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The day we had kisses from a dolphin and a seal !!
Coffs Harbour Travel Blog
We left Sydney at 7 am on the 3rd of Jan...New Year, new adventure we thought. The bus ride to Coffs Harbour took 9 hours so we were felling a little groggy when we got there (I especially felt bad as I was up from 3am the night before with terrible insomnia - sorry to those at home who I pestered with my phone calls!). We took a walk down to the sea that first afternoon as there was a sand castle competition on the beach with some very impressive entries and walked around the fun fair on the way back to our hostel. The next day's weather was not the best and we walked around the town and along the beach again (it turns out that the weather was hot enough for us to catch the sun...
A kiss from Zippy.
I have lovely lines on my arms!). We didn't do any going out in Coffs as we had plans for lots of socalising in Surfers paradise, instead opting to chat with the couple in our room, the bloke from Cardigan, and her from Devon. They both went to Swansea University, and stayed on for a year after their degrees, so we had lots to talk about! They were really cool and we were glad of the good company over our time there.
Our last day in Coffs was the best. We went to the local sea world type attraction called 'Pet Porpoise Pool' (although by their own admission they don't have any popoises). This place is the ONLY place in the world where you can interact with the animals without getting into the water with them. Before the water show, we were all alowed to have a kiss from Ella the seal and Zippy the dolphin! This was very cool.
By the sea at Coffs Harbour.
You could even put your hand in the pool to stroke the dolphins and throw balls for them to catch and play with. All the creatures there had been rescued and some were getting ready to be set back into the wild (I don't much like the idea of zoos and things) so I found this comforting to know. You could see how happy the animals are there. The show was excellent, the dolphins and seals doing countless tricks, all very impressive.
They also have other animals too, kangaroos, peacocks, fairy penguins (which you could feed fish to) and a snake and reptile section with a show in which you could hold and feel them too. We had a fab afternoon there and popped down to the beach for a bit afterwards too...a good day.
This was to take 7 hours on the bus and we were not best pleased when we found out that the only bus they could get us on was the over night bus that left Coffs at 3:30 am! We slept most of the way to Surfers Paradise (thank God). I was awake at about 6:30 am and taking in the scenery from the front windscreen of the bus as we were sitting directly behind the bus driver. We were travelling through the middle of nowhere at this point.
John was snoring beside me with his head on my shoulder and the bus driver was on the phone whilst driving (I am not quite sure what the laws are about that sort of thing over here; in Mexico, they advertise mobiles by having a large billboard picture of someone on the phone whilst driving!!). All of a sudden a kangaroo jumped out into the middle of the road, then another.
At the sandcastle competition.
..I started shaking John awake because I was so chuffed to see my first 'wild' kangaroo. "Aaahh, look John!" I squeeled "look at the kangaroos!" As John awoke another, smaller kangaroo jumped out too..the bus driver tapped on his breaks to let them pass, but in vain as the young joey decided to stop and look at our on-comming bus. There was just enough time for the bus driver to say "here we go" before we had a much closer look at the kangaroo than we were expecting. The poor little joey's guts splatted literally all the way up the front windcreen of the bus! "Thanks a lot for that!" John said to me and tried his best to go back to sleep (I had to explain later that this was not a nightmare, but it really did happen). The bus driver even had to pull over as some of the joey was tuck underneath the bus! It was then that I noticed the 'kangaroo bars' on the front of the bus for exactly this type of occasion...I don't feel half as bad as I did for knocking over that rabbit on the way to Cardiff now!!
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The relationship of acid-soluble glycogen to yeast flocculation.
A relationship between yeast flocculation and intracellular acid-soluble glycogen has been established which has been substantiated using flocculation mutants (mutants with altered capacities to flocculate) as well as a normal strain of Saccharomyces carlsbergensis. Sound evidence exists to implicate physiological differences in carbohydrate metabolism (glycogen storage) to this physical property of brewing significance.
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Common femoral artery antegrade and retrograde approaches have similar access site complications.
Ipsilateral antegrade access (AA) is an alternative access option for contralateral retrograde access (RA) in treating infrainguinal occlusive disease. Our goal was to assess whether AA is associated with higher access site complications. The Vascular Quality Initiative database was searched from 2010 to 2017 for all infrainguinal peripheral vascular interventions. Cases without access through the common femoral artery or those with multiple accesses were excluded. Access types were classified on the basis of whether the approach was AA or RA. Propensity matching and multivariable analyses were performed to determine the effect of AA on access site complications. There were 45,816 access events identified, 6600 (14.4%) AA and 39,216 (85.6%) RA cases. Patients with AA were older (70.7 vs 69.1 years) and more frequently male (66.5% vs 59.1%), white (79.4% vs 74.6%), and on Medicare (58.4% vs 56%); they were more likely to have end-stage renal disease (12.1% vs 11%), and they were less frequently obese (29.3% vs 36.1%) and less likely to be currently smoking (25.5% vs 28.7%), to be diabetic (56% vs 59.8%), to have chronic obstructive pulmonary disease (20.7% vs 21.8%), and to ambulate independently (69.8% vs 72.5%; P < .05 for all). Patients with AA were more likely to have a history of a prior percutaneous vascular intervention (9.3% vs 7%), inflow bypass (6.2% vs 1.8%), and leg bypass (12.6% vs 8.9%; P < .001 for all). The AA technique was more frequently used in the setting of tissue loss (51.8% vs 45.1%) and for tibial intervention (46.3% vs 35.3%; P < .001 for both). There were no significant differences between AA and RA in overall hematoma (3% vs 2.7%; P = .21) or hematoma requiring intervention (0.4% vs 0.4%; P = .75) rates. There was no significant difference in access site occlusion or stenosis between AA and RA (0.2% vs 0.3%; P = .68). These findings were confirmed with 2:1 matching based on preoperative data and type of intervention. Multivariable analysis demonstrated that AA is not associated with increased risk of any hematoma (odds ratio [OR], 1.15; 95% confidence interval [CI], 0.98-1.35; P = .082) or hematoma requiring intervention (OR, 0.88; 95% CI, 0.57-1.35; P = .56). Multivariable analysis of the matched data confirmed these findings between AA and RA for hematoma (OR, 0.88; 95% CI, 0.73-1.06; P = .17) and hematoma requiring intervention (OR, 1.17; 95% CI, 0.7-1.95; P = .55). AA is safe, and it was not found to be associated with increased access site complications, such as hematoma, in the large Vascular Quality Initiative sample. This approach remains a viable alternative to traditional RA.
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Tag Archives: kill
You can’t wear it Like a coat And not expect some Holes to form And stains to stay Nor mud to cake As you fall unto Unbeaten paths You can’t expect To not stumble Through the fields Of the apex predator Without damage incurred You can’t wash it Without losing memory It’s clear but onlyContinue reading “Cullfield”
He wasn’t doing Very well In his tiny little fish bowl Living longer than we All expected Sinking towards the bottom Yet putting up a fight And eating his Fish flake food What a boring life What a tragic strife To never have challenge And to die a captive Wonder wonder wonder How a fishContinue reading “Fireballing the Goldfish”
Ellensberg Laying on the bed In the master bedroom While you’re sitting on the chair Beside And I subtly reach out my hand To see if you’ll notice it And spark an idea for you To grab it and hold I stretch and stretch Trying to get comfy But you know, in the moment ItContinue reading “Ellensberg”
Comeback Try again. Threaten me. You think you’ve got More guts than me? How many teeth do you Think you need? I could check if what Insults you’ve prepared Are backed by your Weak spine. I’ve seen your kind Before And I’ve got more Bite than all of you. Step back, Stand down, Or backContinue reading “Comeback”
Switchblade Fog evaporates With the stinging heat Of ultraviolence. Droplets of amber And sap bleed to Creep like centipedes Down the branches And trunks Of rubber tree forests. So the fog is gone As the sun stabs Dawn into the woods. Oxygen is sunk in From the outside Like golden gore. Gas from monolithic treesContinue reading “Switchblade”
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Eigenlicht Kusanagi I couldn’t clutch A bone of jagged dread More tightly In my clenched fist To my clenched chest In my right hand A bag of whispers Yelled to me “Push forward.” “Saw through.” “Say something.” “Look away.” And in the left A dreadful jag Of bone as bled By yesterday Whispering “It’s okay.”Continue reading “Eigenlicht Kusanagi”
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Nest Hawk-like gaze Conveys unphased A calculated expedition An adventure equipped for Carefully Where we took pictures And pulled red yarn Around nails and targets There came one now Staking out the scene On a condo in some second floor Bare-carpeted with exposed beams Here in the nest you’ve seen Everyone on the sidewalk belowContinue reading “Nest”
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Introduction {#S1}
============
Before relocating to a hot climate, athletes, military personnel and occupational workers are advised to complete 5--14 days of heat acclimation to reduce thermal strain during exercise-heat stress, improve performance, and reduce susceptibility to exertional heat illness ([@B11]; [@B32]). Recommendations for heat acclimation suggest that daily exposures should elevate body temperatures (≥38.5°C) and initiate perfuse sweating through exercise-heat stress ([@B45]; [@B32]; [@B8]; [@B38]). Hallmark heat acclimation adaptations include: an earlier onset and increase in sweating rate, a reduction in resting and exercising core body temperature, and reductions in cardiovascular strain and skin temperature that in turn, reduce perceptual strain and improve exercise capabilities in the heat ([@B19]; [@B29]; [@B26]; [@B45]). Despite the known benefits of heat acclimation, only 15% of athlete's heat acclimatized as part of their preparation for the hot and humid conditions in Beijing, at the 2015 IAAF World Championships ([@B33]). One explanation for poor athlete engagement with heat acclimatization is that protocols rely on sufficiently stressful natural environmental conditions in the days preceding competition to induce adaptation, which cannot be controlled or guaranteed ([@B21]). In addition, conventional exercise-heat-acclimation protocols are costly and impractical for non-acclimatized individuals who reside in cooler climates. Furthermore, hallmark adaptations are transient and decay quickly without regular exposure to the heat ([@B49]; [@B14]; [@B35]). As such, recommendations suggest that heat acclimation protocols should be completed in the days preceding relocation to a hot climate; likely compromising competition taper or pre-deployment training ([@B20]; [@B38]). However, completing an accessible and time efficient alternative method of heat acclimation prior to or during pre-competition taper, such as post-exercise hot water immersion (HWI) ([@B54]) or sauna bathing ([@B41]), may minimize disturbances to training and taper ([@B38]).
Information detailing heat acclimation methods and the induced adaptations is extensive; whereas, research concerning the decay or retention of adaptation is limited ([@B14]). Traditionally, heat acclimation decay is thought to occur rapidly ([@B50]; [@B1]), with 1 day of adaptation lost every 2 days spent without heat exposure ([@B22]). In addition, those adaptations that occur first, such as an expansion in plasma volume and a reduction in exercising heart rate, are thought to exhibit the most rapid decay ([@B49]; [@B30]; [@B3]; [@B15]). The number of heat exposures appears to influence the rate of decay ([@B14]). For example, adaptations from short-term heat acclimation (\<7 exposures) are typically retained for 7 days but lost after 14 days ([@B49]; [@B20]; [@B28]). Conversely, adaptations following medium-term protocols (7--14 exposures) are in part, retained for up to 26 days ([@B48]; [@B13]; [@B34]). Despite heat acclimation adaptations being retained for longer following medium-term heat acclimation, short-term exercise based protocols remain the preferred preparatory method. Nevertheless, the rapid decay of adaptation from short-term heat acclimation dictates that these protocols should be completed in the 7 days preceding relocation to a hot climate. These recommendations contradict those associated with pre-competition taper, which state that accumulated fatigue should be minimized 14 days prior to competition ([@B27]; [@B6]). Recently, six daily exposures to post-exercise HWI was demonstrated to improve exercise performance in the heat through the initiation of heat acclimation adaptations; including, a reduction in rectal core temperature (*T*~re~) at rest and during exercise-heat stress, despite no significant changes in plasma volume or whole body sweat rate (WBSR) ([@B54]). The initiation of heat acclimation was attributed to immersion in hot water, as no effect on thermoregulatory measures at rest and during exercise-heat stress was observed in a control group, who performed 6 days of submaximal exercise followed by a thermoneutral (34°C) water immersion ([@B54]). Furthermore, the magnitude of adaptations from post-exercise HWI were similar in endurance trained and recreationally active individuals and compared favorably to exercise-heat-acclimation ([@B47]; [@B53]). However, it remains unknown whether the length of adaptation retention following post-exercise HWI necessitates the completion of the protocol during a 2-week pre-competition taper and thus, suffers the same practical restraints associated with short-term exercise-heat-acclimation.
The primary aim of the current study was to assess whether adaptations are retained, 1 and 2 weeks following 6-days post-exercise HWI heat acclimation. We hypothesized that similarly to short-term exercise-heat-acclimation, adaptations would demonstrate decay at 2 weeks ([@B20]). In addition, our previous work has suggested that post-exercise HWI does not provide a large expansion in plasma volume or increase whole body sweating rate ([@B54]); adaptations commonly considered as hallmarks of heat acclimation. As such, the secondary aim of the current study was to provide a more comprehensive appraisal of blood compartment and sweating adaptations, using the optimized carbon monoxide (CO) rebreathing technique and esophageal core body temperature (*T*~es~) to measure the sensitivity and drive for sweating.
Materials and Methods {#S2}
=====================
Participants {#S2.SS1}
------------
Thirteen recreationally active males (mean ± SD, age: 23 ± 3 years; body mass: 74 ± 7 kg; ~max~: 58 ± 9 mL⋅kg^--1^⋅min^--1^) provided written informed consent to participate in the current study. All participants were healthy, non-smokers, free from any known immune, cardiovascular or metabolic diseases, and were not taking any medication. Participants had also not been regularly exposed to hot environmental conditions (including saunas and hot baths) in the 3-months prior to commencing testing. This study was received approval from the Bangor University Ethics Committee and was conducted in accordance with the Declaration of Helsinki (2013).
Study Design {#S2.SS2}
------------
To confirm the induction of heat acclimation, participants completed an experimental trial before (PRE) and after (POST) the daily intervention. Four participants were removed from the study after the POST experimental trial as they did not comply with the study protocol. To assess the retention of adaptations, the remaining nine participants completed an experimental trial 1 week (WK 1) and 2 weeks (WK 2) after the intervention. The heat acclimation intervention involved a 40-min submaximal treadmill run in temperate conditions followed by ≤40-min HWI (40°C) completed on six consecutive days. As we have previously demonstrated no thermoregulatory benefit of a 6-day post-exercise thermoneutral water immersion (34°C: to control for training and/or hydrostatic effects), we deemed it unnecessary to include this additional control group ([@B54]).
Preliminary Measurements {#S2.SS3}
------------------------
~max~ was assessed in temperate conditions (20°C) using a continuous incremental exercise test on a motorized treadmill (HP Cosmos Mercury 4.0, Nussdorf-Traunstein, Germany), as described previously ([@B16]). The running speed that elicited 65% ~max~ was then determined and verified using the interpolation of the running speed --  relationship. The individualized running speed was used for the submaximal running performed during each experimental trial and during the daily exercise prior to HWI. As endurance training can induce partial heat acclimation, participants were instructed to reduce their regular training by the duration completed in the laboratory. Physical activity time (\>3 METS) was assessed for the duration of the study using an activity tracker (Fitbit Flex, San Francisco, CA, United States).
Experimental Trials {#S2.SS4}
-------------------
Twenty-four hours prior to, and on the day of the experimental trials participants were instructed to not consume any alcohol, diuretics or caffeine, and to refrain from any additional exercise. Participants completed a diet diary in the 24 h prior to the first experimental trial (PRE) and were asked to replicate this dietary intake prior to all experimental trials (POST, WK 1, and WK 2). As sleeping patterns can influence thermoregulation ([@B39]), participants were instructed to sleep between 2200 h and 0700 h to ensure a similar circadian pattern prior to each experimental trial. An Actigraph (Actigraph GT3X Version 4.4.0, Actigraph, Pensacola, FL, United States) was worn on the non-dominant arm with epoch length set to 1 min to analyze participants sleep quality and sleep duration using Actilife + Sleep Version 6 (Actigraph, Pensacola, FL, United States).
On the day of each experimental trial, participants arrived at the laboratory at 0730 h and were provided with a standardized breakfast (0.03 MJ⋅kg^--1^; 0.2 g⋅kg^--1^ protein, 1.0 g⋅kg^--1^ CHO, and 0.3 g⋅kg^--1^ fat) and a bolus of water equivalent to 7 mL⋅kg^--1^ of body mass. At 0800 h participants completed 20-min seated rest, dressed in t-shirt, running shorts, socks and trainers, in temperate conditions (20°C). A venous blood sample was taken without stasis and assessed for hemoglobin (Hb) concentration and hematocrit percentage. In addition, total Hb mass, blood volume, and plasma volume was assessed using the optimized CO rebreathing technique (in a subsample; *n* = 9). A mid-flow urine sample was analyzed for urine specific gravity using a handheld refractometer (Atago Uricon-Ne refractometer, NSG Precision cells, New York, United States) to confirm participants were hydrated (urine specific gravity \< 1.03) ([@B2]). If participants did not meet the hydration criteria (*n* = 1), they were provided with a 500 mL bolus of water and urine specific gravity was reanalyzed; exercise began only when urine specific gravity \< 1.03. A rectal thermistor and an esophageal thermistor (in a subsample; *n* = 8) was fitted, which measured rectal (*T*~re~) and esophageal temperature (*T*~es~) continuously throughout the experimental trial. A pre-exercise nude body mass was recorded using a digital platform scale (Model 705; Seca, Hamburg, Germany) and the participants were instrumented for the exercise protocol. To establish baseline measures, participants rested for a further 30 min in temperate conditions (20°C).
At 0945-h, dressed in running shorts, socks and trainers, the participant entered the environmental chamber (Delta Environmental Systems, Chester, United Kingdom) which was maintained at 33°C, 40% RH, and completed a 40-min treadmill run at 65% ~max~ (1% gradient). During this time, no fluids were consumed; *T*~re~, *T*~es~, skin temperatures, and heart rate were monitored continuously; and rating of perceived exertion (RPE; 6--20 scale) ([@B5]) and thermal sensation (1--13 scale) ([@B23]) were recorded every 10 min. Local forearm sweating rate was measured every 20 s to assess the drive for sweating onset and sweating sensitivity, as previously described ([@B9]). Oxygen uptake (), and respiratory exchange ratio (RER) were assessed from 60-s expired gas samples collected by Douglas bag method immediately prior to the 10th, 20th, 30th, and 40th min of exercise. On completion of the experimental trial participants exited the environmental chamber and rested for 15 min in temperate conditions, at which point a nude body mass was recorded to estimate WBSR. Participants remained in the laboratory until their *T*~re~ ≤ 38.5°C, during which they consumed a bolus of water equivalent to their sweat losses.
Post-exercise HWI Heat Acclimation {#S2.SS5}
----------------------------------
Post-exercise HWI heat acclimation was completed on six consecutive days, as previously described ([@B54]). During the intervention, participants were instructed to consume their normal diet and fluid intake, including caffeine and alcohol (≤3 units per day) and to report to the laboratory on six consecutive days between 0600 h and 0830 h. Prior to exercise, a nude body mass was taken and participants were fitted with a rectal thermistor and heart rate monitor. *T*~re~ and heart rate were continually monitored throughout the submaximal exercise and HWI. Dressed in running shorts, socks and trainers, participants ran for 40 min at 65% ~max~ (1% gradient) on a motorized treadmill in a temperate environment (20°C). A 5 mL⋅kg^--1^ of body mass bolus of water was consumed in the first 20 min of exercise. At the cessation of exercise, dressed in shorts, participants began a semi-recumbent HWI (2--3 min transition), and submerged to the neck in a temperate room (≈ 20°C). The water was maintained at 40°C for the duration of the immersion. Immersion ended after 40 min unless the participant removed them self due to discomfort or *T*~re~ exceeded 39.9°C. Upon removal from the HWI, participants rested in temperate conditions (20°C) for 15 min, at which point a nude body mass was recorded to estimate WBSR. Participants remained in the laboratory until their *T*~re~ ≤ 38.5°C.
Monitoring Heat Acclimation Retention {#S2.SS6}
-------------------------------------
During the 2 weeks following the 6-day post-exercise HWI intervention, participants were permitted to shower but instructed to avoid significant heat exposure, including exercising in hot conditions and taking hot baths or saunas. In addition, participants were instructed to maintain their normal diet and fluid intake, including caffeine and alcohol (≤3 units per day), whilst resuming their normal exercise routine. Participants completed an experimental trial WK 1 and WK 2 after the POST experimental trial; adopting identical procedures to the PRE and POST trial.
Measurement and Instrumentation {#S2.SS7}
-------------------------------
### Body Temperatures {#S2.SS7.SSS1}
Rectal core temperature and esophageal core body temperature and were measured using a flexible, sterile, disposable thermistor (Henleys Medical Supplies Ltd., Herts, United Kingdom) and recorded using a data logger (YSI model 4000A, YSI, Dayton, United States). The rectal thermistor was inserted 10 cm beyond the rectal sphincter. The esophageal thermistor was inserted through the nasal fossae to a depth of 25% of the participant's height ([@B25]). To assess cumulative hyperthermia, an area under the curve analysis (AUC) was performed on the daily *T*~re~ (\>38.5°C) during the intervention and recovery (≈ 25 min), as previously described ([@B10]). Skin thermistors (Grant EUS-U, Cambridge, United Kingdom) were attached to the right side of the body (on the chest at a midpoint between the acromion process and the nipple, the lateral mid-bicep, the anterior mid-thigh, and lateral calf) and recorded using a portable data logger (Grant SQ2020, Cambridge, United Kingdom). Mean skin temperature (*T*~sk~) was calculated using a four-site weighted equation ([@B36]).
### Sweating Responses {#S2.SS7.SSS2}
Local forearm sweating rate was measured by dew point hygrometry during all experimental trials as previously described ([@B16]). Core temperature (*T*~re~ and *T*~es~) at sweating onset and sweating sensitivity using *T*~es~ were calculated by plotting individual relationships between local forearm sweating rate and core temperature as previously described ([@B9]). Changes in dry nude body mass were used to estimate WBSR during all experimental trials and intervention days.
### Blood Sample Collection and Analysis {#S2.SS7.SSS3}
Following a 20-min seated rest, venous blood samples (6-mL) were collected from an antecubital vein without stasis into an EDTA vacutainer (BD, Oxford, United Kingdom). Aliquots of whole blood were used for the immediate determination of Hb concentration (g.dL^--1^) in duplicate (Hemocue, Sheffield, United Kingdom) and hematocrit in triplicate (capillary tube method).
### Optimized CO Rebreathing Technique {#S2.SS7.SSS4}
Total Hb mass (g), blood volume (mL) and plasma volume (mL) were determined in accordance with the optimized CO rebreathing technique ([@B40]). Following a 20-min seated rest, participants were instructed to inhale 0.8--1.0 mL⋅kg^--1^ bolus of CO (99.9%), followed by rebreathing a 3 L O~2~ bolus (99.5%) using a closed glass spirometer. Prior to the CO rebreathing procedure and 4 min after, participant's exhaled to residual volume into a CO gas meter (Drager Pac 3500, Pittsburgh, PA, United States). Prior to, 6 min and 8 min after the rebreathing procedure, earlobe capillary blood samples were assessed for carboxyhaemoglobin concentration (% COHb; ABL80 CO-OX Flex hemoximeter Radiometer; Copenhagen, Denmark). Total Hb mass was used to determine blood volume \[(Hb mass/Hb concentration) × 100\], red blood cell volume \[mL; blood volume × (hematocrit/100)\] and plasma volume (blood volume -- red blood cell volume). Before commencing data collection, a preliminary reliability study (*n* = 9; triplicate measures) confirmed that the experimenter typical error of measurement was ±2.0% for total Hb mass, ±3.2% for blood volume and ±5.1% for plasma volume.
Statistical Analysis {#S2.SS8}
--------------------
A sample size estimation (G^∗^Power 3.1.2) with an alpha level of 0.05 and power of 0.8, determined that nine participants were required to detect a significant reduction in end-exercise *T*~re~ (0.3°C) following short-term heat acclimation. To ensure adequate power and allowing for dropout, 13 participants were recruited. Data is presented as mean and standard deviation (SD) and statistical significance was accepted at *P* \< 0.05. All data were checked for normality and sphericity. A paired sample *t-*test was used to assess for differences in thermoregulatory variables, heart rate, HWI time and AUC during the intervention (day 1 vs. day 6), and the induction of heat acclimation adaptations (PRE vs. POST; *n* = 13). A two-way repeated measures analysis of variance (ANOVA), with Greenhouse Geisser correction to the degrees of freedom (where necessary), was used to compare adaptations (e.g., end-exercise *T*~re~) to post-exercise HWI with a previous control intervention ([@B54]). A one-way repeated measures ANOVA with Greenhouse Geisser correction to the degrees of freedom (where necessary) was used to assess the induction and retention of heat acclimation adaptations (PRE, POST, WK 1 and WK 2; *n* = 9). When a main effect of time was observed, results were followed up using Tukey's *post hoc* comparison. For non-parametric data (resting *T*~re~), a Friedman test was used to assess the induction and retention of heat acclimation adaptations. When a statistical significance was found, a Wilcoxon Signed Rank tests was used to identify where the difference occurred. The magnitude of effect was reported using Cohen's *d*, where 0.2, 0.5, and 0.8 represent small, medium and large effects, respectively ([@B12]). Pearson's correlations were used to determine the strength of the relationship between the reduction in resting and end-exercise *T*~re~ and total AUC during the heat acclimation intervention. All data was analyzed using SPSS version 24 (IBM Corporation, NY, United States), or GraphPad Prism Version 5.02 (GraphPad Software Inc., La Jolla, United States).
Results {#S3}
=======
Post-exercise HWI Intervention {#S3.SS1}
------------------------------
All 13 participants completed a 40-min submaximal treadmill run followed by HWI (≤40 min) on six consecutive days. During the 6-day intervention, the endogenous stimulus for adaptation was maintained with a similar change in *T*~re~ and AUC between day 1 and day 6 of the daily intervention (*P* \> 0.05; [Table 1](#T1){ref-type="table"}). The stimulus for adaptation was maintained due to an increase in HWI duration (*P* \< 0.05; [Table 1](#T1){ref-type="table"}). For example, on day 1, 10 of the 13 participants removed themselves from the HWI due to discomfort; whereas, on day 6, all participants completed the 40-min HWI protocol ([Table 1](#T1){ref-type="table"}).
######
The influence of 40-min submaximal running at 65% ~max~ in temperate conditions followed by post-exercise hot water immersion in 40°C water to the neck (*n* = 13) on thermoregulatory variables, heart rate, and immersion time.
**Day 1** **Day 6**
------------------------------------------------- -------------- -----------------
**Submaximal exercise**
Change in *T*~re~ (°C) 1.17 ± 0.25 1.08 ± 0.29
End-exercise *heart* rate (beats⋅min^--1^) 153 ± 11 143 ± 10^∗∗^
**Hot water immersion**
End-immersion *T*~re~ (°C) 39.34 ± 0.30 39.24 ± 0.30
Change in *T*~re~ (°C) 0.87 ± 0.28 0.98 ± 0.15
Immersion time (min) 33 ± 7 40 ± 0^∗∗^
*n* completing 40 min immersion 3 of 13 13 of 13
**Submaximal exercise and hot water immersion**
WBSR (L⋅h^--1^) 0.97 ± 0.29 1.09 ± 0.27^∗∗^
AUC (°C⋅min^--1^) 27 ± 16 25 ± 13
T
re
, rectal core temperature; WBSR, whole body sweat rate; AUC, area under the curve.
∗∗
P
\< 0.01 day 6 different to day 1. Data displayed as mean ± SD.
Heat Acclimation Adaptations {#S3.SS2}
----------------------------
Prior to the PRE and POST experimental trials, sleep duration (7 ± 1 h), sleep efficiency (87 ± 9%), and USG (1.018 ± 0.009) were similar (*P* \> 0.05). Heat acclimation adaptations were achieved following post-exercise HWI (PRE vs. POST; *n* = 13), including a reduction in end-exercise *T*~re~ (*P* \< 0.01, *d* = 1.0). For comparison, a 6-day control intervention, described previously ([@B54]), did not reduce end-exercise *T*~re~ at POST (0.00 ± 0.21°C; *P* \> 0.05; *n* = 7). Six days of post-exercise HWI also initiated reductions in: resting *T*~re~ (*P* \< 0.01, *d* = 1.3); *T*~re~ at sweating onset (*P* \< 0.01, *d* = 1.1); end-exercise heart rate (*P* \< 0.01, *d* = 1.0); end-exercise PhSI (*P* \< 0.01, *d* = 1.0); end-exercise *T*~sk~ (*P* \< 0.01, *d* = 1.0); end-exercise RPE (*P* \< 0.01, *d* = 0.9); end-exercise thermal sensation (*P* \< 0.05, *d* = 0.9); mean  (*P* \< 0.01, *d* = 0.3); and mean energy expenditure (*P* \< 0.01, *d* = 0.4). No PRE to POST differences were observed for *T*~re~ -- *T*~sk~ gradient, WBSR or mean RER (*P* \> 0.05).
For completeness, in the nine participants who completed the 2-week retention protocol a main effect of time (*P* \< 0.05) was observed in heat acclimation adaptations. Whereby, similar to the thirteen participants above, reductions from PRE to POST (*P* \< 0.05) were noted in: resting *T*~re~ ([Figure 1](#F1){ref-type="fig"}); *T*~re~ at sweating onset; end-exercise *T*~re~ ([Figure 1](#F1){ref-type="fig"}); end-exercise heart rate ([Figure 2A](#F2){ref-type="fig"}); end-exercise PhSI; end-exercise *T*~sk~ ([Figure 2C](#F2){ref-type="fig"}); end exercise RPE ([Figure 2B](#F2){ref-type="fig"}); end-exercise thermal sensation ([Figure 2D](#F2){ref-type="fig"}); mean ; and mean energy expenditure. Of the nine participants who completed the retention protocol, seven experienced a reduction in resting *T*~re~ at POST ([Figure 1C](#F1){ref-type="fig"}). End-exercise *T*~re~ was reduced in all nine participants at POST ([Figure 1F](#F1){ref-type="fig"}); and end-exercise heart rate and end-exercise *T*~sk~ were lower in eight of the nine participants ([Supplementary Material A,B](#SM1){ref-type="supplementary-material"}). No main effect of time was observed for end-exercise *T*~re~-- *T*~sk~ gradient, WBSR or mean RER (*P* \> 0.05).
~max~ in the heat (33°C, 40% RH). Bars show mean ± SD **(A,D)** or mean ± SD of the change from PRE, at POST, WK 1, and WK 2 **(B,E)**. Lines represent individual responses **(C,F)**. ^∗^*P* \< 0.05, ^∗∗^*P* \< 0.01 less than PRE.](fphys-10-01080-g001){#F1}
~max~ in the heat (33°C, 40% RH). Bars show mean ± SD of the change from PRE, at POST, WK 1, and WK 2. ^∗^*P* \< 0.05, ^∗∗^*P* \< 0.01 less than PRE (*post hoc* effect).](fphys-10-01080-g002){#F2}
Heat Acclimation Retention {#S3.SS3}
--------------------------
Heat acclimation adaptations following post-exercise HWI were retained for 2 weeks; contrary to our expectation. The retention of heat acclimation was evidenced by the reduction in resting *T*~re~ from PRE to POST (*P* \< 0.05, *d* = 1.0), PRE to WK 1 (*P* \< 0.05, *d* = 1.1), and PRE to WK 2 (*P* \< 0.01, *d* = 1.2; [Figure 1](#F1){ref-type="fig"}). Furthermore, the reduction in thermal strain following exercise-heat stress was also retained; with a reduction in end-exercise *T*~re~ observed from PRE to POST (*P* \< 0.05, *d* = 0.7); PRE to WK 1 (*P* \< 0.01, *d* = 1.0) and PRE to WK 2 (*P* \< 0.01, *d* = 1.0; [Figure 1](#F1){ref-type="fig"}). At WK 2 a reduction in resting *T*~re~ (vs. PRE) was observed in eight of the nine participants. The reduction in end-exercise *T*~re~ (vs. PRE) was retained in seven of the nine participants at WK 2 (−0.52 ± 0.25°C). The two participants who demonstrated decay were among the smallest responders to the intervention at POST. Of additional interest, following 7--14 days without exposure to daily heat stress, there was a trend for the magnitude of reduction in resting *T*~re~ to increase from POST to WK 1 and WK 2 (*P* \> 0.05, [Figure 1](#F1){ref-type="fig"}). As such, to observe the full extent of the adaptive benefits, an extended period of recovery may be necessary after the post-exercise HWI intervention. Furthermore, the reduction in resting *T*~re~ at WK 2 appears to drive the reduction in end-exercise *T*~re~ (Pearson's correlation*, r* = 0.69, *P* \< 0.05). The thermal stimulus during the post-exercise HWI intervention also appeared to influence the magnitude of reduction in resting and end-exercise *T*~re~ at WK 2. Correlation analyses suggest that a greater benefit in these adaptations was observed in those who experienced a greater thermal stimulus (total AUC) during the post-exercise HWI intervention (resting *T*~re~; *r* = −0.53, *P* = 0.15, end-exercise *T*~re~; *r* = −0.48, *P* = 0.19); albeit, these correlations were non-significant.
Other heat acclimation adaptations were retained 2 weeks after the cessation of post-exercise HWI. Thus, reductions from PRE to WK 2 were observed for measures of: *T*~re~ at sweating onset (*P* \< 0.01, *d* = 0.8); and end exercise heart rate (in eight of nine participants; *P* \< 0.01, *d* = 0.9; [Figure 2A](#F2){ref-type="fig"} and [Supplementary Material A](#SM1){ref-type="supplementary-material"}); PhSI (*P* \< 0.01, *d* = 1.0); *T*~sk~ (in eight of nine participants; *P* \< 0.01, *d* = 1.3; [Figure 2C](#F2){ref-type="fig"} and [Supplementary Material B](#SM1){ref-type="supplementary-material"}); RPE (*P* \< 0.05, *d* = 0.9; [Figure 2B](#F2){ref-type="fig"}); and thermal sensation (*P* \< 0.01, *d* = 1.4; [Figure 2D](#F2){ref-type="fig"}). However, the observed reductions from PRE to POST in mean  and mean energy expenditure were not observed at WK 1 or WK 2 (*P* \> 0.05). The retention of heat acclimation was demonstrated despite a reduction in weekly activity time during the 2-week retention protocol (7 ± 3 h per week) compared to that during 6 days of post-exercise HWI (10 ± 4 h per week; *P* \< 0.05, *d* = 0.9).
Influence of Post-exercise HWI on Blood Compartment and Sweating Responses {#S3.SS4}
--------------------------------------------------------------------------
Appraisal of blood compartment changes demonstrate that six daily exposures to post-exercise HWI did not provide significant PRE to POST increases in: resting total Hb mass (+3 ± 5%; *P* \> 0.05, *d* = 0.25; [Figure 3A](#F3){ref-type="fig"}); blood volume (+4 ± 6%; *P* \> 0.05, *d* = 0.32; [Figure 3B](#F3){ref-type="fig"}); and plasma volume (+ 6 ± 9%; *P* \> 0.05, *d* = 0.47; [Figure 3C](#F3){ref-type="fig"}). Indeed, the effect of the 6-day intervention on plasma volume was variable, with only five of the nine participants experiencing an expansion greater than the *a priori* determined experimenter error. Examination of the influence of post-exercise HWI on sweating responses suggest that, in line with *T*~re~ at sweating onset, *T*~es~ at sweating onset during exercise-heat stress reduced from PRE to POST (−0.34 ± 0.17°C, *P* \< 0.01, *d* = 1.0). However, no other elements of the sweating response altered; with no PRE to POST change in sweating sensitivity (PRE, 0.52 ± 0.23 mg⋅min^--1^⋅cm^--2^; POST, 0.59 ± 0.31 mg⋅min^--1^⋅cm^--2^; [Figure 4A](#F4){ref-type="fig"}) or the drive for sweating onset (delta change in *T*~es~; PRE, 0.38 ± 0.11°C; POST, 0.42 ± 0.21°C; [Figure 4B](#F4){ref-type="fig"}).
{#F3}
~max~) in the heat (33°C, 40% RH) before (PRE) and after (POST) heat acclimation. Error bars removed for clarity.](fphys-10-01080-g004){#F4}
Discussion {#S4}
==========
The present study is the first to examine the retention of heat acclimation adaptations following 6 days of post-exercise HWI. In accordance with our previous findings, post-exercise HWI induced heat acclimation adaptations in all participants ([@B54]). Contrary to our hypothesis, and the notion that adaptations following short-term exercise-based protocols decay by 2 weeks, the new and noteworthy findings provide evidence of the retention of heat acclimation for at least 2 weeks following the post-exercise HWI intervention. For example, a similar extent of adaptation at POST, WK 1, and WK 2 was observed for measures of resting *T*~re~, *T*~re~ at sweating onset, and end-exercise *T*~re~, heart rate, *T*~sk~, RPE and thermal sensation ([Figures 1](#F1){ref-type="fig"}, [2](#F2){ref-type="fig"}); despite no significant changes in plasma volume or WBSR. The induction and retention of heat acclimation is likely due to the large daily elevations in both core (change in *T*~re~ ≈ 2.1°C) and skin temperatures (*T*~sk~ = 40°C) during immersion in hot water to the neck. We have confidence that immersion in hot water provides these adaptations, as we have previously demonstrated no thermoregulatory benefits from 6 days of submaximal exercise and immersion in thermoneutral water ([@B54]). Exposure to the dual thermal stimulus during immersion in hot water (elevated core and skin temperature) appears to initiate the reduction in resting core temperature; attenuating thermal strain during exercise-heat stress for at least 2 weeks following the HWI intervention. Recommendations state that a 2-week pre-competition taper with a reduction in training volume (≈ 50%) optimizes athletic performance ([@B6]); although, smaller reductions in training volume (15--20%) 7 days from competition have yielded successful performances in elite athletes ([@B46]; [@B43]). The retention of adaptation from post-exercise HWI for at least 2 weeks indicates that taking a hot bath after training in temperate conditions can be completed during the pre-taper phase, without compromising supercompensatory adaptations ([@B46]).
The retention of heat acclimation for at least 2 weeks following post-exercise HWI appears favorable compared to short-term exercise-heat-acclimation and aligns more closely with the retention timeframe following medium-term protocols ([@B48]; [@B20]; [@B13]). However, despite evidence of heat acclimation retention 12--26 days following medium-term protocols, a portion of the induced adaptation is lost (20--35%) ([@B30]; [@B48]). A recent meta-analysis suggested that adaptation decay is dependent upon extent of induced adaptation and estimated a rate of decay of ≈ 2.5% every day without exposure to the heat ([@B14]). Accordingly, the two participants who gained the smallest benefit from post-exercise HWI at POST demonstrated decay at WK 2. Surprisingly, there was no evidence of adaptation decay after 2 weeks in seven of the nine participants (end-exercise *T*~re~; −0.52°C). On the contrary, the mean data suggests a further gain in the extent of adaptation for resting (+40%) and end-exercise *T*~re~ (+11%) was observed despite no exposure to any significant heat stress. It is possible that the experimental trial at WK 1 provided a thermal stimulus to maintain adaptation ([@B35]); however, the endogenous thermal stimulus during this trial was relatively low (end-exercise *T*~re~, 38.3°C). Therefore, the favorable retention of adaptations following post-exercise HWI is more likely due to the large daily elevations in core and skin temperatures during immersion to the neck in hot water. Exposure to a large dual thermal stimulus augments the magnitude of adaptation and provides benefits including: a reduction in resting and exercising core temperature, that decay at a slower rate ([@B30]; [@B48]). Whereas, widely regarded hallmark heat acclimation adaptations, such as an expansion in plasma volume ([@B3]), occur following exposure to a smaller accumulative thermal stimulus and decay rapidly ([@B49]; [@B30]). The current data confirms the reduction in thermal strain from post-exercise HWI is initiated by the reduction in resting *T*~re~ (≈−0.3°C), not through significant changes in blood compartments or sweating responses within the conditions of our experimental trial. As previously suggested ([@B53]), the semi-recumbent body position and/or hydrostatic squeeze during HWI may limit plasma volume expansion; and a greater number of exposures may be required to initiate an increase in WBSR. Therefore, as sweating occurs following a similar rise in *T*~re~ after post-exercise HWI ([Figure 4](#F4){ref-type="fig"}), the reduction in resting *T*~re~ likely initiates the attenuation in *T*~re~ at sweating onset and during exercise-heat stress ([@B54], [@B52], [@B53]). Furthermore, the reduction in resting *T*~re~ at POST was maintained at WK 2 (−0.36°C), supporting the notion that adaptations requiring exposure to a larger thermal stimulus are retained for longer ([@B49]; [@B30]; [@B3]; [@B13]; [@B15]). Interestingly, the retention of the reduction in resting *T*~re~ at WK 2 (−0.36°C) appears to be fully responsible for the attenuation in thermal strain during exercise-heat stress (end-exercise *T*~re~; −0.36°C). As such, the induction of adaptations provided through exposure to large daily elevations in core and skin temperatures, such as a reduction in resting core temperature, may initiate the retention of heat acclimation for at least 2 weeks following post-exercise HWI. In addition, due to the ease of assessing resting core temperature in temperate conditions, this measurement could be utilized as a metric to outline the extent of induced adaptation and, following definition of the slope of decay, to forecast the timeframe of adaptation retention.
A reduction in resting core temperature has previously been linked to alterations in basal metabolic rate following both endurance training and seasonal heat acclimatization ([@B4]; [@B7]). In line with these observations, a large and meaningful reduction in resting core temperature (−0.32°C) occurs following long-term exercise-heat-acclimation (≥15 exposures) ([@B31]; [@B47]). Whereas, both short and medium-term exercise-heat-acclimation induce a smaller attenuation in resting core temperature (≈−0.2°C), according to a recent meta-analysis ([@B47]). Surprisingly, after six daily exposures to post-exercise HWI a large reduction in resting *T*~re~ is observed (≈−0.3°C) ([@B54], [@B52], [@B53]). Comparison of the HWI protocol with the extant exercise-heat-acclimation literature may explain the difference in the magnitude of adaptation. For example, immersion to the neck in hot water exposes individuals to a high core temperature (end-immersion *T*~re~; 39.3°C) and perhaps more importantly, to a large exogenous thermal stimulus, where skin temperatures likely equilibrate with water temperature (≤40 min, ≈ 40°C) ([@B54], [@B52], [@B53]). Whereas, exercise-heat-acclimation protocols which utilize the controlled hyperthermia technique clamp *T*~re~ at 38.5°C ([@B18]; [@B20]) and do not elevate skin temperatures to the same magnitude as HWI. Therefore, exposure to the large dual thermal stimulus during HWI, which is considered to promote a more complete state of adaptation ([@B17]; [@B37]), may provide the large magnitude of adaptation and accelerate the occurrence of a reduction in resting core temperature. Specifically, the elevation in skin temperature during HWI to the neck may activate warm-sensitive neurons and induce hypothalamic neural network changes, which reduce resting core temperature ([@B44]; [@B51]; [@B42]). Interestingly, the reduction in resting *T*~re~ observed at WK 1 and WK 2 was greater than that observed at POST (≈−0.1°C); thus, supporting previous work that suggests a period of recovery in cool conditions may augment the reduction in resting *T*~re~ ([@B13]). This augmentation of adaptation may represent a delay in physiological remodeling following exposure to the heat ([@B24]) and warrants further investigation to improve the integration of heat acclimation into training programs.
Heat acclimation recommendations suggest that daily exercise-heat-stress is the most effective method for acclimating to the heat ([@B45]; [@B32]). In accordance with our recent work ([@B54], [@B52], [@B53]), the present findings offer an alternative approach, by demonstrating that taking a hot bath following exercise in temperate conditions is an effective, practical, and accessible heat acclimation strategy. For example, post-exercise HWI improves endurance performance in the heat ([@B54]) and induces heat acclimation adaptations ([@B52], [@B53]), which in the majority of participants are retained for at least 2 weeks. Furthermore, incorporating a hot bath into post-exercise washing routines on 6 days reduces interference with training/taper while ensuring that athletes are adapted to the heat prior to travel for competition. As such, an athlete may be less reliant on natural acclimatization upon arrival, where environmental conditions may not be sufficiently challenging to induce adaptations ([@B33]; [@B21]). To ensure safety, practitioners and athletes utilizing the post-exercise HWI protocol should limit immersion duration (≤40 min), be mindful to monitor physiological measures, and terminate exposures if intolerance symptoms arise (e.g., high core temperature and/or sensations of thermal strain). We recognize that the current research does not illustrate the timeframe of decay from post-exercise HWI in all participants or directly compare the magnitude and retention of adaptation with exercise-heat-acclimation. Future research should examine the influence of the large daily elevations in skin temperature during HWI on heat acclimation adaptation. In addition, investigations should confirm the underpinning mechanisms for the retention of heat acclimation and examine the effect of post-exercise HWI on training load and recovery, whilst establishing if the maintenance of adaptations translates to performance. To improve the practicality of HWI, future studies should also establish whether meaningful adaptation and retention timeframes are observed following protocols of fewer or a greater number of HWI exposures.
Conclusion {#S5}
==========
Heat acclimation adaptations from post-exercise HWI are retained for at least 2-weeks. As such, for athletes who reside in temperate conditions, taking a hot bath following routine training on six consecutive days during the pre-taper phase represents a simple, practical and effective heat acclimation strategy.
Data Availability {#S6}
=================
The datasets generated for this study are available on request to the corresponding author.
Ethics Statement {#S7}
================
This study received ethical approval from the Ethics Committee of the School of Sport, Health and Exercise Sciences, Bangor University.
Author Contributions {#S8}
====================
NW had primary responsibility for the final content. All authors were involved in the conception of the project and development of the research plan, performed the data analysis, interpreted the data, and prepared the manuscript. MZ led the data collection.
Conflict of Interest Statement {#conf1}
==============================
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We would like to thank Claire Potter, David Harding, Liam Renton, Michael Gregson, Jason Edwards, and Kevin Williams for their valuable assistance with data collection. We are also indebted to the participants for their time and co-operation.
Supplementary Material {#S10}
======================
The Supplementary Material for this article can be found online at: <https://www.frontiersin.org/articles/10.3389/fphys.2019.01080/full#supplementary-material>
######
Click here for additional data file.
[^1]: Edited by: Julien Périard, University of Canberra, Australia
[^2]: Reviewed by: Luke Pryor, University at Buffalo, United States; Jian Cui, Pennsylvania State University, United States; Jamie Stanley, South Australian Sports Institute, Australia
[^3]: This article was submitted to Exercise Physiology, a section of the journal Frontiers in Physiology
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On Saturday, the Detroit Lions announced they were releasing running back Theo Riddick.
Well, it did not take too long for Riddick to find a new home as he will reportedly be heading to the Denver Broncos later this week.
Barring the unexpected, it appears coveted free agent RB Theo Riddick will sign with the Broncos later this week, per source. Saints were also in on Riddick and several other teams called on former Lion. Appears Elway about to give Joe Flacco a new weapon. #9sports — Mike Klis (@MikeKlis) August 1, 2019
During his six seasons with the Lions, Riddick rushed for 1,023 yards on 288 carries and caught 285 passes for 2,238 yards. In all, he scored 19 touchdowns during his time in Detroit.
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UCF: New head coach Josh Heupel returns enough talent to the nation's highest-scoring offense to keep lighting up the scoreboard under dark-horse Heisman candidate QB McKenzie Milton. Heupel made a name for himself with his work as Missouri's offensive coordinator, but after UCF's perfect 13-0 season, the best coaching he can do for this team on offense might be letting them stick to what worked a year ago. The defense is another story. The Knights lost a ton of talent all over the field, so new defensive coordinator Randy Shannon will have his work cut out for him. Even if that unit regresses a little, UCF is still the best team in the conference.
MEMPHIS: Riley Ferguson and Anthony Miller are no longer around, but it's pretty clear that head coach Mike Norvell's spread offense can adapt to any player who's running the show. The Tigers are going to put up points, especially considering talented running backs Darrell Henderson and Patrick Taylor return to make plays behind what could be the conference's best O-line. On the other side of the ball, Memphis has some talent in its secondary. The Tigers aren't going to shut anybody out, but they can create turnovers and aren't going to completely let their offense down.
PREVIEW
No. 10 UCF looks to keep rolling at Memphis
Memphis coach Mike Norvell has mentioned ahead of Saturday's home game against No. 10 Central Florida that the Tigers are facing a better team than the unbeaten Knights featured in last year's AAC championship game.
Central Florida won that game 62-55 in double overtime, preserving their perfect record. The Knights would finish 13-0 under former coach Scott Frost after defeating Auburn in the Peach Bowl.
Josh Heupel is coaching Central Florida now after Frost left for Nebraska and the Knights have continued their dominance, starting 5-0 to increase their winning streak to 18 games.
They are 2-0 in the American Athletic Conference, tied atop the East division with No. 25 Cincinnati and Temple. Memphis is 4-2 overall and in fifth place in the West with a 1-2 record.
"They're probably playing even faster than what they did last year," Norvell said of Central Florida during the AAC's weekly teleconference. "Their tempo is at warp speed. They're snapping the ball anywhere from 5 to 10 seconds after the previous play, which is extraordinary."
Central Florida is third in the nation in total offense with 574.4 yards per game, which is more than last year's average of 530.5. The Knights have scored 38 or more points in each game this season.
Junior quarterback McKenzie Milton is 13th nationally throwing for 300.2 yards a game while completing 102 of 171 passes for 1,501 yards with 15 touchdowns and only four interceptions. He has also rushed for 215 yards on 37 carries with five touchdowns.
"They're playing at a dominant stage regardless of who they played," Norvell said.
Milton, who has started 28 consecutive games, had an injury scare in last week's 48-20 win over SMU. He took a hit while trying to earn a first down, sandwiched by SMU defenders. He lay on the ground for a few minutes as trainers tended to him. He managed to walk off the field.
"We tell him to get down, but he doesn't like to do that too often," Heupel said. "We want to keep him as healthy as possible without eliminating or taking away a portion of his game. Certainly, glad he was healthy and able to play."
Memphis is equally efficient to last season, Heupel said, despite the Tigers featuring a new quarterback in Brady White. Heupel said during the teleconference that White is efficient and that he is impressed with running back Darrell Henderson's speed and vision.
White is completing almost 70 percent of his passes (69.2 percent), hitting 108 of 156 passes for 1,549 yards with 15 touchdowns and only one interception. His passing rating of 183.08 tops the AAC and is seventh nationally.
Henderson tops the AAC with 155.7 yards rushing a game, gaining 934 yards on 79 carries with 12 touchdowns. He leads the nation with his rushing yards and 11.8 yards per carry.
Heupel also mentioned Memphis is more physical than the teams Central Florida has faced this season.
"That's kind of the secret to their sauce," Heupel said during the AAC teleconference. "They got dynamic players and they're really physical and that's typically true of really good football teams."
Both teams are ranked in the nation's top 10 in total offense. Memphis is No. 6, averaging 547.2 yards a game.
Central Florida boasts a defense that is allowing only 17.4 points per game, but Memphis, which is allowing 24.5 points a game, has a higher ranked defense at No. 38 (348.7 yards allowed a game) compared to the Knights at No. 47 (356.4).
If the game comes down to the quarterback, Central Florida has the No. 3 pass-defense team in the AAC, limiting opponents to 174.6 yards a game through the air. The Knights' sophomore cornerback Richie Grant has three interceptions, which is tied for the league lead with Tulsa's Cooper Edmiston.
"They were a well-coached team this last year and they're a really well-coached team this year," Norvell said. "It's just a little bit different presentation."
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Perchloromethyl mercaptan, CCl3SCl, excited with synchrotron radiation in the proximity of the sulfur and chlorine 2p edges: dissociative photoionization of highly halogenated species.
We have investigated the dissociative photoionization of shallow-core excited CCl3SCl by using multicoincidence time-of-flight mass spectrometry and synchrotron radiation in the S 2p and Cl 2p edges. The relative abundances of the ionic fragments and their kinetic energy release values were obtained from both PEPICO (photoelectron photoion coincidence) and PEPIPICO (photoelectron photoion photoion coincidence) spectra. The dynamic of the ionic fragmentation of S and Cl 2p excited CCl3SCl has been studied and compared with those of CCl4. Features determined in the present study seem to be relevant aspects for explaining the dissociation of highly chlorinated species under the action of VUV irradiation. The fragmentation pattern shows that chlorine ion (Cl+) is prominently formed upon both S and Cl 2p excitations.
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Monday, March 31, 2014
With "Fall of the Mutants" behind us and the continued expansion of the line (as well as bi-weekly shipping and "Inferno") still ahead, April looks to be another straightforward (if fill-in laden) month.
Sunday, March 30, 2014
After an odd three week hiatus (after having been shelved during the Olympics), SNL returned this week with another episode that landed firmly in "middling" territory, one of those outings with no real stinker of a sketch but no real standouts either, despite the best efforts of the host. Like most hosts with a background in sketch and/or stand-up comedy, Louis C.K. acquitted himself well and seemed perfectly comfortable with what he was asked to do. For the most part, he simply played some combination of quirky or put-upon straight men, but that's what he does well, and he did it well here. But after all that time off, you'd have hoped the show would have come back with a bit more energy.
This wasn't the funniest or most groundbreaking episode, but I'll give it credit for being relatively original plot-wise, covering some ground it hasn't covered before, which is a pretty rare accomplishment here in the 25th season.
Plot
On Muir Isle, Kitty awakens from a dream in which the X-Men are still alive but slaves of Mojo, trying to capture Phoenix for him. Elsewhere, Meggan finds Captain Britain drunk and despondent after the death of his sister Psylocke, and she leaves to find him help. On Muir Isle, Kitty and Nightcrawler realize they both had the same dream. They are interrupted by the arrival of Gatecrasher and Technet, interdimensional bounty hunters seeking Phoenix, followed shortly by Meggan. A fight breaks out, and Technet manages to capture Meggan and Kitty while Nightcrawler escapes. Meanwhile, Rachel Summers, Phoenix, escapes from Mojoworld and arrives in London, pursued by the Warwolves. Elsewhere, Nightcrawler seeks out Captain Britain, but finds him still a drunken wretch and leaves, admonishing him, In London, Phoenix is captured by Technet, prompting a scuffle between the Warwolves and the bounty hunters.
Plot
With their father away at a conference, the grounded Power children are waiting for their mother to come home from work when the power goes out. After hearing on the radio that the blackout was caused by The Horsemen of Apocalypse, Katie, the only one not grounded, flies off to find their mother on the subway to make sure she's alright. In one of the subway tunnels she encounters Pestilence and is able to escape, but not before getting sick. When Katie doesn't return, the rest of Power Pack track her down and help her heal. They then see Apocalypse's ship crash into the Empire State Building and try stop it, only to encounter Cyclops and Marvel Girl. Pestilence attacks again, but she's hit by debris and Power Pack is unable to save her. After Cyclops and Marvel Girl leave to stop Apocalypse, Power Pack works together to prevent the ship from crashing into the Statute of Liberty, triggering an explosion that blows off enough to ship's tail pipe to save the statute and the tourists inside. After seeing X-Factor emerge triumphant from the ship, they race home, getting there just ahead of their mother. They admit they left the house, but she is too grateful they're okay to punish them further.
Plot
Famine arrives in Kansas and begins laying waste to farmland. Meanwhile, Steve Rogers, the Captain, former Captain America, and his allies are flying aboard their private plane when they receive word of Famine's attack, and Captain tells the pilot to plot a course for Kansas. At Ft. Meade, John Walker, the current Captain America, runs into Freedom Force and learns of the death of the X-Men as well as Famine's attack. He is tasked with stopping her. In Kansas, the Captain, Falcon, Nomad and D-Man attack Famine. She is able to take out Nomad and Falcon, but with D-Man subduing her mount, the Captain defeats Famine. However, she is teleported away before he can take her into custody. Later, Captain America arrives on the scene, well after the battle has completed. Two weeks later, the Captain meets with Tony Stark, who provides him with a new shield to use in his new identity.
Tuesday, March 25, 2014
What's worse: a narrative blithely ignoring a flaw in its structure, trundling along, refusing to give voice to the problem, or a narrative which at least acknowledges an issue, but then attempts to resolve it in a relatively slapdash way?
The main thrust of this episode, which returns us to the "Robin freak out" part of the wedding weekend to which we flashforwarded last season (which prompted Ted to tell us the tale of breaking Victoria out of the same church at her wedding), has Robin finally putting to words what anyone watching the show realized long ago: Barney lies a lot, and even his biggest romantic gestures to Robin were built around hideously elaborate lies. It's good to know that Robin has realized this, and it's good to see the show's writers acknowledge it as well.
This prompts Robin to run off, right into the Mother. To her (and the show's credit), the Mother doesn't miraculously talk Robin out of fleeing her wedding: she just tells her to at least stop and take some deep breaths before making a big decision (it's the kind of advice you could plausibly get from a stranger at your wedding whom you just ran into, and not the kind of advice you get from your best friend's future wife, so I appreciate the restraint). This allows Barney the time to catch up with her and and unknowingly tell her exactly what she needs to hear: that he will never lie to her again.
This episode began with Sergeant Abraham and his crew, Tara and Glenn walking the railroad tracks. Glenn, not having said anything, sees a message from Maggie to go to Terminus and then breaks into a dead sprint. I believe I've made this point before but that scene really crystallized for me how Glenn and Maggie’s characters are solely defined by their relationship.
Glenn’s lone motivation is to be with Maggie. Maggie’s lone motivation is to be with Glenn. Other than that all I can say is…they’re relatively nice people? I guess?
Saturday, March 22, 2014
Around the Web
This week, I've got a slightly revised and updated version of my To Better Know a Hero post on Black Widow up on Sound on Sight. Check it out before you see Captain America: Winter Solider.
The Simpsons: The Winter of His Discontent
This felt like the warmed up leftovers of two plots (Homer embraces the lifestyle of the elderly, Bart is befriend by Nelson after helping him out) from two previous episodes ("The Two Mrs. Nahasapeemapetilons" and "The Haw-Hawed Couple"), with an extended parody of The Warriors tagged onto the end.
Plot
Outside Apocalypse's ship, police arrive and attempt to arrest X-Factor, but when they hear an explosion nearby, the cops allow X-Factor to investigate. Elsewhere, Apocalypse watches from his new base as he recalls Famine from Kansas. In Manhattan, X-Factor arrives at the site of the explosion, and helps rescue people trapped inside the burning building. As they finish, one of the cops tips them off to a collapsed building nearby, and they rush off to help, rescuing more people. At the police's suggestion, Marvel Girl telekinetically takes the wounded to Roosevelt Hospital. At the hospital, Beast runs into Trish Tilby, and she learns about his condition. X-Factor continues to help at the hospital throughout the night, until they're told things are under control. As they leave, they're approached once again by the police, but are told they're no longer under arrest. Thanks to all the reporters covering their acts of heroism, the city is now considering them heroes.
Plot
On the Animates' island, Rahne is hysterical over the death of Doug as Illyana teleports the remaining Right soldiers to Limbo. When she returns to the island, the New Mutants say goodbye to Bird-Brain and the Animates, then teleport home with Doug's body. Meanwhile, Magneto arrives at the Hellfire Club amidst the devastation caused by Apocalypse and his Horsemen, and learns of the X-Men's battle in Dallas. Back at the mansion, the New Mutants all react to Doug's death in their own way before calling Magneto at the Hellfire Club. As they wait for him to return, they watch the footage of the X-Men seemingly dying in Dallas. Just then, Magneto arrives and learns of Doug's death. His sadness quickly gives way to anger, as he suspends the New Mutants in midair, asking if that's the only way he can keep them safe.
Plot
Inside the lobby of Eagle Plaza, the X-Men find themselves beset by both demons and Viet Cong soldiers. As Neal Conan records and broadcasts their actions, Madelyne comes across an image from the past: a young Forge casting a spell, powered by the souls of the dead soldiers around him, which calls forth demons to destroy the Viet Cong. High above in Roma's Starlight Citadel, the Adversary gloats to the captive Roma, Forge and Storm. Psylocke senses the real Forge in the citadel and Rogue tries to fly to it, but is rebuffed by fierce winds. However, trusting to his hollow bones and luck, the X-Men use Longshot as a kite, and he manages to sail over the winds, dragging the rest of the X-Men and Neal behind him. Reaching the citadel, Rogue absorbs a measure of the Adversary's power and sorcerous abilities. Just then, Colossus, who as Roma's ringer was not accounted for by the Adversary, flies into the Adversary, his organic steel body shredding the Adversary's outer form, severely weakening him. Rogue then opens a portal, and the X-Men combine their powers to force the Adversary through it.
Tuesday, March 18, 2014
In a testament to not judging an episode by its DVR description, this turned out to be much better than I was expecting when the episode synopsis had me questioning the logic of shoehorning in another "heretofore unseen but he's been there all along" friend of the gang three episodes from the end, as if there aren't more important things to be covering. In execution, however, the idea worked better, as Gary Blauman (who has made brief appearances before) was merely a vehicle to tell the story of Ted's first date with the Mother as well as an excuse to give us a series wrap on a bunch of supporting players from the past.
Now, I wasn't exactly dying to know what the future holds for Carl the Bartender or that Blah-Blah's name was actually Carol, but the montage at the end of the episode was exactly the kind of thing I like to see from a show as it nears the end, especially a show constructed like this one, when the ending is planned out with plenty of advance knowledge and in which the futures of various characters can be revealed without breaking the model of the show. We know the broad strokes, at least, of what the future holds for the main characters; only fitting then that we learn a little bit about the futures of the various supporting players in their lives as well. That it came in a mostly funny episode that sidestepped most of the season's biggest problems, all the better.
Monday, March 17, 2014
The Good: This episode was an interesting character study. It featured some significant character moments and dirty laundry was aired. This episode also brought up an interesting moral dilemma without an easy answer.
The Bad: More wheel spinning; nobody is closer to Terminus. This episode heavily featured Carol. Their seemed to be an acceptance that Carol’s decision to kill the two people at the prison was right one.
Saturday, March 15, 2014
Around the Web
Two more reviews from me at Sound on Sight: the penultimate chapter of the "X-Files Conspiracy" crossover, and the penultimate chapter of "Trial of Jean Grey". It was a penultimate week, apparently.
We're still a few weeks away from going live (we want to get a few under our belt and work out the kinks before we start posting), but you can be sure I'll pimp the hell out of it here once it goes up. In the meantime, you can follow the show on twitter @sbtb_reviewed, and check out our under-construction tumblr here.
The Simpsons: The Man Who Grew Too Much
Always nice to see a Sideshow Bob episode centered around something other than Bob trying to kill Bart. But let's not pretend the act one reveal of Sideshow Bob is at all shocking when Fox has been pimping his appearance in commercials all week.
Plot
Apocalypse and the captive X-Factor watch as the Horsemen attack Manhattan. As Apocalypse gloats, Beast is able to deactivate Iceman's inhibitor belt, enabling him to ice up and free his teammates. They attack Apocalypse, damaging a transformer that causes the ship to suck light and energy from the city, plunging it into darkness. After Apocalypse ejects Marvel Girl and Cyclops from the ship, they decide to try and stop the Horsemen. As Pestilence heads into the subway tunnels, Marvel Girl and Cyclops split up to face Famine and War. Famine seemingly defeats Marvel Girl, at which point Apocalypse teleports her to Kansas, to smash American's bread basket. Meanwhile, Cyclops beats War by targeting his mount, and reunites with Marvel Girl. Aboard the ship, Beast accidentally destroys the ship's cloaking mechanism and stabilizers, causing it to appear in the sky above the city and then to smash into buildings, causing panic in the streets.
Plot
The Animator brings the captured New Mutants deeper into his complex, where he imprisons them before ordering his Animates to destroy a failed batch of fellow creatures. Back in New York, Magneto flies off to the Hellfire Club to use their equipment to search for the missing New Mutants. Meanwhile, Roberto and Warlock discover the maps their friends had been studying and deduce their relative location. Leaving a note for Magneto, they fly off to find their teammates. Meanwhile, the Animator is contacted by Cameron Hodge, seeking reassurance that the Animator is still working to find a way to stop mutations. Though he insists he is, Hodge decides to visit the island himself. Worried the Right will usurp his work, the Animator decides to flee. But when the New Mutants convince the Animates guarding them that the Animator intends to kill the Animates, they break free and overpower the Animates. Believing they've won, the New Mutants prepare to take an elevator to the island's surface, but when it opens, Hodge and a group of Right soldiers emerge.
Plot
In Dallas, the X-Men, along with a captive Mystique, are gathered inside Eagle Plaza when Longshot notes that sunlight is pouring in through the hole in the night sky. Outside, the captured X-Men attempt to escape, but their battle stops short when Dallas is suddenly transformed into a chaotic landscape of different eras, from the prehistoric to the futuristic. Meanwhile, Forge and Storm find themselves on a parallel Earth created by the Adversary to be their prison, and Storm cares for the injured Forge. In Dallas, the X-Men and Freedom Force call a truce in order to help defend the city as reporters Neal Conan and Manoli Wetherell broadcast to the world their efforts to save civilians from various extratemporal menaces.
Tuesday, March 11, 2014
Well, at least this episode didn't foreshadow the death of a major character...
Aside from that though, this wasn't a half bad episode. Certainly, as has been the case all season, the wedding-centric storyline was pretty lame. Tracey Ullman was fine as Robin's mother, but all the "I'm marrying a man just like my father" panic was not only cliche, but incredibly forced and not at all funny (one line aside). And, of course, the ending ominously sets up yet another ride on the Ted/Robin merry-go-round (this time begun by Robin), which we at least all knew was coming based on previous flashforwards.
But not only did the main plot of the episode circle back around to a plot point we'd all groused about previously (the abrupt way Lily conceded the argument to Marshall, and where she went in the middle of the night), but it also relied less on obvious callbacks to past gags on the show (Boats Boats Boats aside). Most importantly, it was funny. Granted, I'm a sucker for the Captain, even though he's always been more of a cartoon than an actual character, but I can't deny laughing at his forced attempts to work boats into everything. And Ted's Hercule Poirot-esque drawing room whodunit breakdown may just be the comedic highlight of Josh Radnor's season (though just like the Captain, I'm a complete sucker for any gags built around The Mosby Boys. Blame my love of The Three Investigators).
Then again, maybe for the first time ever this season, perhaps I'm just glad the Mother wasn't in this one. It's amazing what a difference ending on the reveal of Marshall and Lily's future daughter rather than a grim portent of death does for one's enjoyment of an episode.
Survival. That’s the name of the game in a zombie apocalypse. Luckily, humans are hard wired for survival. We naturally seek out food, water, shelter. We naturally avoid pain and look for safety. We naturally try to keep ourselves alive. (Well, for the most part. The brain can be confused by modern technology. Oh, and drugs. Drugs can confuse the brain in a variety of different ways.)
At the lowest level these survival instincts are regulated by neurotransmitters. They tell us when to eat, sleep and everything else we need to survive. Of course, there’s another survival instinct that often gets overlooked. It’s the instinct primarily controlled by the neurotransmitter oxytocin. It’s the instinct to do the nasty.
No, this isn't your weekly installment of “Dramatically Oversimplifying Neuroscience.” It’s just readily apparent that the characters showcased in the appropriately name Walking Dead episode “Alone” are all being governed by oxytocin.
Sunday, March 9, 2014
Though by no means one of the season's standout episodes, this was a marked improvement over last week's limp Jim Parsons-hosted affair. Lena Dunham wasn't exactly asked to stretch, mostly just playing it straight (though she did get in a decent Liza Minelli impression towards the end), and was occasionally overshadowed by a surprising bevy of guests, but she handled herself well, even recovering nicely from a flubbed line at one point. It might just be the timing of it, but this seemed like a pretty strong episode, continuing the season-long up-and-down streak.
Other Thoughts
Liam Neeson popping up in the cold open made for a decent joke in and of itself (I'm a sucker for "actors are really their characters" bits), but the payoff (Obama starring in an action film parody) wasn't all that great.
Saturday, March 8, 2014
Putting aside my bitterness over losing my Oscar pool by one point, this wasn't a terrible show, though it wasn't a terribly good one either. Ellen turned in a perfectly cromulent monologue, then became far too obsessed with going out into the crowd (which, I know, is her schtick). Some of that material worked, some of it didn't. The pizza thing mostly did, largely because, as fabricated as it may have been, the reactions to it felt genuine. There's something undeniably entertaining about seeing people like Meryl Streep and Brad Pitt fishing around for change or Harrison Ford's excitement at the prospect of pizza, just like regular people!
Plot
After their battle with the Right, X-Factor finds themselves inside a strange ship. Apocalypse appears and welcomes them to his home. Cyclops orders an attack, but Apocalypse easily bests them, telling them of his long life and taunting them about their actions as mutant hunters. Apocalypse offers them a place at his side as he prepares to unleash his Horsemen on Manhattan. X-Factor refuses and attacks the Horsemen as Apocalypse watches. Though Caliban is quickly forgotten, X-Factor manages to best the Horsemen until Death appears.
Plot
Landing on the island from which Bird-Brain came, the New Mutants find themselves surrounded by angry human-like animals, animates, similar to Bird-Brain. Below, a scientist working for the Right who calls himself the Animator, and who is responsible for the creation of the animates, detects the arrival of the New Mutants. Not wanting to draw the attention of Cameron Hodge, he calls the Right and tells them to stay away from the island while he deals with the mutants. Above, Bird-Brain is able to calm the animates with the food he brought, but then they turn on him, saying Bird-Brain has become too much like man, who is the enemy. In New York, Roberto and Warlock return to the mansion after their adventures with the Beat Street Club. They are reunited with an equally overjoyed and angry Magneto, but quickly discover the rest of the New Mutants are gone.
Plot
In Edinburgh, a recovering Colossus sketches the X-Men, to the amusement of a group of local kids, though a fight quickly breaks out amongst the children regarding whether or not mutants are dangerous. As they run off, Colossus is approached by a mysterious woman who offers to read his palm in exchange for a sketch. When he looks up from his sketch pad, the woman is gone, in her place of a small statute of himself, and when he looks at his drawing, it's of another woman entirely. Elsewhere, the Adversary, still in the form of Naze, arrives in Roma's otherdimensional citadel, where he's imprisoned Roma, the guardian of the Omniverse and the woman whom appeared on Colossus' drawing. With Storm and Forge removed from the board, the Adversary gloats that chaos will finally reign in the universe, though Roma thinks to herself that the game isn't over, and that players exist of whom the Adversary is unaware.
Tuesday, March 4, 2014
If we are to take the implication of the final scene of this episode at face value, it seems that at some point between that scene, set in 2024, and 2030 (the year of SagetTed's narration), the Mother is going to die (presumably of a terminal illness, since they seem aware of her impending death in this episode). Now, the idea that the Mother's death is what prompts SagetTed to tell his kids this ridiculously long story has long been a theory proposed by some fans (along with a corollary that this would allow him to be with Robin in the future, hence explaining the show's seemingly odd fascination with that relationship in spite of its titular premise), but I've always assumed that was just a whacky fan theory (akin to how fans theorized that all the plot threads on Lost would eventually pay off).
Monday, March 3, 2014
The more things change the more things stay the same. You can have society collapse, the dead rise and the average life expectancy cut down to an eighth of what it was. No matter what happens, though, certain constants remain. One those constants, apparently, is that underage teens will always seek out alcohol.
This is the first episode, I believe, that focused on only one piece of the fractured group. It simply stayed with Daryl and Beth as they search for and then drink the aforementioned booze. Once they reach the end of their journey they realize they've learned something about each other and themselves. It’s just your typical teenage comedy film…with zombies.
Sunday, March 2, 2014
Boy, this show did not come out of the Olympics break strong. That Peter Pan sketch wasn't awful, but when it led off the night, I wasn't exactly filled with enthusiasm for the rest of the show, and that mostly panned out. Parsons was mainly a non-entity, showing up in a fair number of sketches but rarely asked to play anything other than comically put upon or lovably goofy, two beats he reliably hits as Sheldon. He seemed to be having a good time; it just would have been nice if the sketches had been better.
In the first really tight race of the night, it's a dead heat between pop culture darling Jennifer Lawrence and newcomer Lupita Nyong'o. The pair have shared the pre-Oscar hardware (including a Globe and BAFTA win for Lawrence). History tends to favor Nyong'o: she's in the more traditionally-Academy-friendly film, while back-to-back Oscar wins are rare indeed for actors (Lawrence, who won Best Actress last year for Silver Linings Playbook, would in fact be the first actor to run the lead/supporting table in consecutive years).
That said, recent Oscar history suggests we shouldn't put too much stock in Oscar history, and while 12 Years a Slave is in the thick of the Best Picture race, it doesn't seem to have the same widespread support as, say, Gravity or American Hustle. I...I just don't know, guys. I'm going to go with Nyong'o for now (if you believe 12 Years a Slave has a shot at Best Picture, and I do, then it's going to need to pickup some additional wins), but I'll be going back and forth right up to the ceremony, and it may come down to a coin flip.
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While his administration and congressional leaders continued to hammer out a trillion-dollar COVID-19 stimulus package, President Trump signed into law Wednesday evening the Families First Coronavirus Response Act, the second bipartisan coronavirus relief bill Congress has passed so far — the first providing around $8 billion in emergency funding for emergency prevention and response efforts. So what’s in the “Families First” bill? Below is a breakdown of its key provisions.
The Families First law addresses the following key priorities, among others:
provides additional funding for nutrition and food assistance programs, particularly in light of schools being shutdown and additional needs for elderly assistance programs expands paid leave benefits expands unemployment benefits provides coronavirus testing at no cost to consumers temporarily increases the Medicaid federal medical assistance percentage
Food and Nutrition Assistance Funding: Families First infuses significant federal money — nearly a billion dollars’ worth — into various nutrition assistance programs, available through Sept. 30, 2020. The provisions include $500 million for the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) and $400 million for the emergency food assistance program. Another $100 million is allocated for programs in U.S. territories: Northern Mariana Islands, Puerto Rico and American Samoa. The law loosens restrictions on who can received Supplemental Nutrition Assistance Program (SNAP) benefits and specifies that qualified households will be eligible for the food assistance programs if their schools have been closed for five consecutive days.
Paid Leave: As summarized by NPR, Families First requires employers with fewer than 500 employees to provides two weeks of paid sick leave to employees who cannot work for COVID-19 related reasons, whether they have contracted the virus, need to self-isolate, must care for children whose schools have been shutdown, or must care for someone who is sick or quarantined. The law specifies that employers cannot force employees to find a replacement or take other forms of paid time off. To help businesses in covering paid leave costs, the bill provides tax credits to employers. Self-employed persons will also get a tax credit if they must take sick leave as a result of COVID-19. Additionally, the law expands paid family and medical leave to up to three months.
Unemployment Benefits: The law provides almost $1 billion in state grants to help processing for expanded unemployment benefits and provides additional emergency relief funds to states that have already maxed out unemployment benefits.
Free COVID-19 Testing: Families First makes coronavirus testing completely free for the public, providing waivers so that consumers does not have to pay deductible or copays.
Temporary Medicaid Expansion: The law “temporarily increase[s] the Medicaid federal medical assistance percentage (FMAP),” increasing by 6.2% federal payments to the states to cover Medicaid costs.
Below is the full text of the congressional summary of the Families First Coronavirus Response Act (read full text of the bill here):
Families First Coronavirus Response Act
This bill responds to the coronavirus outbreak by providing paid sick leave and free coronavirus testing, expanding food assistance and unemployment benefits, and requiring employers to provide additional protections for health care workers.
Specifically, the bill provides FY2020 supplemental appropriations to the Department of Agriculture (USDA) for nutrition and food assistance programs, including
the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC);
the Emergency Food Assistance Program (TEFAP); and
nutrition assistance grants for U.S. territories.
The bill also provides FY2020 appropriations to the Department of Health and Human Services for nutrition programs that assist the elderly.
The supplemental appropriations provided by the bill are designated as emergency spending, which is exempt from discretionary spending limits.
The bill modifies USDA food assistance and nutrition programs to
allow certain waivers to requirements for the school meal programs,
suspend the work requirements for the Supplemental Nutrition Assistance Program (SNAP, formerly known as the food stamp program), and
allow states to request waivers to provide certain emergency SNAP benefits.
In addition, the bill requires the Occupational Safety and Health Administration to issue an emergency temporary standard that requires certain employers to develop and implement a comprehensive infectious disease exposure control plan to protect health care workers.
The bill also includes provisions that
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Estrogen and progesterone activate spinal kappa-opiate receptor analgesic mechanisms.
Rats and humans manifest elevated response thresholds to aversive stimuli during gestation and parturition. This pregnancy-associated antinociception is mediated, in part, by a spinal cord dynorphin/kappa antinociceptive system. Simulating the maternal pregnancy blood concentration profile (in non-pregnant animals) of 17-beta-estradiol (E2) and progesterone (P) produces an opioid antinociception which closely approximates that of actual pregnancy. The current study was initiated in order to determine whether sex steroid-induced antinociception involves a spinal cord kappa-opiate receptor-coupled system (as does the antinociception of actual gestation). Additionally, sex steroid modulation of the intrathecal (i.t.) antinociceptive effectiveness of a kappa agonist was investigated. The opioid antinociception associated with simulating the pregnancy blood concentration profile of E2 and P (hormone-stimulated pregnancy, HSP) is significantly antagonized by i.t. administration of nor-binaltorphimine, an antagonist highly specific for the kappa-opiate receptor. This indicates that exposure (of non-pregnant animals) to the pregnancy blood profile of E2 and P activates a spinal cord kappa-opiate receptor analgesic system, as occurs during actual gestation. Furthermore, during HSP, antinociceptive responsiveness to i.t. U50,488H (kappa-selective) is significantly enhanced (approximately 40%). This effect is abolished in animals treated concomitantly with steroid hormones and systemic naltrexone or i.t. nor-binaltorphimine. In contrast to the effects of steroid treatment on antinociceptive responsiveness to i.t. U50,488H, no alteration in antinociceptive responsiveness to i.t. sufentanil was observed on day 19 of HSP over all doses tested (0.1-1 nmol). Thus, during HSP (and actual gestation), a less robust constituent of intrinsic opioid pain-attenuating systems in the spinal cord is recruited. pF to mediate, at least in part, the maternal antinociception of gestation. pF, positive modulation of the spinal cord kappa analgesic system occurs post-synaptically. This laboratory previously reported that simulating the pregnancy blood concentration profile of E2 and P also positively modulates spinal dynorphin content and the processing of its precursor, suggesting a presynaptic loci of action. Thus, female rats possess a spinal dynorphin/kappa analgesic system that can be positively modulated, pre-synaptically as well as post-synaptically, by circulating sex steroids.
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Identification and analysis of icCu/Zn-SOD, Mn-SOD and ecCu/Zn-SOD in superoxide dismutase multigene family of Pseudosciaena crocea.
Superoxide dismutases (SODs) belong to a significant and ubiquitous family of metalloenzymes for eliminating excess reactive oxygen species (ROS). In this paper, the complete open reading frames (ORFs) of intracellular Cu/Zn-SOD (icCu/Zn-SOD), Mn-SOD and extracellular Cu/Zn-SOD (ecCu/Zn-SOD) were identified from the large yellow croaker (Pseudosciaena crocea, designated as LycSOD1, LycSOD2 and LycSOD3). The sequences were 465 bp, 678 bp and 645 bp (GenBank accession no. KJ908287, KJ908285 and KJ908286), encoding 154, 225 and 215 amino acid (aa) residues respectively. The deduced aa sequences of LycSOD1, LycSOD2 and LycSOD3 shared high identity to the known icCu/Zn-SODs, Mn-SODs and ecCu/Zn-SODs with BLASTp and Phylogenetic analysis. Two conserved Cu-/Zn-binding sites (H-44, H-47, H-64, H-121 for Cu binding and H-64, H-72, H-81, D-84 for Zn binding in LycSOD1, H-98, H-100, H-115, H-164 for Cu binding and H-115, H-163, H-166, D-169 for Zn binding in LycSOD3) and one conserved manganese coordinating sites (H-57, H-101, D-186, H-190 in LycSOD2) were identified. The total length of DNA sequences of LycSOD1, LycSOD2 and LycSOD3 were 3447 bp, 3387 bp and 3886 bp respectively, and there were 4 introns and 5 exons in Cu/Zn-SODs (LycSOD1 and LycSOD3), but only 3 exons and 2 introns in LycSOD3. Spatial expression analysis indicated the highest mRNA expression of three SODs all appeared in liver among eight detected tissues, the highest expression level was LycSOD1, then LycSOD2 and the lowest was LycSOD3 for almost each tissue. The expression of LycSOD1, LycSOD2 and LycSOD3 mRNA were all up-regulated in liver after Vibrio alginolyticus stimulation. The temporal expression peak of LycSOD1 and LycSOD2 were around 9-fold and 8-fold compared to control respectively, whereas, LycSOD3 got the highest level at 48 h post-injection (about 4.2-fold). All the results gave several new and useful evidences for further understanding the regulatory mechanism of superoxide dismutases in the innate immune system of sciaenidae fish.
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An amplified electrochemical strategy using DNA-QDs dendrimer superstructure for the detection of thymine DNA glycosylase activity.
A triple-signal amplification strategy was proposed for highly sensitive and selective detection of thymine DNA glycosylase (TDG) by coupling a dendrimer-like DNA label with the electrochemical method and quantum dots (QDs) tagging. The DNA-QDs dendrimer-like superstructure was designed by DNA hybridization and covalent assembling. Benefiting from outstanding performance of the amplification strategy, this assay showed high sensitivity, extraordinary stability, and easy operation. The limit of detection could reach 0.00003 U µL(-1) with a splendid specificity. The TDG content in different concentration of HeLa cell was also determined. This assay opens a new horizon for both qualitative and quantitative detection of TDG, holding great promise for potential application in cancer cell research and clinical diagnostics.
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Stocks fell sharply Tuesday morning as Wall Street braced for President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE to impose higher tariffs on Chinese imports after a breakdown in trade negotiations with Beijing.
The Dow Jones Industrial Average closed with a loss 473 points by noon, a 1.8-percent drop, after briefly falling below 26,000 points. The S&P 500 index closed down 1.7 percent, while the Nasdaq composite sank by 2 percent.
The sell-off started during the first hours of trading, following an announcement Monday evening by Treasury Secretary Steven Mnuchin Steven Terner MnuchinHillicon Valley: DOJ proposes tech liability shield reform to Congress | Treasury sanctions individuals, groups tied to Russian malign influence activities | House Republican introduces bill to set standards for self-driving cars Treasury: Trump's payroll tax deferral won't hurt Social Security Treasury sanctions individuals, groups tied to Russian malign influence activities MORE and U.S. Trade Representative Robert Lighthizer Robert (Bob) Emmet LighthizerWhiskey, workers and friends caught in the trade dispute crossfire GOP senator warns quick vote on new NAFTA would be 'huge mistake' Pelosi casts doubt on USMCA deal in 2019 MORE that Trump would raise tariffs on $200 billion worth of Chinese goods, from 10 percent to 25 percent, on Friday.
ADVERTISEMENT
Trump announced his intent to raise tariffs on Chinese imports in a pair of Sunday tweets, spurring a steep sell-off in global financial markets Monday morning. But while Asian markets took heavy losses on the news, the Dow recovered almost all of a 470-point drop by the end of Monday trading.
An increase in U.S. tariffs on Chinese goods would be a major setback to trade talks between Washington and Beijing at a time when both sides appeared to be closing in on a deal.
Trump’s threat Sunday to raise tariffs and impose new taxes on more than $300 billion in imports was a surprising turn in negotiations that the president previously said would yield a deal “very soon.”
Several media outlets reported Monday that talks with China hit a roadblock after Beijing refused to agree to measures to halt intellectual property transfers that would require a change to Chinese law.
"We felt we were on track to get somewhere. Over the course of last week we have seen an erosion of commitments by China," Lighthizer said Monday, according to Bloomberg News. He added there were still significant issues to be hammered out in talks.
Chinese Vice Premier Liu He, Beijing's lead on trade negotiations, was scheduled to visit Washington on Thursday, a day before the tariff increase would go into effect.
Trump imposed a 10 percent tariff on $200 billion in Chinese imports last year and delayed the scheduled increase to 25 percent in January as negotiations proceeded. The president has also imposed a 25 percent tariff on $50 billion in Chinese goods.
If Trump follows through with his threat to impose tariffs on an additional $300 billion in Chinese imports, it would likely subject all goods from the country to import taxes.
Updated at 4:35 p.m.
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TAIPEI (Taiwan News) -- Early this morning (July 26), a fight broke out between Taiwanese tourists and Chinese tourists at a hot pot restaurant in Kaohsiung.
At 5 a.m. this morning, a fight broke out between Taiwanese and Chinese tourists at a well-known mala hot pot restaurant in Kaohsiung's Lingya District, reported Apple Daily. One table had a group of Taiwanese tourists, while the other table was full of Chinese tourists.
Just as the Taiwanese were getting up to pay their bill and leave, the Chinese tourists allegedly stared at the Taiwanese. The Chinese tourists' glares were enough to ignite a massive brawl, according to the report.
Soon hot pot bowls, cups, wooden chairs, and broth became weapons. The restaurant was in shambles in a matter of minutes.
Restaurant staff desperately called the police, who swiftly arrived on the scene. Police arrested a Chinese national who had refused to cooperate with officers, while the rest of the combatants were taken in for questioning.
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---
abstract: 'Theoretical modelling and observations of AGN jets suggest that the non-thermal electrons emitting the observed radiation should (i) carry an amount of energy comparable to the magnetic fields ($U_e\sim U_B$), which is likely the case if the magnetic fields play a dynamically important role in the jet’s acceleration process; (ii) cool efficiently in a dynamical time ($t_{\rm cool}\lesssim t_{\rm dyn}$), which is suggested by the fact that a large fraction of the jet’s kinetic energy is promptly converted into radiation. These expectations are at odds with the results of the simplest one-zone Self-Synchro-Compton (SSC) model for the Spectral Energy Distribution (SED) of BL Lacs. Indeed, the model predicts $U_e\gg U_B$ and $t_{\rm cool}\gg t_{\rm dyn}$ for most of the objects. Here we closely investigate one of the key assumptions of this model, namely that the momentum distribution of the non-thermal electrons is isotropic. We find that this assumption may be an oversimplification. If the magnetic energy is dissipated via a turbulent MHD cascade, the highest energy electrons may instead retain a small pitch angle. Since the synchrotron emissivity is suppressed when the pitch angle is small, this effect may importantly affect the modelling of the SED. As an illustrative example, we present an anisotropic model for the electron momentum distribution such that $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$ at the same time. Our model manages to simultaneously solve the two problems with one only more free parameter with respect to the usual isotropic one-zone SSC model.'
author:
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E. Sobacchi$^{1,2}$[^1] & Y. E. Lyubarsky$^1$\
$^1$ Physics Department, Ben-Gurion University, P.O.B. 653, Beer-Sheva 84105, Israel\
$^2$ Department of Natural Sciences, The Open University of Israel, 1 University Road, P.O.B. 808, Raanana 4353701, Israel
bibliography:
- '2d.bib'
title: On the magnetisation and the radiative efficiency of BL Lac jets
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**v**
BL Lacertae objects: general – galaxies: jets – radiation mechanisms: non-thermal – plasmas – MHD – turbulence
Introduction {#sec:introduction}
============
The super massive black holes residing in the centre of galaxies are able to launch jets that reach relativistic velocities. These jets produce remarkably non-thermal spectra. Observations suggest that a significant fraction (typically $\sim 15\%$) of the jet’s total energy is promptly radiated [e.g. @Nemmen2012]. In order to achieve such a high radiative efficiency, the energy dissipation process must involve the efficient acceleration and the subsequent fast cooling of a population of non-thermal particles.
AGN jets are thought to be powered by the rotational energy of the super massive black hole, which is channeled into the outflowing plasma via electromagnetic stresses [e.g. @Blandford1976; @Lovelace1976; @BlandfordZnajek1977]. In this scenario the energy budget of the jet is initially dominated by the Poynting flux, which is gradually converted into the plasma kinetic energy while the flow is accelerated. Theoretical investigation of the energy dissipation process suggests that in this regime the emitting electrons and the electromagnetic fields may carry comparable amounts of energy [see for example @Sironi2015].
Among blazars (i.e. AGN with the jet pointing towards the observer), BL Lacs are the ideal laboratory to test our theoretical understanding of the physics of relativistic jets. These objects are particularly attractive due to their simplicity, since they do not show any emission from the black hole accretion disc, as sometimes is the case for Flat Spectrum Radio Quasars (FSRQ). The Spectral Energy Distribution (SED) of BL Lacs can therefore be simply interpreted as due to Self-Synchro-Compton emission from a population of non-thermal electrons [e.g. @Tavecchio2010].
In order to fit the SED, one has to assume a broken power law for the energy distribution of the electrons. One needs just to specify (i) the number density of the non-thermal electrons; (ii) the Lorentz factor $\gamma_{\rm b}$ of the electrons at the break; (iii) the size $R$, (iv) the magnetic field $B$, and (v) the Doppler factor $\delta$ of the dissipation region. As discussed by @Tavecchio1998, all the parameters of the model are univocally determined by the observed SED.
Despite the apparent simplicity of this model, it is challenging to give a convincing physical interpretation of the results. The reason for this is twofold [see for example @TavecchioGhisellini2016]: (i) the model predicts that the magnetic fields carry just a tiny fraction of the electrons energy, contrary to the theoretical expectation that the two energies are in an approximate equipartition; (ii) the cooling time of the electrons at the break is much longer than the dynamical time, which imply that the jet is extremely radiatively inefficient and raises the further problem to explain the origin of the break itself. Note that a low radiative efficiency would be difficult to reconcile with the observations of @Nemmen2012, who instead found that a significant fraction of the jet’s energy is promptly radiated.
It has been suggested that relaxing the assumption of a one-zone emission model may help to solve this controversy [see for example @TavecchioGhisellini2016]. Though a two-zone emission model can likely provide $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$ for any individual object, we argue that extending this interpretation to the entire BL Lac sample may require some fine tuning. Indeed, since in BL Lacs the luminosity of the synchrotron peak is typically comparable to the luminosity of the IC peak of the SED [e.g. @Tavecchio2010], one would expect the magnetic energy density $U_B$ to be comparable to the radiation energy density $U_\gamma$. In any model with $U_e\sim U_B$, this immediately implies that $U_e\sim U_\gamma$. In a one-zone model, $U_e\sim U_\gamma$ is naturally achieved if the electrons efficiently radiate their energy in a dynamical time. However, if $U_\gamma$ is due to an external radiation field, as is the case in two-zone emission models, it seems to us that there is not any good a priori reason why $U_e\sim U_\gamma$.
The tension mentioned above motivates a closer examination of the one-zone SSC emission model that is usually adopted to interpret the SED of BL Lacs. Here we challenge one of the key assumptions of this paradigm, namely that the momentum distribution of the non-thermal electrons is isotropic. We show that, if the magnetic energy is dissipated via a turbulent MHD cascade, the highest energy electrons may retain a small pitch angle, which suppresses their synchrotron emission. Taking this effect into account may importantly affect the modelling of the BL Lac SED. Indeed, as an illustrative example we present an anisotropic model for the electron momentum distribution such that (i) the non-thermal electrons and the magnetic fields carry comparable amounts of energy, and (ii) the electrons at the break efficiently cool in a dynamical time. Our model has just one more free parameter than the standard isotropic model.
The paper is organised as follows. In Section \[sec:motivation\] we discuss the reason why the highest energy electrons may retain a small pitch angle. In Section \[sec:model\] we describe the predictions of our anisotropic model for the electron momentum distribution. In Section \[sec:comparison\] we compare these predictions with a model that instead assumes an isotropic momentum distribution. In Section \[sec:results\] we present our main results. Finally, in Section \[sec:conclusions\] we summarise our conclusions. Throughout this paper we always work in the frame of the source, or equivalently we assume that the source is at redshift $z=0$.
Motivation for an anisotropic model {#sec:motivation}
===================================
A crucial point in the hydromagnetic jet launching paradigm is understanding how the magnetic energy is dissipated. Since the physical scale of the jet typically exceeds the Larmor radius of the non-thermal particles by many orders of magnitude, it is natural to assume that the energy is brought down to the dissipation scale by a turbulent MHD cascade. In the following we assume the cascade to be injected at the outer scale $R$ of the dissipation region.[^2] In a relativistic, optically thin plasma the photon viscosity is unable to damp the cascade, which should then proceed unimpeded down to microscopic scales [see for example @Zrake2018].
Dissipation of MHD turbulence leads to longitudinal particle heating
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The most important property of MHD turbulence is its strong anisotropy, with the turbulent eddies becoming strongly elongated in the direction of the background magnetic field at small scales. As first proposed by @GoldreichSridhar1995, in the course of the turbulent cascade the ratio of the longitudinal scale of the eddies, $\lambda_\parallel$, to the Alfvén velocity remains equal to the ratio of the perpendicular scale, $\lambda_\perp$, to the turbulent velocity (this condition is known as “critical balance”). From this condition, one finds that $\lambda_\perp$ and $\lambda_\parallel$ are related by $$\lambda_\perp/\lambda_\parallel \sim \sqrt{\lambda_\parallel/R}\;,$$ where $R$ is the outer scale, while the cascade is described by a Kolmogorov spectrum in the perpendicular direction.
@ThompsonBlaes1998 extended the theory to the extreme relativistic regime, when the plasma inertia is negligible (force-free MHD). They argued that an anisotropic cascade is formed also in this case, and that the dissipation occurs at the scale of the current starvation, i.e. when there are not enough charge carriers in the plasma to maintain the currents associated with the Alfvén waves. As pointed out by @Thompson2006, in this case the dissipation of relativistic MHD turbulence heats the particle in the longitudinal direction, and a particle distribution that is strongly elongated in the direction of the background magnetic field might therefore be expected. @Thompson2006 [@ThompsonGill2014; @GillThompson2014] suggested that the rapid variability of the GRB prompt emission may be attributed to this anisotropy.
The statement that in collisionless plasmas the anisotropic MHD turbulence decays by heating/accelerating particles along the background magnetic field is general. Indeed, the dissipation occurs at the wave-particle resonances $$\label{eq:res}
\omega - {\bf k}\cdot{\bf v} = n\Omega_{\rm L} \;,$$ where $\omega$ and ${\bf k}$ are the frequency and the wavenumber, ${\bf v}$ is the particle velocity, $\Omega_{\rm L}\equiv eB/\gamma mc$ is the particle relativistic Larmor frequency, and $n$ is an integer. The cyclotron resonance condition, $n\neq 0$, is satisfied when the longitudinal scale of the wave packet, $\lambda_\parallel$, is of the order of the particle Larmor radius, $r_{\rm L}\equiv c/\Omega_{\rm L}$. Since typically $r_{\rm L}\ll R$, due to the strong anisotropy of MHD turbulence a particle crosses many wave packets during one Larmor orbit and the energy gain averages out. Hence, wave-particle interactions mediated by the cyclotron resonance can be neglected. It was first noticed by @Gruzinov1998 [@Quataert1998; @QuataertGruzinov1999] that in this case the dissipation occurs at the Landau resonance, $n=0$. Since the two physical mechanisms of wave-particle interaction at the $n=0$ resonance are due to (i) the longitudinal electric field of the wave and (ii) the interaction between the effective particle’s magnetic moment and the longitudinal magnetic perturbation, one is led to the conclusion that the turbulent energy is primarily dissipated onto the longitudinal particle motion.
It has also been found that the turbulent fluctuations tend to align with one another forming small scale current sheets [e.g. @Boldyrev2006; @BeresnyakLazarian2006; @Mason2006], which could be disrupted via magnetic reconnection thus providing an additional dissipation mechanism [e.g. @BoldyrevLoureiro2017; @Mallet2017a; @Mallet2017b; @LoureiroBoldyrev2017]. Note that the background magnetic field, which is much larger than the reconnecting field and lies in the same plane of the current sheet, plays the role of a guide field. Since the magnetic energy is transferred to the plasma particles at the Landau resonance between the particles and the tearing mode that disrupts the current sheet, also in this case one would expect the particles to be heated in the longitudinal direction.
Even if the perpendicular heating is negligible, in a weakly magnetised plasma the fire-hose instability quickly erases any momentum anisotropy [e.g. @Parker1958; @Lerche1966]. However, since the fire-hose instability develops once $P_\parallel-P_\perp>B^2/4\pi$ (where $P_\parallel$ and $P_\perp$ are the parallel and perpendicular pressure components respectively), one immediately sees that this instability is not effective if the magnetic to plasma energy ratio exceeds $1/2$. Moreover, a significant angular spread, say $\langle\sin^2\theta\rangle\sim 1/2$ where $\theta$ is the particle pitch angle, is expected only when the energy ratio drops to very small values. In the following we argue that in the highly magnetised regime (i) some plasma instability may still be able to make the electron momentum distribution isotropic; (ii) such an instability may be ineffective for the most energetic electrons, which concludes our argument.
Momentum isotropisation in a highly magnetised plasma by the resonance instability of Alfvén waves
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If the energy of the system was initially stored in the magnetic field, most of the energy release occurs around the equipartition stage when the fire-hose instability does not work. Another isotropisation mechanism is the cyclotron instability that develops at the anomalous cyclotron resonance ($n=-1$ in Eq. \[eq:res\]). In this case, particles with super-Alfvén velocities excite Alfvén waves and at the same time their pitch angle increases, the energy being taken from the longitudinal motion. This process is analogous to the classic cosmic-ray scattering by Alfvén waves [e.g. @Lerche1967; @KulsrudPearce1968].
In the following we assume the momenta of all the particles to be initially directed along the magnetic field. To fix ideas, let the background magnetic field $B$ be directed in the positive $z$ direction. The Alfvén wave velocity $v_{\rm A}$ is mildly relativistic at the equipartition stage. In order to determine the stability properties of the plasma, we adapt an argument due to @Kulsrud2005 to the case we are interested in.
### Electron-positron plasma
We first study the case of an electron-positron plasma. Let us consider a right circularly polarised wave packet with wavelength $\lambda_\parallel$ propagating in the positive $z$ direction. Such a wave is emitted by the positrons at the $n=-1$ resonance, which propagate in the positive $z$ direction, and is absorbed by the electrons at the $n=1$ resonance, which propagate in the negative $z$ direction. Using $n=-1$ in Eq. , we may calculate the Lorentz factor of the resonant positrons as $$\gamma_{e^+ {\rm ,res}}\sim \frac{1}{1-\beta_{\rm A}}\frac{eB\lambda_\parallel}{m_e c^2}\;,$$ where $\beta_{\rm A}\equiv v_{\rm A}/c$. In a similar way, the Lorentz factor of the resonant electrons is obtained substituting $n=1$ into Eq. , which gives $$\gamma_{e^- {\rm ,res}}\sim \frac{1}{1+\beta_{\rm A}}\frac{eB\lambda_\parallel}{m_e c^2}\;.$$ Assuming that the pairs are distributed according to a power law with energy index $\sim -2$, which is ultimately motivated by the observed SED [e.g. @Tavecchio2010], one finds the number density of resonant positrons, $$\label{eq:nres_0}
n_{e^+{\rm,res}}\sim \frac{n_e}{2\gamma_{e^+ {\rm ,res}}} \sim n_e \frac{1-\beta_{\rm A}}{2} \frac{m_e c^2}{eB\lambda_\parallel}\;,$$ and the number density of resonant electrons, $$\label{eq:nres_01}
n_{e^-{\rm,res}}\sim \frac{n_e}{2\gamma_{e^- {\rm ,res}}} \sim n_e \frac{1+\beta_{\rm A}}{2} \frac{m_e c^2}{eB\lambda_\parallel}\;,$$ where $n_e\sim n_{e^+}+n_{e^-}$ is the total number density of the pairs.
The momentum of the resonant positrons is $p_{e^+{\rm, res}}\sim \gamma_{e^+ {\rm ,res}}m_ec$, while the momentum of the resonant electrons is $p_{e^-{\rm, res}}\sim \gamma_{e^- {\rm ,res}}m_ec$. Let $\delta B$ be the amplitude of the wave packet. Since the pitch angle of the positrons diffuses on a time scale $t_{e^+{\rm,diff}}\sim \Omega_{\rm L}^{-1}\left(\delta B/B\right)^{-2}\sim \left(\gamma_{e^+ {\rm ,res}}m_e c/eB\right)\left(\delta B/B\right)^{-2}$ and the pitch angle of the electrons diffuses on a time scale $t_{e^-{\rm,diff}}\sim \left(\gamma_{e^- {\rm ,res}}m_e c/eB\right)\left(\delta B/B\right)^{-2}$, one finds $$\label{eq:emission_p}
\frac{\Delta p_{e^+{\rm ,res}}}{\Delta V \Delta t} \sim \frac{n_{e^+{\rm ,res}}p_{e^+{\rm, res}}}{t_{e^+{\rm,diff}}} \sim eB n_{e^+{\rm ,res}} \left(\frac{\delta B}{B}\right)^2\;,$$ and $$\label{eq:absorption_p}
\frac{\Delta p_{e^-{\rm ,res}}}{\Delta V \Delta t} \sim \frac{n_{e^-{\rm ,res}}p_{e^-{\rm, res}}}{t_{e^-{\rm,diff}}} \sim eB n_{e^-{\rm ,res}} \left(\frac{\delta B}{B}\right)^2\;.$$ These are respectively the momentum density gained (lost) by the wave per unit time due to the resonant interaction with the positrons (electrons). Since $n_{e^+{\rm ,res}}<n_{e^-{\rm ,res}}$, the emission term is smaller than the absorption term and the wave is damped.
Hence, in an electron-positron plasma the instability does not develop and we expect the particle distribution to remain strongly elongated in the direction of the background magnetic field. The synchrotron emissivity depends on the magnetic field through the combination $B\sin\theta$, where $\theta$ is the pitch angle [e.g. @RybickiLightman1979]. Hence, we see that if $\theta\ll 1$ the magnetic field in the dissipation region might be significantly stronger than what it is inferred assuming an isotropic momentum distribution for the non-thermal electrons. Note, however, that the cooling time remains the same even in the limit $\theta\ll 1$.
### Electron-positron-ion plasma
The presence of an even small (in terms of number density) ion component may completely change the results obtained for an electron-positron plasma. It is important to realise that the amplitude of the right circularly polarised wave considered in the previous section grows due to the resonant interaction with the protons moving in the positive $z$ direction. The fundamental difference with respect to the pair plasma is that there are not negatively charged ions, which would be the analogous of the electron component, that damp the wave. Hence, the amplitude of the wave grows if the number of resonant protons and positrons, which emit the wave, exceeds the number of resonant electrons, which absorb the wave.
In the following we consider the case when the pairs dominate the number density ($n_e\gg n_p$), but the protons dominate the rest mass density of the jet ($n_p m_p\gg n_e m_e$), which is motivated by a number of independent arguments in the literature [e.g. @SikoraMadejski2000; @GhiselliniTavecchio2010]. We assume that (i) the pairs are distributed according to a power law with energy index $\sim -2$, and (ii) the proton energy distribution is steeper than the electron one, as discussed in more detail below, in which case most of the proton’s energy is carried by mildly relativistic particles. Hence, the proton to electron energy density is $U_p/U_e \sim n_pm_p/n_e m_e \log\left(\gamma_{\rm b}\right)$. Using a typical break Lorentz factor $\gamma_{\rm b}\sim 10^4-10^6$ for the non-thermal pairs [e.g. @Tavecchio2010], one finds $U_p/U_e\sim \left(100-200\right)\times n_p/n_e$. Hence, if $n_e\sim \left(10-100\right)\times n_p$ [e.g. @SikoraMadejski2000], the energy carried by the protons does not typically exceed that carried by the pairs by a large factor.
Using the same argument as to derive Eq. -, one can calculate the momentum density gained by the wave per unit time due to the interaction with the resonant ($n=-1$) protons, which gives $$\label{eq:pwave1}
\frac{\Delta p_{p{\rm ,res}}}{\Delta V\Delta t} \sim e B n_{p{\rm,res}} \left(\frac{\delta B}{B}\right)^2\;.$$ Combining Eqs. -, one sees that the emission is larger than the absorption, and hence the wave grows, if $$\label{eq:inst}
n_{p{\rm,res}} + n_{e^+{\rm,res}} \gtrsim n_{e^-{\rm,res}}\;.$$ This is the condition for a particle distribution with all the momenta directed along the background magnetic field to be unstable. If the instability develops, the electrons are isotropised by the absorption of the resonant waves, while the positrons and the protons are isotropised by the emission. In Appendix \[sec:appendix\] we calculate the growth rate of the instability, showing that it is fast enough (with respect, for example, to the dynamical time) for the instability to be indeed effective once the condition is satisfied.
In order to make further progress we need to make some assumptions on the proton energy distribution, which determines $n_{p{\rm ,res}}$. First of all, note that if the wavelength is shorter than the proton non-relativistic Larmor radius ($\lambda_\parallel\lesssim m_pc^2/eB$), the number density of the resonant protons equals the total number density of the protons, namely $n_{p{\rm,res}}\sim n_p$. For longer wavelengths, $n_{p{\rm,res}}$ depends on the details of the heating process.
In the following we assume that the protons are distributed according to a power law with energy index $-s$. We take $s>2$, namely we assume that the proton distribution is steeper than the pair distribution. This choice is motivated by the fact that, as a result of the dissipation of non-relativistic MHD turbulence, the proton to electron heating ratio is a decreasing function of the magnetisation, and is already smaller than unity when the thermal and the magnetic energy are in equipartition [e.g. @QuataertGruzinov1999; @Howes2010]. However, one should realise that the extrapolation of these results to the relativistic regime is far from obvious, and would require further investigation.
Since the Lorentz factor of the resonant protons is $\gamma_{p{\rm ,res}}\sim eB\lambda_\parallel/m_pc^2$, one finds $$\label{eq:nres_1}
n_{p{\rm,res}}\sim n_p \times
\begin{cases}
1 & {\rm if} \quad \lambda_\parallel\lesssim m_pc^2/eB\\
\left(\frac{m_p c^2}{eB\lambda_\parallel}\right)^{s-1} & {\rm if} \quad \lambda_\parallel\gtrsim m_pc^2/eB \;.
\end{cases}$$ The important point is that the number of the resonant protons can exceed the number of resonant pairs ($n_{p{\rm,res}}\gtrsim n_{e{\rm,res}}$) even when the pairs dominate the total number density ($n_p\ll n_e$). The reason for this is the large proton to electron mass ratio, $m_p/m_e\gg 1$, which implies that the Lorentz factor of the protons resonating with a given $\lambda_\parallel$ is significantly smaller than the Lorentz factor of the pairs resonating with the same wave.
Using Eqs. and for $n_{e^+{\rm ,res}}$ and $n_{e^-{\rm ,res}}$, and Eq. for $n_{p{\rm ,res}}$, we see that the condition is equivalent to $$\label{eq:lambda_res_1}
\frac{n_e m_e}{n_p m_p}\frac{m_pc^2}{eB} \lesssim\lambda_\parallel\lesssim \left(\frac{n_p m_p}{n_e m_e}\right)^{\frac{1}{s-2}}\frac{m_pc^2}{eB}\;,$$ where we have used the fact that $\beta_{\rm A}$ is of order unity. The Lorentz factor of the pairs resonating with the largest unstable $\lambda_\parallel$ can be found from $\gamma_{\rm iso}m_e c^2/eB\sim \lambda_\parallel$, which finally gives $$\label{eq:gamma_iso}
\boxed{\gamma_{\rm iso}\sim \left(\frac{n_p m_p}{n_e m_e}\right)^{\frac{1}{s-2}}\frac{m_p}{m_e} }\;.$$ The pairs with $\gamma\lesssim\gamma_{\rm iso}$ are isotropised due to the resonant interaction with the waves, while those with $\gamma\gtrsim\gamma_{\rm iso}$ retain a small pitch angle and thus do not radiate by synchrotron.
Since $\gamma_{\rm iso}\gtrsim m_p/m_e \sim 2\times 10^3$, it is possible that $\gamma_{\rm iso}\lesssim\gamma_{\rm b}$ in a significant fraction of BL Lacs, where the break Lorentz factor can be as large as $10^5-10^6$ [e.g. @Tavecchio2010]. As we discuss in the next section, this fact is important for the modelling of the BL Lac SED. Finally, note that the exact value of $\gamma_{\rm iso}$ depends on the poorly known details of the particle heating in relativistic MHD turbulence, which determine $s$, and on the composition of the jet.
Predictions of the model {#sec:model}
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![Main features of our model. The energy distribution of the electrons in BL Lac jets is described by a broken power law (see Eq. \[eq:N\]) extending from $\gamma_{\rm min}$ to $\gamma_{\rm max}$. The electrons at the break ($\gamma\sim\gamma_{\rm b}$) produce the Inverse Compton peak of the SED. The distribution becomes strongly elongated in the direction of the magnetic field for $\gamma\gtrsim\gamma_{\rm iso}$. Since the synchrotron emission by the electrons with $\gamma\gtrsim\gamma_{\rm iso}$ is suppressed due to their small pitch angles, when $\gamma_{\rm iso}\lesssim\gamma_{\rm b}$ the synchrotron peak of the SED is produced by the electrons with $\gamma\sim\gamma_{\rm iso}$.[]{data-label="fig:model"}](./scenario.pdf){width="49.00000%"}
The main features of our model are sketched in Figure \[fig:model\]. In the following all the physical quantities are defined in the frame of the dissipation region. Following @Tavecchio1998, we assume that the energy distribution of the non-thermal electrons is described by $$\label{eq:N}
N\left(\gamma\right) =
\begin{cases}
K \gamma^{-s_1} & {\rm if}\quad \gamma_{\rm min}<\gamma<\gamma_{\rm b}\\
K \gamma_{\rm b}^{s_2-s_1} \gamma^{-s_2} & {\rm if}\quad \gamma_{\rm b}<\gamma<\gamma_{\rm max}
\end{cases}$$ where the scaling constant $K$ has units of cm$^{-3}$. The spectral indices $s_1$ and $s_2$ can be determined directly from the SED; one typically finds $s_1= 1.8-2.2$ and $s_2 = 3.5-5$ [@Tavecchio2010]. In the following we adopt a fiducial value $s_1=2$.
As discussed in Section \[sec:motivation\], we make the further assumption that the momentum of the electrons becomes approximately aligned with the direction of the magnetic field when $\gamma\gtrsim\gamma_{\rm iso}$.[^3] Since the synchrotron emission is suppressed when the pitch angle is close to zero, if $\gamma_{\rm iso}\lesssim\gamma_{\rm b}$ our model predicts the synchrotron radiation to peak at a frequency $$\label{eq:nus}
\boxed{ \nu_{\rm s} = 3.7\times 10^6 \gamma_{\rm iso}^2 B \delta} \;,$$ where $\delta$ is the Doppler factor, $\gamma_{\rm iso}$ is given by Eq. , and $\nu_{\rm s}$ is measured in Hz. The peak luminosity can be written as $$\label{eq:Ls1}
L_{\rm s} = V\delta^4 \int N\left(\gamma\right) P_{\rm s} \left(\gamma\right) {\rm d}\gamma \sim V\delta^4 N\left(\gamma_{\rm iso}\right) \gamma_{\rm iso} P_{\rm s} \left(\gamma_{\rm iso}\right)\;,$$ where $V=4\pi R^3/3$ and $$\label{eq:Ls2}
P_{\rm s} \left(\gamma_{\rm iso}\right) = \frac{4}{3}\sigma_{\rm T}c U_{\rm B} \gamma_{\rm iso}^2 \;,$$ being $U_B=B^2/8\pi$ the magnetic energy density.[^4] Combining Eqs. and we finally get $$\label{eq:Ls}
\boxed{L_{\rm s} = \frac{2}{9}\sigma_{\rm T}c B^2 R^3 K \gamma_{\rm iso} \delta^4}\;,$$ where we have used our fiducial $s_1=2$. Here $c$ is the speed of light and $\sigma_{\rm T}$ is the Thompson cross section.
The non-thermal electrons scatter the synchrotron photons to produce the IC peak of the SED. The resulting spectrum depends on the scattering regime of the photons at the synchrotron peak. These photons are scattered in the Thompson regime if $$\label{eq:cond}
\gamma_{\rm b}h\nu_{\rm s}<\delta m_e c^2\;,$$ and in the Klein-Nishina regime otherwise. Here $h$ is the Planck constant and $m_e$ is the electron mass. We discuss the two cases separately below.
Thompson regime {#sec:thompson}
---------------
The peak of the IC component is produced by the electrons at the break scattering the photons at the synchrotron peak. The peak frequency can be calculated as $$\label{eq:nuc}
\nu_{\rm c} = \frac{4}{3}\gamma_{\rm b}^2 \nu_{\rm s}\;.$$ The peak luminosity can be written as $$\label{eq:Lc1}
L_{\rm c} = V\delta^4 \int N\left(\gamma\right) P_{\rm c} \left(\gamma\right) {\rm d}\gamma \sim V\delta^4 N\left(\gamma_{\rm b}\right) \gamma_{\rm b} P_{\rm c} \left(\gamma_{\rm b}\right)\;.$$ Here $$\label{eq:Lc2}
P_{\rm c}\left(\gamma_{\rm b}\right) = \frac{4}{3}\sigma_{\rm T}c U_\gamma \gamma_{\rm b}^2 \;,$$ being $U_\gamma=L_{\rm s}/4\pi R^2 c \delta^4$ the radiation energy density of the synchrotron photons. Combining Eqs. and we finally get $$\label{eq:Lc}
L_{\rm c} = \frac{4}{9}\sigma_{\rm T}RK \gamma_{\rm b} L_{\rm s}\;,$$ where we have used our fiducial $s_1=2$.
In order to calculate the cooling time, it is important to realise that in our model the radiative losses of the electrons at the break are dominated by the IC. Hence, the cooling time is $$\label{eq:tcool1}
t_{\rm cool} = \frac{\gamma_{\rm b} m_e c^2}{P_{\rm c}\left(\gamma_{\rm b}\right)} \;.$$ The ratio between the cooling time $t_{\rm cool}$ and the dynamical time $t_{\rm dyn}=R/c$ can be presented as $$\label{eq:tcool}
\frac{t_{\rm cool}}{t_{\rm dyn}} = \frac{3\pi m_e c^3 R \delta^4}{\sigma_{\rm T} L_{\rm s} \gamma_{\rm b}}\;.$$
Klein-Nishina regime
--------------------
In this case the peak of the IC component is produced by the electrons at the break scattering the photons whose energy equals $m_e c^2$ in the electron’s frame. By construction, the frequency of these photons is below the synchrotron peak. The frequency of the IC peak is then $$\label{eq:nucKN}
\nu_{\rm c} = \frac{4}{3}\frac{m_e c^2}{h} \gamma_{\rm b} \delta\;.$$
The calculation of $L_{\rm c}$ and $t_{\rm cool}$ can be carried out as in the Thompson regime, with the only difference that only the photons with frequency smaller than $\delta m_e c^2/h\gamma_{\rm b}=3\nu_{\rm c}/4\gamma_{\rm b}^2$ contribute to the effective $U_\gamma$. Since this suppresses $P_{\rm c}$ by a factor of $\left(3\nu_{\rm c}/4\gamma_{\rm b}^2\nu_{\rm s}\right)^{1/2}$, one finds $$L_{\rm c} = \frac{4}{9}\sigma_{\rm T}RK L_{\rm s} \left(\frac{3\nu_{\rm c}}{4\nu_{\rm s}}\right)^{1/2}$$ and $$\frac{t_{\rm cool}}{t_{\rm dyn}} = \frac{3\pi m_e c^3 R \delta^4}{\sigma_{\rm T} L_{\rm s}} \left(\frac{4\nu_{\rm s}}{3\nu_{\rm c}}\right)^{1/2} \;,$$ which are the analogous of Eqs. and respectively.
Final remarks
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The requirement that the observed emission varies on time scales comparable with the dynamical time puts one more constraint to the model, namely $$\label{eq:tvar}
\boxed{R=c\delta t_{\rm var}}\;.$$ where $t_{\rm var}$ is the observed variability time scale. Substituting $\gamma_{\rm b}$ from Eq. into Eq. , one finds $$\label{eq:tau}
\boxed{\sigma_{\rm T}RK = \frac{9L_{\rm c}}{4L_{\rm s}} \left(\frac{4\nu_{\rm s}}{3\nu_{\rm c}}\right)^{1/2}}\;.$$ It is simple to realise that Eq. is valid also in the Klein-Nishina regime. Note that Eqs. , , , do not contain $\gamma_{\rm b}$ any more, which allows one to determine $K$, $R$, $B$, $\delta$. Combining Eqs. and , and taking into account the condition , one eventually finds $$\label{eq:gammab}
\boxed{\gamma_{\rm b}=\max\left[\left(\frac{3\nu_{\rm c}}{4\nu_{\rm s}}\right)^{1/2}, \left(\frac{3h\nu_{\rm c}}{4\delta m_e c^2}\right)\right]}\;,$$ which proves that, once $\gamma_{\rm iso}$ is known, all the free parameters of the model are constrained by observations.
If the scattering occurs in the Thompson regime, one can calculate $t_{\rm cool}/t_{\rm dyn}$ isolating $\gamma_{\rm b}$ from Eq. and $R$ from Eq. , and substituting them into Eq. . This finally gives $$\label{eq:delta}
\frac{t_{\rm cool}}{t_{\rm dyn}} = \frac{3\pi m_e c^4 t_{\rm var}}{\sigma_{\rm T} L_{\rm s}} \left(\frac{4\nu_{\rm s}}{3\nu_{\rm c}}\right)^{1/2} \delta^5 \;,$$ which is valid also in the Klein-Nishina regime.
Comparison with an isotropic model {#sec:comparison}
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{width="49.00000%"} {width="49.00000%"}
Predictions of an isotropic model
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The usual one-zone SSC model has five free parameters, which we will name $K_0$, $\gamma_{\rm b0}$, $R_0$, $B_0$, $\delta_0$. Since the momentum distribution of the non-thermal electrons is assumed to be isotropic, both the synchrotron and the IC peaks of the SED are produced by the electrons at the break. The frequency and the luminosity of the synchrotron peak are given by $$\begin{aligned}
\label{eq:nus0}
\nu_{\rm s} & = 3.7\times 10^6 \gamma_{\rm b0}^2 B_0 \delta_0\\
\label{eq:Ls0}
L_{\rm s} & = \frac{2}{9}\sigma_{\rm T}c B_0^2 R_0^3 K_0 \gamma_{\rm b0} \delta_0^4\;.\end{aligned}$$ It is simple to realise that Eqs. and are still valid. Hence $$\begin{aligned}
\label{eq:tvar0}
R_0 & =c\delta_0 t_{\rm var}\\
\label{eq:tau0}
\sigma_{\rm T}R_0 K_0 & = \frac{9L_{\rm c}}{4L_{\rm s}} \left(\frac{4\nu_{\rm s}}{3\nu_{\rm c}}\right)^{1/2} \;.\end{aligned}$$ The analogous of Eq. also holds, which finally constrains all the free parameters of the model from the observations.
In order to make a straightforward comparison with our model, here we define $t_{\rm cool,0}$ taking into account the IC cooling only. One finds $$\label{eq:ratio}
\frac{t_{\rm cool,0}}{t_{\rm dyn,0}} = \frac{3\pi m_e c^4 t_{\rm var}}{\sigma_{\rm T} L_{\rm s}} \left(\frac{4\nu_{\rm s}}{3\nu_{\rm c}}\right)^{1/2} \delta_0^5\;.$$ Note that, since when the momentum distribution is isotropic the synchrotron cooling should be also taken into account, our $t_{\rm cool, 0}$ is longer than the true cooling time by a factor $1+P_{\rm s}/P_{\rm c}=1+L_{\rm s}/L_{\rm c}$. Since typically $L_{\rm s}$ and $L_{\rm c}$ are of the same order, which can be inferred directly from the SED of individual BL Lacs [e.g. @Tavecchio2010], this correction is a factor of a few.
Relation between the physical parameters
----------------------------------------
Since the observed quantities (namely $\nu_{\rm s}$, $\nu_{\rm c}$, $L_{\rm s}$, $L_{\rm c}$, $t_{\rm var}$) are model-independent by definition, one can find a relation between the physical parameters of our model and those of an isotropic model. Comparing Eq. to Eq. it is simple to realise that $$\label{eq:1}
\gamma_{\rm iso}^2 B \delta = \gamma_{\rm b0}^2 B_0 \delta_0\;.$$ Comparing Eqs. and , one finds $$\label{eq:2}
B^2 R^3 K \gamma_{\rm iso} \delta^4 = B_0^2 R_0^3 K_0 \gamma_{\rm b0} \delta_0^4\;.$$ Comparing Eqs. and , one finds $$\label{eq:3}
R/\delta = R_0/\delta_0\;.$$ Finally, comparing Eqs. and , one finds $$\label{eq:4}
R K = R_0 K_0\;.$$ One can solve Eqs. - in order to express the four parameters $K$, $R$, $B$, $\delta$ as a function of the others, which gives $$\begin{aligned}
\label{eq:K_final}
K & = \left(\frac{\gamma_{\rm b0}}{\gamma_{\rm iso}}\right)^{3/4} K_0\\
\label{eq:R_final}
R & = \left(\frac{\gamma_{\rm iso}}{\gamma_{\rm b0}}\right)^{3/4} R_0\\
\label{eq:B_final}
B & = \left(\frac{\gamma_{\rm b0}}{\gamma_{\rm iso}}\right)^{11/4} B_0\\
\label{eq:delta_final}
\delta & = \left(\frac{\gamma_{\rm iso}}{\gamma_{\rm b0}}\right)^{3/4} \delta_0\;,\end{aligned}$$ where $\gamma_{\rm iso}$ is given by Eq. . These expressions give a simple correspondence between the parameters of the two models.
We are now in the position to evaluate how the two models differ in the predicted ratio of (i) the electron to the magnetic energy, and (ii) the cooling to dynamical times. Let $U_B$ and $U_e$ be the energy density of the magnetic fields and the kinetic energy density of the non-thermal electrons respectively. Since $U_B=B^2/8\pi$, we have $U_B=\left(B/B_0\right)^2 U_{B,0}$. One can calculate $U_e=\int \gamma m_ec^2 N\left(\gamma\right) {\rm d}\gamma \sim Km_e c^2 \log\left(\gamma_{\rm b}/\gamma_{\rm min}\right)$, where we have used the distribution with $s_1=2$. Neglecting the weak (logarithmic) dependence on $\gamma_{\rm min}$ and $\gamma_{\rm b}$, one sees that $U_e=\left(K/K_0\right)U_{e,0}$, from which it immediately follows that $U_e/U_B=\left(B_0/B\right)^2 \left(K/K_0\right) \left(U_{e,0}/U_{B,0}\right)$. Using Eqs. and we finally get $$\label{eq:sigma}
\frac{U_e}{U_B} = \left(\frac{\gamma_{\rm iso}}{\gamma_{\rm b0}}\right)^{19/4} \frac{U_{e,0}}{U_{B,0}}\;.$$ Comparing Eqs. and , one sees that $t_{\rm cool}/\delta^5 t_{\rm dyn} = t_{\rm cool,0}/\delta_0^5 t_{\rm dyn,0}$, which using Eq. gives $$\label{eq:time}
\frac{t_{\rm cool}}{t_{\rm dyn}} = \left(\frac{\gamma_{\rm iso}}{\gamma_{\rm b0}}\right)^{15/4} \frac{t_{\rm cool,0}}{t_{\rm dyn,0}} \;.$$ One sees that, in the case $\gamma_{\rm iso}\lesssim\gamma_{\rm b0}$, the ratio of both (i) the electron to the magnetic energy, and (ii) the cooling to the dynamical times predicted by our model can be significantly lower than those predicted by the usual isotropic model.
Results {#sec:results}
=======
Our goal is showing that, assuming that the electron distribution becomes anisotropic at the highest energies, it is possible to have (i) an approximate equipartition between the energy carried by the non-thermal electrons and by the magnetic fields ($U_e\sim U_B$); (ii) the electrons at the break efficiently cooling in a dynamical time ($t_{\rm cool}\lesssim t_{\rm dyn}$). Combining Eqs. and , we see that $$\label{eq:prediction}
\frac{U_e}{U_B} \left(\frac{t_{\rm dyn}}{t_{\rm cool}}\right)^{19/15} \sim \frac{U_{e,0}}{U_{B,0}} \left(\frac{t_{\rm dyn,0}}{t_{\rm cool,0}}\right)^{19/15}\;.$$ In the following we define the parameter $$a \sim \frac{U_e}{U_B} \left(\frac{t_{\rm dyn}}{t_{\rm cool}}\right)^{19/15} \;.$$ Due to Eq. , such a parameter is model-independent (namely, $a\sim a_0$). If $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$ in the anisotropic model, one would expect $a$ to be distributed above a minimum value of order unity.
In order to calculate the parameter $a$ for individual BL Lacs, we use the results of @Tavecchio2010, who fitted the SED of a sample of BL Lacs using an isotropic model for the electron distribution. In the left panel of Figure \[fig:prediction\] we plot $U_{e,0}/U_{B,0}$ versus $t_{\rm cool,0}/t_{\rm dyn,0}$ for all the BL Lacs in the sample of @Tavecchio2010.[^5] One sees that, while both $U_{e,0}/U_{B,0}$ and $t_{\rm cool,0}/t_{\rm dyn,0}$ have a large scatter and most of the BL Lacs have $U_{e,0}/U_{B,0}\gtrsim 1$ and $t_{\rm cool,0}/t_{\rm dyn,0}\gtrsim 1$, these two quantities are correlated and the combination $a_0\sim \left(U_{e,0}/U_{B,0}\right) \left(t_{\rm dyn,0}/t_{\rm cool,0}\right)^{19/15}$ is slightly bigger than unity for the majority of the BL Lacs. In the right panel of Figure \[fig:prediction\] we show the distribution of $a$ for all the BL Lacs in the sample. Approximately $50\%$ of the BL Lacs have $1\lesssim a\lesssim 10$ and $\sim 75\%$ of them have $1\lesssim a\lesssim 100$, while only $\sim 12\%$ of the objects have $a\lesssim 1$. As discussed above, this shows that it is possible to construct an anisotropic model for the electron momentum distribution such that $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$.
Proof-of-concept: an anisotropic model with $\pmb{U_e\sim U_B}$
---------------------------------------------------------------
![Distribution of the ratio between the cooling to the dynamical times ($t_{\rm cool}/t_{\rm dyn}$) for all the BL Lacs in the sample. We assume an anisotropic model with energy equipartition between the non-thermal electrons and the magnetic fields ($U_e\sim U_B$).[]{data-label="fig:times"}](./times.pdf){width="49.00000%"}
![Distribution of $\gamma_{\rm iso}$ for all the BL Lacs in the sample. We assume an anisotropic model with energy equipartition between the non-thermal electrons and the magnetic fields ($U_e\sim U_B$).[]{data-label="fig:gammaiso"}](./gammaiso.pdf){width="49.00000%"}
{width="49.00000%"} {width="49.00000%"} {width="49.00000%"} {width="49.00000%"}
As an illustrative example, in the following we calculate all the parameters of our anisotropic model under the assumption that that $U_e\sim U_B$.[^6] In Figure \[fig:times\] we show the distribution of $t_{\rm cool}/t_{\rm dyn}$, which we calculate using Eq. after finding $\gamma_{\rm iso}$ from Eq. . Approximately $60\%$ of the BL Lacs have $0.1\lesssim t_{\rm cool}/t_{\rm dyn}\lesssim 1$ and $\sim 85\%$ of them have $0.01\lesssim t_{\rm cool}/t_{\rm dyn}\lesssim 1$, while only $\sim 10\%$ of the objects have $t_{\rm cool}/t_{\rm dyn}\gtrsim 1$. This shows that an anisotropic model with $U_e\sim U_B$ naturally predicts the electrons at the break to cool efficiently in approximately a dynamical time. Moreover, since the ratio $t_{\rm cool}/t_{\rm dyn}$ is typically close to unity, one may speculate that the break in the energy distribution of the non-thermal electrons is separating the electrons whose cooling time is slower/faster than the dynamical time. Therefore the system is self-regulating: electrons are accelerated until they begin to loose the acquired energy. At any $\gamma_{\rm iso}$, the parameter $\gamma_{\rm iso}/\gamma_{\rm b}$, which determines both $U_e/U_B$ and $t_{\rm cool}/t_{\rm dyn}$ is self-adjusted.
In Figure \[fig:gammaiso\] we show the distribution of $\gamma_{\rm iso}$, namely the Lorentz factor above which the electron distribution becomes elongated in the direction of the magnetic field. As discussed in Section \[sec:motivation\], we expect $\gamma_{\rm iso}$ to be somewhat larger than the proton to electron mass ratio, $m_p/m_e$. Indeed, only four BL Lacs in the sample require $\gamma_{\rm iso}\lesssim m_p/m_e$, while the large majority ($\sim 84\%$) of the objects have $m_p/m_e \lesssim\gamma_{\rm iso}\lesssim 10^5$, which is in reasonable agreement with our initial prediction (Eq. \[eq:gamma\_iso\]).
In Figure \[fig:parameters\] we show the parameters $K$, $R$, $B$, $\delta$ predicted by our model, which we find using Eqs. -. For comparison, with the thin line we show the distribution that is obtained assuming an isotropic electron distribution. The distribution of the number density of the non-thermal electrons and the distribution of the size of the dissipation region do not change significantly. The distribution of the magnetic field becomes narrower, and the typical field is significantly higher ($\sim 73\%$ of the BL Lacs have $1\;{\rm G}\lesssim B \lesssim 10\;{\rm G}$). Finally, the distribution of the bulk Doppler factor becomes monotonically decreasing, with most of the objects in the range $5\lesssim\delta\lesssim 25$. Interestingly, even if this was not guaranteed a priori, we find only three objects with $\delta\lesssim 5$ (two of them have $4.5\lesssim\delta\lesssim 5$ and only one has $\delta\sim 2$). This reassures us that our results do not systematically violate the lower limit on $\delta$ that is obtained requiring that the dissipation region is optically thin for pair production ($\gamma\gamma\to e^+ e^-$; e.g.@DondiGhisellini1995).[^7]
Conclusions {#sec:conclusions}
===========
In this paper we have closely investigated one of the key assumptions that is usually adopted to interpret the SED of blazars, namely that the momentum distribution of the non-thermal electrons emitting the observed radiation is isotropic. We have found that this assumption may be oversimplified. Indeed, if the magnetic energy is dissipated via a turbulent MHD cascade, particles are primarily accelerated along the background magnetic field. In a highly magnetised plasma, the momentum of the lowest energy electrons may be isotropised by resonant wave-particle interactions. However, this mechanism is likely inefficient for the highest energy electrons, which may therefore retain a small pitch angle.
Motivated by the physics of energy dissipation in turbulent magnetised plasmas, we have presented a simple anisotropic model where the angular distribution of the electrons momenta depends on the single parameter $\gamma_{\rm iso}$: the electron momentum distribution is isotropic if the Lorentz factor is $\gamma\lesssim\gamma_{\rm iso}$, while the pitch angle becomes negligibly small when $\gamma\gtrsim\gamma_{\rm iso}$. The physical parameters of the dissipation region that are derived from the SED modelling are significantly affected by the anisotropy of the electron momentum distribution when $\gamma_{\rm iso}$ is below the spectral break of the distribution (namely, $\gamma_{\rm iso}\lesssim\gamma_{\rm b}$), as might be the case in a significant fraction of BL Lacs. The reason for such a difference with respect to the isotropic scenario is that, if $\gamma_{\rm iso}\lesssim\gamma_{\rm b}$, the synchrotron peak of the SED is produced by the electrons with $\gamma\sim\gamma_{\rm iso}$, while the IC peak is produced by the electrons with $\gamma\sim\gamma_{\rm b}$.
We have shown that, with a reasonable choice of the single parameter $\gamma_{\rm iso}$, it may be possible to construct a one-zone model reproducing the SED of BL Lacs such that (i) the energy carried by the non-thermal electrons and by the magnetic fields are in an approximate equipartition ($U_e\sim U_B$); (ii) the non-thermal electrons efficiently cool in a dynamical time ($t_{\rm cool}\lesssim t_{\rm dyn}$). As discussed in the introduction, the fact that $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$ is in good agreement with a number of theoretical and observational constraints on AGN jets.[^8] Our results may therefore help to solve a controversy that was pointed out by @TavecchioGhisellini2016: indeed, modelling the BL Lac SED with a one-zone Self-Synchro-Compton model that assumes an isotropic momentum distribution for the non-thermal electrons typically gives $U_e\gg U_B$ and $t_{\rm cool}\gg t_{\rm dyn}$. Also note that, since our model predicts the ratio $t_{\rm cool}/t_{\rm dyn}$ to be typically close to unity for the electrons at the break of the energy distribution, one may speculate such a break to be associated with the Lorentz factor above which the cooling time becomes shorter than the dynamical time.
The dissipation of the magnetic energy through a turbulent MHD cascade may also explain the rapid variability that is observed in the spectra of blazars. Since the magnetic field in the emitting region is tangled, the radiation in the proper frame is isotropic when averaged over a suitably long time. However, as originally proposed by @Thompson2006 in the context of GRBs, a fast variability on short time scales may be produced due to the fact that the radiation from a locally anisotropic electron distribution is strongly beamed. In blazars, the high energy variability of the spectrum is often explained by “jet in a jet” scenarios that may result from the magnetic reconnection process inside the jet [see for example @Giannios2009; @Giannios2010; @Nalewajko2011]. We argue that the emission of highly beamed radiation may instead be the generic product of the energy dissipation in magnetically dominated jets.
Throughout this paper we have mostly been concerned about the statistical properties of BL Lacs. Nevertheless, our model can be used to fit the SED of individual objects. In particular, there are a few objects in the sample of @Tavecchio2010 whose SED is difficult to model assuming an isotropic momentum distribution. As discussed by these authors, the reason is that the fit would require extremely large Doppler factors and small magnetic fields. It would be interesting to see if our model helps to improve the quality of the fit for these objects.
Finally, the fact that the highest energy electrons may retain a small pitch angle is based on a number of assumptions, namely (i) the pairs dominate the total number density ($n_e\gg n_p$), but the protons dominate the total mass density ($n_p m_p\gg n_e m_e$) of the jet, which is motivated by a number of independent arguments in the literature [e.g. @SikoraMadejski2000; @GhiselliniTavecchio2010]; (ii) the dissipation of the magnetic energy heats the particles in the direction of the background magnetic field, which is likely the case if the magnetic energy is brought down to the dissipation scale by a turbulent MHD cascade; (iii) the protons are heated less efficiently than the pairs, which is suggested by an analogy with the behaviour of non-relativistic turbulent plasmas. Future studies focusing on the dissipation of the magnetic energy via relativistic MHD turbulence may help to test the correctness of our assumptions (ii) and (iii).
We have not discussed the case of FSRQ yet. In these objects, the strong Compton dominance (which implies that $U_B\ll U_\gamma$) has led different authors to argue that the most promising explanation for the IC peak of the SED is the Comptonization of the radiation provided by a broad-line region or a dusty molecular torus [see for example @Sikora2009; @Ghisellini2010]. Though the presence of an external photon field makes the detailed modelling of the SED more uncertain than for BL Lacs, it has been suggested that in FSRQ jets (i) the amount of energy carried by the non-thermal electrons is comparable to that carried by the magnetic fields, namely $U_e\sim U_B$; (ii) the electrons at the break cool efficiently in a dynamical time, namely $t_{\rm cool}\sim t_{\rm dyn}$ [e.g. @Ghisellini2010; @GhiselliniTavecchio2015], which would make the interpretation of the model’s results less problematic than for BL Lacs. Our model may hardly affect these conclusions in a statistically significant number of FSRQ. The reason is that the typical break Lorentz factor in FSRQ is $\gamma_{\rm b}\sim 10^2$ [e.g. @Ghisellini2010], which is smaller than our expected $\gamma_{\rm iso}\gtrsim 10^3$ (see the discussion in Section \[sec:motivation\] and in particular Eq. \[eq:gamma\_iso\]). Hence, in FSRQ the electrons at the break may become approximately isotropic, and thus produce both the synchrotron and the IC peaks of the SED.
Acknowledgements {#acknowledgements .unnumbered}
================
The authors acknowledge useful discussions with Amir Levinson. This research has received funding from the Israeli Science Foundation (grant 719/14) and from the German Israeli Foundation for Scientific Research and Development (grant I-1362-303.7/2016).
Conditions for the resonance instability of Alfvén waves {#sec:appendix}
========================================================
In Section \[sec:motivation\] we have studied the stability of a highly magnetised plasma where the momenta of all the particles are aligned with the background magnetic field. Right circularly polarised Alfvén waves are damped due to the absorption by the resonant electrons, while they are emitted by the resonant protons and positrons. Hence, the system is unstable if $n_{p{\rm,res}} + n_{e^+{\rm,res}} \gtrsim n_{e^-{\rm,res}}$. One can calculate the damping time scale from $$\frac{\Delta p_{\rm wave}}{\Delta V\Delta t} \sim - \frac{\Delta p_{e^-{\rm ,res}}}{\Delta V \Delta t}\;,$$ where $$\frac{\Delta p_{\rm wave}}{\Delta V\Delta t} \sim -\frac{1}{t_{\rm damp}} \frac{\left(\delta B\right)^2}{8\pi v_{\rm A}}\;.$$ Using Eq. , this finally gives $$\label{eq:tdamp_e}
t_{\rm damp} \sim \frac{B}{8\pi v_{\rm A}e n_{e^-{\rm,res}} }\;.$$ In a similar way, one can calculate the growth rate from $$\frac{\Delta p_{\rm wave}}{\Delta V\Delta t} \sim \frac{\Delta p_{e^+{\rm ,res}}}{\Delta V \Delta t} + \frac{\Delta p_{p{\rm ,res}}}{\Delta V \Delta t}\;,$$ where $$\frac{\Delta p_{\rm wave}}{\Delta V\Delta t} \sim \frac{1}{t_{\rm growth}} \frac{\left(\delta B\right)^2}{8\pi v_{\rm A}}\;.$$ Using Eqs. and , this finally gives $$t_{\rm growth} \sim \frac{B}{8\pi v_{\rm A}e \left(n_{p{\rm,res}} + n_{e^+{\rm,res}}\right)}\;.$$ One immediately sees that the condition $n_{p{\rm,res}} + n_{e^+{\rm,res}} \gtrsim n_{e^-{\rm,res}}$ is equivalent to $t_{\rm growth}\lesssim t_{\rm damp}$.
The instability is effective if $t_{\rm growth}$ and $t_{\rm damp}$ are short with respect to the other relevant time scales of the system. Since the instability develops once $t_{\rm growth}\lesssim t_{\rm damp}$, it is sufficient to check $t_{\rm damp}$ to be short. The wave packet considered above may suffer from the additional damping by the wave-wave interaction with the packets from the turbulent MHD cascade. Following @FarmerGoldreich2004, we estimate the time scale for turbulent damping as $$t_{\rm turb}\sim\frac{\sqrt{R\lambda_\parallel}}{v_{\rm A}}\;,$$ which is much shorter than the dynamical time in the relevant case $\lambda_\parallel\ll R$. Using Eq. to calculate $n_{e^-{\rm ,res}}$, the ratio $t_{\rm damp}/t_{\rm turb}$ may be expressed as $$\frac{t_{\rm damp}}{t_{\rm turb}} \sim \frac{B^2}{8\pi n_e m_e c^2} \sqrt{\frac{\lambda_\parallel}{R}}\;.$$ If the electron and the magnetic energy density are in an approximate equipartition, one sees that $t_{\rm damp}/t_{\rm turb}\sim\sqrt{\lambda_\parallel/R}\ll 1$. Hence, $t_{\rm damp}$ is the relevant time scale of the system, being it of the order of the Larmor time of the resonating electrons.
Finally, note that the particle pitch angle may change due to synchrotron emission, which damps the perpendicular particle motion, and due to IC emission (since the photons are typically scattered exactly in the direction of motion, we argue that IC emission is quite inefficient to produce a diffusion in the pitch angle). The important point is that in our model the cooling time due to both these processes is comparable to the dynamical time (see Figure \[fig:times\]). Since we have shown the instability discussed in Section \[sec:motivation\] to operate on much shorter time scales, we expect that synchrotron and IC processes hardly affect the pitch angle distribution.
[^1]: E-mail: [email protected]
[^2]: Such a turbulent cascade may be triggered by MHD instabilities in a Poynting-dominated jet. Recent PIC simulations have shown that highly tangled magnetic fields may be formed in the kink-unstable region of the jet, resulting in the dissipation of the magnetic energy and the rapid acceleration of a population of non-thermal particles [e.g. @Alves2018; @Nalewajko2018].
[^3]: In principle, the dependence of the pitch angle on the Lorentz factor of the electrons at $\gamma\sim\gamma_{\rm iso}$ can be determined by the slope of the SED at frequencies $\nu\gtrsim\nu_{\rm s}$. This would require a detailed fit of the model to the SED of individual objects, which is out of the scope of the paper.
[^4]: Note that we are assuming the Doppler amplification to be proportional to $\delta^4$, which is the appropriate case if the emitting region moves together with the fluid at the same velocity ${\bf v}$. If instead the emitting region is stationary and the fluid inside moves with uniform velocity ${\bf v}$ (i.e., it turns “on and off” as it enters and leaves the emitting region), the amplification would be proportional to $\delta^3/\Gamma_{\rm jet}$ [e.g. @LindBlandford1985; @Sikora1997].
[^5]: In order to calculate $t_{\rm cool,0}$, (i) we calculate the cooling time due to synchrotron losses only, and (ii) we rescale it by a factor $L_{\rm s}/L_{\rm c}$. We infer the luminosities directly from the SED of individual objects.
[^6]: Five BL Lacs in the sample of @Tavecchio2010 have $U_{e,0}\lesssim U_{B,0}$. For these objects we use the same best fit parameters of the isotropic model adopted by these authors.
[^7]: We have checked this constraint not to be violated for any object in the sample of @Fan2014, who calculated the lower limit on the Doppler factor for 457 blazars. Their sample includes $\sim 80\%$ of the objects in our sample.
[^8]: @Nemmen2012 found a radiative efficiency of about 15% for AGN jets. Taking into account that in Poynting dominated jets the fraction of energy going to heat could hardly exceed 50% [@Peer2017], that the electron spectrum is broad, and there are also protons, one concludes that the cooling time at the break, $t_{\rm cool}$, could not be significantly larger than $t_{\rm dyn}$.
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Many different types of digitally controlled printing systems of ink jet printing apparatus are presently being used. These ink jet printers use a variety of actuation mechanisms, a variety of marking materials, and a variety of recording media. For home applications, digital ink jet printing apparatus is the printing system of choice because low hardware cost make the printer affordable to every one. Another application for digital ink jet printing uses large format printers. It is a further requirement that these large format printers provide low cost copies with an ever improving quality. Ink jet printing technology is the first choice in today's art. Thus, there is a need for improved ways to make digitally controlled graphic arts media, such as billboards, large displays, and home photos for example, so that quality color images may be made at a high-speed and low cost, using standard or special paper.
Ink jet printing has become recognized as a prominent contender in the digitally controlled, electronic printing arena because of its nonimpact, low-noise characteristics, its use of papers from plain paper to specialized high gloss papers and its avoidance of toner transfers and fixing. Ink jet printing mechanisms can be categorized as either continuous ink jet or droplet on demand ink jet. Continuous ink jet printing dates back to at least 1929. See U.S. Pat. No. 1,941,001 to Hansell.
U.S. Pat. No. 3,373,437, issued to Sweet et al. in 1967, discloses an array of continuous ink jet orifices wherein ink droplets to be printed are selectively charged and deflected towards the recording medium. This technique is known as binary deflection continuous ink jet, and is used by several manufacturers, including Elmjet and Scitex.
U.S. Pat. No. 3,416,153, issued to Hertz et al. in 1966, discloses a method of achieving variable optical density of printed spots in continuous ink jet printing using the electrostatic dispersion of a charged droplet stream to modulate the number of droplets which pass through a small orifice. This technique is used in ink jet printers manufactured by Iris.
U.S. Pat. No. 3,878,519, issued to Eaton in 1974, discloses a method and apparatus for synchronizing droplet formation in a liquid stream using electrostatic deflection by a charging tunnel and deflection plates.
U.S. Pat. No. 4,346,387, issued to Hertz in 1982 discloses a method and apparatus for controlling the electric charge on droplets formed by the breaking up of a pressurized liquid stream at a droplet formation point located within the electric field having an electric potential gradient. Droplet formation is effected at a point in the field corresponding to the desired predetermined charge to be placed on the droplets at the point of their formation. In addition to charging tunnels, deflection plates are used to actually deflect droplets.
Conventional continuous ink jet utilizes electrostatic charging tunnels that are placed close to the point where the droplets are formed in a stream. In this manner individual droplets may be charged. The charged droplets may be deflected downstream by the presence of deflector plates that have a large potential difference between them. A gutter (sometimes referred to as a "catcher") may be used to intercept the charged droplets, while the uncharged droplets are free to strike the recording medium. If there is no electric field present or if the break off point from the droplet is sufficiently far from the electric field (even if a portion of the stream before droplets break off is in the presence of an electric field), then charging will not occur.
The on demand type ink jet printers are covered by hundreds of patents and describe two techniques for droplet formation. At every orifice, (about 30 to 200 are used for a consumer type printer) a pressurization actuator is used to produce the ink jet droplet. The two types of actuators are heat and piezo materials. The heater at a convenient location heats ink and a quantity will phase change into a gaseous steam bubble and raise the internal ink pressure sufficiently for an ink droplet to be expelled to a suitable receiver. The piezo ink actuator incorporates a piezo material. It is said to possess piezo electric properties if an electric charge is produced when a mechanical stress is applied. This is commonly referred to as the "generator effect" "The converse also holds true; an applied electric field will produce a mechanical stress in the material. This is commonly referred to as the "motor effect". Some naturally occurring materials possessing this characteristics are: quartz and tourmaline. Some artificially produced piezoelectric crystals are: Rochelle salt, ammonium dihydrogen phosphate (ADP) and lithium sulphate (LH). The class of materials used for piezo actuators in an ink jet print head possessing those properties includes polarized piezoelectric ceramics. They are typically referred to as ferroelectric materials. In contrast to the naturally occurring piezoelectric crystals, ferroelectric ceramics are of the "polycrystalline" structure. The most commonly produced piezoelectric ceramics are: lead zirconate titanate, barium titanate, lead titanate, and lead metaniobate. For the ink jet print head a ferroelectric ceramic is machined to produce ink chambers. The chamber is water proofed by gold plating and becomes a conductor to apply the charge and cause the piezo "motor effect". This "motor effect" causes the ink cavity to shrink, raise the internal pressure, and generate an ink droplet.
Inks for high speed jet droplet printers must have a number of special characteristics. Typically, water-based inks have been used because of their conductivity and viscosity range. Thus, for use in a jet droplet printer the ink must be electrically conductive, having a resistivity below about 5000 ohm-cm and preferably below about 500 ohm-cm. For good flow through small orifices water-based inks generally have a viscosity in the range between about 1 to 15 centipoise at 25 degree C.
Over and above this, the ink must be stable over a long period of time, compatible with the materials comprising the orifice plate and ink manifold, free of living organisms, and functional after printing. The required functional characteristics after printing are: smear resistance after printing, fast drying on paper, and waterproof when dry. Examples of different types of water-based jet droplet printing inks are found in U.S. Pat. Nos. 3,903,034; 3,889,269; 3,870,528; 3,846,141; 3,776,642; and 3,705,043.
The ink also has to incorporate a nondrying characteristic in the jet cavity so that the drying of ink in the cavity is hindered or slowed to such a degree that through occasional spitting of ink droplets the cavities can be kept open. The addition of glycol will facilitate the free flow of ink through the ink jet. Also it is of benefit if ink additives prevent the ink from sticking to the ink jet print head surfaces. Ink jet printing apparatus typically includes an ink jet print head that is exposed to the various environment where ink jet printing is utilized. The orifices are exposed to all kinds of air born particles. Particulate debris accumulates on the surfaces, forming around the orifices. The ink will combine with such particulate debris to form an interference burr to block the orifice or cause through an altered surface wetting to inhibit a proper formation of the ink droplet. That particulate debris has to be cleaned from the orifice to restore proper droplet formation. This cleaning commonly is achieved by wiping, spraying, vacuum suction, and/or spitting of ink through the orifice. The wiping is the most common application.
Inks used in ink jet printers often have the following problems:
1) they require a large amount of energy to dry after printing; PA1 2) large printed areas on paper usually cockle because of the amount of water present; PA1 3) the printed images are sensitive to wet and dry rub; PA1 4) the compositions of the ink usually require an anti-bacterial preservative to minimize the growth of bacteria in the ink; PA1 5) the inks tend to dry out in and around the orifices resulting in clogging; PA1 6) the wiping of the orifice plate causes wear on plate and wiper; PA1 7) the wiper itself generates particles that clog the orifice; PA1 8) cleaning cycles are time consuming and slow the productivity of ink jet printers. It is especially of concern in large format printers where frequent cleaning cycles interrupt the printing of an image; and PA1 9) when a special printing pattern is initiated to compensate for plugged or badly performing orifices, the printing rate declines. PA1 a) a structure defining a cleaning cavity for receiving cleaning liquid; PA1 b) a roller partially submerged in the cleaning liquid; PA1 c) means for rotating the roller so that cleaning liquid coats the roller and is carried by surface tension around the roller; and PA1 d) means for providing relative movement between the orifice plate and the structure so that the orifice plate is positioned adjacent to the cleaning cavity with the rotating roller spaced a distance from the orifice plate so that there is turbulence of the cleaning liquid and such turbulence causes the cleaning fluid to engage the orifice plate and remove debris from the orifices and orifice plate.
Some of these problems may be overcome by the use of polar, conductive organic solvent based ink formulations. However, the use of non-polar organic solvents is generally precluded by their lack of electrical conductivity. The addition of solvent soluble salts can make such inks conductive, but such salts are often toxic, corrosive, and unstable.
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The other night, I found myself in a dilemma: I wanted cake, but I did not want to make cake. I just wanted cake to magically appear in front of me. Eventually, I compromised with myself and decided that I wanted cake badly enough that I was willing to make it so long as I only had to exert the bare minimum amount of time and energy. I went online and started hunting for easy vegan cake recipes, and I couldn’t believe how many great recipes I found. Here are eight of the best cakes I came across. Enjoy!
8 Easy to Make Plant-Based Cakes
#1. Easy Berry Pear Cake
Get the recipe here.
#2. Easy Peanut Butter Mug Cake
My Latest Videos
Get the recipe here.
#3. Easy Lime Cake with Whipped Coconut Cream
Get the recipe here.
#4. The Easiest Chocolate Mug Cake
Get the recipe here.
#5. Chocolate Chip Cookie Dough Mug Cake
Get the recipe here.
#6. Quick and Easy Vegan Chocolate Cupcakes
Get the recipe here.
#7. One Minute Coffee Cake In A Mug
Get the recipe here.
#8. Vegan Cake Batter Blondies
Get the recipe here.
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As well as ordinary shares that you can buy and sell on the stock market, there are also preference shares. This type of share is an interesting mix of equity and debt. Preference shares are very similar to how ordinary shares work, but they carry a guaranteed percentage dividend. Read on to find out more about preference shares and the different types available…
Cumulative preference shares
If a company can’t pay preference share dividends in a particular financial year, the company will pay the amount of these ‘unpaid’ dividends in subsequent years when results allow.
Non-cumulative preference shares
If a company can’t pay preference share dividends in a particular year, the holder of a non-cumulative preference share forfeits the right to this dividend.
Redeemable preference shares
A company issues a redeemable preference share with the provision that the company will be able to redeem this share at some future date. This means the company will be able to ‘buy’ these shares back, and remove them from circulation.
Convertible preference shares
A company who issues a convertible preference share may decide to convert it into an ordinary share.
Participating preference shares
The holder of a participating preference share will not only receive the fixed dividend entitlement; but will also receive the ordinary share dividend too.
So there you have it, the five different types of preference shares there are.
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Q:
Using if/else statement and exit function in Python
The two cases below describe my dilemma. I would like to understand when the code is more stable.
Case A
from sys import argv
a = float( argv[1] )
b = float( argv[2] )
if a == 0.:
exit(1)
else:
print b / a
exit( 0 )
Case B
from sys import argv
a = float( argv[1] )
b = float( argv[2] )
if a == 0.:
exit(1)
print b / a
exit( 0 )
A:
Both methods offer the same stability because, in essence, they do the same thing.
However, the first one uses else unnecessarily. If the code hits the exit(1) line, it immediately exits the script. Meaning, else doesn't contribute anything positive (such as flow-control). In fact, all it does is take up a line and cause unnecessary indenting.
So, if you are wondering which method to choose, I'd say to use the second. It is cleaner and uses less syntax to do the same job.
Also, since exiting a script usually means something unusual and bad happened, using just the if without the else makes it somewhat clearer that you are protecting against a freak occurrence.
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Posted on October 9, 2013
CHICAGO – Wrigley’s Orbit® gum is launching Orbit for Kids, a new sugarfree chewing gum that will help parents and dental practitioners keep kids’ teeth healthy when they are on the go and between checkups.
“Dental disease is the leading chronic illness among children[1]. While parents understand the importance of brushing and flossing twice a day, many don’t realize the importance of proper oral care throughout the day,” said Dr. Amanda Seay, DDS, spokesperson for Orbit for Kids. “A lot of damage can be done to teeth between brushings, so it’s vital to educate patients and parents about easy, and fun, ways to help protect teeth—like chewing Orbit for Kids sugarfree gum.”
Orbit for Kids gum is recognized for its oral care benefits and has been awarded the American Dental Association’s Seal of Acceptance.
“Wrigley has been a pioneer over the last several decades researching and trying to better understand the role of sugarfree gum in promoting oral health,” said Anne Marie Splitstone, senior director of the gum category at Wrigley. “We launched Orbit for Kids to give busy families a new way to help protect teeth on-the-go that everyone will enjoy.”
Seay adds, “It can be difficult to get pediatric patients to form good dental habits. But, kids see gum as a treat, and parents can feel good about giving Orbit for Kids to their family.”
Available in select markets in May and nationwide in July, Orbit for Kids comes in two kid-friendly sugarfree flavors: new Strawberry Banana and Original Bubble Gum. It will be available in 14-tab envelopes (great for parents to hold onto) and Multi-Pack bags with 10, six-tab micro Packs (perfect size for kids!). 14-tab envelopes will be available for an MSRP of $1.29 and 10-ct. Multi-Pack bags for an MSRP of $4.49.
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Hole in the Wall
The producers of Justified like to, if nothing else, experiment with how their season-long storylines play out from season to season. In season 2, we had the long-running singular villain in the form of Mags. Last season, we had two villains -- though, arguably, only one turned out to actually try and kill Raylan -- and this season, were not sure what we have. At the very least, its a thirty-year old mystery that incorporates Raylans father, Arlo.In 1983, an unknown person parachuted to their death with what looked like bricks of cocaine. They were discovered by a man named Sherman and presumably his wife. Somehow, 30 years later, what we can assume Sherman stole from the dead person wound up inside the walls in Arlos home that Raylan is now trying to sell.
Read more »
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Friday, January 22, 2016
Coming Home by Melissa Frost
As a foster care child, Andi never
stays long in one place. She doesn't have a chance to connect with anyone—until
sexy, blue-eyed Devon walks into her life.
Devon claims
to have known her birth parents. He’s even got a photograph to prove it. He
shows up offering her everything she could ever want—a friend, a connection to
her family, and answers.
The only
problem is Devon’s friendship comes with a few complications attached. There’s
the fact that he’s a werewolf, and then there’s the territorial clan out to
start a war with Devon’s pack. What started as a simple journey to learn about
herself turns into a dangerous road trip that could get her killed.
If she can
survive, Andi just might get the answers that have been plaguing her, and she
might just fall in love with her new furry pal along the way.
“I’m still
not convinced.” She informed him of this in a tone that stated quite clearly
she thought him to be a liar. “You’ll have to try harder than that.”
At her
skepticism, Devon gave a grin that could only be described as devilish.
Climbing to his feet, he yanked the zipper down on his coat and shrugged out of
it. He tossed the coat into the snow before lifting his shirt over his head.
As if they
had a mind of their own, her eyes drank in the sight of his bare chest. He was
amazingly sculpted, his arm muscles bunching with every movement. His abs, which
appeared rock solid, mirrored the action. He even had an interesting scar along
his left shoulder that only seemed to add to his sex appeal. She cleared her
throat uncomfortably, willing her body to settle down. She didn’t usually get
so affected by boys.
When his
hands went to his belt buckle and began unfastening it, she gave a squeak of
objection. “What are you doing? Stop taking your clothes off!”
He grinned
over at her. “You wanted to see a werewolf, didn’t you? I’m just obliging.”
“But … but
…”
He stripped
out of his jeans with ease. “Werewolves aren’t freaked out by nudity, Andi. If
you remembered even the slightest bit about your history, you would know that.”
As his
briefs came down, her eyes lifted hurriedly to the sky. She gazed at the clouds
as if they were the most intriguing thing in the entire world. Which was a
complete farce. Standing before her was the first naked boy she’d ever been in
the presence of. She desperately wanted to sneak a peek, yet she was too
freaked out by the idea to even lower her gaze a fraction of an inch.
“Sheesh,
you’re such a human,” Devon said in complaint. “You’re such a prude that you’re
about to miss all the fun.”
Andi
scowled, but her gaze was still lifted skyward so she had no idea if he saw her
or not. As she stood awkwardly gazing at the clouds, she realized how
absolutely absurd this situation was. She was standing in the entrance to a
public park. With a naked boy. In the snow.
“This is
so—” Her protests broke off as an odd popping sound filled the air. She couldn’t
quite place it, but it felt so familiar. It was a noise she’d heard before, but
she couldn’t remember where.
Her eyes
lowered to Devon’s bare shoulders to find them shifting and cracking. His flesh
moved in such an unnatural way, she nearly cried out in alarm. Her own hand
pressing to her lips was the only thing that stopped the sound from escaping.
She watched
with morbid fascination as Devon’s body repositioned and changed itself into
something new. Before her very eyes, his entire being altered, and he
transformed into the shape of a wolf. It took no more than a minute or two, but
the time seemed to stretch on forever.
She
witnessed soft puffs of cream fur appear that seemed to burst right out of his
skin. His fingers elongated, the nails growing out into sharp claws. The urge
to run lasted a mere second before she was stepping forward in fascination.
Her fingers
outstretched toward the furry muzzle that had once been Devon’s nose. She
wasn’t frightened by him in the least. How could she be? He was the wolf!
The one she’d seen outside the school staring into her classroom window.
She knew
instantly he’d been there for her, watching over her as he awaited their
reunion. She bet he had seen it playing out quite differently. Closing her
eyes, she allowed her fingers to brush over the soft fur between his ears.
The
sensation of it shook her to the core. Her body remembered it, recalled it like
it was yesterday. Werewolf fur. She wasn’t sure if it was his fur in particular
that felt so much like home, or if it was werewolf fur in general. Either way,
it startled her just how much she longed to be near him in that moment.
Her eyes
snapped open, and she stumbled back, unsteady on her feet. This was far too
much to absorb in one afternoon. Her mind was racing, and she didn’t even know
where to begin. As a result, she simply plopped down into the snow, stunned.
About the Author:
Melissa Frost grew up loving young
adult novels and continues to immerse herself in the current authors on the
market.
In the
fifth grade, she won a writing competition to work with children’s author
Colleen O'Shaughnessy Mckenna, and it inspired her to write stories of her own.
She never looked back.
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Dose-dense high-dose methylprednisolone and rituximab in the treatment of relapsed or refractory high-risk chronic lymphocytic leukemia.
This study evaluated the efficacy and safety of dose-dense high-dose methylprednisolone (HDMP) plus rituximab (Rtx) in patients with high-risk CLL. Twenty-nine patients with relapsed or progressive CLL with adverse cytogenetics (17p deletion, TP53 mutation, 11q deletion, and/or trisomy 12) and/or progression within 12 months of fludarabine treatment were included. HDMP (1 g/m(2)) was administered daily for 5 days of each treatment course. Rtx was administered on days 1 (375 mg/m(2)) and 5 (500 mg/m(2)) of the first treatment course, on days 1 (500 mg/m(2)) and 5 (500 mg/m(2)) of the second course, and on day 1 (500 mg/m(2)) of courses 3-6. The cycles were repeated every 21 days. The overall response rate (ORR) was 62%, and 28% of patients had stable disease. In 13 patients with 17p deletion/TP53 mutation, ORR was 69%. After 22 months, the median progression-free and overall survivals were 12 and 31 months, respectively. The most frequent toxicity was hyperglycemia, and three deaths occurred in the study. Dose-dense treatment with HDMP and Rtx is an effective therapy with a favorable safety profile in patients with high-risk CLL, including those with 17p deletion/TP53 mutation.
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233 N.W.2d 555 (1975)
Sandra Waltz KRECH, Respondent,
v.
Edward ERDMAN, Appellant.
No. 45026.
Supreme Court of Minnesota.
August 22, 1975.
*556 Douglass, Bell, Donlin, Shultz & Petersen and John C. Wallraff, St. Paul, for appellant.
Robins, Davis & Lyons and Leo F. Feeney, St. Paul, for respondent.
Heard before ROGOSHESKE, TODD and MacLAUGHLIN, JJ., and considered and decided by the court en banc.
PER CURIAM.
This is an action for damages arising out of personal injuries sustained by plaintiff when her automobile was struck from behind by defendant's truck. The jury awarded plaintiff $22,500, and defendant appeals from an order denying him a new trial. We affirm.
Defendant asserts the following grounds for reversal:
(1) The court permitted plaintiff to amend the ad damnum clause of her complaint, increasing it from $23,400 to $75,000.
(2) Although plaintiff did not disclose the identity of a medical expert until the day before trial, the court refused to suppress his evidence.
(3) The court received hospital records which were not disclosed by plaintiff's answers to defendant's interrogatories.
(4) The court commented on the availability of a witness to clarify facts elicited from plaintiff by defendant on cross-examination for impeachment purposes.
(5) One of plaintiff's doctors testified concerning a myelogram examination of plaintiff which was not, in fact, conducted.
(6) Defendant asserts that the damages awarded are excessive.
1. Defendant's insurance coverage was limited to $10,000. The original prayer was for $23,400. Defendant, prior to trial, had been fully advised of his right to retain independent counsel. Although defendant argues that it was an abuse of discretion to permit an increase of the ad damnum clause because it gave the plaintiff a tactical advantage, the fact remains that the amount of the verdict was less than the amount sought in the original complaint. This was a discretionary matter with the court, and we find no prejudice resulted. Bastianson v. Forschen, 293 Minn. 31, 36, 196 N.W.2d 451, 455 (1972).
2. Plaintiff did not disclose until the day before trial that a neurologist would testify on her behalf. Defendant sought to suppress this testimony, and complains that the refusal to do so was highly prejudicial because the doctor was one of only two experts to testify that plaintiff sustained permanent injuries.
We held in Gebhard v. Niedzwiecki, 265 Minn. 471, 477, 122 N.W.2d 110, 114-115 (1963):
"* * * [W]here the after-acquired information is of a material nature or where it will render the answers originally given untruthful, unreliable, or inaccurate, the obligation to disclose such after-acquired information continues.
* * * * * *
*557 "* * * In cases where there is an honest mistake [in failing to disclose] and the harm can be undone, it may frequently occur that a continuance or some other remedy would be adequate but, where the violation is willful and the party guilty of the violation seeks to take advantage of it at a time when the harm cannot be undone, suppression of the evidence may very well be the proper and only available remedy."
As applied to the instant case, the trial court might well have invoked the sanction of suppression had he found that defendant was, to any appreciable degree, prejudiced. We reiterate what was said in Gebhard concerning the ongoing obligation of counsel to keep his adversary apprised of the changes in circumstances which make it necessary to call witnesses or introduce evidence not previously disclosed. Trial courts have a duty to suppress such evidence where counsel's dereliction is inexcusable and results in disadvantage to his opponent. In situations where the failure to disclose is inadvertent but harmful, the court should be quick to grant a continuance and assess costs against the party who has been at fault. Here, however, defendant did not seek a continuance upon learning that the doctor would testify. The trial court was justified in finding that defendant did not sustain prejudice which was attributable to his having had only brief notice of the doctor's appearance. Muckler v. Buchl, 276 Minn. 490, 502, 150 N.W.2d 689, 697 (1967).
3. With respect to the introduction of hospital records not disclosed in answers to interrogatories, it is enough to say counsel for defendant made no objection and, indeed, used the records effectively to rebut testimony introduced by plaintiff. Muckler v. Buchl, supra; Cook Seed Co. v. Welker, 288 Minn. 412, 181 N.W.2d 870 (1970).
4. In cross-examining plaintiff, counsel for defendant called attention to the fact that medical records of the University of Minnesota Health Service contained a statement by an examining doctor that plaintiff attributed some of her disability to her activity while playing basketball. Plaintiff denied having made that statement, and defendant's counsel then asked her if she had taken any steps to have the record corrected. Thereupon, plaintiff's counsel stipulated that the University doctor could be made available to defendant, to which proposal defendant objected, prompting the court to state: "Well, I don't know. If it's important I take it that the doctor can be called." Defendant complains that the court's comment adversely affected his attempt to impeach plaintiff. However, we regard the court's statement as responsive to the objection, and the impact on the jury, if any, trivial and inconsequential.
5. There is no merit to defendant's claim that he was prejudiced by the statement by one of plaintiff's doctors that she had been given a myelogram examination when, in fact, she had not. Not only did the doctor testify that the examination was negative, but the fact that the examination was not given was made clear to the jury by other witnesses.
6. With respect to the question of whether the award was excessive, it is of some significance that the accident occurred in May 1968 and the verdict was not rendered until January 1974. Although the special damages apparently were less than $500 and the award is generous, we are of the opinion that there is competent medical testimony to support the verdict. One doctor gave plaintiff a 20-percent disability of the cervical spine, and another doctor testified her condition was permanent. At the time of trial, plaintiff's injuries were not seriously disabling, but the jury could find that she continued to have substantial pain and discomfort in the area of her shoulder and neck. Although the case is a close one on the issue of damages, the verdict has the approval of the trial court and on this record we are reluctant to disturb it.
Affirmed.
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Item added to cart
Your pickup store:
Overview
Material:
HARDWOOD
Assembled Product Length:
41"
Assembled Product Width:
7.13"
Only at Home Hardware
When you trust your gardening equipment, you do a better job. This 41" Mark's Choice spade, available exclusively at Home Hardware is features a heavy duty stainless steel head with premium straight grain hardwood D-handle.
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Comment Wall
As everyone knows that working in the medical fieldit is getting harder and more dangerous than ever before. We face new challenges in this kind of new world that we live in. As a emergency room charge nurse, I have seen an increase of drug seekers, Ethol abuse and such low life people who don't care what they do to get the drugs they want. We had to lock down our emergency room today for several hours d/t a person who was mad at the hospital for some reason and was going to walk in and shoot us. The stress was high but out team of Doctors, nurses and medics get wonderful. They caught him and now he is in jail!! Great going PCSO. So as you can see, my stress level is really high right now. Have a safe shift and a wonderful weekend. I am going flying ,can't get me up there.
Diane
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##
# This file is part of WhatWeb and may be subject to
# redistribution and commercial restrictions. Please see the WhatWeb
# web site for more information on licensing and terms of use.
# http://www.morningstarsecurity.com/research/whatweb
##
# Version 0.3 # 2016-04-17 # Andrew Horton
# Added website parameter and description
##
# Version 0.2
# removed :certainty=>100
##
Plugin.define "SnomPhone" do
author "Andrew Horton"
version "0.3"
description "VoIP phones and teleconferencing systems"
website "http://www.snom.com/"
# Dorks #
dorks [
'"You can enter a simple telephone number (e.g. 0114930398330) or URI like [email protected]."'
]
# © 2000-2008 <a href="http://snom.com">snom AG</a><br>
# <tr><td class="flyoutLink" colspan="2"><b><a href=http://wiki.snom.com/wiki/index.php/snom300>Manual</a>
# You can enter a simple telephone number (e.g. 0114930398330) or URI like [email protected].
# <td class="headerText" width="705">Welcome to Your Phone!</td>
# <tr><td class="flyoutLink" colspan="2"><b><a href=http://www.snom.com/wiki/index.php/snom360>Manual</a>
# Matches #
matches [
{:name=>"copyright snom.com", :regexp=>/© 2000-20[0-9]+ <a href="http:\/\/snom.com">snom AG<\/a><br>/ },
{:name=>"link to manual1", :regexp=>/<tr><td class="flyoutLink" colspan="2"><b><a href=http:\/\/(wiki|www).snom.com/ },
{:text=>'You can enter a simple telephone number (e.g. 0114930398330) or URI like [email protected].' },
{:certainty=>75, :regexp=>/<td[^>]+>Welcome to Your Phone!<\/td>/ },
]
end
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<This is co-published with Thought Catalog>
So on Monday, I wrote a thing about Christy Mack’s assault at the hands of her ex-boyfriend and the slut-shaming and victim blaming that resulted. It’s a complicated and tangled enough topic that it’s difficult to fit every angle and wrinkle in. But there was one topic that I wanted to get into that didn’t quite fit: how the concept of “manhood” and masculinity ties into the abuse.
So of course, the universe decided to drop yet another opportunity to talk about sex, masculinity and violence… and wrapped up in the ongoing drama that is the geek community. Practically all of my favorite topics, wrapped up in one! Because if there’s anything I needed, it’s another reason to take a whack at the Nerds and Male Privilege hornet’s nest one more time.
Still, never let it be said that I don’t use every part of the news cycle buffalo, because I can’t help but notice similarities between the Christy Mack assault and the harassment of women in the video games industry. Confused? Hear me out…
The Insidious Quest To Steal Your Manhood
One of the ongoing narratives surrounding Christy Mack’s assault – especially the one forward by Koppenhaver himself – is that Mack provoked him by cheating on him with Corey Thomas. In fact, according to the police report, Koppenhaver entered the house at 1:30 AM and found the two of them in bed. As a result, he “did what he had to”… “what he had to” in this case being “beat the ever-loving fuck first out of Thomas and then Mack.”
The important part here isn’t whether Mack was cheating on War Machine – she had broken up with him months ago and had recently started a relationship with Thomas – but the way that he saw it. In his delusional mind, she was still “his property”; as far as he was concerned, Christy Mack and Corey Thomas were cuckolding him – and that is an insult that simply can’t go unanswered. Someone else fucking your wife or girlfriend, you’ve gotta correct that shit. Preferably with your fists. Because otherwise it’s time to turn in your penis because you’re clearly not a man anymore.
See, one of the unspoken tenets of hypermasculinity is that masculinity is an external creation – and that means it’s something that ultimately taken from you. Not just lost, mind you, actively taken. Hypermasculine men – and men who wish to be seen as “manly” are always afraid that their manhood is being taken from them, that they’re being forced into being a bitch.
But there are few acts that are intrinsic to being a “real man” than sex… both in establishing his man-card and in it’s removal. A “real man” is defined by his sexual conquests. The more women he’s slept with, the more of a man he is. But at the same time, those women need to stay his. More importantly however, is that a man can control his woman; after all, he’s supposed to be her superior. A man who isn’t in charge is “pussy-whipped” – he’s beyond pathetic, forced to be servile in hopes of being granted access to sex. When his woman has sex with someone else, it carries the implication is that he’s unable to either please her or keep her under control – all of which insults and degrades his masculinity. Someone else now has access to his woman – his “property”, as it were. This other man has functionally stolen her from him, and with her, his manhood.
In War Machine’s eyes – and those of his many supporters on social media – he was cuckolded, betrayed, wronged. Corey Thomas and Christy Mack being together functionally stole his manhood from him.Of course, it’s bad enough when a man steals your masculinity from him. As twisted as it may be, at least it’s a contest between equals. When a woman – someone who is by definition lesser – robs you of your manhood, it’s an outrage.
This is part of what informs so much of the response to the assault; Christy Mack didn’t just provoke War Machine, she castrated him. To someone who markets himself with the tag of “I do alpha male shit”, this is a sin to great to be borne.It’s an injustice that must be redressed; his manhood must be reclaimed.
And the fastest way to do that? Violence.
As I write this, there is one guy in here for slapping his wife, one here for yelling at his wife, and one here for beating some guy’s ass that disrespected his wife. WTF!? If your wife is being a bitch you can’t slap her, if your wife is yelling at you, God forbid you yell back, and if some asshole hurts your wife, you can not protect her! LMFAO!
Corey Thomas touched Koppenhaver’s property and so he is beaten but allowed to leave. Christy Mack’s participation in his emasculation, however, is the insult on top of injury and so warrants the brunt of his fury. He has to reclaim his masculinity, show that he can control his bitch and re-establish that this is indeed his pussy. And so he breaks her face. He fractures her ribs. He kicks her so hard her liver bursts. Because he’s been made lesser by someone who’s supposed to be beneath him.
But not every man who is looking to re-establish his masculinity is willing or able to inflict it on the woman who’s insulted him and this reclaim his manhood… what is he to do then?
Well… who ever said that the violence needed to be physical?
Zoe Quinn and the Pretty Internet Hate Machine
On Saturday, April 16th, Eron Gjoni posted an extensive – 10,000+ word blog post detailing his relationship and subsequent break-up with Zoe Quinn, the developer of the critically acclaimed indie game/interactive novel Depression Quest. In and of itself it’s the typical writings of a bitter and resentful ex, made more uncomfortable by the repeated postings of private communications between the two. Over the course of the rant, Gjoni accuses Quinn of having cheated on him repeatedly with journalists and members of the gaming industry – calling her “Five Guys Burgers and Fries” in an especially classy moment – illustrating his point with (equally classy) annotated screenshots of their conversations as proof. Gjoni implies repeatedly that Quinn’s alleged relationships with these men was “ethically murky”‘ at best.
Zoe Quinn was already a controversial figure, having endured repeated harassment over the publication of Depression Quest on Steam, Valve Software’s web-based gaming network. Gjoni’s post – and the implications that Quinn didn’t just cheat on him but was whoring herself out – was enough to stir the Internet Hate Machine to life once more, focusing it’s inchoate rage on her. Since then, Quinn has been the subject of repeated harassment including having her personal information shared online, her Tumblr and Twitter accounts being hacked, distribution of nude photos of her via social media and repeated death and rape threats.
The given explanation for this ongoing assault is that it’s about “ethics” and unearthing “corruption in video games journalism”, except for the inconvenient fact that there is no proof of any wrong-doing. Others insist that it’s about Quinn’s “integrity” – as though her sex-life were at all relevant to anything. All we have are accusations of infidelity and a relationship gone bad; a shame if true but ultimately not anyone’s business but the individuals involved. Except it was Gnonji who decided to make it the Internet’s business. Gnonji who decided that the world needed to know about his ex – violating her privacy to parade it around for the judgment of strangers. This has nothing to do with any alleged “corruption” and everything to do with whipping an Internet mob into a frenzy.
And in doing so, make Zoe Quinn into the avatar of every woman who ever did a gamer wrong.
See, just as with War Machine, Gjnoji is telling the world that he has been cuckolded. He’s been insulted. His manhood has been stolen from him. He’s been hurt, wronged even and must exact retribution for her sins against him and his masculinity. Unlike Koppenhaver, Gjoni outsourced the avenging of her “crimes” against him instead. Cry harlot! and let slip the blogs of war.
And as we see so many times, the Internet responded with vigor, eager to savage a woman with threats and accusations, promising rape, promising death, promising to end her career. Demanding to shut her down, shut her up and erase her from the community until she’s nothing but a legend of yet another uppity slut, trying to take advantage of good men with her whorish ways.
They’re Coming For Your Penis! OR: Toxic Masculinity and the Internet Mob
It’s a pattern we have seen over and over again – women attacked, harassed and threatened for the crimes of being a woman online – especially one daring to enter a “man’s” domain. If a woman dares to participate into those worlds deemed the sole province of masculinity in any way other than for the pleasure of men, then she’s seen as suspect at best and malignant at worst. Fake geek girls prowl conventions and nerd gatherings, looking to prey on unsuspecting geeks, exploiting them for nebulous values of “attention”. Anita Sarkeesian – bro-gaming’s Public Enemy #1 – seeks to neuter video games because fuck you, penis! Dina Abou Karam is hired as a community manager for Mighty 9 and suddenly is part of a feminist conspiracy to take over the game. Alice Mercier is harassed by a games journalist and is blamed for maliciously destroying his reputation. Janelle Asselin critiques a comic cover and is deluged by rape threats. Women become instant targets for harassment simply for the crime of saying “hello” during a Halo 3 deathmatch.
All in the name of taking geekdom back from those eeeeeeevil feminists who’re coming to take away your penis games and your comics and other “man stuff”. Women are coming to steal your manliness! Push back! Strike back!
The narrative of the toxic and fragile masculinity can be seen all over these debates, from the attacks on Zoe Quinn, Anita Sarkeesian and others. It’s the battle of “real” men, manly men vs. the White Knights and Social Justice Warriors. The term “White Knight” is tossed about to shame men into not defending women or challenging the sexist harassment. It’s a form of gender policing; “conform to our way of thinking or get your masculinity taken away”. After all, the only possible reason someone might disagree with the gatekeepers of gaming is because they’re trying to ingratiate themselves to women in hopes of sex. White Knights can’t possibly be real men. Real men don’t put pussy on the pedestal; they wave their disgust and resentment of women loud and proud! And what quicker and easier way is there to validate your manliness in the eyes of your peers than by striking back against those emasculating feminists? It’s not enough to simply not purchase Depression Quest – you need to call Zoe Quinn a whore, buying non-existent reviews with sexual favors. You need to threaten to rape women you disagree with because they dare to show their faces online. You need to punish women by threatening to doxx them, to humiliate them with nude photos and use their sex-lives as reasons to invalidate them.
This is why the need to prove one’s “manliness” are so toxic; because it’s a never-ending excuse to lash out at others – women especially – in the name of avenging any perceived, even imagined, injustice. The geek community is supposed to be better than this. We need to be better than this.
But we never will be until we stop letting geek culture be defined by fear and hate.
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Job cuts loom as EADS changes name to Airbus
Tim Hepher, Cyril Altmeyer
6 Min Read
PARIS (Reuters) - EADS EAD.PA will take the name of its flagship brand Airbus and target higher profits by combining defense and space units, Europe’s top aerospace group confirmed on Wednesday, in a move that could involve job cuts.
File photo of an A380 aircraft seen through a window with an Airbus logo during the EADS / Airbus 'New Year Press Conference' in Hamburg January 17, 2012. REUTERS/Morris Mac Matzen/Files
Nine months after bowing to political opposition to his attempt to merge with UK arms firm BAE Systems (BAES.L), Chief Executive Tom Enders declared civil jets the main “growth engine” for EADS investors, who pushed shares to new highs.
After unveiling a strong batch of commercial earnings that included a rise in Airbus order targets, Enders did not rule out job cuts in the group’s 45,000-strong defense and space operations, which will be based in Germany.
“It (the reorganization) means some real restructuring, but we are forced to do it: the defense business is ... shrinking in Europe,” he said.
The company warned the move could lead to restructuring charges later in the year - a standard sign of layoffs ahead. But it also deferred politically sensitive decisions until after German elections in September by promising a detailed review.
The changes will come into affect starting from January 1, allowing time for what could be lengthy talks with unions.
“To keep the company economically successful, the restructuring must take place in a socially acceptable way,” Ruediger Luetjen, head of the company’s European works council and a representative of trade union IG Metall, told Reuters.
STANDOFF
The company is already on a potential collision course with the German government over the allocation of jobs for Airbus A350 jets, in a dispute that shows few signs of easing.
People familiar with the matter say Airbus is unwilling to give guarantees over the share of work on the latest jet as long as Germany holds back a development loan. Berlin, for its part, wants guarantees about work on future Airbus projects.
“The German government will work closely (with EADS) during the upcoming restructuring process and will place great importance on Germany’s interests as an industrial location,” Economy Minister Philipp Roesler said.
EADS was formed in 2000 from a merger of French, German and Spanish assets that incorporated passenger jetmaker Airbus, founded three decades earlier and now a global rival to Boeing.
The name EADS - originally European Aeronautic, Defense & Space Co - was never widely recognized and the group has long discussed changing its name to Airbus. But politics have until now made it difficult to tinker with Europe’s leading symbols.
Enders hopes the decision to unite under a globally recognized brand will galvanize the rest of the business from space rockets to helicopters and encrypted communications.
EADS will be called Airbus Group and will combine defense and space activities in one division together with Airbus Military transporters, currently twinned with passenger jets.
Eurocopter, the world’s largest commercial helicopter maker, will also be renamed Airbus Helicopters.
‘NOBODY AUTONOMOUS’
The decision to co-opt the Airbus brand may test a delicate balance between ‘old EADS’ and the Airbus division, where CEO Fabrice Bregier is widely seen as Enders’ future successor.
Industry sources noted the unit is keeping the one-word name “Airbus” rather than a more hierarchical divisional title like that of its direct counterpart, Boeing Commercial Airplanes.
But by uniting defense and space and rallying behind one brand, EADS is adopting much of the look and feel of its rival, where planemaking has traditionally had less independence.
Enders dismissed media “rumors” about such sensitivities and is seen likely to avoid clashing with Bregier. But he ruled out a return to fiefdoms that beset EADS under past managements.
“Nobody is autonomous on this planet. I have a board and the same goes for division heads in the group,” he told reporters.
Powered by commercial demand for Airbus planes, second-quarter EADS operating profit rose 23 percent to 887 million euros on revenue of 13.945 billion, up 3 percent. Airbus makes up two thirds of sales and is expected to remain dominant.
Analysts were expecting profit of 839 million euros.
EADS raised the 2013 order target for passenger jets by 25 percent to more than 1,000 aircraft, as reported by Reuters earlier in July. Other targets were unchanged.
Shares in EADS closed up 1.4 percent at 44.89 euros.
The new order target puts Airbus on course to beat its 2012 gross order tally of 914 jetliners. Industry sources say business in the pipeline suggests it could reach 1,200 orders.
Airbus is battling to regain leadership of the $100 billion annual jet market after Boeing grabbed top spot last year.
Strategy chief Marwan Lahoud said all divisions would join efforts to increase margins to 10 percent by 2015, from a group average of 5.6 percent in the first half of this year.
That would bring EADS roughly in line with Boeing, though the comparison is blurred by accounting differences that allow the U.S. company to spread some costs over a longer period.
Enders said testing for the A350, the newest Airbus jet, was going “very, very well” but the project remained challenging.
Additional reporting by Joern Poltz, Editing by James Regan and Anthony Barker
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PHP Do While Loop
In this tutorial we will study about do-while loop, by default do-while loop iterates at least once irrespective of condition. Examples in this tutorial will make it more clear.
Do-While Control Structure:
Do-While loop is another type of loop which runs at least once, since this
loop checks the condition after executing the code within. We generally use
Do-While loop when the iteration must run at least once despite of the validity
of the variable. In Do-While loop we need to initialize the variable first the
coding within the loop executes and at last the this loop checks the condition.
We should change the value of the variable within the loop.
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Governor Andrew Cuomo has warned that New York State is running out of time to get enough ventilators to treat the sickest coronavirus patients. Without them, vastly more New Yorkers could die. But the number of ventilators is not the only bottleneck: hospitals around the country are worried that a surge in COVID-19 patients will catch them short of the staff needed to run the lifesaving machines.
In a typical hospital intensive care unit, one nurse takes care of one or two patients at a time, says Ali Raja, a physician and executive vice chair of emergency medicine at Massachusetts General Hospital. Before an individual is put on a ventilator, an anesthesiologist or emergency room doctor must intubate, or feed a tube down the throat of, that person. Such patients need to be anesthetized and immobilized during this process to avoid feeling like they are choking, Raja says. Then there are the respiratory therapists—roughly one for every 10 patients—needed to set up the ventilators and routinely check in on the machines, responding if there are any alarms or malfunctions. In addition, a critical care doctor must check in on each patient twice a day. There is also the worry that the health care workers themselves will become sick with the virus.
“This disease, unlike really anything we’ve seen in 100 years, doesn’t just affect our patients—it affects our staff,” says Raja, who is estimating that 20 to 25 percent of hospital workers might fall ill and be unable to come to work. Major hospitals such as his have the “bench strength,” or backup staff, to continue functioning with such a reduction, Raja says, but “in community hospitals in Massachusetts, that’s really hard to come by.”
About 80 percent of COVID-19 patients can safely recover at home, studies suggest. Even most of those admitted to a hospital can be treated simply with extra oxygen to help them breathe better, without the need for a ventilator to force air into their lungs. But people whose lungs are filled with fluid need the device to allow their body to focus on fighting the virus rather than struggling to breath, Raja says.
“There are questions about which patients we should intubate and whether we should do it earlier or later in their care. But there’s no doubt that ventilators save patients’ lives,” he says. “While COVID-19 has a mortality rate as high as 50 percent in some ICU case series, it would be much higher if we did not intubate those patients who are severely ill.”
Coronavirus patients who are sick enough to require a ventilator need one for an average of nearly three weeks, whereas a few days are sufficient for many people with other conditions, says Eric Schneider, senior vice president for policy and research at the Commonwealth Fund, a private nonprofit organization that promotes a high-performing health care system. This long-term need means that New York may not—as Governor Cuomo has suggested—be able to free up enough ventilators to send to the next national hotspot, Schneider says.
Hospitals and health care workers are beginning to figure out how to treat two patients at a time on one ventilator. In many places, including Raja’s hospital, experts are working to develop ways to double ventilator capacity while still allowing the different adjustments that each patient might need, he says. The same number of nurses would still be required, Raja says, because “there is so much to nursing care beyond ventilator management. Having two patients on one vent doesn't take anything off of their plate.”
Such doubling up is necessary because of a lack of ventilators and the skyrocketing cost of a new one—from about $25,000 before the current outbreak to $50,000 or more now, Schneider says. “States are bidding against the federal government and against each other,” he says, noting that production cannot ramp up fast enough to meet the current demand. “Prices are all over the place.” Without adequate staff, patients cannot be treated safely even if there are enough machines to go around, Schneider and Raja say.
William Padula’s research at the University of Southern California helps support this observation. Padula, an assistant professor of pharmaceutical and health economics, has been studying the global death rates for COVID-19 and has found they are lower in countries that have more nurses per patient. Nations with one extra nurse per 1,000 people save two lives per million coronavirus patients, according to research he conducted with his colleagues at Johns Hopkins University. “You need skilled specialists available in hospitallike settings to manage patient caseloads and, especially, to deal with high-needs patients on respirators or [others] who need special care,” says Padula, who is now expanding his analysis to include doctors.
Peter Marshall, vice chief for medical critical care at the University of Southern California’s Keck School of Medicine, says his hospital is managing fine—at the moment. But he is anxious for the future. Without an emergency room, Keck usually receives patients who are transferred from other hospitals—often the sickest individuals. Right now, Marshall says, his hospital has 15 patients on ventilators and the capacity to handle at least 30. “If this goes on for weeks and weeks, it’s conceivable that we would have shortages,” he says, adding that other Los Angeles hospitals are already nearing capacity.
Raja says the Massachusetts General Hospital system—one of the largest and best-resourced in the country—should be able to handle all but the most extreme level of demand. Partners Healthcare, the nonprofit parent company of Mass General and other Harvard University–affiliated hospitals, has many nurses and anesthetists who have been working in operating rooms but whose duties can be shifted to care for COVID-19 patients. “We have lots of people with the right expertise,” he says. “What I worry about is smaller hospitals that don’t have the bench strength we do.”
There have been concerns about nurses and other health care workers contracting COVID-19 when they are intubating patients, because the process can generate aerosols that may spread the virus. But Raja says it can be done safely with the proper protective equipment. He says a device called a video laryngoscope allows clinicians to stand a few feet from people, rather than directly above them, while intubating those individuals. Intubation takes only about five minutes, in addition to another 15 to 20 for staff to put on appropriate protective gear, he says.
Major hospitals such as Raja’s have disposable tips for their video laryngoscopes, allowing them to be quickly cleaned. In a smaller hospital, the cleaning process alone might take an hour or more, he says. If the staff have to perform back-to-back intubations, they are going to run out of devices and personnel pretty quickly, he adds.
The real fear, Raja says, is the surge that everyone knows is coming in the next two weeks. “We are all expecting a surge [higher] than anything we’ve seen,” he says. “We have plans ready with more beds and more personnel. But we don’t know whether or not those are enough. There are so many different eventualities we might not be ready for, and we just can’t know, until it starts, whether we are.”
Read more about the coronavirus outbreak here.
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Ukrainian Cultural Heritage Village
The Ukrainian Cultural Heritage Village () is an open-air museum that uses costumed historical interpreters to recreate pioneer settlements in east central Alberta, Canada, northeast and east of Edmonton. In particular it shows the lives of Ukrainian Canadian settlers from the years 1899 to 1930. Buildings from surrounding communities have been moved to the historic site and restored to various years within the first part of the twentieth century.
"The Village", as it is colloquially known, has a very strong commitment to historical authenticity and the concept of living history. The Village uses a technique known as first-person interpretation which requires that the costumed performers remain in character at all times (or as much as is feasibly possible). Actors answer all questions as if it is the year their building portrays. Although this technique is startling for some visitors at first, it allows for a much stronger experience of immersion in history than traditional third-person interpretation where the actor acknowledges that he is, in fact, in a museum.
The village is in Lamont County on the Yellowhead highway, on the eastern edge of Elk Island National Park.
Monuments
Alberta Centenary Pioneer Recognition Monument
Cenotaph to the Ukrainian Canadian Soldier
Joseph Olesków Monument – by Leo Mol
Pioneer Family Monument – by Leo Mol
Statue of Vasyl' Stefanyk
Ukrainian Canadian Internment Camp Monument
Chornobyl Disaster Commemorative Cross
Stelmach House
Buildings
The Museum is divided into thematic areas: Overview, Farmsteads, Rural Communities, and Town sites.
Note: the spellings used for names and locations are those from the time to which the building has been restored, and may not match those in use today
Name (indicates the name of the owners or operators of a building and its original location), as well as the time period to which it has been restored
Overview
Provides an introduction to Galician and Bukovynian immigration to Canada by showing the homes of three settler families. Iwan Pylypow was one of two individuals who set off the mass migration of Ukrainians to Canada at the end of the 19th century. His family was Galician. His third house in Canada is preserved at the Village. The second house is that of Mykhailo and Vaselina Hawreliak. The Hawreliaks were a large Ukrainian Bukovynian family who settled in the Shandro area. By the 1920s Mykhailo Hawreliak was quite successful, and the house preserved here has five bedrooms and a cistern that collected rainwater for use in the kitchen. The Nazar Yurko family was also from Bukovyna, but was of Romanian descent.
Pylypow House (Star, Alberta; Built 1906, depicts 1923–1929)
Hawreliak House (Shandro, Alberta; Built 1919, depicts 1925–1928)
Yurko House (Boian, Alberta; Built 1920, depicts 1932)
Farmsteads
Shows different farmyards from different eras/stages of development.
Township Survey Marker (Reconstruction to circa 1892) – marked the corner of a Township (36 square miles), containing 160 acre plots of land for farming that were surveyed prior to the mass influx of European immigration to the Canadian Prairies
The newly arrived immigrants
Burdei – Based on field research and archaeological findings; reconstructed to 1900 - Temporary shelters dug out of the ground or into
the side of a hill were a common feature of the earliest farms of the Ukrainian immigrant settlers.
The Bukovynian settlers
Grekul House (Toporivtsi, Alberta; Built 1915, depicts 1918–1919)
Grekul Granary (Toporivtsi, Alberta; Built 1908-1909, depicts 1918–1919
Grekul Barn (Toporivtsi, Alberta; Built 1915, depicts 1918–1919
Roswiyczuk Granary (North Kotzman, Alberta; Built 1914, depicts 1918)
Makowichuk Barn (South Kotzman, Alberta; Built 1912, depicts 1918)
The Galician settlers
Hlus' House (Buchach, Alberta; Built 1915–1916, depicts 1918)
Hlus' Barn (Buchach, Alberta; Built 1915, depicts 1918)
Hlus' Chicken Coop (Buchach, Alberta; Built 1915, depicts 1918)
Lakusta Barn (Amelia-Cookville, Alberta; Built 1915, depicts 1918)
Lakusta Granary (Amelia-Cookville, Alberta; Built 1912, depicts 1918)
The later immigrants
Slemko House (South Kotzman, Alberta; Built 1912, depicts 1919)
Slemko Granary (South Kotzman, Alberta; Built 1913, depicts 1919)
Slemko Barn (South Kotzman, Alberta Built 1914, depicts 1919)
Pigsty (Based on field research; reconstructed to 1919)
Ukrainian-Canadian farmers
Hewko House (Podola, Alberta; Built 1917–1924, depicts 1930)
Kitt Threshing Machine Shed (Myrnam, Alberta; Built 1922, depicts 1930)
Chernochan Machine Shed (Smoky Lake, Alberta; Built 1915, depicts 1925-1928
Rural community (reflecting 1925–30 time period)
Roadside Shrine (Based on field research; reconstructed to 1919)
Luzan Grocery (Luzan, Alberta; Built 1927, depicts 1929)
Luzan Post Office (Luzan, Alberta; Built 1926, depicts 1929)
Kiew Hall – a community centre; originally independent, later (1930s) affiliated with the Ukrainian Labour Farmer Temple Association (Kiew, Alberta; Built 1924, depicts 1930))
St. Nicholas Russo-Greek Orthodox Church (Kiew, Alberta; Built 1908, depicts 1925–1928)
Kolody Sawmill (Vilna, Alberta; Manufactured 1927, depicts 1929)
"Russia" School and Barn (Musidora, Alberta; Built 1910, depicts 1926–1929)
Russia" School Barn (Musidora, Alberta; Built 1926, depicts 1926–1929)
South River Teacher’s Shack (South River, Alberta; Built 1921, depicts 1927)
St. Nicholas Ukrainian Greek Catholic Church (also known as St. Mary's or Hlus' Church) (Buchach, Alberta; Built 1912, depicts 1930)
Town site (reflecting 1925–30 time period)
St. Vladimir's Ukrainian Greek Orthodox Church (Vegreville, Alberta; Built 1934, depicts 1934–1935)
Wostok Hardware Store (Wostok, Alberta; Built 1937–1938, depicts 1939)
Hilliard Pool Hall (Hilliard, Alberta; Built 1925, depicts 1930)
Hilliard Pool Hall Stable & Garage (Hilliard, Alberta; Built 1925, depicts 1930)
Market Square
Radway Post Office, Telephone Exchange, and Municipal District Office (Radway, Alberta; Built 1920, depicts 1929)
Radway Postmaster’s Garage (Radway, Alberta; Built 1927, depicts 1929)
Radway Livery Barn (Radway, Alberta; Built 1927, depicts 1929)
Pawlenchuk Lot Barn (Smoky Lake, Alberta; Built 1930, depicts 1932)
United Merchants of Alberta General Store (Smoky Lake, Alberta; Built 1932, depicts 1932)
Andrew Alberta Provincial Police Post (Andrew, Alberta; Built 1913, depicts 1925–1928)
Bellis Home Grain Co. Elevator (Bellis, Alberta; Built 1922, depicts 1928)
Bellis Canadian National Railway Station (Bellis, Alberta; Built 1923, depicts 1928)
Morecambe School (Morecambe, Alberta; Built 1929, depicts 1930)
Hilliard Hotel (Hilliard, Alberta; Built 1928, depicts 1929)
Alberta Lumber Co. Office (Lamont, Alberta; Built 1907–1910, depicts 1928)
Alberta Lumber Company Cement Shed (Lamont, Alberta; Built 1906, depicts 1928)
Demchuk Blacksmith Shop (Myrnam, Alberta; Built 1927, depicts 1929)
Demchuk House (Myrnam, Alberta; Built 1928, depicts 1929)
Woodworking Shop (Based on field research; reconstructed to 1930)
Affiliations
The Museum is affiliated with: CMA, CHIN, and Virtual Museum of Canada.
See also
Kalyna Country – an ecomuseum region in East Central Alberta, of which the Village is a part
List of Canadian place names of Ukrainian origin – some of the places where the Village's buildings and machines are from are listed on this page (in the Alberta section)
Narodny dim – community centres with a Ukrainian cultural emphasis concentrated in districts inhabited by Ukrainian Canadians across the Prairie provinces
References
External links
Alberta Community Development – Ukrainian Cultural Heritage Village
University of Alberta – Ukrainian Cultural Heritage Village
Google Map to Ukrainian Cultural Heritage Village from Edmonton, Alberta, Canada Route Map Overhead view
Category:Lamont County
Category:Provincial historic sites of Alberta
Category:Living museums in Canada
Category:Ukrainian-Canadian culture in Alberta
Category:Ukrainian museums in Canada
Category:Open-air museums in Canada
Category:Church museums in Alberta
Category:Farm museums in Alberta
Category:Historic house museums in Alberta
Category:Grain elevator museums in Alberta
Category:Railway station museums in Alberta
Category:Ukrainian culture
Category:1974 establishments in Alberta
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Chronic obstructive pulmonary disease, risk factors, and outcome trials: comparisons with cardiovascular disease.
Chronic obstructive pulmonary disease (COPD) is a major health problem and now ranks fifth in terms of the global burden of disease. Although COPD is a disease that is characterized by progressive respiratory symptoms and functional decline, exacerbations pose the greatest risk for morbidity and early mortality, have a dramatic effect on quality of life, and are the most significant source of health care expenditure. To improve survival and reduce costs, it is critical to develop effective programs designed to reduce the frequency and severity of exacerbations for these patients. With limited health care resources, efficient and effective management of COPD ideally involves identifying and focusing efforts on individuals at particular risk. In the development of an appropriate multimodal strategy, lessons could be learned from the evolution of guidelines and management of cardiovascular disease, in particular heart failure, which has many parallels with COPD in terms of prevalence, prognosis, and impact on patient quality of life. There is a need for large prospective trials in COPD, based on hard clinical outcomes such as death, which, together with physician and patient education, will help to drive improvements in clinical management.
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Conventionally, as bearings usable with a long period of greasing interval or without greasing, oil-containing slip bearings prepared by allowing pores in a Cu-based or Fe-based porous sintered alloy to contain a lubricating oil are widely put into practical use. Selection of the Cu-based or Fe-based porous sintered alloy is determined depending on conditions such as oil lubricating state, sliding speed, contact surface-pressure and the like, and under light-load and high-speed sliding conditions, a bronze-based oil-containing slip bearing is suitably utilized, whereas under high-surface-pressure and low-speed sliding conditions, a Fe—C, Fe—Cu or Fe—C—Cu-based oil-containing slip bearing is suitably utilized (see, for example, Japan Powder Metallurgy Association ed. Parts—Their design and manufacture”, Gijutsu Shoin Co., Ltd., Oct. 20, 1987, p. 327-341). On one hand, there are widely utilized also slip bearings produced by orderly arranging graphite fragments as a solid lubricant on a bearing material made of high tensile brass and bronze, and allowing the graphite fragments to contain a lubricating oil (for example, 500 SP manufactured by Oiles Corp.). On the other hand, prior technologies aiming at improvement in a sliding property under high surface pressure and low speed sliding are shown in the following various patent literatures.
Japanese Patent No. 2832800 adopts a composite sintered alloy having a porosity of 5 to 30 vol % and composed of a copper powder and an iron powder, as an iron-based sintered body in a slip bearing in which a lubricating oil having a kinematic viscosity of 240 cSt to 1500 cSt is impregnated on an iron-based sintered body oil-containing bearing used under sliding conditions of a high surface pressure of 600 kgf/cm2 or more and a sliding speed of 1.2 to 3 m/min, and discloses that it is preferable to perform a carburizing, nitriding or sulfurizing nitriding treatment on a contact surface.
Japanese Patent Application Laid-Open (JP-A) No. 10-246230 discloses that a slip bearing produced by filling a lubricant composition containing a solid lubricant or an extreme-pressure additive having a dropping point of 60° C. or more in semi-solid condition or solid condition at ambient temperature, into pores in an iron-based sintered alloy containing martensite in an iron-carbon alloy base and in which at least one of copper particles and copper alloy particles are dispersed, shows excellent slip bearing performance under a surface pressure of 30 MPa or more.
Japanese Patent Publication (JP-B) No. 6-6725 discloses that a sintered copper alloy having self lubricity suitable for use on a ware plate of a press machine and the like is obtained by sintering under pressure a mixed powder prepared by mixing a copper alloy powder containing 5 to 30 wt % of Ni, 7 to 13 wt % of Sn and 0.3 to 2 wt % of P with 1 to 5 wt % of Mo and 1 to 2.5 wt % of a graphite powder.
JP-A No. 8-109450 discloses a wear resistant sintered alloy for oil-containing bearing characterized in that Cu particles or Cu alloy particles are dispersed in an iron-carbon alloy base having martensite present therein, the content of Cu is from 7 to 30 wt % and, alloy particles having a specific composition as a phase harder than the above-mentioned iron-carbon alloy base are dispersed in an amount of 5 to 30 wt % and the porosity is from 8 to 30 vol %. In this wear resistant sintered alloy for oil-containing bearing, by dispersing a large amount of soft Cu particles in a martensite phase, conformability is improved, and by dispersing alloy particles harder than the martensite of the base, plastic deformation of the base is decreased and load applied on the base alloy in sliding contact state is lowered, to obtain excellent wear resistance even under high surface pressure. Here, this patent literature mentions, as the above-mentioned alloy particles, {circle around (1)} Fe-base alloy particles (high speed steel (Highss) powder particles) containing 0.6 to 1.7 wt % of C, 3 to 5 wt % of Cr, 1 to 20 wt % of W and 0.5 to 6 wt % of V, {circle around (2)} Fe-base alloy particles (high speed steel (Highss containing Mo, Co) powder particles) containing 0.6 to 1.7 wt % of C, 3 to 5 wt % of Cr, 1 to 20 wt % of W, 0.5 to 6 wt % of V and 20 wt % or less of Mo and/or Co, {circle around (3)} Mo—Fe particles (ferro-molybdenum) containing 55 to 70 wt % of Mo, {circle around (4)} Co-base alloy particles (heat resistant and wear resistant alloy powder for build up spraying, trade name: COBAMET manufactured by Cabot) containing 5 to 15 wt % of Cr, 20 to 40 wt % of Mo and 1 to 5 wt % of Si; and the like.
JP-A No. 2001-271129 which is a prior application of the applicant discloses a slip bearing characterized in that hard dispersion materials such as various intermetallic compounds and the like, solid lubricants such as graphite and the like may be contained in an (alpha+beta) two-phase structure having at least a beta phase dispersed in the structure, or a beta phase structure constituting a Cu—Al—Sn-based sintered contact material, and in which, further, the Cu—Al—Sn-based sintered contact material is integrated on the inner circumferential surface of an iron-based backing metal, so as to maintain bearing rigidity and press fit force in press-fitting on a work implement connecting apparatus. In this slip bearing, the above-mentioned Cu—Al—Sn-based sintered contact material is soft as compared with the bearing material containing martensite according to the above-mentioned patent literature 4, and excellent in conformability with a contact opposite member (work implement connecting pin or the like). Therefore, this sliding bearing is an extremely excellent sliding bearing which can be suitably used at extremely low sliding speed (0.6 m/min or less) and a high surface pressure of up to 1200 kgf/cm2.
JP-A No. 7-166278 discloses that a sintered contact material having an excellent lubricating ability, affinity to oil, low friction coefficient and high wear resistance can be obtained by adding 0.5 to 5 wt % of Mo or 0.5 to 15 wt % of Fe—Mo into a bronze-based and/or lead bronze-based sintered contact material containing 4 to 12 wt % of Sn or this and 0.1 to 10 wt % of Pb.
On one hand, comparatively soft lead bronze ingot materials (for example, LBC 2 to 5) are often used as, for example, a contact material for floating bushing of a turbo charger used under high speed, high temperature and oil lubrication conditions, however, from the standpoint of corrosion resistance under high temperature sliding condition (sulfur attack property), free-cutting brass-based and high tensile brass-based alloys containing Pb are suitably used (see, for example, JP-B No. 5-36486). Additionally, Al bronze-based ingot materials are also investigated as the contact material for floating bushing (see, for example, JP-A No. 5-214468).
On the other hand, in the case of, for example, engine metals used under high surface pressure and high speed sliding conditions, an overlay layer made of a soft metal such as Sn and the like is formed on a contact surface of a lead bronze-based sintered bushing to improve conformability and to obtain improved fluid lubricity.
Further, in parts sliding under high surface pressure and high speed conditions (hereinafter, referred to as “sliding part”) of constituent parts of hydraulic pumps/motors used under high surface pressure and high speed sliding conditions likewise, a material containing lead bronze integrated by a cast wrapping method and the like is used as a constituent material, and in sliding parts used under particularly severe sliding conditions, materials having high strength, and excellent seizure resistance and wear resistance such as high tensile brass are used as a constituent material (see, for example, Japan Non-ferrous Metal Casting Association ed., “ENGINEERING DATA BOOK FOR COPPER BASED ALLOY CASTING”, Issued by Materials Process Technology Center (SOKEIZAI CENTER), Jul. 30, 1988, p. 134-155).
In general, it is extremely rare to attain fluid lubricating condition on an oil-containing slip bearing, and particularly under extremely low sliding speed and high surface pressure conditions, the film thickness of a lubricant oil on a bearing surface (contact surface) becomes, due to escape of oil pressure through pores in a sintered material, approximately the surface roughness of the bearing surface or smaller, and in many cases, boundary lubricating sliding conditions including solid friction (adhesion) are provided. Consequently, in slip bearings (bushing, thrust bearings and the like) used under sliding conditions of a surface pressure of 300 kgf/cm2 or more and a sliding speed of 0.01 to 2 m/min, in a work implement connecting portion of construction machines such as, for example, a hydraulic excavator and the like, its seizure resistance and Wear resistance are significantly ruled by material functions of the sliding bearing (composition and structure).
However, the Cu-based and Fe-based porous sintered alloy material according the above-mentioned literature (Japan Powder Metallurgy Association ed. “P/M Parts—Their design and manufacture”, Gijutsu Shoin Co., Ltd., Oct. 20, 1987, p. 327-341) has a problem that it cannot be adapted to extremely low sliding speed and high surface pressure conditions of a sliding speed of 0.01 to 2 m/min and a surface pressure of 300 kgf/cm2 or more, as apparent from FIG. 21 showing the application range of an oil-containing slip bearing generally used (Japan Powder Metallurgy Association ed. “P/M Parts—Their design and manufacture”, Gijutsu Shoin Co., Ltd., Oct. 20, 1987, p. 337, FIG. 6. 19 “Sintered bearing application example”, is cited).
Even a composite sintered alloy material according to Japanese Patent No. 2832800 in which surface treatments such as carburization, nitriding and the like are performed on a composite sintered alloy composed of a copper powder and an iron powder, and an iron-base sintered alloy material according to JP-A No. 10-246230 in which pores are filled with extreme-pressure additives and the like and a martensite structure is contained have a problem that there is a possibility that a sufficient sliding ability is not manifested under extremely low sliding speed (0.01 to 2 m/min), too.
In the sintered copper alloy material according to JP-B No. 6-6725 having self lubricity suitable for use on a ware plate or the like of a press machine, local metal contact with an opposite member tends to occur under sliding conditions in which a lubricating oil film is not easily formed due to extremely low sliding speed and high surface pressure, resultantly there is a problem that sufficient seizure resistance and wear resistance are not obtained easily. Further, there is also a problem that when the addition amount of soft solid lubricants such as graphite, MoS2 and the like dispersed in the sintered copper alloy material is over 2.5 wt %, its strength decreases remarkably.
In the above-mentioned wear resistant sintered alloy for oil-containing bearing according to JP-A No. 8-109450, the plastic deformation of a base is reduced and load applied on a base alloy in sliding contact state is decreased by dispersing a large amount of soft Cu particles in a martensite phase and dispersing alloy particles harder than the martensite in a base, however, it has a problem that an effect of improving adhesion resistance is not sufficient since co-existence of dispersion of soft Cu particles and dispersion (5 to 30 wt %) of hard alloy particles in one alloy is limited and load applied on the base alloy in sliding contact state is concentrated on its hard alloy particles. Further, there is also a problem that by addition of a large amount of alloy particles harder than a martensite in a base and having no self lubricity, a contact opposite material is remarkably attacked by adhesion wearing, and the temperature of a contact surface increases to easily cause a seizure phenomenon. Furthermore, there is a problem that a bearing bushing made of this wear resistant sintered alloy for oil-containing bearing as a constituent material is expensive. There is also an investigation of lowering cost, increasing a sliding ability, improving maintenance and the like by sharing the role of a sliding function to a cheap contact material constituting mutual slip pair, however, a solution is not attained yet.
The Cu—Al—Sn-based sintered contact material suggested in JP-A No. 2001-271129 which is a prior application of the applicant is an extremely excellent bearing material which can be used at extremely low sliding speed (0.6 m/min or less) and a high surface pressure of up to 1200 kgf/cm2, which cannot be attained by conventional bearing materials of iron-carbon alloy base, however, it has a problem that, due to somewhat lack in pressure resistance required in use environments in which earth and sand invade, wearing progresses easily under such use environments.
The sintered contact material according to JP-A NO. 7-1662778 has, when a lubricating function formed by Mo of 5% by area or less or Fe-55 to 70 wt % Mo (ferro-molybdenum phase) of 15% by area or less based on the contact area using a bronze alloy phase as a mother phase is singly performed, problems that, under extreme low sliding speed and high surface pressure conditions such as for the above-mentioned work implement connecting portion, formation of an adhesion portion by local metal contact with an opposite member is not sufficiently prevented and adhesion wearing progresses, and conformability resistance, seizure resistance and wear resistance are not sufficiently attained, and hard MoFe (ferro-molybdenum) particles remarkably attack a contact opposite material. It is easily envisaged to be able to improve a sliding property by regulating the addition amount of Mo at 5 wt % or more, however, there occurs, in this case, a new problem that the structure strength of the sintered contact material is decreased.
The high tensile brass-based and Al bronze-based contact materials containing a lead bronze-based material and lead according to JP-B No. 5-36486 and JP-A No. 5-214468 suitably used as a constituent material of a floating bushing in a turbo charger are recently required to improve seizure resistance and wear resistance under higher speed and higher temperature sliding and to manifest excellent seizure resistance, wear resistance and corrosion resistance even under poor lubrication condition in starting of a turbo charger and the like, however, these contact materials have a problem that (1) a Pb-lack layer after elution of Pb is formed near a contact surface (see, FIG. 22 (a) to (c)), and (2) even after stop of operation of a turbo charger, the temperature at a bearing portion increases to high temperatures around 300° C. due to heat conduction from a turbine and consequently a layer of accumulation of CuS and sludge formed by reaction with S in a lubricating oil is formed on a trace of Pb connecting to the contact surface (see, FIG. 23 (a) to (b)), therefore, a lubricating ability by Pb decreases, and essential improvement against seizure resistance and durability (elongation of life) is impossible. Further, from the standpoint of recent environmental problems, there is a problem that a large amount of Pb contained in a material is not preferable.
Regarding hydraulic pumps/motors, there is recently a tendency of increase in pressure and further decrease in size, therefore, improvement in seizure resistance and wear resistance is desired for sliding parts constituting the hydraulic pumps/motors, however, the conventional lead bronze, bronze and brass-based contact materials according to the above-mentioned literature (Japan Non-ferrous Metal Casting Association ed., “ENGINEERING DATA BOOK FOR COPPER BASED ALLOY CASTING”, Issued by Materials Process Technology Center (SOKEIZAI CENTER), Jul. 30, 1988, p. 134-155) have a problem that they are insufficient in strength, seizure resistance and wear resistance for higher output and further decrease in size.
The present invention has been made in view of the above-mentioned problems, and an object thereof is to provide a thermal spray membrane contact material contact member and contact part, and an apparatus to which they are applied, excellent in seizure resistance and wear resistance under extremely poor lubrication conditions such as high surface pressure and low speed sliding and swinging and the like, and excellent in conformability in sliding and showing excellent seizure resistance and wear resistance even under high speed and high temperature sliding and high surface pressure and high speed sliding.
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The nature of suffering and its relief: a proposal for a redefinition.
Recent advances in our understanding of the nature of suffering and its different dimensions have exposed certain deficits in the current definition of suffering. These shortcomings have impacted negatively on the appropriate formulation of precise treatment objectives for each dimension of suffering within the overall framework of the goals of medicine. Existential suffering offers a clear example where the lack of a universally accepted definition has led to confusion regarding what should constitute appropriate relief for this particular dimension of suffering. In this thought piece, we propose a redefinition of suffering based on three elements: first, suffering refers to a specific state of a person (the essence of suffering); second, this state is characterised by a specific psychosomatic anguish reaction (the manifestation of suffering) and third, this reaction is in response to a perceived threat to the integrity of the person (the cause of suffering). The proposed definition allows for an important and clear distinction to be made between the primary and symptomatic relief of suffering and the role of medicine in each form of relief. The terms of the proposed definition and the distinction between primary and symptomatic relief provide useful tools for further research regarding the different dimensions of suffering and its relief.
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Chikungunya and the nervous system: what we do and do not know.
Chikungunya virus (CHIKV), an alphavirus transmitted by mosquitoes of the Aedes genus, has recently re-emerged, causing epidemics on Indian Ocean Islands and the Indian subcontinent, and an unexpected outbreak in north-eastern Italy. CHIKV infection was first reported to affect the nervous system in the 1960s; in the early 1970s it was found to be associated with meningoencephalopathy, myelitis, and choroiditis, and animal studies appeared to confirm that CHIKV was neurotropic. Nonetheless, CHIKV has never been considered as a 'true' neurotropic virus. The re-emergence of CHIKV infection in areas with efficient clinical facilities has allowed CHIKV-related neurological disease to be better defined both in adults and children. Encephalopathy appears to represent the most common clinical manifestation among newborns infected through mother-to-child transmission. Although data are still scarce, the ratio between cases with and without CNS involvement for CHIKV appears to be comparable with that for other neurotropic viruses. Unfortunately, the neurotropism of CHIKV has not been completely defined, and different animal studies show inconsistencies with regard to the capacity of the virus to invade and replicate in the brain parenchyma. This merits further investigation in light of the emergence of the virus in previously unaffected areas and of the clinical evidence of CNS involvement in a considerable proportion of symptomatic cases.
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RENTON, Wash. -- Seattle Seahawks defensive end Michael Bennett and left tackle Bradley Sowell got into a heated dust-up Sunday that resulted in both players getting pulled from practice.
Seahawks coach Pete Carroll said the fight was the result of Sowell shoving defensive end Josh Shirley to the ground earlier in a one-on-one drill. When Bennett got a turn to face Sowell, the two players mixed it up and ended up on the ground before they were separated.
"He's just fighting for his own a little bit," Carroll said of Bennett. "One of the young guys got knocked around, and he was standing up for him. He's got a lot of pride. He's an incredible competitor, but he's got to make sure he stays poised so he doesn't get himself in trouble. So we had a good illustration of that today."
After the two players were initially separated, and it appeared the situation had calmed down, Bennett charged Sowell a second time. When teammates broke them up, Bennett tossed his helmet.
At one point, Doug Baldwin tried to approach Bennett and calm him down, but Bennett then went after the wide receiver.
Bennett and Sowell spent the remainder of practice on the sidelines. Afterward, they walked off the field together and appeared to be on good terms.
Bennett got kicked out of a practice earlier in training camp. He said at the time that he understood the message Carroll was sending to the team.
"There's a lot riding on this season for our whole football team," Carroll said. "And we have to deal with that. We have really high expectations, and that can heighten the passion and intensity and all of that. That's kind of something we're kind of used to out here.
"I think everything about everything is more intense than it's been. It just seems like the focus has been there to get prepared for this season, and I can't say that we don't like it. We just have to manage it well and perform well. So far we need to do better in games. We're getting too many penalties, and we need to make sure that we're doing right. I don't know if that's part of that or not, but we're working on it to make sure that it isn't.
Michael Bennett got into a practice scuffle Sunday with Bradley Sowell during a one-on-one drill, in which the two mixed it up and ended up on the ground before being separated. AP Photo/Elaine Thompson
"We're very connected," Carroll said. "There's a respect that is here about competing and battling and that you're working to take it as far as you can and still respect the people across from you. And sometimes that line gets crossed a little bit. It's a very competitive world we're in and a very competitive game we play. And these guys care with all their heart. So we have to learn how to deal with that and how to manage that well."
Offensive line coach Tom Cable said the intensity can be a positive as long as it doesn't go too far.
"There's parts of it that are good, but ultimately you don't want either one of them fighting or doing that," Cable said. "And they've got to learn how to manage that because that stuff's going to happen in the game. And if you do it in the game, you're going to get thrown out, and they're going to take your money. So a good lesson for both [Sowell] and Mike. Both guys are wrong, and they've got to learn to do right. And they'll do that."
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Lance Ito
Lance Allan Ito (born August 2, 1950) is a retired American judge best known for presiding over the criminal trial for the O. J. Simpson murder case, held in the Los Angeles County Superior Court in 1995.
Early life and career
Ito was born in Los Angeles, to Jim Ito and Toshi Ito. Both his parents were kept in Japanese American internment camps with their families during World War II. Ito was enrolled in Sunday School at the Mount Hollywood Congregational Church. Ito attended John Marshall High School, where he was student body president and received the Scholar Athlete award in 1968. He earned his bachelor's degree with honors from the University of California, Los Angeles in 1972, and his J.D. degree from the University of California, Berkeley's Boalt Hall in 1975. He then joined the Los Angeles district attorney's office in 1977, working in the hardcore gang unit and the organized crime and terror unit, among others.
In 1981, he married Margaret Ann York, the first woman to attain the rank of Deputy Chief in the Los Angeles Police Department and that department's highest ranking woman officer when she retired in 2002. The two met while at an Eagle Rock murder scene.
Republican Governor George Deukmejian appointed Ito, a Democrat, to the Municipal Court in 1987, and then elevated him to Superior Court in 1989.
Charles H. Keating, Jr. trial
In 1992, he presided over the trial of financier Charles H. Keating Jr. Keating's ensuing ten-year sentence was later overturned on appeal because Ito had neglected to instruct the jury to determine whether Keating intended to defraud investors. It was the prosecution's position that Keating was liable as a matter of strict liability.
O.J. Simpson murder trial
Ito presided over the 1995 murder trial of O. J. Simpson, at which Simpson was acquitted. His decision to allow television coverage of the trial was controversial, and Ito faced criticism for seeming to enjoy the press and for allowing too many sidebars and recesses, etc.
During the trial, the prosecution requested that Ito recuse himself when it came to light that his wife, Margaret York, had been detective Mark Fuhrman's superior officer in the past. Fuhrman had been called to testify by the prosecution regarding his discovery of evidence in the case. During cross-examination, Fuhrman claimed that he had not used racial epithets to refer to African-Americans during the last ten years. Simpson's defense team unearthed tapes in which Fuhrman had used racial epithets as recently as 1988, and they wished to introduce them as evidence to prove that Fuhrman had perjured himself, in order to discredit his testimony. However, in the tapes, Fuhrman disparages York's appearance and suggests that she used her gender to advance in the police force. The prosecution requested that Ito step down because they felt that derogatory remarks toward his wife might bias Ito against Fuhrman, though prosecutors later withdrew the request out of fear that it would result in a mistrial.
Post-Simpson trial career
Ito declined to give interviews regarding the O.J. Simpson murder trial because ethical guidelines for California trial-court judges forbid commenting on pending matters or matters likely to come before the courts. He has noted his disbelief that public interest in the trial extended through the "turgid" DNA section of the trial. He has used his status to work on issues of judicial reform, such as increasing the number of translators and enforcing rules for foreign national defendants in the court.
Los Angeles County announced on April 17, 2012, that Ito's courtroom, along with 55 others, would be closed due to budget cuts. Ito retired in 2015.
Popular culture
Ito was portrayed on Saturday Night Live by Mike Myers.
The Tonight Show with Jay Leno had a recurring skit called "The Dancing Itos" featuring five bearded Asian American dancers
Ito was portrayed by Kenneth Choi in the series The People vs. O.J. Simpson
References
External links
Category:1950 births
Category:American jurists of Japanese descent
Category:American people of Japanese descent
Category:California Democrats
Category:California state court judges
Category:Lawyers from Los Angeles
Category:Living people
Category:O. J. Simpson murder case
Category:Superior court judges in the United States
Category:UC Berkeley School of Law alumni
Category:University of California, Los Angeles alumni
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Crews in Superior recently finished repairing the culvert at Barker's Island from the flooding caused by the storms one year ago, almost to the date, but the 2-4 inches of rain that Superior got overnight was enough to cause serious damage for the second year in a row.
While I was taking these photos, a resident who lived across the street from the culvert struck up a conversation with me and he suspects that because of the flooding in the culvert his basement flooded again for the second year in row and he is considering legal action against the city for the continued flooding problems.
As you can see in the photos below crews are already working to repair the damage which is significantly less than last year.
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Sofia Carson
Sofía Daccarett Char (born April 10, 1993), known professionally as Sofia Carson, is an American actress and singer. Her first appearance on television was as a guest star on the Disney Channel series Austin & Ally. In 2015, she appeared as Evie, the daughter of the Evil Queen, in the Disney Channel Original Movie Descendants, and later reprised her role in Descendants 2 and Descendants 3. In 2016, she appeared as Lola Perez in Adventures in Babysitting, Melanie Sanchez in Tini: The Movie, and Tessa in A Cinderella Story: If the Shoe Fits. In 2019, Carson starred in the Freeform drama series Pretty Little Liars: The Perfectionists.
Early life
Carson was born in Ft. Lauderdale, Florida, to José F. Daccarett and Laura Char Carson, who moved to Florida from Colombia. She chose the artistic name "Carson" after her American maternal grandmother, Lauraine Carson. Through her mother, Carson is related to the Char family of Colombian politicians.
She attended St. Hugh School and graduated from Carrollton School of the Sacred Heart in Miami. She attended In Motion Dance Studio, where she was part of the IMPAC Youth Ensemble program, competing all over the United States. She subsequently attended UCLA, majoring in communications with a minor in French.
Career
In 2012, Carson was signed with BMI as a "singer-songwriter". Her acting career was launched in 2014 when she was cast as guest star, playing Chelsea, on the Disney Channel series Austin & Ally. A few months later, Carson was cast as recurring guest star, playing Soleil, on MTV's series Faking It. In 2014, she was cast in a starring role in the Disney Channel Original Movie Descendants, in which she plays Evie, the daughter of the Evil Queen from Snow White and would later do a version of the soundtrack.
On January 9, 2015, Carson was cast in the co-lead role in the upcoming Disney Channel Original Movie Adventures in Babysitting. Filming began in spring 2015, for an early 2016 television premiere. In March 2016, The Hollywood Reporter announced that Carson landed the leading role in the fourth installment of the A Cinderella Story series, A Cinderella Story: If the Shoe Fits, directed by Michelle Johnston and produced by Dylan Sellers, which was released direct-to-video. In an August 2015 interview Carson stated she was working on her first album. In September 2015 Carson was added on the list of Hollywood Records artists. Previously, some of Disney Channel Europe websites reported the incorporation of Sofia to the label. In March 2016, Hollywood Records and Republic Records officially announced that Sofia had signed a joint worldwide record deal with both companies. Her debut single is "Love Is the Name", an interpolation of Opus' "Live Is Life", and was released on April 8. Carson released a promotional single on August 26, 2016 entitled "I'm Gonna Love You". In January 27, 2017 she released her single "Back to Beautiful" featuring Alan Walker and in February 15, 2017 she released the official music video on YouTube. "Back to Beautiful" was written by Julia Michaels, who also wrote her next single "Ins and Outs". In 2018, Carson was featured in three EDM instant hits: R3hab's "Rumors", Alan Walker's "Different World" and Galantis's "San Francisco", positioning as the most sought after collaborator in this genre.
Carson has performed in NBC's 2015 Thanksgiving Parade, ABC's Disney Parks Christmas Celebration, Univision's Feliz 2016 (New Year's Eve Special) and the 2016 Radio Disney Music Awards, and was a presenter on ABC's Disneyland 60th Anniversary Special. She performed "The Star-Spangled Banner" at the 2017 A Capitol Fourth, an annual concert at the United States Capitol in celebration of Independence Day.
Carson reprised her role as Evie in the 2017 sequel Descendants 2. Carson played the role of Sloane Silver in the second season of Freeform's Famous in Love in 2018. In January 2018, it was announced that Carson would be starring in the television series Pretty Little Liars: The Perfectionists, in the role of Ava Jalali; it was picked up to series by Freeform in May 2018 and premiered in March 2019. She once again played Evie for Descendants 3, the third installment of the franchise, which premiered on August 2, 2019. In July 2019, it was announced that Carson would portray the role of April in the Netflix dance film Feel the Beat.
In August 2019, Carson was designated as the first Global Ambassador of the Latin GRAMMY Cultural Foundation. Her role includes advocating, promoting, and increasing awareness of the foundation's mission and educational programs. Since its establishment five years ago, the Latin GRAMMY Cultural Foundation has donated more than US$5 million in scholarships, grants, musical instrument donations, and educational events in the United States and Ibero-America. In January 2020, Carson was named the new global ambassador of beauty brand Revlon.
Filmography
Discography
Awards and nominations
References
External links
Category:1993 births
Category:21st-century American actresses
Category:21st-century American singers
Category:American people of Colombian descent
Category:American performers of Latin music
Category:American television actresses
Category:American female pop singers
Category:American pop singers
Category:American dance musicians
Category:Hispanic and Latino American musicians
Category:Hispanic and Latino American actresses
Category:Hollywood Records artists
Category:Republic Records artists
Category:Living people
Category:Schools of the Sacred Heart alumni
Category:University of California, Los Angeles alumni
Category:21st-century American women singers
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Bethan Rhys Roberts, Jason Mohammad and guests discuss plans for the new M4 relief road. Would it be money well spent?
Plus poet Patrick Jones asks if there are any great Welsh orators left.
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Choice of "Classic" crust or Mellow "Thin" Crust. Customize to your taste with any of the fresh ingredients listed. Base sauce choices include olive oil & garlic, pesto (GF) and Mellow red sauce (GF). (+15-100 cal). *These items are so good they count as two ingredients. Calories listed per slice
1 Ingredient8.99
2 Ingredients9.99
3 Ingredients10.99
Additional Ingredients1.0
Small 10"
1 Ingredient12.49
2 Ingredients13.99
3 Ingredients15.49
Additional Ingredients1.5
Medium 14"
1 Ingredient15.99
2 Ingredients17.99
3 Ingredients19.99
Additional Ingredients2.0
Large 16"
S7.99
M10.99
L13.99
*Cheese Pizza
Mellow red sauce and mozzarella on Mellow's crust, buttered and sprinkled with parmesan
All pizzas are served as large - 8 slices, medium - 6 slices, small - 4 slices. Calories listed per slice. Bakers Mellow "Thin" Crust; **These pies can be made with our gluten allergy-safe procedures. All gluten-free pizzas are served on our 10" signature gluten-free crust. Gluten-free pizzas and ingredients are priced as small pie plus $2
With side of roasted potatoes (+150 cal) or choice of kettle chips. All BYOB burgers are dressed with lettuce, tomato, pickle and onions. Add two additional ingredients of your choice from the following list:
*All burgers may be cooked to order. Unless otherwise requested, hamburgers are cooked to an internal temperature of 155˚. Consuming raw or undercooked meats, poultry, seafood, shellfish or eggs may increase your risk of foodborne illness. **These pies can be made with our gluten allergy-safe procedures. Learn more about our gluten-free program and procedures on the back cover
Sweets
Order any cookie or brownie as a sundae. We'll top it with all-natural vanilla bean ice cream, dark chocolate truffle sauce, house-made fresh whipped cream and an all-natural bing cherry for an additional $2.75 (+380 cal)
Include plates, serving utensils, cutlery and napkins per order. A minimum order may be required.
12.0
The Boxes
Choose from our signature sandwiches with your choice of kettle chips or chill out pasta salad and two small bites cookies.
Small Tray (8 Whole Sandwiches Cut In Half)80.0
Large Tray (12 Whole Sandwiches Cut In Half)120.0
The Trays
Choose your favorites from the collection of signature sandwiches or ask for the best-sellers; custom tray pricing is available.
The Packages
Choose your favorite Signature Sandwiches, Salads and Sweets by the Dozen that are bound to make any meeting more flavorful. Include plates, serving utensils, cutlery and napkins per order. A minimum order may be required.
Rich, savory and creamy, topped with a roasted mushroom trio, chives and Montamoré®.
Pizza
Pizza is what we're famous for! Every option you can imagine is available. Select from one of our specialty pies listed below, or build your own from our extensive list of premium ingredients. Please contact your local catering department or mellowmushroom.com for more info. Gluten-free options available.
We've taken the flavors in Mellow Mushroom's kitchen and reinvented them into catering options we know you are going to love! Our eco-friendly packaging is designed to travel to your office, home, park or practice. We've created a new twist for all your catering needs, keeping detail in mind. If you have an in-house favorite that's not listed here, let us know and we are more than happy to accommodate you!
We handle every catering order with the care and precision it deserves.
We make everything fresh just for you. Please give us 24 hours notice. Same day ordering is available with menu limitations
Our delivery drivers will be happy to set up your order at your specified location and time. A minimum order and/or delivery fee may apply.
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South Florida Crime
MIAMI (CBSMiami) – The man responsible for three deaths in a violent hit and run accident at Miami intersection in 2011 has pled guilty.
Thursday, Cedric Williams pled guilty and received 20 years in jail followed by 10-years of probation.
His plea came as jurors were deliberating a verdict at his trial. Williams also apologized to the families of the victims.
A sentencing hearing was scheduled for February 6th.
Williams, now 52, admitted to police that he was under the influence of alcohol while driving with an expired license and tag. He was trying to get away from a police car when he crashed into another vehicle in the intersection of NE 2nd Avenue and 82nd Street in January, 2011.
Robert Wissler, 25, was behind the wheel of his Honda Civic when Williams, who was driving a van at a high rate of speed, plowed into him. After the crash witnesses told police they saw the driver of the van limp away into a neighborhood.
Dean Wissler, Robert’s father, said his son had been on a date earlier in the night and that two of his passengers; Lindsey Ennis, 20 of Duluth, Ga., and Kayla Elizabeth Bain, of Putnam Station, NY, were visiting South Florida. All three were killed.
The fourth person in the car, Robert Judd, 69, of North Miami Beach, who was riding in the front passenger seat, was taken to Jackson Memorial Hospital in critical condition.
When Miami police went to William’s house, he refused to come out. Officers from Miami-Dade along with Miami police officers surrounded the home for several hours until his family members convinced Williams to surrender.
In the house, Williams reportedly confessed to his mother that he did it, saying ‘it happened so fast’.
During questioning by police, Williams again reportedly confessed to running a red light and slamming into the car.
He allegedly told investigators he ran from the scene because he had been drinking and he knew he had been driving with a suspended license.
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There and back again
Of course, a title stolen from ‘The Hobbit’ but appropriate just the same. It’s Monday afternoon and the Atlantis is once again tied up to the dock. We came in yesterday on the early morning tide and quickly began the task of ‘demobilization’ – i.e., unloading the tons of scientific gear that were set up on the Atlantis for NAAMES III. It’s remarkable how quickly all that gear can be packed, labels, offloaded, and sent to shipping when demobilization is the one thing standing between 30+ scientists and their trips home. It is a keen motivator to say the least. Only a day and a half after arriving, the labs are shockingly empty. The cramped spaces once filled with instruments, wires, tubing, sampling equipment, and myriad other widgets and gadgets are now empty spaces that echo your voice. The final tasks is sweeping and mopping and then NAAMES III is finished.
Earlier in this trip, one of our bloggers mentioned the duality of time during an ocean voyage. On one hand, exact timing is essential to successful experimentation and for keeping activities running smoothly on a very busy schedule. On the other hand, time seems to hold little meaning as the days blur together and weeks pass with little recognition. This duality is particularly pronounce when the voyage is done. The memory of untying the ship and heading out to sea is still so vivid in our minds that it is seems impossible to accept that nearly a month has passed. On the other hand, it seems equally impossible that the sum of all those endless days and sleepless nights has only amounted to a few weeks.
If you have followed this blog over the past month, I suspect you have both gained a greater appreciation for the science of the NAAMES project and enjoyed some insights on the personal experiences associated with going to sea. A temporary family is always created during these expeditions, but when it is over that family must disperse and return to their normal lives. Today, we are beginning to say our farewells, but the science we do will keep this family attached for a long time to come. NAAMES III has been a tremendous success, and that success is fully attributable to the individuals who have taken part in this adventure, both the scientists and the crew of the Atlantis. It is an amazing team. We have gone there and come back again. I will end this blog as I have during previous NAAMES campaigns in saying that it is the names of NAAMES that set this mission apart.
Written by Michael Behrenfeld
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Production Machining
JAN 2018
Contents of this Issue
Navigation
Page 11 of 135
53.5
MICHAEL GUCKES, MBA
Chief Economist, Gardner Intelligence
Michael has performed economic
analysis, modeling and forecasting
work for almost 20 years among a
range of industries. Michael received
his B.A. in political science and
economics from Kenyon College
and his MBA from The Ohio State
University.
mguckes@gardner web.com
November Index Shows
Expansion at Slower Rate
Supplier deliveries experienced slightly faster growth.
60
55
50
45
40
PRECISION MACHINING INDEX
60
55
50
45
40
35
PRECISION MACHINING NEW ORDERS AND PRODUCTION (3-month moving average)
The November readings of
the Precision Machining Index
indicated a significant slowing of
the industry's growth rate. Index
readings from the 2017 calendar
year have been volatile, however,
with an average monthly reading
of 55.5, the industry has grown
strongly during the calendar year.
The latest figures for new orders and
production fell below their year-to-
date average readings of 58.7 and
59.5, respectively. Significant swings
in the monthly readings during 2017
have resulted in a year of strong yet
volatile growth.
n Production
n New Orders
54.3
7/13 1/14 7/14 1/15 7/15 1/16 7/16 1/17 7/17
7/13 1/14 7/14 1/15 7/15 1/16 7/16 1/17 7/17
GARDNER BUSINESS INDEX: PRECISION MACHINING
10 PRODUCTION MACHINING :: JANUARY 2018
R
egistering 54.3 for November, the Gardner Business Index (GBI): Precision
Machining moved lower after two months of strong expansionary gains. For the
year-to-date period, the index has averaged 55.5 and increased by approximately
1 percent in 2017. Gardner Intelligence's review of the underlying data indicates
that supplier delivery production and new orders lifted the business index higher,
while employment, backlog and exports pulled the index lower. For November, only
exports contracted slightly after having expanded in September and October. All
components of the index moved lower in November except for supplier deliveries,
which recorded slightly faster growth as compared with the prior month.
November saw slower growth in new orders and production as compared with October's
figures. Although the latest figures are below their year-to-date averages, they are well
above the average readings from 2015 and 2016 and compare favorably with the strong
readings of 2014 when the Precision Machining Index experienced solid cyclical growth. In
the three-month period from the beginning of September to the end of November, backlog
has drastically transitioned from record high growth to being almost flat. For the calendar
year, backlog has experienced volatile expansion with only one month of contraction
during that time.
Stay ahead of the curve with Gardner Intelligence.
More information about the Precision Machining Index can be found at gardnerintelligence.com.
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Business Bandwidth Speed Chart
Ohio Ethernet Fiber Service Providers from Ohio Business Ethernet Internet
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To obtain a Business Ethernet Internet Quote for your business in Clermont County, give us a call at (888) 765-8301 or use our online quote Ohio Metro Ethernet, Fast Ethernet and Gigabit Ethernet price tool (on the left) to get an initial estimate on Ethernet over Fiber and Ethernet over Copper in Clermont. Once we receive your information we'll give you a call to discuss your individual Ethernet Bandwidth request.
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---
abstract: 'The free analog of the pressure is introduced for multivariate noncommutative random variables and its Legendre transform is compared with Voiculescu’s microstate free entropy.'
address: 'Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan'
author:
- 'Fumio Hiai$\,^1$'
title: Free analog of pressure and its Legendre transform
---
=22.5truecm =15.5truecm
=-17mm =-6mm
\[section\] \[thm\][Proposition]{} \[thm\][Lemma]{} \[thm\][Corollary]{} \[thm\][Remark]{} \[thm\][Examples]{} \[thm\][Problem]{} \[thm\][Definition]{}
[^1]
Introduction {#introduction .unnumbered}
============
The entropy and the pressure are two fundamental ingredients in both classical and quantum statistical mechanics, in particular, in classical and quantum lattice systems (see [@Is; @BR] for example). They are the dual concepts of each other; more precisely, the entropy function is the Legendre transform of the pressure function and vice versa under a certain duality between the state space and the potential space, and an equilibrium state associated with a potential is usually described by the so-called variational principle (the equality case of the Legendre transform). The free entropy introduced by D. Voiculescu [@V1; @V2] has played a central role in free probability theory as the free analog of the Boltzmann-Gibbs entropy in classical theory. It then would be natural to consider the free probabilistic analog of the pressure. In [@HMP] we indeed introduced the free pressure of real continuous functions on the interval $[-R,R]$ and showed its properties like the statistical mechanical pressure (see Section 1 of this paper).
The aim of the present paper is to introduce the notion of free pressure for multivariate noncommutative random variables and to investigate it in connection with the free entropy. (The contents of Sections 2 and 3 were indeed announced in [@Hi §§4.4].) In [@HMP] we adopted the Legendre transform of the minus free entropy of probability measures to define the free pressure of real continuous functions. The idea here is opposite; we will first introduce the free pressure of noncommutative multivariables in the so-called microstate approach, and then we will examine what is the Legendre transform of the free pressure.
In Section 2 we define, given $N\in\bN$ and $R>0$, the free pressure $\pi_R(h)$ for selfadjoint elements $h$ of the $N$-fold full free product $C^*$-algebra $\cA_R^{(N)}:=C([-R,R])^{\star N}$ and give its basic properties. In Sections 3 and 4 we consider the Legendre transform $\eta_R(\mu)$ of $\pi_R$ for tracial states $\mu$ on $\cA_R^{(N)}$ under the duality between the selfadjoint elements and the tracial states. For an $N$-tuple $(a_1,\dots,a_N)$ of selfadjoint noncommutative random variables in a $W^*$-probability space $(\cM,\tau)$ such that $\|a_i\|\le R$, a tracial state $\mu_{(a_1,\dots,a_N)}$ on $\cA_R^{(N)}$ can be defined by $\mu_{(a_1,\dots,a_N)}(h):=\tau(h(a_1,\dots,a_N))$ for $h\in\cA_R^{(N)}$ where $h(a_1,\dots,a_N)$ is the noncommutative “functional calculus" of $(a_1,\dots,a_N)$. We then define the free entropy-like quantity $\eta_R(a_1,\dots,a_N)$ as $\eta_R(\mu_{(a_1,\dots,a_N)})$ and also $\eta(a_1,\dots,a_N):=\sup_{R>0}\eta_R(a_1,\dots,a_N)$. The properties of $\eta_R(a_1,\dots,a_N)$ are similar to those of Voiculescu’s microstate free entropy $\chi(a_1,\dots,a_N)$ while they do not generally coincide. But it is shown that $\eta_R(a_1,\dots,a_N)\ge\chi(a_1,\dots,a_N)$ holds and equality arises when $a_1,\dots,a_N$ are free. Also, we have $\eta_R(a_1,a_2)=\chi(a_1,a_2)$ if $a_1+ia_2$ is $R$-diagonal (Section 5). In Section 6 we slightly modify $\pi_R$ to define the free pressure $\pi_R^{(2)}(g)$ for selfadjoint elements $g$ of $\cA_R^{(N)}\otimes_\min\cA_R^{(N)}$ and prove that the quantity $\tilde\eta(a_1,\dots,a_N)$ induced from $\pi_R^{(2)}$ via Legendre transform is equal to $\chi(a_1,\dots,a_N)$. In this way, the free entropy can be understood as the Legendre transform of a certain free probabilistic pressure. Finally in Section 7 we consider the Gibbs probability measure on the $N$-fold product of $\bigl\{A\in M_n^{sa}:\|A\|\le R\bigr\}$ associated with $h_0\in\bigl(\cA_R^{(N)}\bigr)^{sa}$, and we examine the asymptotic behavior of its Boltzmann-Gibbs entropy as $n\to\infty$ in relation to $\eta_R(\mu_0)$ of an equilibrium tracial state $\mu_0$ associated with $h_0$, i.e., a tracial state $\mu_0$ on $\cA_R^{(N)}$ satisfying $\pi_R(h_0)=-\mu_0(h_0)+\eta_R(\mu_0)$.
Preliminaries
=============
Let $(\cM,\tau)$ be a tracial $W^*$-probability space, that is, $\cM$ is a von Neumann algebra with a faithful normal tracial state $\tau$, and $\cM^{sa}$ be the set of selfadjoint elements in $\cM$. Let $M_n$ be the algebra of $n\times n$ complex matrices and $M_n^{sa}$ the set of selfadjoint matrices in $M_n$. The normalized trace of $A\in M_n$ is denoted by $\tr_n(A)$ and the operator norm of $A$ by $\|A\|$. In [@V2] D. Voiculescu introduced the free entropy of an $N$-tuple $(a_1,\dots,a_N)$ of noncommutative random variables in $\cM^{sa}$ as follows: For each $R>0$, $\eps>0$ and $n,r\in\bN$ define $$\begin{aligned}
&&\Gamma_R(a_1,\dots,a_N;n,r,\eps)
:=\bigl\{(A_1,\dots,A_N)\in(M_n^{sa})^N:\|A_i\|\le R, \\
&&\hskip2cm
|\tr_n(A_{i_1}\cdots A_{i_k})-\tau(a_{i_1}\cdots a_{i_k})|\le\eps,
\ 1\le i_1,\dots,i_k\le N,\ k\le r\bigr\},\end{aligned}$$ $$\begin{aligned}
\label{F-1.1}
&&\chi_R(a_1,\dots,a_N)
:=\lim_{r\to\infty,\,\eps\to+0}\,\limsup_{n\to\infty}
\biggl({1\over n^2}\log\Lambda_n^{\otimes N}
\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr) \nonumber\\
&&\hskip10cm+{N\over2}\log n\biggr),\end{aligned}$$ where $\Lambda_n^{\otimes N}$ denotes the $N$-fold tensor product of the “Lebesgue" measure $\Lambda_n$ on $M_n^{sa}$: $$d\Lambda_n(A):=2^{n(n-1)/2}\prod_{i=1}^ndA_{ii}
\prod_{i<j}d(\Re\,A_{ij})\,d(\Im\,A_{ij})$$ (the constant $2^{n(n-1)/2}$ comes from the isometric isomorphism between $M_n^{sa}$ and $\bR^{n^2}$). Then the [*free entropy*]{} of $(a_1,\dots,a_N)$ is $$\chi(a_1,\dots,a_N):=\sup_{R>0}\chi_R(a_1,\dots,a_N).$$ The definition being based on the microstate (or matricial) approximation, this$\chi(a_1,\dots,a_N)$ is sometimes called the [*microstate free entropy*]{} in contrast to another Voiculescu’s free entropy $\chi^*(a_1,\dots,a_N)$ in the microstate-free approach in [@V5].
In the case of a single variable $a\in\cM^{sa}$ whose distribution measure (with respect to $\tau$) is $\mu$, $\chi(a)$ coincides with the free entropy $\Sigma(\mu):=\iint\log|x-y|\,d\mu(x)\,d\mu(y)$ of $\mu$ introduced in [@V1] up to an additive constant: $$\chi(a)=\Sigma(\mu)+{1\over2}\log2\pi+{3\over4}.$$
With $R>0$ fixed, let $C_\bR([-R,R])$ be the Banach space of real continuous functions on $[-R,R]$ with sup-norm $\|\cdot\|$, and $\cM([-R,R])$ be the set of probability measures on $[-R,R]$. Consider the dual pairing $$\mu(h):=\int h\,d\mu
\quad\mbox{for $h\in C_\bR([-R,R])$, $\mu\in\cM([-R,R])$}.$$ The free entropy $\chi(\mu):=\Sigma(\mu)+{1\over2}\log2\pi+{3\over4}$ being strictly concave and weakly upper semicontinuous on $\cM([-R,R])$ (see [@HP1 5.3.2] for example), it is natural to consider the [*Legendre transform*]{} of $-\chi(\mu)$ as follows: $$\label{F-1.2}
\pi_R(h):=\sup\bigl\{-\mu(h)+\chi(\mu):\mu\in\cM([-R,R])\bigr\}
\quad\mbox{for $h\in C_\bR([-R,R])$}.$$ This $\pi_R(h)$ is the [*free pressure*]{} of $h$ discussed in [@HMP]. A fundamental result in the theory of weighted potentials ([@ST I.1.3 and I.3.1]) tells us that for each $h\in C_\bR([-R,R])$ there exists a unique $\sigma^h\in\cM([-R,R])$, called the [*equilibrium measure*]{} associated with $h$, such that $$-\sigma^h(h)+\chi(\sigma^h)=\pi_R(h).$$ The last equality characterizing $\sigma^h$ is a kind of the variational principle, a fundamental notion in statistical mechanics. Let us assemble some properties of the free pressure obtained in [@HMP] in the following:
- The function $\pi_R(h)$ on $C_\bR([-R,R])$ is convex and decreasing, i.e., $\pi_R(h_1)\ge\pi_R(h_2)$ if $h_1\le h_2$. Moreover, $$|\pi_R(h_1)-\pi_R(h_2)|\le\|h_1-h_2\|
\quad\mbox{for all $h_1,h_2\in C_\bR([-R,R])$}.$$
- Conversely, $\chi(\mu)$ is the (minus) Legendre transform of $\pi_R(h)$, that is, $$\label{F-1.3}
\chi(\mu)=\inf\bigl\{\mu(h)+\pi_R(h):h\in C_\bR([-R,R])\bigr\}
\quad\mbox{for every $\mu\in\cM([-R,R])$},$$
- For every $h\in C_\bR([-R,R])$, $\pi_R(h)$ is expressed as $$\label{F-1.4}
\pi_R(h)=\lim_{n\to\infty}\Biggl({1\over n^2}\log
\int_{(M_n^{sa})_R}\exp\bigl(-n^2\tr_n(h(A))\bigr)\,d\Lambda_n(A)
+{1\over2}\log n\Biggr),$$ where $(M_n^{sa})_R:=\bigl\{A\in M_n^{sa}:\|A\|\le R\bigr\}$ and $h(A)$ is defined via functional calculus.
- For each $h\in C_\bR([-R,R])$, define a probability measure $\lambda_{R,n}^h$ on $(M_n^{sa})_R$ by $$d\lambda_{R,n}^h(A):={1\over Z_{R,n}^h}\exp\bigl(-n^2\tr_n(h(A))\bigr)
\,\chi_{\{\|A\|\le R\}}(A)\,d\Lambda_n(A)$$ with the normalization constant $$Z_{R,n}^h:=\int_{(M_n^{sa})_R}\exp\bigl(-n^2
\tr_n(h(A))\bigr)\,d\Lambda_n(A),$$ and let $S(\lambda_{R,n}^h)$ be the Boltzmann-Gibbs entropy of $\lambda_{R,n}^h$. Then $$\chi(\sigma^h)=\lim_{n\to\infty}\biggl(
{1\over n^2}S(\lambda_{R,n}^h)+{1\over2}\log n\biggr).$$
Free pressure $\pi_R$ for multivariables
========================================
For each $N\in\bN$ and $R>0$ we write $\cA_R^{(N)}$ for the $N$-fold full (universal) free product $C^*$-algebra of $C([-R,R])$, i.e., $\cA_R^{(N)}:=C([-R,R])^{\star N}$. One can describe $\cA_R^{(N)}$ in a bit more constructive way as below. Consider the (algebraic) noncommutative polynomial $*$-algebra $\bC\<X_1,\dots,X_N\>$ with noncommuting indeterminates $X_1,\dots,X_N$, where the $*$-operation is given by $X_i^*=X_i$. Let $\bC\<X_1,\dots,X_N\>^{sa}$ be the space of selfadjoint polynomials $p=p^*$ in $\bC\<X_1,\dots,X_N\>$. Obviously, $p(A_1,\dots,A_N)\in M_n^{sa}$ whenever $p\in\bC\<X_1,\dots,X_N\>^{sa}$ and $A_1,\dots,A_N\in M_n^{sa}$. One can immediately see that a $C^*$-norm $\|\cdot\|_R$ is defined on $\bC\<X_1,\dots,X_N\>$ by $$\|p\|_R:=\sup\bigl\{\|p(A_1,\dots,A_N)\|:A_1,\dots,A_N\in M_n^{sa},
\ \|A_i\|\le R,\ n\in\bN\bigr\}.$$
\[P-2.1\] The $C^*$-completion of $\bC\<X_1,\dots,X_N\>$ with respect to $\|\cdot\|_R$ is isomorphic to $\cA_R^{(N)}$ by the isomorphism mapping $X_i$ to $f_0(t)=t$ in the $i$th copy of $C([-R,R])$ of $\cA_R^{(N)}$ for $1\le i\le N$.
[[*Proof.*]{}]{}Let ${\frak A}_R^{(N)}$ be the $C^*$-completion of $\bC\<X_1,\dots,X_N\>$ with respect to $\|\cdot\|_R$. Since any $*$-homomorphism of $C([-R,R])$ into $B(\cH)$ is determined by a selfadjoint $a\in B(\cH)$ with $\|a\|\le R$ (the image of $f_0$), what we have to prove is that, for each selfadjoint $a_1,\dots,a_N\in B(\cH)$ with $\|a_i\|\le R$, there exists a $*$-homomorphism $\Phi:{\frak A}_R^{(N)}\to B(\cH)$ such that $\Phi(X_i)=a_i$, $1\le i\le N$. To do so, it suffices to show that $$\|p(a_1,\dots,a_N)\|\le\|p\|_R
\quad\mbox{for all $p\in\bC\<X_1,\dots,X_N\>$}.$$ But this is easy to show. In fact, choose a net of finite-dimensional projections $e_k$ in $B(\cH)$ with $e_k\nearrow\1$. Then, the above inequality follows because $\|p(e_ka_1e_k,\dots,e_ka_Ne_k)\|\le\|p\|_R$ and $p(e_ka_1e_k,\dots,e_ka_Ne_k)\to p(a_1,\dots,a_N)$ strongly.
In view of the above proposition, we consider $\cA_R^{(N)}$ as the $C^*$-completion of $\bC\<X_1,\dots,X_N\>$ with respect to $\|\cdot\|_R$ and write $\|\cdot\|_R$ for the norm of $\cA_R^{(N)}$ as well. For each selfadjoint $a_1,\dots,a_N\in B(\cH)$ with $\|a_i\|\le R$, we can extend $p\in\bC\<X_1,\dots,X_N\>\mapsto p(a_1,\dots,a_N)\in B(\cH)$ to a $*$-homomorphism $\cA_R^{(N)}\to B(\cH)$, written as $$h\in\cA_R^{(N)}\mapsto h(a_1,\dots,a_N)\in B(\cH),$$ which is regarded as the “continuous functional calculus" of the noncommutative $N$-tuple $(a_1,\dots,a_N)$. In particular, for a single selfadjoint $a$ with $\|a\|\le R$, this reduces to the usual functional calculus $h(a)$ for $h\in C([-R,R])$ ($=\cA_R^{(1)}$). There are natural operations on the class of $C^*$-algebras $\cA_R^{(N)}$ ($N\in\bN$, $R>0$).
- When $R_1<R$, the restriction $f\mapsto f|_{[-R_1,R_1]}$, $f\in C([-R,R])$, induces a $*$-homomorphism $r_{R,R_1}:\cA_R^{(N)}\to\cA_{R_1}^{(N)}$. Note that $r_{R,R_1}(p)=p$ for $p\in\bC\<X_1,\dots,X_N\>$.
- For each $R,R_1>0$ the dilation $f\mapsto f((R/R_1)\,\cdot)$ induces a $*$-isomorphism $\rho_{R,R_1}:\cA_R^{(N)}\to\cA_{R_1}^{(N)}$. For a polynomial $p\in\bC\<X_1,\dots,X_N\>$ this is written as $$\qquad\rho_{R,R_1}(p)(X_1,\dots,X_N)=p((R/R_1)X_1,\dots,(R/R_1)X_N).$$ In particular, the $C^*$-algebra $\cA_R^{(N)}$ is independent (up to a $*$-isomorphism) of the choice of $R>0$.
- When $1\le L<N$, $\cA_R^{(L)}$ and $\cA_R^{(N-L)}$ are considered as $C^*$-subalgebras of $\cA_R^{(N)}$ under the identification $\cA_R^{(L)}\star\cA_R^{(N-L)}\cong\cA_R^{(N)}$. For $h_1\in\cA_R^{(L)}$ and $h_2\in\cA_R^{(N-L)}$ we simply write $h_1+h_2$ for the sum of $h_1,h_2$ in $\cA_R^{(N)}$ under this identification. For polynomials $p_1\in\bC\<X_1,\dots,X_L\>$ and $p_2\in\bC\<X_{L+1},\dots,X_N\>$ this is the usual polynomial sum $p_1+p_2\in\bC\<X_1,\dots,X_N\>$.
Let $\bigl(\cA_R^{(N)}\bigr)^{sa}$ be the selfadjoint part of $\cA_R^{(N)}$. Note that $h(A_1,\dots,A_N)\in M_n^{sa}$ whenever $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $A_1,\dots,A_N\in M_n^{sa}$ with $\|A_i\|\le R$. It is immediate to see that the function $h(A_1,\dots,A_N)$ on $(M_n^{sa})_R^N$ is continuous, where $(M_n^{sa})_R^N$ is the $N$-fold product of $(M_n^{sa})_R$. The following definition is the direct multivariate extension of the formula (see also ):
\[D-2.2\][For each $R>0$ and $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ define $$\begin{aligned}
\label{F-2.1}
&&\pi_R(h):=\limsup_{n\to\infty}
\Biggl({1\over n^2}\log\int_{(M_n^{sa})_R^N}
\exp\bigl(-n^2\tr_n(h(A_1,\dots,A_N))\bigr)
\,d\Lambda_n^{\otimes N}(A_1,\dots,A_N) \nonumber\\
&&\hskip10cm+{N\over2}\log n\Biggr).\end{aligned}$$ We call this $\pi_R(h)$ the [*free pressure*]{} of $h$ (with parameter $R>0$). ]{}
Basic properties of free entropy $\pi_R(h)$ are summarized in the following. This and the above definition extend the properties (I) and (III) in Section 1 to noncommutative multivariables.
\[P-2.3\]
- $\pi_R(h)$ is convex on $\bigl(\cA_R^{(N)}\bigr)^{sa}$.
- If $h_1,h_2\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $h_1\le h_2$, then $\pi_R(h_1)\ge\pi_R(h_2)$.
- $|\pi_R(h_1)-\pi_R(h_2)|\le\|h_1-h_2\|_R$ for all $h_1,h_2\in\bigl(\cA_R^{(N)}\bigr)^{sa}$.
- If $R>R_1>0$ and $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$, then $\pi_{R_1}(r_{R,R_1}(h))\le\pi_R(h)$.
- If $R,R_1>0$ and $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$, then $\pi_{R_1}(\rho_{R,R_1}(h))=\pi_R(h)+N\log(R_1/R)$.
- Let $h_1\in\bigl(\cA_R^{(L)}\bigr)^{sa}$ and $h_2\in\bigl(\cA_R^{(N-L)}\bigr)^{sa}$ where $1\le L<N$, and $h_1+h_2$ be given as in (c) above. Then $\pi_R(h_1+h_2)\le\pi_R(h_1)+\pi_R(h_2)$. In particular when $L=1$, $\pi_R(h_1+h_2)=\pi_R(h_1)+\pi_R(h_2)$.
[[*Proof.*]{}]{}(1)Let $h_1,h_2\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $0<\alpha<1$. For $A_1,\dots,A_N\in(M_n^{sa})_R$ set $$\begin{aligned}
f_k(A_1,\dots,A_N)&:=&\exp\bigl(-n^2\tr_n(h_k(A_1,\dots,A_N))\bigr),
\qquad k=1,2, \\
f(A_1,\dots,A_N)&:=&\exp\bigl(-n^2\tr_n(
(\alpha h_1+(1-\alpha)h_2)(A_1,\dots,A_N))\bigr).\end{aligned}$$ Since the Hölder inequality gives $$\begin{aligned}
\int_{(M_n^{sa})_R^N}f\,d\Lambda_n^{\otimes N}
&=&\int_{(M_n^{sa})_R^N}f_1^\alpha f_2^{1-\alpha}
\,d\Lambda_n^{\otimes N} \\
&\le&\Biggl(\int_{(M_n^{sa})_R^N}f_1\,d\Lambda_n^{\otimes N}\Biggr)^\alpha
\Biggl(\int_{(M_n^{sa})_R^N}f_2\,d\Lambda_n^{\otimes N}\Biggr)^{1-\alpha},\end{aligned}$$ we have $$\begin{aligned}
&&{1\over n^2}\log\int_{(M_n^{sa})_R^N}f\,d\Lambda_n^{\otimes N}
+{N\over2}\log n \\
&&\qquad\le\alpha\Biggl({1\over n^2}\log
\int_{(M_n^{sa})_R^N}f_1\,d\Lambda_n^{\otimes N}+{N\over2}\log n\Biggr) \\
&&\qquad\qquad+(1-\alpha)\Biggl({1\over n^2}\log
\int_{(M_n^{sa})_R^N}f_2\,d\Lambda_n^{\otimes N}+{N\over2}\log n\Biggr),\end{aligned}$$ which implies that $$\pi_R(\alpha h_1+(1-\alpha)h_2)\le\alpha\pi_R(h_1)+(1-\alpha)\pi_R(h_2).$$
\(2) is obvious because the assumption implies that $h_1(A_1,\dots,A_N)\le h_2(A_1,\dots,A_N)$ for all $A_i\in(M_n^{sa})_R$.
(3)By the definition of $\|\cdot\|_R$, for any $A_1,\dots,A_N\in
(M_n^{sa})_R$ we get $$|\tr_n(h_1(A_1,\dots,A_N))-\tr_n(h_2(A_1,\dots,A_N))|
\le\|h_1-h_2\|_R$$ so that $$\begin{aligned}
&&\exp\bigl(-n^2\tr_n(h_1(A_1,\dots,A_N))\bigr)
\exp\bigl(-n^2\|h_1-h_2\|_R\bigr) \\
&&\qquad\le\exp\bigl(-n^2\tr_n(h_2(A_1,\dots,A_N))\bigr) \\
&&\qquad\le\exp\bigl(-n^2\tr_n(h_1(A_1,\dots,A_N))\bigr)
\exp\bigl(n^2\|h_1-h_2\|_R\bigr).\end{aligned}$$ This immediately implies that $$\pi_R(h_1)-\|h_1-h_2\|_R\le\pi_R(h_2)\le\pi_R(h_1)+\|h_1-h_2\|_R.$$
\(4) is obvious because $r_{R,R_1}(h)(A_1,\dots,A_N)=h(A_1,\dots,A_N)$ for $A_i\in(M_n^{sa})_{R_1}$.
(5)For $h_1:=\rho_{R,R_1}(h)$ and $\alpha:=R_1/R$, since $h_1(A_1,\dots,A_N)=h(\alpha^{-1}A_1,\dots,\alpha^{-1}A_N)$ for $A_i\in(M_n^{sa})_{R_1}$, we get $$\begin{aligned}
&&\int_{(M_n^{sa})_{R_1}^N}\exp\bigl(-n^2
\tr_n(h_1(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad=\int_{(M_n^{sa})_{R_1}^N}\exp\bigl(-n^2\tr_n
(h(\alpha^{-1}A_1,\dots,\alpha^{-1}A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad=\alpha^{n^2N}\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n(h(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N}\end{aligned}$$ thanks to the trivial formula $d\Lambda_n(\alpha
A)/d\Lambda_n(A)=\alpha^{n^2}$. Hence $\pi_{R_1}(h_1)=\pi_R(h)+N\log\alpha$.
(6)Since $(h_1+h_2)(A_1,\dots,A_N)=h_1(A_1,\dots,A_L)+h_2(A_{L+1},\dots,A_N)$ for $A_i\in(M_n^{sa})_R$, we get $$\begin{aligned}
&&\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n((h_1+h_2)(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad=\int_{(M_n^{sa})_R^L}\exp\bigl(-n^2
\tr_n(h_1(A_1,\dots,A_L))\bigr)\,d\Lambda_n^{\otimes L} \\
&&\qquad\qquad\times\int_{(M_n^{sa})_R^{N-L}}\exp\bigl(-n^2
\tr_n(h_2(A_{L+1},\dots,A_N))\bigr)\,d\Lambda_n^{\otimes{N-L}}\end{aligned}$$ and hence $$\begin{aligned}
&&{1\over n^2}\log\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n((h_1+h_2)(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N}
+{N\over2}\log n \\
&&\quad={1\over n^2}\log\int_{(M_n^{sa})_R^L}\exp\bigl(-n^2
\tr_n(h_1(A_1,\dots,A_L))\bigr)\,d\Lambda_n^{\otimes L}
+{L\over2}\log n \\
&&\qquad+{1\over n^2}\log\int_{(M_n^{sa})_R^{N-L}}\exp\bigl(-n^2
\tr_n(h_2(A_{L+1},\dots,A_N))\bigr)\,d\Lambda_n^{\otimes{N-L}}
+{N-L\over2}\log n,\end{aligned}$$ which gives the required inequality. Also, the above equality together with the formula (with limit) gives the last assertion.
Legendre transform $\eta_R$ of free pressure
============================================
We first define the (minus) Legendre transform of the free pressure $\pi_R$ in the purely algebraic situation.
\[D-3.1\][Let $\Sigma\<X_1,\dots,X_N\>$ denote the set of selfadjoint linear functionals $\mu$ on $\bC\<X_1,\dots,X_N\>$ such that $\mu(\1)=1$, where the selfadjointness of $\mu$ means $\mu(p^*)=\overline{\mu(p)}$ for $p\in\bC\<X_1,\dots,X_N\>$. For each $R>0$ and $\mu\in\Sigma\<X_1,\dots,X_N\>$ define $$\eta_R(\mu):=\inf\bigl\{\mu(p)+\pi_R(p):
p\in\bC\<X_1,\dots,X_N\>^{sa}\bigr\}.$$ ]{}
The following is obvious by definition.
\[P-3.2\] For each $R>0$, $\eta_R(\mu)$ is a concave function on $\Sigma\<X_1,\dots,X_N\>$, and it is upper semicontinuous in the sense that if $\mu,\mu_k\in\Sigma\<X_1,\dots,X_N\>$ for $k\in\bN$ and $\mu_k(p)\to\mu(p)$ as $k\to\infty$ for all $p\in\bC\<X_1,\dots,X_N\>$, then $$\eta_R(\mu)\ge\limsup_{k\to\infty}\eta_R(\mu_k).$$
Let $\cT\bigl(\cA_R^{(N)}\bigr)$ denote the set of all tracial states on $\cA_R^{(N)}$. As is easily seen, $\mu\in\Sigma\<X_1,\dots,X_N\>$ can (uniquely) extend to an element of $\cT\bigl(\cA_R^{(N)}\bigr)$ (in this case we also write $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$) if and only if the following three conditions are satisfied:
- $\mu\ge0$ in the sense that $\mu(p^*p)\ge0$ for all $p\in\bC\<X_1,\dots,X_n\>$,
- $|\mu(p)|\le\|p\|_R$ for all $p\in\bC\<X_1,\dots,X_N\>$,
- $\mu$ is tracial in the sense that $\mu(p_1p_2)=\mu(p_2p_1)$ for all $p_1,p_2\in\bC\<X_1,\dots,X_N\>$.
\[L-3.3\] If $\mu\in\Sigma\<X_1,\dots,X_N\>$ and $\mu\notin\cT\bigl(\cA_R^{(N)}\bigr)$ (i.e., $\mu$ does not extend to an element of $\cT\bigl(\cA_R^{(N)}\bigr)$), then $\eta_R(\mu)=-\infty$.
[[*Proof.*]{}]{}Assume that $\mu\in\Sigma\<X_1,\dots,X_N\>$ and $\eta_R(\mu)>-\infty$, and we prove that the above conditions (a)–(c) hold.
(a)Suppose $\mu(p^*p)<0$ for some $p\in\bC\<X_1,\dots,X_N\>$; then for each $\alpha>0$ we get $\pi_R(\alpha p^*p)\le\pi_R(0)$ by Proposition \[P-2.3\](2). Therefore, $$\eta_R(\mu)\le\mu(\alpha p^*p)+\pi_R(\alpha p^*p)
\longrightarrow-\infty\quad\mbox{as $\alpha\to\infty$},$$ a contradiction.
(b)Suppose $|\mu(p)|>\|p\|_R$ for some $p\in\bC\<X_1,\dots,X_N\>^{sa}$. We may suppose $\mu(p)<-\|p\|_R$. Since Proposition \[P-2.3\](3) gives $\pi_R(\alpha p)\le\|\alpha
p\|_R+\pi_R(0)$ for $\alpha>0$, we get $$\begin{aligned}
\eta_R(\mu)&\le&\mu(\alpha p)+\pi_R(\alpha p) \\
&\le&\alpha\bigl(\mu(p)+\|p\|_R\bigr)+\pi_R(0)\longrightarrow-\infty
\quad\mbox{as $\alpha\to\infty$},\end{aligned}$$ a contradiction. Hence we have shown that $|\mu(p)|\le\|p\|_R$ for all $p\in\bC\<X_1,\dots,X_N\>^{sa}$. Thanks to this and (a) already proven, it follows that $\mu$ extends to a bounded positive linear functional on the $C^*$-algebra $\cA_R^{(N)}$. Since $\mu(\1)=1$, the extended $\mu$ has norm one.
(c)It suffices to show that $\mu(i(p_1p_2-p_2p_1))=0$ for all $p_1,p_2\in\bC\<X_1,\dots,X_N\>^{sa}$. Suppose $\mu(i(p_1p_2-p_2p_1))<0$ for some $p_1,p_2\in\bC\<X_1,\dots,X_n\>^{sa}$. For $\alpha>0$ we get $\pi_R(i\alpha(p_1p_2-p_2p_1))=\pi_R(0)$ because $\tr_n(i\alpha(p_1p_2-p_2p_1)(A_1,\dots,A_N))=0$ for any $A_i\in M_n^{sa}$. Therefore, $$\begin{aligned}
\eta_R(\mu)&\le&\mu(i\alpha(p_1p_2-p_2p_1))
+\pi_R(i\alpha(p_1p_2-p_2p_1)) \\
&=&\alpha\mu(i(p_1p_2-p_2p_1))+\pi_R(0)\longrightarrow-\infty
\quad\mbox{as $\alpha\to\infty$},\end{aligned}$$ a contradiction.
The above lemma says that the essential domain $\bigl\{\mu\in\Sigma\<X_1,\dots,X_N\>:\eta_R(\mu)>-\infty\bigr\}$ is included in $\cT\bigl(\cA_R^{(N)}\bigr)$. In the next theorem we show that $\pi_R(h)$ for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $\eta_R(\mu)$ for $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$ are the Legendre transforms of each other with respect to the Banach space duality $\mu(h)$ for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}$, the selfadjoint part of $\bigl(\cA_R^{(N)}\bigr)^*$. In this way, the Legendre transform formulas and are extended to the noncommutative multivariate setting, where $C_\bR([-R,R])$ and $\cM([-R,R])$ are replaced by $\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $\cT\bigl(\cA_R^{(N)}\bigr)$, respectively.
\[T-3.4\]
- For every $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$, $$\eta_R(\mu)=\inf\bigl\{\mu(h)+\pi_R(h):
h\in\bigl(\cA_R^{(N)}\bigr)^{sa}\bigr\}.$$ Hence, $\eta_R(\mu)$ is concave and weakly\* upper semicontinuous on $\cT\bigl(\cA_R^{(N)}\bigr)$.
- For every $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$, $$\pi_R(h)=\sup\bigl\{-\mu(h)+\eta_R(\mu):
\mu\in\cT\bigl(\cA_R^{(N)}\bigr)\bigr\}.$$
[[*Proof.*]{}]{}(1) is obvious from Definition \[D-3.1\] because $\bC\<X_1,\dots,X_N\>^{sa}$ is dense in $\bigl(\cA_R^{(N)}\bigr)^{sa}$.
(2)The Legendre transform of $\pi_R(h)$ on $\bigl(\cA_R^{(N)}\bigr)^{sa}$ with respect to the Banach space duality between $\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $\bigl(\cA_R^{(N)}\bigr)^{*,sa}$ is $$\begin{aligned}
(\pi_R)^*(\mu)&:=&\sup\bigl\{-\mu(h)-\pi_R(h):
h\in\bigl(\cA_R^{(N)}\bigr)^{sa}\bigr\} \\
&=&-\inf\bigl\{\mu(h)+\pi_R(h):h\in\bigl(\cA_R^{(N)}\bigr)^{sa}\bigr\}
\quad\mbox{for $\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}$}.\end{aligned}$$ Suppose $\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}$ and $\mu(\1)\ne1$; then for $\alpha\in\bR$ we get $$\mu(\alpha\1)+\pi_R(\alpha\1)=\alpha(\mu(\1)-1)+\pi_R(0)$$ thanks to $\pi_R(\alpha\1)=-\alpha+\pi_R(0)$. Hence $(\pi_R)^*(\mu)=+\infty$. This and Lemma \[L-3.3\] imply that $$(\pi_R)^*(\mu)=\cases
-\eta_R(\mu) & \text{if $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$}, \\
+\infty & \text{if $\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}
\setminus\cT\bigl(\cA_R^{(N)}\bigr)$}.
\endcases$$ Since $\pi_R(h)$ is convex and continuous on $\bigl(\cA_R^{(N)}\bigr)^{sa}$, it is the Legendre transform of $(\pi_R)^*(\mu)$ on $\bigl(\cA_R^{(N)}\bigr)^{*,sa}$ so that $$\begin{aligned}
\pi_R(h)
&=&\sup\bigl\{-\mu(h)-(\pi_R)^*(\mu):
\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}\bigr\} \\
&=&\sup\bigl\{-\mu(h)+\eta_R(\mu):\mu\in\cT\bigl(\cA_R^{(N)}\bigr)\bigr\},\end{aligned}$$ as desired.
Since $\cT\bigl(\cA_R^{(N)}\bigr)$ is weakly\* compact, for each $h_0\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ there exists a $\mu_0\in\cT\bigl(\cA_R^{(N)}\bigr)$ such that $$\pi_R(h_0)=-\mu_0(h_0)+\eta_R(\mu_0).$$ This equality condition is a kind of variational principle, so we call such $\mu_0$ an [*equilibrium tracial state*]{} associated with $h_0$. We see by the above proof that such a $\mu_0\in\cT\bigl(\cA_R^{(N)}\bigr)$ is characterized as an element of $\bigl(\cA_R^{(N)}\bigr)^{*,sa}$ which supports at $h_0$ the function $\pi_R(h)$ on $\bigl(\cA_R^{(N)}\bigr)^{sa}$. Thus, the general theory of conjugate (or Legendre) functions says (see [@ET I.5.3] for example) that the uniqueness of an equilibrium tracial state associated with $h_0\in\cA_R^{sa}$ is equivalent to the differentiability of $\pi_R(h)$ at $h_0$; or equivalently, $$\lim_{t\to0}{\pi_R(h_0+tp)-\pi_R(h_0)\over t}$$ exists for every $p\in\bC\<X_1,\dots,X_N\>^{sa}$ (the above limit then equals $\mu_0(p)$). In the single variable case ($N=1$), as mentioned in Section 1, there is a unique equilibrium measure $\sigma^{h_0}$ associated with each $h_0\in C_\bR([-R,R])$ ($=\bigl(\cA_R^{(1)}\bigr)^{sa}$), so that we have $$\lim_{t\to0}{\pi_R(h_0+th)-\pi_R(h_0)\over t}=\sigma^{h_0}(h)
\quad\mbox{for every $h\in C_\bR([-R,R])$}.$$ However, in the multivariate case, it seems quite a difficult problem to show the differentiability of $\pi_R(h)$ (even at $h_0=0$ for instance). It might be worth noting a general result that the function $\pi_R$ is differentiable at points in a dense $G_\delta$ subset of $\bigl(\cA_R^{(N)}\bigr)^{sa}$. Indeed, this is true for any Lipschitz continuous convex function on a separable Banach space (see the proof of [@DS V.9.8]).
Quantity $\eta(a_1,\dots,a_N)$ for multivariables
=================================================
We apply the quantity $\eta_R(\mu)$ for $\mu\in\Sigma\<X_1,\dots,X_N\>$ to introduce a free entropy-like quantity for noncommutative multivariables in a tracial $W^*$-probability space $(\cM,\tau)$.
\[D-4.1\][For each $a_1,\dots,a_N\in\cM^{sa}$ define $\mu_{(a_1,\dots,a_N)}\in\Sigma\<X_1,\dots,X_N\>$ by $$\mu_{(a_1,\dots,a_N)}(p):=\tau(p(a_1,\dots,a_N)).$$ We further define $$\eta_R(a_1,\dots,a_N):=\eta_R(\mu_{(a_1,\dots,a_N)});$$ namely, $$\eta_R(a_1,\dots,a_N)
=\inf\bigl\{\tau(p(a_1,\dots,a_N))+\pi_R(p):
p\in\bC\<X_1,\dots,X_N\>^{sa}\bigr\},$$ and $$\eta(a_1,\dots,a_N):=\sup_{R>0}\eta_R(a_1,\dots,a_N).$$ ]{}
If $(a_1,\dots,a_N)\in\cM^{sa}$ and $R\ge\max_i\|a_i\|$, then we have $\mu:=\mu_{(a_1,\dots,a_N)}\in\cT\bigl(\cA_R^{(N)}\bigr)$ because of the the functional calculus $h\in\cA_R^{(N)}\mapsto h(a_1,\dots,a_N)\in\cM$. In this case, $\eta_R(a_1,\dots,a_N)$ is also given as $$\eta_R(a_1,\dots,a_N)
=\inf\bigl\{\tau(h(a_1,\dots,a_N))+\pi_R(h):
h\in\bigl(\cA_R^{(N)}\bigr)^{sa}\bigr\},$$ and we further see that $\{a_1,\dots,a_N\}''$ ($\subset\cM$) is isomorphic to the von Neumann algebra $\pi_\mu\bigl(\cA_R^{(N)}\bigr)''$ by the isomorphism defined by $a_i\mapsto\pi_\mu(X_i)$, $1\le i\le N$, where $\pi_\mu$ is the GNS representation of $\cA_R^{(N)}$ associated with $\mu$. (A related result in connection with Connes’ embedding problem is found in [@Br §9].)
The next proposition in the single variable case is a direct consequence of (II) in Section 1.
\[P-4.2\] For every $a\in\cM^{sa}$ with $\|a\|\le R$, $$\eta(a)=\eta_R(a)=\chi(a).$$
The following is obvious by definition and Proposition \[P-3.2\].
\[P-4.3\] For each $R>0$, $\eta_R(a_1,\dots,a_N)$ is upper semicontinuous on $(\cM^{sa})^N$ in strong topology, that is, if $(a_1,\dots,a_N)$ and $(a_1^{(k)},\dots,a_N^{(k)})$ are in $(\cM^{sa})^N$ for $k\in\bN$ and $a_i^{(k)}\to a_i$ strongly as $k\to\infty$ for $1\le i\le N$, then $$\eta_R(a_1,\dots,a_N)\ge
\limsup_{k\to\infty}\eta_R(a_1^{(k)},\dots,a_N^{(k)}).$$
The following properties immediately follow from (4) and (6) of Proposition \[P-2.3\].
\[P-4.4\] Let $a_1,\dots,a_N\in\cM^{sa}$.
- If $R>R_1>0$, then $\eta_{R_1}(a_1,\dots,a_N)\le\eta_R(a_1,\dots,a_N)$.
- For $1\le L<N$ and $R>0$, $$\begin{aligned}
\eta_R(a_1,\dots,a_N)
&\le&\eta_R(a_1,\dots,a_L)+\eta_R(a_{L+1},\dots,a_N), \\
\eta(a_1,\dots,a_N)
&\le&\eta(a_1,\dots,a_L)+\eta(a_{L+1},\dots,a_N).\end{aligned}$$
For Voiculescu’s free entropy, it is known that $\chi_R(a_1,\dots,a_N)=\chi(a_1,\dots,a_N)$ whenever $R\ge\max_i\|a_i\|$. However, the similar property for $\eta_R$ that $\eta_R(a_1,\dots,a_N)=\eta(a_1,\dots,a_N)$ for such $R$ is unknown.
\[T-4.5\]
- For every $a_1,\dots,a_N\in\cM^{sa}$ and $R>0$, $$\begin{aligned}
\eta_R(a_1,\dots,a_N)&\ge&\chi_R(a_1,\dots,a_N), \\
\eta(a_1,\dots,a_N)&\ge&\chi(a_1,\dots,a_N).\end{aligned}$$
- If $a_1,\dots,a_N\in\cM^{sa}$ are free and $R\ge\max_i\|a_i\|$, then $$\eta(a_1,\dots,a_N)=\eta_R(a_1,\dots,a_N)=\chi(a_1,\dots,a_N).$$
[[*Proof.*]{}]{}(1)Let $p\in\bC\<X_1,\dots,X_N\>^{sa}$ and $\delta>0$ be given. One can choose $r\in\bN$ and $\eps>0$ such that, for each $n\in\bN$, $(A_1,\dots,A_N)\in\Gamma_R(a_1,\dots,a_N;n,r,\eps)$ implies $$|\tr_n(p(A_1,\dots,A_N))-\tau(p(a_1,\dots,a_N))|<\delta.$$ This gives $$\begin{aligned}
&&\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n(p(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad\ge\exp\bigl(-n^2\tau(p(a_1,\dots,a_N))-n^2\delta\bigr)
\,\Lambda_n^{\otimes N}\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr)\end{aligned}$$ so that $$\begin{aligned}
&&{1\over n^2}\log\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n(p(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad\ge-\mu_{(a_1,\dots,a_N)}(p)-\delta+{1\over n^2}\log
\Lambda_n^{\otimes N}\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr).\end{aligned}$$ Therefore, $$\mu_{(a_1,\dots,a_N)}(p)+\pi_R(p)+\delta\ge\chi_R(a_1,\dots,a_N).$$ Since $p\in\bC\<X_1,\dots,X_N\>^{sa}$ and $\delta>0$ are arbitrary, we have $$\eta_R(a_1,\dots,a_N)\ge\chi_R(a_1,\dots,a_N),$$ which gives the other inequality as well.
(2)We have $$\begin{aligned}
\eta_R(a_1,\dots,a_N)
&\le&\eta_R(a_1)+\dots+\eta_R(a_N)
\quad\mbox{(by Proposition \ref{P-4.4}\,(2))} \\
&=&\chi(a_1)+\dots+\chi(a_N)
\qquad\mbox{(by Proposition \ref{P-4.2})} \\
&=&\chi(a_1,\dots,a_N)\end{aligned}$$ by the additivity of $\chi(a_1,\dots,a_N)$ in the free case ([@V2]). The converse inequality is in (1).
By Proposition \[P-4.4\] and Theorem \[T-4.5\] we notice that $\eta(a_1,\dots,a_N)$ admits the same maximal value as $\chi(a_1,\dots,a_N)$ when restricted on $\|a_i\|\le R$. In fact, the maximum is attained when $a_1,\dots,a_N$ are free and each $a_i$ has the arcsine distribution supported on $[-R,R]$.
\[R-4.6\][For $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$ we denote by $\chi(\mu)$ the free entropy $\chi(\pi_\mu(X_1),\dots,\pi_\mu(X_N))$ via the GNS representation $\pi_\mu$ of $\cA_R^{(N)}$ associated with $\mu$. According to [@V3], if $\chi(a_1,\dots,a_N)>-\infty$ for selfadjoint variables $a_1,\dots,a_N$ in a tracial $W^*$-probability space, then $\{a_1,\dots,a_N\}''$ is a (non-hyperfinite, even non-$\Gamma$) II$_1$ factor. This shows in particular that if $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$ is not factorial (or not extremal in $\cT\bigl(\cA_R^{(N)}\bigr)$), then $\chi(\mu)=-\infty$. Choose two different $\mu_1,\mu_2\in\cT\bigl(\cA_R^{(N)}\bigr)$ such that $\chi(\mu_1)$ and $\chi(\mu_2)$ are finite; then for $\mu_0:=(\mu_1+\mu_2)/2$ we get $\eta(\mu_0)>-\infty$ thanks to the concavity of $\eta$ (Theorem \[T-3.4\](1)), but $\chi(\mu_0)=-\infty$. Hence, $\eta$ and $\chi$ are not equal in general; $\chi(\mu)$ for $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$ is far from concave. ]{}
The following two propositions are analogous to [@V2 Propositions 3.6 and 3.8]. But it does not seem that $\eta$ enjoys the change of variable formulas established in [@V2; @V4] for $\chi$.
\[P-4.7\]
- If $A=[\alpha_{ij}]_{i,j=1}^N\in M_N(\bR)$ and $\beta_1,\dots,\beta_N\in\bR$, then $$\eta\Biggl(\sum_{j=1}^N\alpha_{1j}a_j+\beta_1\1,\dots,
\sum_{j=1}^N\alpha_{Nj}a_j+\beta_N\1\Biggr)
=\eta(a_1,\dots,a_N)+\log|\det A|.$$
- If $a_1,\dots,a_N$ are linearly independent, then $\eta(a_1,\dots,a_N)=-\infty$.
[[*Proof.*]{}]{}(1)Write $b_i:=\sum_{j=1}^N\alpha_{ij}a_j+\beta_j\1$ for $1\le i\le N$. Here, assume that $A$ is invertible (the singular case will be seen after proving (2)), and define $\Psi:(M_n^{sa})^N\to(M_n^{sa})^N$ by $$\Psi(A_1,\dots,A_N)
:=\Biggl(\sum_{j=1}^N\alpha_{1j}A_j+\beta_1I,\dots,
\sum_{j=1}^N\alpha_{Nj}A_j+\beta_NI\Biggr).$$ It is known (see [@HP1 6.2.2]) that $d(\Lambda_n^{\otimes N}\circ\Psi)/d\Lambda_n^{\otimes N}=|\det A|^{n^2}$. For each $R>0$ and $q\in\bC\<X_1,\dots,X_N\>^{sa}$ set $$R':=\max_{1\le i\le N}\Biggl(\sum_{j=1}^N|\alpha_{ij}|R+|\beta_i|\Biggr),$$ $$p(X_1,\dots,X_N):=q\Biggl(\sum_{j=1}^N\alpha_{1j}X_j+\beta_1\1,
\dots,\sum_{j=1}^N\alpha_{Nj}X_j+\beta_N\1\Biggr).$$ Then we get $$\begin{aligned}
\pi_{R'}(q)&\ge&\limsup_{n\to\infty}\Biggl({1\over n^2}\log
\int_{\Psi\bigl((M_n^{sa})_R^N\bigr)}\exp\bigl(-n^2
\tr_n(q(B_1,\dots,B_N))\bigr)\,d\Lambda_n^{\otimes N}
+{N\over2}\log n\Biggr) \\
&=&\limsup_{n\to\infty}\Biggl({1\over n^2}\log\int_{(M_n^{sa})_R^N}
\exp\bigl(-n^2\tr_n((q\circ\Psi)(A_1,\dots,A_N))
\bigr)\,d(\Lambda_n^{\otimes N}\circ\Psi) \\
&&\hskip8cm+{N\over2}\log n\Biggr) \\
&=&\pi_R(p)+\log|\det A|\end{aligned}$$ so that $$\begin{aligned}
\tau(q(b_1,\dots,b_N))+\pi_{R'}(q)
&\ge&\tau(p(a_1,\dots,a_N))+\pi_R(p)+\log|\det A| \\
&\ge&\eta_R(a_1,\dots,a_N)+\log|\det A|.\end{aligned}$$ Therefore, $$\eta_{R'}(b_1,\dots,b_N)\ge\eta_R(a_1,\dots,a_N)+\log|\det A|.$$ By reversing the roles of $(a_1,\dots,a_N)$ and $(b_1,\dots,b_N)$ we have $$\eta(b_1,\dots,b_N)=\eta(a_1,\dots,a_N)+\log|\det A|.$$
(2)We may assume that $a_1=\alpha_2a_2+\dots+\alpha_Na_N$ with $\alpha_i\in\bR$. For every $\eps>0$, since $a_1=\eps a_1+(1-\eps)\alpha_2a_2+\dots+(1-\eps)\alpha_Na_N$, we get by (1) $$\eta(a_1,\dots,a_N)=\eta(a_1,\dots,a_N)+\log\eps,$$ implying $\eta(a_1,\dots,a_N)=-\infty$. Finally, when $A$ is singular, it follows from (2) just proven that both sides of the equality in (1) are $-\infty$.
\[P-4.8\] Let $a_1,\dots,a_N,b_1,\dots,b_N\in\cM^{sa}$ be such that $b_1=a_1$ and $b_i-a_i\in\{a_1,\dots,a_{i-1}\}''$ for $2\le i\le N$, and let $R_0:=\max_i\|b_i-a_i\|$. Then $$\begin{aligned}
\eta_R(a_1,\dots,a_N)&\le&\eta_{R+R_0}(b_1,\dots,b_N)
\quad\mbox{if $R\ge\max_i\|a_i\|$}, \\
\eta_R(b_1,\dots,b_N)&\le&\eta_{R+R_0}(a_1,\dots,a_N)
\quad\mbox{if $R\ge\max_i\|b_i\|$}.\end{aligned}$$ Hence, $$\eta(a_1,\dots,a_N)=\eta(b_1,\dots,b_N).$$
[[*Proof.*]{}]{}When $R\ge\max_i\|a_i\|$, as noted just after Definition \[D-4.1\], $\mu:=\mu_{(a_1,\dots,a_N)}\in\cT\bigl(\cA_R^{(N)}\bigr)$ and $\{a_1,\dots,a_N\}''$ is isomorphic to $\pi_\mu\bigl(\cA_R^{(N)}\bigr)''$ by the isomorphism $\psi$ defined by $\psi(a_i)=\pi_\mu(X_i)$, $1\le i\le N$. For each $2\le i\le N$, since $\psi(b_i-a_i)\in\{\pi_\mu(X_1),\dots,\pi_\mu(X_{i-1})\}''$, using Kaplansky density theorem and an argument with functional calculus, one can choose a sequence of selfadjoint elements $h_i^{(k)}$, $k\in\bN$, in $C^*(X_1,\dots,X_{i-1})$ ($\subset\cA_R^{(N)}$) such that $\|h_i^{(k)}\|_R\le\|\psi(b_i-a_i)\|=\|b_i-a_i\|$ and $\pi_\mu(h_i^{(k)})\to\psi(b_i-a_i)$ strongly as $k\to\infty$. Hence, there exists a sequence $p_i^{(k)}\in\bC\<X_1,\dots,X_{i-1}\>^{sa}$, $k\in\bN$, such that $\|p_i^{(k)}\|_R\le\|b_i-a_i\|$ and $\psi\bigl(p_i^{(k)}(a_1,\dots,a_{i-1})\bigr)
=\pi_\mu\bigl(p_i^{(k)}(X_1,\dots,X_{i-1})\bigr)\to\psi(b_i-a_i)$ strongly; hence $p_i^{(k)}(a_1,\dots,a_{i-1})\to b_i-a_i$ strongly as $k\to\infty$. Set $b_1^{(k)}:=b_1=a_1$ and $b_i^{(k)}:=a_i+p_i^{(k)}(a_1,\dots,a_{i-1})$ for $2\le i\le N$. Then $\|b_i^{(k)}\|\le\|a_i\|+\|b_i-a_i\|\le R+R_0$ and $b_i^{(k)}\to b_i$ strongly as $k\to\infty$. Define $\Psi^{(k)}:(M_n^{sa})^N\to(M_n^{sa})^N$, $\Psi^{(k)}(A_1,\dots,A_N)=(B_1,\dots,B_N)$, by $B_1:=A_1$ and $B_i:=A_i+p_i^{(k)}(A_1,\dots,A_{i-1})$ for $2\le i\le N$. Notice that $\Lambda_n^{\otimes N}$ is $\Psi^{(k)}$-invariant: $\Lambda_n^{\otimes N}\circ\Psi^{(k)}=\Lambda_n^{\otimes N}$. If $(A_1,\dots,A_N)\in(M_n^{sa})_R^N$, then $\Psi^{(k)}(A_1,\dots,A_N)\in(M_n^{sa})_{R+R_0}^N$ because of $\|B_i\|\le\|A_i\|+\|p_i^{(k)}\|_R\le R+R_0$.
For each $q\in\bC\<X_1,\dots,X_N\>^{sa}$, setting $p^{(k)}\in\bC\<X_1,\dots,X_N\>^{sa}$ by $$p^{(k)}(X_1,\dots,X_N):=q\bigl(X_1,X_2+p_2^{(k)}(X_1),
\dots,X_N+p_N^{(k)}(X_1,\dots,X_{N-1})\bigr),$$ we get $$\begin{aligned}
&&\pi_{R+R_0}(q) \\
&&\quad\ge\limsup_{n\to\infty}
\Biggl({1\over n^2}\log\int_{\Psi\bigl((M_n^{sa})_R^N\bigr)}\exp\bigl(-n^2
\tr_n(q(B_1,\dots,B_N))\bigr)\,d\Lambda_n^{\otimes N}
+{N\over2}\log n\Biggr) \\
&&\quad=\limsup_{n\to\infty}\Biggl({1\over n^2}\int_{(M_n^{sa})_R^N}
\exp\bigl(-n^2\tr_n((q\circ\Psi^{(k)})(A_1,\dots,A_N))\bigr)
\,d\Lambda_n^{\otimes N}+{N\over2}\log n\Biggr) \\
&&\quad=\limsup_{n\to\infty}\Biggl({1\over n^2}\int_{(M_n^{sa})_R^N}
\exp\bigl(-n^2\tr_n(p^{(k)}(A_1,\dots,A_N))\bigr)
\,d\Lambda_n^{\otimes N}+{N\over2}\log n\Biggr) \\
&&\quad=\pi_R(p^{(k)}).\end{aligned}$$ Therefore, since $p^{(k)}(a_1,\dots,a_N)=q(b_1^{(k)},\dots,b_N^{(k)})$, $$\begin{aligned}
\tau\bigl(q(b_1^{(k)},\dots,b_N^{(k)})\bigr)+\pi_{R+R_0}(q)
&\ge&\tau\bigl(p^{(k)}(a_1,\dots,a_N)\bigr)+\pi_R(p^{(k)}) \\
&\ge&\eta_R(a_1,\dots,a_N)\end{aligned}$$ so that letting $k\to\infty$ gives $$\tau(q(b_1,\dots,b_N))+\pi_{R+R_0}(q)\ge\eta_R(a_1,\dots,a_N),$$ which yields $$\eta_{R+R_0}(b_1,\dots,b_N)\ge\eta_R(a_1,\dots,a_N).$$
Since the assumption implies that $a_i-b_i\in\{b_1,\dots,b_{i-1}\}''$ for $2\le i\le N$, the other direction follows by reversing the roles of $(a_1,\dots,a_N)$ and $(b_1,\dots,b_N)$.
Equality $\eta=\chi$ for $R$-diagonal variables
===============================================
Let $(\cM,\tau)$ be a tracial $W^*$-probability space as before. When $x$ is a non-selfadjoint element in $\cM$, Voiculescu’s (microstate) free entropy of $x$ is defined as $\chi(a_1,a_2)$ where $a_1$ and $a_2$ are the real and imaginary parts of $x$, i.e., $a_1=(x+x^*)/2$ and $a_2=(x-x^*)/2i$. When $a_1$ and $a_2$ are free, we have $\eta(a_1,a_2)=\chi(a_1,a_2)$ by Theorem \[T-4.5\](2). In this section we show that this equality remains true for [*$R$-diagonal*]{} variables. The notion of $R$-diagonal was introduced by A. Nica and R. Speicher [@NS], where it was shown that for $x\in\cM$ with ${\rm ker}\,x=\{0\}$, $x$ is $R$-diagonal if and only if it admits the polar decomposition $x=u|x|$ with a Haar unitary $u$ free from $|x|=(x^*x)^{1/2}$.
The “Lebesgue" measure on $M_n$ is defined as $$d\hat\Lambda_n(X):=\prod_{i,j=1}^nd(\Re X_{ij})\,d(\Im X_{ij}).$$ Recall the following correspondences of measures under the transformations of Descartes decomposition and of polar decomposition (see [@HP1 6.5.4 and 4.4.7]).
- Under the transformation $X\in
M_n\mapsto(A_1,A_2)\in(M_n^{sa})^2$ with $X=A_1+iA_2$, the measure $\hat\Lambda_n$ on $M_n$ corresponds to the product measure $$\Lambda_n\otimes\Lambda_n\quad\mbox{on $(M_n^{sa})^2$}.$$
- Let $\cU_n$ be the unitary group of order $n$ and $M_n^+$ the set of positive semidefinite $n\times n$ matrices. Under the transformation $X\in M_n\mapsto(U,X^*X)\in\cU_n\times M_n^+$ where $U$ is the unitary part of $X$ (uniquely determined for non-singular matrices $X$, the other case being $\hat\Lambda_n$-negligible), $\hat\Lambda$ on $M_n$ corresponds to the product measure $$\gamma_n\otimes\bigl(C_n\Lambda_n|_{M_n^+}\bigr)
\quad\mbox{on $\cU_n\times M_n^+$}$$ where $\gamma_n$ is the Haar probability measure on $\cU_n$ and $$C_n:={\pi^{n(n+1)/2}\over2^{n(n-1)/2}\prod_{j=1}^{n-1}j!}.$$
\[T-5.1\] For every $x=a_1+ia_2\in\cM$ with $a_1,a_2\in\cM^{sa}$, $$\eta(a_1,a_2)\le\chi(x^*x)+{1\over2}\log{\pi\over2}+{3\over4}.$$
[[*Proof.*]{}]{}For each real polynomial $q(t)$ we set $p\in\bC\<X_1,X_2\>^{sa}$ by $$p(X_1,X_2):=q((X_1+iX_2)^*(X_1+iX_2)).$$ Obviously, we have $$\begin{aligned}
q(x^*x)&=&p(a_1,a_2), \\
q(X^*X)&=&p(A_1,A_2)
\quad\mbox{for $X=A_1+iA_2$, $A_1,A_2\in M_n^{sa}$}.\end{aligned}$$ For each $R\ge\|x\|$, since $$\bigl\{A_1+iA_2:(A_1,A_2)\in(M_n^{sa})_R\bigr\}
\subset(M_n)_{2R}:=\bigl\{X\in M_n:\|X\|\le2R\bigr\},$$ we get $$\begin{aligned}
&&\int_{(M_n^{sa})_R}\exp\bigl(-n^2
\tr_n(p(A_1,A_2))\bigr)\,d\Lambda_n^{\otimes 2}(A_1,A_2) \\
&&\qquad\le\int_{(M_n)_{2R}}\exp\bigl(-n^2
\tr_n(q(X^*X))\bigr)\,d\hat\Lambda_n(X)\quad\mbox{(by (a))} \\
&&\qquad=C_n\int_{(M_n^+)_{4R^2}}\exp\bigl(-n^2
\tr_n(q(A))\bigr)\,d\Lambda_n(A)\quad\mbox{(by (b))}\\
&&\qquad\le C_n\int_{(M_n^{sa})_{4R^2}}\exp\bigl(-n^2
\tr_n(q(A))\bigr)\,d\Lambda_n(A),\end{aligned}$$ where $(M_n^+)_{4R^2}:=\bigl\{A\in M_n^+:\|A\|\le4R^2\bigr\}$. Therefore, $$\begin{aligned}
\pi_R(p)&=&\limsup_{n\to\infty}\Biggl({1\over n^2}
\log\int_{(M_n^{sa})_R}\exp\bigl(-n^2
\tr_n(p(A_1,A_2))\bigr)\,d\Lambda_n^{\otimes 2}(A_1,A_2)
+\log n\Biggr) \\
&\le&\limsup_{n\to\infty}\Biggl({1\over n^2}
\log\int_{(M_n^{sa})_{4R^2}}\exp\bigl(-n^2
\tr_n(q(A))\bigr)\,d\Lambda_n(A)+{1\over2}\log n\Biggr) \\
&&\qquad+\lim_{n\to\infty}\biggl({1\over n^2}\log C_n
+{1\over2}\log n\biggr) \\
&=&\pi_{4R^2}(q)+{1\over2}\log{\pi\over2}+{3\over4}.\end{aligned}$$ This implies that $$\begin{aligned}
\eta_R(a_1,a_2)&\le&\tau(p(a_1,a_2))+\pi_R(p) \\
&\le&\tau(q(x^*x))+\pi_{4R^2}(q)+{1\over2}\log{\pi\over2}+{3\over4}.\end{aligned}$$ Taking the infimum of the above over $q$ yields $$\begin{aligned}
\eta_R(a_1,a_2)&\le&\eta_{4R^2}(x^*x)
+{1\over2}\log{\pi\over2}+{3\over4} \\
&=&\chi(x^*x)+{1\over2}\log{\pi\over2}+{3\over4}\end{aligned}$$ by Proposition \[P-4.2\] thanks to $4R^2\ge\|x^*x\|$, completing the proof.
\[C-5.2\] If $x\in\cM$ and $\chi(x^*x)=-\infty$ (in particular, this is the case if ${\rm ker}\,x\ne\{0\}$), then $$\eta(a_1,a_2)=\chi(a_1,a_2)=-\infty.$$
[[*Proof.*]{}]{}Since $$\chi(a_1,a_2)\le\chi(x^*x)+{1\over2}\log{\pi\over2}+{3\over4}=-\infty$$ by [@HP1 6.6.3], Theorem \[T-5.1\] gives the conclusion.
\[C-5.3\] If $x=a_1+ia_2$ with $a_1,a_2\in\cM^{sa}$ is $R$-diagonal and $R\ge\|x\|$, then $$\eta(a_1,a_2)=\eta_R(a_1,a_2)=\chi(a_1,a_2).$$
[[*Proof.*]{}]{}By Corollary \[C-5.2\] we may assume ${\rm ker}\,x=\{0\}$; then $x$ admits the polar decomposition as mentioned in the first paragraph of this section. By Theorem \[T-5.1\], $$\eta_R(a_1,a_2)\le\eta(a_1,a_2)
\le\chi(x^*x)+{1\over2}\log{\pi\over2}+{3\over4}.$$ But, it is known (see [@HP1 6.6.8] and [@NSS]) that $$\chi(a_1,a_2)=\chi_R(a_1,a_2)
=\chi(x^*x)+{1\over2}\log{\pi\over2}+{3\over4}.$$ Since $\chi_R(a_1,a_2)\le\eta_R(a_1,a_2)$ by Theorem \[T-4.5\](1), we have the conclusion.
Modified quantity $\tilde\eta(a_1,\dots,a_N)$
=============================================
Although the free entropy-like quantity $\eta(a_1,\dots,a_N)$ is different from $\chi(a_1,\dots,a_N)$ as mentioned in Remark \[R-4.6\], it is a natural one from the viewpoint of “free variational principle." In this section we introduce a modified version of $\eta(a_1,\dots,a_N)$, which is shown to coincide with $\chi(a_1,\dots,a_N)$ in general. For each $R>0$ we consider the minimal $C^*$-tensor product $\cA_R^{(N)}\otimes_\min\cA_R^{(N)}$, whose norm is denoted by $\|\cdot\|_{R,\min}$. The algebraic tensor product $\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>$ is naturally considered as a (dense) $*$-subalgebra of $\cA_R^{(N)}\otimes_\min\cA_R^{(N)}$. Let $a_1,\dots,a_N$ be selfadjoint operators in $B(\cH)$. For $q(X_1,\dots,X_N)=\sum c_{i_1\dots i_k,j_1\dots j_l}
X_{i_1}\cdots X_{i_k}\otimes X_{j_1}\cdots X_{j_l}$ in $\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>$, we define $$q(a_1,\dots,a_N):=\sum c_{i_1,\cdots i_k,j_1\cdots j_l}
a_{i_1}\cdots a_{i_k}\otimes a_{j_1}\cdots a_{j_l}
\in\cA_R^{(N)}\otimes_\min\cA_R^{(N)}.$$ When $\|a_i\|\le R$, since the functional calculus $h(a_1,\dots,a_N)$ for $h\in\cA_R^{(N)}$ is a $*$-homomorphism of $\cA_R^{(N)}$ into $B(\cH)$ (see Section 2), one can define the tensor product $*$-homomorphism $\Phi\otimes\Phi:\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\to
B(\cH)\overline\otimes B(\cH)=B(\cH\otimes\cH)$. We denote $(\Phi\otimes\Phi)(g)$ by $g(a_1,\dots,a_N)$ for $g\in\cA_R^{(N)}\otimes_\min\cA_R^{(N)}$. This extends $q(a_1,\dots,a_N)$ above for $q\in\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>$.
\[D-6.1\][For each $R>0$ and $g\in\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$ define $$\begin{aligned}
&&\pi_R^{(2)}(g):=\limsup_{n\to\infty}\Biggl({1\over n^2}
\log\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
(\tr_n\otimes\tr_n)(g(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\hskip10cm+{N\over2}\log n\Biggr).\end{aligned}$$ ]{}
Properties of $\pi_R^{(2)}(g)$ is similar to those of $\pi_R(h)$ in Proposition \[P-2.3\]; for example,
- $\pi_R^{(2)}(g)$ is convex on $\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$,
- $|\pi_R^{(2)}(g_1)-\pi_R^{(2)}(g_2)|\le\|g_1-g_2\|_{R,\min}$ for all $g_1,g_2\in\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$.
\[D-6.2\][Let $\Sigma^{(2)}\<X_1,\dots,X_N\>$ denote the set of selfadjoint linear functionals $\nu$ on $\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>$ such that $\nu(\1)=1$. For each $R>0$ and $\nu\in\Sigma^{(2)}\<X_1,\dots,X_N\>$ define $$\eta_R^{(2)}(\nu):=\inf\bigl\{\nu(q)+\pi_R^{(2)}(q):
q\in(\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>)^{sa}\bigr\}.$$ ]{}
One can see as Lemma \[L-3.3\] that if $\nu\in\Sigma^{(2)}\<X_1,\dots,X_N\>$ and $\eta_R^{(2)}(\nu)>-\infty$, then $\nu\in\cT\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)$, that is, $\nu$ (uniquely) extends to a tracial state on $\cA_R^{(N)}\otimes_\min\cA_R^{(N)}$. Hence the essential domain of $\eta^{(2)}$ is included in $\cT\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)$. Furthermore, as in Theorem \[T-3.4\], $\pi_R^{(2)}(g)$ for $g\in\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$ and $\eta_R^{(2)}(\nu)$ for $\nu\in\cT\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)$ are the Legendre transforms of each other with respect to the Banach space duality between $\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$ and the selfadjoint part of $\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^*$.
\[D-6.3\][For each $a_1,\dots,a_N\in\cM^{sa}$ define $$\tilde\eta_R(a_1,\dots,a_N)
:=\eta_R^{(2)}(\mu_{(a_1,\dots,a_N)}\otimes\mu_{(a_1,\dots,a_N)}),$$ where $\mu_{(a_1,\dots,a_N)}\in\Sigma\<X_1,\dots,X_N\>$ was given in Definition \[D-4.1\] and $\mu_{(a_1,\dots,a_N)}\otimes\mu_{(a_1,\dots,a_N)}$ is an element of $\Sigma^{(2)}\<X_1,\dots,X_N\>$ defined by the algebraic tensor product of $\mu_{(a_1,\dots,a_N)}$ and itself. Furthermore, define $$\tilde\eta(a_1,\dots,a_N):=\sup_{R>0}\tilde\eta_R(a_1,\dots,a_N).$$ ]{}
Note that if $R\ge\max_i\|a_i\|$, then $\mu_{(a_1,\dots,a_N)}\in\cT\bigl(\cA_R^{(N)}\bigr)$ and so $\mu_{(a_1,\dots,a_N)}\otimes\mu_{(a_1,\dots,a_N)}\in
\cT\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)$.
\[T-6.4\] For every $a_1,\dots,a_N\in\cM^{sa}$ and $R>0$, $$\eta_R(a_1,\dots,a_N)\ge\tilde\eta_R(a_1,\dots,a_N)
=\chi_R(a_1,\dots,a_N),$$ $$\eta(a_1,\dots,a_N)\ge\tilde\eta(a_1,\dots,a_N)
=\chi(a_1,\dots,a_N).$$
[[*Proof.*]{}]{}By Theorem 4.5(1) it is enough to prove $\tilde\eta_R=\chi_R$. (A direct proof of $\eta_R\ge\tilde\eta_R$ is also easy from definition.) For each $q\in(\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>)^{sa}$ notice that $$(\mu_{(a_1,\dots,a_N)}\otimes\mu_{(a_1,\dots,a_N)})(q)
=(\tau\otimes\tau)(q(a_1,\dots,a_N))$$ is a polynomial (of at most order $2$) of mixed moments $\tau(a_{i_1}\cdots a_{i_k})$ with $k\le K$ for some $K\in\bN$. This is same for $(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))$ with $A_1,\dots,A_N\in M_n^{sa}$. Thus, for any $\delta>0$, one can choose $r\in\bN$ and $\eps>0$ such that, for each $n\in\bN$, if $(A_1,\dots,A_N)\in\Gamma_R(a_1,\dots,a_N;n,r,\eps)$ then $$\big|(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))
-(\tau\otimes\tau)(q(a_1,\dots,a_N))\big|<\delta.$$ Then, the proof of $\tilde\eta_R(a_1,\dots,a_N)\ge\chi_R(a_1,\dots,a_N)$ is the same as in the proof of Theorem \[T-4.5\](1).
To prove the converse inequality, let $\alpha>\chi_R(a_1,\dots,a_N)$ and $\beta>0$. There exist $r\in\bN$ and $\eps>0$ such that $$\limsup_{n\to\infty}\biggl({1\over n^2}\log\Lambda_n^{\otimes N}
\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr)+{N\over2}\log n\biggr)<\alpha.$$ Set $$I:=\{(i_1,\dots,i_k):1\le i_1,\dots,i_k\le N,\ 1\le k\le r\}$$ and define $q\in(\bC\<X_1,\dots,X_N\>\otimes\bC\<X_1,\dots,X_N\>)^{sa}$ by $$\begin{aligned}
&&q(X_1,\dots,X_N) \\
&&\quad:={\beta\over\eps^2}\sum_{(i_1,\dots,i_k)\in I}
\bigl(X_{i_1}\cdots X_{i_k}-\tau(a_{i_1}\cdots a_{i_k})\1\bigr)\otimes
\bigl(X_{i_1}\cdots X_{i_k}-\tau(a_{i_1}\cdots a_{i_k})\1\bigr)^*.\end{aligned}$$ We notice $(\tau\otimes\tau)(q(a_1,\dots a_N))=0$ and $$(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))
={\beta\over\eps^2}\sum_{(i_1,\dots,i_k)\in I}
\big|\tr_n(A_{i_1}\cdots A_{i_k})-\tau(a_{i_1}\cdots a_{i_k})\big|^2$$ for $A_1,\dots,A_N\in M_n^{sa}$. Since $$(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))\ge\beta
\quad\mbox{if $(A_1,\dots,A_N)\not\in
\Gamma_R(a_1,\dots,a_N;n,r,\eps)$},$$ we get $$\begin{aligned}
&&\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\qquad\le\Lambda_n^{\otimes N}\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)
\bigr)+e^{-n^2\beta}\Lambda_n^{\otimes N}\bigl((M_n^{sa})_R^N\bigr)\end{aligned}$$ so that $$\begin{aligned}
&&\Biggl(\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2(\tr_n\otimes\tr_n)
(q(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N}\Biggr)^{1/n^2} \\
&&\qquad\le\Bigl(\Lambda_n^{\otimes N}
\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr)\Bigr)^{1/n^2}
+e^{-\beta}\Bigl(\Lambda_n^{\otimes N}
\bigl((M_n^{sa})_R^N\bigr)\Bigr)^{1/n^2}.\end{aligned}$$ Since $$\limsup_{n\to\infty}n^{N/2}\Bigl(\Lambda_n^{\otimes N}
\bigl(\Gamma_R(a_1,\dots,a_N;n,r,\eps)\bigr)\Bigr)^{1/n^2}
\le e^\alpha$$ and $$\begin{aligned}
\lim_{n\to\infty}n^{N/2}\Bigl(\Lambda_n^{\otimes N}
\bigl((M_n^{sa})_R^N\bigr)\Bigr)^{1/n^2}
&=&\lim_{n\to\infty}\Bigl(n^{1/2}\Bigl(\Lambda_n
\bigl((M_n^{sa})_R\bigr)\Bigr)^{1/n^2}\Bigr)^N \\
&=&\Bigl(R(\pi/2)^{1/2}e^{3/4}\Bigr)^N\end{aligned}$$ (see [@HP1 §5.6]), we have $$\begin{aligned}
&&\limsup_{n\to\infty}n^{N/2}\Biggl(\int_{(M_n^{sa})_R^N}
\exp\bigl(-n^2(\tr_n\otimes\tr_n)(q(A_1,\dots,A_N))\bigr)
\,d\Lambda_n^{\otimes N}\Biggr)^{1/n^2} \\
&&\qquad\le e^\alpha+e^{-\beta}
\Bigl(R(\pi/2)^{1/2}e^{3/4}\Bigr)^N\end{aligned}$$ so that $$\pi_R^{(2)}(q)\le\alpha+\log\Bigl(1+e^{-\alpha-\beta}
\Bigl(R(\pi/2)^{1/2}e^{3/4}\Bigr)^N\Bigr).$$ Since $(\tau\otimes\tau)(q(a_1,\dots,a_N))=0$, this implies that $$\tilde\eta_R(a_1,\dots,a_N)
\le\alpha+\log\Bigl(1+e^{-\alpha-\beta}
\Bigl(R(\pi/2)^{1/2}e^{3/4}\Bigr)^N\Bigr).$$ Letting $\beta\to+\infty$ and then $\alpha\searrow\chi_R(a_1,\dots,a_N)$ we obtain $\tilde\eta_R(a_1,\dots,a_N)\le\chi_R(a_1,\dots,a_N)$, completing the proof.
Some known properties of $\chi(a_1,\dots,a_N)$ may be shown based on Theorem \[T-6.4\]. For instance, the change of variable formulas in [@V2; @V4] can be proven for $\tilde\eta(a_1,\dots,a_N)$ in a bit more easily than for $\chi(a_1,\dots,a_N)$.
Gibbs ensemble asymptotics
==========================
For each $R>0$ and $n\in\bN$ we define the “micro" pressure function $P_{R,n}(h)$ for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ by $$P_{R,n}(h):=\log\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
\tr_n(h(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N}(A_1,\dots,A_N).$$ This is nothing but the usual (classical) pressure of the continuous function $n^2\tr_n(h(A_1,\dots,A_N))$ on $(M_n^{sa})_R^N$. The definition is $$\label{F-7.1}
\pi_R(h)=\limsup_{n\to\infty}\biggl({1\over n^2}P_{R,n}(h)
+{N\over2}\log n\biggr)
\quad\mbox{for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$}.$$ For each $h_0\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ we define the Gibbs probability measure $\lambda_{R,n}^{h_0}$ on $(M_n^{sa})_R^N$ corresponding to the function $n^2\tr_n(h_0(A_1,\dots,A_N))$ by $$\begin{aligned}
d\lambda_{R,n}^{h_0}(A_1,\dots,A_N)
&:=&{1\over Z_{R,n}^{h_0}}\exp\bigl(-n^2
\tr_n(h_0(A_1,\dots,A_N))\bigr) \\
&&\qquad\quad\times\chi_{(M_n^{sa})_R^N}(A_1,\dots,A_N)
\,d\Lambda_n^{\otimes N}(A_1,\dots,A_N),\end{aligned}$$ where the normalization constant $Z_{R,n}^{h_0}:=\exp\bigl(P_{R,n}(h_0)\bigr)$. Furthermore, we define $$\mu_{R,n}^{h_0}(h):=\int_{(M_n^{sa})_R^N}
\tr_n(h(A_1,\dots,A_N))\,d\lambda_{R,n}^{h_0}(A_1,\dots,A_N)
\quad\mbox{for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$}.$$ It is immediate to see that $\mu_{R,n}^{h_0}\in\cT\bigl(\cA_R^{(N)}\bigr)$. The next lemma is elementary and well known.
\[L-7.1\] With the above definitions, the function $P_{R,n}$ is convex on $\bigl(\cA_R^{(N)}\bigr)^{sa}$ and differentiable at any $h_0\in\bigl(\cA_R^{(N)}\bigr)^{sa}$. The supporting function of $P_{R,n}$ at $h_0$ is $$-n^2\mu_{R,n}^{h_0}(h)+S(\lambda_{R,n}^{h_0}),
\qquad h\in\bigl(\cA_R^{(N)}\bigr)^{sa},$$ where $S(\lambda_{R,n}^{h_0})$ is the Boltzmann-Gibbs entropy: $$S(\lambda_{R,n}^{h_0}):=-\int_{(M_n^{sa})_R^N}
{d\lambda_{R,n}^{h_0}\over d\Lambda_n^{\otimes N}}
\log{d\lambda_{R,n}^{h_0}\over d\Lambda_n^{\otimes N}}
\,d\Lambda_n^{\otimes N}.$$
\[P-7.2\] Let $h_0\in\cA_R^{sa}$.
- There exists an equilibrium tracial state $\mu_0\in\cT\bigl(\cA_R^{(N)}\bigr)$ associated with $h_0$ such that $$\liminf_{n\to\infty}\biggl(
{1\over n^2}S(\lambda_{R,n}^{h_0})+{N\over2}\log n\biggr)
\le\eta_R(\mu_0)\le\limsup_{n\to\infty}\biggl(
{1\over n^2}S(\lambda_{R,n}^{h_0})+{N\over2}\log n\biggr).$$
- Assume that the limit $$\pi_R(h_0)=\lim_{n\to\infty}\biggl(
{1\over n^2}P_{R,n}(h_0)+{N\over2}\log n\biggr)$$ exists. Then any limit point of the sequence $\bigl\{{1\over n^2}S(\lambda_{R,n}^{h_0})+{N\over2}\log n\bigr\}$ is attained as the value $\eta_R(\mu_0)$ of some equilibrium tracial state $\mu_0$ associated with $h_0$. In particular, if $\mu_0$ is a unique equilibrium tracial state associated with $h_0$, then $$\label{F-7.2}
\eta_R(\mu_0)=\lim_{n\to\infty}\biggl(
{1\over n^2}S(\lambda_{R,n}^{h_0})+{N\over2}\log n\biggr).$$
[[*Proof.*]{}]{}(1)First, note that $\cT\bigl(\cA_R^{(N)}\bigr)$ is a compact metrizable space in the weak\* topology. Hence, there exists a subsequence $\{n(k)\}$ of $\{n\}$ such that $$\pi_R(h_0)=\lim_{k\to\infty}\biggl({1\over n(k)^2}
P_{R,n(k)}(h_0)+{N\over2}\log n(k)\biggr)$$ and $\mu_{R,n(k)}^{h_0}$ weakly\* converges to some $\mu_0\in\cT\bigl(\cA_R^{(N)}\bigr)$. By Lemma \[L-7.1\] we get $$\begin{aligned}
\mu_0(h_0)+\pi_R(h_0)
&=&\lim_{k\to\infty}\biggl(\mu_{R,n(k)}^{h_0}(h_0)
+{1\over n(k)^2}P_{R,n(k)}(h_0)+{N\over2}\log n(k)\biggr) \\
&=&\lim_{k\to\infty}\biggl({1\over n(k)^2}
S(\lambda_{R,n(k)}^{h_0})+{N\over2}\log n(k)\biggr)\end{aligned}$$ and for every $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ $$\begin{aligned}
\mu_0(h)+\pi_R(h)
&=&\lim_{k\to\infty}\mu_{R,n(k)}^{h_0}(h)
+\limsup_{n\to\infty}\biggl({1\over n^2}P_{R,n}(h)
+{N\over2}\log n\biggr) \\
&\ge&\limsup_{k\to\infty}\biggl(\mu_{R,n(k)}^{h_0}(h)
+{1\over n(k)^2}P_{R,n(k)}(h)+{N\over2}\log n(k)\biggr) \\
&\ge&\lim_{k\to\infty}\biggl({1\over n(k)^2}
S(\lambda_{R,n(k)}^{h_0})+{N\over2}\log n(k)\biggr)
=\mu_0(h_0)+\pi_R(h_0).\end{aligned}$$ By Theorem \[T-3.4\](1) this implies that $\mu_0$ is an equilibrium tracial state associated with $h_0$ and $\eta_R(\mu_0)=\mu_0(h_0)+\pi_R(h_0)$. Hence we have the conclusion.
(2)Let $\{n(k)\}$ be a subsequence of $\{n\}$ for which the limit $$\alpha:=\lim_{k\to\infty}\biggl({1\over n(k)^2}S(\lambda_{R,n(k)}^{h_0})
+{N\over2}\log n(k)\biggr)$$ exists. We may assume that $\mu_{R,n(k)}^{h_0}\to\mu_0$ weakly\* for some $\mu_0\in\cT\bigl(\cA_R^{(N)}\bigr)$. Then, as in the proof of (1), we get $\mu_0(h_0)+\pi_R(h_0)=\alpha\le\mu_0(h)+\pi_R(h)$ for all $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$, and the result follows.
Although the formula has been shown under the existence of limit in the definition of $\pi_R(h_0)$ as well as the strong assumption of unique equilibrium, the above proposition provides the noncommutative multivariate version of the property (IV) in Section 1. The existence of limit of this kind seems one of the major questions in random matrix theory, and recently a similar limit behavior has been investigated by A. Guionnet [@Gu] for several particular noncommuting polynomials of interest.
To get rid of the convergence problem, we are tempted to introduce the free pressure by using the limit via a ultrafilter, as Voiculescu defined the free entropy $\chi^\omega$ in [@Va]. Let $\omega$ be a fixed free ultrafilter, i.e., $\omega\in\beta\bN\setminus\bN$. Since the inside of the $\limsup$ in is a bounded sequence, we can define $$\pi_R^\omega(h):=\lim_{n\to\omega}\biggl(
{1\over n^2}P_{R,n}(h)+{N\over2}\log n\biggr)$$ for each $R>0$ and $h\in\cA_R^{sa}$. Then $\pi_R^\omega$ has the same properties as $\pi_R$, and we define its Legendre transform with respect to the duality between $\bigl(\cA_R^{(N)}\bigr)^{sa}$ and $\bigl(\cA_R^{(N)}\bigr)^{*,sa}$ by $$\eta_R^\omega(\mu):=\inf\bigl\{\mu(h)+\pi_R^\omega(h):
h\in\bigl(\cA_R^{(N)}\bigr)^{sa}\bigr\}
\quad\mbox{for $\mu\in\bigl(\cA_R^{(N)}\bigr)^{*,sa}$}.$$ As before we have $\eta_R^\omega(\mu)=-\infty$ unless $\mu\in\cT\bigl(\cA_R^{(N)}\bigr)$ and $$\pi_R^\omega(h)=\sup\bigl\{-\mu(h)+\eta_R^\omega(\mu):
\mu\in\cT\bigl(\cA_R^{(N)}\bigr)\bigr\}
\quad\mbox{for $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$}.$$ Similarly, we define for $g\in\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)^{sa}$ $$\begin{aligned}
&&\pi_R^{(2)}(g):=\limsup_{n\to\omega}\Biggl({1\over n^2}
\log\int_{(M_n^{sa})_R^N}\exp\bigl(-n^2
(\tr_n\otimes\tr_n)(g(A_1,\dots,A_N))\bigr)\,d\Lambda_n^{\otimes N} \\
&&\hskip10cm+{N\over2}\log n\Biggr).\end{aligned}$$ and for $\nu\in\cT\bigl(\cA_R^{(N)}\otimes_\min\cA_R^{(N)}\bigr)$ $$\eta_R^{(2),\omega}(\nu):=\inf\bigl\{\nu(h)+\pi_R^{(2),\omega}(h):
h\in(\cA_R\otimes\cA_R^{op})^{sa}\bigr\}.$$ Furthermore, for each $a_1,\dots,a_N\in\cM^{sa}$ define $$\begin{aligned}
\eta_R^\omega(a_1,\dots,a_N)&:=&\eta_R^\omega(\mu_{(a_1,\dots,a_M)}), \\
\eta^\omega(a_1,\dots,a_N)&:=&\sup_{R>0}\eta_R^\omega(a_1,\dots,a_N), \\
\tilde\eta_R^\omega(a_1,\dots,a_N)&:=&
\eta_R^{(2),\omega}(\mu_{(a_1,\dots,a_N)}\otimes\mu_{(a_1,\dots,a_N)}), \\
\tilde\eta^\omega(a_1,\dots,a_N)&:=&
\sup_{R>0}\tilde\eta_R^\omega(a_1,\dots,a_N).\end{aligned}$$
The next proposition can be shown as Theorems \[T-4.5\] and \[T-6.4\].
\[P-7.3\] For every $a_1,\dots,a_N\in\cM^{sa}$ and $R>0$, $$\eta_R^\omega(a_1,\dots,a_N)\ge\tilde\eta_R^\omega(a_1,\dots,a_N)
=\chi_R^\omega(a_1,\dots,a_N),$$ $$\eta^\omega(a_1,\dots,a_N)\ge\tilde\eta^\omega(a_1,\dots,a_N)
=\chi^\omega(a_1,\dots,a_N).$$
\[P-7.4\] Let $h_0\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ and define $$\mu_{R,\omega}^{h_0}(h):=\lim_{n\to\omega}\mu_{R,n}^{h_0}(h),
\qquad h\in\bigl(\cA_R^{(N)}\bigr)^{sa}.$$ Then $\mu_{R,\omega}^{h_0}$ is an equilibrium tracial state associated with $h_0$ in the sense that $$\pi_R^\omega(h_0)=-\mu_{R,\omega}^{h_0}(h_0)
+\eta_R^\omega(\mu_{R,\omega}^{h_0}).$$ Moreover, $$\eta_R^\omega(\mu_{R,\omega}^{h_0})=\lim_{n\to\omega}\biggl(
{1\over n^2}S(\lambda_{R,n}^{h_0})+{N\over2}\log n\biggr).$$
[[*Proof.*]{}]{}It is immediate to see that $\mu_{R,\omega}^{h_0}\in\cT\bigl(\cA_R^{(N)}\bigr)$. By Lemma \[L-7.1\] we get for every $h\in\bigl(\cA_R^{(N)}\bigr)^{sa}$ $$\begin{aligned}
\mu_{R,\omega}^{h_0}(h)+\pi_R^\omega(h)
&=&\lim_{n\to\omega}\biggl(\mu_{R,n}^{h_0}(h)+{1\over n^2}
P_{R,n}(h)+{N\over2}\log n\biggr) \\
&\ge&\lim_{n\to\omega}\biggl({1\over n^2}S(\lambda_{R,n}^{h_0})
+{N\over2}\log n\biggr) \\
&=&\mu_{R,\omega}^{h_0}(h_0)+\pi_R^\omega(h_0).\end{aligned}$$ This implies the conclusion.
Finally, it is worth noting that the Gibbs ensemble asymptotics (or random matrix approximation) provides a useful tool to obtain free probabilistic analogs of classical problems. For example, the free transportation cost inequality established by Ph. Biane and D. Voiculescu [@BV] in case of single variables was re-proven in [@HPU] by using this tool, and the multivariate case will be discussed in our forthcoming paper.
[99]{}
Ph. Biane and D. Voiculescu, A free probabilistic analogue of the Wasserstein metric on the trace-state space, [*Geom. Funct. Anal.*]{} [**11**]{} (2001), 1125–1138.
O. Bratteli and D. W. Robinson [*Operator Algebras and Quantum Statistical Mechanics 2*]{}, Second edition, Springer-Verlag, Berlin-Heidelberg, 1997.
N. P. Brown, Invariant means and finite representation theory of $C^*$-algebras, Preprint, 2003.
N. Dunford and J. T. Schwartz, [*Linear Operators, Part I: General Theory*]{}, Interscience, New York, 1958.
I. Ekeland and R. Temam, [*Convex Analysis and Variational Problems*]{}, North-Holland, Amsterdam-Oxford, 1976.
A. Guionnet, First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models, Preprint, 2002.
F. Hiai, Free relative entropy and $q$-deformation theory, in: [*Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads*]{}, N. Obata et al. (eds.), QP-PQ, Vol. 16, World Scientific, 2002, pp. 97–142.
F. Hiai, M. Mizuo and D. Petz, Free relative entropy for measures and a corresponding perturbation theory, [*J. Math. Soc. Japan*]{} [**54**]{} (2002), 679–718.
F. Hiai and D. Petz, [*The Semicircle Law, Free Random Variables and Entropy*]{}, Mathematical Surveys and Monographs, Vol. 77, Amer. Math. Soc., Providence, 2000.
F. Hiai, D. Petz and Y. Ueda, Free transportation cost inequalities via random matrix approximation, [*Probab. Theory Related Fields*]{}, to appear.
R. B. Israel, [*Convexity in the Theory of Lattice Gases*]{}, Princeton Univ. Press, Princeton, 1979.
A. Nica, D. Shlyakhtenko and R. Speicher, Maximality of the microstates free entropy for $R$-diagonal elements, [*Pacific J. Math.*]{} [**187**]{} (1999), 333–347.
A. Nica and R. Speicher, $R$-diagonal pairs - a common approach to Haar unitaries and circular elements, in [*Free Probability Theory*]{}, D.V. Voiculescu (ed.), Fields Inst. Commun. [**12**]{}, Amer. Math. Soc, 1997, pp. 149–188.
E. B. Saff and V. Totik, [*Logarithmic Potentials with External Fields*]{}, Springer-Verlag, Berlin-Heidelberg-New York, 1997.
D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory, I, [*Comm. Math. Phys.*]{} [**155**]{} (1993), 71–92.
D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory, II, [*Invent. Math.*]{} [**118**]{} (1994), 411–440.
D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory III: The absence of Cartan subalgebras, [*Geom. Funct. Anal.*]{} [**6**]{} (1996), 172–199.
D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory, IV: Maximum entropy and freeness, in [*Free Probability Theory*]{}, D.V. Voiculescu (ed.), Fields Inst. Commun. [**12**]{}, Amer. Math. Soc., 1997, pp. 293–302.
D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory, V, Noncommutative Hilbert transforms, [*Invent. Math.*]{} [**132**]{} (1998), 189–227.
D. Voiculescu, A strengthened asymptotic freeness result for random matrices with applications to free entropy, [*Internat. Math. Res. Notices*]{} [**1998**]{}, 41–63.
[^1]: $^1\,$Supported in part by Grant-in-Aid for Scientific Research (C)14540198 and by the program “R&D support scheme for funding selected IT proposals" of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.
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All New MKast and Developer's Blog Now Live on Worldscollide.com
October 24, 2008
All New MKast and Developer's
Blog Now Live on Worldscollide.com
This Week's MKast Features Mortal
Kombat Team Members, Steve Beran and Dave Pindara
Today, Midway announced that the
next episode of MKast, the official Mortal Kombat podcast, is now live at
www.worldscollide.com
along with an all new Developer's Blog. This week's MKast has Art Director,
Steve Beran and Dave Pindara, Technical Art and Environment Lead, joining Hans
and Hector in the sound booth to discuss their involvement within the Mortal
Kombat vs. DC Universe project. In the latest Developer's Blog, Hector focuses
on the new Kombo Challenge Mode and its significance to Trophies and
Achievements found in Mortal Kombat vs. DC Universe. With the MKast and the
Developer's Blog, enthusiasts and fans alike can stay up-to-date on the latest
news and updates for Mortal Kombat vs. DC Universe.
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699 F.Supp. 1119 (1988)
Richard BARANOWSKI and B.E.S. Environmental Specialists, Inc.
v.
The ENVIRONMENTAL PROTECTION AGENCY and Lee M. Thomas, Administrator, Environmental Protection Agency and Harvey G. Pippen, Jr., Director, EPA Grants Administration Division and John C. Martin, EPA Inspector General and P. Ronald Gandolfo, EPA Divisional Inspector General for Audit.
Civ. A. No. 88-8359.
United States District Court, E.D. Pennsylvania.
November 23, 1988.
*1120 Gregory T. Magarity, Wolf, Block, Schorr and Solis Cohen, Philadelphia, Pa., by Nancy Ezold, for plaintiffs.
Catherine L. Votaw, Asst. U.S. Atty., Philadelphia, Pa., for defendants.
FINDINGS OF FACT AND CONCLUSIONS OF LAW
KATZ, District Judge.
FINDINGS OF FACT
1. Plaintiff B.E.S. Environmental Specialists, Inc. ("BES") is a large contractor under the Superfund program.
2. Plaintiff Richard Baranowski is an officer of BES.
3. On September 30, 1988, EPA issued a subpoena to BES, seeking the production of cost records in connection with an audit of specified contracts between BES and EPA, and of all delivery orders awarded to BES under a contract between EPA and another EPA clean-up contractor. The subpoena was issued because plaintiffs had been stonewalling EPA's audit efforts. The Assistant U.S. Attorney recommended enforcement proceedings.
4. Plaintiff BES did not comply with this subpoena.
5. On September 29, 1988, EPA had issued Notices of Proposed Disbarment to BES and Baranowski. These Notices suspended plaintiffs from further contracting with EPA, and gave plaintiffs 30 days to submit information against the proposed debarment.
6. Plaintiffs did not exercise their right to submit materials opposing the proposed debarment.
7. On October 31, 1988, plaintiffs filed this suit, with a motion for preliminary injunction in which they asked the Court to enjoin defendants from (1) conducting audits contemplated by the subpoena, (2) continuing the suspension and (3) continuing the debarment process.
8. In April, 1987, a federal grand jury indicted BES and Baranowski on seven counts of making false claims and false statements against the United States, in connection with BES's contract to clean up a Superfund site in Berks County, Pennsylvania called the Brown's Battery Breaking site. After a non-jury trial, the district court acquitted BES and Baranowski of all the criminal charges.
9. The subpoena decision was made by Deputy Inspector General Anna Virbick, upon the request of Divisional Inspector General for Audits P. Ronald Gandolfo, with the background memorandum of James Clark, an attorney with EPA's Office of General Counsel, Inspector General Division. The agent in the criminal case, Martin Squitieri, now Divisional Inspector General for Investigations, did not participate *1121 in the decision to issue the September 30, 1988 subpoena to BES.
10. The documents listed in the September 30, 1988 subpoena are necessary for the proper conduct of an audit.
11. The scope of the subpoena is reasonable in light of the agency's purpose to protect the taxpayers' investment in the Superfund program. The subpoena seeks documents which are relevant to this purpose.
12. Although some burden is necessarily imposed by complying with the subpoena, the subpoena at issue is not unduly broad or burdensome. EPA also eased any burden by permitting production at BES's offices instead of EPA's offices, and by seeking to audit only completed contracts.
13. The burden on the contractor must be evaluated in view of the fact that BES entered into the contracts which permit the agency access to the records in question.
14. EPA's Office of Inspector General issued the September 30, 1988 subpoena for several reasons. First, the criminal charges and transcript of the criminal trial revealed problems of concern to EPA. Second, BES is a large and important EPA contractor under the Superfund program. Third, BES had refused to comply with its contractual obligation to produce records.
15. The subpoena was not the product of individual or institutional vindictiveness or retaliation.
16. The prior audits were not in depth, and did not take into account the record of the criminal trial.
17. There is a reasonable basis for the agency to allege "special circumstances, such as indications of fraud" in light of the criminal transcript and exhibits as described at the hearing. Whether the administrative record will support any such finding is another matter, which must await development of a full record at an administrative hearing.
18. BES has not received final payment on the Brown's Battery contract. BES has a contractual obligation to produce the records starting three years following final payment on the contract.
19. The Director of the Grants Administration Division (the "Director") is EPA's debarring official. The Director is the only EPA official who has the authority to debar or suspend a contractor or to issue a notice proposing a debarment or suspension.
20. The Director initiates a debarment proceeding by sending a notice of proposed debarment to the respondent.
21. EPA afforded BES an opportunity for a hearing.
22. Based on the hearing and the entire administrative record, the debarring official makes a decision. This decision must be made within 30 days after the hearing or receipt of the respondent's written information unless the debarring official extends this period for good cause.
23. A notice of proposed debarment precludes the issuing agency from awarding contracts to the respondent pending resolution of the debarment proceeding. The notices contain a statement to this effect.
24. The agency debarring official and hearing officer serve as neutral fact-finders. They have their own independent legal advisor. They act independently of the views and interests of advocates of debarment in the agency.
25. On July 17, 1987, the Director issued Notices of Suspension to BES and Baranowski based on the April 14, 1987 indictment.
26. On October 13, 1987 the acquittal removed the sole basis for the suspension and it was terminated.
27. Early in 1988, Martin Squitieri, an EPA special agent in Investigations who had worked on the criminal investigation of BES and Baranowski, gave James Clark, of the Inspector General Division of the Office of the General Counsel, the transcript of the criminal trial and the trial exhibits. He also informed Mr. Clark about evidence that Mr. Baranowski had given gratuities to Thomas Massey, EPA's on-scene coordinator at the Brown's Battery site. Agent *1122 Squitieri asked Mr. Clark to study the case to determine whether some civil or administrative action would be warranted against BES or Baranowski. Mr. Clark had not participated in either the fraud or the gratuities investigations.
28. In 1988, Mr. Clark and Agent Squitieri met with Mr. Meunier, the Chief of EPA's Debarment Compliance Section, Mr. Feldman, a contracts lawyer in EPA's Office of General Counsel, and others. The persons at the meeting believed: a) in light of the evidence of various forms of misconduct on the part of Mr. Baranowski and BES, the firm did not appear to be the kind of firm that EPA wanted implementing the Superfund program; b) because BES had been acquitted, debarring the firm would be difficult; c) Mr. Clark should draft a memorandum in support of proposed debarment of BES and Baranowski; and d) the approval of the Superfund program and the Procurement and Contracts Management Division should be obtained before asking the Director to initiate any debarment action.
29. After the meeting, Mr. Clark drafted a memorandum of information ("MOI") in support of proposed debarment. The MOI alleged that BES had made fraudulent claims against EPA on the Brown's Battery job, that Mr. Baranowski had given gratuities to an EPA employee, and that BES had refused to give EPA auditors access to audit papers available under the audit access clauses of BES's contracts and subcontracts.
30. After completion of the MOI, Mr. Clark met with Mr. Meunier, Mr. Feldman, and others. Those present agreed that EPA should seek to debar BES and Baranowski.
31. After obtaining the necessary concurrences, Mr. Clark, Mr. O'Connor, and Mr. Meunier signed off the MOI and sent it to EPA's debarring official, Harvey Pippen, for his consideration.
32. On September 29, 1988, Director Harvey Pippen made an independent judgment to issue EPA's notices proposing to debar plaintiffs from receiving both federal procurement contracts and EPA assisted contracts, and attaching the MOI. The notice of proposed debarment stated that if the charges in the MOI were true, then cause for debarment existed. It provided that in accordance with 48 CFR § 9.406-3 of the Federal Acquisition Regulations (the "FAR"), EPA would not award any contracts to BES or Baranowski pending resolution of debarment notices. It also notified plaintiffs that they had thirty days in which to ask for a hearing. Mr. Clark played no role in drafting the notices of proposed debarment.
33. BES and Baranowski have not exercised their right to submit information and argument or to request an administrative hearing.
34. There are no exceptional circumstances that would justify bypassing the administrative process in this manner.
35. EPA's administrative procedures satisfy the requirements of the regulations and due process.
36. Mr. Clark, the agency attorney in this matter, played the lead role in preparing the Memorandum of Information in Support of Proposed Debarment of BES and Richard Baranowski, which was essentially the debarment complaint.
37. Mr. Pippen based his decision to issue the notices of proposed debarment to plaintiffs entirely on the Memorandum of Information in Support of Proposed Debarment of BES and Richard Baranowski.
38. The agency's notices of proposed debarment with attached MOI gave plaintiffs adequate notice of the allegations and of their procedural rights.
39. Defendants did not deny plaintiffs any information to which they are entitled.
40. EPA bears a lesser burden of proof in a debarment than the beyond a reasonable doubt standard of proof required in a criminal case.
41. Plaintiffs have not shown a probability of success on their claim to stop the debarment process. The MOI presents evidence of several instances of alleged misconduct which, if true, would be cause for debarment. Defrauding the government, *1123 giving government employees gratuities to influence their official actions, and refusing to give government auditors access to records, if proven in the administrative hearing, are each probably causes for debarment. The audit proceedings were separately pursued by the agency and were not a ruse to set up the debarment proceedings.
42. The MOI alleges that plaintiff Baranowski conspired with John Del Vecchio to boost Del Vecchio's price for supplying clay to the Brown's Battery site and to pass that fraudulently increased price on to EPA. That allegation is based on the immunized trial testimony of John Del Vecchio, testimony of other witnesses, and documentary evidence. The testimony of witnesses at the criminal trial and the trial exhibits may have probative value even though the prosecution had failed to prove plaintiffs guilty beyond a reasonable doubt.
43. BES allegedly submitted payment requests to EPA representing that it owned equipment that was actually rented and charged EPA the rate appropriate for owned equipment. Examples of these payment requests are attached to EPA's MOI.
44. EPA has some evidence (e.g., charge card records and the corporate ledger) showing that Baranowski took Mr. Massey, EPA's on-scene coordinator at the Brown's Battery site, on a Canadian vacation. Baranowski allegedly bricked in Massey's carport. There is a dispute as to whether Massey paid for the brick wall. There may be a dispute about the allegedly paid vacation.
45. The credit card records and hotel receipts are not "matters occurring before the grand jury" because they are independently created business records the disclosure of which neither compromises grand jury secrecy nor reveals the grand jury's scope or direction. Even if the credit card and hotel records and the other evidence derived from grand jury subpoenas were "matters occurring before the grand jury," the administrative proceedings are based largely on other issues, stopping the debarment would be a disproportionate sanction and the charge card records could be obtained by an administrative subpoena. Moreover, it is premature to determine whether any future debarment will even rest on any matters derived from grand jury subpoenas. The subpoena and debarment actions are based on other evidence having no relation to "matters occurring before the grand jury." The fraud charges are based on the criminal trial transcript and exhibits. The gratuity charges are based on hotel receipts, the employee's time card, the investigation in Canada, the BES general ledger which was a trial exhibit and the statements of the persons who did the brick work. The plaintiffs' failure to provide information requested during audit had nothing to do with any grand jury investigation.
46. EPA has been seeking access to records from various projects that BES has performed for EPA since March 25, 1988. BES's refusal to give agency auditors the access to these records which their contracts require could constitute a violation of the terms of a Government contract. 48 CFR § 9.406-2(b)(1); 40 CFR § 32.200(c).
47. Plaintiffs have not shown that EPA or any of its employees are engaged in an improper campaign to harass plaintiffs. EPA's subpoena and debarment actions are motivated by concern for the agency's legitimate business interests, not by any personal or institutional vendetta. EPA's debarring official is a neutral fact finder insulated from any bias on the part of other EPA employees.
48. Plaintiffs have not shown sufficient irreparable harm between now and the time their debarment case can be resolved administratively to justify the relief they seek.
49. Plaintiffs are not foreclosed from completing their multi-million dollar existing contracts with EPA nor from bidding additional contracts in the hope that BES will be eligible to receive contracts when the awards occur. The suspension incident to the debarment proceedings does not foreclose plaintiffs from dealing with Government agencies besides EPA.
*1124 50. Granting a preliminary injunction would harm the agency's orderly conduct of its business and the public interest in the responsible conduct of the agency's affairs.
CONCLUSIONS OF LAW
1. EPA has met its burden of establishing
(1) that the subpoena is within the agency's statutory authority and has a legitimate purpose.
(2) that the information sought is relevant to EPA's inquiry and necessary.
(3) that the demand is not unreasonably burdensome or broad and agency procedures have been followed.
The subpoena was not issued for an improper purpose, such as harassment, nor would its enforcement constitute an abuse of the Court's process.
2. EPA has shown that the subpoena is within the agency's statutory authority.
3. The subpoena seeks relevant information, and is not unduly broad or burdensome.
4. Defendants did not issue the subpoena for an improper purpose.
5. The subpoena should be enforced.
6. The Court lacks subject matter jurisdiction to intervene in an ongoing debarment process, absent exceptional circumstances.
7. Plaintiffs have failed to prove a reasonable probability of success on the merits of their claim that such exceptional circumstances exist.
8. Plaintiffs have failed to exhaust their administrative remedies. The administrative proceeding is not yet final.
9. Plaintiffs have not shown a probability of prevailing on their claim that EPA has denied them due process.
10. Plaintiffs have not shown a probability of success on their claims that the suspension was not adequately founded.
11. Plaintiffs have not shown that EPA's debarment activities were improperly motivated.
12. Plaintiffs have not shown sufficient irreparable harm if the preliminary injunction is denied to justify the relief sought.
13. The equities favor denying the requested injunctive relief. No exceptional circumstances exist to justify disruption of the administrative processes.
ORDER
AND NOW, this 23rd day of November, 1988, after a hearing, plaintiff's motion for preliminary injunction is DENIED and defendants' motion to enforce the September 30, 1988 subpoena is GRANTED. Plaintiffs shall furnish EPA with the documents specified in the September 30, 1988 subpoena within 15 days or later date as the Inspector General shall establish.
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Baltimore police have arrested Anita Jones (pictured) after they say she fatally stabbed her husband inside John Hopkins Hospital
Baltimore police have arrested a woman they say fatally stabbed her husband inside John Hopkins Hospital in Baltimore.
Police arrested 30-year-old Anita Jones on Saturday and charged her with first-degree murder stemming from the stabbing death of 33-year-old Christopher Yancey.
On Friday, police in Baltimore said a man was found dead of multiple stab wounds in his young son's room at the hospital.
Police spokesman T.J. Smith said in a statement that officers were called to the room at around 2.30pm after hearing reports of a disturbance.
Smith commented that the man was in his son's room with the boy's mother.
Their 14-year-old son was there to undergo a minor medical procedure. The stabbing occurred when the boy's parents were left in a private room alone together.
When they arrived hospital staff told them that Jones and Yancey had been arguing in a room.
Christopher Yancey, 33, was found stabbed to death inside the hospital Friday afternoon
Jones then came out and told staff that Yancey had cut himself. Staff members found Yancey suffering from multiple lacerations. He was pronounced dead. Jones left the hospital before officers arrived.
Police say no weapon was found in the hospital room, and Yancey's injuries were determined to be inconsistent with suicide.
Police spokesman T.J. Smith (picturerd) said that officers were called to the room at around 2.30pm
Smith says the man was stabbed in the upper body.
The hospital said in a statement that the stabbing was an isolated incident.
'We would like to extend our deepest sympathies to the family of the deceased,' Johns Hopkins Hospital spokeswoman Kim Hoppe said.
Since this is a police investigation, we must defer all inquiries to them,' she added.
Friday's killing marked Baltimore's 281st homicide in Baltimore in 2017, a record for the city.
The world-renown hospital has been at the epicenter of violent events within its parameters before.
The most-notable incident occurred in 2010, when a Virginia man entered the hospital and shot his mother’s doctor, killed his mother and then killed himself, according to The Baltimore Sun.
The man, Paul Warren Pardus, blamed Dr. David B. Cohen for paralyzing his mother during surgery. Dr. Cohen survived the homicide attempt.
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Innovation from Spectre Screws
WHEN it comes to woodscrews – or even fastenings in general – we have a bewildering choice nowadays.
The cordless drill driver and modern woodscrews have made what was a chore into a simple job with, usually, much better results than we could have expected 20 years ago, writes PETER BRETT.
Who drills pilot holes these days? Or who greases screws before twisting them in with a big screwdriver like we used to?
The Spectre USPs
The new Spectre screws are labelled as Advanced Multi-Purpose Woodscrews, so are aimed at jobbing builders, joiners, carpenters and others. They need a good product at a good price, when a premium screw is not required.
FORGEFIX carefully chose the features most needed for general users and, based on my experience of using woodscrews in a variety of applications, the design is pretty well spot on.
Starting with the quick-start type 17 slash point, it is very sharp so getting a good start is almost as easy as just pushing it into the wood where you need the screw to be.
In addition to the cut out to clear the starting hole quickly, the first few mm of the thread has a small sawtooth that literally cuts its way through the wood and helps prevent splitting.
I tried the screws close to the edges of both hard and softwood, and it is not an idle claim.
Brian Trevaskiss, Marketing Manager at FORGEFIX, said: "Users don’t have to open the box, they just need to offer up their sample screw to the scale to compare.
" This is simple stuff – but no-one else has thought of this before. I am sure retailers will love it.
"There is also the option to purchase larger quantity boxes of the most popular sizes that represent a 10% saving on the equivalent normal size boxes.
"As for the screws – yes, they work well. They are anti-corrosion coated, and come in 48 sizes with, as mentioned above, options for bulk trade boxes.
Point of sale display
FORGEFIX is to be commended for coming up with a few excellent ideas to help end users (and even shop counter staff) to choose the right size screws.
This will also help with the annoying problem of finding clumsily opened boxes half full of screws on a display - usually the result of a customer trying to find exactly the length and gauge of the screw they want.
The new bright yellow and black boxes have the size and gauge of the screws written in big letters (even without my glasses I can read them) on one side of the box.
On the other side is an actual size representation of the head, so the user will know what size and type of driver to use. Below it is a centimetre scale with the screw imposed on it.
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Lightsticks content toxicity: effects of the water soluble fraction on the oyster embryonic development.
Lightsticks are artifacts used as attractors in a type of commercial fishery, known as surface longline gear. Despite the excessive use, the contamination risks of these devices have not yet been properly investigated. This research aimed to fill up this gap by determining the chemical composition and the toxicity of lightsticks recently activated, compared to those one year after activation and to the ones collected on the beaches. The analyzes were carried out by Gas Chromatography coupled with Mass Spectrometry (GC-MS). Additionally, the variations in composition and the toxicity of their sea Water Soluble Fractions (WSF) were evaluated based on the WSF-effects of Crassostrea rhizophorae embryonic development. The GC-MS analysis made possible the identification of nineteen substances in the water soluble fraction of the lightsticks, such as dibutyl phthalate (DBP) and dimethyl phthalate (DMP). The value of the WSF-effective concentration (EC50) was in an average of 0.35%. After one year of the lightsticks activation, the toxicity was even higher (0.65%). Furthermore, other substances, also present in the lightsticks-WSF caused persistent toxicity even more dangerous to the environment than DBP and DMP. This essay discusses their toxicity effects and possible environment damages.
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Soul Mate Dream Date Finalists: Vote for the Winner
More than 120 couples entered the Soul Mate Dream Date contest to win a cutsom Memphis date. I've narrowed the field down to five finalists, and now it's your turn to pick the winner.
There were so many good stories, and choosing five was tough. I really enjoyed reading all of your stories about your sweethearts – you guys are seriously lucky.
Thanks to everyone who voted.I'm happy to announce that the winners of the dream date are Catherine and Kevin, who won with 33 percent of the vote. Congrats, you crazy kids!
Here's what's at stake: a custom Memphis dream date, including dinner for two, an activity and a night's stay at the Westin Memphis Beale Street.
Now let's meet the finalists:
Couple no. 1: Jeff and Annie
Jeff and Annie met when they both worked at the Movie and Pizza Co. in Harbortown (she was a server, he was a delivery driver). Years after they worked together, they finally hit it off while singing karaoke at Yosemite Sam's. Jeff wrote the entry, and he loves Annie's caring and encouraging nature (she's a teacher) and her sense of humor.
This is too sweet. Surjit and Nimmi's story was submitted by their son J.R. They met in India in1969, when he was a student and she was a nurse, after Surjit's family told him they had a woman they'd like him to meet. "Having somewhat of an arranged marriage, my parents were able to learn to love each other after the fact of being married and not before," J.R. wrote. "Their marriage is one that has evolved from not only learning about a new person and being in a new country and culture, to a marriage where two people have truly found their best friend, companion and confidant. This past January, my parents celebrated their 44th anniversary."
On their dream date, they want to: Have drinks at a nice cocktail bar, go to dinner and have some quiet time alone together.
Couple no. 3: Catherine and Kevin
Catherine and Kevin's busy work schedules kept them from being able to meet many dateable people. They found each other on Match.com about a year ago, and it's been love ever since. Catherine, who works as a pediatric doctor, describes her music professor partner this way: "As you might not imagine of someone who plays the tuba, Kevin is handsome, well-dressed, ambitious, and suave". She loves his goofy sense of humor, his involvement in his work, and the way that he always makes time for her.
On their dream date, they want to: have dinner at Iris, Flight or Paulettes and then go to a musical at the Orpheum.
Couple no. 4: Danielle and Allyson
Danielle and Allyson met in a college dorm, where they initially bonded over their favorite websites. Danielle admires Allyson's drive, her smile, and her shy streak.
On their dream date, they'd like to: Danielle said it best – " I would like the opportunity to take her somewhere where she (Allyson) feels appreciated. Because we are both in college, it's hard for me to be able to do these things and it would be great if I could do that for her because she works so hard all the time."
Couple no. 5: Cynthia and Nick
Nick and Cynthia met for the first time at the Cooper-Young Regional Beer Festival, but, because it's a drinking festival, Cythnia's memory of their first encounter is a little blurry. They met for the first time again a few weeks after the festival, at the home of a mutual friend. She loves the way that he's always wanted to include her in his plans and that he's committed, respectful, motivated and honest.
On their dream date, they'd like to: have dinner downtown at a local restaurant and then see some live music. They're homebrewers and craft beer enthusiasts, so a good beer list is a must.
You can vote for your favorite couple once per day until 12 p.m. on Feb. 14. The couple with the most votes at that time will win the prize. Happy voting!
Edit: I fixed the glitch in the poll that was allowing multiple votes from different browsers. If you vote more than once now, it'll say "thank you, your vote has already been counted" and will not count the any votes past the first one.
Share this Post
Author: Holly Whitfield
I write about what’s going on with Memphis music, food, arts, events, sports, people, and culture. Memphians love Elvis and barbeque with a passion that must be seen to be believed, but there is so much more to this place.
I'm so excited to be one the top 5!!! You guys rock and I am so appreciative of this opportunity. Thank you guys so much for the consideration!!! I know that this surprise will be one that she will never forget!
As the son who wrote the story for my parents (couple #2), I would like to extend congrats on from myself and on behalf of my parents to Catherine & Kevin. May your lives be filled with the same amount of happiness and joy that my parents have experienced for the past 44 years and counting. Cheers!!
Wow, what an honor! Thank you Kerry, and thank you everyone who voted! Congrats to the other 4 couples; you all sound like fantastic pairs of lovebirds! May you have a very Happy Valentine's Day with the one you love!
Although I'm sure the winners are as worthy as anyone, I don't like the way they won. It wasn't the couple, but Kevin's aunt did something I think is unfair to the others. She is a member of a very large message board, and asked people to vote for Catherine and Kevin. And people did. Not because they read the stories and made a decision on which one they liked best, but voted for the win because, well, why not? This gives an unfair advantage to one entry over another as there are several thousand members on that forum. It's ballot-stuffing rather than voting for a favorite, and I think it stinks.
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Attaching a new blu-ray to another system help?
Ok so i brought a 60gig off Ebay and i knew it came without a blu ray drive so i brought one as well.. But i didn't know a logic board had to come with it.. ANYWAY i asked the owner where is the original logic board that attaches to the drive.. and no answer as yet.
My question is.. Can you just buy another bluray drive with the logic board connected on that drive and put it into the ps3 system?
Ok i did some testing.. i swapped my good 60gb ps3 blu ray to the other 60gig ps3 system and it just didnt pick it up. I would follow your method PS3news but the firmware on the system that needs the new blu ray drive is 3.66.. any ideas?
Do i need to get the orginal board off the guy i brought the ps3 system from and hopefullly he still has that broken blu ray drive with the board attached to the drive?
Let me get this straight as im a Noob ill admit it:
I got a 60gb console off ebay with no bluray drive in it.. The seller did not include the circit board from the blu ray drive.. Now does that mean if i was to buy a 60gb blu ray drive off ebay with its circut board will it not work?
Does the Blu Ray drive "marry" it self to the systems mother board or just the circut board the blu ray drive its attached to?
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1. Introduction
===============
Nickel (Ni) is a prevalent metal in the ecosystem of both geographical distribution and human activities. It exists as an essential element of more than one hundred compounds, and it was widely used in industry and commerce \[[@B1-ijerph-10-07310],[@B2-ijerph-10-07310],[@B3-ijerph-10-07310]\]. Naturally, the most common oxidative state of Ni is the +2 valence, and Ni salts such as nickel chloride (NiCl~2~), sulphate, nitrate, carbonate, hydroxide, acetate and oxide are valuable in commerce \[[@B4-ijerph-10-07310],[@B5-ijerph-10-07310],[@B6-ijerph-10-07310]\]. Water-soluble Ni salts such as NiCl~2~, nitrate, sulphate are easily absorbed \[[@B2-ijerph-10-07310],[@B7-ijerph-10-07310],[@B8-ijerph-10-07310]\]. Ni gets into human and animals mainly through inhalation, drinking water and food, and among these pathways, food are the most important \[[@B2-ijerph-10-07310]\].
Ni is considered as an essential metal nutrient for many species \[[@B9-ijerph-10-07310],[@B10-ijerph-10-07310],[@B11-ijerph-10-07310]\]. It has been reported that Ni is vital for some hormones (like prolactin, adrenaline, noradrenaline and aldosterone) and proper function of the immune system, and its deficiency will inhibit growth, reduce reproductive rate and alter glucose and lipid metabolism, and intracellular Ni can change membrane properties and influence ox/red systems \[[@B12-ijerph-10-07310],[@B13-ijerph-10-07310],[@B14-ijerph-10-07310],[@B15-ijerph-10-07310]\]. Depigmentation of the skin, thickened legs, swollen hocks, growth retardation and anemia has been reported in chicks fed on a Ni deficient diet \[[@B15-ijerph-10-07310]\]. However, Ni and its compounds could also be toxic to human beings and animals \[[@B1-ijerph-10-07310],[@B2-ijerph-10-07310],[@B3-ijerph-10-07310]\]. Previous studies have proved that long-term exposure to Ni is deleterious to the upper respiratory tract, skin, kidney, immune system \[[@B16-ijerph-10-07310],[@B17-ijerph-10-07310],[@B18-ijerph-10-07310],[@B19-ijerph-10-07310]\], embryos, and the breeding system \[[@B8-ijerph-10-07310],[@B20-ijerph-10-07310],[@B21-ijerph-10-07310]\]. Even short-term exposure to Ni can significantly influence the cardiovascular system \[[@B18-ijerph-10-07310],[@B19-ijerph-10-07310]\]. Ni in the body can also disturb the metabolic balance of other elemental metals, which suppresses the toxicity and carcinogenicity of nickel. Nickel toxicity mainly results from the ability to replace other metal ions in enzymes and proteins or to bind to cellular compounds containing O-, S-, and N-atoms \[[@B4-ijerph-10-07310],[@B22-ijerph-10-07310],[@B23-ijerph-10-07310]\].
It had been reported that Ni can enhance lipid peroxidation (LPO) and cause cellular damage and reduced glutathione (GSH) contents, and catalase (CAT) and glutathione peroxidase (GSH-Px) activities in the liver and kidney of rats \[[@B24-ijerph-10-07310],[@B25-ijerph-10-07310]\]. Ni-ion accumulation may be responsible for the generation of reactive oxygen species (ROS) and the enhancement of LPO, and NiCl~2~ is related to DNA oxidation and DNA strand breaks in rat's liver \[[@B23-ijerph-10-07310]\]. NiCl~2~-induced human lymphocyte toxicity may be mediated by oxygen radical intermediates \[[@B26-ijerph-10-07310]\]. Our earlier study has proved that NiCl~2~ can cause oxidative damage in the intestinal tract of broiler \[[@B27-ijerph-10-07310]\]. Data also show that oxidative stress caused by Ni is important in the mechanism of Ni toxicity \[[@B24-ijerph-10-07310],[@B25-ijerph-10-07310],[@B28-ijerph-10-07310],[@B29-ijerph-10-07310],[@B30-ijerph-10-07310]\].
Previous studies show that Ni can cause DNA damage, inhibit DNA repair in mammalian cells \[[@B31-ijerph-10-07310],[@B32-ijerph-10-07310],[@B33-ijerph-10-07310]\]. Some articles describe that Ni can induce cell apoptosis, and the mechanisms have been well documented. Ni (II) can directly generate ROS, activate Caspase-3 expression, increase Caspase-3-like protease activity, and then cause cell death in mice \[[@B34-ijerph-10-07310],[@B35-ijerph-10-07310]\]. It has been also reported that nickel ferrite nanoparticles-induced oxidative stress mediates apoptosis in cultured A549 cells \[[@B36-ijerph-10-07310]\].
Spleen is a peripheral immune organ in the body. Ni is considered to be toxic to the immune system. Ni (II) exposure has multiple effects on the immune system, including thymic involution, decreasing T cell number and natural killer cell activity in the spleen of mice \[[@B35-ijerph-10-07310]\]. A previous article has reported that Ni (II) can reduce cell viability and proliferation of Jurkat T cells, which are similar to human T lymphocytes \[[@B34-ijerph-10-07310]\]. Animal studies show that NiCl~2~ can accumulate in the spleen of mice \[[@B29-ijerph-10-07310]\], and promote immunosuppression \[[@B37-ijerph-10-07310]\]. Ni could accumulate in the spleen and cause changes both in number and size of the giant cells \[[@B38-ijerph-10-07310],[@B39-ijerph-10-07310]\]. NiCl~2~ and NiS can also influence cellular proliferation in the spleen \[[@B40-ijerph-10-07310],[@B41-ijerph-10-07310]\]. Studies on CBA/J and C57BL/6J mice show that NiCl~2~ significantly reduced the NK cell activity in the spleen of mice \[[@B42-ijerph-10-07310],[@B43-ijerph-10-07310]\], but the mechanisms of the effects of Ni compounds on splenocytes are still unknown \[[@B44-ijerph-10-07310]\].
At present, studies on NiCl~2~ in chickens mainly focus on bone of male broiler, egg productivity, feather and fatting programs, and biochemical parameters in liver and blood \[[@B45-ijerph-10-07310],[@B46-ijerph-10-07310],[@B47-ijerph-10-07310]\], and very limited research focuses on the effects of NiCl~2~ on the splenic apoptosis and oxidative stress in animals and human beings.
Taking previous research on laying hens \[[@B48-ijerph-10-07310]\], the concentration in the environment \[[@B49-ijerph-10-07310]\], and our preliminary experiment into consideration, we choose to add dosages of 300, 600 and 900 mg/kg NiCl~2~ to the basal diet of broilers and then we attempted to systematically investigate how Ni induced apoptosis and oxidative stress in the spleen, and the association between these effects in broiler. Thus, the activities of superoxide dismutase (SOD), CAT and GSH-Px, and the ability to inhibit hydroxyl radical, and GSH and malondialdehyde (MDA) contents were used to measure the oxidative stress in the spleen, and mRNA expression and contents of Bax, Bcl-2 and Caspase-3, and apoptotic cells detected by ELISA, qRT-PCR, terminal dexynucleotidyl transferase (TdT)-mediated dUTP nick end labeling (TUNEL) and FCM were used to investigate the apoptotic condition in the spleen caused by NiCl~2~.
2. Materials and Methods
========================
2.1. Chickens and Diets
-----------------------
These were described previously \[[@B27-ijerph-10-07310]\]. Two hundred and forty one-day-old healthy avian broilers were randomly divided into four groups by body weight with 60 broilers in each group. Broilers were housed in cages with electrical heater and were provided with diets and water *ad libitum* for 42 days. A corn-soybean basal diet formulated by the National Research Council (NRC) \[[@B50-ijerph-10-07310]\] was the control diet. NiCl~2~ was mixed into the corn-soybean basal diet to produce experimental diets containing 300, 600 and 900 mg/kg NiCl~2~, respectively.
2.2. Detection of the Splenocyte Apoptosis by TUNEL and FCM
-----------------------------------------------------------
### 2.2.1. TUNEL Assay
Five broilers in each group were euthanized at 14, 28 and 42 days of age for gross examination. Spleens were removed, fixed in 4% neutral buffered paraformaldehyde, and embedded in paraffin. The terminal dexynucleotidyl transferase (TdT)-mediated dUTP nick end labeling (TUNEL) assay was performed in the deparaffinized section (5 μm thick) with an apoptosis detection kit (EMD Biosciences, Inc. La Jolla, CA, USA) according to the manufacturer's instructions. Briefly, splenic slices were rehydrated in a series of xylene and ethanol solutions and then incubated in a humidified chamber at room temperature for 20 min with proteinase K (Cat. No: JA 1477, EMD Biosciences, Inc. La Jolla, CA, USA). Slices were then rinsed with tris-buffered saline (TBS). The entire specimens were covered with 3% H~2~O~2~ and then incubated at room temperature for 5 min. Slices were rinsed with TBS. TUNEL enzyme (Cat. No. JA 1559, EMD Biosciences, Inc. La Jolla, CA, USA) and label solution (Cat. No. JA 1560, EMD Biosciences, Inc. La Jolla, CA, USA) were mixed and applied to slices, which were incubated again in the humidified chamber for 1 h at 37 °C. Slices were thoroughly rinsed with TBS. Stop buffer, block buffer, and conjugate were applied in turn. Diaminobenzidine solution was applied for 10--15 min to stain the nuclei of apoptotic cells. The methyl green solution was used to counterstain the nuclei of normal cells. Slices were dehydrated in a series of three ethanol baths and twice xylene baths, 5 min for each. The positive cells were quantified using Image-Pro Plus 5.1 (Media Cybernetics, Inc. Bethesda, MD, USA). Five slices were measured in each group and five microscopic areas (randomly chosen) were measured in each slice. Then the numbers were averaged.
### 2.2.2. Annexin V Apoptotic Detection by FCM
At 14, 28 and 42 days of age, five broilers in each group were humanely killed, and then the spleens were removed immediately and ground to form a cell suspension, which was then filtered with 300-mesh nylon screen. The cells at a concentration of 1×10^6^ cells/mL were washed twice with cold PBS (phosphate buffer solution, pH 7.2-7.4), and suspended in 1×binding buffer (Cat. No: 51-66121E, BD, Co. Ltd. San Diego, CA, USA). 100 μL of the cell suspension was transferred to a 5ml culture tubes, and then 5 μL of Annexin V-FITC (Cat. No: 51-65874X, BD, Co. Ltd. San Diego, CA, USA) and 5 μL of PI (Cat. No: 51-66211E) were added. The mixture was gently swirled to misce bene and incubated for 15 min at 25 °C in the dark. 400 μL of 1× binding buffer was added to each tube, and finally analysis by FCM (BD FACS Calibur, BD, Co. Ltd. San Diego, CA, USA) was conducted within 1 h.
2.3. Determination of Bax, Bcl-2 and Caspase-3 in the Spleen
------------------------------------------------------------
### 2.3.1. Detection of Bax, Bcl-2 and Caspase-3 mRNA Expression Levels by qRT-PCR
At the age of 14, 28 and 42 days, spleens of five broilers in each group were removed and immediately stored in liquid nitrogen. Adding liquid nitrogen into a mortar, the spleens were ground into a homogenized powder with a pestle. The powder was filled into EP tubes immediately, then, stored at −80 °C for future usage.
Total RNA was extracted from the powder of the spleen by RNAiso Plus (9108/9109, Takara Tomy, Tokyo, Japan). The mRNA was then reverse transcribed into cDNA using PrimScript^TM^ RT reagent kit with gDNA Eraser (RR047A, Takara). The cDNA was used as a template for qRT-PCR analysis. Sequence of primers was obtained from GenBank of NCBI. Primers were designed with Primer 5, and synthesized by BGI Tech (Shenzhen, China) ([Table 1](#ijerph-10-07310-t001){ref-type="table"}).
For qRT-PCR reactions, 25 μL mixture was made by using SYBR^®^ Premix Ex Taq^TM^ Ⅱ (DRR820A, Takara), containing 12.5 μL Tli RNaseH Plus, 1.0 μL of forward and 1.0 μL of reverse primer, 8.5 μL RNAase-free waters and 2 μL cDNA. Reaction conditions were set to 3 min at 95 °C for 1 cycle, followed by 44 cycles of, 30s at Tm of a specific primer pair, followed by 1 cycle of 10 s at 95 °C, 72 °C for 10 s, and 10 s at 95°C, using Thermal Cycler (C1000, Bio-Rad, Hercules, CA, US). β-actin was used as an internal control gene. Results were analyzed with the method of 2 ^-ΔΔCT^.
ijerph-10-07310-t001_Table 1
######
Nucleotides used as primers in qRT-PCR analysis of mRNA expression in the spleen.
Primer Sequence (5'→3') Accession Number
----------- ----------------------- ---------------------- -----------
Bax F TCCTCATCGCCATGCTCAT XM_422067
R CCTTGGTCTGGAAGCAGAAGA XM_422067
Bcl-2 F GATGACCGAGTACCTGAACC NM_205339
R CAGGAGAAATCGAACAAAGGC NM_205339
Caspase-3 F TGGCCCTCTTGAACTGAAAG NM_204725
R TCCACTGTCTGCTTCAATACC NM_204725
β-actin F TGCTGTGTTCCCATCTATCG L08165
R TTGGTGACAATACCGTGTTCA L08165
### 2.3.2. Detection of Bax, Bcl-2 and Caspase-3 Contents by ELISA {#sec2dot3dot2-ijerph-10-07310}
At 14, 28 and 42 days of age, spleens of five broilers from each group were humanely removed. Then spleens were immediately removed, and chilled to 0 °C in 0.85% NaCl solution. The spleens were rinsed with icy isotonic saline (0.9% wt/vol NaCl) before being weighed. A 10% homogenate of spleen was produced by using glass homogenizers and centrifugation at 3,000 × g for 10 min at 4 °C. The supernatant was conserved for further analysis. The concentrations of Bax, Bcl-2, Caspase-3 were assayed by ELISA Kit for chicks (MyBioSource, Inc. San Diego, CA USA) \[[@B51-ijerph-10-07310]\]. Bax (REF: MBS043584), Bcl-2 (REF: MBS260943) and Caspase-3 (REF: MBS023920). The contents of Bax, Bcl-2 and Caspase-3 were determined by the standard curve and were expressed as nanograms per milliliter.
2.4. Detection of Oxidative Stress Parameters in the Spleen
-----------------------------------------------------------
Preparation of the splenic homogenate was described in [Section 2.3.2](#sec2dot3dot2-ijerph-10-07310){ref-type="sec"} above. After determining the amount of total protein in the supernatant of splenic homogenate with the Bradford method (a rapid and accurate method for the estimation of protein concentration, which relies on the binding of the dye Coomassie Blue G250 to protein) \[[@B52-ijerph-10-07310]\], the SOD, CAT and GSH-Px activities, and ability to inhibit hydroxyl radical, and MDA and GSH contents in the supernatant were detected according to the instruction of the reagent kits (SOD: Cat. No: A001-1, LOT: 201211; CAT: Cat. No: A007, LOT: 201211; GSH-Px: Cat. No: A005, LOT: 201211; abilities to inhibit hydroxyl radical: Cat. No: A018, LOT: 201211; GSH: Cat. No: A006, LOT: 201211; MDA: Cat. No: A003-2, LOT: 201211; total protein: Cat. No: A045-2, LOT: 201211, Nanjing Institute of Jiancheng Biological Engineering, Nanjing, China). The absorbance of SOD, CAT, GSH-Px, abilities to inhibit hydroxyl radical, MDA, GSH and total protein were measured at 550, 240, 412, 550, 532, 420 nm and 590 nm respectively, and data were gained by using a microtiter plate reader (Thermo, Waltham, MA, USA).
2.5. Statistical Analysis
-------------------------
The significance of difference among four groups was analyzed by variance analysis. The analysis was performed using one-way analysis of variance (ANOVA) test of SPSS 16.0 for Windows, and results were presented as means ± standard deviation (*X* ± SD). A value less than 0.05 (*p* \< 0.05) was considered significant when compared to the control group.
3. Results
==========
3.1. Changes of Splenocyte Apoptosis
------------------------------------
TUNEL assays showed that the nuclei of positive cells were stained in brown ([Figure 1](#ijerph-10-07310-f001){ref-type="fig"}, [Figure 2](#ijerph-10-07310-f002){ref-type="fig"} and [Figure 3](#ijerph-10-07310-f003){ref-type="fig"}). The results in [Figure 4](#ijerph-10-07310-f004){ref-type="fig"} show that the number of apoptotic splenocytes was significantly higher (*p* \< 0.05 or *p* \< 0.01) in the 300 mg/kg, 600 mg/kg and 900 mg/kg groups from 14 to 42 days of age than those in the control group.
{#ijerph-10-07310-f001}
{#ijerph-10-07310-f002}
{#ijerph-10-07310-f003}
{#ijerph-10-07310-f004}
Apoptosis detection by FCM showed that the percentages of apoptotic splenocytes were significantly increased (*p* \< 0.05 or *p* \< 0.01) in the 600 and 900 mg/kg groups from 14 to 42 days of age, and in the 300 mg/kg group at 42 days of age when compared with those of the control group, as shown in [Figure 5](#ijerph-10-07310-f005){ref-type="fig"}.
{#ijerph-10-07310-f005}
3.2. Changes of Bax, Bcl-2 and Caspase-3 mRNA Expression Levels and Contents in the Spleen
------------------------------------------------------------------------------------------
Changes of Bax, Bcl-2 and Caspase-3 mRNA expression levels were shown in [Figure 6](#ijerph-10-07310-f006){ref-type="fig"}, and changes of Bax, Bcl-2 and Caspase-3 contents were shown in [Figure 7](#ijerph-10-07310-f007){ref-type="fig"}.
{#ijerph-10-07310-f006}
{#ijerph-10-07310-f007}
3.3. Changes of the Oxidative Stress Parameters in the Spleen
-------------------------------------------------------------
Changes of the SOD, CAT and GSH-Px activities, the ability to inhibit hydroxyl radical, GSH and MDA contents were shown in [Figure 8](#ijerph-10-07310-f008){ref-type="fig"}.
{#ijerph-10-07310-f008}
4. Discussion
=============
At present, very limited studies focus on NiCl~2~-induced apoptosis and oxidative stress in the spleen of animals and human. Thus, the aim of this study is to investigate the oxidative stress, alternations of Bax, Bcl-2 and Caspase-3 mRNA expression levels and contents, and apoptosis in the spleen of broilers induced by dietary NiCl~2~, and to reveal the association between splenocyte apoptosis and alternations of Bax, Bcl-2 and Caspase-3 mRNA expression levels and contents, and oxidative stress, and to provide new experimental evidence to clarify the mechanism of NiCl~2~ toxicity on spleen and splenic functions.
Apoptosis is the programmed cell death in eukaryotes, which is essential for development and tissue homeostasis by providing a protective mechanism to clean out aged or damaged cells \[[@B53-ijerph-10-07310],[@B54-ijerph-10-07310]\]. It can be activated by various stimuli, including ultraviolet (UV) irradiation and serum starvation \[[@B55-ijerph-10-07310]\]. Cell death through apoptosis is tightly controlled by changes, interactions and post-translational modifications (including proteolytic cleavage and phosphorylation) of proteins \[[@B56-ijerph-10-07310]\]. In the present study, the results of FCM and TUNEL assays showed that dietary NiCl~2~ in excess of 300 mg/kg could increase the percentage of splenocyte apoptosis, which was consistent with the alternations of Bax, Bcl-2 and Caspase-3 mRNA expression levels and contents in the spleen due to the close relationship between apoptosis and apoptosis proteins.
Apoptosis mainly has two pathways: the intrinsic and the extrinsic ones. The former involves initial mitochondrial perturbation resulting from cellular stress or cytotoxicity \[[@B55-ijerph-10-07310],[@B57-ijerph-10-07310],[@B58-ijerph-10-07310]\]. The Bcl-2 protein family is the major regulators and effectors of the intrinsic pathway \[[@B59-ijerph-10-07310]\]. Bcl-2 locates mainly on the outer membrane of mitochondria, and its overexpression protects cells from apoptosis caused by various stimuli. The Bcl-2 family can be categorized into the anti-apoptotic proteins (Bcl-2-like proteins such as Bcl-2 and Bcl-X~L~), and the pro-apoptotic proteins (such as Bax-like and the BH3-only proteins) \[[@B59-ijerph-10-07310]\]. The activation of the pro-apoptotic proteins will induce cytochrome c release from mitochondria into the cytoplasm \[[@B60-ijerph-10-07310],[@B61-ijerph-10-07310],[@B62-ijerph-10-07310],[@B63-ijerph-10-07310]\]. However, Bcl-2-like proteins can prevent Bax-induced cell death by blocking cytochrome c release \[[@B53-ijerph-10-07310]\]. The increase in Bax mRNA expression levels and contents and the decrease in Bcl-2 mRNA expression levels and contents in our study caused the cytochrome c release and apoptosis initiation in the spleen. Caspase is a family of single-chain synthesized zymogens playing central roles in apoptotic signaling and execution \[[@B64-ijerph-10-07310],[@B65-ijerph-10-07310]\]. The executor-Caspase-3 can be activated both by the intrinsic and the extrinsic apoptotic pathways. In the intrinsic one, cytochrome c enters the cytoplasm, and activates a chain-reaction of caspase family and the cell demise \[[@B66-ijerph-10-07310]\]. It is reported that Ni (II)-induced ROS can activate Caspase-3 expression, increase Caspase-3-like protease activity, and then cause cell death in mice \[[@B34-ijerph-10-07310],[@B35-ijerph-10-07310]\]. The results showed that the significantly increased Caspase-3 mRNA expression levels and contents in the NiCl~2~-added groups promoted apoptosis in the spleen.
There are enzymatic and non-enzymatic internal defense systems to prevent the oxidative stress in the body \[[@B67-ijerph-10-07310]\]. Endogenous antioxidants such as SOD, GSH-Px, CAT and GSH, and the ability to inhibit hydroxyl radical are important bio-markers of the anti-oxidative system. These endogenous antioxidants are able to inhibit overproduced free radicals (including ROS), and avoid excess lipid peroxidation. SOD can break up ROS and repair cellular damage caused by ROS. Ni ion accumulation may be responsible for the generation of ROS and the enhancement of LPO \[[@B23-ijerph-10-07310]\], and NiCl~2~ is related to DNA oxidation and DNA strand breaks in rat's liver \[[@B23-ijerph-10-07310]\]. Hydroxyl radical can affect cellular structure protectors (such as CAT, SOD and GSH) \[[@B68-ijerph-10-07310]\]. Additionally, Ni can enhance lipid peroxidation (LPO) and caused cellular damage and reduced GSH contents, and CAT and GSH-Px activities in the liver and kidney of rats \[[@B24-ijerph-10-07310],[@B25-ijerph-10-07310]\]. GSH is considered to be an important bio-marker in LPO and is important in maintaining the cellular redox status \[[@B67-ijerph-10-07310]\]. Reduction of GSH is a marker of oxidative stress \[[@B21-ijerph-10-07310],[@B69-ijerph-10-07310]\] and can significantly enhance NiCl~2~-induced apoptosis \[[@B70-ijerph-10-07310]\]. Thus, the reduced activities of GSH-Px and CAT may be closely associated to the reduction of GSH contents. The interaction of the antioxidants may be the main reason which caused the reduction of activities of SOD, CAT and GSH-Px and the decreased content of GSH as shown in [Figure 8](#ijerph-10-07310-f008){ref-type="fig"}.
Free radicals (including ROS and ∙OH) are products of metabolic reactions and byproducts of immune reactions, and can damage cellular lipids, proteins and DNA \[[@B71-ijerph-10-07310]\]. LPO may be a contributing factor in Ni-induced tissue oxidative stress \[[@B22-ijerph-10-07310]\]. In the LPO process, free radicals attack lipids, and abstract electrons from the cell membrane through a chain reaction \[[@B63-ijerph-10-07310],[@B72-ijerph-10-07310]\], and cause the generation of MDA ([Figure 8](#ijerph-10-07310-f008){ref-type="fig"}), which inhibits activity of antioxidants. LPO can reduce membrane fluidity and integrity, and increase membrane fragility \[[@B73-ijerph-10-07310],[@B74-ijerph-10-07310]\]. There is no doubt that NiCl~2~-induced oxidative stress to the spleen impairs the splenic function.
The changes of the abovementioned oxidative stress parameters showed that NiCl~2~ caused oxidative damage in the spleen, which is consistent with the increased percentages of splenocyte apoptosis. Previous studies have revealed that ROS and oxidative damage are strongly related to the induction of apoptosis \[[@B67-ijerph-10-07310]\]. Thus, the results in the present study revealed the NiCl~2~-induced oxidative damage in the spleen caused alterations of Bax, Bcl-2 and Caspase-3 mRNA expression levels and contents, and finally resulted in splenocyte apoptosis *via* the intrinsic apoptosis pathway as well as oxidative damage.
5. Conclusions
==============
In conclusion, dietary NiCl~2~ in excess of 300 mg/kg causes apoptosis, alters Bax, Bcl-2 and Caspase-3 mRNA expression levels and contents, and results in oxidative stress in the spleen of broilers. Also, splenocyte apoptosis is closely related, to not only the alternations of Bax, Bcl-2 and Caspase-3 mRNA expression levels, but also oxidative stress. Consequently the splenic immunity and blood filtration functions are impaired in broilers. This study provides new experimental evidences and an animal model for further understanding the mechanism of the effects of NiCl~2~ on the spleen.
This study was supported by the Program for Changjiang Scholars and Innovative Research Team at Universities (IRT 0848) and the Education Department (09ZZ017) and Scientific Department of Sichuan Province.
The authors declare no conflict of interest. Our experiments involving the use of broilers, and the use of chickens and all experimental procedures involving animals were approved by Sichuan Agricultural University Animal Care and Use Committee.
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Notes:
The Racial Dissimilarity Index measures the percentage of the non-hispanic white population in a county which would have to change Census tracts to equalize the racial distribution between white and non-white population groups across all tracts in the county.Starting with the 2016 observations, the calculation has been changed so that counties with only one census tract have missing data. Zero values represent counties where the proportions of non-white population and non-hispanic white population are the same.
Suggested Citation:
U.S. Bureau of the Census,
White to Non-White Racial Dissimilarity Index for Dane County, WI [RACEDISPARITY055025],
retrieved from FRED,
Federal Reserve Bank of St. Louis;
https://fred.stlouisfed.org/series/RACEDISPARITY055025,
February 22, 2019.
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Studied Homeopathic Remedies
Asafoetida
Colocynthis
Lycopodium
The symptoms of irritable bowel syndrome (IBS) include one or more of the following: alternating diarrhea and constipation, intestinal gas, bloating and cramping, abdominal pain, painful bowel movements, mucous discharge, and undigested food in the stool. Despite all these distressing symptoms, people with IBS have normal intestines, so far as any medical examination can show. Thus the condition belongs to a category of diseases that physicians call functional. This term means that while the function of the bowel seems to have gone awry, no injury or disturbance of its structure can be discovered.
The cause of IBS remains unknown, although stress is thought to play a role.
One homeopathic remedy,
Asafoetida
, has been evaluated as a potential treatment for irritable bowel syndrome. In this 14-week,
double-blind trial
, about 100 people with irritable bowel syndrome received
Asafoetida
D3 or placebo.
1
The results indicated that participants taking the homeopathic remedy improved to a greater extent than those taking placebo.
Traditional Homeopathic Treatments for Irritable Bowel Syndrome
In
classical homeopathy
, there are many possible homeopathic treatments for irritable bowel syndrome, to be chosen based on various specific details of the person seeking treatment.
The classic
symptom picture
of
Asafoetida
, the remedy tested in the double-blind study described above, includes constipation alternating with profuse, offensive, watery diarrhea, abdominal distention with much flatulence, and the sensation of a lump in the throat that is relieved by swallowing and belching. Symptoms are worse after eating, from sitting, at night, and on the left side, but relieved by pressure and by motion in the open air.
The remedy
Colocynthis
may be suggested when abdominal pain is described as cutting or cramping, often coming in waves, and relieved by firm pressure or by doubling over. Pain is increased by eating or drinking, as well as by the emotions of anger or indignation. Pain often reaches its peak just prior to diarrhea.
Homeopathic
Lycopodium
may be recommended when symptoms include band-like pain around the waist, severe flatulence and bloating, and frequent heartburn.
Other Natural Options
For herbs, supplements, and other alternative treatments that may be useful for this condition, see the full
Irritable Bowel Syndrome
article.
For a thorough explanation of homeopathy, including dilution of therapies, see the
Homeopathy Overview
.
Revision Information
This content is reviewed regularly and is updated when new and relevant evidence is made available. This information is neither intended nor implied to be a substitute for professional medical advice. Always seek the advice of your physician or other qualified health provider prior to starting any new treatment or with questions regarding a medical condition.
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---
bibliography:
- 'bibliography.bib'
---
[**On Robustness Analysis of Stochastic Biochemical Systems by Probabilistic Model Checking** ]{}\
Luboš Brim, Milan Česka, Sven Dražan, David Šafránek$^{\ast}$\
Systems Biology Laboratory, Faculty of Informatics, Masaryk University, Brno, Czech Republic\
$\ast$ E-mail: [email protected]
Abstract {#abstract .unnumbered}
========
This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions.
The framework is applied to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We succeeded to extend previous studies performed on deterministic models (ODE) and show that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Introduction
============
Robustness is one of the fundamental features of biological systems. According to Kitano [@Kitano2004] *“robustness is a property that allows a system to maintain its functions against internal and external perturbations”*. To formally analyse robustness, we must thus precisely identify model of a biological system and define formally the notions of a system’s function and its perturbations. In this paper, we propose a novel framework for robustness analysis of stochastic biochemical systems. To this end, inspected systems are described by means of stochastic biochemical kinetics models, system functionality is defined by its logical properties, and system perturbation is modelled as a change in stochastic kinetic parameters or initial conditions of the model.
Processes occurring inside living cells exhibit dynamic behaviours that can be observed and classified as carrying out a certain function – maintaining stable concentrations, responding to a change of the environment, growing etc. Kinetic models with parameters are used to formally capture cell dynamics. To observe and analyse a dynamic behaviour on a kinetic model, all its numerical parameters must be instantiated to a specific value. This poses a challenge since the precise values of all parameters (kinetic constants, initial concentrations, environmental conditions etc.) may not be known, may be known but without a given accuracy of measurement or may in principle form an interval instead of being a single value (e.g. non-homogeneous cell populations, different structural conformations of a molecule leading to multiple kinetic rates etc.). This implies that the behaviour of a kinetic model for a given single parametric instantiation and its derived functionality may not provide an adequate result and it is therefore unavoidable to take into account possible uncertainties, variance and inhomogeneities.
The concept of robustness addresses this aspect of functional evaluation by considering a weighted average of all behaviour across a *space of perturbations* each altering the model parameters (hence its behaviour) in a particular way and having a certain probability of occurrence. A general definition of robustness was introduced by Kitano [@Kitano2007]: $$R^{\mathcal{S}}_{\mathcal{A},\mathbf{P}} = \int_{\mathbf{P}}{\psi(p)D^{\mathcal{S}}_{\mathcal{A}}(p)dp}$$ where $\mathcal{S}$ is the system, $\mathcal{A}$ is the function under scrutiny, $\mathbf{P}$ is the space of all perturbations, $\psi(p)$ is the probability of the perturbation $p\in \mathbf{P}$ and $D^{\mathcal{S}}_{\mathcal{A}}(p)$ is an *evaluation function* stating how much the function $\mathcal{A}$ is preserved under a perturbation *p* in the system $\mathcal{S}$.
For the macroscopic view as provided by the deterministic modelling framework based on ordinary differential equations (ODEs), the concept of robustness has been widely studied. There exist many mature analytic techniques based on static analysis as well as dynamic numerical methods for effective robustness analysis of ODE models. In circumstances of low molecular/cellular numbers such as in signalling [@ueda2007stochastic], immunity reactions or gene regulation [@Gillespieetal05], intrinsic and extrinsic noise plays an important role and thus these processes are more faithfully modelled stochastically. However, the existing methods and tools are not adequate for rigorous and effective analysis of stochastic models with uncertain parameters. In order to bridge this gap we adapt the concept of robustness to stochastic systems.
The main challenge of the adaptation lies in the interpretation of the evaluation function $D^{\mathcal{S}}_{\mathcal{A}}(p)$. We discuss several definitions of the evaluation function that give us different options how to quantify the ability of the system to preserve the inspected functionality under a parameters perturbation. We show how absolute and relative robustness of the stochastic systems can be captured and analysed using our framework.
Semantics of stochastic biochemical kinetics models can be defined by *Continuous Time Markov Chains* (CTMCs) where the evolution of the probability density vector describing the population of particular species is given by the chemical master equation (CME) [@Gillespie1977]. A function of a system in the biological sense is any intuitively understandable behaviour (e.g., stability of *ERK* signal effector population in high concentration observed in a given time horizon). In order to define the robustness of a system formally we need to make precise the intuitive and informal concept of functionality. Our framework builds on the formal methods where the functionality of a system is expressed indirectly by its logical properties. This leads to a more abstract approach emphasising the most relevant aspects of a system function and suppressing less important technicalities. We use stochastic temporal logics, namely the bounded time fragment of *Continuous Stochastic Logic (CSL)* [@Aziz1996csl] further extended with *rewards* [@Kwiatkowska2006rewards] (e.g., $\mathsf{P}_{\geq 0.9}[ \mathsf{G}^{[t_1,t_2]} (ERK > \textit{high})]$). To broaden the scope of possibly captured functionality we extend CSL with a class of *post-processing functions* defined over probability density vectors. We show that the bounded fragment of CSL with rewards and post-processing functions can adequately capture many biological relevant behaviours that are recognisable in finite time intervals.
Our framework is based on probabilistic model checking techniques that compute the probability with which a given CTMC satisfies a given CSL formula. The computation can be conducted using Monte Carlo based methods such as Gillespie’s stochastic stimulation algorithm [@Gillespie1977] or numerical methods such as uniformisation [@Stewart2009uniformization]. Although Monte Carlo based methods (often denoted as statistical model checking) can produce detailed simulations for stochastically evolving biochemical systems, computing a statistical description of their dynamics that is necessary for evaluating $D^{\mathcal{S}}_{\mathcal{A}}(p)$, such as the probability density, mean, or variance, requires a large number of individual simulations. Moreover, if $\mathcal{A}$ describes a behaviour that occurs rarely, the evaluation of $D^{\mathcal{S}}_{\mathcal{A}}(p)$ requires an extremely large number of simulations to be performed to obtain sufficient accuracy. As was shown in [@munsky2006finite] in such situations numerical methods are substantially more efficient. Since rigorous stochastic robustness analyses may require to compute precise probabilities of all behaviours, we build our framework on probabilistic numerical methods.
To analyse the robustness of the CTMC $\mathcal{C}$ with respect to the CSL formula $\Phi$ over the space of perturbations $\mathbf{P}$, which can be discrete but still very large or continuous and thus infinite, one needs to efficiently compute or approximate the evaluation function $D^{\mathcal{C}}_{\Phi}$, i.e, the values $D^{\mathcal{C}}_{\Phi}(p)$ for all $p\in \mathbf{P}$. One of the possible approaches (recently used in [@Bartocci2013]) is to effectively sample the perturbation space $\mathbf{P}$ and use standard statistical or numerical methods to obtain values in grid points. These values can be afterwards interpolated linearly or polynomially. Using adaptive grid refinement such an approach provides an arbitrary degree of precision. A disadvantage of this method is the fact that the obtained result is an approximation not providing any minimal and maximal upper bounds. Therefore such an approach can neglect sharp changes or discontinuities in the landscape of the evaluation function $D^{\mathcal{C}}_{\Phi}$.
It is worth noting that the evaluation function can be discontinuous or may change its value rapidly on a very small perturbation interval in situations when the given CSL formula contains nested probability operators. In particular, this is inevitable to formulate hypothesis requiring the detailed temporal program [@Alon2004] of the biological system (e.g., temporal ordering of events). The actual shape of the evaluation function arises from the combination of such a formula and the particular model. Especially, high sensitivity of a model to the perturbed parameter can intensify rapid changes in the evaluation function. An example of a formula with a nested probability operator is mentioned in Section \[sec:functionality\].
To evaluate the function $D^{\mathcal{C}}_{\Phi}$ we employ in our framework another approach that is based upon our min-max approximation method recently published in [@CAV2013]. The method guarantees strict upper and lower estimates of $D^{\mathcal{C}}_{\Phi}(p)$ without neglecting any sharp changes or discontinuities. This method exploits numerical techniques for probabilistic model checking, can provide arbitrary degree of precision and thus can be considered as an orthogonal approach to the adaptive grid refinement. The framework further extends the min-max approximation to a more general class of stochastic biochemical models (i.e., incorporation of stochastic Hill kinetics) and a more general class of quantitative properties (i.e., including post-processing functions) and allows us to compute the robustness of such systems. In our framework we provide the user not only a numerical value giving the robustness of the system but possibly also a landscape visualisation of the evaluation function.
We demonstrate the applicability of the proposed method by means of two biological case studies – a model predicting dynamics of a gene regulatory circuit controlling the $G_1/S$ phase transition in the cell cycle of mammalian cells, and two models representing different topologies of a general two-component signalling mechanism present in procaryotic cells. Both cases are examples of cellular processes where stochasticity plays a crucial role especially because of low numbers of molecules involved.
The former case study exploits the usability of the method to analyse bistability (and its robustness) in the stochastic framework and thus provides a stochastic analysis analogy to the study presented in [@Swatetal04] under the deterministic (ODE) setting. Robustness is employed to characterise parameterisations of the model with respect to the tendency of the molecule population to choose one of the possible steady states irreversibly deciding whether the cell will or will not commit to *S*-phase. The results show that intrinsic and extrinsic noise caused by randomness in protein-DNA binding/unbinding events and other processes controlling the chemical affinity of involved molecules can significantly affect the cell decision. In our model, the intrinsic noise of chemical reactions is inherently captured by stochastic mass action kinetics whereas the extrinsic noise is considered by means of parameter uncertainty.
The latter case study focuses on analysing the effect of intrinsic noise on the signalling pathway functionality. In particular, two topologically different variants of a two-component signalling pathway are exploited for different levels of input signal and different levels of intrinsic noise appearing in transcription of the two signalling components. The considered topologies have been compared in the previous study presented by Steuer et al. [@steuer2011robust] where robustness has been analysed in the setting of deterministic (ODE) models. Here the signalling mechanism is remodelled in the stochastic setting and robustness is employed to quantify under which circumstances the individual topologies are less amenable to intrinsic noise of the underlying protein transcription mechanism. The results show that the stochastic approach can uncover facts unpredictable in the deterministic setting.
Formal analysis of complex stochastic biological systems employing both the numerical and the statistical methods generally suffers from extremely high computational demands. These computational demands are even more critical if we need to analyse systems with uncertain parameters which is also the case of our framework. However, our framework has been designed in order to be adapted to high performance computing platforms (e.g. multi-core workstations and massively parallel general-purpose graphic processing units) and also to be successfully combined with existing acceleration methods, see e.g. [@munsky2006finite; @Henzinger2009; @Didier]. Although the acceleration is a subject of our future research (inspired by our previous results [@BBS10]), we already employ the fact that the min-max approximation method can be efficiently parallelised. In the second case study where the analysis of the inspected perturbation space requires an extensive numerical computation, we utilise a high performance multi-core workstation to achieve the acceleration. Fundamentally different approaches to overcome the time complexity of stochastic analyses of complex biological systems build on a moment closure computation and on a fluid approximation, see e.g. [@Verena2013; @Bortolussi2012]. These approaches are briefly discussed in the related work.
The main contributions of this paper can be summarised in the following way:
1. The adaptation of the general concept of robustness of Kitano [@Kitano2007] to the class of stochastic systems modelled by CTMCs. The key step of the adaptation is a definition of the evaluation function that reflects the quantitative aspects of stochastic models and their behaviours. We discuss several definitions of the function allowing for different ways of capturing stochastic robustness.
2. Introduction of a novel framework based on formal methods to evaluate robustness of the stochastic system with respect to the functionality given by a stochastic temporal property and to *perturbations in reaction rate parameters and initial conditions*. The framework significantly extends the min-max approximation method published in [@CAV2013], namely with the support for Hill kinetics and post-processing functions.
3. Demonstration of the fact that our concept of robustness can capture and quantify the ability of the stochastic systems to maintain their functionality. We apply our framework to two biologically relevant case studies. Namely, it is the gene regulation of mammalian cell cycle where we explore the impact of stochasticity in low molecule numbers to bistability of a regulatory circuit controlling G1/S transition and analysis of noise behaviour in different topologies of two-component signalling systems. The case studies show that our framework provides deeper understanding of how the validity of an inspected hypotheses depends on reaction rate parameters and initial conditions.
Related work
------------
The discussion on related work can be roughly divided into two parts. First, we summarise the existing methods for parameter exploration and robustness analysis of stochastic models. Second, we briefly mention the methods and tools allowing for robustness analysis of ODE models.
In the field of stochastic models, parameter estimation methods and the concept of robustness are not as established yet as in the case of ODE models. We have recently published a method [@CAV2013] where the CSL model checking techniques are extended in order to systematically explore the parameters of stochastic biochemical kinetic models. In [@Verena2012] a CTMC is explored with respect to a property formalised as a deterministic timed automaton (DTA). It extends [@Verena2011] to parameter estimation with respect to the acceptance of the DTA. Most approaches to parameter estimation [@Reinker; @Verena2011; @Petzold2012] rely on approximating the maximum likelihood. Their advantage is the possibility to analyse infinite state spaces [@Verena2011] (employing dynamic state space truncation with numerically computed likelihood) or even models with no prior knowledge of parameter ranges [@Petzold2012] (using Monte-Carlo optimisation for computing the likelihood). In [@Verena2013] the moment closure approach is considered to capture the distribution of highly populated species in combination with discrete stochastic description for low populated species. The method is able to cope with multi-modal distributions appearing in multi-stable systems. The method introduced in [@Bortolussi2012] exploits fluid (limit) approximation techniques and in that way enables an alternative approach to CSL model checking of stochastic models. Despite the computational efficiency, a shared disadvantage of all the mentioned methods is that they rely on approximations applicable only to models that include highly populated species. This is not the case of, e.g., gene regulation dynamics.
Approaches based on Markov Chain Monte-Carlo sampling and Bayesian inference [@Wilkinson; @Clarke; @Cago] can be extended to sample-based approximation of the evaluation function, but at the price of undesired inaccuracy and high computational demands [@Bernardini; @Paolo]. Compared to these methods, our method provides the upper and lower bounds of the result which makes it more reliable and precise but at the price of higher computational demands. The most relevant contribution to this domain has been recently introduced by Bartocci et al. [@Bartocci2013]. To our best knowledge this is the only related work addressing robustness of stochastic biochemical systems. The work is based on the idea to directly adapt the concept of behaviour oriented robustness to stochastic models. Individual simulated trajectories of the CTMC are locally analysed with respect to a formula of Signal Temporal Logic (STL), a linear-time temporal logic interpreted on simulated time sequences. For each simulated trajectory, the so-called satisfaction degree representing the distance from being (un)satisfied is computed, thus resulting into a randomly sampled distribution of the satisfaction degree. This distribution thus gives modellers another source of information in addition to probability of formula satisfaction (percentage of valid trajectories in the sampled set). In comparison, our method directly (and exactly) computes the probability of formula satisfaction for a different kind of temporal logic – the branching-time CSL logic. This allows to express more intricate properties that require branching time, e.g., multi-stability. On the other hand, our method as conceptually based on transient analysis does not allow to compute local analysis of individual trajectories, i.e., to obtain a satisfaction degree would require non-trivial elaboration at the level of numerical algorithms.
In the domain of ODE models, there exist several analytic methods for effective analysis under parameter uncertainty. They build on static analysis (stoichiometric analysis, flux balance analysis) as well as dynamic numerical methods (simulation, monitoring by temporal formulae, sensitivity analysis) implemented in tools (e.g. [@Hoops2006copasi; @Loew2001vcell; @Fages2004biocham]). Robustness analysis with respect to functionality specified in terms of temporal formulae has been introduced recently [@Fainekos2009robustness; @Rizketal09]. There exist two major approaches how to define and analyse robustness. If only parameters of the model are perturbed, we speak of a *behaviour oriented approach* to robustness. This approach has been explored by Fainekos & Pappas [@Fainekos2009robustness], further extended by A. Donzé et al. [@Donze2010robust] and implemented in the toolbox Breach [@Donze2010breach]. Another option could be to perturb the model structure i.e. the reaction topology, as this is done in many gene knock-out biological experiments. Such changes are in principle discrete and the problem of robustness computation for such perturbations would reduce to solving many individual instances of the same problem for each discrete topology. However identifying model behaviour shared among individual perturbations can lead to more efficient analysis [@Barnat12coloredmc].
Yet another way to look at perturbations is from the perspective of property uncertainty. If the system is considered fixed and all parameters exactly known, the uncertainty then lies in the property of interest. For a specific property such as “The concentration of X repeatedly rises above 10 and drops below 5 within the first 20 minutes” where all three numerical constants can be altered, we explore how much would they have to be altered in order to affect the property validity in the given model. This approach has been adopted for ODEs by F. Fages et al. [@Rizketal09] and implemented in the tool BIOCHAM [@Fages2004biocham]. When only parameters of the property are perturbed, it is the case of a *property oriented approach* to robustness.
Methods {#sec:methods}
=======
Methodology Overview
--------------------
In this paper we propose a formal framework that allows to analyse the robustness of stochastic biochemical systems with respect to a space of perturbing parameters. The framework consists of the following objects:
- *a finite state stochastic biochemical system given by a set of chemical species participating in a set of chemical reactions*
Each of the reaction is associated with a stochastic rate function that for a fixed stochastic rate constant returns the rate of the reaction. To formalise such system we use a population based finite state continuous time Markov Chain (CTMC), i.e, a state of the CTMC is given by populations of particular species and the evolution of the CTMC is driven by the chemical master equation (CME) [@Gillespie1977; @Didier].
- *a perturbation space defined by a Cartesian product of uncertain stochastic rate constants given as value intervals with minimal and maximal bounds*
Additionally, the perturbation space may also be expanded by initial conditions of the system (i.e, interval for the size of a population of a particular species) encoded in the initial state of the CTMC. The given stochastic system and the perturbation space induce a *set of parameterised* CTMCs.
- *set of paths that describe the evolution of a fully instantiated stochastic system (i.e., in which all stochastic rate constants and the initial state are specified) over time*
For a state of the system and a finite time there is a unique probability measure of all paths starting in that state that defines *probability distribution* over states occupied by the system at the given time. Each perturbation from a given perturbation space possibly leads to a different probability distribution.
- *stochastic temporal property interpreted over the paths and states of CTMC enabling to specify an a priori given quantitative hypothesis about the system*
We primarily focus on the *bounded time fragment of Continuous Stochastic Logic* (CSL) [@Aziz1996csl] further extended with rewards [@Kwiatkowska2006rewards]. For most cases of biochemical stochastic systems the bounded time restriction is adequate since a typical behaviour is recognisable in finite time. Additionally, we also consider properties given by a class of post-processing functions defined over probability distributions at the given finite time.
The main goal of our framework is to analyse how the validity of an *a priori* given hypothesis expressed as a temporal property depends on uncertain parameters of the inspected stochastic system. For this purpose we adapt the general definition of robustness [@Kitano2007] to the class of stochastic systems. While the concept of robustness is well established for deterministic systems [@Donze11rob-behaviour; @Rizk09rob-property], it has not been adequately addressed for stochastic systems. The key difference is the fact that evolution of a stochastic system is given by a set of paths in contrast to a single trajectory as in the case of a deterministic system. Hence a stochastic system at the given time is described by a probability distribution over states of the corresponding CTMC in contrast to the single state representation of a deterministic system. Therefore, the definition of robustness for stochastic systems requires a more sophisticated interpretation of the evaluation function that determines how the quantitative temporal property is preserved under a perturbation of the system’s parameters.
Similarly to Kitano, we define robustness of stochastic systems as the integral of an evaluation function. In our case the evaluation function $D^{\mathcal{C}_p}_{\Phi}$ for each parameter point *p* from the inspected perturbation space $\mathbf{P}$ returns the quantitative model checking result for the respective CTMC $\mathcal{C}_p$ and the given property $\Phi$. We show how robustness can be effectively over/under-approximated for a class of quantitative temporal properties using new techniques for model checking of parameterised CTMCs. Moreover, if the property can be expressed using only the bounded time fragment of CSL with rewards (i.e., without post-processing functions) we can extend the approach to global quantitative model checking techniques. They enable to compute the model checking result for all states of a CTMC with the same price as for a single state and thus to analyse the perturbation of initial conditions in a much more effective way. Finally, we demonstrate how robustness can capture and quantify the ability of a stochastic system to maintain its functionality described by such class of properties.
Since the inspected perturbation space is in principle dense the set of parameterised CTMCs to be explored is infinite. It is thus not possible to compute the model checking result for each CTMC individually. The straightforward approach to overcome this problem could be to sample points from the perturbation space and use existing model checking techniques for fully instantiated CTMCs. That way we can obtain precise model checking results in the grid points and then interpolate them linearly or polynomially. Although an adaptive grid refinement could provide an arbitrary degree of precision, it does not guarantee strict lower and upper bounds. Hence such an approach could neglect sharp changes or discontinuities of the evaluation function. Since we want to guarantee strict bounds of obtained results, we extend our previously published method [@CAV2013]. This method allows to compute strict minimal and maximal bounds on the quantitative model checking results for all CTMCs $\left\{ \mathcal{C}_p \mid p \in \mathbf{P} \right\}$ for a given perturbation space $\mathbf{P}$.
Models
------
The formalism used to model a biochemical system is essential since it not only dictates the possible behaviours that may or may not be captured, but also determines the means of detecting them. ODEs enable the study of large ensembles of molecules in population count and species diversity since they abstract from the individualistic properties of each molecule such as position or its stochastic behaviour and take as its variables only concentrations of each species. Stochastic models such as CTMCs abstract positions of molecules but maintain their individual reactions. Even more detailed models such as Brownian dynamics which keep track of positions but abstract from the geometry and orientation of each molecule could be used. However as the amount of information about each individual molecule increases the computational complexity of proving some property to hold over all the behaviours of a model becomes quickly infeasible even for small models.
In our framework we focus on stochastic biochemical systems that can be formalised as a finite state system $\mathcal{S}$ defined by a set of *N* *chemical species* in a well stirred volume with fixed size and fixed temperature participating in *M* *chemical reactions*. The number $X_i$ of molecules of each species $S_i$ has a specific bound and each reaction is of the form $u_1 S_1 + \ldots + u_N S_N \longrightarrow v_1 S_1 + \ldots + v_N S_N$ where $u_i, v_i \in \mathbb{N}_0$ represent *stoichiometric coefficients*.
A *state* of a system in time $t$ is the vector $\mathbf{X}(t) = (X_1(t),
X_2(t), \ldots, X_N(t) )$. When a single reaction with index $r \in \{1, \ldots,
M\}$ with vectors of stoichiometric coefficients $U_r$ and $V_r$ occurs the state changes from $\mathbf{X}$ to $\mathbf{X}' = \mathbf{X} - U_r + V_r$, which we denote as $\mathbf{X} \stackrel{r}{\rightarrow} \mathbf{X}'$. For such reaction to happen in a state $\mathbf{X}$ all reactants have to be in sufficient numbers and the state $\mathbf{X}'$ must reflect all species bounds. The *reachable state space* of $\mathcal{S}$, denoted as $\mathbb{S}$, is the set of all states reachable by a finite sequence of reactions from *an initial state* $\mathbf{X}_0$. The set of indices of all reactions changing the state $\mathbf{X}_i$ to the state $\mathbf{X}_j$ is denoted as $\mathsf{reac}(\mathbf{X}_i,\mathbf{X}_j) =
\{r \mid \mathbf{X}_i \stackrel{r}{\longrightarrow} \mathbf{X}_j \}
$. Henceforward the reactions will be referred directly by their indices.
According to [@Gillespie1977; @Didier] the behaviour of a stochastic system $\mathcal{S}$ can be described by the CTMC $\mathcal{C} = (\mathbb{S},
\mathbf{X}_0, \mathbf{R})$ where the transition matrix $\mathbf{R}(\mathbf{X}_i,\mathbf{X}_j)$ gives the probability of a transition from $\mathbf{X}_i$ to $\mathbf{X}_j$. Formally, the transition matrix is defined as: $$\mathbf{R}(\mathbf{X}_i,\mathbf{X}_j) \stackrel{def}{=} \sum_{r \in \mathsf{reac}(\mathbf{X}_i,\mathbf{X}_j) } f_r(\mathbf{k}_r, \mathbf{X}_i)$$ where $f_r$ is a *stochastic rate function* and $\mathbf{k}_r$ is a vector of all numerical parameters occurring in $f_r$ such as a *stochastic rate constant* $k_r$, stoichiometry exponents, Hill coefficients etc.
In case of mass action kinetics the stochastic rate function has the simple form of a polynomial of reacting species populations. That is $ f_r(\mathbf{k}_r,
\mathbf{X}_i) = k_r \cdot C_{r,i}$ where $C_{r,i} \stackrel{def}{=} \prod_{l =
1}^{N}\binom{\mathbf{X}_{i,l}}{u_l}$ corresponds to the population dependent term such that $\mathbf{X}_{i,l}$ is the *l*th component of the state $\mathbf{X}_{i}$ and $u_l$ is the stoichiometric coefficient of the reactant $S_l$ in reaction $r$. However, sometimes the mass action kinetics is not sufficient, especially, when the reactions are not elementary but are rather an abstraction of several reactions with unknown precise dynamics (e.g. gene transcription) or if including all elementary reactions would cause the analysis to be computationally infeasible. In such cases dynamics are typically approximated by Hill functions [@Hill1910], a quasi-steady-state approximation [@Madsen2012] of the law of mass conservation. For sake of simplicity of our presentation we will further assume that for each reaction $r$ the vector $\mathbf{k}_r$ is one-dimensional and thus $\mathbf{k}_r = k_r$, the proposed methods can however be directly used also for multi-dimensional vectors of constants. To comply with standard notation in the area of CTMC analysis henceforward the states $\mathbf{X}_i \in \mathbb{S}$ will be denoted as $s_i$.
The probability of a transition from state $s_i$ to $s_j$ occurring within *t* time units is $1 - e^{-\mathbf{R}(s_i,s_j) \cdot t}$, if such a transition cannot occur then $\mathbf{R}(s_i,s_j) = 0$. The time before any transition from $s_i$ occurs is exponentially distributed with an overall *exit rate* $E(s_i)$ defined as $E(s_i) = \sum_{s_j \in
\mathbb{S}}{\mathbf{R}(s_i,s_j)}$. A path $\omega$ of CTMC $\mathcal{C}$ is a non-empty sequence $\omega=s_0,t_0,s_1,t_1\ldots$ where $\mathbf{R}(s_i,s_j)>0$ and $t_i\in \mathbb{R}_{\geq 0}$ is the amount of time spent in the state $s_i$ for all $i \geq 0$. For all $s\in \mathbb{S}$ we denote by $Path^{\mathcal{C}}(s)$ the set of all paths of $\mathcal{C}$ starting in state $s$. There exists the unique probability measure on $Path^{\mathcal{C}}(s)$ defined, e.g., in [@Kwiatkowska2007]. Intuitively, any subset of $Path^{\mathcal{C}}(s)$ has the unique probability that can be effectively computed. For the CTMC $\mathcal{C}$ the transient state distribution $\pi^{\mathcal{C},s,t}$ gives for all states $s'\in \mathbb{S}$ the transient probability $\pi^{\mathcal{C},s,t}(s')$ defined as the probability, having started in the state *s*, of being in state $s'$ at the finite time *t*.
Perturbations
-------------
In our approach we have focused on the behavioural approach for stochastic systems and thus we will now define a set of perturbed stochastic systems and their CTMCs. Let each stochastic rate constant $k_r$ have a value interval $[k_r^{\bot},k_r^{\top}]$ with minimal and maximal bounds expressing an *uncertainty range* or *variance* of its value. A *perturbation space* $\mathbf{P}$ induced by a set of stochastic rate constants $k_r$ is defined as the Cartesian product of the individual value intervals $\mathbf{P} =
\prod_{r=1}^{M}[k_r^{\bot},k_r^{\top}]$. A single *perturbation point* $p
\in \mathbf{P}$ is an *M*-tuple holding a single value of each rate constant, i.e., $p = (k_{1_p}, \ldots , k_{M_p})$.
A stochastic system $\mathcal{S}_p$ with its stochastic rate constants set to the point $p\in \mathbf{P}$ is represented by a CTMC $\mathcal{C}_p =
(\mathbb{S}, s_0, \mathbf{R}_p)$ where transition matrix $\mathbf{R}_p$ is defined as: $$\mathbf{R}_p(s_i,s_j) \stackrel{def}{=} \sum_{r \in \mathsf{reac}(s_i,s_j) } f_r(k_{r_p}, s_i)$$ A *set of parameterised* CTMCs induced by the perturbation space $\mathbf{P}$ is defined as $\mathbf{C} = \{ \mathcal{C}_p \mid p \in \mathbf{P} \}$.
Additionally, we consider the perturbation of initial conditions of the stochastic system that are represented by different initial states of the corresponding CTMC. In this case we extend the perturbation space such that a single perturbation point $p\in \mathbf{P}^e = \mathbb{I} \times \mathbf{P}$ where $\mathbb{I} \subseteq \mathbb{S}$ is an *M*+1-tuple holding a single value of an initial state and a single value of each rate constant, i.e., $p =
(s_p,k_{1_p}, \ldots , k_{M_p})$ and CTMC $\mathcal{C}_p =(\mathbb{S}, s_p,
\mathbf{R}_p)$.
Functionality {#sec:functionality}
-------------
To be able to automatically analyse a system’s function $\mathcal{A}$ under scrutiny there must be a formal way of expressing a function of a system. A function of a system in the biological sense is any intuitively understandable behaviour such as response, homoeostasis, reproduction, respiration or growth. It can be a high level concept such as chemotaxis as well as a low level one e.g. reaching of a state with a given number of molecules of a specific species.
The inspected function can usually be described by a *property* that is understood as an abstraction of a system’s behaviour expressed in some temporal logic and given as a formula of that logic. Unlike the intuitive concept of a biological function mentioned above, a property may be formally verified over a formal model of a system and proven to hold or to be violated. Since the concept of robustness builds on the notion of a function that can be measured, we focus on a quantitative logic for stochastic systems. We use *continuous stochastic logic* (CSL) [@Aziz1996csl; @Baier2003mcctmc] extended with *reward* operators [@Kwiatkowska2006rewards]. Reward operators allow us to further broaden the scope of possibly captured behaviour. They enable to express properties such as the probability of a system being in the specified set of states over a time interval or the probability that a particular reaction has occurred.
Full CSL with rewards can express properties concerning a system in near future as well as the infinite steady state situation. In this paper we focus only on the *bounded time fragment of CSL*. This fragment allows us to speak only about behaviour within a finite time horizon. For most cases of biochemical stochastic systems, such as intracellular reaction cascades or multi-cellular signalling, the bounded time restriction is adequate since a typical behaviour is recognisable within finite time intervals [@KwiatkowskaBIO].
As we show later on, there exist several biologically relevant properties that cannot be directly expressed by CSL with rewards. Therefore, we employ a class of post-processing functions to specify and analyse robustness of stochastic systems with respect to such properties. The key idea of these functions is to process and aggregate the transient state distribution at the given finite time.
Let $\mathcal{C} =\left(\mathbb{S}, s_0, \mathbf{R}, L \right)$ be a labelled CTMC such that *L* is a labelling function which assigns to each state $s \in
\mathbb{S}$ the set *L(s)* of atomic propositions that are valid in state $s$. We consider the specification of the inspected property using the bounded time fragment of CSL with rewards and post-processing functions. The syntax of this logic is defined in the following way. A state formula $\Phi$ is given as $$\Phi::= \mathsf{true} \mid a \mid \neg\Phi \mid \Phi \wedge \Phi \mid
\mathsf{P}_{\sim p}[\phi] \mid \mathsf{R}_{\sim r}[\mathsf{C}^{\leq t}] \mid
\mathsf{R}_{\sim r}[\mathsf{I}^{=t}] \mid \mathsf{E}_{\sim r}[\mathsf{I}^{=t}]$$ where $\phi$ is a path formula given as $\phi::= \mathsf{X}\mbox{~}\Phi \mid$ $\Phi\mbox{~}\mathsf{U}^{I}\mbox{~}\Phi$, *a* is an atomic proposition, $\sim \in \left\{ <, \leq, \geq, > \right\}$, $p \in [0,1]$ is a probability, $r
\in \mathbb{R}_{\geq 0}$ is an expected reward and $I = [a,b]$ is a bounded time interval such that $a,b \in \mathbb{R}_{\geq 0} \wedge a \leq b$. Path operators $\mathsf{G}$ (always) and $\mathsf{F}$ (eventually) are derived in the standard way using the operator $\mathsf{U}$. In order to specify properties containing rewards ($\mathsf{R}_{\sim r}[\mathsf{C}^{\leq t}]$ is the *cumulative reward* acquired up to time *t*, $\mathsf{R}_{\sim
r}[\mathsf{I}^{= t}]$ is the *instantaneous reward* in time *t*) the CTMC $\mathcal{C}$ is enhanced with reward (cost) structures. Two types of reward structures can be used, *a state reward* and *a transition reward*. For sake of simplicity, we consider in this paper only state rewards, however, the proposed methods can be easily extended to transition rewards as well. The state reward $\rho(s)$ defines the rate with which a reward is acquired in state $s\in \mathbb{S}$. A reward of $t \cdot \rho(s)$ is acquired if $\mathcal{C}$ remains in state *s* for *t* time units.
Since the function $\rho$ has to be defined before the actual analysis of the CTMC, the rewards for particular states have to be known prior to the specification of the property. This fact limits the class of properties that can be expressed using such structures. For example, noise expressed by a *mean quadratic deviation* (*mqd*) of the population probability distribution of a species at a given time cannot be specified using CSL with rewards. To compute the *mqd* we need to know the mean of the distribution to be able to obtain the corresponding coefficients and encode them into state rewards.
To overcome this problem we introduce the abstract state operator $\mathsf{E}_{\sim r}[\mathsf{I}^{=t}]$ which *evaluates* the state distribution $\pi^{\mathcal{C},s_0,t}$ at the given time instant *t* by a user provided real-valued *post-processing* function $Post(\pi^{\mathcal{C},s_0,t})$ and compares it to $\sim r$. At the end of this section we show how to define $Post$ in order to specify biologically relevant properties such as noise using the *mqd*. The *mqd* is also used in the second case study to analyse a noise in different variants of signalling pathways.
The formal semantics of the bounded fragment of CSL with rewards and post-processing functions is defined similarly as the semantics of full CSL and thus we refer the readers to original papers. The key part of the semantics is given by the definition of the satisfaction relation $\vDash$. It specifies when a state $s$ satisfies the state formula $\Phi$ (denoted as $s \vDash \Phi$) and when a path $\omega$ satisfies the path formula $\phi$ (denoted as $\omega
\vDash \phi$). The informal definition of $\vDash$ is as follows:
- $s \vDash \mathsf{E}_{\sim r}[\mathsf{I}^{=t}]$ iff $Post(\pi^{\mathcal{C},s,t})$ satisfies $\sim r$.
- $s \vDash \mathsf{P}_{\sim p}[\phi]$ iff the probability of all paths $\omega \in Path^{\mathcal{C}}(s) $ that satisfy the path formula $\phi$ (denoted as $Prob^{\mathcal{C}}(s,\phi)$) satisfies $\sim p$, where
- $\omega$ satisfies $\mathsf{X}\mbox{~}\Phi$ iff the second state on $\omega$ satisfies $\Phi$
- $\omega$ satisfies $\Phi\mbox{~}\mathsf{U}^{I}\mbox{~}\Psi$ iff there exists time instant $t\in I$ such that the state on $\omega$ occupied at $t$ satisfies $\Psi$ and all states on $\omega$ occupied before $t'\in [0,t)$ satisfy $\Phi$
- $s \vDash \mathsf{R}_{\sim r}[\mathsf{C}^{\leq t}]$ iff the sum of expected rewards over $Path^{\mathcal{C}}(s)$ *cumulated* until $t$ time units (denoted as $Exp^{\mathcal{C}}(s,\mathsf{X}_{\mathsf{C}^{\leq t}})$) satisfies $\sim r$
- $s \vDash \mathsf{R}_{\sim r}[\mathsf{I}^{= t}]$ iff the sum of expected rewards over all paths $\omega \in Path^{\mathcal{C}}(s)$ at time *t* (denoted as $Exp^{\mathcal{C}}(s,\mathsf{X}_ {\mathsf{I}^{= t}})$) satisfies $\sim\!r$.
A set $Sat_{\mathcal{C}}(\Phi)=\{s \in \mathbb{S} \mid s \vDash \Phi \}$ denotes the set of states that satisfy $\Phi$.
Note that the syntax and semantics can be easily extended with “quantitative” formulae in the form $\Phi ::= \mathsf{P}_{= ?}[\phi] \mid
\mathsf{R}_{= ?}[\mathsf{C}^{\leq t}] \mid \mathsf{R}_{= ?}[\mathsf{I}^{= t}]
\mid \mathsf{E}_{=?}[\mathsf{I}^{=t}]$, i.e., the topmost operator of the formula $\Phi$ returns a quantitative result, as used, e.g., in PRISM [@KNP11]. In this case the result of a decision procedure is not in the form of a boolean yes/no answer but the actual numerical value of the probability $Prob^{\mathcal{C}}(s,\phi)$, the expected reward $Exp^{\mathcal{C}}(s,\mathsf{X})$ for $\mathsf{X} \in \{ \mathsf{X}_
{\mathsf{I}^{= t}}, \mathsf{X}_ {\mathsf{C}^{\leq t}}\}$ or the value of $Post^{\mathcal{C}}(s,t)$. The computation of a numerical value is of the same complexity class as the computation of a result to be compared leading to a boolean answer, although in some cases the comparison may be carried out on less precise or preliminary results. As we will show the quantitative result is much more suitable for robustness analysis.
To demonstrate that the bounded time fragment of CSL with rewards and post-processing functions can adequately capture relevant biological behaviours and thus be successfully used in the robustness analysis of stochastic biochemical systems, we list several formalisations of such behaviours.
- *stochastic reachability* - $\mathsf{P}_{\geq 0.8}[ \mathsf{F}^{[5,10]} ( A \geq 3)]$ expresses the property “The probability that the population of *A* exceeds 3 between 5 and 10 time units is at least $80\%$”.
- *stochastic stability* - $\mathsf{P}_{=?}[ \mathsf{G}^{[0,5]} ( A \geq 1 \wedge A \leq 3 )]$ represents the quantitative property “What is the probability that the population of *A* remains between 1 and 3 during the first 5 time units?”
- *stochastic temporal ordering of events* - $\mathsf{P}_{<0.2}[(A \le 2)\ \mathsf{U}^{[2,3]}\ \mathsf{P}_{\geq 0.95} [ ( 2 < A
\leq 5)\ \mathsf{U}^{[0,10]} (A > 5)]]$ expresses the stochastic version of the following temporal pattern: “Species A is initially kept below 2 until it reaches 5 and finally exceeds 5.” The formula quantifies both the time constrains of the events and the probability that the events occur. It expresses that “The probability that the system has following probabilistic temporal pattern is less that $20\%$: the population of *A* is initially kept below 2 until the system between 2 and 3 times units reaches the states satisfying the subformula $\mathsf{P}_{\geq 0.95} [ ( 2 < A \leq 5)\ \mathsf{U}^{[0,10]} (A > 5)]]$." The subformula specifies the states where “The probability that the population of *A* remains greater than 2 and less or equal 5 until it exceeds 5 within 10 time units, is greater than $95\%$."
- *cumulative reward property* - $\mathsf{R}_{<5}[\mathsf{C}^{\leq 100}]$, where $\forall s\in \mathbb{S}\ \rho(s) = 1$ if $0 \leq A \leq 3$ in *s*, captures the property that “The overall time spent in states with population of *A* between 0 and 3 within the first 100 time units, is less than 5 time units”, which can also be understood as “The probability of the system being in a state with population of *A* between 0 and 3 within the first 100 time units is less then 5%”.
- *noise as mean quadratic deviation* - $\mathsf{E}_{<10}[\mathsf{I}^{=100}]$, where the post-processing function is defined as $Post(\pi) = \sum_{s \in \mathbb{S}}{\lvert s(A) - mean(\pi,A)\rvert^2 \cdot \pi(s)}$, $s(A)$ gives the population of *A* in state *s* and $mean(\pi,A)$ is the mean of the distribution $\pi$ defined as $mean(\pi,A) = \sum_{s \in \mathbb{S}}{s(A) \cdot \pi(s)}$. This property states that “The mean quadratic deviation of the distribution of species *A* at time instant $t=100$ must be less then 10”.
The $\mathsf{E}$ operator could in principle be extended to allow for intervals and be interpreted as an integral of a user-provided post-processing function over the given time interval. This could lead e.g. to the noise over time interval which is more natural then an instantaneous noise, however the computation complexity of such an operator would be very large.
![[**Running example.**]{} The example model contains one species *X* with the population bounded to 40, two reactions: production of *X* ($\emptyset \rightarrow X$ with rate $k_1$), degradation of *X* ($X \rightarrow \emptyset$ with rate $k_2 \cdot [X]$, $k_2 = 0.01$) and initial population of *X* is 15. The corresponding CTMC has 41 states (initial state $s_0$ corresponds to state with initial population). The inspected formula $\Phi$ represents the quantitative property “What is the probability that the population of $X$ is between 15 and 20 at time 1000?” The perturbation space $\mathbf{P}$ is given by the interval of the rate $k_1 \in [0.1,0.3]$. On the right, there are depicted three transient distributions at time 1000 for three different values of $k_1$ and the resulting probability for the formula $\Phi$ obtained as the sum of probabilities in states with populations from 15 to 20.[]{data-label="fig:decomposition"}](decomposition){width="\textwidth"}
Robustness
----------
Let us recap the general definition of Kitano [@Kitano2007] to show how it can be interpreted and how we propose to use it in the context of stochastic systems.
$$R^{\mathcal{S}}_{\mathcal{A},\mathbf{P}} = \int_{\mathbf{P}}{\psi(p)D^{\mathcal{S}}_{\mathcal{A}}(p)dp} \hspace{1cm} D^{\mathcal{S}}_{\mathcal{A}}(p) = \left\{
\begin{array}{cl}
0 & p \in \mathbf{B} \subset \mathbf{P} \\
f_{\mathcal{A}}(p)/f_{\mathcal{A}}(0) & p \in \mathbf{P} \setminus \mathbf{B}
\end{array} \right.$$
### Functionality evaluation
Kitano proposed that the evaluation function $D^{\mathcal{S}}_{\mathcal{A}}(p)$ stating how much the functionality $\mathcal{A}$ is preserved in perturbation *p* should be defined using a subspace $\mathbf{B}$ of all perturbations where the system’s function is completely missing and the rest $\mathbf{P} \setminus \mathbf{B}$ where the functions’ viability is somehow altered. This definition is meaningful e.g. in cases where the perturbation would lead to a system not having the function at all (speed of reproduction of a dead cell) or in cases where a plain measurement would provide a function’s value, however, in reality the system would lack the function altogether (inside temperature during homoeostasis experiment in conditions when an organism loses thermal control and has temperature of environment). These examples have in common that the information about a system lacking its function is provided from outside because if it could be deducible from the system’s state alone it could be incorporated into the evaluation function $D^{\mathcal{S}}_{\mathcal{A}}(p)$ itself.
For perturbations $p \in \mathbf{P} \setminus \mathbf{B}$ where the system maintains its function at least partially, Kitano proposes to express the evaluation function $D^{\mathcal{S}}_{\mathcal{A}}(p) = f_{\mathcal{A}}(p)/f_{\mathcal{A}}(0)$ relatively to the ground unperturbed state $f_{\mathcal{A}}(0)$. This is meaningful e.g. for naturally living systems where the ground state is measurable and is considered as an optimal performance state. Such a definition could then enable the comparison of a common property of different species. For example, a reproduction rate for a mouse and a sequoia tree with respect to perturbations of their environment. If a mouse has 20 offsprings per year in base temperature and 22 offsprings for a 2 degrees Kelvin rise then the evaluation function $D^{\mathcal{S}_M}_{\mathcal{A}}(+2 K) = 22/20 = 1.1$. While if a sequoia has 1000 seedlings in ground temperature and 1200 for a 2 degrees Kelvin rise then $D^{\mathcal{S}_S}_{\mathcal{A}}(+2 K) = 1200/1000 = 1.2$.
We can see that the relativistic nature of Kitano’s definition enables comparison of otherwise incomparable organisms and their robustness to perturbations. In our example, the sequoia is more robust to the single perturbation of temperature by $+2K$ than the considered species of mice. However, in cases when no ground state is given the absolute value can be more adequate. The next subsection shows that robustness in stochastic systems can be defined in several different ways providing both the absolute and relative interpretations.
### Robustness in Stochastic systems
Let $\mathcal{S}$ be a stochastic system with CTMC $\mathcal{C} = \left(\mathbb{S}, s_0, \mathbf{R}, L \right)$, let $\mathbf{P}$ be a space of perturbations to the stochastic kinetic constants of $\mathcal{C}$ and let $\Phi$ be a formula of the bounded time fragment of CSL with rewards and evaluation functions formalising the system’s function $\mathcal{A}$. Since the evaluation of $\Phi$ is inherently dependent on the initial conditions of the system that are encoded using the initial state $s_0$, we consider the evaluation function in the form $D^{\mathcal{C},s_0}_{\Phi}$.
In cases where the set of perturbed stochastic kinetic constants $\mathbf{P}$ is actually extended by initial conditions to $\mathbf{P}^e$, then for a single perturbation point $p = (s_p, k_{1_p}, \ldots , k_{M_p}) \in \mathbf{P}^e$ we consider the initial state $s_0$ of $\mathcal{C}$ to be substituted by $s_p$ in all subsequent expressions, otherwise it remains the original $s_0$.
Let us first define an auxiliary *Eval* function which is then used in the definition of $D^{\mathcal{C},s_0}_{\Phi}$: $$Eval_{\Phi}^{\mathcal{C}}( s_0) = \left\{
\begin{array}{cl}
Prob^{\mathcal{C}}(s_0,\phi) & \mbox{if~} \Phi \equiv \mathsf{P}_{\star}[\phi] \\[0.3em]
Exp^{\mathcal{C}}(s_0,\mathsf{X}_{\mathsf{C}^{\leq t}}) & \mbox{if~} \Phi \equiv \mathsf{R}_{\star}[\mathsf{C}^{\leq t}] \\[0.3em]
Exp^{\mathcal{C}}(s_0,\mathsf{X}_{\mathsf{I}^{= t}}) & \mbox{if~} \Phi \equiv \mathsf{R}_{\star}[\mathsf{I}^{= t}] \\[0.3em]
Post(\pi^{\mathcal{C},s_0,t}) & \mbox{if~} \Phi \equiv \mathsf{E}_{\star}[\mathsf{I}^{= t}]
\end{array} \right.
\label{eg:eval}$$ where $\star \in \{=?, \sim\! r\}$. Given these specifications the evaluation function $D^{\mathcal{C},s_0}_{\Phi}$ can be restated in several different ways:
$$\begin{aligned}
D^{\mathcal{C},s_0}_{\Phi}(p) &= \left\{
\begin{array}{clcl}
\hspace{1cm} 0 \hspace{1cm} & p \in \mathbf{B} \subset \mathbf{P} & \vee & Eval_{\Phi}^{\mathcal{C}_p}(s_0) \nsim r \\[0.5mm]
1 & p \in \mathbf{P} \setminus \mathbf{B} & \wedge & Eval_{\Phi}^{\mathcal{C}_p}(s_0) \sim r
\end{array} \right.
\label{eq:sem_boolean}\\
D^{\mathcal{C},s_0}_{\Phi}(p) &= \left\{
\begin{array}{cl}
\hspace{1cm} 0 \hspace{1cm} & p \in \mathbf{B} \subset \mathbf{P} \\[0.8mm]
\frac{Eval_{\Phi}^{\mathcal{C}_p}(s_0)}{r} & \mbox{else if~} \sim \in \{ \geq, > \} \\[0.8mm]
\frac{r}{ Eval_{\Phi}^{\mathcal{C}_p}(s_0)} & \mbox{else if~} \sim \in \{ \leq, < \}
\end{array} \right.
\label{eq:sem_relative}\\
D^{\mathcal{C},s_0}_{\Phi}(p) &= \left\{
\begin{array}{cl}
\hspace{1cm} 0 \hspace{1cm} & p \in \mathbf{B} \subset \mathbf{P} \\[0.5mm]
Eval_{\Phi}^{\mathcal{C}_p}(s_0) & \mbox{else}
\end{array} \right.
\label{eq:sem_absolute}\\
D^{\mathcal{C},s_0}_{\Phi}(p) &= \left\{
\begin{array}{cl}
\hspace{1cm} 0 \hspace{1cm} & p \in \mathbf{B} \subset \mathbf{P} \\[0.8mm]
\lvert Eval_{\Phi}^{\mathcal{C}_p}(s_0) - X \rvert^2 & \mbox{else, ~} X = agr \{Eval_{\Phi}^{\mathcal{C}_p}(s_0) \mid \mathcal{C}_p \in \mathbf{P} \} \wedge agr\in \{min,max,avg \}
\end{array} \right.
\label{eq:sem_relative2} \end{aligned}$$
The first definition of the evaluation function (\[eq:sem\_boolean\]) is possible for the specification where the topmost operator of the formula $\Phi$ includes the threshold $r$ (i.e. $\star = \sim \! r$). Because $D^{\mathcal{C},s_0}_{\Phi}(p)$ returns a qualitative result robustness $R^{\mathcal{C}}_{\Phi,\mathbf{P}}$ specifies the measure of all perturbations in $\mathbf{P}$ for which the property holds in a strictly boolean sense – it is the fraction of $\mathbf{P}$ where the property is valid. This definition can be used, e.g., in the property $\Phi_A = \mathsf{P}_{\geq 0.8}[ \mathsf{F}^{[0,5]} (X > 300)]$ which specifies that in $80\%$ of cases the population of X is larger than 300 within 5 seconds. For this property and a model with a parameter $k \in [0,10]$ the robustness gives us the fraction of the parametric interval $[0,10]$ for which the model satisfies $\Phi_A$.
In the second definition (\[eq:sem\_relative\]) $D^{\mathcal{C},s_0}_{\Phi}(p)$ returns the quantitative value that is relative to the threshold *r*. Therefore, robustness can be interpreted as the average relative validity of the property over $\mathbf{P}$. If *r* corresponds to the validity of $\Phi$ in conditions considered natural for the inspected system $\mathcal{S}$ (i.e, to the unperturbed state) then this interpretation complies with the original definition of Kitano. Let us consider the same property $\Phi_A$ and the same parametric space $k \in [0,10]$. If in $60\%$ of model behaviours the population of X is larger than 300 within 5 seconds than the robustness is 0.6/0.8 = 0.75. If the probability is different in each *k* then the robustness gives us the average value that meets our expectations.
The third definition (\[eq:sem\_absolute\]) is possible for specifications using the quantitative semantics of formula $\Phi$ (i.e. $\star = ?$). The robustness gives the mean validity over all $\mathbf{P}$ regardless of any probability threshold *r*. This interpretation is convenient when there are no *a priori* assumptions about the system expected behaviour.
Finally, to express the fact that the system behaviour remains the same (with respect to the evaluation function) across the space of perturbations we introduce the fourth definition (\[eq:sem\_relative2\]). It uses an aggregation function to compute a mean value and then express the variance from the mean. This definition enables us to compare models which have same numerical values of robustness in the sense of definition (\[eq:sem\_absolute\]) but which achieve the average value with very different landscapes of evaluation function.
While the last three definitions require the precise computation of the probability value in every $p \in \mathbf{P}$, the first definition is amenable to approximate solutions. In this case it suffices to ensure that the probability is larger or smaller then *r*. In many cases it can be achieved without computing the precise value and thus statistical model checking techniques can be efficiently used. In both case studies we use definition (\[eq:sem\_absolute\]), since we do not consider any ground unperturbed state. We assume $\mathbf{B}$ to be an empty set and expect all the lack of functionality $\mathcal{A}$ to be fully expressible in terms of the property $\Phi$.
Robustness computation
----------------------
Now we look how robustness $R^{\mathcal{C}}_{\Phi,\mathbf{P}^e}$ can be efficiently computed by using the evaluation function $D^{\mathcal{C},s_0}_{\Phi}$. Let us first consider the case where the space of perturbations $\mathbf{P}$ does not contain different initial states.
As will be shown in the next section the computation of $Eval^{\mathcal{C}_p}_{\Phi}(s_0)$ even for a single perturbation point $p$ is rather complex, therefore a computation of the integral over the whole space of perturbations is not possible in an explicit sense. Instead a way to approximate the upper and lower bounds $R_{\Phi,\mathbf{P},\top}^{\mathcal{C}}$ and $R_{\Phi,\mathbf{P},\bot}^{\mathcal{C}}$ is introduced enabling the approximation of the value of the integral as $$\begin{array}{rcl}
R_{\Phi,\mathbf{P}}^{\mathcal{C}} &\stackrel{def}{=}& \displaystyle\int_{\mathbf{P}}{\psi(p)D^{\mathcal{C}}_{\Phi}(p)dp} \\[0.6em]
R_{\Phi,\mathbf{P}}^{\mathcal{C}} &\simeq& \displaystyle\frac{1}{2}\left(
R_{\Phi,\mathbf{P},\top}^{\mathcal{C}} + R_{\Phi,\mathbf{P},\bot}^{\mathcal{C}} \right) \pm Err_{\Phi,\mathbf{P}}^{\mathcal{C}} \hspace{1cm}
Err_{\Phi,\mathbf{P}}^{\mathcal{C}} = \displaystyle\frac{1}{2}\left( R_{\Phi,\mathbf{P},\top}^{\mathcal{C}} - R_{\Phi,\mathbf{P},\bot}^{\mathcal{C}} \right)
\end{array}$$
The computation of $R_{\Phi,\mathbf{P},\top}^{\mathcal{C}}$ and $R_{\Phi,\mathbf{P},\bot}^{\mathcal{C}}$ is due to the approximation of the upper $D^{C}_{\Phi,\mathbf{P},\top}$ and lower $D^{\mathcal{C}}_{\Phi,\mathbf{P},\bot}$ bounds for values of the evaluation function $D^{\mathcal{C}}_{\Phi}(p)$ over $\mathbf{P}$ $$D^{\mathcal{C}}_{\Phi,\mathbf{P},\top} \geq max \left\{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \right\}\hspace{1cm} D^{\mathcal{C}}_{\Phi,\mathbf{P},\bot} \leq min \left\{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \right\}$$ Because such an approximation would be too course for most cases a finite decomposition of the perturbation space $\mathbf{P}$ into perturbation subspaces $\mathbf{P} = \mathbf{P}_1 \cup \ldots \cup \mathbf{P}_n$ is used which then under the assumption of equal probability of all perturbations gives better robustness bounds. Hence we get that: $$R_{\Phi,\mathbf{P},\top}^{\mathcal{C}} = \sum_{i = 1}^{n}{\frac{|\mathbf{P}_i|}{|\mathbf{P}|} \cdot D_{\Phi,\mathbf{P}_i,\top}^{\mathcal{C}}} \hspace{1cm}
R_{\Phi,\mathbf{P},\bot}^{\mathcal{C}} = \sum_{i = 1}^{n}{\frac{|\mathbf{P}_i|}{|\mathbf{P}|} \cdot D_{\Phi,\mathbf{P}_i,\bot}^{\mathcal{C}}}
\label{eq:robustness_sum}$$
Let us now consider the case in which the space of perturbations is extended with initial states $\mathbf{P}^e = \mathbb{I} \times \mathbf{P}$ where $\mathbb{I} \subseteq \mathbb{S}$ and $\mathbf{P}$ is non-singular, for this case the integral defining robustness is actually a finite sum of integrals: $$R_{\Phi,\mathbf{P}^e}^{\mathcal{C}} \stackrel{def}{=} \displaystyle\sum_{s \in \mathbb{I}}{\frac{1}{|\mathbb{I}|} \displaystyle\int_{p \in \mathbf{P}}{\psi(p)D^{\mathcal{C}}_{\Phi}(p)dp}} = \frac{1}{|\mathbb{I}|} \displaystyle\sum_{s \in \mathbb{I}}{ R_{\Phi,\mathbf{P}}^{\mathcal{C}} }$$ where $\psi(p)$ gives the probability of perturbation *p* with respect to $\mathbf{P}$. This expression is valid for uniform distributions of the initial states over the whole space of perturbations $\mathbf{P}^e$, however, it can be straightforwardly modified for non-uniform distributions. Using the expression the robustness computation for perturbations containing a single initial state can be easily extended to perturbations containing different initial states. Moreover, in Section \[sec:GMC\], we show that for most properties the model checking procedure (utilised in the robustness computation) returns results for an arbitrary set of initial states $\mathbb{I} \subseteq \mathbb{S}$ with the same time complexity as for a single state.
The accuracy of the approximation can be further improved using the *piece-wise linear approximation* of robustness. This concept is illustrated in Figure \[fig:pla\_approx\]. Since the spaces $\mathbf{P}_i$ and $\mathbf{P}_{i+1}$ have a common point *p* (in a general *n* dimensional perturbation space $2^n$ subspaces intersect in a single point *p*), we can use this to obtain a more precise range of values for the value of the property $\Phi$ in *p* as $$D_{\Phi,p,\top}^{\mathcal{C}} = min\left\{ D_{\Phi,\mathbf{P}_i,\top}^{\mathcal{C}} \mid p \in \mathbf{P}_i \right\} \text{ and } D_{\Phi,p,\bot}^{\mathcal{C}} = max\left\{ D_{\Phi,\mathbf{P}_i,\bot}^{\mathcal{C}} \mid p \in \mathbf{P}_i \right\}.$$
Under the assumption that the value of a property does not change rapidly over sufficiently small subspaces $\mathbf{P}_i$ the resulting upper and lower bound of robustness can then be computed from linear interpolation of grid points *p*. The decision in which cases such an assumption is acceptable is up to user since there is in general no efficient way of resolving this situation. In such a case the overall piecewise linear approximation of robustness will usually have a higher precision albeit without the guarantee of strict upper and lower bounds.
![[**Piecewise linear approximation of robustness.**]{} An improved approximation is shown in dark green, it is computed by linearly interpolating grid points in which the upper and lower bounds of a property may be computed more precisely as the minimum resp. maximum of the values from all parameter subintervals sharing boundary grid points. The obtained result is more precise that the original robustness (in light pink) albeit without the conservative guarantee on bounds.[]{data-label="fig:pla_approx"}](0017_pla_reduced){width="\textwidth"}
To understand how $D_{\Phi,\mathbf{P}_i,\top}^{\mathcal{C}}$ and $D_{\Phi,\mathbf{P}_i,\bot}^{\mathcal{C}}$ can be efficiently computed first the methods for transient analysis and global CSL model checking based on *uniformisation* are revisited [@Baier2000mcviatran; @Kwiatkowska2007]. Afterwards we present the *min-max approximation* [@CAV2013] that allows us to approximate the quantitative model checking result for continuous sets of parameterised CTMCs. The key idea is to employ a method called *parameterised uniformization* – a modification of the standard uniformization technique presented in [@CAV2013]. Finally, we show how to control the *approximation error* in order to obtain the required error bound.
### Transient analysis
The aim of transient analysis is to compute a transient probability distribution. Given an initial distribution $\pi^{\mathcal{C}, s_0, 0}$ (i.e. $\pi^{\mathcal{C}, s_0, 0}(s) = 1$ if $s_0 = s$, and 0, otherwise) at time 0 of a CTMC $\mathcal{C} = \left( \mathbb{S}, s_0, \mathbf{R}\right)$ what will the transient state distribution $\pi^{\mathcal{C},s_0,t}$ look like in some future yet finite time $t \in \mathbb{R}_{\geq 0}$.
Transient analysis of a CTMC may be efficiently carried out by a standard technique called *uniformization* [@Kwiatkowska2007]. The transient probability in time *t* is obtained as a sum of expressions giving the state distributions after *i* discrete reaction steps of the respective *uniformized* discrete time Markov chain (DTMC) weighted by the *i*th probability of the Poisson process. It is the probability of *i* such steps occurring in time *t*, assuming the delays between steps of the CTMC $\mathcal{C}$ are exponentially distributed with *rate* $q$. Formally, for the rate $q$ satisfying $q \geq max\{E^{\mathcal{C}}(s) \mid s\in \mathbb{S}\}$ (*E* is the exit rate of state *s*) the uniformized DTMC $\mathsf{unif}(\mathcal{C})$ is defined as $\mathsf{unif}(\mathcal{C}) = \left( \mathbb{S}, s_0, \mathbf{Q}^{\mathsf{unif}(\mathcal{C})} \right)$ where $$\mathbf{Q}^{\mathsf{unif}(\mathcal{C})}(s,s') = \left\{
\begin{array}{cl}
\frac{\mathbf{R}(s,s')}{q} & \mbox{if~~} s \neq s' \\
1-\sum_{s'' \neq s}{\frac{\mathbf{R}(s,s'')}{q}} & \mbox{otherwise.}
\end{array} \right.$$ and the $i$th Poisson probability in time $t$ is given as $\gamma_{i,q \cdot t}= e^{-q \cdot t} \cdot \frac{\left(q\cdot t\right)^i}{i!}$. The transient probability can be computed as follows: $$\pi^{\mathcal{C}, s_0, t} = \sum^{\infty}_{i=0}{\gamma_{i,q
\cdot t} \cdot \pi^{\mathcal{C},s_0,0} \cdot (
\mathbf{Q}^{\mathsf{unif}(\mathcal{C})})^i} \approx
\sum^{R_{\epsilon}}_{i=L_{\epsilon}}{\gamma_{i,q \cdot t} \cdot
\pi^{\mathcal{C},s_0,0} \cdot ( \mathbf{Q}^{\mathsf{unif}(\mathcal{C})})^i}.$$ Although the sum is in general infinite, for a given precision $\epsilon$ the lower and upper bounds $L_{\epsilon}, R_{\epsilon}$ can be estimated by using techniques such as of Fox and Glynn [@FoxGlynn1988] which also allow for efficient solutions of the Poisson process. In order to make the computation of uniformization feasible the matrix-matrix multiplication is reduced to a vector-matrix multiplication, i.e., $$\pi^{\mathcal{C}, s_0, 0} \cdot
(\mathbf{Q}^{\mathsf{unif}(\mathcal{C})})^i = ( \pi^{\mathcal{C}, s_0, 0} \cdot
(\mathbf{Q}^{\mathsf{unif}(\mathcal{C})} )^{i-1} ) \cdot
\mathbf{Q}^{\mathsf{unif}(\mathcal{C})}.$$
Standard uniformization can be intractable when the system under study is too complex, i.e., contains more than in order of $10^7$ states and the upper estimate $R_{\epsilon}$, denoting the number of vector-matrix multiplications as iterations, is high (more than in order of $10^6$). Therefore, many approximation techniques have been studied in order to reduce the state space and to lower the number of iterations $R_{\epsilon}$. State space reductions are based on the observation that in many cases (especially in biochemical systems) a significant amount of the probability mass in a given time is localized in a manageable set of states. Thus neglecting states with insignificant probability can dramatically reduce the state space while the resulting approximation of the transient probability is still sufficient. Methods allowing efficiently state-space reduction are based on finite projection techniques [@munsky2006finite; @Henzinger2009] and dynamic state space truncation [@Didier].
Since the number of iterations $R_{\epsilon}$ inherently depends on the uniformization rate *q* that has to be greater then the maximal exit rate of all the states of the system, a variant of standard uniformization, so-called *adaptive* uniformization [@Moorsel94], has been proposed. It uses a uniformization rate that adapts depending on the set of states the system can occupy at a given time, i.e, after a particular number of reactions. In many cases, a significantly smaller rate *q* can be used and thus the number of iterations $R_{\epsilon}$ can be significantly reduced during some parts of the computation. Moreover, adaptive uniformization can be successfully combined with reduction techniques mentioned above [@Didier]. The downside of adaptive uniformization is that the Poisson process has to be replaced with a general *birth* process which is more expensive to solve. See, e.g [@Moorsel94], for more details.
For sake of simplicity, we present our methods for the computation of $D_{\Phi,\mathbf{P}_i,\top}^{\mathcal{C}}$ and $D_{\Phi,\mathbf{P}_i,\bot}^{\mathcal{C}}$ using standard uniformization. However, our method can be successfully combined with the aforementioned techniques.
### Global CSL Model Checking {#sec:GMC}
The aim of the global model checking technique is to efficiently compute for any CSL formula $\Phi$ the values $Eval_{\Phi}^{\mathcal{C}}(s)$ for all states $s \in \mathbb{S}$. On the other hand, the goal of local model checking technique is to compute $Eval_{\Phi}^{\mathcal{C}}(s)$ for a single state $s \in \mathbb{S}$. The crucial advantage of the global approach is the fact that it has the same asymptotic and also practical complexity as the local approach. Therefore, the global model checking technique is much more suitable for robustness analysis over perturbations of initial conditions that are encoded as the initial state of the corresponding CTMC.
Global model checking returns the vector of size $|\mathbb{S}|$ such that the *i*th position contains the model checking result provided that $s_i$ is the initial state. Let $\mathcal{C} =\left(\mathbb{S}, \mathbf{R}, L \right)$ be a labelled CTMC where the initial state is not specified. The crucial part of this method is to compute the vector of probabilities $\overline{Prob}^{\mathcal{C}, \phi}$ for any path formula $\phi$ and the vector of expected rewards $\overline{Exp}^{\mathcal{C}, \mathsf{X}}$ for $\mathsf{X} \in \{ \mathsf{X}_ {\mathsf{I}^{= t}}, \mathsf{X}_ {\mathsf{C}^{\leq t}}\}$ such that for all $s\in \mathbb{S}$ the following holds: $$\overline{Prob}^{\mathcal{C}, \phi}(s) = Prob^{\mathcal{C}}(s,\phi) \wedge \overline{Exp}^{\mathcal{C}, \mathsf{X}}(s) = Exp^{\mathcal{C}}(s,\mathsf{X})$$
In local model checking the computation of $Prob^{\mathcal{C}}(s,\phi)$ and $Exp^{\mathcal{C}}(s,\mathsf{X})$ is reduced to the computation of the transient probability distribution $\pi^{\mathcal{C},s,t}$, see [@Baier2000mcviatran; @Kwiatkowska2007] for more details. Thus, for different initial states $s$ we have to compute the corresponding transient probability distributions separately. The key idea of the global model checking method is to use *backward transient analysis*. The result of backward transient analysis is the vector $\tau^{\mathcal{C},\mathbb{A},t}$ such that for arbitrary set of states $\mathbb{A}$, the value $\tau^{\mathcal{C},\mathbb{A},t}(s)$ is the probability that $\mathbb{A}$ is reached from $s$ at the time *t*. Without going into details the vector $\tau^{\mathcal{C},\mathbb{A},t}$ can be computed in a very similar way using the uniformized DTMC $\mathsf{unif}(\mathcal{C})$ as in the case of vector $\pi^{\mathcal{C},s,t}$. Only vector-matrix multiplications is replaced by matrix-transposed-vector multiplication and $\tau^{\mathcal{C},\mathbb{A},0}(s) = 1$ if $s\in\mathbb{A}$, and $0$, otherwise.
The global model checking technique can not be used if $\Phi$ includes the operator $\mathsf{E}_{\sim r}[I^{=t}]$. In such a case we have to compute the value $Post(\pi^{\mathcal{C},s,t})$. Hence the local model checking technique has to be employed, i.e., we first compute the vector $\pi^{\mathcal{C},s,t}$ and then apply the user specified function *Post*.
Now we briefly show how the vector $\overline{Prob}^{\mathcal{C}, \phi}$ is computed using backward transient analysis. Since the definition of next operator $\mathsf{X}\ \Phi$ does not rely on any real time aspects of CTMCs, its evaluation stems from the probability of the next reaction that can be easily obtained from the transition matrix $\mathbf{R}$. The evaluation of the until operator $\Phi_1 \mathsf{U}^{I} \Phi_2$ depends on the form of the interval $I$ and is separately solved for the cases of $I=[0,t_1]$ and $I=[t_1, t_2]$ where $t_1, t_2 \in \mathbb{R}_{\geq 0}$. It is based on a modification of the uniformized infinitesimal generator matrix $\mathbf{Q}^{\mathsf{unif}}$ where certain states are made absorbing. This means that all outgoing transitions are ignored in dependence on the validity of $\Phi_1$ and $\Phi_2$ in these states.
For any CSL formula $\Phi$, let $\mathcal{C}[\Phi] = \left( \mathbb{S}, s_0, \mathbf{R}[\Phi], L \right)$, where $\mathbf{R}[\Phi](s,s') = \mathbf{R}(s,s')$, if $s \vDash \Phi$, and $0$, otherwise. The formula $\phi = \Phi_1 \ \mathsf{U}^{[0,t]} \ \Phi_2$ can be evaluated using the vector $\tau^{\mathcal{C},\mathbb{A},t}$ in the following way: $$\overline{Prob}^{\mathcal{C}, \phi} = \tau^{\mathcal{C}[\neg \Phi_1 \wedge \Phi_2], \mathbb{A}, t} \mbox{~where~} s \in \mathbb{A} \mbox{~iff~} s \vDash \Phi_2.$$ For the formula $\phi = \Phi_1 \ \mathsf{U}^{[t_1,t_2]} \ \Phi_2$ the evaluation is split into two parts: staying in states satisfying $\Phi_1$ until time $t_1$ and reaching a state satisfying $\Phi_2$, while remaining in states satisfying $\Phi_1$, within time $t_2-t_1$. The formula $\phi$ can be evaluated using the vector $\tau^{\mathcal{C},\overline{v},t}$ that takes a vector $\overline{v}$ instead of a set $\mathbb{A}$ (i.e., $\tau^{\mathcal{C}, \overline{v}, 0} = \overline{v}$) in the following way: $$\overline{Prob}^{\mathcal{C}, \phi} = \tau^{\mathcal{C}[\neg \Phi_1], \overline{v}, t_1} \mbox{~where~} \overline{v} = \tau^{\mathcal{C}[\neg \Phi_1 \wedge \Phi_2], \mathbb{A}, t_2-t_1} \mbox{~and~} s \in \mathbb{A} \mbox{~iff~} s \vDash \Phi_2.$$
The backward transient analysis can be also used in the case of reward computation. Since operator $\mathsf{R}_{\sim p}[\mathsf{I}^{= t}]$ expresses the expected reward at time $t$, the vector $\overline{Exp}^{\mathcal{C}, \mathsf{X}_{\mathsf{I}^{= t}}}$ can be computed as follows: $$\overline{Exp}^{\mathcal{C}, \mathsf{X}_{\mathsf{I}^{= t}}} = \tau^{\mathcal{C}, \overline{v}, t} \mbox{~where~} \overline{v} = \rho \mbox{~such that~} \rho \mbox{~is the given state reward structure.}$$ For evaluation of the operator $\mathsf{R}_{\sim p}[\mathsf{C}^{\leq t}]$ we have to use *mixed Poisson probabilities* (see, e.g., [@Kwiatkowska2006rewards; @Kwiatkowska2007]) in the backward transient analysis. It means that during the uniformization the Poisson probabilities $\gamma_{i,q \cdot t}$ are replaced by the mixed Poisson probabilities $\bar{\gamma}_{i,q \cdot t}$ that can be computed as: $$\bar{\gamma}_{i,q \cdot t} = \frac{1}{q} \cdot \left( 1- \sum_{j = 1}^{i} \gamma_{j,q \cdot t} \right) \mbox{.}$$ Using the given state reward structure $\rho$ we can compute the vector $\overline{Exp}^{\mathcal{C}, \mathsf{X}_ {\mathsf{C}^{\leq t}}}$ in the following way:
$$\overline{Exp}^{\mathcal{C}, \mathsf{X}_ {\mathsf{C}^{\leq t}}} = \tau^{\mathcal{C}, \overline{v}, t} \mbox{~where~} \overline{v} = \rho \mbox{~and the mixed Poisson probabilities~} \bar{\gamma}_{i,q \cdot t} \mbox{~are used.}$$
To recap the overall method of stochastic model checking of CTMCs over CSL formulae we present the methods from an abstract perspective. The evaluation of a structured formula $\Phi$ proceeds by bottom-up evaluation of a set of atomic propositions, probabilistic or expected reward inequalities and their boolean combinations. This evaluation gives us a discrete set of states that are further used in the following computation. The process continues up the formula until the root is reached. The final verdict is reported either in the form of a boolean yes/no answer or as the actual numerical value of the probability or the expected reward. This process can be easily extended for the operator $\mathsf{E}_{\sim r}[I^{=t}]$, however, the local model checking method has to be used.
### Min-max approximation
The key idea of min-max approximation is to approximate the *largest set of states satisfying* $\Phi$, and the *smallest set of states satisfying* $\Phi$ with respect to the space of perturbations $\mathbf{P}$. Let $\mathbf{C}$ be a set of parameterised CTMCs induced by the space of perturbations $\mathbf{P}$ in the system $\mathcal{S}$. We compute the approximation $Sat^{\top}_{\mathbf{C}}(\Phi)$ and $Sat^{\bot}_{\mathbf{C}}(\Phi)$ such that $$Sat^{\top}_{\mathbf{C}}(\Phi) \supseteq \bigcup_{\mathcal{C}_p \in \mathbf{C}} Sat_{\mathcal{C}_p}(\Phi) \ \wedge \ Sat^{\bot}_{\mathbf{C}}(\Phi) \subseteq \bigcap_{\mathcal{C}_p \in \mathbf{C}} Sat_{\mathcal{C}_p}(\Phi)$$ where $s\in Sat_{\mathcal{C}_p}(\Phi)$ iff $s\vDash \Phi$ in CTMC $\mathcal{C}_p$. To obtain such approximations we extended the satisfaction relation $\vDash$ and showed that it is sufficient for an arbitrary path formula $\phi$, and $\mathsf{X} \in
\{\mathsf{X}_ {\mathsf{C}^{\leq t}}, \mathsf{X}_ {\mathsf{I}^{= t}}\}$ to compute the vectors $\overline{Prob}^{\mathbf{C}, \phi}_{\top},\ \overline{Prob}^{\mathbf{C}, \phi}_{\bot},\ \overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\top}$ and $\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\bot}$ such that for each $s\in \mathbb{S}$ the following holds: $$\label{eq:glob}
\begin{array}{rl}
\overline{Prob}^{\mathbf{C}, \phi}_{\top}(s) & \geq max\{ \overline{Prob}^{\mathcal{C}_p, \phi}(s) \mid \mathcal{C}_p \in \mathbf{C} \} \\
\overline{Prob}^{\mathbf{C}, \phi}_{\bot}(s) & \leq min \{ \overline{Prob}^{\mathcal{C}_p, \phi}(s) \mid \mathcal{C}_p \in \mathbf{C} \} \\
\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\top}(s) & \geq max\{ \overline{Exp}^{\mathcal{C}_p, \mathsf{X}}(s) \mid \mathcal{C}_p \in \mathbf{C} \} \mbox{~for~} \mathsf{X} \in \{ \mathsf{X}_ {\mathsf{I}^{= t}}, \mathsf{X}_ {\mathsf{C}^{\leq t}} \}\\
\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\bot}(s) & \leq min\{ \overline{Exp}^{\mathcal{C}_p, \mathsf{X}}(s) \mid \mathcal{C}_p \in \mathbf{C} \} \mbox{~for~}\mathsf{X} \in \{ \mathsf{X}_ {\mathsf{I}^{= t}}, \mathsf{X}_ {\mathsf{C}^{\leq t}} \}.\\
\end{array}$$
The min-max approximation can be easily extended to the operator $\mathsf{E}_{\sim r}[I^{=t}]$. For the given state $s \in \mathbb{S}$ and the time *t* it is sufficient to compute the values $Post^{\mathbf{C}}_{\top}(s,t)$ and $Post^{\mathbf{C}}_{\top}(s,t)$ such that the following holds: $$\label{eq:loc}
\begin{array}{rl}
Post^{\mathbf{C}}_{\top}(s,t) & \geq max\{ Post(\pi^{\mathcal{C}_p,s,t}) \mid \mathcal{C}_p \in \mathbf{C} \} \\
Post^{\mathbf{C}}_{\bot}(s,t) & \leq min\{ Post(\pi^{\mathcal{C}_p,s,t}) \mid \mathcal{C}_p \in \mathbf{C} \}. \\
\end{array}$$
The approximated sets ${Sat}^{\top}_{\mathbf{C}}(\Phi)$ and ${Sat}^{\bot}_{\mathbf{C}}(\Phi)$ are further used in the computation of $D_{\Phi,\mathbf{P},\top}^{\mathcal{C},s}$ and $D_{\Phi,\mathbf{P},\bot}^{\mathcal{C},s}$. If the topmost operator of the formula $\Phi$ is $\mathsf{P}_{= ?}[\phi]$ then $$D_{\Phi,\mathbf{P},\bot}^{\mathcal{C},s} =
\overline{Prob}^{\mathbf{C}, \phi}_{\bot}(s) \wedge D_{\Phi,\mathbf{P},\top}^{\mathcal{C}, s} =
\overline{Prob}^{\mathbf{C}, \phi}_{\top}(s).$$ If the topmost operator of the formula $\Phi$ is $\mathsf{R}_{= ?}[\mathsf{C}^{\leq t}]$ and $\mathsf{R}_{= ?}[\mathsf{I}^{= t}]$ then $$D_{\Phi,\mathbf{P},\bot}^{\mathcal{C},s} =
\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\bot}(s) \wedge D_{\Phi,\mathbf{P},\top}^{\mathcal{C},s} =
\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\top}(s) \mbox{~for~} \mathsf{X} =\mathsf{X}_
{\mathsf{C}^{\leq t}} \mbox{~and~} \mathsf{X} = \mathsf{X}_ {\mathsf{I}^{= t}} \mbox{, respectively}.$$ Similarly, if the topmost operator of the formula $\Phi$ is $\mathsf{E}_{= ?}[\mathsf{I}^{= t}]$ then $$D_{\Phi,\mathbf{P},\bot}^{\mathcal{C}, s} = Post^{\mathbf{C}}_{\bot}(s,t)
\wedge D_{\Phi,\mathbf{P},\top}^{\mathcal{C}, s} =
Post^{\mathbf{C}}_{\top}(s,t).$$
### Parameterised uniformisation {#sec:parameteriseduniformisation}
Recall that the most crucial part of the robustness computation is given by the fact that the space of perturbations of stochastic rate constants $\mathbf{P}$ is dense and thus the set $\mathbf{C}$ is infinite. Therefore, it is not possible to employ the standard model checking techniques to compute the result for each CTMC $\mathcal{C}_p \in$ $\mathbf{C}$ individually.
In order to overcome this problem we employ parameterised uniformisation introduced in [@CAV2013]. It is a modification of the standard uniformisation technique that allows us to compute strict approximations of the minimal and maximal transient probability with respect to the set $\mathbf{C}$, moreover, the modification preserves the asymptotic time complexity of standard uniformisation. For the given state $s \in \mathbb{S}$ and time $t \in \mathbb{R}_{\geq 0}$ the parameterised uniformisation returns vectors $\pi^{\mathbf{C}, s, t}_{\top}$ and $\pi^{\mathbf{C}, s,
t}_{\bot}$ such that for each state $s' \in \mathbb{S}$ the following holds: $$\pi^{\mathbf{C}, s, t}_{\top}(s') \geq max\{\pi^{\mathcal{C}_p, s, t}(s') \mid \mathcal{C}_p \in \mathbf{C}\} \ \wedge \ \pi^{\mathbf{C}, s, t}_{\bot}(s') \leq min\{\pi^{\mathcal{C}_p, s, t}(s') \mid \mathcal{C}_p \in \mathbf{C}\}$$
The modification is based on the computation of the local maximum (minimum) of $\pi^{\mathcal{C}_p, s, t}(s')$ over all $\mathcal{C}_p \in \mathbf{C}$ for each state *s’* and in each iteration $i$ of standard uniformisation. It means that in the *i*th iteration of the computation for a state *s’* we consider only the maximal (minimal) values in the relevant states in the iteration *i-1*, i.e., the states that affect $\pi^{\mathcal{C}_p, s, t}(s')$.
In [@CAV2013] we have defined the function $\sigma(s)$ (formally $\sigma(p,s,\pi)$) which for each state $s \in \mathbb{S}$, perturbation point $p\in \mathbf{P}$ and probability distribution $\pi$ (or pseudo-distribution with the sum smaller or larger than $1$) returns the difference of probability mass inflow and outflow to/from state *s*. If all reactions are described by mass action kinetics the resulting $\sigma$ functions are monotonic with respect to any single perturbed stochastic rate constant $k_r$. This allows us to efficiently compute for each state $s'$ the local maximum (minimum) of $\pi^{\mathcal{C}_p, s, t}(s')$ over all $\mathcal{C}_p \in \mathbf{C}$ corresponding to $\mathbf{P}$.
However, in the case of more complex rate functions than those resulting from mass action kinetics, the corresponding $\sigma(s)$ function does not have to be in general monotonic over $k_r \in [k_r^{\bot},k_r^{\top}]$ for all states *s*. This makes the computation of local extremes with respect to $k_r$ more complex however still tractable. In the following let us assume the space of perturbations $\mathbf{P} = [k_r^{\bot},k_r^{\top}] \times \mathbf{P}'$ will be decomposed along the $k_r$ axis.
The key idea is for each state *s* to be able to efficiently decompose $\mathbf{P}$ into subspaces $\mathbf{P} = \mathbf{P}_1 \cup \ldots \cup \mathbf{P}_n$, such that for each $\mathbf{P}_i$ the function $\sigma(s)$ over $\mathbf{P}_i$ is monotonic and then use the original method. The problem is a computation of such a strict decomposition into monotonic subspaces is computationally demanding. Therefore we use a simplification, by off-line functional analysis we identify properties of $\sigma$ functions for a given class of reaction kinetics and then obtain a partial decomposition of $\mathbf{P}$ based on function derivations into subspaces where monotonicity is guaranteed. For the remaining subspaces $\mathbf{P}_j$ where monotonicity of $\sigma$ is not guaranteed we employ a less accurate approximation.
We decompose the function $\sigma(s)$ over ${\mathbf{P}_j}$ into functions $\alpha^{s,\mathbf{P}_j}_k$ and $\beta^{s,\mathbf{P}_j}_l$ such that: $$\sigma(s) = \sum_{k=1}^K \alpha^{s,\mathbf{P}_j}_k - \sum_{l=1}^L \beta^{s,\mathbf{P}_j}_l$$ and each $\alpha^{s,\mathbf{P}_j}_k$ and $\beta^{s,\mathbf{P}_j}_l$ is monotonic. This allows us to use the original method to compute the maximum and minimum of the functions $\alpha^{s,\mathbf{P}_j}_k$ and $\beta^{s,\mathcal{P}_j}_l$ over the interval $\mathbf{P}_j$, denoted as $max(\alpha^{s,\mathbf{P}_j}_k)$, $min(\alpha^{s,\mathbf{P}_j}_k)$, $max(\beta^{s,\mathbf{P}_j}_k)$ and $min(\beta^{s,\mathbf{P}_j}_k)$, respectively. Note that, this decomposition can be easily obtained from the definition of the rate function $f_r$. Now the maximum and minimum of $\sigma(p,s)$ over $\mathbf{P_j}$ can be approximated in the following way: $$max\{\sigma(p,s) \mid p \in \mathbf{P}_j\} \leq \sum_{k=1}^K max(\alpha^{s,\mathbf{P}_j}_k) - \sum_{l=1}^L min(\beta^{s,\mathbf{P}_j}_l)$$ $$min\{\sigma(p,s) \mid p \in \mathbf{P}_i\} \geq \sum_{k=1}^K min(\alpha^{s,\mathbf{P}_i}_k) - \sum_{l=1}^L max(\beta^{s,\mathbf{P}_j}_l).$$ This approximation increases the inaccuracy of parameterised uniformisation, however, the subspaces $\mathbf{P}_j$ where the monotonicity of $\sigma(s)$ is not guaranteed are usually small and together with perturbation space decomposition introduced in the following section keep on getting smaller. Hence, the additional inaccuracy of the presented extension is manageable. Despite the fact that the time demands of this approximation are orders of magnitudes lower than other numerical methods computing maximum/minimum of $\sigma(s)$ over $\mathbf{P}_i$, they still significantly slow down the computation of parameterised uniformisation.
The aforementioned parameterised uniformisation can be straightforwardly employed also for backward transient analysis. It means that we can efficiently compute the vectors $\tau^{\mathbf{C},\mathbb{A},t}_{\top}$ and $\tau^{\mathbf{C},\mathbb{A},t}_{\bot}$ such that for the given set of states $\mathbb{A}$ and each state $s \in \mathbb{S}$ the following holds: $$\tau^{\mathbf{C}, \mathbb{A}, t}_{\top}(s) \geq max\{\tau^{\mathcal{C}_p, \mathbb{A}, t}(s) \mid \mathcal{C}_p \in \mathbf{C}\} \ \wedge \ \tau^{\mathbf{C}, \mathbb{A}, t}_{\bot}(s) \leq min\{\tau^{\mathcal{C}_p, \mathbb{A}, t}(s) \mid \mathcal{C}_p \in \mathbf{C}\}$$
Once we know how to compute the vectors $\tau^{\mathbf{C}, \mathbb{A}, t}_{\top}$ and $\tau^{\mathbf{C}, \mathbb{A}, t}_{\bot}$ the global model checking technique for non-parameterised CTMCs can be directly employed. To obtain the vectors $\overline{Prob}^{\mathbf{C}, \phi}_{\top},\ \overline{Prob}^{\mathbf{C}, \phi}_{\bot},\ \overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\top}$ and $\overline{Exp}^{\mathbf{C}, \mathsf{X}}_{\bot}$ satisfying Equation \[eq:glob\], it is sufficient to replace the backward transient distribution $\tau^{\mathcal{C}, \mathbb{A},t}_{\bot}$ by the vectors $\tau^{\mathbf{C}, \mathbb{A}, t}_{\top}$ and $\tau^{\mathbf{C}, \mathbb{A}, t}_{\top}$. However for a general class of user-defined post-processing functions *Post*, the vectors $\pi^{\mathbf{C}, s, t}_{\top}$ and $\pi^{\mathbf{C}, s,t}_{\bot}$ cannot be directly used to compute values of $Post^{\mathbf{C}}_{\top}(s,t) = Post(\pi^{\mathbf{C}, s, t}_{\top})$ nor $Post^{\mathbf{C}}_{\bot}(s,t) = Post(\pi^{\mathbf{C}, s, t}_{\bot})$ that would satisfy Equation \[eq:loc\] since there is no guarantee about the projective properties of the function *Post*.
Now we show the main idea how to compute $Post^{\mathbf{C}}_{\top}(s,t)$ and $Post^{\mathbf{C}}_{\bot}(s,t)$ for the post-processing function *Post* defined as the mean quadratic deviation of a probability distribution. This function allows us to quantify and analyse a noise in different variants of signalling pathways that are studied in the second case study. The post-processing function is defined as $Post(\pi) = \sum_{s \in \mathbb{S}}{\lvert s(A) - mean(\pi,A)\rvert^2 \cdot \pi(s)}$, where $s(A)$ gives the population of *A* in state *s* and $mean(\pi,A)$ is the mean of the distribution $\pi$ defined as $mean(\pi,A) = \sum_{s \in \mathbb{S}}{s(A) \cdot \pi(s)}$.
Let us suppose we have an upper and lower bound on the probability distribution $\pi_{\top}, \pi_{\bot}$ obtained by the parameterised uniformisation. It means that $\forall \mathcal{C}_p \in \mathbf{C}$ and $\forall s \in \mathbb{S}. \ \pi_{\bot}(s) \leq \pi^{\mathcal{C}_p}(s) \leq \pi_{\top}(s)$. To find the maximal value $max \left\{ Post(\pi^{\mathcal{C}_p}) \mid \mathcal{C}_p \in \mathbb{C} \right\}$ means to find the distribution $\pi^{max}$ such that $\sum_{s \in \mathbb{S}}{\pi^{max}(s)} = 1$, $\forall s\in \mathbb{S}. \ \pi_{\bot}(s) \leq \pi^{max}(s) \leq \pi_{\top}(s)$ and the probability mass in $\pi^{max}$ is distributed with the farest distance from the mean. Clearly, such a distribution has a maximal mean quadratic deviation. Note that the number of distributions satisfying the first two conditions is uncountable. Thus we cannot employ direct searching strategy.
Our searching strategy builds on the observation that only distributions that localise most of the mass as far as possible from the mean (i.e., maximizing the mean quadratic deviation and still meeting the bounds $\pi_{\bot}, \pi_{\top}$), have to be considered. These distributions can be linearly ordered with respect to the sum of mass *x* localised at the low populated part of the state space. It can be shown that the function that evaluates $Post$ on all these distributions is piece-wise quadratic with respect to *x* and has $O(|\mathbb{S}|)$ segments. Therefore, $O(|\mathbb{S}|)$ many steps are sufficient to compute $max \left\{ Post(\pi^{\mathcal{C}_p}) \mid \mathcal{C}_p \in \mathbb{C} \right\}$.
To compute the minimal value $min \left\{ Post(\pi^{\mathcal{C}_p}) \mid \mathcal{C}_p \in \mathbb{C} \right\}$ we proceed analogously, i.e., only the distributions that localise most of the mass as close as possible to the mean are considered. This leads again to a piece-wise quadratic function. It is also important to note that the perturbation space decomposition presented in the next section allows us to obtain the values $Post^{\mathbf{C}}_{\top}(s,t)$ and $Post^{\mathbf{C}}_{\bot}(s,t)$ with the desired precision.
![[**Perturbation space refinement.**]{} Part (A) depicts three resulting probabilities (green dots) of the formula $\Phi$ for three values of the rate $k_1$ corresponding to three perturbation points $p \in \mathbf{P}$ from Figure \[fig:decomposition\] for the initial state $s_0$ denoted as $Prob^{\mathcal{C}_p}(s_0,\Phi)$. The shape of $Prob^{\mathcal{C}_p}(s_0,\Phi)$ for all $p\in \mathbf{P}$ is estimated upon these three points by polynomial interpolation and shown as a black curve. The top four parts (A), (B), (C) and (D) illustrate the min-max approximation of $Prob^{\mathcal{C}_p}(s_0,\Phi)$ for all $p\in \mathbf{P}$ using the decomposition of $\mathbf{P}$ into 2, 4, 8 and 16 subspaces. The exact shape of the probability function for $\Phi$ is visualised as the red thick curve in the (D) and is compared to the initial estimate. Two types of errors are illustrated: the approximation error is depicted as yellow rectangles and the uniformisation error as the pink rectangles. As can be seen a more refined decompositions reduces both types of errors in each further refined subspace. The bottom parts (E) and (F) depict how the errors arise and how they can be reduce using perturbation space decomposition.[]{data-label="fig:refinement"}](minmax_all){width="\textwidth"}
### Perturbation space decomposition
As we already mentioned, a finite decomposition $\mathbf{P} = \mathbf{P}_1 \cup \ldots \cup \mathbf{P}_n$ into perturbation subspaces is used in order to obtain more accurate approximation of the evaluation function $D^{\mathcal{C}}_{\Phi}$ over the perturbation space $\mathbf{P}$. Before we describe perturbation space decomposition we briefly discuss the key characteristics of parameterised uniformisation that helps us to understand the source of the inaccuracy. The most important fact is that parameterised uniformisation for the set $\mathbf{C}$ in general does not correspond to standard uniformisation for any CTMC $\mathcal{C}_p \in \mathbf{C}$. The reason is that we consider a behaviour of a parameterised CTMC that has no equivalent counterpart in any particular $\mathcal{C}_p$. First, the parameter $k_r$ (minimizing/maximizing the inspected value) is determined locally for each state. Therefore, in a single iteration there can exist two different states such that in one state the parameterised uniformisation selects $k_r=k_r^{\top}$ while in another state it selects $k_r=k_r^{\bot}$. Second, the parameter is determined individually for each iteration and thus for a state $s_i$ the parameter $k_r$ can be chosen differently in individual iterations.
Inaccuracy of the proposed min-max approximation related to the computation of parameterised uniformisation, called *unification error*, is given as: $$(D^{\mathcal{C}}_{\Phi,\mathbf{P},\top} - max \{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \}) +
(min \{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \} - D^{\mathcal{C}}_{\Phi,\mathbf{P},\bot}).$$ Apart from the unification error our approach introduces an inaccuracy related to approximation of the evaluation function, called *approximation error*, given as: $$max \{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \} - min \{ D^{\mathcal{C}}_{\Phi}(p) \mid p \in \mathbf{P} \}.$$ Finally, the *overall error* of the min-max approximation, denoted as $\mathsf{Err}^{\mathcal{C}}_{\Phi, \mathbf{P}}$, is defined as a sum of both errors, i.e., $D^{\mathcal{C}}_{\Phi,\mathbf{P},\top} - D^{\mathcal{C}}_{\Phi,\mathbf{P},\bot}$. Figure \[fig:refinement\] illustrates both types of errors. The approximation error is depicted as yellow rectangles and the unification error is depicted as the purple rectangles.
We are not able to effectively distinguish the proportion of the approximation error and the unification error nor to reduce the unification error as such. Therefore, we design a method based on the perturbation space decomposition that allows us to effectively reduce the overall error of the min-max approximation to a user specified *absolute error bound*, denoted as $\textsc{Err}$.
In order to ensure that the min-max approximation meets the given absolute error bound $\textsc{Err}$, we iteratively decompose the perturbation space $\mathbf{P}$ into finitely many subspaces such that $\mathbf{P} = \mathbf{P}_1 \cup \ldots \cup
\mathbf{P}_n$ and each partial result satisfies the overall error bound, i.e., $\forall \ j: 1 \leq j \leq n: \mathsf{Err}^{\mathcal{C}}_{\Phi, \mathbf{P}_j} \leq \textsc{Err}$. Therefore, the overall error equals to $$\mathsf{Err}^{\mathcal{C}}_{\Phi, \mathbf{P}}= \sum_{j =
1}^{n}{\frac{|\mathbf{P}_j|}{|\mathbf{P}|} \left(D^{\mathcal{C}}_{\Phi,\mathbf{P}_j,\top} - D^{\mathcal{C}}_{\Phi,\mathbf{P}_j,\bot} \right)} \leq \sum_{j =
1}^{n}{\frac{|\mathbf{P}_j|}{|\mathbf{P}|} \textsc{Err}} = \textsc{Err}.$$ Figure \[fig:refinement\] illustrates such a decomposition and demonstrates convergence of $\mathsf{Err}^{\mathcal{C}}_{\Phi, \mathbf{P}_j}$ to 0 provided that the evaluation function $D^{\mathcal{C}}_{\Phi}$ over $\mathbf{P}$ is continuous.
For sake of simplicity, we present the parametric decomposition only on the computation of $\pi^{\mathbf{C}, s, t}_{\star}$ and $\tau^{\mathbf{C}, \mathbb{A}, t}_{\star}$ for $\star \in \{\top,\bot\}$ and $\mathbf{P}$ since it can be easily extended to the computation of $D_{\Phi,\mathbf{P},\star}^{\mathcal{C}}$ for any formula $\Phi$. The key part of the parametric decomposition is to decide when the inspected subspace should be further decomposed. The condition for the decomposition is different for $\pi^{\mathbf{C}, s, t}_{\star}$ and $\tau^{\mathbf{C}, \mathbb{A}, t}_{\star}$. Since the vector $\pi^{\mathbf{C}, s, t}_{\star}$ gives us the transient probability distribution from the state $s$ that is further used to compute $D^{\mathcal{C},s}_{\Phi,\mathbf{P},\star}$, we consider the following condition. The space $\mathbf{P}$ (represented by the CTMC $\mathbf{C}$) is decomposed if during the computation of parameterised uniformisation in an iteration $i$ it holds that: $$\sum_{k =1}^{|\mathbb{S}|} {\pi^{\mathbf{C}, s, i}_{\top}(s_k)} - \sum_{k =1}^{|\mathbb{S}|} {\pi^{\mathbf{C}, s, i}_{\bot}(s_k)} > \textsc{Err}$$ where $ \pi^{\mathbf{C}, s, i}_{\star}$ denotes the corresponding approximation of $\pi^{\mathbf{C}, s, 0} \cdot (\mathbf{Q}^{\mathsf{unif}(\mathbf{C})})^i$.
In contrast to $\pi^{\mathbf{C}, s, t}_{\star}$, the value $\tau^{\mathbf{C}, \mathbb{A}, t}_{\top}(s)$ for each state $s\in \mathbb{S}$ is further used to $D^{\mathcal{C},s}_{\Phi,\mathbf{P},\star}$ and thus we consider the different condition. The space $\mathbf{P}$ is decomposed if during the computation of parameterised uniformisation in an iteration $i$ for any state $s$ it holds that: $$\tau^{\mathbf{C}, \mathbb{A}, i}_{\top}(s) - \tau^{\mathbf{C}, \mathbb{A}, i}_{\bot}(s) > \textsc{Err}.$$
If the decomposition takes place we cancel the current computation and decompose the perturbation space $\mathbf{P}$ to $n$ subspaces such that $\mathbf{P} = \mathbf{P}_1 \cup
\ldots \cup \mathbf{P}_n$. Each subspace $\mathbf{P}_j$ defines a new set of CTMCs $\mathbf{C}_j = \{\mathcal{C}_j \mid j \in \mathbf{P}_j \}$ that is independently processed in a new computation branch. Note that we could reuse the previous computation and continue from the iteration $i-1$. However, the most significant part of the error is usually cumulated during the previous iterations and thus the decomposition would have only a negligible impact on error reduction.
*A minimal decomposition with respect to the perturbation space $\mathbf{P}$* defines a minimal number of subspaces *m* such that $\mathbf{P} = \mathbf{P}_1 \cup \ldots
\cup \mathbf{P}_{m}$ and for each subspace $\mathbf{P}_j$ where $1 \leq j \leq m$ holds that $\mathsf{Err}^{\mathcal{C},s}_{\Phi, \mathbf{P}_j} \leq \textsc{Err}$ where $\mathsf{Err}^{\mathcal{C},s}_{\Phi, \mathbf{P}_j} = D^{\mathcal{C}, s}_{\Phi,\mathbf{P}_j,\top} - D^{\mathcal{C},s}_{\Phi,\mathbf{P}_j,\bot}$. Note that the existence of such decomposition is guaranteed only if the evaluation function $D^{\mathcal{C},s}_{\Phi}$ over $\mathbf{P}$ is continuous. If the evaluation function is continuous there can exist more than one minimal decomposition. However, it can not be straightforwardly found. To overcome this problem we have considered and implemented several heuristics allowing to iteratively compute a decomposition satisfying the following: (1) it ensures the required error bound whenever $D^{\mathcal{C},s}_{\Phi}$ over $\mathbf{P}$ is continuous, (2) it guarantees the refinement termination in the situation where$D^{\mathcal{C},s}_{\Phi}$ over $\mathbf{P}$ is not continuous and the discontinuity causes that $\textsc{Err}$ can not be achieved. To ensure the termination an additional parameter has to be introduced as a lower bound on the subspace size. Hence this parameter provides a supplementary termination criterion.
### Implementation
We delivered a prototype implementation of the framework for the robustness analysis on top of the tool PRISM 4.0 [@KNP11]. This tool provides the appropriate modelling and specification language. Our implementation builds on sparse engine that uses data structures based on the sparse matrices. They provides suitable representation of models for the time efficient numerical computation.
In the case that large number of perturbation subspaces is required to obtain the desired accuracy of the approximation the sequential computation can be extremely time consuming. However, our framework allows very efficient parallelization since the the computation of particular subspaces is independent and thus can be executed in parallel. Our implementation enables the parallel computation and thus the robustness analysis can be significantly accelerated using high performance parallel hardware architectures.
Results
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Gene Regulation of Mammalian Cell Cycle
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We have applied the robustness analysis to the gene regulation model published in [@Keletal00], the regulatory network is shown in Fig. \[fig:modelg1s\] (left). The model explains regulation of a transition between early phases of the mammalian cell cycle. In particular, it targets the transition from the control $G_1$-phase to *S*-phase (the synthesis phase). $G_1$-phase makes an important checkpoint controlled by a *bistable regulatory circuit* based on an interplay of the retinoblastoma protein *pRB*, denoted by *A* (the so-called tumour suppressor, HumanCyc:HS06650) and the retinoblastoma-binding transcription factor $E_2F_1$, denoted by *B* (a central regulator of a large set of human genes, HumanCyc:HS02261). In high concentration levels, the $E_2F_1$ protein activates the $G_1$/$S$ transition mechanism. On the other hand, a low concentration of $E_2F_1$ prevents committing to *S*-phase.
Positive autoregulation of *B* causes bi-stability of its concentration depending on the parameters. Especially, of specific interest is the degradation rate of *A*, $\gamma_{A}$. In [@Swatetal04] it is shown that for increasing $\gamma_{A}$ the low stable mode of *B* switches to the high stable mode. When mitogenic stimulation increases under conditions of active growth, rapid phosphorylation of *A* starts and makes the degradation of unphosphorylated *A* stronger (the degradation rate $\gamma_{A}$ increases). This causes *B* to lock in the high stable mode implying the cell cycle commits to *S*-phase. Since mitogenic stimulation influences the degradation rate of *A*, our goal is to study the population distribution around the low and high steady state and to explore the effect of $\gamma_{A}$ by means of the evaluation function.
It is necessary to note that the original ODE model in [@Swatetal04] has been formalised by means of Hill kinetics representing the cooperative action of transcription factor molecules. Since Hill kinetics cannot be directly transferred to stochastic modelling [@Garaietal12; @Sanftetal11], we have reformulated the model in the framework of stochastic mass action kinetics [@Gillespie1977]. The resulting reactions are shown in Fig. \[fig:modelg1s\] (right). Since the detailed knowledge of elementary chemical reactions occurring in the process of transcription and translation is incomplete, we use the simplified form as suggested in [@Gillespieetal05]. In the minimalist setting, the reformulation requires addition of rate parameters describing the transcription factor–gene promoter interaction while neglecting cooperativeness of transcription factors activity. Our parameterisation is based on time-scale orders known for the individual processes [@Yang2003] (parameters considered in $s^{-1}$). Moreover, we assume the numbers of *A* and *B* are bounded by 10 molecules. Correctness of the upper bounds for *A* and *B* was validated by observing thousand independent stochastic simulations. We consider minimal population number distinguishing the two stable modes. All other species are bounded by the initial number of DNA molecules (genes *a* and *b*) which is conserved and set to 1. The corresponding CTMC has 1078 states and 5919 transitions.
![[**Model of regulation of the mammalian cell cycle.**]{} The core gene regulatory module controlling the $G_1/S$-phase transition in the cell cycle of mammalian cells [@Keletal00] is depicted in the upper part. The retinoblastoma protein *pRB* (A) \[HumanCyc:HS06650\] interacts with the retinoblastoma-binding transcription factor $E_2F_1$ (B) \[HumanCyc:HS02261\]. In high concentration levels, the $E_2F_1$ protein activates the $G_1/S$ transition mechanism. On the other hand, a low concentration of $E_2F_1$ prevents committing to $S$-phase. Positive autoregulation of $E_2F_1$ causes bi-stability.\
Stochastic mass action reformulation of the $G_1/S$ regulatory circuit is shown in the table below. The gene regulation is modelled by means of a set of second-order reactions simplifying the elementary processes behind transcription. In particular, the model includes the interactions among transcription factors (*A*, *B* stand for *pRB* and $E_2F_1$, respectively) and respective genes and protein production/degradation reactions. The interactions are represented by reversible TF-gene binding reactions in the second row of the table (genes are denoted by small letters). Individual protein production reactions controlled by these interactions are represented by the irreversible gene expression reactions in the first row of the table. Protein degradation is modelled as spontaneous by means of first-order reactions. Kinetic coefficients are set only approximately provided that they are considered equal for all instances of a particular process (binding, dissociation, promoted protein production). The only exception is the spontaneous (basal) expression of *b* which is set to a low rate. This mimics the fact that $E_2F_1$ is only rapidly produced under the circumstances of self-activation [@Swatetal04]. Degradation parameters are left unspecified.[]{data-label="fig:modelg1s"}](cs1_model){width="50.00000%"}
We consider two hypotheses: (1) stabilisation in the low mode where $B<3$, (2) stabilisation in the high mode where $B>7$. Both hypotheses are expressed within time horizon 1000 seconds reflecting the time scale of gene regulation response. According to [@Swatetal04], we consider the perturbation space $\gamma_{A}\in
[0.005,0.5]$. For both hypothesis we consider three different settings of $\gamma_{B}$: $\gamma_B=0.05$, $\gamma_B=0.10$, and $\gamma_B=0.15$.
We employ two alternative CSL formulations to express the hypothesis (1). First, we express the property of being inside the given bound during the time interval $I=[500,1000]$ using globally operator: $\mathsf{P}_{=?}[\mathsf{G}^I\, (B< 3)]$. The interval starts from 500 seconds in order to bridge the initial fluctuation region and let the system stabilise. The resulting landscape visualisation is depicted in Figure \[fig:cs1\_until\_0-2\] together with the robustness values computed for individual cases. Since the stochastic noise causes molecules to repeatedly escape the requested bound, the resulting probability is significantly lower than expected. Namely, in the case $\gamma_B=0.05$ the resulting probability is close to 0 for almost all considered parameter values implying very small robustness. Increasing of the *B* degradation rate causes an observable increase in robustness.
![[**Results of robustness analysis for hypothesis (1) using a until operator.**]{} Hypothesis (1) requires stabilisation of $E_2F_1$ in the low concentration mode ($B<3$). A CSL formula with the until operator is used in this case. Each of the curves represents the evaluation function over $\gamma_A$ degradation obtained for a particular setting of $\gamma_B$. More precisely, the horizontal axis shows the perturbation of *pRB* degradation rate and the vertical axis shows the probability of the hypothesis to be satisfied. In the upper left corner, robustness values are shown for each of the curves. The values are displayed with the absolute error quantifying the precision of the approximate method. For comparison, the values are computed also on piece-wise affine approximations of the evaluation function. It can be seen that the robustness values are small which is due to the fact that fluctuations of molecular numbers cause frequent exceeding of the required bound in the considered time horizon.[]{data-label="fig:cs1_until_0-2"}](cs1_until_0-2){width="\textwidth"}
In order to avoid fluctuations of affecting the result, we use a cumulative reward property to capture the fraction of the time the system has the required number of molecules within the time interval $[0,1000]$: $\mathsf{R}_{=?}[\mathsf{C}^{\leq t}](B<3)$ where $t = 1000$ and $\mathsf{R}_{=?}[\mathsf{C}^{\leq t}](B \sim X)$ denotes that state reward $\rho$ is defined such that $\forall s\in \mathbb{S}.\rho(s) = 1$ iff $B \sim X$ in $s$. The resulting landscape visualisation is shown in Figure \[fig:cs1\_reward\_0-2\]. Here the effect of increase of robustness value with respect to increasing $\gamma_B$ is significantly stronger.
After normalising the robustness values, we can observe that the model is significantly more robust with respect to the cumulative reward-based formulation of the hypothesis. This goes with the fact that the reward property neglects the frequent fluctuations in the given time horizon.
When focusing on the phenomenon of bistability, we can conclude that the most significant variance in the molecule population with respect to the two stable modes is observed in the range $\gamma_A=[0.15,0.3]$ with $\gamma_B=0.10$. Here the distribution of the behaviour targeting the low and high mode is diversified nearly uniformly (especially for $\gamma_A=0.2$). Note that in this case there is a significant amount of behaviour (around $40\%$) not converging to either of the two modes.
![[**Results of robustness analysis for hypothesis (1) using a reward operator.**]{} Hypothesis (1) requires stabilisation of $E_2F_1$ in the low concentration mode ($B<3$). A CSL formula with cumulative reward operator is used in this case. Each of the curves represents the evaluation function over $\gamma_A$ degradation obtained for a particular setting of $\gamma_B$. More precisely, the horizontal axis shows the perturbation of *pRB* degradation rate and the vertical axis shows the probability of the hypothesis to be satisfied. In the upper left corner, robustness values are shown for each of the curves. The values are displayed with the absolute error quantifying the precision of the approximate method. For comparison, the values are computed also on piece-wise affine approximations of the evaluation function. It can be seen that the robustness values change rapidly with different settings of $\gamma_B$. This observation goes with the fact that with faster degradation of $E_2F_1$ there is a higher probability that the positively self-regulated protein is locked in the stable mode of no production. The decrease of the value with increasing $\gamma_A$ is due to the weakening effect of inhibition by *pRB*.[]{data-label="fig:cs1_reward_0-2"}](cs1_reward_0-2){width="\textwidth"}
To encode the hypothesis $2$ we employ the reward-based formulation: $\mathsf{R}_{=?}[\mathsf{C}^{\leq t}](B>7)$. The time interval is set to be the same as in the previous case ($t=1000$). The resulting landscape visualisations for individual settings of $\gamma_B$ are depicted in Figure \[fig:cs1\_reward\_8-10\]. It can be observed that the effect of $\gamma_B$ is now inverse which goes with the fact that higher rate of $E_2F_1$ degradation causes the rapid dynamics of the protein and decreases the amenability of the cell to commit to *S*-phase (by making the hypothesis $1$ more robust than hypothesis $2$).
![[**Results of robustness analysis for hypothesis $2$.**]{} Hypothesis (2) requires stabilisation of $E_2F_1$ in the high concentration mode ($B>7$). A CSL formula with cumulative reward operator is employed. Each of the curves represents the evaluation function over $\gamma_A$ degradation obtained for a particular setting of $\gamma_B$. The horizontal axis shows the perturbation of *pRB* degradation rate and the vertical axis shows the probability of the hypothesis to be satisfied. In the upper left corner, robustness values are shown for each of the curves. The values are displayed with the absolute error quantifying the precision of the approximate method. For comparison, the values are computed also on piece-wise affine approximations of the evaluation function. It can be seen that the robustness values change rapidly with different settings of $\gamma_B$. This observation goes with the fact that with faster degradation of $E_2F_1$ there is a lower probability that the positively self-regulated protein is locked in the stable mode of no production. In particular, the high stable mode is preferred for lower values of $\gamma_B$. The increase of the value with increasing $\gamma_A$ is due to the weakening effect of inhibition by *pRB*.[]{data-label="fig:cs1_reward_8-10"}](cs1_reward_8-10){width="\textwidth"}
An interesting observation coming out of the analysis is that the selection of an initial state has only a negligible impact on the result. This is exploited in Figure \[fig:cs1\_init\_states\_combine\] where we have selected 11 states uniformly distributed throughout the state space. Although low initial numbers of *B* slightly decrease robustness of hypothesis (2), the difference is not very big.
More detailed insight can be inferred from Figure \[fig:cs1\_selected\_interval\_statemap\] where hypothesis (2) evaluation is exploited for a small perturbation of $\gamma_A$ with respect to the entire initial state space. The considered perturbation is highlighted in Figure \[fig:cs1\_init\_states\_combine\] by the grey vertical line. The colour intensity of the grid shows the upper bound of the cumulative reward evaluated for the respective initial state. It can be seen that the hypothesis is really insensitive to selection of initial states. Only the initial zero level of *B* causes a decrease of the resulting value. Moreover, this happens (naturally) just in two kinds of states: (*i*) no molecule of *B* is bound to any of the genes, i.e., self-activation of *b* is inactive and the expression of *b* occurs in the spontaneous mode having a low rate 0.05; (*ii*) a molecule of *A* is bound to *b* thus imposing the inhibition of *b* and causing the same scenario.
![[**Landscape visualisation for hypothesis (2) and several selected initial states.**]{} The landscape visualisation of hypothesis (2) (stabilisation of $E_2F_1$ in the high concentration mode $B>7$) is shown for several selected initial states of the whole state space. A CSL formula with cumulative reward operator is employed. Each of the curves represents the evaluation function over $\gamma_A$ degradation obtained for a particular initial state and $\gamma_B$ set to 0.05. The legend shows the amount of individual species in particular initial states and the robustness of the hypothesis is given together with the absolute error. The results obtained by piece-wise affine approximation are also shown. It can be seen that the hypothesis is only negligibly sensitive to initial conditions. Especially, only states with zero initial concentration of $E_2F_1$ cause $E_2F_1$ to attain low molecular numbers thus lowering the robustness of the hypothesis. The grey vertical line shows the small perturbation in $\gamma_A$ which is further explored in detail in Figure \[fig:cs1\_selected\_interval\_statemap\].[]{data-label="fig:cs1_init_states_combine"}](cs1_init_states_combine){width="\textwidth"}
![[**Analysis of hypothesis (2) for all initial states.**]{} Hypothesis (2) (stabilisation of $E_2F_1$ in the high concentration mode $B>7$) is computed and visualised for all initial states in the considered perturbation space $(\gamma_A,\gamma_B) \in [0.10168, 0.10555] \times [0.05]$. Because we assume at most a single molecule of DNA in the system, state variables denoting genes and gene-protein complexes have a binary domain. There are only two variables having a larger domain (0-10), in particular, these are the proteins *pRB* and $E_2F_1$. Therefore each of the (binary) combinations is visualised for the entire domain of *A* and *B* in a separate box. The colour intensity of each box in the grid shows the upper bound of the cumulative reward evaluated for the respective initial state. It can be seen that the hypothesis is mostly insensitive to selection of initial states. Only the initial zero level of $E_2F_1$ (*B, bB, aB*) causes a decrease of the resulting value. States selected in Figure \[fig:cs1\_init\_states\_combine\] are highlighted in red.[]{data-label="fig:cs1_selected_interval_statemap"}](cs1_selected_interval_statemap){width=".8\textwidth"}
Robustness of two-component signalling systems response
-------------------------------------------------------
Signalling pathways make the main interface between cells and their environment. Their main role is to sense biochemical conditions outside the cell and to transfer this information into the internal logical circuits (gene regulation) of the cell. Since signal processing is realised by several dedicated protein complexes (signalling components), it is naturally amenable to intrinsic noise in these protein populations caused by stochasticity of transcription/translation processes. Robust input-output signal mapping is crucial for cell functionality. Many models and experimental studies have been conducted attempting to explain mechanisms of robust signal processing in procaryotic cells, e.g., [@Batchelor21012003; @Shinar11122007].
In order to construct robust signalling circuits in synthetically modified procaryotic cells, Steuer et al. [@steuer2011robust] has suggested and analysed a modification of a well-studied two-component signalling pathway that is insensitive to signalling component concentration fluctuations. The study has been performed by using a simplified model consisting of the two signalling components each considered in both phosphorylated and unphosporylated forms. The first component, the histidine kinase *H*, is a membrane-bound receptor phosphorylated by an external signalling ligand *S*. In its phosphorylated form *Hp*, the histidine kinase transfers the phospho-group onto the second component – the response regulator *R*. That way it activates the response regulator by transforming it into the phosphorylated form *Rp* which is diffusible and functions as the internal signal for the cell. The basic topology of the pathway is depicted in Figure \[fig:sigtopol\]A. The modification suggested by Steuer et al. is depicted in Figure \[fig:sigtopol\]B. The difference is in the addition of catalytic activation of *Rp* dephosporylation by the unphosphoshorylated histidine kinase *H*. In [@steuer2011robust] it has been rigorously proven that under the deterministic setting this modification leads to globally robust steady-state response of the signalling pathway that is not achievable with the basic topology.
We reformulate the model in the stochastic setting and employ our method to provide detailed analysis of the input-output signal response under fluctuations in population of both signalling components. In contrast to [@steuer2011robust] where average steady-state population is analysed with respect to fluctuations in signalling components, our analysis refines the steady population in terms of distributions. That way we obtain for a stable input signal a detailed view of distribution of the output response. In particular, instead of studying the effect of perturbations on the average population, we see how perturbations affect the distribution, i.e., the variance (fluctuation) in the output response. That way the stochastic framework gives a more detailed insight into the input-output signal response mechanism.
The biochemical model of both topology variants is given in Figure \[fig:sigtopol\]C. The input signal *S* is considered to be fixed and therefore it makes a constant parameter of the model. The signalling components in both phosporylated and unphosporylated forms make the model variables *H, Hp, R*, and *Rp*.
![[**Model of a two-component signalling pathway.**]{} (A) Basic topology of the two-component signalling pathway. (B) Modified topology of the two-component signalling pathway, additionally, histidine kinase *H* catalyses dephosporylation of the response regulator *R*. (C) Reactions specifying the biochemical model of the two considered topologies of the two-component signalling pathway. Phosphorylation of the first component *H* catalysed by the input signal *S* and phosporylation of the second component *R* are shared by both topologies, the only difference is in the second component dephophorylation. Additionally, we consider unregulated proteosynthesis/degradation reactions for both topology variants. Reaction topology in (A) and (B) was created using CellDesigner [@Celldesigner]. []{data-label="fig:sigtopol"}](cs2_model){width="50.00000%"}
Depending on which topology is chosen the original deterministic model [@steuer2011robust] exhibits different relationships between the steady-state concentrations of the input signal *S* and the output signal *Rp*:
$$\begin{aligned}
Rp \text{ steady-state in model 1} \hspace{2cm}& Rp \text{ steady-state in model 2}\\
[Rp]=\frac{k_1}{k_{31}}[S][H] \hspace{3cm} &\hspace{1.5cm} [Rp]=\frac{k_1}{k_{32}}[S]\end{aligned}$$
In particular, it can be seen that the steady-state concentration of the output signal \[*Rp*\] in model 1 is affected not only by the input signal *S* but also by the number of unphosphorylated receptors *R*, this can be interpreted in such a way that the concentration of the signalling components should be kept stable in order to obtain the robust output. This is, however, not an issue in model 2 where *Rp* depends only on *S*. Since the steady-state analysis has been carried out under the deterministic setting additionally imposing assumptions of conserved total amounts of *H + Hp* and *R + Rp*, it is appropriate only for high molecular populations.
The question we want to answer is “Is there a difference in the way the two models handle noise (fluctuations) for low molecular numbers of signalling components?” In such conditions, populations of *H + Hp* and *R + Rp* can not be considered conserved since the proteins are subject to degradation and production. Production of proteins from genes as well as degradation is inherently noisy as it has been demonstrated in the previous case study. Different levels of noise can be affected by, e.g., regulatory feedback loops or varying numbers of gene copies. Even for a noiseless output signal *S* these internal fluctuations of protein concentrations transfer noise to *Rp*. We formalise our question in terms of the CSL property $\mathsf{E}_{=?}[\mathsf{I}^{=t}]$ which asks for the value of a post-processing function in a future time *t*, where the post-processing function is defined as the *mean quadratic deviation* of the distribution of *Rp*.
For the model to have low numbers of molecules to exhibit stochastic fluctuations and enable responses to varying levels of *S* we have chosen $k_{p} = 0.3$ *molecules*$\cdot s^{-1}$ and $k_{d} = 0.01 \mbox{~} s^{-1}$ which leads to an average total population of 30 molecules for both $H + Hp$ and $R + Rp$. To make the analysis straightforward we assume same speed of degradation of phosphorylated and unphosphorylated variants of each protein.
To reduce the size of the state space we have truncated total populations to $25 \leq H + Hp \leq 35$ and $25 \leq R + Rp \leq 35$ which leads to $116281$ states in total. The initial state is considered with populations $s_0 = (H = 30, Hp = 0, R = 30, Rp = 0)$. The state space reduction has a significant impact on the measured absolute values of noise but conserves general trends as is shown in Figure \[fig:cs2\_truncation\_noise\].
In order to control fluctuations in protein production we extend our model with two populations of genes, one for *H* and one for *R*, respectively, and for each of the genes we introduce an autoregulatory negative feedback loop via binding of the proteins to their corresponding genes. That way we restrict the protein production. By modifying the number of gene copies in the cell and the rate of protein-gene binding we are able to regulate the overall noise in the transcription. This approach however leads to rapid increase in state space size because of the necessary introduction of new variables representing genes and protein-gene complexes thus making the analysis inefficient. To this end, we decided to abstract from details of the underlying autoregulatory mechanism and to model it using a sigmoid production function which mimics the desired behaviour accordingly. By numerical analysis, we have verified that such an approximation can be employed in the stochastic framework. The function is defined in the following way: $$\emptyset \stackrel{sig(k_p,n)}{\longrightarrow} X \hspace{4em} sig(k_p,n) = \frac{2}{1 + \left( \frac{X}{30} \right)^n} \cdot k_p$$ where $n$ is the so-called Hill coefficient controlling the steepness of the sigmoid (caused by cooperativity of transcription factors in protein-gene interactions) and $k_P$ is the maximal production rate. We use this approach for modelling the production of both species *H* and *R* by sigmoid coefficients denoted $n_H$ and $n_R$, respectively. The sigmoid function regulates the population by enabling production when it is below average and represses it when the population is above the average. The larger *n* is the more steep the sigmoid function is leading to stronger regulation and lower noise. The case *n=0* corresponds to an unregulated model and when increased to *n=20* it corresponds to over 10 copies of each gene in the fully modelled feedback loop mechanism. The effect of different levels of sigmoid regulation to noise can be seen in a simplified birth death model in Figure \[fig:cs2\_truncation\_noise\].
![[**Influence of state space truncation to mean quadratic deviation of a distribution.**]{} A simple birth death model is considered to show the influence of different settings of the state space truncation on the measured noise evaluated in the form of a *mean quadratic deviation* (*mqd*) of the state space distribution. The model has a single species *X* and two reactions $\emptyset \stackrel{sig(0.3,n)}{\longrightarrow} X, X \stackrel{0.01}{\longrightarrow} \emptyset$ which stabilise the population around an average of 30. For different values of the sigmoid coefficient *n* we can see different *mqd* values, the larger the *n* the smaller the noise. If *X* is restricted to $25\leq X\leq 35$ the overall noise is smaller since the probability mass can not spread to states placed further from the mean. In a less restricted version with populations between 20 and 40 the noise is about $2.5\times$ larger. If sigmoid regulation is weak and the regulation is strong then the difference in the amount of noise is less then 20%.[]{data-label="fig:cs2_truncation_noise"}](cs2_truncation_noise){width="\textwidth"}
To see long term effects of intrinsic noise we decided to examine the system in the situation when the output response is stabilised. Since the min-max approximation method cannot be employed with steady-state computation, transient analysis in a suitable time horizon has been performed instead. To estimate the closest time *t* when the system behaviour can be observed stable, we have computed values of output response noise for the unregulated variant of the model (*n = 0*) using standard numerical steady state numerical analysis (we employed the tool PRISM [@KNP11]) and compare it to probability distributions obtained by transient analysis in $t=20$, $t=50$ and $t=100$ seconds. Consequently, we have compared the probability distribution in the steady state with the probability distribution in $t=100$ seconds. The results clearly show that that the difference in distributions is negligible and the transient distribution can be considered stable after $t=100$.
To further speed up the computation, we have precomputed the distribution of *H* and *R* in the time horizon $t=100$ without enabling phosphorylation reactions. This has lead to a significant reduction to $121$ states. Starting with the achieved probability distribution, we have subsequently computed the transient analysis with enabled phosporylation reactions in next $5$ seconds. The rationale behind is that the protein production and degradation are two orders of magnitude slower than phosphorylation. Therefore total populations of *H* and *R* dictate the time at which the system is nearly stable and thus the next $5$ seconds are sufficient for the fast-scale phosporylation to stabilise the fractions $\frac{H}{Hp}$ and $\frac{R}{Rp}$.
To compute the noise (variance) in *Rp* we employ the *mean quadratic deviation* post-processing function for state space distributions. Our goal is to compare the levels of *Rp* noise in both models for different levels of the output signal *S* and for different values of intrinsic noise appearing in protein production (controlled by sigmoid coefficients $n_H$ and $n_R$). After computing lower and upper bounds of the state space distributions, we have computed the lower and upper bounds of the post-processing function using the algorithm informally introduced in Section \[sec:parameteriseduniformisation\]. Consequently, we obtain robustness values for the output response $R_p$ over the respective perturbation subspaces in the form *average* $\pm$ *error*. Finally, we define the perturbation space of the interest. In particular, for the signal we choose the value interval $S \in [2.0, 20.0]$ and for sigmoid coefficients $n_H, n_R \in [0.1, 10.0]$.
Since the full computation over the 3-dimensional perturbation space has turned out to be intractable, we have to find a way how to reduce its dimension. To this end, we focus on a subspace $S = 15.0, (n_H,n_R) \in [3.0,4.0] \times [3.0,4.0]$ where both models have symmetric sensitivity to both sigmoid production coefficients $n_H, n_R$. This symmetry allows us to merge $n_H, n_R$ into a single coefficient *n*. Results are visualised in Figure \[fig:cs2\_models\_nhnr\] where it can be seen that in Model 1 the influence of $n_H$ and $n_R$ is almost perfectly symmetrical with $n_H$ being slightly more influential. In Model 2 the influence is evidently stronger in $n_R$ but the response seems to be symmetrical enough to justify the sigmoid coefficients merging. An interesting property of parameterised uniformization and the perturbation space decomposition algorithm can be seen in Figure \[fig:cs2\_models\_nhnr\] where the decomposition of the perturbation spaces around both sigmoid coefficients set to $3.1$ is very dense. This is due to the non-linearity of the sigmoid production functions which leads to non-monotonicity of probability inflow/outflow differences in states during parameterised uniformization (see Section \[sec:methods\]). In order to preserve conservativeness of estimates we have to locally over/under approximate these inflow/outflow rates thus leading to increase of error. To obtain the desired level of accuracy, we dynamically refine all those subspaces where this has occurred.
Finally, we inspect selected subintervals of the perturbation space given by five exclusive intervals of the input signal value domain, $S \in [2,3] \cup [6,7] \cup [10,11] \cup [14,15] \cup [19,20]$, and three distinct levels of production noise represented by sigmoid coefficient $n \in \left\{0.1, 4.0, 10.0\right\}$. The results of this main experiment can be seen in Figure \[fig:cs2\_model12\_rp\_noise\] and Figure \[fig:cs2\_model12\_hr\_noise\]. The trends that can be seen in Figure \[fig:cs2\_model12\_rp\_noise\] are that for lower signals up to *S=10*. Model 2 has encountered lower noise in *Rp* than Model 1 but in the higher signal region it is outperformed by Model 1 which quickly converges to values between $8$ and $10$. However, *Rp* noise produced in Model 2 linearly increases with increasing value of the input signal *S*. For most of the inspected subspaces a stronger regulation of *H* and *R* production by the sigmoid coefficient *n* leads to a reduction of *Rp* noise. An exception to this observation can be seen in Model 2 at the signal interval $[19.0, 20.0]$ where this trend is inverted. To show that this is an emergent behaviour arising from the nontrivial interaction of phosphorylation and dephosphorylation reactions not present in the basic production and degradation of components *H* and *R*, their respective influences are displayed in Figure \[fig:cs2\_model12\_hr\_noise\]. There we can see that in Model 1 both *H* and *R* follow an initial increase of noise with increasing *S* but then the noise stabilises. This leads us to a hypothesis that the regulation of noise in signalling components dynamics looses its influence as signal *S* increases. This is however due to the fact that more *S* leads to faster phosphorylation of *H* which effectively reduces the population of *H* thus also reducing its absolute noise. In the case of Model 2 the situation is different since we can observe a permanent increase of noise in both *H* and *R* populations. The inversion of noise with increased regulation seen in \[fig:cs2\_model12\_rp\_noise\] and closely shown in Figure \[fig:cs2\_model2highsignal\] has not yet been explained satisfactorily.
![[**Influence of genetic regulation on noise in model 1 and 2.**]{} In the upper part two schemes noise of *Rp* in model 1 is computed over perturbations of both sigmoid production constants $n_H$ and $n_R$ in $[3.0,4.0] \times [3.0,4.0]$. The upper and lower bounds on noise (mean quadratic deviation of the resulting probability distribution projected onto populations of *Rp*) are recomputed into the form *average* $\pm$ *error*, the average values are shown on the left and errors are shown on the right. The densely subdivided subspaces around the value $3.1$ are due to conservative over/under approximations in the computation of the probability distribution in states where inflow and outflow of the probability mass is not strictly a monotonous function over the given perturbation interval, thus the error is locally increased and the subspaces must be further divided to obtain the required precision. The lower two schemes show the same results for model 2. By comparing both results we can see that model 1 has an overall lower noise and also computation error given the same level of refinement then model 2, in model 1 the results are symmetrical with respect to perturbations in $n_H$ and $n_R$ with $n_H$ having a slightly larger influence. In model 2 $n_R$ has a larger influence, however we considered the difference negligible and combined both parameters into a single sigmoid production constant *n*.[]{data-label="fig:cs2_models_nhnr"}](cs2_model12_nRnH_3-4){width="\textwidth"}
![[**Comparison of models by *Rp* noise robustness.**]{} Robustness *Rp* noise in both models has been computed with respect to perturbations of signal *S* over five selected intervals of the input signal $S \in [2,3] \cup [6,7] \cup [10,11] \cup [14,15] \cup [19,20]$ and for three distinct levels of the intrinsic noise in signalling component dynamics represented by sigmoid coefficient $n \in \left\{0.1, 4.0, 10.0\right\}$. Perturbations were not computed over the whole interval $(S,n) \in [2, 20] \times [0.1, 10.0]$ due to very high computational demands. From the computed values of individual refined subspaces as well as the aggregated robustness values for each input signal interval we can see that for lower values of signal *S* (up-to 10) Model 2 embodies lower output response noise then Model 1 (spontaneous dephosphorylation). While output response noise in Model 1 tends to converge to values between 8 and 10, Model 2 exhibits a permanent (almost linear) increase in the output response noise over most of the studied portion of the perturbation space. A super-linear increase of the noise is observed for strong input signals. Another interesting aspect is that while with increasing levels of gene regulation given by sigmoid coefficient *n* the overall noise in *Rp* decreases over the whole interval of signal values for Model 1 and most of it for Model 2, there is an anomaly in Model 2 in the high signal region \[19.0, 20.0\] where with decreasing noise in *R* and *H* (see Figure \[fig:cs2\_model12\_hr\_noise\]) the noise in *Rp* increases. We have not yet explained this phenomenon satisfactorily.[]{data-label="fig:cs2_model12_rp_noise"}](cs2_models_combine_all_kn){width="\textwidth"}
![[**Noise in populations or *H* and *R* in both models.**]{} Noise in *H* (A) and *R* (B) in both models has been computed with respect to perturbations of signal *S* over five selected intervals $S \in [2,3] \cup [6,7] \cup [10,11] \cup [14,15] \cup [19,20]$ and for three distinct levels of inherent production noise represented by sigmoid coefficient $n \in \left\{0.1, 4.0, 10.0\right\}$. We can see that in all cases with increasing regulation by *n* the intrinsic noise in the dynamics of each of the signalling components decreases.[]{data-label="fig:cs2_model12_hr_noise"}](cs2_hr_noise_combine){width="\textwidth"}
![[**High signal region in model 2.**]{} A closeup of the high signal region in model 2, where increasing levels of regulation by the sigmoid coefficient *n* leads to a paradoxical increase of output response noise instead of decrease. Even though the inaccuracy is large we consider the trend to be strong and thus real.[]{data-label="fig:cs2_model2highsignal"}](cs2_model_2_all_kN_19-20_combine){width="\textwidth"}
Discussion
==========
In this paper we proposed a novel framework for robustness analysis of stochastic biochemical systems. It allows us to quantify and analyse how the validity of a hypothesis formulated as a temporal property depends on the perturbations of stochastic kinetic parameters and initial concentrations. The framework extends the quantitative model checking techniques and numerical methods for CTMCs and adapts them to the needs of stochastic modelling in biology. Therefore, in contrast to statistical methods such as Monte Carlo simulation and parameter sampling our framework is customizable with respect to the required precision of computation. This is obtained by providing the lower and upper bounds of the results.
Case studies have demonstrated that the framework can be successfully applied to the robustness analysis of nontrivial biochemical systems. They have shown how to use CSL to specify properties targeting transient behaviour under fluctuations. From the first case study we can conclude that the reward-based formulation of stability properties is more appropriate to distinguish the individual parameter settings under the requested range of uncertainty. The inspected biological hypothesis in the second case study can not be directly formulated using CSL with rewards. Therefore, we have employed post-processing functions to express and study the mean quadratic deviation of the molecule population distribution of the signal response regulator protein.
The time complexity of our framework in practice depends mainly on the size of the state space, the number of reaction steps that have to be considered, and the number of perturbation sets that have to be analysed to provide the desired precision. The size of the state space is given by the number of species and their populations. The framework is suitable for low populations and is relevant especially in the case of gene regulation. In the first case study we have considered only a single molecule of DNA and thus the state space of resulting CTMC was manageable. In the second case study we had to abstract from the feedback loop mechanism using a sigmoid production function to reduce the state space and to make the analysis feasible. If such an abstraction can not be used, our framework can be effectively combined with general state space reduction methods for CTMCs, e.g., finite projection techniques [@munsky2006finite; @Henzinger2009] and dynamic state space truncation [@Didier]. The number of reaction steps can be reduced using separation of fast and slow reactions as demonstrated in the second case study or using adaptive uniformisation [@Moorsel94; @Didier].
In the first case study several hundreds of perturbation subsets had to be analysed and the overall robustness analysis took a few hours. However, in the second case study several thousands of perturbation subsets were required to achieve reasonable precision. In order to speedup the computation we analysed the subsets in parallel using a high performance multi-core workstation were the analysis took several hours. To further improve the accuracy of the robustness analysis without decreasing the performance, we have employed a piecewise linear approximation. It allows us to obtain more precise result without increasing the number of perturbation sets, however, it does not guarantee the conservative error bounds.
The presented method as employed in the first case study gives us a tool for exact analysis of bistability from the global point of view (with respect to all initial conditions, the considered time bound, and the given range of parameters). It can be considered as an analogy to bifurcation analysis known from the ODE world. When comparing our approach with the bifurcation analysis performed in [@Swatetal04], our approach provides a detailed mesoscopic insight into the analysed phenomenon. Instead of identifying just the points where the population diverges, we obtain the precise knowledge of how the population is distributed around the two stable states. Especially, the method shows that reachability of the cancer-inducing high stable mode of the retinoblastoma-binding transcription factor is almost always possible despite the initial state of the regulatory system. The exhaustive analysis is performed with uncertainty in the degradation parameters of the two most important cell-cycle regulating proteins. However, if the degradation of the tumour suppressor protein is sufficiently high, there is always possibility allowing the population to switch into the safe low stable mode. Moreover, robustness of having the possibility to avoid the cell malfunction is positively affected by increasing the retinoblastoma-binding transcription factor degradation. In contrast to [@Swatetal04], the switching mechanism is described at the single cell level which allows to quantify the portion of population amenable to mall-function and thus can provide a preliminary guide to further analysis targeting elimination of the undesired behaviour.
The second case study has shown new insights into the phenomenon of noise in two-component signalling pathways appearing in procaryotic organisms. The previous study [@steuer2011robust] conducted in the framework of deterministic models targeted global robustness of steady concentrations of output signalling components by means of analytically finding invariant perturbation space. The result has shown that a synthetic pathway topology including additional catalysis of signal response regulator by histidine kinase leads to globally robust input-output signal mapping with respect to fluctuations in signalling components concentration. On the contrary, the basic topology without histidine-modulated dephosphorylation does not fulfil global robustness. Since signalling pathways are understood to be amenable to intrinsic noise due to relatively low molecule populations of signalling proteins (typically hundreds of molecules), the respective stochasticity might affect the input-output signal response. To this end, we have reformulated the model in the stochastic framework and instead of studying the effect of perturbations on the average population, we study in detail how perturbations affect the distribution, i.e., the variance (fluctuation) in the output response. Our study has shown that both pathway topologies result with fluctuations in output response, but robustness of input-output mapping varies in both models with increasing the level of the (constant) input signal. For low input signals the synthetic topology gives response with smaller variance in the output whereas for high input signals the output variance rapidly increases. Therefore the basic topology seems to be more suitable for processing of strong signals while the synthetic topology is more appropriate for low level signals. Our study has also shown that both topologies are quite robust with respect to scaling the noise in signalling components dynamics.
Acknowledgments {#acknowledgments .unnumbered}
===============
This work has been supported by the Czech Science Foundation grant No. GAP202/11/0312. M. Češka has been supported by Ministry of Education, Youth, and Sport project No. CZ.1.07/2.3.00/30.0009 - Employment of Newly Graduated Doctors of Science for Scientific Excellence. D. Šafránek has been supported by EC OP project No. CZ.1.07/2.3.00/20.0256.
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Ageing and dopamine uptake by subcellular fractions of the C57BL/6J male mouse brain.
The uptake of dopamine (DA) by synaptosomes from the hypothalamus and striatum was reduced in healthy ageing mice at DA concentrations below 10(-7) M. Kinectic analysis indicates that ageing increases the Km of high affinity DA uptake processes by about 35%, but does not alter alter Vmax. l-Tyrosine and serotonin uptake at low concentrations was unaltered by ageing in the striatum and hypothalamus; no changes of L-norepinephrine uptake were found in the hypothalamus. We conclude that ageing may selectively affect DA uptake processes by neuronal membranes.
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Small solid particles may be changed or loaded into a vertical vessel to form within the vessel single or multiple beds of such particles. For example, solid adsorbents or packing may be charged to a column or solid catalysts may be changed to a reactor.
Formerly, such solid materials have been charged to a particular vessel by such methods as loading buckets, pouring, or the "sock" method. By this "sock" method, a hopper containing the solid particles is connected to the vessel to be charged by an attached hose, which hose extends down into the reactor near its bottom or to the surface of the solid particles being introduced into the vessel. The solid particles are released from the bottom of the hose by slowly elevating the hose. The bed of solid particles that is formed in the vessel develops a cone at its upper surface. As the solid particles are loaded into the vessel, the bed of solid particles is more or less uniformly distributed over the cross-sectional area of the vessel by raking. By this method of loading solid particles, such as catalyst particles, voids will inherently form in the bed as it is produced in the vessel. Such voids result in non-uniform bed densities. The cone can be avoided by having a man slowly guide the bottom of the hose or "sock" and uniformly fill the reactor; however, non-uniform densities still occur.
Subsequently, small solid particles have been charged to various vessels by means of a catalyst or particle loading device or apparatus, such as the apparatus described in U.S. Pat. No. 3,854,637. For such an apparatus to provide a more uniform bed of solid particles, the distributing plate or baffle at the bottom of the apparatus must remain horizontal. If it does not, non-uniformity of the particle bed will develop.
It has now been found that the apparatus for loading solid particles into a vertical vessel, whatever the apparatus may be, will be maintained in such a position that its distributing plate or baffle will remain in a horizontal position, if the apparatus that is described hereinafter is employed.
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Tick Tock: Circadian Regulation of Plant Innate Immunity.
Many living organisms on Earth have evolved the ability to integrate environmental and internal signals to determine time and thereafter adjust appropriately their metabolism, physiology, and behavior. The circadian clock is the endogenous timekeeper critical for multiple biological processes in many organisms. A growing body of evidence supports the importance of the circadian clock for plant health. Plants activate timed defense with various strategies to anticipate daily attacks of pathogens and pests and to modulate responses to specific invaders in a time-of-day-dependent manner (gating). Pathogen infection is also known to reciprocally modulate clock activity. Such a cross talk likely reflects the adaptive nature of plants to coordinate limited resources for growth, development, and defense. This review summarizes recent progress in circadian regulation of plant innate immunity with a focus on the molecular events linking the circadian clock and defense. More and better knowledge of clock-defense cross talk could help to improve disease resistance and productivity in economically important crops.
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Loan watch: Harry Wilson strikes again for Derby
Harry Wilson continued his rich vein of form for Derby County with another set-piece goal in a 3-1 win over Birmingham City on Saturday.
The on-loan Liverpool winger put Frank Lampard’s team ahead in the game as they came from one down to claim three points that lifted them to fourth in the Championship.
Wilson – who also saw a later free-kick hit the post – beat the goalkeeper from a narrow angle on the right with a low effort aided by a deflection.
“It was on target and the defender stuck his leg out – you make your own luck,” said Lampard.
“We deserved that for how we played in the second half. And Harry hit the post later on. We had numerous chances; it was a comfortable 3-1 in the end, which I wouldn’t have expected to say at half-time.”
The Wales international has now scored four goals in 14 appearances since joining Derby in the summer.
Elsewhere, Loris Karius played the whole game for Besiktas as they were beaten 1-0 by Istanbul Basaksehir in the Turkish Super Lig.
It was the same story for Adam Bogdan in the Scottish Premiership, Hibernian losing to the only goal of the game at home to St. Johnstone.
There was better news in the division for Ovie Ejaria and Ryan Kent, who played 87 and 90 minutes respectively in Rangers’ 2-0 win at St. Mirren.
Ben Woodburn was sent on for the final 10 minutes of Sheffield United’s 1-0 defeat at Nottingham Forest, Herbie Kane was part of the Doncaster Rovers team beaten by Charlton Athletic, and Corey Whelan played the first half for Crewe Alexandra as they lost 2-0 against Northampton Town.
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Vietnam says fishing boat rammed and sunk by Chinese ship A Vietnamese government official says a Vietnamese fishing boat capsized after being rammed by a Chinese vessel in Paracel Islands, which are claimed by both countries
HANOI, Vietnam -- A Vietnamese fishing boat capsized after being rammed by a Chinese vessel in the South China Sea's contested Paracel Islands, a Vietnamese official said Friday. China said its boat came upon the fishing vessel after it started sinking and sought help for the crew.
The boat was fishing near Discovery Reef when the incident occurred Wednesday, said the Vietnamese official, who spoke on condition of anonymity because he is not authorized to speak to the press. The Paracel archipelago is claimed by both Vietnam and China, which took control of the islands in 1974.
An online report by the newspaper Tuoi Tre said the five crewmen aboard the Vietnamese boat clung to the bow of their upturned vessel for two hours until they were rescued by another Vietnamese fishing boat.
The official Chinese Communist Party newspaper reported that a Chinese government vessel received a distress call from a Vietnamese fishing boat and sailed to the area, where it found the boat partly sunk. The online report, quoting Chinese Foreign Ministry spokesman Lu Kang, said the Chinese ship immediately contacted China's maritime search and rescue center to dispatch a rescue vessel and the five Vietnamese fishermen were rescued.
Lu said nothing about a vessel, Chinese or otherwise, ramming the Vietnamese ship other than to cite the original Vietnamese report. He also didn't specifically say that the Chinese ship rescued the fishermen.
China's territorial claims extend far into the South China Sea, and it maintains a robust maritime presence that includes driving away non-Chinese fishing boats. Its coast guard performs most such actions, assisted by ships of the maritime militia — ostensibly civilian fishing boats that can swiftly be mobilized. There have been several previously reported incidents of Vietnamese fishing boats being attacked by Chinese vessels.
China has also built up reefs and islands, transforming them into military installations to further its claim to the disputed waterway and its resources, a major point of regional tension. A standoff between the countries in 2014 after China parked an oil rig near the Paracel Islands sparked deadly riots in Vietnam.
———
Associated Press writer Christopher Bodeen in Beijing contributed to this story.
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Controlling group A meningococcal disease is a public health priority. Every 10--12 years, the region of sub-Saharan Africa extending from Senegal to Ethiopia, known as the meningitis belt, experiences major epidemics of meningococcal meningitis \[[@CIV626C1]\]. These epidemics have been most commonly caused by group A *Neisseria meningitidis*.
Since 2001, the Meningitis Vaccine Project, a partnership between the World Health Organization (WHO) and PATH, funded by the Bill & Melinda Gates Foundation, has aimed to eliminate group A meningococcal disease through the development of an affordable group A meningococcal conjugate vaccine that induces immunologic memory and a long-lasting immune response \[[@CIV626C2]\].
This effort led to the licensure, followed by WHO prequalification, of PsA-TT (MenAfriVac, Serum Institute of India, Ltd) in June 2010 after 4 clinical studies (phase 1, 2, and 2/3) that included a total of 1915 subjects, of whom 1126 from age 1 to 34 years had received at least 1 dose of PsA-TT, and which demonstrated its safety and superior immune response compared with the group A--containing polysaccharide vaccine \[[@CIV626C3]--[@CIV626C8]\]. Two additional clinical studies (phase 3), a lot consistency study in India and a large safety study in Africa, were ongoing at the time of prequalification and submitted to regulatory authorities as part of the early postlicensure requirements.
Here we present the results of the large phase 3 safety trial conducted in 2010 in Bamako, Mali, to collect additional data on the safety profile of PsA-TT in a randomized controlled setting \[[@CIV626C9]--[@CIV626C12]\], while allowing sufficient exposure to detect potential rare vaccine-related adverse reactions, where "rare" is conventionally defined as ≤1 per 1000 vaccinees \[[@CIV626C13]\].
METHODS {#s2}
=======
Study Design and Oversight {#s2a}
--------------------------
This phase 3, double-blind, randomized, active controlled clinical study (PsA-TT-006) was designed to evaluate the safety of a single intramuscular injection of the study vaccine up to 3 months after vaccination, in healthy residents of the study area; it was intended to increase the safety database and to further document the safety specifications of PsA-TT. The study was performed in children, adolescents, and adults aged 1--29 years, recruited at the Center for Vaccine Development in Bamako, Mali. Six thousand eligible subjects were randomized in a 2:1 ratio to receive either the study vaccine (PsA-TT, MenAfriVac, Serum Institute of India; group 1, n = 4004) or the reference vaccine (PsACWY, Mencevax ACWY, GlaxoSmithKline; group 2, n = 1996). The sample size was stratified into 3 age groups (children 1--10 years, adolescents 11--17 years, and adults 18--29 years of age) to ensure a balanced safety information across the target population of 1--29 years of age \[[@CIV626C14]\]. Each participant made 1 vaccination visit and 3 follow-up visits (at 4 days, 28 days, and 84 days after vaccination). Only the staff members at the study sites who were directly responsible for preparing the vaccines were aware of group assignments; the subjects and their families, other site staff members, investigators, and sponsors were blinded and unaware of group assignments throughout the study period.
The main criteria for exclusion were a history of allergic disease or known hypersensitivity to any component of the 2 study vaccines and/or following administration of vaccines included in the local program of immunization; administration of any other vaccine within 30 days prior to administration of study vaccines or planned vaccination during the first 28 days after the study vaccination; or pregnancy or lactation (prelicensing vaccine trials did at that time not usually include pregnant and lactating women). A negative pregnancy test was required before vaccination for all women of childbearing potential (ie, postmenarcheal or married women). The study was conducted in accordance with the study protocol and was designed and conducted in accordance with the Good Clinical Practice guidelines established by the International Conference on Harmonisation and with the Declaration of Helsinki. The participating community approved the study, and written informed consent was obtained before enrollment from all subjects between 18 and 29 years of age and from all parents or guardians of subjects \<18 years of age. In addition, written informed assent was obtained from subjects 10--17 years of age as appropriate within the participating community. The study was approved by the PATH and WHO ethics committees, as well as by the ethics committee and the national regulatory authority in Mali.
Vaccines {#s2b}
--------
A reconstituted dose of PsA-TT (0.5 mL) contained 10 µg of group A polysaccharide conjugated to 10--33 µg of tetanus toxoid, 2.85 mg of mannitol, 0.72 mg of sucrose, 0.3 mg aluminium(III) ion as aluminum phosphate as adjuvant, TRIS buffer, 0.01% thiomersal (preservative), and 0.9% sodium chloride, and water for injection.
A reconstituted dose of reference vaccine, PsACWY (0.5 mL), contained 50 µg of purified polysaccharide from each of the *N. meningitidis* groups A, C, Y, and W, sucrose, trometamol, sodium chloride, phenol, and sterile water for injection.
The vaccines were injected intramuscularly, in the right thigh for children \<2 years of age, and in the right deltoid for children aged ≥2 years, adolescents, and adults.
Safety Evaluation {#s2c}
-----------------
Subjects were observed for 30 minutes after vaccination to record and treat immediate reactions. Subjects were monitored for local and systemic postimmunization reactions during daily home visits by nurses and doctors using diaries for 4 days, unsolicited adverse events (AEs) were assessed for 1 month, and serious adverse events (SAEs) were assessed throughout the course of the study for 3 months. Subjects (or their parents or guardians) were asked about tenderness and induration at the injection site; fever, vomiting, and diarrhea (for all subjects); lethargy, irritability, and loss of appetite (for subjects between 1 and 10 years of age); and headache, fatigue, myalgia, and arthralgia (for subjects \>10 years of age). Solicited reactions within 4 days after vaccination were presumed to be vaccine related. Assessment of causality in the case of unsolicited AEs was performed by the study investigators based on clinical judgment. An independent data and safety monitoring board was established.
Statistical Analysis {#s2d}
--------------------
The primary objective of this study was to evaluate the safety up to 3 months (84 days) after a single dose of PsA-TT, in terms of vaccine-related SAEs. The primary analysis on the primary endpoint was descriptive.
The safety of a single dose of PsA-TT was compared to that of 1 dose of PsACWY, in terms of local and systemic reactions, AEs, and SAEs. Differences between the 2 vaccine groups were tested using a Cochran--Mantel--Haenszel test adjusting for age group for percentage of subjects with at least 1 postimmunization reaction (local or systemic), percentage of subjects reporting the presence of each reactogenicity parameter (however, for lethargy, irritability, and loss of appetite in those aged 1--10 years, the comparison was made by Fisher exact test at a 2-sided significance level of α = .05), and percentage of subjects with at least 1 AE or SAE. Because lethargy, irritability, and loss of appetite were only collected in the age group of 1--10 years, Fisher exact test was used to compare the 2 vaccine groups for percentage of subjects with at least 1 of these 3 postimmunization reactions.
All safety analyses were carried out on the intention-to-treat dataset. Data were analyzed with SAS software, version 9.1.3. A 2-sided significance level of .05 was used for testing. Calculations of the sample size, required to assess the primary objective with sufficient power, were based on the probability of observing a rare AE as derived by a Poisson approximation \[[@CIV626C15]\]. When the incidence rate (R0) of a particular AE is sufficiently low and a sample size is sufficiently large, the probability of observing an AE can be approximated by that of a Poisson distribution with parameter λ = nR0. If no vaccine-related SAE was observed in the estimated 4000 participants who were supposed to receive a single dose of the PsA-TT vaccine, one can conclude with a 95% confidence that the incidence of the vaccine-related SAE for PsA-TT vaccine is \<1 in 1333 vaccinated individuals.
RESULTS {#s3}
=======
Study Population {#s3a}
----------------
Of the 6077 randomized subjects, 6000 were vaccinated between 22 February and 9 October 2010: 4004 in the PsA-TT group and 1996 in the PsACWY group (Figure [1](#CIV626F1){ref-type="fig"}). All vaccinated subjects were included in the analyses. The duration of study participation for each subject was 3 months: all subjects completed the initial vaccine period of 28 days, and all but 4 subjects completed the study with an additional 56 days of follow-up (Figure [1](#CIV626F1){ref-type="fig"}). Demographic and clinical characteristics of the subjects are summarized in Table [1](#CIV626TB1){ref-type="table"}. Table 1.Age, Sex, Height, and Weight of Study SubjectsAge Group, yVaccine GroupNo.Median Age, Years (Min--Max)Female, No. (%)Median Height, cm (Min--Max)Median Weight, kg (Min--Max)1--10PsA-TT7998 (1--10)396 (49.6)125.5 (70.0--159.2)22.0 (7.0--59.0)PsACWY4017 (1--10)187 (46.6)124.0 (70.0--172.0)22.0 (7.0--55.0)11--17PsA-TT160014 (11--17)737 (46.1)156.5 (122.0--193.0)\*47.0 (20.0--94.5)\*\*PsACWY80014 (11--17)368 (46.0)155.0 (128.0--183.4)\*45.0 (23.0--90.0)\*\*18--29PsA-TT160521 (18--29)542 (33.8)167.2 (145.1--195.0)61.0 (36.0--129.0)PsACWY79521 (18--29)252 (31.7)167.3 (137.0--199.0)61.0 (36.5--103.0)TotalPsA-TT400416 (1--29)1675 (41.8)159.0 (70.0--195.0)51.0 (7.0--129.0)PsACWY199616 (1--29)807 (40.4)157.6 (70.0--199.0)50.0 (7.0--103.0)[^2][^3][^4] Figure 1.Study population. Abbreviations: PsACWY, group A, C, W, Y meningococcal polysaccharide vaccine; PsA-TT, group A meningococcal polysaccharide-tetanus toxoid conjugate vaccine.
Safety {#s3b}
------
### Primary Endpoint {#s3b1}
No vaccine-related SAE occurred during the 3 months of follow-up. Therefore, no further analyses were required on the primary criterion.
### Secondary Endpoints {#s3b2}
Postimmunization reactions and AEs are shown in Table [2](#CIV626TB2){ref-type="table"}. No allergic or anaphylactic reaction occurred immediately after immunization. Rates of systemic reactions during the first 4 days after immunization, rates of AEs during the first 28 days after immunization, and SAEs within 84 days after immunization were similar among vaccine groups. Table 2.Overall Vaccine Safety ProfileLocal ReactionSystemic Reaction^a^Adverse EventSerious Adverse EventWithin 4 d PostimmunizationWithin 4 d PostimmunizationWithin 28 d PostimmunizationWithin 84 d PostimmunizationAge Group, yVaccine GroupNo.No.% (95% CI)No.% (95% CI)No.% 95% CI)No.% (95% CI)1--10PsA-TT799729.0 (7.1--11.2)111.4 (.7--2.4)10012.5 (10.3--15.0)70.9 (.4--1.8)PsACWY401164.0 (2.3--6.4)51.2 (.4--2.9)6115.2 (11.8--19.1)30.7 (.2--2.2)11--17PsA-TT160018911.8 (10.3--13.5)322.0 (1.4--2.8)1197.4 (6.2--8.8)110.7 (.3--1.2)PsACWY800354.4 (3.1--6.0)192.4 (1.4--3.7)799.9 (7.9--12.2)50.6 (.2--1.5)18--29PsA-TT160526516.5 (14.7--18.4)734.5 (3.6--5.7)18711.7 (10.1--13.3)161.0 (.6--1.6)PsACWY795354.4 (3.1--6.1)405.0 (3.6--6.8)9211.6 (9.4--14.0)60.8 (.3--1.6)TotalPsA-TT400452613.1^b^ (12.1--14.2)1162.9 (2.4--3.5)40610.1 (9.2--11.1)340.8 (.6--1.2)PsACWY1996864.3^b^ (3.5--5.3)643.2 (2.5--4.1)23211.6 (10.2--13.1)140.7 (.4--1.2)[^5][^6][^7]
However, the rate of local reactions was 3 times as high in the PsA-TT group as in the PsACWY group (13.1% vs 4.3%; *P* \< .0001). All but 2 mild indurations were injection-site tenderness, with a between-group rate difference increasing with age of the subjects. Intensity of tenderness was rated 1 (mild pain to touch) for all subjects in the PsACWY group and for most of the subjects in the PsA-TT group. In the PsA-TT group, tenderness intensity rated 2 (significant pain to touch) was reported as follows: 0 children, 7 adolescents (3.7% of 189 adolescents who reported tenderness), and 21 adults (8.0% of 264 adults who reported tenderness). Only 1 adult reported a tenderness of intensity 3 (significant pain on moving the limb).
Rates of systemic reactions were low (2.9% in PsA-TT vs 3.2% in PsACWY) and increased with age of the subjects: 1.4% vs 1.2% in children; 2.0% vs 2.4% in adolescents, and 4.5% vs 5.0% in adults in the PsA-TT vs PsACWY groups, respectively. Headache, fatigue, myalgia, and arthralgia (solicited only among adolescents and adults) were the most frequently reported systemic postimmunization reactions, with 3.0% vs 3.4% of the subjects in the PsA-TT vs PsACWY group, respectively, reporting at least 1 of these 4 reactions. Headache was the most frequently reported reaction: 2.3% in PsA-TT vs 2.8% in PsACWY, twice as frequent in adults than in adolescent subjects. Fatigue was reported more frequently in the PsACWY group (1.1% vs 0.5% in the PsA-TT group; *P* = .0160). Overall, local and systemic postimmunization reactions were mild, transient, and resolved without sequelae.
A total of 10.1% subjects in the PsA-TT group and 11.6% of subjects in the PsACWY group reported at least 1 unsolicited AE. Commonly reported AEs were infections and infestations according to system organ class (SOC), mainly malaria, upper respiratory tract infections, schistosomiasis, and rhinitis. Adverse events were transient and resolved without sequelae, and no vaccine-related unsolicited AEs were recorded.
Within 3 months after vaccination, 48 subjects---34 subjects (0.8%) in the PsA-TT group and 14 (0.7%) in the PsACWY group---reported experiencing 50 serious AEs, all of which were vaccine unrelated (Table [3](#CIV626TB3){ref-type="table"}). One adolescent had vascular disorder according to SOC (severe malignant hypertension) and died 57 days after vaccination with PsA-TT; the event was unrelated to the study vaccine. Twenty-nine subjects (0.7%) in the PsA-TT group and 14 (0.7%) in the PsACWY group reported a total of 45 SAEs that were infections and infestations according to SOC, mainly malaria (34 cases). The remaining 4 SAEs were 2 cases of injury, poisoning, and procedural complications (multiple injuries, forearm fracture), and 1 case each of gastrointestinal disorders (appendicitis) and surgical and medical procedures (induced abortion) and were reported in 4 subjects in the PsA-TT group. Most of the cases of SAEs were severe (43/50) or moderate (7/50), but all, except for the fatal case, recovered without sequelae. The overall comparison adjusted for age groups showed no statistically significant difference in the percentage of subjects with at least 1 SAE between the 2 vaccine groups with respect to SAEs after vaccination. There was no difference when comparing the rates within each follow-up period of before or after the first 28 days postimmunization. Table 3.Summary of Subjects With Severe Adverse Events by Primary System Organ ClassAge Group, yVaccine GroupPrimary System Organ ClassInfections and Infestations^a^Gastrointestinal DisordersInjury, Poisoning, and Procedural ComplicationsSurgical and Medical ProceduresVascular Disorder^b^AllNo.No. (%)No. (%)No. (%)No. (%)No. (%)No. (%)1--10PsA-TT7996 (0.8)0 (0.0)1 (0.1)0 (0.0)0 (0.0)7 (0.9)PsACWY4013 (0.7)0 (0.0)0 (0.0)0 (0.0)0 (0.0)3 (0.7)11--17PsA-TT16009 (0.6)0 (0.0)0 (0.0)1 (0.1)1 (0.1)11 (0.7)PsACWY8005 (0.6)0 (0.0)0 (0.0)0 (0.0)0 (0.0)5 (0.6)18--29PsA-TT160514 (0.9)1 (0.1)1 (0.1)0 (0.0)0 (0.0)16 (1.0)PsACWY7956 (0.8)0 (0.0)0 (0.0)0 (0.0)0 (0.0)6 (0.8)TotalPsA-TT400429 (0.7)1 (0.0)2 (0.0)1 (0.0)1 (0.0)34 (0.8)PsACWY199614 (0.7)0 (0.0)0 (0.0)0 (0.0)0 (0.0)14 (0.7)[^8][^9][^10]
For detailed data on solicited local and systemic reactions, AEs, and SAEs, see the [Supplementary Tables](http://cid.oxfordjournals.org/lookup/suppl/doi:10.1093/cid/civ626/-/DC1).
### Pregnancies {#s3b3}
Within the study period, 4 pregnancies were reported 1--2 months after vaccination among 3 adults and 1 adolescent. Three subjects had normal live-born deliveries 8--9 months after vaccination, and 1 had a voluntary termination of pregnancy at 2 months after vaccination.
DISCUSSION {#s4}
==========
This study increased the safety database while further documenting the safety specifications of PsA-TT in a randomized controlled setting. No vaccine-related SAE occurred during the 84-day follow-up of 4004 subjects vaccinated with a single dose of PsA-TT, which supports that PsA-TT vaccine is safe. Indeed, rare events are conventionally defined as those whose frequency is ≤1 per 1333 vaccinated individuals \[[@CIV626C13], [@CIV626C16]\]. Rare events could be ruled out, as no vaccine-related SAEs were observed among the 4004 subjects vaccinated with PsA-TT.
When compared to the licensed PsACWY vaccine, local reactogenicity appeared to be more frequent in the PsA-TT vaccine group, with a high number of instances of tenderness at the injection site (3 times as frequent). This was also seen in previous studies \[[@CIV626C4]--[@CIV626C8]\] and can be explained by the presence of TT as a carrier protein and aluminum as an adjuvant. Occurrence and intensity of tenderness increased with the age of the vaccinated subjects and were more frequent among adults. However, the rates of systemic reactions, AEs, and SAEs were similar in both vaccine groups. All AEs, whether they were serious or not, were unrelated to the study vaccines and consisted mainly of infection and infestations, whose distribution was consistent with the pattern of the age-related morbidity in Mali.
In conclusion, this study confirmed the excellent safety profile of 1 dose of MenAfriVac when administered to its entire target population of 1--29 years of age, thus supporting the prospects of large vaccine deployment in countries of the African meningitis belt.
Supplementary Data {#s5}
==================
[Supplementary materials](http://cid.oxfordjournals.org/lookup/suppl/doi:10.1093/cid/civ626/-/DC1) are available at *Clinical Infectious Diseases* online (<http://cid.oxfordjournals.org>). Supplementary materials consist of data provided by the author that are published to benefit the reader. The posted materials are not copyedited. The contents of all supplementary data are the sole responsibility of the authors. Questions or messages regarding errors should be addressed to the author.
###### Supplementary Data
***Acknowledgments.*** We thank the study participants and their communities; the teams at the Center for Vaccine Development--Mali, the Meningitis Vaccine Project, DiagnoSearch Life Science, and the Serum Institute of India; the Malian Ministry of Health and the World Health Organization (WHO) office in Mali for their advice and support throughout the study; the study monitors at the Agence Africaine de Recherche en Santé Humaine under the leadership of Dr Véronique Mazarin-Diop; Professor Brian Greenwood and Dr Margaret Bash for invaluable guidance; and Dr Jean-François Etard, Dr Lorna Renner, Aissata Doumbia Diarra, and Dr Rebecca Grais of the data and safety monitoring board.
***Disclaimers.*** 1) The authors and editors alone are responsible for the views expressed in this publication and they do not necessarily represent the views, decisions, or policies of the institutions with which they are affiliated; 2) The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of PATH or the WHO concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Dotted and dashed lines on maps represent approximate border lines for which there may not yet be full agreement; 3) The mention of specific companies or of certain manufacturers' products does not imply that they are endorsed or recommended by PATH or the WHO in preference to others of a similar nature that are not mentioned. Errors and omissions excepted, the names of proprietary products are distinguished by initial capital letters.
***Financial support.*** This work was supported by the Meningitis Vaccine Project (PATH) with a grant from the Bill & Melinda Gates Foundation.
***Supplement sponsorship.*** This article appears as part of the supplement "The Meningitis Vaccine Project: The Development, Licensure, Introduction, and Impact of a New Group A Meningococcal Conjugate Vaccine for Africa," sponsored by the Meningitis Vaccine Project through a grant from the Bill & Melinda Gates Foundation.
***Potential conflicts of interest.*** M.-P. P. has received institutional grant support from PATH, Gavi the Vaccine Alliance, the Shefa Fund hosted by the Swiss Philanthropy Foundation, the National Philanthropic Trust, the Research Council of Norway, and the US Agency for International Development, and has received travel support from PATH and the Research Council of Norway. All other authors report no potential conflicts.
All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed.
[^1]: Present affiliation: independent consultant.
[^2]: Abbreviations: PsACWY, group A, C, W, Y meningococcal polysaccharide vaccine; PsA-TT, group A meningococcal polysaccharide-tetanus toxoid conjugate vaccine.
[^3]: \* *P* = .0093 for the comparison of PsACWY vs PsA-TT in the age group 11--17 years using analysis of variance (ANOVA).
[^4]: \*\* *P* = .0204 for the comparison of PsACWY vs PsA-TT in the age group 11--17 years (ANOVA).
[^5]: Abbreviations: CI, confidence interval; PsACWY, group A, C, W, Y meningococcal polysaccharide vaccine; PsA-TT, group A meningococcal polysaccharide--tetanus toxoid conjugate vaccine.
[^6]: ^a^ Subjects reporting at least 1 of fever, vomiting, and diarrhea: age group 1--10 years, 1.0% of subjects (95% CI, .4%--2.0%; n/N = 8/799) in the PsA-TT group and 0.7% of subjects (95% CI, .2%--2.2%; n/N = 3/401) in the PsACWY group; 11--17 years, 0.3% of subjects (95% CI, .1%--.7%; n/N = 5/1600) in PsA-TT and 0.4% of subjects (95% CI, .1%--1.1%; n/N = 3/800) in PsACWY; and 18--29 years, 0.6% of subjects (95% CI, .3%--1.1%; n/N = 9/1605) in PsA-TT and 0.6% of subjects (95% CI, .2%--1.5%; n/N = 5/795) in PsACWY. Subjects reporting at least 1 of lethargy, irritability, and loss of appetite: age group 1--10 years, 0.8% of subjects (95% CI, .3%--1.6%; n/N = 6/799) in the PsA-TT group and 0.5% of subjects (95% CI, .1%--1.8%; n/N = 2/401) in the PsACWY group. Subjects reporting at least 1 of headache, fatigue, myalgia, and arthralgia: age group 11--17 years, 1.8% of subjects (95% CI, 1.2%--2.6%; n/N = 29/1600) in PsA-TT and 2.1% of subjects (95% CI, 1.2%--3.4%; n/N = 17/800) in PsACWY; 18--29 years, 4.2% of subjects (95% CI, 3.3%--5.3%; n/N = 68/1605) in PsA-TT and 4.7% of subjects (95% CI, 3.3%--6.4%; n/N = 37/795) in PsACWY.
[^7]: ^b^ *P* \< .0001 for the comparison of PsACWY vs PsA-TT using Cochran--Mantel--Haenszel test adjusting for age group. The difference was due to more tenderness reported in the PsA-TT than PsACWY group.
[^8]: Abbreviations: PsACWY, group A, C, W, Y meningococcal polysaccharide vaccine; PsA-TT, group A meningococcal polysaccharide--tetanus toxoid conjugate vaccine.
[^9]: ^a^ Only 2 subjects reported \>1 SAE: 1 subject aged 1--10 years in the PsA-TT group and the other aged 1--10 years in the PsACWY group reported 2 SAEs that were infections and infestations.
[^10]: ^b^ One SAE that was vascular disorder (malignant hypertension) resulted in death of a subject aged 11--17 years in the PsA-TT group.
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Q:
PHP, structural or OOP based language?
I would like to discuss why is PHP called a structural language? what are the OO concepts that cannot be implemented using PHP?
A:
Classification of programming languages is an art as most languages falls in many categories. In this case it's simple enough though. PHP is an imperative OO language, like C++. That is, you can select to use objects and classes if you like, but you don't have to.
As regards to what you can and cannot do with objects in PHP, I don't really see anything missing. But "missing" is a relative term here, as some OO languages have more features and others less. For instance, some consider language-supported properties to be a hallmark of OO, something that is lacking in both Java and PHP. Still Java is undoubtedly in the OO camp.
Judging from Wikipedia, the fundamental concepts in OO is:
Class
Instance
Method
Message passing
Abstraction
Encapsulation
Inheritance
(Subtype) polymorphism
Decoupling
All this is part of PHP.
On a personal note, I haven't found anything in PHPs OO implementation that is lacking. There is lots of stuff in PHP that is seriously flawed, inconsistent and just weird, but that is another issue. It's OO constructs are good enough to be called complete.
A:
I consider PHP language to be object-capable, not object-oriented. That's because most of the built-in constructs are not object-oriented. Take an array or a string for example. In object oriented language, you'd use it's methods to manipulate it. In fully fledged object-oriented language everything is an object.
On the other hand PHP is object-capable, you can write code, that will be OOP. Instead of using for example normal arrays, you can use data structures from SPL, which actually are OOP. The only problem with that is, it's an extension, not a part of the language itself.
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Tag: best blender
Auto-iQ system is one of the most advanced blender technology nowadays. This feature allows you to select and control blender settings that suit your food preparing process. Furthermore, this system offers convenience in making healthy drinks, soup, and other foods. Ninja Blenders is the best-selling brand of this device in the market right now. This manufacturer is popular for their auto-iQ blenders.
Are you looking for a blender that can do all the tough crushing job? Then, what you need is the Ninja Mega Kitchen blender. This product from Ninja Blenders is a popular option for individuals who want an all-around feature in their blenders. This one can perform every difficult task which your regular food processor can do. It can crush ice, nuts, fruits, and vegetables, and mix it perfectly. The reason behind Ninja Mega Kitchen Blender is its 1500-watt motor power which is amazingly high for this kind of kitchen device. Moreover, this appliance has a 2-HP motor which makes it possible for this product to prepare all types of food blend. Aside from this product’s motor power, Ninja Mega Kitchen features Auto-iQ technology. It means that this device could not only create shakes and smoothies but also it can prepare dough, crush and pulse. In addition, this blender has powerful blades that can break the ice and make a healthy smoothie easy and quick. If you want to enjoy your healthy drink with friends, this blender is a nice choice since it has a large pitcher capacity which can hold a total of 72 ounces of food blend. The only drawback of this device is its expensive price. Still, investing in this kind of blender is worth your money.
Nutri Ninja Duo Nutrient Extraction Blender
Here is another creation of Ninja Blender that you must see for yourself. The Nutri Ninja BL680 Duo nutrient extraction blender is a must-have because of its top-notch quality, durability, and power. Parallel to Ninja Mega Kitchen Blender, this product of the same brand has a 1500 watt motor base and 2 Horsepower which are both excellent qualities of the kitchen tool. Therefore, using this blender, you can prepare lots of drinks and food recipes to a large group of foodies minus the kitchen disasters. If you always experience problems in making tasty baby foods, worry no more for Nutri Ninja Duo can do the job for you. This device can make better baby foods for your infant compared to those regular baby food processors. The high motor power and strong blades of this device can crush, chop and create dough better rather than a traditional food processor. This product of Ninja Blender is one of its creations with Auto-iQ system input. Thus, through its various settings, you can control how you want to prepare your food and have the best outcome. Ninja Blender has more help to offer for your kitchen duties. Learn more about this brand’s products on Blend It Nutrition.
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Background
==========
Radiotherapy remains an essential treatment for patients with cancer and is associated with a number of short term and long term side effects \[[@B1]\]. One of these side effects includes radiation-induced skin reactions (RISR), also known as radiation dermatitis, which affects up to 90 % of cancer patients receiving radiotherapy \[[@B2]-[@B4]\]. Approximately, 85 % of these patients experience a moderate-to-severe skin reaction \[[@B5],[@B6]\]. The reactions are the combined result of a decrease in functional stem cells, changes in the skin's endothelial cells, inflammation, and skin cell necrosis and death of the skin \[[@B7]\]. Radiation-induced skin reactions are often characterised by oedema, erythema, changes in pigmentation, fibrosis and ulceration \[[@B8]\]. Signs and symptoms may include skin dryness, itching discomfort, pain, warmth, and burning \[[@B9]\]. Radiation-induced skin reactions have an impact on pain and quality of life in this patient group \[[@B10]\], and if severe, may necessitate changes to the patient's radiation schedule \[[@B11]\]. Therefore, managing skin reactions is an important priority in caring for this patient group \[[@B9]\].
The development of RISR may begin immediately, with increasing toxicity occurring at 2--3 weeks, with effects accumulating across the course of treatment, and may persist up to 4 weeks after treatment ends \[[@B4]\]. Hypothesised risk factors influencing RISR reported in the literature are both intrinsic or extrinsic \[[@B12]\]. The intrinsic factors are age, general health, ethnic origin, co-existing diseases, UV exposure, hormonal status \[[@B12]\] and genetic factors \[[@B13]\]. The extrinsic factors include the dose, volume, and number of fractions of radiation, radio-sensitizers, concurrent chemotherapy and the site of treatment \[[@B12]\]. Of these hypothesised factors, smoking status \[[@B14]\] and BMI \[[@B14],[@B15]\] are the major influencing factors supported by empirical data. A range of interventions are used for prophylaxis and management of these reactions. These interventions include (i) topical preparations (both steroidal and non-steroidal), (ii) dressings, (iii) systematic treatment such as amifostine, oral hydrolytic enzymes, pentoxifylline and zinc supplement, (iv) alternating modes of radiation delivery. The latest published systematic review including 39 trials before 2008 reported that only topical corticosteroid agents, among other interventions mentioned above, were found to significantly reduce the severity of some RISR, but not the levels of pain and itching \[[@B5]\]. Further, it is not yet clear which corticosteroid is superior to other non-steroidal agents \[[@B5]\]. This systematic review, together with a number of other previous reviews concluded that the uses of these interventions are not yet supported by conclusive evidence and warrant further investigations \[[@B4],[@B5],[@B10],[@B16],[@B17]\]. Current evidence indicates that there is a paucity of conclusive evidence which can inform health professionals on effective skin management of RISR \[[@B18],[@B19]\].
A natural oil-based emulsion, as known as Moogoo Udder Cream®, is a Queensland owned product that comprises allantoin, purified water, sweet almond oil, olive oil, rice bran oil, emulsifying wax, milk protein, aloe vera, vitamin E, glycerol caprylate, piroctone alamine and guarsilk. Anecdotal reports by patients with RISR and radiation oncologists in a number of Australian cancer centres suggest that Moogoo Udder Cream® may be effective in promoting healing, comfort, and pain relief. This product is being increasingly used in some other Australian cancer centres in for managing RISR, however there is not yet empirical evidence supporting this claim. This study aims to investigate the effects of Moogoo Udder Cream® against aqueous cream (which is current standard of care) in patients with RISR.
Objective of the study
======================
The aim of this study is to assess the efficacy of Moogoo Udder Cream® against aqueous cream for managing RISR in patients with breast cancer/lung cancer and head and neck cancer receiving radical radiotherapy.
Methods and materials
=====================
Design
------
A double-blind randomised controlled trial design will be used in this study.
Research questions
------------------
1\. Is there any difference in incidence of Grade 2,3 and 4 RISR between patients with breast, lung and head and neck cancers who receive Moogoo Udder Cream® and those who receive aqueous cream at week 5?
2\. Do patients with breast, lung and head and neck cancers who receive Moogoo Udder Cream® for their RISR have a different level of quality of life compared to those who receive aqueous cream at week 5?
3\. Do patients with breast, lung and head and neck cancers who receive Moogoo Udder Cream® for their RISR have a different level of pain compared to those who receive aqueous cream at week 5?
4\. Do patients with breast, lung and head and neck cancers who receive Moogoo Udder Cream® for their RISR have a different level of itching compared to those who receive aqueous cream at week 5?
5\. Is there any difference in time to grade 2, 3 and 4 of RISR between patients with breast, lung and head and neck cancers who receive Moogoo Udder Cream® and those who receive aqueous cream?
6\. Are there any differences in RISR, pain, itch and quality of life between groups at all other time points assessed (i.e. week 1,2,3,4,6 of radiation treatment, and 4 weeks post treatment completion)?
Sampling frame
--------------
Participants in this study will all be patients receiving radical radiotherapy for lung cancer, breast cancer and head and neck cancer at the Royal Brisbane and Women's Hospital (see Table [1](#T1){ref-type="table"}). A sample of consecutive eligible and consented patients will be recruited into the study. The research nurse will screen all patients for eligibility at the Radiation Treatment Department over the study duration period.
######
Recruitment criteria for this study
**Recruitment criteria**
----------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------
**Inclusion criteria** **Exclusion criteria**
· Age \>18 years · Patients who are unable to consent
· Patients who have a definitive diagnosis of breast cancer, lung cancer or head and neck cancer · Patients with pre-existing skin rash, ulceration or open wound in the treatment area
· Patients who are receiving radiotherapy (\>50 Gy) either as primary treatment or postoperative treatment to their chest, breast or head and neck. · Patients with known allergic and other systemic skin diseases even not directly affecting irradiated fields.
· Patients with any known allergic reactions towards any ingredient of either the Moogoo Udder Cream® or the aqueous cream and failed the patch test.
Baseline characteristics
------------------------
Baseline characteristics are demographic and clinical variables which include personal factors and radiotherapy factors (see Table [2](#T2){ref-type="table"}). These variables are expected to be important for explaining the primary and secondary outcomes in this patient group.
######
Summary of baseline characteristics and data collection
**Independent variables** **Data collection**
--------------------------- ------------------------------------------------------------------------
Personal factors Age
Gender
Ethnicity
Stage of cancer (Staging, nodal involvement)
Comorbidity
Prior chemotherapy/radiotherapy
Concurrent chemotherapy/biotherapy (e.g. monoclonal anti-bodies)
Body mass index
Smoking
Cup-size (breast and axilla)
Radiotherapy factors Daily dose (Gy/fraction)
Planning target volume (cm3)
Total dose to region of interest
Site of radiotherapy
Radiation technique (External beam via Tomotherapy/Linear accelerator)
Boost (Yes or no)
Number of boost treatments
Outcomes
--------
### Primary outcome
#### Severity of skin reaction (assessment by the clinician)
The Common Terminology Criteria for Adverse Events (CTCAE- Version 4.0) will be used to assess the severity of RISR \[[@B20]\]. This instrument is well used and well validated in radiation oncology for assessing radiation dermatitis \[[@B21]\]. This assessment will be undertaken weekly by a research nurse with extensive clinical experience in radiation oncology on a weekly basis during their weekly progress evaluation clinic during their treatment period. This scoring system is widely used in practice and research. The research nurse will be instructed prior to the beginning of the study to score the worst toxicity present, at the time of assessment within the treatment field.
Secondary outcomes
------------------
### Quality of life (skin specific) (self-administered by the patient)
Skindex-16 is a 16-item self-administered survey instrument developed by Chren and her research team in 2001 to measure the effects of skin condition on quality of life \[[@B22],[@B23]\]. Skindex-16 comprises three scales to assess patient emotion, symptoms and functioning. Item responses are standardized from 0 (no effect) to 100 (maximal effect). The scale demonstrated good psychometric properties: reliability at 72 hours (r = 0.68-0.90) and internal consistency (Cronbach's Alpha = 0.76-0.86). This tool has been increasing used in patients with skin toxicities resulted from their anti-cancer treatment \[[@B23]-[@B25]\]. Permission to use this tool has been granted by the author.
### Modified brief pain inventory (self- administered by the patient)
This study will use three measures from the Brief Pain Inventory (BPI), those of the average, best, and worst pain, and pain relief scores from the preceding seven days \[[@B26]\]. The participant will be asked to rate their pain level at the irradiated area. The time of interest of the original BPI is modified from "the past 24 hours" to "the past 7 days" for the specific purpose of this study. The BPI has been selected as it is a brief and easy tool for the assessment of pain within both the clinical and research settings. It has been well validated in both the chronic pain and cancer settings. The scale of 0 to 10 is simple for patients to use and reflects common clinical assessment of pain.
### Itching (self- administered by the patient)
Itching will be scored on a numeric analogue scale of 0--10 in the treated skin (0 = no itching at all), (10 = itching as bad as you can imagine).
### Treatment interruptions
Treatment interruptions due to severe skin reactions will be documented throughout the study (Yes/No). This decision is determined and routinely documented by the treating medical officers.
### Adverse events
Adverse events will be assessed by the research nurse. Adverse events will include allergic reactions from the allocated treatment and will be assessed using the Common Toxicity Criteria for Adverse Events version 4.0. (CTCAE v4) \[[@B18]\].
Sample size
-----------
A sample size of at least 81 in each arm would be required to detect a 20 % difference in the skin reactions scores using a 2-sided significant level of 0.05 and a power of 80 %. Assuming that approximately 5 % will be lost to follow-up; an additional 5 in each group will be required so the final sample will require 172 patients (86 per arm). All eligible patients will be approached consecutively. According to the local statistics of RBWH Cancer Care Services \[[@B27]\], 746 patients receive radical radiotherapy for breast cancer, lung cancer and head and neck cancer over a twelve-month period. Thus, the sample size proposed is achievable over a period of seven months.
Randomisation
-------------
Eligible and consenting patients will be randomly allocated to the intervention group to receive Moogoo Udder Cream®, or the control group to receive aqueous cream.
Sequence generation
-------------------
Blocked randomisation will be performed, with a block size of six, by a computer generated random number list prepared by an investigator who has no clinical involvement in the trial. Stratification by irradiated sites (breast, lung or head and neck), BMI categories (underweight \<18.50, normal = 18.50-24.99, overweight =25-29.9, obesity \> 30) and smoking status (smoking and non-smoking) will be carried out.
Allocation concealment and blinding
-----------------------------------
After the research nurse has obtained the patient's consent. The research nurse will then allocate participants to either receive Cream 1 (Group 1), or receive Cream 2 (Group 2) according to the generated sequence. This proposed study is a double-blind study. Blinding will be accomplished by not disclosing to the research nurse, medical officers, radiation therapists, nurses or participants which preparation used for skin treatment for each of the participants.
Both topical preparations (Moogoo Udder Cream® and aqueous cream) are white in colour, have similar consistency, and have no distinct odour. There are no other differentiating features. Both topical preparations will be provided and coded as Cream 1 or Cream 2 by the manufacturer in identical containers. The manufacturer will only disclose what Cream 1 and Cream 2 are at the completion of data collection. Subsequently, baseline data will be collected.
Procedures
----------
During the first visit, the doctor or nurse will introduce the study to eligible patients. If the patient is interested in the study; the research nurse will approach the patient and explain to him/her details of the study. At this time, the information sheet will be provided and informed consent will be obtained.
Any participant with known allergy to any ingredient of Moogoo Udder Cream® or the aqeuous cream will receive a patch test to determine a potential reaction with either cream. The patch test entails application of a small amount of the Moogoo Udder Cream® and the aqueous cream to two different sites distal to the irradiated area. This is reviewed after 24 hours for any reaction (a 24 hour timeframe was advised by literature and the RBWH Dermatology specialists). If after 24 hours, the patient is found to have a reaction to either cream, they will not be randomised onto the trial.
Patients allocated to Group one will receive Cream 1. Group two will receive Cream 2. Patients will be asked to start topical application of their allocated cream on the area of skin being irradiated at the onset of radiotherapy, twice a day or more as needed depending on the occurrence of RISR and pain, until the skin reaction subsides. The amount of cream dispensed to each patient will be recorded throughout treatment. If moist desquamation occurs, the topical preparation will be discontinued in the area of skin breakdown and dressings will be applied until the wound heals as per standard care. Patients will be asked to still continue with the topical preparation onto irradiated area that has no breakdown. All participants are given written instructions on how to apply the allocated treatment (see Figure [1](#F1){ref-type="fig"}).
{#F1}
All other skin care advice given to both groups of patients will be the same, as per the local policy of the Royal Brisbane and Women's Hospital. All patients will be advised to
wear loose, comfortable cotton clothing in the area being treated
use a gentle detergent
not wear an under wire bra if they are treated for breast cancer
avoid temperature extremes and use lukewarm water to wash
not use hot or ice packs
not use a harsh soap or shampoo on irradiated skin
keep irradiated skin dry
air skin 2--3 times a day
not use a blade razor on irradiated skin
not expose irradiated skin to the sun
not rub or scratch irradiated skin; patients may apply cool moist washers if skin feels itchy or hot
pat skin dry with a soft towel after washing or air dry
not use any tapes, band aids, or dressing unless advised by their clinicians.
not use other topical preparations in the treatment area
rinse off immediately in fresh water if swimming in a pool or salt water (if the skin is intact)
Discontinuation
---------------
If discontinuation of study skin care products occurs due to allergy (or another patient reason), substitution of alternative creams is at the treating clinician's discretion. Application of both study skin products should cease, as un-blinding for an individual may reveal product types for future patients even though the labelling of the products as 1 or 2 is randomised and the products are very similar in appearance. A variety of other skin products are available so it is unnecessary to continue with either of the study products.
Discontinuation of the study creams does not constitute withdrawal from the study and scheduled assessments should continue as described in this protocol.
Data collection
---------------
Table [3](#T3){ref-type="table"} outlines the measures used in this study. At baseline and weekly during treatment, data will be collected when patients are in the radiation oncology department. At completion of radiotherapy, patients will be given the diaries to complete at home at week 1, week 2 and week 3 post-treatment. The research nurse will contact the patient via telephone to remind them to complete the diaries. At week 4 post-treatment, all patients who have completed their treatments will return to the radiation oncology department for a routine medical review. At this time, they will be asked to complete the final questionnaire and have the severity of their skin reaction assessed by the research nurse.
######
Table of study measure
**Measures** **Administered by** **Baseline (i.e. Day −7 to Day 0 of radiation treatment)** **Weekly during treatment (i.e. Day 5, 10, 15, 20, 25, 30 of radiation treatment)** **Week 1, week 2 and week 3 post treatment (i.e. Day 5, 10, 15 post radiation treatment)** **4 weeks after radiation treatment Review appointment (Face to face)**
------------------------------------------------------------- --------------------- ------------------------------------------------------------ ------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------- -------------------------------------------------------------------------
Personal factors (see Table [1](#T1){ref-type="table"}) Research nurse \*
Radiotherapy factors (see Table [1](#T1){ref-type="table"}) Research nurse \*
CTCAE Research nurse \* \* \*
Modified Brief Pain Inventory Patient \* \* \* \*
Itching Patient \* \* \* \*
Skindex-16 Patient \* \* \* \*
Data analysis
-------------
Patient characteristics between arms will be compared using the chi-square test for discrete variables and the *t*-test for continuous variables. Acute reactions will be evaluated using Kaplan-Meier actuarial plots (time to event) with the log-rank test for significance. Grade reaction plots at the particular time points (weeks) will be plotted and compared with 95 % confidence intervals for both arms. Uni-variate regression models will determine the significance of factors to be included in the multivariate regression model. A generalized linear interactive modelling package (GLIM4) will be used.
Discussion
==========
Despite advances of radiologic technology and supportive care, RISR are still not well managed. There is a lack of efficacious interventions in managing RISR. While anecdotal evidence suggests that Moogoo Udder Cream® may be effective in managing RISR, research is needed to substantiate this claim. This paper presents the design of a double blind randomised controlled trial that will evaluate the effects of Moogoo Udder Cream® versus aqueous cream for managing in RISR in patients with cancer.
Ethical considerations
----------------------
This study protocol has been reviewed and approved by the Royal Brisbane and Women\'s Hospital Human Research Ethics Committee.
Competing interests
===================
The products used in this trial will be provided by the manufacturer (Moogoo Skin Care) free of charge. None of the investigators own any shares of the tested products in any form. We declare that this is an investigator initiated trial. There is no limitation for the investigators to publish the results in peer-reviewed journals.
Authors' contributions
======================
RJC drafted and coordainted the development of the manuscript. All authors contributed to the development of this protocol. LT conducted the sample size calculation and developed the data analysis plan. All authors read and approved the final manuscript.
Acknowledgements
================
This study received research a grant from the Office of Medical and Health Research, Queensland Health, and received sponsorship from Moogoo Skincare. We declare that this is an investigator-intiated study and Moogoo Skincare does not have any involvement in the conduct of the study.
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Beautiful, super-soft, feminine top by Deletta for Anthropologie. Flattering, sheer flutter sleeves. Ties can also be worn loose (untied). Rich, rust-orange color. Looks great loose over jeans/slacks or tucked in to a high-waisted skirt!
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Introduction {#Sec1}
============
The solute carrier family 26 (SLC26), also known as the sulfate permease (SulP) family, facilitates the transport of a broad variety of organic and inorganic anions^[@CR1]^. Members of this family are found in all kingdoms of life and operate predominantly as secondary transporters (symporters and exchangers)^[@CR2]--[@CR4]^. As an exception, prestin (SLC26A5) functions as a voltage-sensitive motor protein that evokes robust length changes in outer hair cells and thereby contributes to cochlear amplification^[@CR5],[@CR6]^. The relevance of the SLC26 family in maintaining anion equilibria is underlined by the causative role of mammalian SLC26 proteins in diseases such as congenital chloride diarrhea^[@CR7]^ and cytotoxic brain edema^[@CR8]^.
SLC26 proteins are composed of a membrane-inserted transport domain and a carboxy-terminal cytoplasmic STAS (sulfate transporter and anti-sigma factor antagonist) domain. The SLC26--STAS domain is relevant for intracellular trafficking^[@CR9],[@CR10]^ and protein--protein interactions^[@CR11]--[@CR13]^. Its deletion impairs substrate transport by the membrane domain^[@CR4],[@CR10],[@CR14]^. The crystal structure of SLC26Dg, a prokaryotic SLC26 protein from *Deinococcus geothermalis*, revealed a spatially separated membrane and STAS domain^[@CR4]^. The SLC26Dg membrane domain holds two intertwined inverted repeats of seven transmembrane segments (TMs). Despite a poor sequence homology, the SLC26 family shares this 7-TM-inverted repeat (7TMIR) architecture with the SLC4 and SLC23 families that transport bicarbonate and nucleobases plus vitamin C, respectively^[@CR15]--[@CR22]^. The 14 TMs are arranged in two subdomains: a compact core domain that holds the substrate binding site as inferred from the location of the nucleobases in the SLC23 crystal structures^[@CR20]--[@CR22]^, and an elongated gate domain that shields one side of the core domain. A mounting body of evidence^[@CR16],[@CR19],[@CR22],[@CR23]^ suggests that these proteins operate based on an elevator alternating-access mode of transport^[@CR24]^ involving a rigid-body translation-rotation of the core domain with respect to the gate domain.
Dimeric states have been previously observed for pro- and eukaryotic members of the SLC4^[@CR25]--[@CR27]^, SLC23^[@CR28]^, and SLC26^[@CR4],[@CR29]--[@CR32]^ families. Recent structures subsequently confirmed this oligomeric state for SLC4^[@CR17]--[@CR19]^ and SLC23^[@CR21],[@CR22]^ proteins and indicated that in both families the gate domains form the main interaction surface between protomers, though each family appears to hold a distinct dimer interface. As the crystal structure of SLC26Dg captured the protein in a monomeric state, the mode of interaction between SLC26 protomers has remained elusive. Interestingly, the protomers within the SLC26 dimer have been found to interact functionally^[@CR29],[@CR33]^ despite the presence of a complete translocation path in each individual protomer. Here, we provide structural and mechanistic insights in the allosteric interactions between SLC26 protomers. We integrated pulsed electron--electron double resonance (PELDOR, also known as double electron--electron resonance) distance measurements and in vitro transport studies with structural modeling and refinement using molecular dynamics (MD) simulation to determine the architecture of the membrane-embedded SLC26 dimer and characterize its functional relevance.
Results {#Sec2}
=======
Resolving the SLC26Dg dimer interface in the lipid membrane {#Sec3}
-----------------------------------------------------------
To define the SLC26Dg dimer interface, we used interspin distance constraints derived from PELDOR experiments. As SLC26Dg is monomeric in its detergent-solubilized state, we reconstituted spin-labeled protomers in lipid membranes to assure dimer formation^[@CR4]^. As the gate domain in the SLC4^[@CR17]--[@CR19]^ and SLC23^[@CR21],[@CR22]^ families establishes the main protomer--protomer contacts in the membrane (Fig. [1a, b](#Fig1){ref-type="fig"}), we engineered spin labels at 13 different positions on the termini of gate domain helices in SLC26Dg. One additional central position in the core domain (TM8) was also selected (Fig. [1c](#Fig1){ref-type="fig"}). By site-directed modification of single-cysteine mutants, we efficiently introduced the probe 1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl-methanethiosulfonate (MTSSL)^[@CR34]^ (Supplementary Table [1](#MOESM1){ref-type="media"}, Supplementary Fig. [1](#MOESM1){ref-type="media"}). Size-exclusion chromatography and transport assays in proteoliposomes demonstrated that all mutants were folded well and active (Supplementary Fig. [2](#MOESM1){ref-type="media"}).Fig. 1Dimer interfaces in 7TMIR proteins. **a** Side view of the membrane domains of NBCe1 (PDB: 6CAA) and UraA (PDB: 5XLS). Core and gate domain are colored orange and gray, respectively, with residues within 4 Å of the opposing protomer in pink. **b** Top views of the dimeric arrangements of NBCe1 and UraA. For each dimer, the gate domain of one of the protomers follows a rainbow coloring scheme (blue-to-red for N-to-C direction). TMs central in the respective dimers are numbered. **c** Side view of the membrane domain of SLC26Dg (PDB: 5DA0). Residues mutated to cysteine for site-directed spin labeling are colored blue. The circled numbers indicate the respective TMs
Systematic analysis of all positions led to the identification of three labeled positions, K353R1, V367R1, and L385R1, that gave well-defined interspin distance distributions centering around 4.4 ± 0.2, 3.9 ± 0.3, and 1.8 ± 0.1 nm, respectively (Fig. [2b--d](#Fig2){ref-type="fig"}). These positions are located in TM13 and TM14 and place this region in close proximity to the center of the SLC26Dg dimer interface. This particular dimer arrangement combined with the short phase memory time (*T*~*M*~) of the spins in membranes (Supplementary Fig. [3](#MOESM1){ref-type="media"}) did not allow to accurately determine the long interspin distances between other helices (Supplementary Fig. [4](#MOESM1){ref-type="media"}). An exponential decay was observed for the PELDOR measurement of the detergent-solubilized protein (Fig. [2a](#Fig2){ref-type="fig"}), supporting the notion that the identified region is part of the native SLC26Dg dimer interface formed in the lipid membrane. Given the spin-labeling efficiencies of 70--100%, the obtained modulation depths of the PELDOR time traces are in the range expected for a dimer (Supplementary Table [1](#MOESM1){ref-type="media"}), suggesting that the majority of the protomers in the membrane is part of a dimer.Fig. 2Interspin distances in the SLC26Dg dimer. **a** Primary PELDOR data of detergent-solubilized K353R1. **b**--**d** Left panels: background-corrected PELDOR time traces for membrane-reconstituted K353R1, V367R1, and L385R1 (black traces), overlaid with the fit from Tikhonov regularization (green), and forward-calculated PELDOR time traces from BioEn spin-label rotamer refinement of the MD simulation model (magenta, dashed; *θ* = 10). Right panels: distance distributions obtained by Tikhonov regularization (green), overlaid with the distance distributions resulting from BioEn analysis of the MD simulation model (magenta, dashed). Original PELDOR data in Supplementary Fig. [2](#MOESM1){ref-type="media"}. **e** C~α~-atom root mean squared distance (RMSD) values of the core, gate, TM13, and 14 relative to the monomer crystal structure as a function of MD time (1 μs)
Structural model of the SLC26Dg membrane dimer interface {#Sec4}
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On the basis of the PELDOR data and the SLC26Dg crystal structure, we constructed a dimer model. First, to obtain an equilibrated structure for rigid-body docking, monomeric SLC26Dg without its carboxy-terminal STAS domain was embedded in a palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayer and submitted to 1 μs of MD simulations. We observed considerable flexibility of the gate domain in comparison with the core domain (Fig. [2e](#Fig2){ref-type="fig"}). In particular, TM13 and TM14 exhibited significant motions in the monomer, in line with their suspected involvement in the membrane dimer interface. Owing to the observed flexibility, we used several relaxed monomer conformations obtained at 110 ns intervals of MD for docking. For each conformation, a rigid-body search restricted by C2 symmetry with an axis normal to the membrane was performed and the rotation angle that showed the best overall fit with the PELDOR data was determined. Using this approach, we identified a candidate dimer structure based on a monomer conformation observed at 440 ns of MD and a polar plane angle of 210 ± 5° (Supplementary Fig. [5](#MOESM1){ref-type="media"}). An alternative rigid-body docking approach guided by the inferred distance distributions resulted in a very similar dimer model (Supplementary Fig. [6](#MOESM1){ref-type="media"}). The initial C2 symmetric MD dimer was then relaxed by additional MD simulation. The forward-calculated PELDOR traces for the relaxed dimer, after gentle spin-label rotamer refinement^[@CR35]^, are in excellent agreement with the experimental background-corrected time-domain data (Fig. [2b--d](#Fig2){ref-type="fig"}, left panels, Supplementary Fig. [7](#MOESM1){ref-type="media"}). The structure of this SLC26Dg membrane domain dimer model is shown in Fig. [3](#Fig3){ref-type="fig"}. Simulations performed on this model for two additional positions, V129R1 (TM5) and L248R1 (TM8), agree with the experimental data as well (Supplementary Fig. [4a](#MOESM1){ref-type="media"}). For the other nine positions in the gate domain, simulations predict mean interspin distances in the range of 6.3--10.6 nm, which could not be accurately determined owing to the short *T*~*M*~ (Supplementary Fig. [4b](#MOESM1){ref-type="media"} and Supplementary Fig. [3](#MOESM1){ref-type="media"}).Fig. 3Model of the SLC26Dg dimer interface. **a** Side view of the SLC26Dg membrane domain in the same orientation as Fig. [1a](#Fig1){ref-type="fig"}. Core and gate domain are colored orange and gray, respectively, with residues within 4 Å of the opposing protomer in pink. **b** Top views of the dimeric arrangement of SLC26Dg. The gate domain of one of the protomers follows a rainbow coloring scheme (blue-to-red for N-to-C direction)
The model of the SLC26Dg dimer displays a protomer--protomer membrane interface that is remarkably different from the membrane interfaces observed for the SLC4 and SLC23 families, both in its location and in its size^[@CR17]--[@CR19],[@CR21],[@CR22]^. Whereas the membrane dimer interfaces of SLC4 and SLC23 proteins center around TM6, and TM5 plus TM12, respectively, the midpoint of the SLC26Dg dimer is TM14. Furthermore, although the membrane dimer interface of SLC4 and SLC23 proteins involves extensive interactions covering large fractions of the exposed membrane surface of their gate domains, the membrane interface of SLC26Dg is relatively small. Also, in comparison with other oligomeric membrane proteins, the surface buried by dimerization of the membrane domain is modest^[@CR36]^. This observation agrees with the complete absence of dimerization in detergent and suggests that other factors, such as subunit-bridging lipids or the cytoplasmic STAS domain may contribute to the stabilization of the dimeric state.
STAS domain affects central regions in the dimer {#Sec5}
------------------------------------------------
The cytoplasmic STAS domain is one of the major structural constituents that distinguishes the SLC26 family from the SLC4 and SLC23 families, which do not hold carboxy-terminal domains^[@CR16]^. Although deletion of the STAS domain compromises the transport capacity of the SLC26Dg membrane domain, the structure of the membrane domain is not altered^[@CR4]^. As the STAS domain immediately follows the central TM14, we further determined to what extent the STAS domain contributes to the dimer interface.
As evidenced from the PELDOR time trace for L385R1 in SLC26Dg^ΔSTAS^, deletion of the STAS domain did not affect the ability of the membrane domain to form dimers (Supplementary Fig. [8](#MOESM1){ref-type="media"}). STAS domain deletion resulted in a small increase in the mean L385R1 distance from 1.8 ± 0.1 to 2.1 ± 0.1 nm, that, given the narrow distance distribution, rather suggests a rearrangement of the MTSSL rotamers than a physical separation of the protomers. The complete disappearance of oscillations in the primary PELDOR data of SLC26Dg^ΔSTAS^-K353R1 and -V367R1 in TM13 suggests that either similar rearrangements of spin-label rotamers or an increased flexibility at these positions may underlie these changes (Supplementary Fig. [8](#MOESM1){ref-type="media"}). The latter could not be confirmed owing to the limited time window of the dipolar evolution. Thus, although deletion of the STAS domain appears to affect the environment around the spin labels in TM13 and TM14, the STAS domain itself is not a prerequisite for dimerization.
SLC26Dg dimer interface represents the SLC26 family {#Sec6}
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To further validate the SLC26Dg membrane dimer model and determine to what extent it represents the SLC26 family in general, we used oxidative cross-linking in biological membranes. Owing to its central position, we focused on TM14 (Fig. [3b](#Fig3){ref-type="fig"}). Oxidative cross-linking of single-cysteine variants at several positions in TM14 of SLC26Dg, fused to superfolder green fluorescent protein (GFP) to facilitate detection, leads to the appearance of a band with lower electrophoretic mobility (Fig. [4a](#Fig4){ref-type="fig"}). We assign this band to SLC26Dg homodimers because an identical anomalous shift was observed on cross-linking in proteoliposomes (Supplementary Fig. [9](#MOESM1){ref-type="media"}). Cross-links were observed for residues located at both ends of TM14, but not for residues facing the interior of the bilayer in line with a general lower reactivity of cysteines at this position^[@CR37]--[@CR39]^. The ability of cysteine residues in TM14 of SLC26Dg to form a disulfide bond with the opposing protomer further validates our SLC26Dg dimer model (Fig. [4b](#Fig4){ref-type="fig"}).Fig. 4Oxidative cysteine cross-linking between TM14 of SLC26Dg. **a** In gel GFP fluorescence analysis of disrupted *E. coli* cells expressing single-cysteine variants of SLC26Dg fused to superfolder GFP. Following oxidative cross-linking, samples were analyzed by non-reducing SDS-PAGE. Cysteine-free SLC26Dg (cysless) and L144C (TM5) represent negative controls. Black and white arrows indicate dimeric and monomeric SLC26Dg. Source data are provided as a Source Data file. **b** Side view of the SLC26Dg dimer model. Core and gate domain are colored orange and gray, respectively. Positions in TM14 susceptible to cross-linking are colored in green, non-susceptible residues are colored pink. The gate domain of the right protomer is depicted in surface representation. TM13 of the left protomer is contoured. The circled numbers indicate the respective TMs
Although the known dimer interfaces between SLC4 and SLC23 families differ greatly, a high degree of similarity is observed between members of the same family^[@CR17]--[@CR19],[@CR21],[@CR22]^. This suggests that the dimer interfaces for this fold are specific to a family. To test this, we used the same TM14 cross-linking approach on SLC26 proteins from *Sulfitobacter indolifex* and *Rattus norvegicus*, which hold 23% and 21% sequence identity to SLC26Dg, respectively (Supplementary Fig. [10](#MOESM1){ref-type="media"}, [11](#MOESM1){ref-type="media"}). For both proteins, we observed the formation of TM14 disulfide cross-links between protomers, which provides evidence that the membrane dimer interface may be very similar, if not conserved, throughout the SLC26 family.
Functional relevance of the SLC26Dg dimer {#Sec7}
-----------------------------------------
The observation of a structural SLC26Dg dimer led us to ask whether this oligomeric state is important for function. As both protomers have independent binding sites and non-overlapping translocation paths, the relevance of the dimeric state is not evident. Functional interactions between protomers in oligomeric proteins can be revealed by mixing protomers with different functional characteristics and analyzing the resulting hetero-oligomers. We opted to create an inactive variant by locking the protein in the inward-facing conformation using disulfide cross-linking. Based on the crystal structure, we selected Ile-45 on the extracellular side of TM1 (core) and Ala-142 in TM5 (gate) as most suited positions concerning cross-linking efficiency and ability to lock the protein (Fig. [5a](#Fig5){ref-type="fig"}). Oxidative cross-linking of SLC26Dg-CL-I45C/A142C, hereafter named SLC26Dg-IL (inward-locked), resulted in a nearly complete shift in the electrophoretic mobility of the protein that could be restored by the addition of the reductant dithiothreitol (DTT) (Fig. [5b](#Fig5){ref-type="fig"}). Likewise, fumarate transport of the cross-linked mutant in proteoliposomes was close to background activity, but could be fully recovered to wildtype activity by the addition of DTT, indicating that the protein was well-folded and reconstituted (Fig. [5c](#Fig5){ref-type="fig"}).Fig. 5Generation and functional characterization of SLC26Dg-IL. **a** Surface representation of MD-simulated SLC26Dg clipped through the funnel toward the putative substrate-binding site. Cytoplasmic water molecules in a \~ 10 Å slab at the clipping plane are shown. Ile-45 and Ala-142 indicate the relative position of the cysteine mutants in the core (orange) and gate (gray) domain, respectively. **b** SDS-PAGE analysis of purified and cross-linked SLC26Dg-IL monomers in the absence and presence of DTT. Single and double stars indicate not-cross-linked and cross-linked protein, respectively. **c** Functional characterization of membrane-reconstituted and cross-linked SLC26Dg-IL (dark blue), wildtype SLC26Dg (orange), and both proteins mixed in equal ratio's (pink). Closed and open symbols indicate the absence and presence of a pre-incubation step with DTT. **d** Initial transport rates of membrane-reconstituted and cross-linked samples containing wildtype and SLC26Dg-IL mixed in different ratio's. Dark blue, pink, and orange dashed curves indicate the anticipated curves assuming an activity of the heterodimers corresponding to 0, 50, and 100% of the wildtype homodimers. These models were calculated assuming stochastic dimer formation (e.g., mixing WT:IL protomers in a 50:50 ratio results in 25% WT--WT, 50% WT--IL, and 25% IL--IL dimers) and specific transport activities of 32.3 or 6.8 nmol fumarate per mg WT or IL homodimer per min, respectively, and heterodimer activities corresponding to 0, 50, or 100% of WT homodimer. Data points represent mean and standard deviations of three technical replicates. Source data are provided as a Source Data file
As SLC26Dg is monomeric in detergent and dimerizes only after reconstitution in the lipid membrane, we achieved stochastic formation of heterodimers as demonstrated by the decreased TM14 cross-linking upon the addition of SLC26Dg-IL in a control experiment (Supplementary Fig. [12](#MOESM1){ref-type="media"}). Interestingly, the initial transport rates of proteoliposomes holding different ratios of wildtype and SLC26Dg-IL followed a positive quadratic relationship (Fig. [5d](#Fig5){ref-type="fig"}). The activity of the heterodimers exceeded the expected values for independent functioning of protomers, which is half the sum of the activities of the wildtype and SLC26Dg-IL homodimers (Fig. [5d](#Fig5){ref-type="fig"}, straight line). In fact, in the most parsimonious model for the quadratic dependence of the activity on the mixing ratio, only the SLC26Dg-IL homodimer is inactive and all other dimers have the same activity. This could imply that either only one protomer is active in a dimer or the activity of a wildtype protomer is doubled when paired with an inward-locked protomer. In any case, the robust coupling evident in this transport activity data is a strong indication that dimerization is functionally relevant.
Discussion {#Sec8}
==========
The structural model of the SLC26Dg membrane domain dimer interface, based on electron paramagnetic resonance (EPR) measurements on membrane-reconstituted protein and validated by cysteine cross-linking in biological membranes, places TM14 of the gate domain at the center of the SLC26Dg dimer. Further cross-linking studies on additional prokaryotic and mammalian homologs suggest that this interface might be evolutionary conserved in the SLC26 family. Nevertheless, amino-acid sequence alignments of TM14 show no conserved features between or even within prokaryotic and mammalian SLC26 proteins, other than a GxxxG-like motif toward the extracellular side of TM14 (Supplementary Fig. [13](#MOESM1){ref-type="media"}). Though this motif often mediates dimerization in single-pass membrane proteins^[@CR40]^, its role in multi-pass membrane proteins lies more likely in folding of the protomers^[@CR41]^. Besides, this specific region of TM14 is not directly involved in protomer--protomer interactions in our model. Specificity of the SLC26 protomer--protomer interaction may instead arise from general complementarity of the interacting surfaces combined with other, potentially conserved features such as interfacial lipids (*vide infra*). The central position of the gate domain in the SLC26 membrane dimer interface corresponds well with the SLC4 and SLC23 families in which the gate domains also form the major contacts between the membrane domains^[@CR17]--[@CR19],[@CR21],[@CR22]^. However, although the dimer interfaces seem conserved within a family, the regions involved in the protomer--protomer contacts seem to differ greatly among the three families.
It appears likely that these different dimeric arrangements represent stable constellations between which the protomers do not alternate during transport. The structures of dimeric SLC4 and SLC23 proteins in different conformations^[@CR17]--[@CR19],[@CR21],[@CR22]^ have identical contact surfaces within each family. This is further supported by repeat-swap homology modeling of AE1, which indicated that no changes in the dimerization interface were required during the transition from the outward-facing structure to the inward-facing model^[@CR23]^. Transitions between interfaces seem further unlikely owing to the requirement for significant rearrangements in structural elements, such as the cytoplasmic region following TM12 in SLC4A1 and SLC4A4^[@CR17],[@CR18]^, which also appears stable and blocking alternative interfaces in SLC26Dg (Supplementary Fig. [14](#MOESM1){ref-type="media"}). Finally, our PELDOR data on SLC26Dg, especially the well-defined distance distributions for the interface region, strongly disagrees with a dynamic interface. A stable oligomer interface is in line with other observations on unrelated elevator proteins^[@CR42],[@CR43]^.
The buried surface resulting from dimerization in the SLC26Dg membrane domain amounts to \~ 350 Å^2^, which is small, not only in comparison with the SLC4 and SLC23 family whose membrane interfaces measure \~ 1000 Å^2^ and \~ 2000 Å^2^ ^[@CR44]^, respectively, but also in relation to other oligomeric membrane proteins^[@CR36]^. It is likely that additional extrinsic factors contribute to extend and stabilize the SLC26 membrane dimer interface, e.g., interfacial lipids that were recently reported to stabilize an SLC23 dimer^[@CR45]^ and other oligomeric membrane proteins^[@CR36]^. In this respect, the STAS domain appears to be relevant as well. The short linker region connecting TM14 and the STAS domain implies its close proximity to the membrane dimer interface. In addition, the STAS domain affects TM13 and TM14 at the center of the dimer interface (Supplementary Fig. [8](#MOESM1){ref-type="media"}). Given that isolated SLC26--STAS domains do not appear to form dimers^[@CR13],[@CR46],[@CR47]^, we expect the STAS-mediated effect on the gate domain to result from a direct interaction between the STAS domain and the membrane domain. This interaction may also form the basis for the enhanced transport rates observed in the presence of the STAS domain^[@CR4],[@CR10],[@CR14]^.
All 7TMIR proteins form structural dimers in the membrane, but the general relevance of this oligomeric state for their function is not clear. The available structures of the SLC4, SLC23, and SLC26 proteins all indicate that the complete substrate translocation path is contained within one protomer. This is supported by the recessive inheritance mode of SLC26-linked diseases^[@CR29],[@CR48]^ and further confirmed by the functional characterization of heterodimers composed of a wildtype and an inactive mutant protomer. Most of these heterodimers were found to be active for NBCe1^[@CR49]^ (SLC4), UraA^[@CR22]^ (SLC23), and SLC26Dg (SLC26, this work), though for UapA (SLC23), inactive heterodimers were observed as well^[@CR21]^. With the exception of SLC26Dg, these studies were carried out in the context of whole cells, employed different mutations that interfered in diverse ways with substrate transport, and, in case of NBCe1 and UraA, involved the use of concatemeric constructs. This diversity in experimental approaches makes it difficult to precisely compare these data. Nevertheless, although the inferred specific activity of the heterodimers of NBCe1 (50% active) suggests that the protomers can operate independently, the apparent negative and positive dominance observed for UapA, and UraA plus SLC26Dg, respectively, indicates that the dimeric state may have a functional role as well. This notion is further supported by studies on rat prestin (SLC26A5) heterodimers composed of protomers that in the context of a homodimer hold a very different voltage-dependence of their non-linear capacitance. For these heterodimers an intermediate phenotype was observed, suggesting a strong co-operative interaction in which the two protomers jointly determine the voltage-dependence of the conformational changes^[@CR29]^.
Though the mechanistic basis for functional interactions in 7TMIR dimers is currently unclear, important insights were obtained from the characterization of monomeric 7TMIR proteins. Monomeric variants of UraA, generated by the introduction of bulky residues at the dimer interface, bind substrate with wildtype affinities and are thus expected to be well-folded, but are incapable of facilitating transport^[@CR22]^. In our study, we characterized the transport properties of individual protomers as well, but in the context of a dimer. These SLC26Dg-WT protomers, embedded in WT--IL heterodimers, are fully active. In fact, the WT--IL heterodimers have the same activity as wildtype homodimers. Together these observations highlight the relevance of the interaction between opposing gate domains for facilitating transport. This interaction may stabilize an essential conformation of the gate domain required for transport, as suggested previously^[@CR22]^ and in line with our observation that the transport-incompetent SLC26Dg^ΔSTAS^ undergoes small rearrangements in the gate domain. Alternatively, the gate--gate domain interaction may provide a stable membrane-embedded scaffold that enables the vertical translation of the core domain and its anticipated deformation of the bilayer. In this context, the inward-locked SLC26Dg protomer may serve as an extended scaffold that fixates the gate domain even better in the membrane, providing a rational for the apparent increase in transport rate observed for the wildtype protomer in the heterodimer. Though the similar transport rates of wildtype homodimers and WT--IL heterodimers may also imply that only one protomer is active in the SLC26Dg dimer, the latter appears in conflict with the intermediate non-linear capacitance observed for rat prestin heterodimers^[@CR29]^. Additional structures of dimeric 7TMIR proteins in multiple states will be required to further pinpoint the role of the gate domain.
Understanding the transport mechanism of 7TMIR proteins requires that proteins are not studied only as individual protomers, but also in the context of the dimer, their functionally relevant oligomeric state. Structures of SLC4 and SLC23 proteins have provided exceptional insight into protomer interactions by providing snapshots of dimeric constellations, but the structure of a dimeric SLC26 protein has been elusive. Here, we have determined the architecture of dimeric, membrane-embedded SLC26Dg using an integrated structural biology approach. The SLC26 dimer interface is unique and distinguishes itself from SLC4 and SLC23 proteins. We have demonstrated that the interface is not dynamic, and that the carboxy-terminal STAS domain, although not required for dimerization, affects regions central in the dimer. Finally, our heterodimer studies have underlined the functional significance of the dimer. Together these structural, dynamic, and functional characterizations provide the framework for further studies on the SLC26 family and offer mechanistic insights that may extend to other elevator proteins as well.
Methods {#Sec9}
=======
Site-specific mutagenesis of SLC26 transporters {#Sec10}
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Cysteine residues were introduced into pINITcat-SLC26Dg by Quikchange mutagenesis or a two-step PCR method (mega-primer approach; primer sequences in Supplementary Data [1](#MOESM2){ref-type="media"}). Sequence-validated pINITcat-SLC26Dg variants were subsequently subcloned into pBXC3GH by FX cloning^[@CR50]^ for protein expression and purification.
Protein expression and purification {#Sec11}
-----------------------------------
*Escherichia coli* MC1061 (ATCC 53338) containing pBXC3GH-SLC26Dg or the variants was cultivated in 9 L TB/ampicillin in a fermenter (Bioengineering). Cells were grown at 37 °C until an OD~600~ ≈ 2 was reached, after which the temperature was gradually decreased to 25 °C over the course of 1 h. Expression was induced by the addition of 0.005% (w/v) [l]{.smallcaps}-arabinose and continued for 16 h. Cell pellets were resuspended in 50 m[m]{.smallcaps} potassium phosphate (KPi), pH 7.5, 150 m[m]{.smallcaps} NaCl, and 1 m[m]{.smallcaps} MgSO~4~ and incubated for 1 h at 4 °C in the presence of 1 mg/mL lysozyme and traces of DNase I before disruption with an APV Gaulin/Manton homogenizer. The lysate was cleared by low-spin centrifugation, and membrane vesicles were obtained by ultracentrifugation. Vesicles were resuspended to 0.5 g/mL in 50 m[m]{.smallcaps} KPi, pH 7.5, 150 m[m]{.smallcaps} NaCl and 10% glycerol (buffer A). All subsequent steps were carried out at 4 °C. Membrane proteins were extracted for 1 h at a concentration of 0.1 g/mL buffer A supplemented with 1--1.5% (w/v) *n*-decyl-*β*-maltoside (DM, Glycon). Solubilized SLC26Dg was purified by immobilized metal affinity chromatography (IMAC). Target protein was immobilized on Ni-NTA resin and impurities were removed with 20 column volumes (CV) washing with 20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl (buffer B) supplemented with 50 m[m]{.smallcaps} imidazole, pH 7.5 and 0.2% DM. Protein was eluted with buffer B containing 300 m[m]{.smallcaps} imidazole and cleaved by HRV 3 C protease during dialysis against buffer B without imidazole. Histidine-tagged GFP and protease were removed by IMAC, and cleaved protein was concentrated and subjected to size-exclusion chromatography (SEC) on a Superdex 200 Increase 10/300 column (GE Healthcare) equilibrated with 20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl, and 0.2% DM (buffer C).
Site-directed spin labeling of SLC26Dg cysteine mutants {#Sec12}
-------------------------------------------------------
Cultivation and isolation of membrane vesicles were essentially performed as detailed above, but buffers for resuspending cells and membrane vesicles were supplemented with 3 m[m]{.smallcaps}, and 1 m[m]{.smallcaps} DTT, respectively. IMAC purification was conducted in the same way as described in the previous section but 5 m[m]{.smallcaps} 2-mercaptoethanol was included in all purification buffer to preserve the reduced state of the cysteine residues. Peak fractions from SEC purification were pooled and 2-mercaptoethanol was removed with Econo-Pac 10DG desalting column (Bio-rad), which was pre-equilibrated with buffer C. The concentration of eluted protein was adjusted to 7.5 µ[m]{.smallcaps} with buffer C. The labeling of cysteine residue was initiated by stepwise addition of 100 m[m]{.smallcaps} MTSSL spin label (in dimethyl sulfoxide, Toronto Research Chemicals) in the protein solution to a final concentration of 300 µ[m]{.smallcaps} and incubated at room temperature for 45 min with gentle agitation. The spin-labeled protein was further concentrated and free label was removed using Micro Bio-Spin 6 Chromatography Columns (Bio-rad) pre-equilibrated with buffer C.
Membrane reconstitution of SLC26Dg {#Sec13}
----------------------------------
Proteoliposomes were prepared using the detergent-doped liposomes method^[@CR4],[@CR51]^. Dry pellets of [l]{.smallcaps}-α-phosphatidylcholine (derived from soybean, Sigma) were dissolved in chloroform, dried in a rotary evaporator, resuspended to 20 mg/ml and sonicated in buffer containing 50 m[m]{.smallcaps} KPi, pH 7.5. After three freeze--thaw cycles, large unilamellar vesicles were prepared by extrusion through a polycarbonate filter with pore diameters of 400 nm. Liposomes were diluted to 4 mg/ml and destabilized beyond *R*~sat~ with Triton X-100. SEC-purified SLC26Dg in 0.2% DM was added to the liposomes at a weight ratio of 1:50 (protein/lipid) for transport assays or 1:20 (protein/lipid) for PELDOR measurements, and detergent was subsequently removed by the addition of Biobeads. For radioisotope transport assays, proteoliposomes were harvested by centrifugation for 1.5 h at 250,000 × *g* and resuspended in 50 m[m]{.smallcaps} sodium phosphate (NaPi), pH 7.5, 2 m[m]{.smallcaps} MgSO~4~ to a lipid concentration of 20 mg/ml. After three freeze--thaw cycles, proteoliposomes were stored in liquid nitrogen until analysis. For PELDOR measurements, proteoliposomes were harvested by centrifugation for 20 min at 250,000 × *g* and resuspended in 50 m[m]{.smallcaps} KPi, pH 8.0 to a final spin concentration of 80--130 µ[m]{.smallcaps}.
PELDOR EPR {#Sec14}
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All the PELDOR experiments were performed at Q-band frequencies (33.7 GHz) using a Bruker E580 spectrometer equipped with an EN 5170 D2 cavity, 150 W traveling-wave tube (Applied Systems Engineering Inc.) microwave amplifier, and an ELEXSYS SuperQ-FT accessory unit. The temperature was kept at 50 K using a ITC 502 temperature control unit (Oxford Instruments) and a continuous-flow helium cryostat (CF935, Oxford Instruments). For all samples, 20 % (v/v) deuterated glycerol was added. For measurement, a 10 μL sample was transferred into a 1.6 mm outer diameter quartz EPR tubes (Suprasil, Wilmad LabGlass) and immediately frozen in liquid nitrogen. The dead-time free four-pulse PELDOR sequence with a phase-cycled *π*/2-pulse was used^[@CR52],[@CR53]^. Typical pulse lengths were 22 ns (*π*/2 and π) for the observer pulses and 12 ns (*π*) for the pump pulse. The delay between the first and second observer pulse was increased by 16 ns for eight steps to average deuterium modulations. The frequency of the pump pulse was set to the maximum of the echo-detected field swept spectrum to obtain maximum inversion efficiency. The observer frequency was set 70 MHz lower. Distance distributions were determined using DeerAnalysis^[@CR54]^. The normalized primary PELDOR data *V*(t)/*V*(0) were processed to remove the intermolecular contribution and the resulting form factors *F*(t)/*F*(0) were fitted with a model-free Tikhonov regularization to determine the distance distributions. The MATLAB-based MMM^[@CR55]^ software was used for simulation of interspin distances on the form factor-based dimer model.
CW EPR {#Sec15}
------
Continuous wave (CW)-EPR spectra were recorded to determine the spin-labeling efficiency. The spectra were recorded at a Bruker ELEXSYS E500 spectrometer (9.4 GHz) at room temperature with the following parameter settings: microwave power of 2.00 mW, modulation amplitude of 0.15 mT, and modulation frequency of 100 KHz.
MD simulation of the SLC26Dg monomer {#Sec16}
------------------------------------
The crystal structure of the membrane domain of SLC26Dg monomer (PDB: 5DA0)^[@CR4]^ was used in all-atom explicit solvent MD simulation for equilibration and to uncover structural flexibility. The WT MD simulation model included residues Q14 to S392. The unresolved region between TM12 and TM13 (T334, L335, T336, V337) was modeled using Modeller^[@CR56]^. The transmembrane domain of SLC26Dg was embedded into 241 POPC lipids and 13185 TIP3P water molecules^[@CR57]^ were added (total system size 77650 atoms). We used GROMACS 5.1.3^[@CR58]^ to perform simulations with a time step of 2 fs at a constant temperature (303.15 K) set with a Nosé-Hoover thermostat^[@CR59]^ using a coupling constant of 1.0 ps. A semi-isotropic Parrinello-Rahman barostat^[@CR60]^ was used to maintain a pressure of 1 bar. The all-atom CHARMM36 force-field was used for the simulation of protein and lipids^[@CR61],[@CR62]^. We performed the monomer MD simulation for \~1.1 μs.
Modeling of the SLC26Dg dimer using PELDOR time traces {#Sec17}
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The conformation of monomeric SLC26Dg at 440 ns of the MD simulation was used for investigation of the dimeric state. We performed rigid-body docking by placing a second protomer against the first protomer. We imposed C2 symmetry by rotating the second protomer in steps of 10 and 5 degrees about axes normal to the membrane plane centered at protomer two and one, respectively, and then bringing the two protomers to contact. For conformations without steric clashes, we forward calculated the PELDOR signals assuming uniform spin-label rotamer distributions^[@CR63]^. We found that the interface had to be formed by TM13 and TM14 to match the PELDOR data for L385R1. Details on the selection of conformations and dimer modeling procedures are indicated in Supplementary Fig. [5](#MOESM1){ref-type="media"}.
Modeling of the SLC26Dg dimer using distance distributions {#Sec18}
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In addition to the docking using PELDOR time traces, the SLC26Dg conformation at 440 ns of the MD simulation was used for rigid-body docking using mean ± SD of the PELDOR distance distributions (*P*(*r*)s) and C2 symmetry as the restraints. To determine the initial dimer structure model, rigid-body docking was performed using a grid search approach as implemented in the MMMDock tool of the Matlab-based software MMM^[@CR55],[@CR63]^. The experimental distance distributions for the positions K353R1 (4.4 ± 0.2 nm), V367R1 (3.9 ± 0.3 nm), and L385R1 (1.8 ± 0.1 nm) were used as the restraints, because the corresponding PELDOR time traces show clear oscillations. As the STAS domain of the SLC26Dg monomer is in a non-physiological orientation in the crystal structure, the STAS domain was deleted and the MD refined monomer was used as the starting structure. Assuming C2 symmetry for the dimer (*γ* = 0) and a parallel orientation (*z* = 0), a grid of the angle values for *α* (between 0--360° with 10° steps) and *β* (between 0--180° with 5° steps) and of the translation parameters *x* and *y* (between ± 7.5 nm with 0.25 nm steps) was generated.
For each model corresponding to a particular parameter set (*α*~i~, *β*~i~, *x*~i~, *y*~i~), mean distances for the positions K353R1, V367R1, and L385R1 were simulated. To obtain the initial grid search dimer model, the model with the minimum root mean square deviation (RMSD) to the input values was chosen. The parameter set from this initial search (*α*~0~ = 360°, *β*~0~ = 5°, *x*~0~ = 5 nm, *y*~0~ = 1 nm) served as the starting point for subsequent refinement, where small changes of the parameters further minimized the RMSD. As the refinement does not sample the whole possible parameter space, it was used after a global grid search to avoid becoming caught in local minima of the error surface. The parameters for the final model are *α* = 359.93°, *β* = 5.49°, *x* = 5.034 nm, *y* = 1.022 nm.
MD simulation of the SLC26Dg dimer {#Sec19}
----------------------------------
To relax the SLC26Dg dimer conformation (docked based on PELDOR time traces), we performed an additional MD simulation. The dimer was embedded into 648 POPC lipids and 37227 TIP3P water molecules (total system size 210,115 atoms). We used the same settings for the dimer MD simulation as described above for the monomer MD simulation. We performed the MD simulation for \~ 200 ns.
BioEn spin-label reweighting {#Sec20}
----------------------------
We calculated PELDOR signals for SLC26Dg dimer conformations saved along the MD simulation at 1-ns intervals. For each saved conformation, we performed a spin-label rotamer refinement^[@CR35]^ by (1) attaching MTSSL labels^[@CR63]^, (2) calculating PELDOR traces for each label position (K353, V367, L385) and rotamer combination, and (3) ensemble-reweighting the spin-label rotamers using the Bayesian inference of ensembles (BioEn)^[@CR64],[@CR65]^ maximum-entropy method for each individual dimer conformation. We selected the conformation at 107 ns as the SLC26Dg dimer conformation with minimal total *χ*^2^ for further analysis. L-curve analysis was used to identify suitable confidence parameters *θ*~*i*~ that trade off consistency between the simulated data at each site and experiment (using a chi-squared metric *χ*^2^) and the changes in the ensemble weights (using relative entropy $\documentclass[12pt]{minimal}
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\begin{document}$$S_{KL}^{(i)}$$\end{document}$ for label positions *i* = 1,2,3)^[@CR35]^. Corresponding marginalized reweighted rotamer weights are visualized in Supplementary Fig. [4](#MOESM1){ref-type="media"}.
Radioisotope transport assays {#Sec21}
-----------------------------
For transport studies, proteoliposomes were thawed and extruded through a 400 nm polycarbonate filter. Extruded proteoliposomes were pelleted by centrifugation for 20 min at 250,000 × *g* at 15 °C and resuspended to a final lipid concentration of 100 mg/ml in 50 m[m]{.smallcaps} NaPi, pH 7.5, 2 m[m]{.smallcaps} MgSO~4~. The sample was homogenized with a 26 gauge needle and stored at room temperature until use. Radioisotope transport studies were performed on stirred samples at 30 °C. To initiate transport, proteoliposomes were diluted 40-fold into the external buffer (50 m[m]{.smallcaps} KPi, pH 6.0, 2 m[m]{.smallcaps} MgSO~4~ containing 24 µ[m]{.smallcaps} of \[^14^C\]-fumarate (Moravek) and 100 n[m]{.smallcaps} valinomycin). At appropriate time points, 100 μL samples were taken and immediately diluted with 2 mL ice-cold external buffer, followed by rapid filtration on 0.45 μm nitrocellulose filters. After washing the filters with another 2 mL buffer, the radioactivity associated with the filter was determined by scintillation counting.
Oxidative cross-linking of SLC26Dg-IL {#Sec22}
-------------------------------------
SLC26Dg-IL (I45C/A142C, inward-locked) was expressed and purified as described method for cysteine variants used in PELDOR studies. The eluted and HRV 3 C protease-cleaved protein was subjected to SEC in buffer C supplemented with 3 m[m]{.smallcaps} DTT. Proteins from peak fractions were pooled and DTT was removed with an Econo-Pac 10DG desalting column (Bio-rad) which was pre-equilibrated with buffer C. The concentration of protein was adjusted to \~ 7 µ[m]{.smallcaps} and oxidative cross-linking was initiated by adding a 10-fold concentrated CuPhen stock (3 m[m]{.smallcaps} CuSO~4~, 9 m[m]{.smallcaps} 1,10-phenanthroline monohydrate, freshly prepared) into the protein solution. The sample was incubated at room temperature for 45 min with gentle agitation and subsequently 0.5 [m]{.smallcaps} Na-EDTA, pH 7.0 was added to a final concentration of 20 m[m]{.smallcaps} to quench the reaction. The locked protein was injected for SEC to remove the cross-linking reagent and peak fractions were pooled and used for subsequent reconstitution and transport studies.
Oxidative cross-linking of cysteine mutants along TM14 {#Sec23}
------------------------------------------------------
*E. coli* MC1061 containing pBXC3sfGH holding the gene coding for cysteine variants of SLC26Dg fused C-terminally to superfolder GFP^[@CR66]^ were cultivated in 700 µL of TB/Amp in a 96 deep well plate. Cells were grown at 37 °C until an OD~600~ ≈ 1 was reached, after which the temperature was gradually decreased to 25 °C over the course of 1 h. Expression was induced by the addition of 0.005% [l]{.smallcaps}-arabinose and proceeded for 16 h. Cells were pelleted and resuspended in 500 µL of 50 m[m]{.smallcaps} KPi, pH 7.5, 1 m[m]{.smallcaps} MgSO~4~, 10% glycerol, 3 m[m]{.smallcaps} DTT, 1 m[m]{.smallcaps} phenylmethylsulfonyl fluoride with trace amounts of DNase I. After 20 min incubation on ice, cell disruption was carried out by 1 min sonification on ice at output level 4, and a 50% duty cycle (Sonifier 250, Branson). Unbroken cells and debris were removed by 5 min centrifugation at 13,000 × *g*. The supernatant was collected and DTT was removed by a Bio-Spin 6 column (Bio-rad) which was pre-equilibrated with 50 m[m]{.smallcaps} NaPi, pH 7.2. Oxidative cross-linking was initiated by adding a 10-fold concentrated CuPhen stock (3 m[m]{.smallcaps} CuSO~4~, 9 m[m]{.smallcaps} 1,10-Phenanthroline monohydrate, freshly prepared) into the vesicle solution. Samples were incubated at room temperature for 20 min and terminated by adding 100 m[m]{.smallcaps} *N*-ethylmaleimide and 0.5 [m]{.smallcaps} Na-EDTA, pH 7.0 in a final concentration of 5 m[m]{.smallcaps} and 20 m[m]{.smallcaps}, respectively. The reaction mixture was mixed with sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) sample buffer and the degree of cross-linking was determined by 8% SDS-PAGE and in gel GFP fluorescence imaging (ImageQuant LAS4000).
Preparation of CHO cell membrane vesicles {#Sec24}
-----------------------------------------
CHO/dhFr^-^ cells (ATCC CRL-9096) were cultivated as described previously^[@CR67]^. After 24 to 36 h of transfection, CHO cells expressing eGFP-tagged rat prestin (cysteine-free) or single-cysteine variants (V499C and I500C located at the cytoplasmic end of TM14^[@CR68]^) were treated with trypsin, harvested and washed with phosphate-buffered saline (PBS) containing 10 m[m]{.smallcaps} DTT. The cells were resuspended in disruption buffer (20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl, 10% glycerol, 1 m[m]{.smallcaps} MgSO~4~, 3 m[m]{.smallcaps} DTT, 20 µg/mL DNase I, 1 tablet of EDTA-free protease inhibitor cocktail) and lysed by six series of 5 sec sonification at 100% amplitude with 1 min incubation on ice in between (Sonoplus GM mini 20, Bandelin). The unbroken cells were removed by centrifugation at 1500 × *g* for 5 min and the membranes were obtained by ultracentrifugation at 50,000 rpm for 1 h (TLA110 rotor). The membrane pellet was resuspended in membrane resuspension buffer (20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl, 10% glycerol, 3 m[m]{.smallcaps} DTT) to a final protein concentration of \~ 0.7 mg/mL.
Oxidative cross-linking in CHO cell membrane vesicles {#Sec25}
-----------------------------------------------------
The resuspended rat prestin membrane vesicles were pelleted at 200,000 × *g* for 30 min at 4 °C. After centrifugation, the membrane vesicles were gently washed with 20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl, 10% glycerol without disturbing the pellet. The cross-linking reaction was initiated by homogeneously resuspension of membrane vesicles in the same amount of cross-linking buffer (20 m[m]{.smallcaps} HEPES, pH 7.5, 150 m[m]{.smallcaps} NaCl, 10% glycerol, 300 µ[m]{.smallcaps} CuSO~4~, 900 µ[m]{.smallcaps} 1,10-phenanthroline monohydrate, freshly prepared) and incubated at room temperature for 20 min. The cross-linking reaction was quenched by addition of 0.5 [m]{.smallcaps} Na-EDTA to a final concentration of 20 m[m]{.smallcaps}. To decrease anomalous migration of rat prestin in SDS-PAGE, cross-linked vesicles were treated with PNGaseF (New England BioLabs) at 37 °C for 1.5 h. The reaction mixture was mixed with non-reducing SDS-PAGE sample buffer and the degree of cross-linking was determined by 8% SDS-PAGE and in gel GFP fluorescence imaging (ImageQuant LAS4000).
Reporting summary {#Sec26}
-----------------
Further information on research design is available in the [Nature Research Reporting Summary](#MOESM5){ref-type="media"} linked to this article.
Supplementary information
=========================
{#Sec27}
Supplementary Information Supplementary Data 1 Peer Review File Description of Additional Supplementary Files Reporting Summary
Source Data
**Journal peer review information:** *Nature Communications* thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.
**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
These authors contributed equally: Yung-Ning Chang, Eva A. Jaumann, Katrin Reichel,
Supplementary information
=========================
**Supplementary Information** accompanies this paper at 10.1038/s41467-019-10001-w.
We acknowledge professor Thomas Prisner for his support on the EPR measurements. We thank Melanie Engelin and Kai Steinmetz for their support in mutagenesis, and Dr. Brinda Vallat for assistance with the PDB-Dev deposition. We acknowledge financial support from the Max Planck Society (KR, GH), the International Max Planck Research School (IMPRS) of the MPI of Biophysics in Frankfurt (EAJ), and the German Research Foundation via the Cluster of Excellence Frankfurt (Macromolecular Complexes; GH, ERG), the SPP1608 (Ultrafast and temporally precise information processing: normal and dysfunctional hearing; OL 240/4--2 to DO), and the SFB807 (Transport and Communication across Biological Membranes; GH, BJ, ERG).
YNC prepared samples for EPR and designed and performed cross-linking and functional studies under supervision of ERG. EAJ designed and performed EPR measurements under supervision of BJ. KR designed and performed MD simulations and spin-label ensemble refinement under supervision of GH. JH expressed rat prestin under supervision of DO. GH, BJ, and ERG designed the research. ERG drafted the manuscript. All authors analyzed and interpreted the data and contributed to the manuscript.
Data supporting the findings of this manuscript are available from the corresponding authors upon reasonable request. A reporting summary for this Article is available as a Supplementary Information file. The source data underlying Figs. [4](#MOESM6){ref-type="media"}a, [5b--d](#MOESM6){ref-type="media"}, and Supplementary Fig. [2c](#MOESM1){ref-type="media"} are provided as a Source Data file. Our structural model of the SLC26Dg dimer is deposited at PDB-Dev under accession code PDBDEV_00000031.
The code used for spin-label rotamer reweighting is freely available at <https://github.com/bio-phys/BioEn>.
Competing interests {#FPar1}
===================
The authors declare no competing interests.
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The New England Electric System’s "direct installation" Small Commercial and Industrial Program (Small C/I Program) addresses the unique needs of small businesses with power requirements of less than 50 kW, a customer class that is vital to the resilience of the local economy. Small C/I customers have been hard to attract with rebates for the purchase of energy-efficient equipment, but by paying 100% of the cost of auditing customers' facilities and installing energy-efficient equipment and backed by the credibility of the utility, this program has demonstrated the potential for very high penetration rates while remaining cost effective. Perhaps the most elegant aspect of the program is that it is administered by a skeleton staff in coordination with regional labor and product vendors. These trade allies market the program, do the retrofit analyses, provide the equipment, and do the installations. This keeps the utility’s overhead low (and thus administrative costs low) and stimulates business in the local economy. All product is purchased locally to stimulate local distribution of energy-efficient goods while bolstering the economy.
While the NEES Companies do a first rate job of analyzing DSM program data, their programs are relatively young and thus critical impact evaluations are not yet complete. Many of the assumptions built into the savings data therefore are based on early estimates from the program’s Rhode Island pilot. NEES uses adjustment factors, based on limited subsets from the pilot, for estimating savings for the system-wide program
In 1991 the Small C/I program resulted in average customer savings of 7,256 kWh, up significantly from its pilot average of 4,011 kWh. To date the program has resulted in total cumulative savings of 54 GWh when factoring in NEES’s engineering estimate of savings. The measures installed in 1991 had an average measure lifetime of 15 years. In terms of capacity the program has delivered a total of 14.27 MW of peak summer capacity.
This program has been a key example of the cost effectiveness of direct installation. Since the program’s inception NEES has spent nearly $20 million on this effort, resulting in an a 1991 cost of saved energy of 5.15 cents per kWh. While paying an average of nearly $5,000 per installation, and nearly $17,000 for schools, NEES has demonstrated the benefit to the utility and to its ratepayers of such a program. NEES has pioneered incentive mechanisms that has made its DSM activities profitable for consumers and shareholders alike. Perhaps most encouraging are a host of lessons learned through the program, further lowering administrative costs and resulting in the implementation of efficiency measures in over 95% of solicited customers.
Southern California Edison (SCE) is unquestionably a national DSM leader. SCE has spent nearly a billion dollars on DSM since 1973. Its Low-Income Relamping Program is the oldest program of its kind operating today. SCE has cultivated a unique, synergistic relationship with community-based organizations (CBOs) to market and deliver the program. The CBOs provide a variety of social services to specific portions of the low-income community. For instance, the Maravilla Foundation specifically serves the Latin American community. These organizations are uniquely suited to provide energy services and education, as well.
SCE has had difficulty using traditional DSM approches and utility personnel to provide assistance services to its low-income customers. Many of these customers are recent immigrants to the United States, who often tend to be distrustful of governments and large institutions such as the utility. By paying the full costs of the compact fluorescent lamps and using the CBOs to interact with the customers, SCE can provide services to these customers in a nonthreatening manner. This relationship also provides SCE with a cost-effective means for fulfilling its PUC-mandated obligation to provide assistance to low-income customers. The CBOs benefit by earning much needed funds which aid in the operation of their organizations.
Although the general quality of data obtained from SCE is good, two shortfalls exist. First are concerns regarding the calculation of energy savings and in particular duty factors, persistence, etc. The other shortfall exists in quantifying the administrative costs of the program. The relamping effort is a sub-program of the larger Customer Assistance Program (CAP) for which cost data are not separated among the sub-programs.
To date, Southern California Edison has installed over 1.3 million compact fluorescent lamps through this program. These lamps have resulted in energy savings of 121 GWh and peak capacity savings of 14 MW, since the program's inception in 1985. From 1985 to 1991, the program has cost a total of $23.5 million. In the 1991 program year, the program saved 3 MW while providing over 5 lamps per home at an average cost per participant of $75.
Pacific Gas & Electric's Customized Electric Rebate Program is a "free-form" program where commercial, industrial, and agricultural customers can receive financial assistance for implementing electrical efficiency measures, subject to PG&E's approval. The program is designed to accommodate more complex projects than those covered by the menu-driven Direct Rebate Program. Projects range from commercial lighting retrofits, to industrial process changes, to agricultural irrigation efficiency measures. Customers learn of the Customized Rebate Program through personal contact with their PG&E customer representative; little direct marketing is conducted.
The program provides rebates based upon the quantity of energy that an efficiency measure saves in the first year of its operation. Rebates have varied between 2 and 7¢/kWh, since the program's inception in 1983, and are currently 6¢/kWh or 40% of the project cost, whichever is less. The maximum rebate per account is $300,000. (Gas efficiency measures are covered by the Customized Gas Rebate Program for which other rebate levels apply.)
As a result of the California Collaborative Process, PG&E has been allowed to earn a return on its DSM expenditures. Therefore, it has placed greater emphasis on carefully documenting its DSM programs' savings and costs. For the Customized Electric Rebate Program, PG&E is conducting billing analyses, metering of customers' facilities and operations, and on-site validation of measures installed. Due to these efforts, data reported after 1989 are much more easily analyzed and compared than data produced in previous years. Our analysis will therefore only examine data from 1990 and 1991.
During 1990 and 1991, the program realized 380 GWh of cumulative energy savings and 40.6 MW of cumulative capacity savings. The cost of this saved energy was 0.72¢/kWh at a 5% real discount rate. PG&E's program expenditure was $22 million, of which $19 million were rebates. The average cost per participant was $5,893.
One of the benefits of the Customized Electric Rebate Program is that it provides the utility with information on which types of energy saving projects and technologies are popular with its customers. If PG&E wishes to encourage such projects and technologies, it can determine standard rebates and procedures for them and incorporate them into the Direct Rebate program.
In 1990 the voters of Burlington, Vermont authorized the Burlington Electric Department (BED) to issue an $11 million bond to invest in energy efficiency. Many voters took the opportunity to make it clear that they favored energy efficiency over the prospect of buying additional increments of Hydro-Quebec's James Bay power, another element in the resource plan.
As part of its overall efficiency initiative BED staff opted to employ a lightbulb leasing mechanism that had been pioneered at Taunton, Mass. Municipal Lighting Plant. There, Joe Desmond had a rather elegant idea. By leasing customers compact fluorescent lamps wouldn't it be possible for a utility to offer positive cash flow for customers (where bill savings were greater than lease payments), while at the same time providing savings for the utility at low cost? The "Smartlight" program has been refined in Burlington and is the largest program of its kind in the country.
In the first fifteen months of the program BED had distributed almost 25,000 bulbs to over five thousand residential customers. After 20 months BED had installed 26,602 bulbs, averaging 3.4 lamps per customer, for estimated savings of 1,300 MWh/year. Burlington Electric, with a total of 33,647 energy-efficient lamps distributed in the community, is now in the process of extending leasing to commercial lighting.
BED's Smartlight Program also was able to effectively use college students on summer vacation to educate sustomers about energy efficiency and the leasing mechanism, and to install the lamps in appropriate applications. Selct students were retained during the school year to perform installations.
One of the interesting lessons learned from Burlington's Smartlight program is that the lease payments themselves have been a relatively insignificant aspect of the program. BED program managers feel that the point is the education of their customers, and their commitment to have the lamps only in cost effective sockets. The profile concludes with a discussion of the relative merits of the leasing concept versus direct installation programs for residential lighting.
BED provides a fascinating case study of an innovative, positive cash flow, DSM implementation strategy. Costs of the program are somewhat elusive, as lamps placed today have a net present value in terms of lease payments. This, however, is offset in part by attrition rates of the lamps. Finally, the savings data is complicated by the fact that a certain percentage of installed lamps maintain active leases, while another subset are likely in service but their leases have been broken.
The Osage Municipal Utility’s Comprehensive DSM program has been heralded as one of the most effective DSM efforts ever. In large part, Weston D. Birdsall, Osage’s recently-retired General Manager, is to be credited to this exemplary DSM effort. Birdsall believed and proved that the citizens of a small community could collectively take responsibility for their energy use (both electric and gas) and profit! By marshalling the support from all members of the community, from schoolchildren to professionals, Osage’s success in terms of gross savings and the remarkably low costs of the savings, has yet to be replicated.
The Osage program was designed to reduce the utility bills of all customers to improve the economic well-being of the community. Its other purpose was to reduce the growth rate of electric peak demand to delay the need to expand its generating capacity. Both objectives were met, the town actually experienced three electricity rate reductions and the capacity additions are still not necessary. For a total cost of less $500,000 over eighteen years, Osage has been able to save some 92.4 GWh, 4 MW, and about 8 million therms of gas since 1974. Furthermore, 100% of OMU's customers have participated in the program, at an average cost of only about $100 per customer total, or just over $6 per customer per year!
The most unique element of the Osage effort is the positive relationship that the utility has built with its customers. Through a series of educational programs and successful DSM measures, OMU has earned the trust of its customers. Once the people in the community realized that the utility was trying to help them reduce their bills and save money, it became successively easier to implement programs and achieve high participation rates.
Not only was OMU successful in achieving its main goals but an indirect benefit of economic development was realized. By keeping rates relatively low and helping businesses and industries reduce their energy consumption the economic viability of these businesses was also increased. This not only helped businesses and industries expand but also attracted new ones. Thus, the Osage community has enjoyed a stable local economy and unemployment rates far below the national average.
Through your kind contribution of $50, $100, $250, $500, or even $1000, you can help us raise the $10,000 needed to build the well in the next 3-6 months and you can be part of this very real community effort that will positively impact every person in Mapintade. read more...
Our Achievements
About IIEC
The International Institute for Energy Conservation (IIEC) was founded in 1984 to dramatically increase the use of energy efficiency (EE) as an important clean energy approach in developing countries. Through our regional offices, we have been effective in bringing about progress in EE policy and implementation that has both reduced energy consumption by thousands of MWs and fostered economic development in the countries we serve. The IIEC works with stakeholders across all sectors to connect international best practice with the unique needs of the communities in which we operate, combining sound EE and renewable energy policy with hands-on implementation in order to reduce greenhouse gas emissions and encourage sustainable development.
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Interaction of cytochrome c with liposomes: covalent labeling of externally bound protein by the fluorescent probe, azidonaphthalenedisulfonic acid, enclosed in the inner aqueous compartment of unilamellar vesicles.
The photoreactive fluorescent probe, 3-azidonaphthalene-2,7-disulfonic acid (ANDS) was encapsulated in the inner aqueous compartment of small unilamellar liposomes, prepared from egg phosphatidylcholine (PC) +/- 20 mol% dihexadecylphosphate (DHP). After adding cytochrome c externally to a suspension of these vesicles, the probe was activated by ultraviolet irradiation, and the protein was separated from the lipids. When negatively charged (egg PC/DHP) vesicles at low ionic strength were used, which form an electrostatic complex with cytochrome c, the protein was labeled by ANDS. This process depended on irradiation time, and was inhibited by increasing the ionic strength of the medium. Labeling was not observed with isoelectric (egg PC) vesicles. These observations suggest that electrostatic binding of cytochrome c to the bilayer is accompanied by intramembrane penetration to such a depth that the protein can communicate with the inner membrane-water interface.
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Charge transfer coefficient
Charge transfer coefficient, and symmetry factor (symbols α and β, respectively) are two related parameters used in description of the kinetics of electrochemical reactions. They appear in the Butler–Volmer equation and related expressions.
The symmetry factor and the charge transfer coefficient are dimensionless.
According to an IUPAC definition, for a reaction with a single rate-determining step, the charge transfer coefficient for a cathodic reaction (the cathodic transfer coefficient, αc) is defined as:
The anodic transfer coefficient (αa) is defined by analogy:
where:
: stoichiometric number, i.e., the number of activated complexes formed and destroyed in the overall reaction (with n electrons)
: universal gas constant
: absolute temperature
: number of electrons involved in the electrode reaction
: Faraday constant
: electrode potential
: partial cathodic (anodic) current
Significance
The charge transfer coefficient signifies the fraction of the interfacial potential at an electrode-electrolyte interface that helps in lowering the free energy barrier for the electrochemical reaction. The electroactive ion present in the interfacial region experiences the interfacial potential and electrostatic work is done on the ion by a part of the interfacial electric field. It is charge transfer coefficient that signifies this part that is utilized in activating the ion to the top of the free energy barrier.
Batteries and fuel cells
In operating batteries and fuel cells, charge transfer coefficient is the parameter that signifies the fraction of overpotential that affects the current density. This parameter has had a mysterious significance in electrochemical kinetics for over three quarters of the previous century. It can also be said that charge transfer coefficient is the heart of electrode kinetics.
Symmetry factor
The symmetry factor (or barrier symmetry factor) is a coefficient similar to the transfer coefficient, but applicable only to single-step reactions.
The sum of anodic symmetry factor and cathodic symmetry factor is equal to one:
References
Category:Dimensionless numbers of chemistry
Category:Electrochemistry
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Q:
In Symfony sub-request, $this->container is null
I want to implement a batch request api using symfony.
So, I using the sub-request in symfony. But in each controller, the $this->container is null. Because I am using service container in my project.
So, the batch request parameter like below:
{request: [{"url":"/api/user?username=test"}, {"url":"/api/thread?id=123"}]}
And the source code like below:
I want to generate some sub-request to reduce outside HTTP request.
foreach($request_list as $k => $v) {
parse_str(parse_url($v['url'], PHP_URL_QUERY), $params);
$req = Request::create(
parse_url($v['url'], PHP_URL_PATH),
"POST",
$params
);
$context = new RequestContext();
$context->fromRequest($req);
$route = $this->get('router');
$matcher = new UrlMatcher($route->getRouteCollection(), $context);
$dispatcher = new EventDispatcher();
$dispatcher->addSubscriber(new RouterListener($matcher));
$resolver = new ControllerResolver();
$kernel = new HttpKernel($dispatcher, $resolver);
$response = $kernel->handle($req, HttpKernelInterface::SUB_REQUEST);
$res[$k] = $response->getContent();
}
Can you give my some hints? Thanks!
A:
Why do you want to make simple task so complex?
In your controller you can just create new Request object and pass it to the existing (already instantiated) HttpKernel instance:
foreach($request_list as $k => $v) {
parse_str(parse_url($v['url'], PHP_URL_QUERY), $params);
$req = Request::create(
parse_url($v['url'], PHP_URL_PATH),
"POST",
$params
);
$httpKernel = $this->container->get('http_kernel');
$response = $httpKernel->handle(
$request,
HttpKernelInterface::SUB_REQUEST
);
$res[$k] = $response->getContent();
}
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CNN and NYT Are Deliberately Obscuring Who Perpetrated the Afghan Hospital Attack - etiam
https://theintercept.com/2015/10/05/cnn-and-the-nyt-are-deliberately-obscuring-who-perpetrated-the-afghan-hospital-attack/
======
cryoshon
At first I thought this article was Greenwald getting a bit overzealous, but
after reading what the NYT/CNN actually wrote, I can agree that they were
intentionally trying to hide the fact that the US bombed the hospital.
There's absolutely no question about who attacked the hospital, and yet both
the NYT and CNN seem to hem and haw and use distracting, meaningless language
to distance the US from the slaughter of civilians. I expect about as much
from both of those news rags of course, but still, it seems as though for some
reason they are getting their strings pulled specifically to obfuscate. Based
off of the evasive language they used, I'd suspect some kind of Ministry of
Culture to be patrolling-- of course, there is no such overt thing.
The bewildering part is that other mainstream media outlets that are usually
of poor journalistic integrity in favor of government interests are reporting
that the US was in fact the striker, unambiguously, with no pretense of
deniability. Even the US military accepts that it called in a bad airstrike!
This makes the exceptional effort expended on deception by the NYT and CNN
very confusing.
------
mark_l_watson
Well, many news topics receive very different treatment in the USA than the
get in most of the rest of the world. I debate this with friends: I will point
out a descrepency and they resist the idea that their news is not legit. I
guess this attitude is understandable but I believe that access to accurate
news is vital for democracy.
~~~
cryoshon
Conversely, the powers that be are likely of the view that strong propaganda
is vital for democracy. See: Edward Bernays, father of PR.
------
cafard
I can only ask, who else does anybody think is flying in that area? It sure
isn't the Taliban Air Force, because the Taliban doesn't have one.
~~~
Someone1234
Nobody. But there is more than one way to blow up a hospital, for example
mortars, rocket propelled grenades, just a bomb planted in the hospital.
Someone else /could/ have done it, they didn't, but they /could/ have in
theory.
I have no idea why CNN and NYT are more cagy than the US military themselves
about this incident. It isn't like the USG are trying to cover this up from
what I can tell.
------
phantom_oracle
I'm not too familiar with how geopolitics/warfare rules work, but will this
constitute a war-crime and/or crime against humanity?
~~~
cryoshon
Doubtful. At the very most, it'd be considered a war crime, if intent can be
proven, which it probably can't be to the standards of a court. And even then,
the US won't send anyone to be prosecuted to international courts, so the best
we can hope for is internal military discipline, which probably won't happen
meaningfully.
I assume this strike was a mistake; hitting a civilian hospital from a
multinational organization is begging for bad PR, and PR is what wins
guerrilla wars.
------
transfire
When will we stop accepting excuses?
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USC football to play Alabama in 2016 for first time since 1985
USC and Alabama college football programs agreed to open the 2016 season with a Labor Day weekend game played at AT&T Stadium in Arlington, Texas.
The game will be played on Sept. 3, 2016, when USC was scheduled to host New Mexico at the Coliseum. The New Mexico game will now be played on Sept. 19, 2020.
“At USC, we have always tried to schedule as many outstanding non-conference opponents as possible because we believe that should be part of the experience our players get when they come here,” USC coach Steve Sarkisian said. “The Trojans versus the Crimson Tide in Arlington will certainly be such a game.”
USC has not played Alabama since 1985, a 24-3 Crimson Tide victory in the Aloha Bowl. Alabama leads the series 5-2.
The highly anticipated game will add luster to USC’s future non-conference schedules, which in recent years lacked the big-name opponents common in the Pete Carroll era. USC does have a home-and-home series scheduled with Texas in 2017-18.
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Sunday, January 31, 2016
Former General Secretary of the Convention People’s Party (CPP), Ivor Kobina Greenstreet, pulled a major surprise over the weekend when he beat three others, including favourite Samia Yaaba Nkrumah, to become the party’s flagbearer for the 2016 general election.
He has been elevated from the General Secretary position to presidential candidate. With his election, he will have to contend with the New Patriotic Party’s (NPP’s) Nana Addo Dankwa Akufo-Addo and the incumbent National Democratic Congress’ (NDC’s) John Mahama in the November elections.
Ivor polled an overwhelming 1,288 votes, representing 64.7 percent of the 2,006 total votes cast, while Samia had 579, representing 29 percent, followed by new face Joseph Agyapong and Bright Akwetey, who together polled less than 10% with 83 and 42 votes respectively at a congress held at the Trade Fair Site, La in Accra.
Bribery
Samia has since been crying foul, claiming Greenstreet bribed his way through to be elected to the position by doling out cash ranging between GH¢200 and GH¢500.
United Front
Moments after being declared winner, Mr Greenstreet, a lawyer by profession, indicated his preparedness to work with his three other contenders to ensure a united front, going into the 2016 general election.
“We will emerge united. There are going to be no divisions and I will do everything in my power… Samia Nkrumah is my sister, Bright is my brother, Joe Agyapong is also my brother; we will work together and you will hear from us in our discussions with our colleagues about our theme for our campaign because in CPP we work as a team,” were his exact words.
He continued, “I am merely a flagbearer and when you hold a flag, you are holding it for a group of people, which is the party. I will honour my commitment to work with them for the best movement of the party CPP.”
He appealed to his colleagues, “Let us all come together; let us all take away our ego and our pride because we are here to serve not ourselves but Ghanaians.”
Going forward, he said, the CPP would serve as a vehicle for frustrated Ghanaians who are tired of the “bogus and empty promises” of the Mahama-led National Democratic Congress administration.
Vote Buying
Despite earlier caution by the party’s National Chairman, Professor Edmund Delle, against unfounded allegations and character assassination by the aspirants, Samia Yaaba Nkrumah, immediate past Chairperson of the CPP and daughter of Ghana’s first president, told journalists that Mr Ivor Greenstreet engaged in vote buying.
“I’m obviously not happy with the results, but I accept them. The fact of the matter is that every delegate was paid GH¢200 and GH¢500 actually, amongst many other things. So, it was down to money and of course, we cannot be happy about that,” she alleged.
CPP leading member Professor Agyemang Badu Akosa also believes delegates voted for money. Prof Akosa, who tipped Samia to win with more than 80 percent of votes, expressed his disappointment with the delegates after the results were declared.
He said it was sad that delegates decided to sell their votes.
Saturday, January 30, 2016
The Convention People’s Party (CPP) goes to polls today to elect a flagbearer to lead the Nkrumahist party to the 2016 general election scheduled for November 7.
The National Delegates’ Congress, which is scheduled to take place at the Trade Fair Site in La, Accra, would see 2,600 delegates from all 275 constituencies across the country in attendance.
Four persons are gunning for the topmost position, including immediate past party Chairperson Samia Yaaba Nkrumah and former General Secretary Ivor Kobina Greenstreet.
Others are Lawyer Bright Akwetey and new entrant Joseph Agyapong, a businessman.
But the contest is seen as a straight fight between Samia and Ivor Greenstreet, even though the two others are equally confident of pulling surprises.
Even though a live television debate organised for the four to sell their messages to the delegates did not end up with a clear winner, it proved to be an interesting event since it offered them an opportunity to market themselves.
Samia, who is basking in her father’s glory, said when given the opportunity to lead the country, she would finish Dr Kwame Nkrumah’s (her late father’s) unaccomplished seven-year development plan for Ghana and adapt it to the current situation.
She however suffers the disadvantage of being considered a not-too-successful chairperson when she presided over the party. Samia is also seen as a divisive leader and has been accused of pushing Dr Nduom out of the party.
Mr Greenstreet is positioning himself as a unifier, asking delegates to vote for him because he would galvanise and energise all the talents in the party with greater charisma. He prides himself with the assertion of some delegates that he has a “clean heart and loyal to the rank and file; he also has very deep knowledge of issues of governance, economy and the welfarist philosophy of the CPP.”
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Mr Akwetey, an ardent Nkrumahist who is aspiring to lead the CPP as a presidential candidate for the third time, says “watching the CPP, once the touchstone of political power in Ghana and institutional machinery that laid the foundation for the prosecution of the progressive agenda of our nation, sink to such depths of virtual dormancy has provoked me to liberate the priceless heritage.” He pledged to fight corruption in the country with an iron fist.
On his part, new face Joseph Agyapong said the country needs to build systems, including a national database, for the sustainable development of the country. His campaign of injecting resources into the party, coupled with the display of cars and logistics, is indeed boosting his chances.
Delegates say they would support whoever is given the mandate to lead the party after the presidential primaries.
Task
Whoever wins today’s contest would be burdened with the task of forming a formidable CPP to match the New Patriotic Party (NPP) and the National Democratic Congress (NDC) in the 2016 elections.
Police Readiness
More than 500 police personnel have been dispatched by the Accra Regional Police Command to provide security at the CPP congress.
The personnel, according to Commissioner of Police (COP) Dr George Akuffu Dampare, Regional Police Commander, would make sure that the election is held smoothly without any disturbances whatsoever.
Wednesday, January 27, 2016
Price of sachet water is expected to go up from GH20p to GH30p starting from February 1.
Consumers would pay GH¢5 per bag of sachet drinking water, which was currently being sold on the market at GH¢3.
According to the National Association of Sachet and Packaged Water Producers (NASPWP), the increment was as a result of the outrageous tariff increases by the Public Utilities and Regulatory Commission (PURC) in December last year.
The PURC in December last year increased electricity and water tariffs by 59.2% and 67.2% respectively, while a 27 percent tax was slapped on petroleum products by government.
Magnus Nunoo, President of NASPWP, speaking to journalists in Accra yesterday, said the current cost of production for sachet water had been increased by 195 percent from GH¢3.8 to GH¢11.21 per cubic meter while bottled water had also been increased by 400 percent from GH¢10.07 to GH¢50.76.
He called on PURC to come out with reduced and fair charges for all commercial and industrial users – be it sachet water, bottled water, soft drink producers.
“The tariffs our members received when their December bills came this month are remarkably different from the 67 percent that the whole world was made to believe. The progressive rate system must be made to work in order to determine final bills that companies have to pay rather than the seeming subsidy offered to some industries,” Mr Nunoo said.
He added that the new prices were arrived at based on the assumption that the PURC would heed their call to adjust water rates to a standard commercial rate of GH¢10.7 in order to avoid another price change.
Encourage Alcohol Production
Mr Nunoo disclosed that recent hike in water tariff would lead to an increase in alcohol consumption.
He noted that while NASPWP was being charged GH¢51 for the production of bottled water, alcoholic beverage producers were being charged GH¢10, indicating that the profitability of the players were at variance.
“If one takes a bottle of beer of say one litre and a bottle of water for two products, and the two different companies have Ghana Water Company as supplier of waster for the two products, why should the PURC allow Ghana Water Company to charge the company that produces water 5 times as much as the alcohol producing company? In terms of pricing and profitability of the two products, the price of water comes no where near that of beer or any of the hard liquors which is over 95 percent water,” Mr Nunoo noted.
He stated that “if the PURC is showing such bias, what moral lessons are we teaching our youth?”
Presidential aspirants of the Convention Peoples Party (CPP) have condemned the Mahama-led government for engaging the International Monetary Fund (IMF) with the aim of trying to revive the ailing economy.
The three-year IMF bail-out is expected to come with stringent conditions such as job cuts in the public service in order to reduce the wage bill as well as a cap on the amount of loans Ghana can contract with the public debt now hovering around GH¢65billion (almost 60 per cent of GDP ratio).
Speaking at the maiden edition of the debate organized for presidential aspirants of the CPP at the TV Africa studios in Accra on Tuesday, Samia Nkrumah, one of four of the presidential aspirants stated that by accepting the conditions imposed by the IMF, it was clear that the current government did not believe in the dignity of Ghanaians.
Samia Nkrumah is in the race with Ivor Greenstreet, former General Secretary of the CPP; Bright Akwetey and Joseph Agyapong. One of them would be given the mandate to lead the party in the 2016 elections at the CPP presidential primaries on Saturday.
“It is very clear to all of us that the conditions imposed by the IMF are simply not working. The system has failed completely and it is very obvious that if you had a government that believed in the dignity of the people, there is no way you are going to accept these conditions,” Samia said.
She said government should be able to stand up to the stringent conditions attached to the lMF bail-out just like the CPP did in the 60’s.
“I want to see the day when we are confident enough to be able to say no or to say enough is enough when certain proposals are brought to us. Give the CPP a second chance to run this country and you will see the difference. We are able to say no, not because we are stubborn or rigid but because we have our own economic plan that can cater for the needs of the people of Ghana. What we need is our economic independence. Fellow Ghanaians, this is what we have to do and this is what we have to do soon and with a sense of urgency before things get very difficult,” she added.
Ivor Greenstreet disclosed that due to the mismanagement of the economy and resources, government had no choice than to go to the IMF “cup in hand as beggar to go and borrow to try and take us out of a situation that we ourselves have caused.”
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Joe Agyapong wondered why the current government kept running back to the IMF and agreeing on conditions that were clearly not helping our economy.
“We have come to know that taking money from the IMF is not helping this nation; it is rather destroying this nation by the day. A lot of people are unemployed because of this IMF conditions. We cannot keep doing this everyday,” Mr Agyapong noted.
However, Bright Akwetey called for the criminalization of galamsey and the creation of state-owned industries to help drive away the IMF.
“We need to stop exporting our raw materials like gold and our oil and add more value to it before we export. If we want to wean Ghana off the IMF prescription, we need to take control of our economy and be self-reliant. We need to control employment to generate taxes. If we do not localize control over our resources, we will live to regret it,” Mr Akwetey said.
Fight Against Corruption
Mr Akwetey, who is aspiring for the third time (after 2008 and 2012) to lead the CPP as presidential candidate, said if CPP was given the nod, he would fight corruption with an iron fist with the help of the anti-corruption institutions in the country.
“I would also fight corruption with an iron fist. In fighting corruption, I would go back to the anti-corruption institutions. The previously called Serious Fraud Office, now EOCO has been emasculated by not being provided enough facilities, opportunities and the funding to carry out their work,” he said.
He argued that the creation of the Ghana Youth Employment and Entrepreneurial Development Agency (GYEEDA) and Savannah Accelerated Development Authority (SADA) among others were palliatives which do not solve the alarming unemployment rate.
The event, which was moderated by Prof. Kwame Kakari, brought together a host of CPP faithful to support the aspirants.
Monday, January 25, 2016
Contrary to the approved 59.2 percent increase in electricity tariff by the Public Utilities and Regulatory Commission (PURC), consumers have been slapped with a 75 percent increase.
This is due to a directive by the PURC to Electricity Company of Ghana (ECG) to charge additional costs.
A group calling itself Pre-paid Demonstrators has threatened to hit the streets if the ECG does not resolve the technical challenges that have resulted in the undue charges.
In December 2015, PURC announced increases in utility tariffs, with 59.2 percent increase for electricity and 67.2 percent for water. But since then, some consumers have complained that their electricity credits run out rashly.
The group, in a statement sighted by Nii Ogbamey Tetteh, blamed the situation on “unpardonable and unrealistic” technical challenges.
“Consumers with the pre-paid meters are currently experiencing difficult times with many being cheated as we may put it. The situation has been blamed on technical challenges which for us is unpardonable and unrealistic because we strongly believe that while authorities announce increment in utility, it should take steps to enhance the delivery and quality of services rendered to Ghanaians,” the statement signed by Kwabena Berima, Public Relations Officer (PRO) for the group said.
Pre-paid Demonstrators called on ECG to withhold the increment of electricity tariff until the technical challenge was rectified.
“We also wish to call for the refund of monies consumers may have lost in view of the so-called technical challenge. We will soon hit the streets to protest against this burden on us. Any well-meaning Ghanaian affected by this should support this laudable initiative to demand accountability, equity and quality of services from our providers.”
Exorbitant charges
Consumers are paying extra 5 percent for a streetlight levy and another 5 percent increase for the national electrification charge. Furthermore, consumers pay a regular monthly service fee ranging from GH¢6.33 to about GH¢60 depending on the quantum of consumption and user classification.
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This simply means if for instance a consumer buys GH¢20 worth of power, which initially could last averagely for about two weeks for a regular household, it may now take less than a week.
Meanwhile, John Jinapor, Deputy Minister of Power, has admitted that some deductions were wrong and that the ECG would rectify the problem.
“The system was configured to rise from the 1st of every month but they informed me that the tariff adjustment took effect on the 15th so it calibrated as if it was charging customers on the 1st. I have asked them to work on their systems and to rectify that so that we do not have a repeat of that problem,” he said.
From the information ECG gave to me, they have a prepayment meter customer base of 531,014. Out of that, they have credited back to about 333,902 so they are in the process of rectifying that, the deputy minister added.
Thursday, January 21, 2016
Dr. Mohammed Amin Adam, Executive Director of African Center for Energy Policy (ACEP), says with the implementation of the deregulated policy, the fortnight adjustment of prices of petroleum products is no longer necessary.
Speaking to Nii Ogbamey Tetteh in an interview, the ACEP boss stated that with abolition of the fortnight fuel price adjustment, the decline or rise in crude oil prices would reflect immediately on the domestic market.
“This is why ACEP called for daily adjustment of prices because if we have deregulation, why do you have the fortnight window? It is no longer necessary. If international prices of fuel products fall today, we must see it reflecting in the domestic prices of petrol and diesel and not to wait until two weeks, otherwise consumers will not benefit from the decline in international prices,” Dr. Adam said.
He added that Ghanaians should have seen a reduction in domestic prices of petroleum products with the recent drop of crude oil prices on the international market.
“But because of government’s reliance of the fortnight fuel price adjustment, if there would be any reduction at all, it would take two weeks to reflect at the pumps.”
The price of crude oil on the international market as at yesterday was $27 per barrel, but consumers in Ghana are paying more at the pumps due to the heavily imposed taxes and levies by government.
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“You should know that the prices of petroleum in Ghana are adjusted fortnightly. So if you have a reduction in fuel prices today or even in the petroleum product price today international petroleum product prices today, you will not see a reduction in domestic price until the window for price adjustment is triggered and new prices are expected to be brought out by the BDCs and OMCs,” he noted.
He stated that the recent increases in petroleum prices domestically were due to the imposition of taxes and levies.
“Indeed, at the time the increases were announced, crude oil prices, as well as international price of petroleum products were declining. So we should have seen a decline in domestic prices of petroleum products.”
Wednesday, January 20, 2016
Leslie Dwight Mensah, an economist at the Institute of Fiscal Service (IFS), says government should reduce the prices of petroleum products if the current decline in the price of crude oil on the international market persists for a week or two.
The price of crude oil on the international market dropped to $25 per barrel yesterday but consumers in Ghana are paying more at the pumps.
According to him, the last time domestic prices of petroleum products were increased, crude oil was below $30 a barrel on the international market.
“If this situation persists for another week or two, then it is probable we would see a reduction at the pumps on the Ghanaian market.
The last time the domestic prices were set, crude oil was below $30 so once the price has fallen below $30, since that time, then the decline between the period of the last increase and now should reflect very soon in the decline in domestic pump prices,” Mr Mensah told Nii Ogbamey Tetteh in an interview.
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He said the introduction of the energy sector levy, among others in recent times, had caused a drastic increase in the prices of petroleum products instead of consumers witnessing a fall in pump prices.
“That levy substituted the reduction that we would have seen at the pumps. So whereas there is a decline in the world market price and we should be witnessing a fall in pump prices, we have seen an increase which is rather unfair to the consumer,” he added.
He continued: “The upward adjustment in petrol prices came about because of the energy sector levy, and we have not seen the benefit of the decline of crude in the world market because Ghanaian consumers were due some reduction but then the government came in with the tax or a levy.
“The decrease that we, consumers, should have been granted has been captured by the government through that energy sector levy and their justification is that they have debts to pay in the energy sector. My view is that that is unfair to the Ghanaian consumer,” he said.
He said that with the Western sanctions on Iran lifted allowing Tehran to resume oil exports, the price of crude oil on the international market would reduce further.
Monday, January 18, 2016
Private Universities Students’ Association of Ghana (PUSAG) has decried President Mahama’s directive to the Ministry of Health to consider graduate nurses from public institutions before their counterparts from the private institutions.
According to the leadership of PUSAG, government’s decision to employ graduate nurses only from the public institution would not help address the unemployment situation in the country.
Richard Odame, National President of PUSAG, in a statement, called on President Mahama to grant graduate nurses from both public and private institutions equal opportunities to be absorbed into the system.
“The advent and existence of private institutions in the country have contributed meaningfully to improving the literacy rate while breeding captains of both the private and public sectors of the country. It has also reduced the burden on government’s low infrastructure resources to provide quality education for the numerous students who complete senior high schools yearly with good grades. At this point, quality will be paramount in decision-making and would fuel decisions of who to admit into job schemes,” Mr Odame said.
President Mahama, speaking on how government would address joblessness during the recent press briefing, stated emphatically that the situation was as a result of the Ministry considering graduate nurses from private institutions first and relegating the interest of their counterparts from the public institutions to the background.
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““We want to respectfully bring to the attention of the President and the government the need to reconsider the intention of his statement,” Mr Odame said.
He disclosed that almost all the private universities and institutions operate under public institution through affiliations.
“Why then should the case be that student nurses and the entire general graduates from public institutions be given priority over their contemporary counterparts in private institutions. This clearly means that students from private institutions are also products of the public institutions so by default equal opportunities should be granted,” he noted.
Nana Yaw Osei-Darkwa, founding president of Youth Icons Ghana and a non-violence activist, says the ongoing debate over the two Guantanamo Bay detainees who are being held in Ghana should be limited strictly to security and not religion.
According to him, the religious twist to the debate by various stakeholders and political commentators is a threat to the peace and stability of the country.
The John Mahama-led administration recently brokered a deal with the Obama administration to house two ex-detainees from the dreaded Guantanamo Bay military facility for a period of two years.
Three major Christian groups — the Ghana Catholic Bishops’ Conference (GCGC), the Christian Council of Ghana (CCG) and the Ghana Pentecostal and Charismatic Council (GPCC)—and other civil society groups have called on government to return the ex-convicts to where they came from.
Mr Osei-Darkwa stated that government needed to appreciate the various concerns raised by Ghanaians about the two suspected Al-Qaeda detainees who were being held in the country.
He said it was legitimate for citizens to express fear over the two detainees due to the terrorism link.
No Religious Comments
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Mr Osei-Darkwa mentioned that religious leaders should stay away from making further public comments on the debate and resort to closed-door consultations so that their comments wouldn’t be twisted or misconstrued to heighten tension between religious groups.
“Why should we try to set ourselves against each other because we accepted two strangers into our fold? Government commentators must appreciate the apprehension of Ghanaians and find very creative ways of helping to address the legitimate fears of the people of Ghana because the word terrorism anywhere in the world sparks fear. Happenings in Nigeria, France, Kenya, USA, among several other nations of the world in 2015 with regard to terrorists’ attacks serve as a legitimate basis for the fear of the citizens,” he said.
He charged all political leaders and their communicators to exercise the highest sense of responsibility in their pronouncements because the country is too tensed for reckless and irresponsible comments.
“I am very worried about the way things are going regarding the introduction of a dangerous twist of religion to the debate. I am particularly worried because the discussions as far as I am concerned must be restricted purely within the remit of security and nothing else,” Mr Osei-Darkwa noted.
Nana Osei-Darkwa disclosed that Ghana is a beautiful country where people of different faiths, tribes, traditions and cultures have co-existed for decades to the admiration of the world.
“We must not let the debate over two Guantanamo detainees lead to the dangerous abyss of setting one religion against the other. Do you know that in other jurisdictions a Christian can not enter the mosque let alone visit the National Chief Imam? I am a staunch and avowed Christian but have on countless occasions had one-on-one discussions with the National Chief Imam who is a great man with a warm heart of compassion who accepts all,” he noted.
He continued: “The shape of the world today does not permit us the luxury of soft-mindedness. A nation or civilisation that continues to produce soft-minded men and women purchases its own spiritual death on an instalment plan.”
He also advised the media to be very circumspect in their reportage on the issue.
Thursday, January 14, 2016
(from right) Dr. Dey presenting the items to a representative of the New life orphanage
Dr Dzifa Dey, a Physician Specialist & Rheumatologist and Lecturer at the School of Medicine and Dentistry, University of Ghana Medical School, says five out of every Ghanaian get diagnosed with Autoimmune Disease (AD) on weekly basis.
According to her, the condition which makes the immune system to attack other internal organs until they are totally destroyed has become a worldwide concern.
Speaking to Nii Ogbamey Tetteh at a New Year party organised by ‘The Rheumatology Initiative’ (TRI Ghana) to celebrate with people living with ADs and the children of New Life Orphanage in Accra, Dr Dey, who is also the Director of TRI Ghana, said the term ‘Autoimmune Disease’ (AD) refers to a varied group of illnesses that involve the immune system attacking specific organs in the body.
“Research shows that autoimmune diseases are on the increase worldwide. Almost every week, we have about five people with lupus –another form of AD- on admission in Ghana. It is becoming more common and we are yet to find out whether it has to do with the environment or we are diagnosing it more because we are more aware of it. You can never be sure until a lot of studies or research have gone into it,” Dr Dey stated.
She added that there are a group of conditions that are referred to as autoimmune condition but in all of the ADs, the underlying problem is that the body’s immune system becomes misdirected and attacks the very organs it is designed to protect.
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Dr Dey also noted that autoimmune diseases are not curable but can be managed with medication and proper lifestyle.
“You need constant monitoring and constant treatment to make sure that all your organs are not affected. But once it affects your brain and kidney, it becomes difficult to manage. You will need very strong drugs that we call neurosuppressants to try and suppress the immune system. But the condition can be life-threatening if you leave it untreated,” she warned.
Some of the patients living with the disease told the paper that though they could not go about their usual day-to-day activities like they used to, proper medication and counselling from TRI Ghana had helped them to live an almost normal life.
The Rheumatology Initiative (TRI Ghana) is a non-profit organisation dedicated to providing education, advocacy and research into autoimmune rheumatic conditions in Ghana and Africa.
“Our basic aim is to try and reassure patients, educate them enough about this condition so that they can be accepting of the treatment and management, and encourage them to live healthy lifestyles,” she said.
Dr Dey, on behalf of TRI Ghana, also donated bags of rice, stationery and toiletries worth thousands of Ghana Cedis to New Life Orphanage.
Wednesday, January 13, 2016
Haris Broumidis, Chief Executive of Vodafone Ghana, has predicted a growth in revenue driven by money transfer and payments using a handset and Machine-2-Machine (M2M) services to take the telecommunication industry to the next level across the country this year.
According to Mr Broumidis, 2016 would open doors and avenues for further consolidation of the gains made in the telecommunications industry.
“At Vodafone, we would continue to focus on new ways of providing unmatched customer experience. We see Vodafone Cash and M2M as two platforms that will become game-changers for us,” the Vodafone Ghana boss said.
He added that the telecommunications industry was expected to see heightened competition this year, following the deployment of LTE and the constant striving for high revenue yields and subscriber increases by telecom companies.
“These notwithstanding, prevalent issues such as regulatory interventions, the tax regime, aggressive competition and a tough economic environment still remain. Mobile money and M2M are, however, set to be the two key elements that will dictate the pace in the industry this year. Vodafone Ghana recently launched “Vodafone Cash”, its version of the famous M-Pesa platform that has transformed the economies of East Africa. The product is expected to bridge the huge gap between the banked and unbanked across the country,” Mr Broumidis said.
In a related development, Vodafone is of the view that across the rest of the world, the concept of unified communications will take center stage this year.
According to a statement published in its 2015/2016 Annual report, consumer and enterprise customers in most developed economies are yearning for a unified approach where fixed, mobile and TV services, will all be bundled together for access everywhere.
The statement added that traditional revenue sources – mobile voice and texts – have reached maturity, hence the demand for data will shoot up in 2016, driven by rising smartphone and tablet penetration and usage, as well as improvements in mobile network capability.
Consumers who would be paying an amount of GH¢1 billion annually in three to four years to settle debts accumulated over the years in the country’s power sector.
Mohammed Amin Adam, Executive Director of ACEP, who disclosed this recently at a press conference in Accra, said “Apart from paying high electricity tariffs, it is unfair for consumers to be asked to also pay debts accumulated from the inefficiencies of Volta River Authority (VRA) and Electricity Company of Ghana (ECG), as well as government’s neglect of its responsibility to the utilities through petroleum levies.”
He continued: “We also know that the balance sheets of the utilities are not good due to a number of factors, the central factor being the huge indebtedness of the utilities. In spite of this dilemma, it is our considered opinion that this levy will provide sustainable resources for addressing the energy sector investment challenges and thereby help end the crises we have in our power sector.”
In 2015, he said government, under the Ghana Millennium Challenge Compact II, confirmed the payment of its debts to ECG over a period but refused to make provision for the payments in the 2016 Budget.
“Without providing for these payments in the 2016 Budget, we are not surprised that government is now considering repayment of the debt through this new levy.”
He urged government to audit and publish the true state of the debts of the utilities, the legislative instrument providing a sunset clause to determine the exact period over which the debts would be paid and also abolish the levy as soon as the debt is completely paid so that it does not become like the unending TOR Debt Recovery Levy.
Dr Adam therefore cautioned government to ensure that the revenue to be generated from the Power Generation & Infrastructure Support Levy on Petroleum Products would be used to address the crisis.
Tuesday, January 12, 2016
The Ghana National Fire Service (GNFS) says there was a reduction in fire outbreaks in the first two weeks of January 2016 compared to the same period last year.
According to DOII Timothy Osafo-Affum, acting Public Relations Officer for GNFS, the reduction was as a result of on-going fire safety campaigns across the country.
DOII Osafo-Affum, who was speaking to the media yesterday, said in fire prevention, protection and precautionary measures were crucial.
“It is heart-warming to note that our previous and current efforts are steadily yielding dividends, a comparative analysis of major fire outbreaks shows that there has been a radical reduction in the first two weeks of January 2016 as compared to January 2015,” he stated.
He added that from January 1-10 this year, the Greater Accra region recorded 51 fire outbreaks, which represented a drastic reduction over that of 2015.
DOII Osafo-Affum said trend analysis of fire outbreaks showed that the months of November and February each year was the peak period for fire outbreaks.
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“The recent fire outbreaks at the Kumasi Central Market, Kumasi Kayayei, Tuobodom Senior High School, among others, have raised public concerns about fire safety in the country. Fire safety is therefore a shared responsibility of all stakeholders and the general public; so if we want to see an end to these preventable fires, then the public has a bigger role to play. This is because they are closer to the ‘flash-spots’ across the country than the fire personnel,” he added.
The Acting PRO disclosed that the Harmattan season reduces the temperature of all combustible materials making them burn at a certain temperature.
“The GNFS has consistently been up to the task, honest market women and men, the clergy and traditional leaders can bear us witness. To the best of our professional capabilities and resource-availability, we have always executed proactive strategies to forestall fire outbreaks in Ghana. Apart from forming taskforce and training 500 Fire Volunteers to augment the existing ones to patrol and monitor areas deemed to be fire-prone, we intensified our fire safety education and awareness in churches, mosques, market-places, lorry parks and rural communities in order to ensure effective and efficient control fire,” he said.
DOII Osafo-Affum urged the general public to report any recalcitrant individual, who consciously or unconsciously causes fire outbreaks.
“Bushfire Prevention Law (PNDC LAW 226) is to be strictly enforced. We are therefore urging the general public to volunteer information that will lead to the arrest and prosecution of anyone whose actions or inactions will result in bushfires.”
Sunday, January 10, 2016
Uncontrollable fire on Friday swept through a large portion of the Achimota Forest, destroying a major part of the reserve.
When Nii Ogbamey Tetteh visited the scene, major parts of the forest had been razed down with smoke still emanating from some tree stumps.
A vast area of the forest close to the Abelemkpe roundabout, towards the Greater Accra Regional Forestry Commission office, had been lost to the fire which according to an eyewitness started around 11:45am.
Another eyewitness told the paper that attempts by some workers of the Forestry Commission, together with the police and other volunteers, to bring the fire under control while they awaited the Fire Service team to get to the scene proved futile due to the high harmattan winds.
The Fire Service personnel from the Abelemkpe fire station were said to have fought the raging fire for close to an hour before extinguishing it.
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Though the cause of the fire was not immediately known, Edith Ansah, the Greater Accra Regional Manager of the Forestry Commission, said she suspected that the fire was ignited by wee smokers who were smoking in the forest.
“I suspect that the wee smokers went in there to do their own thing but failed to completely put out their flames. Last year around this time, the same thing happened and we had parts of the forest burnt as well,” Madam Ansah told Nii Ogbamey Tetteh in an interview.
“My reason is that from what we saw, the fire started right in the middle of the forest or let’s say right within the forest. But if it started outside, I would have said a passer-by had thrown away a cigarette stump which had caused it,” she added.
“Though we patrol the forest a lot, these smokers lurk around till my patrol team go for lunch or break and as soon as they leave, the boys go in there to do their own thing,” she said.
She urged Ghanaians to be very careful in handling fire close to bushes or forest areas in this dry season to avert fire destroying the country’s forest and game reserves.
Within the past 62 hours, Ghana has recorded several fire outbreaks and it is feared that more incidents could occur during this severe harmattan period if precautionary measures are not put in place.
Friday, January 8, 2016
The African Center for Energy Policy (ACEP) has accused government of overburdening Ghanaians by imposing many taxes on petroleum products.
According to Mohammed Amin Adam, Executive Director of ACEP, the imposition of the 17.5 percent Special Petroleum Tax (SPT) on some selected petroleum products amounts to double taxation.
Speaking to the media yesterday in Accra, Mr Adam estimated that based on volumes of petroleum consumption (petrol, diesel and LPG) in 2015, the new levies would generate an incremental revenue of GH¢3.2 billion annually.
“All the levies and taxes imposed on the products are also taxed in the Special Petroleum Tax, which is Tax on Tax, because the SPT is a tax on the ex-pump price which already contains all these levies and taxes.”
He added that instead of paying ex-pump prices based on the levies and taxes like the TOR Debt Recovery Levy,Power Generation and Infrastructure Support Levy, among others, consumers were made to pay ex-pump prices based on the levies and taxes in addition to the SPT, which was already contained in the ex-pump price.
“We estimate that the double taxation alone would cost the consumer GH¢675 million annually on petrol, diesel and LPG,” he noted.
Special Petroleum Tax (SPT), which was introduced on selected petroleum products in 2014, generated GH¢183,438,611.54 in its first year and GH¢748,545,275.65 in the first half of 2015.
The ACEP boss urged government to revise the trend to bring relief to Ghanaians.
Levies on petroleum product prices
ACEP said there had been different versions of relative impact of the levies on the ex-pump price of petroleum products.
It continued that its analysis on the contrary showed that the effects of the levies on ex-pump prices were much greater and punitive. “We estimate that the levies had led to an increase in the ex-pump price of petrol per litre by 33 percent, 40 percent on diesel per litre and 22 per litre on LPG per kilogram.
“Also with the current levies, the tax component in proportion to the ex-pump prices of petrol and diesel are 41 percent and 42 percent respectively. The IMF shows that average tax share in ex-pump prices of petrol and diesel in developing countries ranges between 22 percent and 30 percent. Therefore, the share of taxes in the petroleum prices in Ghana is one of the highest in the developing world.
TOR Debt Recovery Levy
ACEP said it still maintained that consumers had overpaid the TOR debt, indicating that at the time the levy was instituted, the total debt stood at GH¢450 million. By 2009, it said the total debt had grown to GH¢900 million due to non-application of the revenues to service the debt, as well as interest accumulation.
“Our analysis shows that between 2009 and 2015, total collection from the levy is in excess of GH¢1.9 billion. This effectively amortizes the debt assuming an interest rate of 10 percent.
“We therefore find it difficult to comprehend why consumers should continue to pay this debt. Ostensibly, the TOR debt recovery levy has over the years been misapplied aided by the weak oversight of parliament.”
Price Stabilization & Recovery Levy
It mentioned: “The levy imposed on petrol is GH¢0.12 per liter, diesel is GH¢ 0.10 per liter and LPG is GH¢10 per kilogram. These levies translate into an increase in ex-pump price by 5 percent for petrol, 4 percent for diesel and 4 percent for LPG. The levy to be collected is much more than required to stabilize prices and subsidize premix and residue fuel oil in this price era,” he noted.
However, Mr Amin commended government for abolishing the exploration levy, which ACEP had been campaigning against for the past two years.
The National Democratic Congress (NDC) has called for the arrest of Dr Mahamudu Bawumia, vice presidential candidate of the opposition New Patriotic Party (NPP), for his recent exposé about the credibility of the voter register.
Speaking to the media yesterday at the NDC headquarters in Accra, the party’s General Secretary, Johnson Asiedu Nketia, rubbished Dr Bawumia’s presentation to the Electoral Commission (EC) concerning alleged registration of foreign nationals by the commission. He described the claim as false and fabricated, for which he (Bawumia) should be arrested.
He insisted that the evidence presented by Dr Bawumia was “photoshoped” and could only be allowed on social media and not serious institutions like the Supreme Court and the EC.
The NDC in recent times has turned its attack dogs on Dr Bawumia, trying to tarnish his reputation despite a series of predictions he made about the economy that came to pass.
Diplomats’ Frustration
At a retreat held at Royal Senchi, Akosombo last December, Ghanaian diplomats expressed dissatisfaction with the NDC party and government’s response to economic issues raised by Dr Bawumia.
According to them, the international community seemed to lap all the analysis made on media platforms by Dr Bawumia, an economist and running mate of Nana Akufo-Addo.
The diplomats therefore called for a means of taming his rising star.
This might have informed the NDC leadership to make Dr Bawumia their target, making Asiedu Nketia to lash out at the NPP vice presidential candidate.
The NDC chief scribe stated, “The NDC condemns in no uncertain terms the fraudulent conduct and calls on the police to immediately investigate the matter. In particular, we are calling for the arrest of Dr Bawumia on the basis that he engaged in falsification and fabrication of public records to deceive public officials.
“The reason why we are calling for the arrest of Mahamudu Bawumia is that, I am not a lawyer, but I have heard people say that if you fabricate public documents, if you falsify public documents with the intention of deceiving people, our laws should have a way of dealing with you.
“In the Supreme Court they printed fake pink sheets and tendered them in evidence; all that was done was that the Supreme Court rejected them. Nothing has happened afterwards.
“And they came to deceive the Electoral Commission again by printing fake Togolese register, put people’s pictures on the register and presented it as Togolese.
“How can a PhD [holder] who wants to be a vice president in this country sink that low?” he claimed.
Mr Asiedu Nketia, popularly called General Mosquito, alleged that Dr Bawumia in 2013 falsified various documents and presented them to the Supreme Court during the election petition case. “The same man has falsified another document to the EC.
“It should not happen when you are presenting evidence to a constitutional body like the Supreme Court or the electoral body and you be let off the hook like that… otherwise our democracy will be in danger,” he said.
It would be recalled that Dr Bawumia, former Deputy Governor of the Bank of Ghana, last year made some stunning revelations about flaws in the voter register, providing impetus for various civil society groups to demand a replacement of the electoral roll.
Dr Bawumia’s disclosure about the presence of the names of about 80,000 Togolese on the register particularly ruffled various stakeholders.
EC’s Rejection
The NDC also endorsed the EC’s decision not to compile a new register ahead of the 2016 elections.
Mr Asiedu Nketia disclosed that EC’s rejection of the demand vindicates the NDC’s position on the subject.
NPP’s Response
The Acting General Secretary of the New Patriotic Party (NPP), John Boadu, in reaction to Mr Nketia’s utterances, rather called on the security agencies to start chasing President John Dramani Mahama.
John Boadu, reacting on Asempa FM’s ‘Ekosii Sen’ programme yesterday, said Asiedu Nketia should have rather called for the arrest of the president since “he is known for public deceit.”
“Why would Asiedu Nketia call for the arrest of Bawumia when there are bigger thieves that have stolen the country’s money walking around…has he forgotten of President Mahama and Alfred Agbesi Woyome?” he quizzed.
Prominent among what he described as the gross deceit of the public by President John Mahama was the promise to end the four-year power crisis (dumsor) which has crippled the country’s industrial sector.
“Did the president not promise at an IEA forum in 2012 of ending dumsor by 2013? What have we seen on that…nothing…so the president lied big time and must be arrested,” he charged.
Mr John Boadu further sought to know if businessman Alfred Agbesi Woyome had paid the fraudulent judgement debt he was asked by the court to refund into the state’s coffers.
“The year 2015 has ended so if he has not paid the money, then I believe the NDC could have done more service to the country by calling on the security agencies to pursue him to refund the money and that would have been a more prudent venture…,” he noted.
The Acting NPP General Secretary further said that the party had handed over the EC’s letter to its special committee that worked on the voter register and that they would expose the ‘hollow arguments’ of the EC in claiming that Ghana does not need a new voter register at a press conference the party would organize.
He however stated that he and the NPP were not surprised by the response of the EC to the NPP as “the EC, since time immemorial, has always kicked against ‘any ideas from the NPP.’”
Mr Boadu was astonished to see the NDC jubilating about the recommendations of the panel of five established by the EC to examine the calls for a new electoral roll since the panel members are not the ones to make a final decision on the way forward.
Obiri Boahen Fires
Deputy General Secretary of the NPP, Nana Obiri Boahen, also lambasted Asiedu Nketia, describing him as a “certified schizophrenia.”
A livid Nana Obiri Boahen explained that the actions and inactions of the NDC chief scribe were enough attestation that he was suffering from a ‘chronic brain disorder.’
He expressed shock at the conduct of the ruling party.
He said “assuming without admitting that the allegation was true, calling for the prosecution of Dr Bawumia is the sole preserve of the EC and not the NDC.”
He fumed, “Is Asiedu Nketia now the spokesperson of the EC? But I’m not surprised because Asiedu Nketia is a certified schizophrenia patient.”
Ohemaa Mercy and a host of other Ghanaian gospel musicians on Christmas day thrilled worshippers to live ministrations at the seventh edition of Alabaster Praise Concert at the Assemblies of God (AG) Tema New Town branch.
The annual concert, organized by Divine Instruments (DI) of New Life Assemblies of God, is aimed at providing an ultimate worship experience for all Christians and an opportunity to win souls for Christ through music.
Guest artiste, Ohemaa Mercy; host choir, Divine Instruments; guest choir, Jewels of Praise and other ministers did not only minister the crowd’s favourites, but also interacted with the fans, making their performance very engaging.
Main act of the evening, Ohemaa Mercy, led the congregation through non-stop renditions of popular worship tunes. The songstress’ praise jam session saw the crowd holding up their mobile phones, singing out loud, jumping and dancing to her popular tunes like ‘Wo Fri Mo’, ‘Wo Beye Kese’ and others.
Commenting on the Alabaster Praise dream, President DI, Hannah Doughan, said the ministry came up with the concert as an avenue to reach out to the youth through music, worship, choreography and a host of voluntary social projects.
Ohemaa Mercy
“Within six years, Divine Instruments has made inroads by bringing seasoned ministers like Cecilia Marfo, Joe Mettle, Diana Hopeson, former MUSIGA President, Francis Amo, Vine Praise, Gifty Osei, Jim Emmit Konadu, De Joe and the Levitical Order and others to lead hundreds of worshippers to the throne room of God during the concert.
A member of the planning committee and a music director of DI, Paa Kwesi Forson, entreated fans of the group to look forward to the eight edition of the concert in 2016, adding that the group has already hit the drawing board to prepare for the 2016 edition.
Wednesday, January 6, 2016
Obrafour is mournful on this Nature produced number. He has always been the one to hold his head and lament, but this song is the saddest I've ever felt him.
Why is it even possible, how is it even allowed, that as a man approaches the age of legacy, he's this broken? But Obrafour, who has nothing else to prove to us musically, still harbours such intense grief.
The issues he touches on, in this song, are neither surprising about him or to us, so here, it's not necessarily what he says, but how he says it:
It is for his rap we revere him; always clean and decent, deep and mature, specific and practical truth --but we respect him for his singing too; brief, pleasant and easily familiar. Some of his vocal deliveries, his hooks especially, have been highly successful here; Saa Okodiɛ no, Swedru Agona, Abena, Ohene. Now these are recent but of course he's had memorable choruses since "Pae Mu Ka."
Then again, you can't ignore what he says in the song...you just can't! It directly affects you. Don't worry, I'm not interested in what or who you are, he's speaking directly to you, because it's about greed, and envy, and disregard for the truth, and apostles of evil, struggle and global strife, and as usual, dirty politics. And he's ruthless! He goes everywhere. Oh you think you're anointed so you can't be touched? Ooh he's got something special for you in verse 1. Let's take one or two of them, shall we:
Don't worry, I'll translate. The above lines refer to how we have discarded God's laws and have become wise in our own eyes and are swindling people, how it is the followers of God who are most surprising; that even though they are aware of a judgement, they ( "pastors") have changed the apparel of the word of God. In the same verse, he wonders why pastors are putting their abilities, oil and water up for sale, as God first gave them their gifts for free. He cites Peter in the Bible, saying that unlike contemporary pastors, he healed for free.
He also mentions something poignant: the words in the Bible are definite, but interpretations differ, so depending on how good you can spin understanding, you'll be successful, which is why pastors would scold their members and call it a sermon.
Wahu Nyame Nipa?
His singing on Nkontompo is especially emotional, he's wailing, even. In the chorus, when he says "me werɛ aho", it makes you shake your head slowly. He doesn't have a very good voice, he's never had, but what he lacks in vocal space, he makes up for with raw, honest emotion...and on so many levels, emotional honesty is more important than vocal talent; Joseph Hill, Amakye Dede, Kanye West sometimes, and Sarkodie, on Mary.
"Ewiase bɛn po ni?"
Religion is service to a deity and and the obsession with odd ritual. Love is good intentions toward the one standing next to us. Menocchio says that it's more important to love one's neighbour than to love God. Deep down, we do not disagree with this, so that's it: love trumps religion.
Indeed it's the theme of every religion, it's the central message of every great leader or rabi who has ever treaded here, so religion is a love too. Even without bothering to research, I am certain that religion has the most influence on us. The biggest gatherings are crusades and the Hajj. The most widely read stuff are religious literature...but you already knew that, so let's progress the argument.
Let's be objective, all through history, religion too...the politics of its philosophy has, on its own, been responsible for some of the most monumental acts of hatred to the brain, heart, knees and toes. It's a shamefully wide range, from bloodshed to noise pollution.
His second verse is just as spirited. There are abbrasively truthful words on shameless corruption, pointless propaganda, the various versions of the truth, religious extremism, the love for money alone, how we stifle those who speak up and how we've turned this country into hell all by ourselves. It's remarkable how he's stuffed all that in the space of one verse. Obrafour is a lyricist, and there's no debate there. Who else do you know that can sing, rap, preach, advise, talk about love and women, and still maintain a dignity and depth? Who else do you know who can do all this with proverbs and in Twi?
Obrafour is our ultimate social commentator. It is what we have come to know him for, and why we have grown to trust him. Periodically, he has had to remind us that it's in a chaos, and not a bliss, that we are so comfortable. It is in that way that he has constantly remained relevant to us...like our community Imam or grandmother.
Our Imam is tired. Our grandmother is spent.
The village old man has lost hope. For all of their adult lives, they've been saying the same thing: "wise up, my child, wise up". And if you've said the same thing over and over, and all you see is scanty change, you too would be tired.Obrafour embodies these emotions in Nkontompo.
The instrumentation is rich and complex. It tells a story too...a parallel story. The electric guitar for instance, shows us a facial expression of strain, pain, and the verge of giving up. The horns suggest a danger and the piano invokes sustained sadness. Indeed, one reason the song stands out is how deep horn and organ sounds are sustained, right from the beginning. It's dark and dangerous, profoundly gothic...and we instantly know something troubling is pending.
A lot of things are happening in the song, it's a picture of disaster, or the scene after a massacre which you can't look away from. It's a gorgeous and disturbing paradox: I have mentioned that the spine of the song is how some sounds are sustained, but at the same time, many of the sounds in the song are choppy and piercing. Like the message of the song, it's supposed to make you uncomfortable. It pulls at your skin and keeps you attentive.
It's a kind of homage to Da Hammer --the instrumentation. The horns and distinguished kicks especially, which are Hammer's trademark sound, seem to be mined from somewhere special unto the song...and influence is no sin so...
But Red Eye, or Nature (when he's producing beats and not rapping hard and demented in Ga) too, has always been eccentric and warlike...more experimental too with other rhythms than Hammer would touch. From his early work with 2 Toff, the group he belongs to, to Kwaw Kesse, to Edem, he has constantly proven to be a strong and versatile hand. For 2 Toff, he worked on " Yɛ Na Bra", on which they featured Castro. Several years on, on "Meawezo" the song on which they announced their comeback after a long exile from Ghana's music industry, he rendered a parallel sound which was both modern and at the same time, invoked the nostalgia of "Yɛ Na Bra".
Nature might have done way more for Kwaw Kesse's "Poppin" than we may be praising him for (if we are praising him at all), as all Kwaw did, really, was to give a fun chorus. Both reggae songs Nature did for Edem are infectious; "Make Money" and "Ghetto Arise" are testimony to the diversity of his talent.
Nature too, has been a fan of the trumpet, which, like I have said elsewhere, works excellently as warrior melody and death announcement. He's also remorseless with the guitar, and it's remarkable.
Truth is truth, and common sense lays around. It doesn't have to come from the high and mighty for it to be truer.
Obrafour is just a man, it's all he's been this whole time. He's faced the valleys of the shadows, he testifies in his song "My Praise", he's had public banters with fellow rappers and felt good about it, which is a bad example and might reduce drastically his moral leverage should he advise younger rappers to bury the hatchet. He's imperfect, but the "blameless" ones may have failed us. All we need to speak up to life and against it, is to be a man or woman, and that refers to you and me...Obrafour too.
"M'asɛm tia yi eko ma yɛn nyinaa"
He's a tired old man, but he's a special kind of tired and old. He's our favourite old man...tired or not. It's not all he is though; he's anointing the up and coming ( Dues), he believes in God's protection over the helpless ( Aboa Onni Dua) and he's exploring love (Pimpinaa,Twe Ma Me). He's protesting against life, and embracing it all at once. It is well.
Nkontompo means lies, and it is an official single off Obrafour's latest album, Obrafoforo.
Tuesday, January 5, 2016
Richard Adjei, Chief Executive of Kasapreko Company Limited, says owing to the power crisis in the country, his outfit would switch to solar energy by the end of the year to run its facility effectively.
According to him, the switch to solar power is expected to cost the company about $ 5 million and it would provide more than 30 percent of power needed to run the state-of-the-art factory.
Mr Adjei disclosed this in an interview with Nii Ogbamey Tetteh when a group of 60 students from the Harvard University in the US visited the company’s head office off the Spintex Road.
He said the move was part of the company’s 2016 strategy to help tackle pollution.
“By the close of this year, we would have 16,000 meter cube solar panels that can power more than 30 percent of our facility. There are a lot of climate change issues that the world is facing and we want to help anti-pollution issues,” Mr Adjei stated.
He added that currently the company that has the capacity to produce over 110,000 bottles of beverages and water per hour, spends about GH¢150,000 every month on diesel to power their generators during power outage.
The students were taken on a tour of the new $70 million bottling plant, which was recently commissioned by President John Mahama to obtain first-hand information in the production of both alcoholic and non- beverages at Kasapreko.
Dina Pomeranz, an Assistant Professor of Business Administration at Harvard Business School and the leader of the team, said the team chose world-class brands like Kasapreko Company Limited based on the global presence of the company over the past 26 years.
She noted the 10-day tour of Ghana was part of efforts to teach the students how to do business internationally.
“The business potential in Ghana is huge, and it is very important for our students to learn how to do business in such a country.
“We think it is very important that our students learn how to do business in a different cultural context. The goal of the visit is to open the eyes of the students to different markets around the world,” she noted.
Dr. Adjei, Group Chairman and Founder of the company, who led the students on the tour, disclosed that the company started with five workers in a garage at Nungua 27 years ago.
It has now grown into a multinational beverage company employing over 600 workers.
He urged the students to set high academic standards and adhere to them to achieve success in their chosen careers.
Dr. Adjei hinted that the company, which has made inroads in Nigeria and South Africa, would by the close of 2016 start exporting its products to the US.
Friday, January 1, 2016
General Secretary of the Ghana Rugby Football Union, Abdul Azziz, has expressed satisfaction over the level of player participation and spectatorship in the local rugby league.
According to him, there was high level of skills development on the part of players, which was helping to improve the standard of the game to attract more viewers.
“Gradually, we are improving. Last year we used to play on virtually empty fields but these days, people are beginning to patronize our games.”
He was speaking in an interview at the end of the first round of rugby league matches played at the Accra Stadium over the weekend.
Mr. Azziz however expressed worry over the lack of corporate and governmental support for the game, attributing it to the fact that rugby was new in Ghana, to many people.
“It takes time for people to pick up new sports. Everybody’s attention is on football but we cannot put all our eggs in one basket,” he said.
“We always fall on the president of the union (Herbert Mensah) who pays almost everything as far as this activity is concerned. We cannot allow the situation where the president has to be the financier for all activities of Rugby,” he added.
He therefore called on organizations and the government to give the game a facelift adding that the association was focused on identifying talented young people to be trained by competent coaches.
Mr. Azziz said the league, expected to resume on January 30, 2016, would continue with more games to be played locally as well as major events scheduled to take place in Lome, Togo.
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About Me
I am a Creative Arts Writer who is also into Strategic Communications, Public Relations, Photography and IT consultancy. I am also Social media enthusiast and an alumni of the Ghana Institute of Journalism (GIJ).
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Tyler Kornfield
Tyler Kornfield (born February 9, 1991) is an American Olympic cross-country skier.
Early and personal life
Kornfield was born and raised in Anchorage, Alaska, the son of Ed and Robin Kornfield. His father was originally from Philadelphia, Pennsylvania, moved to Alaska in 1978, and worked for the United States Department of the Interior, Office of Aviation Services (OAS), as Chief of Fleet Services. He has a sister, named Tamra.
He attended high school at Service High School in Anchorage, graduating in 2009. He then attended that University of Alaska Fairbanks in Fairbanks, Alaska, graduating in 2013 with a degree in Mechanical Engineering.
Skiing career
Kornfield began skiing at age three. His club is the Alaska Pacific Nordic Center. His club coach is Erik Flora, and his Team USA national coach is Chris Grover. He competed for the University of Alaska Fairbanks Nanooks in both Nordic skiing and cross-country running.
In 2009, he was Alaska state champion in the 7.5k classic race. In January 2010, Kornfield came in second in the US National Championships Spring (SP) 1.5 km race. In January 2012, he won the US National Championships SP 1 km race.
At the 2013 Fédération Internationale de Ski (FIS) U23 World Championships, Kornfield came in 19th in sprint freestyle. In January 2015, he took second at the US National Championships SP 1 km race. In February 2017, Kornfield won the US Super Tour SP 1.6 km race. In January 2018, he won the US National Championships Classic 30 km race.
Kornfield competed for the United States at the 2018 Winter Olympics in the men's 15 kilometre freestyle, coming in 74th out of 119 competitors and in the Men’s 50 kilometer classic, coming in 48 out of 69 competitors.
References
External links
Website
Instagram page
Twitter page
Category:1991 births
Category:Living people
Category:Jewish American sportspeople
Category:American male cross-country skiers
Category:Olympic cross-country skiers of the United States
Category:Cross-country skiers at the 2018 Winter Olympics
Category:Sportspeople from Anchorage, Alaska
Category:University of Alaska Fairbanks alumni
Category:Alaska Nanooks skiers
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A COPY OF THE OFFICIAL REGISTRATION AND FINANCIAL INFORMATION FOR FRANKLIN'S FRINEDS MAY BE OBTAINED FROM THE DIVISION OF CONSUMER SERVICES BY CALLING TOLL-FREE (800) 435-7352 WITHIN THE STATE OR VISITING THEIR WEBSITE. REGISTRATION DOES NOT IMPLY ENDORSEMENT, APPROVAL, OR RECOMMENDATION BY THE STATE. Florida registration CH38383. No fees paid to professional fund-raising consultant or solicitor. The organization receives 100% of each donation.
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In light of recent statements by President Donald Trump calling for retaliation against NFL players engaged in the free exercise of their First Amendment rights, this editorial – originally published on Jun 23, 2017 – has once again become relevant. MintPress brings you the original piece by Eric Draister in its entirety.
Like a million and a half other bleary-eyed workers, I commute into Manhattan early every morning. My train ride takes me right through the foul-smelling no-man’s-land that is the wetlands between East Rutherford and Secaucus, New Jersey – a methane-laden marsh that is beautiful in a “don’t dig or you’ll find a low-level mob guy’s skeleton” kind of way.
And, as I stare off into the hazy distance, dominating the skyline is that bulging, pimple-shaped eyesore that is MetLife Stadium, home of the NFL’s New York Giants and New York Jets.
And on this sticky, humid, gray June morning, I peer out the dirt-encrusted window of the NJ transit train out towards the stadium, sitting empty in anticipation of the upcoming football season, when every Sunday it will be transformed into America’s equivalent of Chartres or the Temple at Karnak – a sacred and holy space complete with the images and symbols of venerated saints of past glory, and hordes of devout worshipers clamoring for a glimpse of greatness, desperate for the communal belonging that comes with the price of admission.
And when the Giants and Jets begin their 2017 NFL seasons, they will do so with significant quarterback questions: The Giants, with their past-his-prime two-time Super Bowl champion Eli Manning, and the Jets with a God-knows-who collection of cast-offs and scrubs (Josh McCown? Bryce Petty? Christian Hackenberg? A bucket of sand?). One team has a desperate need for an NFL-level starter, while the other surely needs an insurance policy on their over-35 and consistently mediocre franchise quarterback, Eli Manning.
Both teams reside in a massive, high-profile football market. Both teams represent a city that boasts a majority of people of color. Both teams have a history of employing “controversial” players, some of whom have had significant legal and public relations troubles; the Giants kept serial wife-beater Josh Brown on the roster until public pressure forced them to release him.
And yet both teams have refused to even offer a tryout to the lone NFL-level starting quarterback who is still available just two and a half months before the season starts.
And why have both teams chosen to move forward with subpar starting and/or backup quarterbacks rather than offering a tryout to an unsigned free agent QB who remains head, shoulders, arms, waist, knees and toes above every other available QB?
Because that man is named Colin Kaepernick. And because that man has chosen to use his fame to draw attention to the institutionalized, systemic racism and violence that primarily targets people of color.
But oh, we’re told by the preening sycophants of so-called sports journalism – almost without exception just corporate mouthpieces with communications degrees – that it’s not racism that keeps Kaepernick off NFL rosters; it’s not the blacklisting of an athlete for the dangerous sin of being both black and politically radical.
No, it’s a purely football decision because Kaepernick is just not very good … or so they tell us.
Of course, no one would argue that Kap is Aaron Rodgers or Tom Brady. But “not very good”? Really?
Is Kaepernick worse than Josh McCown, Mark Sanchez, Josh Johnson, Geno Smith, Aaron Murray, Case Keenum, David Fales or Austin Davis? If your response to reading those names was “Who the hell are those people?” then you’d be joining the tens of millions of other football fans who would ask the same question. Still, every one of those scrub QBs has landed a spot on an NFL team.
But perhaps the even better question is: “Why is this even up for debate?”
Kaepernick’s real-world performance on the second-worst team in the NFL (the San Francisco 49ers finished 2-14 in 2016) was more than adequate. In fact, Kap was one of the better QBs in the league when he got a chance to start, even on a horrendous dumpster fire of a football team. Now, let’s look at some numbers. Forgive me non-football fan readers, but this is important:
According to the NFL’s official research organization , Kaepernick threw 16 touchdowns and only four interceptions while going 1-10 as a starter. That was good for the sixth-lowest interception percentage in the NFL, just behind Aaron Rodgers and Derek Carr, two poster boys of the NFL who were considered contenders for the Most Valuable Player award in 2016. Kaepernick finished the 2016 season 16 th among QBs in adjusted yards per attempt (better than two Pro Bowl QBs). Kaepernick finished 17 th in QB rating. Kaepernick finished 13 th in touchdown percentage. He finished second in total rushing yards among QBs despite starting just 11 games, as well as posted the best yards per carry of any player with at least 50 carries.
In short, any objective analysis of Kaepernick’s level of play shows that he is at worst a middle of the road, average NFL QB, which should make him sought after by every single organization and earn him tens of millions of dollars. Consider the fact that Brock Osweiler last year signed a $72 million contract and performed as one of the worst QBs in the NFL, performing far worse than Kaepernick in every offensive category. And yet Kap remains unemployed. Why?
Radical Liberation Politics in a Reactionary, Oppressive League
Kaepernick’s lack of a job is less about him than it is the NFL and American society as a whole. As the numbers show – and many experts agree – Kaepernick’s performance is, by any statistical measure, worthy of an NFL job. So there must be another reason for his fall from grace.
As ESPN’s Bomani Jones eloquently wrote:
“Stop hiding behind code. Stop trumpeting the idea that sports are the ultimate meritocracy, then shrugging and say ‘thems the breaks’ in the face of a visible potential case of discrimination. It’s intellectually disingenuous at best, indefensible cowardice at worst and sounds eerily like the worst of past evaluations and coverage of black athletes…And, then perhaps, we could address the cruelest irony of this. Kaepernick’s stand was a refusal to pay homage to American ideals because he couldn’t ignore America’s reality. Now, writers and fans are ignoring those same ideals and their defense of that outlook is … it’s reality.”
Indeed, it is good old-fashioned racism and white supremacy at work in the Kaepernick saga, not some putrid garbage about reading defenses, being a pocket passer or getting rid of the ball too slowly.
It is, once again, a professional sports league dominated by the same rich white billionaires who revel in ostentatious displays of hero worship for U.S. military – it makes no difference whether those wars are unjust, illegal, imperialist wars, mind you – and other agents of the state such as politicians and cops.
So, NFL owners and the league think Kaepernick is not NFL material? That he is a black eye (pardon the pun) for the game? Well, let’s remember just what kind of league we’re talking about. This is the same NFL that:
Attempted to cover up and suppress information from studies establishing a correlation between football and brain damage .
. Proclaims itself to be a proud sponsor of breast cancer awareness and research with its pink-colored merchandise, but only actually gives 8 percent of the money consumers spend on pink gear to cancer research . In fact, the NFL takes 1.25 percent of the profits – and even more when they are the direct retailer.
Maintained tax exempt status until 2015 , despite being one of the most profitable organizations in the world. I wonder how many schools, hospitals and infrastructure projects didn’t get funded because of tax revenue that cities and states were cheated out of thanks to NFL accounting practices that have saved the league hundreds of billions of dollars over many decades.
Refused for years to extend or expand long-term health benefits to former players, despite mountains of evidence regarding the long-term negative health impacts of football.
Routinely allows teams to blackmail cities and their citizens into providing public funding for billion-dollar stadiums, while the billionaire owners rake in the profits.
And on and on and on. We’re talking about the same league that has all but canonized Ray Lewis, despite the fact that he was directly implicated in a double murder and, at the very least, was guilty of helping to cover it up. Instead, Lewis pled down to a misdemeanor and went on to spend years as one of the most well-known faces of the NFL.
Somehow, Lewis was not an embarrassment or a black eye for the league. Nor was Hall of Famer Michael Irvin booted from the league when he was found in a hotel room with a crack pipe, drugs and prostitutes. Nor is the NFL’s “tough guy QB” darling Ben Roethlisberger, a world-class rapist who, when he’s not too busy sexually assaulting young women, remains the face of the Pittsburgh Steelers, one of the NFL’s most storied and hallowed franchises.
Standing out and refusing to be silent
So what does all this tell us about Kaepernick’s situation? It’s simple, really.
It’s not that the NFL doesn’t want its players to speak. It’s that it doesn’t want its players to speak about things that matter.
It’s not that Kaepernick speaks up on behalf of oppressed communities. It’s that Kaepernick directly confronts the forces that engage in such oppression.
It’s not that Kaepernick isn’t an NFL quarterback. It’s that Kaepernick isn’t a silent, smiling NFL quarterback basking in the glow of his multi-million dollar toys and endorsement deals.
What the NFL really wants is a league full of Tom Bradys: White, smiling yes-men who date supermodels and say things like, “What’s going on in the world? I haven’t paid much attention. I’m just a positive person.”
Tom Brady is a hero and an icon, hailed as perhaps the greatest QB to ever play the game. But while his accomplishments on the field are second to none, he remains a privileged, narcissistic, Trump-loving mush-head who has zero interest in the communities from which many of his on-field teammates hail.
In contrast, Kaepernick has donated hundreds of thousands of dollars to worthy, grassroots organizations working in communities of color. Just in March and April, Kaepernick’s donations included, but were not limited to:
Life After Hate, Inc. – an organization that works with individuals and organizations dealing with racism and intolerance ($50,000).
Leaders of a Beautiful Struggle – a Baltimore-based group that works to improve living conditions for black communities in Baltimore.
Silence is Violence – a New Orleans-based group that works to build a “safe and equitable New Orleans.”
Assata’s Daughters – a Chicago group that focuses on black female empowerment in the tradition of Assata Shakur ($25,000).
H.O.M.E. (Helping Oppressed Mothers Endure) – a Georgia-based group that is using Kap’s donation to purchase beds for single mothers and their children ($25,000).
Grassroots Leadership (Texas Advocates for Justice) – Four weekend-long intensive workshops with community members who have been incarcerated. The goal of TAJ workshops is to develop leadership in the movement to confront mass incarceration and end reliance on the criminal justice system by training approximately 30 new Texas Advocates for Justice members in each workshop ($25,000).
American Friends Service Committee Arizona – covering the costs of behavioral health treatment for formerly incarcerated/convicted people participating in AFSC programs.
It should also be noted that Kap spearheaded a campaign to secure a plane, as well as food, water and other supplies, for the people of Somalia. The campaign raised more than $1 million in its first 24 hours. As Kap announced at the time via Instagram:
We got the plane! Now it's time to raise money to help get food and water to the people of Somalia. You can donate on the go fund me page, the link is in my bio. This was done out of Love, so we are using the hashtag #LoveArmyForSomalia A post shared by colin kaepernick (@kaepernick7) on Mar 17, 2017 at 1:16pm PDT
In hours, Kap was able to achieve what the U.S. government and every multi-billion-dollar corporation and foundation simply could not.
Notice also that the organizations Kap is backing are all community-focused, grassroots groups that will directly apply donations to their initiatives. These are not large non-profit NGOs that pay generous salaries to their management while only distributing a portion of donations to those in need.
Put simply, Kap is directly financing the defense and development of economically marginalized and oppressed communities – something that the NFL itself has always talked about, but never done.
Building a legacy of empowerment and justice
Colin Kaepernick is an NFL QB who deserves a job. He may not be the best QB in the NFL, nor will he be a Hall of Famer whose name will be etched into the history of professional football. If anything, the powers that be would like to see him erased completely.
Unfortunately for the NFL and the cop-worshiping, military fetishists draping themselves in Old Glory (and the Confederate rebel flag), Kaepernick is not going quietly into that good night. He won’t be receding anonymously into obscurity.
No, Kap is making himself a household name for all the right reasons. And the NFL simply cannot stand it.
There are kids in New York City who will go to school in September sporting free backpacks purchased with Kaepernick foundation money. There are single mothers in Georgia who will lie down with their children on beds provided for free thanks to Kaepernick’s donations. There are young black leaders in Baltimore who will help build their community, thanks to Kap’s money.
Kaepernick could never play another NFL game as long as he lives, and he’ll still be a hero and a legend to millions.
For Kap, his legacy is important. It’s just that he’s finally realized that his legacy will be in uplifting oppressed communities, not in his stat line.
He will be remembered not as another quarterback, but as the man who stood up to racism, imperialism and white supremacy, paid for it dearly, and never regretted it for a second.
Top photo | San Francisco 49ers quarterback Colin Kaepernick listens to a question at a news conference after an NFL football game against the Chicago Bears on Sunday, Dec. 4, 2016, in Chicago. The Bears won 26-6. (AP/Charles Rex Arbogast)
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Investigation of the impact of feeding Lactobacillus plantarum CRL 1815 encapsulated in microbially derived polymers on the rat faecal microbiota.
The aim of this study was to evaluate the impact of the administration of microencapsulated Lactobacillus plantarum CRL 1815 with two combinations of microbially derived polysaccharides, xanthan : gellan gum (1%:0·75%) and jamilan : gellan gum (1%:1%), on the rat faecal microbiota. A 10-day feeding study was performed for each polymer combination in groups of 16 rats fed either with placebo capsules, free or encapsulated Lact. plantarum or water. The composition of the faecal microbiota was analysed by fluorescence in situ hybridization and temporal temperature gradient gel electrophoresis. Degradation of placebo capsules was detected, with increased levels of polysaccharide-degrading bacteria. Xanthan : gellan gum capsules were shown to reduce the Bifidobacterium population and increase the Clostridium histolyticum group levels, but not jamilan : gellan gum capsules. Only after administration of jamilan : gellan gum-probiotic capsules was detected a significant increase in Lactobacillus-Enterococcus group levels compared to controls (capsules and probiotic) as well as two bands were identified as Lact. plantarum in two profiles of ileum samples. Exopolysaccharides constitute an interesting approach for colon-targeted delivery of probiotics, where jamilan : gellan gum capsules present better biocompatibility and promising results as a probiotic carrier. This study introduces and highlights the importance of biological compatibility in the encapsulating material election, as they can modulate the gut microbiota by themselves, and the use of bacterial exopolysaccharides as a powerful source of new targeted-delivery coating material.
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48 F.3d 1234NOTICE: Federal Circuit Local Rule 47.6(b) states that opinions and orders which are designated as not citable as precedent shall not be employed or cited as precedent. This does not preclude assertion of issues of claim preclusion, issue preclusion, judicial estoppel, law of the case or the like based on a decision of the Court rendered in a nonprecedential opinion or order.
CORTEX FOUR, INC., Plaintiff-Appellant,v.MARQUETTE ELECTRONICS, INC., Defendant-Appellee.
No. 95-1076.
United States Court of Appeals, Federal Circuit.
Jan. 24, 1995.
DCT
1
DISMISSED.
ORDER
The parties having so agreed, it is
2
ORDERED that the proceeding is DISMISSED under Fed.R.App.P. 42(b).
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The present invention relates to a sheet holding mechanism of an apparatus, such as a copying machine, a printer or the like, for transferring data onto a recording sheet.
Heretofore, copying machines, printers and the like have been known for transferring data onto recording sheet.
Such an apparatus is arranged so that a recording sheet introduced from a recording-sheet introducing port into the apparatus is subjected to a predetermined processing, such as copying, printing and the like before being ejected from a sheet eject port.
An ejection sheet tray is normally attached to one side where the sheet eject port of the apparatus is located and sheets of recording sheet ejected from the sheet exhaust port are placed and stacked on the sheet tray.
However, the sheet tray has to be larger in size than the maximum size of the recording sheet that the apparatus can deal with. Accordingly, the apparatus needs a wide space for installation only because of the sheet tray, despite the fact that the tendency is for the apparatus to be made compact.
In view of the installation space and operability, it is needless to say advantageous if the angle of the sheet tray is freely adjustable. Notwithstanding, difference in angle between the sheet eject from the sheet eject port and the sheet tray may cause sheet-jamming. The problem is that the sheet cannot be ejected onto the sheet tray smoothly.
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The South Region heads to Atlanta for the Sweet 16, with top-seed Kentucky still the favorite to move onto New Orleans. The Wildcats crushed play-in winner Western Kentucky by 15 points, then went bigger and beat Iowa State by 16 in the next round. Meanwhile, Indiana cruised in its first game over New Mexico State and squeezed by last year's Cinderella, VCU, in a very close game to set up a rematch with Kentucky. The bottom of the bracket included one of this year's shocking moments when No. 15 Lehigh took down No. 2 Duke, only the sixth time in NCAA Tournament history that a seed that low won a game. However, Lehigh's road ended there, as it lost by 12 to Sweet 16 participant Xavier, who took down the Fighting Irish of Notre Dame in its first game. The final spot in the Sweet 16 is filled by Baylor, which won its first two games by a combined 25 points, beating No. 14 South Dakota State and No. 11 Colorado to reach Atlanta. With Kentucky eyeing revenge against Indiana, will any of these teams have enough to keep the Wildcats from reaching the Final Four? Let's look at what's ahead.
No. 4 Indiana vs. No. 1 Kentucky
Key Matchup: Kentucky's Terrence Jones against Indiana's Christian Watford. We've all seen the highlight of Watford's remarkable game-winner against the Wildcats on Dec. 10, but what people forget is that Watford led all players in scoring that day with 20 points while Jones and teammate Anthony Davis combined for just 10. This is a much different Kentucky squad, though slowing down Watford will still be the key. Davis is arguably the best defender in the country, but it likely will be Jones who tries to slow Watford, leaving Davis to deal with another talented freshman, Cody Zeller. Jones turned the ball over six times during the teams' first meeting and struggled to find any sort of offensive rhythm, whereas Watford clearly had his way against Big Blue. If Jones, who is averaging 15.0 points and 10.5 rebounds in the NCAA Tournament, can keep close to Watford, the Wildcats should be able to make their way through to the Elite Eight.
Kentucky will Win IF: they can limit the Hoosiers front court. Watford and Zeller have both been solid so far in the NCAA Tournament, and while Jordan Hulls and Will Sheehey have been good contributors, limiting the big men will have a huge impact toward the Wildcats walking away with a victory. Indiana was 11-2 this season when Watford scored at least 15 points (losing at Michigan State and to Wisconsin in the Big Ten Tournament), so Jones and Davis will have to do their best to contain the junior forward. Kentucky has a number of players who can score, such as Doron Lamb, Michael Kidd-Gilchrist and Marquis Teague, so if Jones and Davis focus on the defensive side of the ball, they'll find themselves heading to the Elite Eight.
Indiana will Win IF: it continues to make shots. The Hoosiers were the eighth-best shooting team in the country this season and the second best from three-point land. Meanwhile, Kentucky led the nation in blocked shots, highlighted by Davis' 4.6 per game average. Indiana shot nearly 60 percent from the field and 54 percent from three-point range against New Mexico State and then 52 percent and 46 percent against a very good VCU squad to reach the Sweet 16. If the Hoosiers can keep up the good shooting against another talented defensive team, they'll be in a great position to upset the Wildcats again.
Player to Watch: Kentucky's Anthony Davis. The probable National Player of the Year is a much different player than when these two teams first faced off in early December. He has recorded a double-double in seven of the last nine games and is averaging 15.5 points, 10.5 rebounds, 4.0 assists and 4.5 blocked shots during the NCAA Tournament. He'll have his hands full matching up against either Watford or Zeller, but they'll have a tough time slowing him as well. The Wildcats are undefeated when Davis scores at least 13 points, so if Kentucky can get him going, it should continue to roll.
Prediction: Kentucky was the No. 1 team in the country when it lost to Indiana earlier this season and are the No. 1 team again for this matchup. However, the Wildcats are much better than they were in early December and should be easy favorites in this game. Davis and Jones are peaking at just the right time and while Watford can be a handful, the likes of Kidd-Gilchrist, Lamb and Teague figure to be too much for the Hoosiers to handle. With a number of top teams already bounced from the NCAA Tournament, Kentucky has become a near unanimous national championship favorite and should be able to pass the Hoosiers on its way to New Orleans.
No. 10 Xavier vs. No. 3 Baylor
Key Matchup: Xavier's Tu Holloway vs. Baylor's Brady Heslip. Holloway was a pre-season All-American and had the Musketeers to a ranking as high as No. 8 in the country before the ugly brawl with Cincinnati knocked their season off track. However, he turned it around just in time for the NCAA Tournament and is a trouble spot for Baylor, and especially Heslip. Heslip, though, has been a solid scorer of his own lately. While the Xavier star is averaging 23.0 points per game in the Tournament, Heslip is averaging 22.0, including making 14-of-22 shots from three-point range. Both players can light it up, though Holloway has shown he can shut down opposing guards, such as when he forced Lehigh's C.J. McCollum to miss 17-of-22 shots during their third-round matchup. If Holloway can do the same to Heslip, Xavier could take home the victory; if not, Baylor will advance.
Xavier will Win IF: Kenny Frease can dominate the paint. The 7-footer did just that against Lehigh to the tune of 25 points and 12 rebounds, shooting 11-of-13 from the field. The Baylor front line of Quincy Acy and Perry Jones III is very talented, though they could very well struggle trying to stop such a big load. Holloway will get his shots, but if Frease can get consistent looks near the bucket, the Musketeers will have a great shot of advancing to the Elite Eight.
Baylor will Win IF: its guards can continue to produce. Heslip has been lethal from three-point land lately, and Pierre Jackson has done an excellent job of running the show for the Bears. While Baylor has some great athletes in the frontcourt, it's the guards who make the team roll. If they can keep Tu Holloway from getting hot, while putting in some buckets of their own, Baylor has a great chance to move on.
Player to Watch: Baylor's Perry Jones III. The Bears are simply a different team when Jones is making shots, as evidenced by their back-to-back wins in the Big 12 Tournament when Jones dropped a 31-11 against Kansas State and then an 18-7 against Kansas the day after. He has tremendous upside and likely will be an NBA lottery pick, but he's far from a consistent player, which has limited Baylor somewhat this season. Xavier doesn't have a great defensive matchup for him, so if Jones can get going, Baylor could very well advance to the Elite Eight.
Prediction: Xavier isn't as much of an underdog as you'd expect in a No. 10 vs. No. 3 matchup. The Musketeers were a top-10 team earlier in the season and seem to be putting it all together in the NCAA Tournament. However, Baylor has been ranked consistently this season and has a solid starting five that can compete with almost anyone. Jackson has done a great job of leading the Bears lately, including a 15-point, 10-assist effort against Colorado in the third round. He and Heslip should be enough to overcome anything Holloway can throw at them, bringing the Bears into the Elite Eight.
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Drosophila reproductive behavior will be studied using genetic tools. Questions on the control, by the various parts of the nervous system, of different features of courtship will be asked with genetic mosaics (following up our earlier studies). What parts of the dorsal brain must be male to allow the early steps of courtship to be performed? Are intermediate steps of courtship controlled by the brain, and if so, by the same parts? The later steps of courtship are controlled by male thoracic tissues: is the thoracic ganglion critically involved in such control? For female behaviors, which tissues must have a female genotype in order that a mosaic be receptive to courtship and copulation, or be able to carry out the post-copulation rejection behaviors? -- Several behavioral mutants affecting courtship have been characterized by behavioral observation and manipulation. Different mutants influence the early, middle, or late stages of courtship sequence. The causes of these reproductive defects will be analyzed, beginning with studies of mosaics: For instance, where in the fly must a small genetic duplication--carrying the normal allele of a gene involved in aberrant male-female and male-male interactions--be present in order that normal behavior occur? Some of the experiments here, on mutants and mosaics, will concern the possible genetic control of particular neural oscillators--those that drive motor output in the courtship lovesong. Also, we are dissecting the control of copulation--its basic duration, the relationship of that duration to sperm transfer, and the details of actions involved in its termination. -- The various mutants may affect the development or the functioning of the nervous system. In this light, we will analyze conditional alleles of certain of the mutants, to ask which stage of the life cycle is influenced by the genetic variants. -- We are asking several questions on triggers and inhibitions of courtship behaviors, influenced by putative pheromones. These experiments are related, not only to studies of normal males and females, but also very strongly to the investigations of behavioral mutants, and to the behavioral dissection of the brain in genetic mosaics.
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<html><head><style type='text/css'>body { font-family: 'Arial'; font-size: 10pt; color: #000000}</style></head><body>Using Mofi I can see my access point and when I tap on "connect to AP" it seems to connect (the circle changes from grey to orange) but I don't see an IP address. If I open a terminal and run ifconfig all I have is eth0, lo, and usb0.<br><br><br></body></html>
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Q:
Philips #00 screwdriver for MacBook Pro 2013 NZ does not fit
I need to remove the back plane of an early 2013 MacBook Pro, sold in New Zealand.
According to questions on here:
What screwdriver size is needed for MacBook Pro mid 2012 back cover?
Screwdriver for 13-inch MacBook Pro
I need a Philips #00 screwdriver, which I bought as part of this set:
https://www.mitre10.co.nz/shop/fuller-mini-ratchet-screwdriver-set-12-piece-black-and-yellow/p/125687?gclid=EAIaIQobChMI6r23zfPW2wIVlY2PCh0H7QxNEAQYCCABEgKXaPD_BwE&gclsrc=aw.ds
However, the screwdriver doesn't fit. Specifically it seems the blades of it are actually to thick to get into the screws.
Is this something I can specify as part of the screwdriver to look for? Or is size #00 possibly different in different parts of the world?
A:
I've seen occasional mismatches in sets for $20 in the US and certainly some really bad $10 sets in the US. Not knowing the relative prices I don't know if that's expensive for New Zealand. My gold standard is a wiha tool.
https://www.kctoolco.com/wiha-26100-00-x-40mm-precision-phillips-screwdriver/ for $5 US
I would get a good tool for the ones you'll use a lot like #00 and if you can afford it - a nice set. Another gold standard seller for me in the US is DigiKey Electronics: Here's their #00 Phillips selection
Hopefully this lets you evaluate if you got a dud blade or just a low quality set in general. If it's really not able to fit - contact your seller to get advice if you can.
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BOTANICAL NAME:
Family:
Status:
Star thistle is declared noxious in the Southern Tablelands and South East Region only in Bombala LCA, in class 4, although it can be quite common elsewhere on the tablelands.
Description
Most thistles are erect single-stemmed or branching biennial herbs ranging from 30cm to 2m high depending on species and growing conditions. They are characterised by having long spines on the leaf margins and stems. The plant begins life as a rosette, from which an elongated flowering stem arises. Flower heads consist of numerous small flowers clustered into cylindrical or hemispherical heads at the branch tips, and surrounded by spiny bracts. Flower colour is pink to purple for most of the species found in the region, except for a few with yellow flowers.
Star thistle is distinctive in often being quite short (about 40cm), though it may reach 1m high, and densely branched from the base. The rosette leaves are narrow, grey-green, deeply lobed right to the central vein (midrib) and not spiny. The purple flower heads are enclosed in bracts which have extremely long bone coloured spines. For additional thistle photos, check the entries for Scotch thistle, nodding thistle and soldier thistle.
preferred habitat and impacts
Thistles are invasive weeds of pasture, reducing carrying capacity. The broad flat rosette habit in the early stages of growth smothers surrounding grass plants, and the density of stands which can occur after disturbance such as over-grazing or cultivation can choke out all other vegetation. Unpalatable to stock because of the spines, they are favoured by heavy grazing. The spiny nature of thistle plants restricts stock and human movement in infested pasture.
Thistles are a more troublesome weed in the drier tablelands and slopes of southern NSW than on the coast, and more species are present in these areas. Black or spear thistle is the most common thistle found on both the coast and the tablelands, but other thistle species are quite uncommon on the coast.Thistles are also environmental weeds, invading grasslands and grassy woodlands.
dispersal
Seed of star thistle lacks the tuft of fine hairs which aids wind dispersal in some thistle species, so is mostly moved around by water, in soil and on animals, vehicles and machinery. The seed tends to stay in the spiny heads and the long spines help these to adhere to animals, bags, machinery and so on.
look-alikes
All thistles are broadly similar in appearance and star thistle is distinguished by its compact habit, spineless leaves and the long bone coloured spines on the bracts. Its rosette leaves are similar to other thistles in the genus Centaurea, of which the commonest locally is St Barnaby's thistle (Centaurea solstitialis). However, it has yellow flowers and less ferocious spines.
Some plants have a resemblance to thistles although they are not closely related. The weed Mexican poppy (Argemone ochroleuca) has thistle-like spiny foliage which is silvery grey in colour. It is in the poppy family, and has a cream coloured poppy flower and a prickly seed capsule which splits at the top to release numerous small black seeds. It grows to about 1m high. Wild teazel (Dipsacus fullonum) has more elongated cylindrical heads of mauve flowers with long spiny bracts at the base, and short prickles on stems and the vein on the leaf underside, but not on leaf margins. It is also a weed.
There is a native plant with thistle-like foliage, the blue devil (Eryngium rostratum). It is a plant of native grasslands and grassy woodlands on the tablelands and slopes, and is very unlikely to be found on the coast. It has blue flowers in branched heads, and is not in the daisy family. Its leaves are narrow, deeply lobed with very narrow lobes and not spiny, so young plants could be mistaken for star thistle.
control
Small infestations of thistles can be chipped out, but may regrow if the cut is not made deeply enough. Hold the top of the plant down to the ground with one foot to get the spiny leaves away from your hands while chipping, or catch them while still in the rosette stage, when they are very much easier to cut. Spot spraying or boom spraying can be used for larger infestations. Slashing can be effective on star thistle but viable seed may form on the cut plants if slashing is done after heads have been fertilised.
Goats and donkeys may help reduce seed-set by eating the flowers, although the very long spines of star thistle might prove a better deterrent to browsing than the shorter spines of most other species.
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1971–72 Nationalliga A season
The 1971–72 Nationalliga A season was the 34th season of the Nationalliga A, the top level of ice hockey in Switzerland. Eight teams participated in the league, and HC La Chaux-de-Fonds won the championship.
First round
Final round
Relegation
External links
Championnat de Suisse 1971/72
Swiss
Category:National League (ice hockey) seasons
Category:1971–72 in Swiss ice hockey
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Rahm Emanuel for president? Not so fast
Mayor Rahm Emanuel of Chicago, who left a dream job as President Barack Obama's Chief of Staff, has been rumored as a possible contender for the 2016 Democratic party presidential nomination, along with Hillary Clinton. While it cites the acerbic Emanuel's prowess in fundraising and politics, and his media contacts as reasons for possibly succeeding his former boss, the post had more to say:
Emanuel allies insist that he has done much good for the city but it’s clear from the headlines that the dominant story of his time in office so far is the rising murder rate. The Chicago homicide rate in January was its highest in more than a decade and the Windy City has become a national talking point — and not in a good way — when it comes to violence. There’s been little recent credible polling on Emanuel but he has to have taken a hit from all the negative publicity surrounding the murders. And, even if he hasn’t, it’s hard to imagine Emanuel’s potential 2016 opponents wouldn’t dredge up some of those violence stats if he did make a bid.
Well, now there is recent credible polling on Emanuel, and it’s not good for the mayor. A Crain’s/Ipsos poll out Thursday finds that the mayor’s popularity has fallen sharply since voters were last surveyed in September:
In Chicago, that gives Mr. Emanuel a net minus 16 rating, down from the plus 4 he had in September, when 37 percent approved and 33 percent disapproved.
Notably, the share of those disapproving of Mr. Emanuel's job performance hasn't moved much, going from 33 percent to 35 percent. The big shift has occurred in the “mixed feelings” category — up from 21 percent to 30 percent — and the “not sure” category, which went from 12 percent in September to 16 percent from Feb. 12 to 15, when the survey was conducted.
That may suggest that Mr. Emanuel has paid a political price in battling the Chicago Teachers Union, pushing for government worker pension reform and struggling to reverse a spike in murders that has continued for more than a year.
The Washington Post then speculates that Mayor Emanuel might not want to give up on running for mayor to run for the president's chair. Fighting the teachers union last year over a strike cost him politically, as has the ongoing wave of violence in the City of Broad Shoulders. Rahm would be up for re-election in 2015, thus interfering with the necessary lead time for building a presidential bid. Running on a slim chance of a presidential nomination could endanger his chances of winning re-election since his support among unions is currently soft. Democrats contacted by the Washington Post would not dismiss a possible bid for Rahm, but voiced concerns over the "tire tracks" he has left on some opponents in getting what he wants.
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USA lifts some of toughest economic sanctions on Sudan
Saudi Arabia has succeeded in persuading the United States administration to lift economic sanctions imposed on Sudan.
Lifting the sanctions on Sudan is part of a process begun by former President Barack Obama at the end of his term and was opposed by human rights groups.
"Ties between Sudan and USA date back to before Sudan's independence and we are looking forward to fully normalizing relations and we feel that the Americans are now having the same desire", the top diplomat said.
"Sudan regards it as a positive development in the history of the Sudanese-U.S. relations and a natural outcome of a frank, transparent and constructive dialogue that reviewed all concerns between the two countries", it added.
Though Sudan will remain, for now, on the USA list of state sponsors of terrorism, alongside Iran and Syria, and thus subject to other restrictive measures, the new decision reflects a U.S. assessment that the state has made progress in meeting Washington's demands, including cooperation on counter-terrorism, working to resolve internal conflicts and allowing more humanitarian aid into Darfur and other rebellious border areas.
Sudan's President Omar al-Bashir remains wanted by the International Criminal Court for alleged war crimes.
Sudan has previously accused Egypt of opposing the lifting of United Nations sanctions on Sudan over the conflict in its western Darfur region. Officials in Sudan's capital city of Khartoum also agreed not to pursue an arms deals with North Korea, as the sanctions are lifted.
The U.S. had worked to isolate Sudan since the military coup that brought al-Bashir to power in 1989. Last week the Trump administration removed Sudan from its controversial list of countries whose citizens travel to the United States is severely restricted.
Heather Nauert, spokesperson for the US State Department, said in a statement that the decision followed "a focused, 16-month diplomatic effort to make progress with Sudan".
The US state department announced its decision to revoke the penalising measures - in place since 1997 - on Friday. A further round of sanctions was put in place in 2006 in response to Sudanese forces' actions in the troubled Darfur region.
Related:
Cuba says during the second and third visits, it let the US import special equipment and granted access to all facilities. The total of Americans affected has now reached 22, with another medically confirmed case being announced on Tuesday.
Barron split the team lead in tackles with LB Alec Ogletree , each posting seven tackles, according to press-box statistics. The same happened to defensive coordinator Rod Marinelli who had no answers at all for the offensive game plan of McVay's.
While coal is expected to remain the largest source of electricity generation in 2022, its lead over renewables will be halved. By the end of 2016, China had increased its solar PV capacity by almost 800 times, with more than 77 gigawatts now installed.
Officials tell ABC News that the suspect was speeding when he barreled through a police barricade and hit a police officer . Just before midnight, police said , the suspect led officers on a high-speed chase while driving a U-Haul truck.
In the meantime, ICE has stepped up immigration arrests in sanctuary cities, drawing the protest from state and local officials. President Donald Trump's administration ramped up its crackdown on so-called sanctuary cities this week when U.S.
He said: "The tendency is to go with players with first-team experience because you have evidence of how they will react". Michael O'Neill: We were great in the second half, especially after being 2-0 down against that level of opposition.
According to Microsoft's listing, the Samsung Odyssey headset will begin shipping on the 6th of November, with a $499 price tag. Samsung's Oculus Rift and HTC VIVE competitor has officially been listed on Microsoft's store, detailing its specs and price.
Workers at the plant are not allowed to leave the compounds without permission and have no access to telephones or email. Information for this article was contributed by Martha Mendoza, Leonardo Haberkorn, Han Guan Ng, Fu Ting, Kelvin K.
Stephen Paddock's girlfriend Marilou Danley said through her lawyer Wednesday that the Las Vegas gunman was not the man she knew. While Danley was away, Paddock wired $100,000 to an account in the Philippines, according to senior law enforcement officials.
Street Fighter 5 arcade mode coming in January
Extra battle is another new distraction that tasks players with completing timed challenges and win exclusive costumes. Street Fighter fans will be happy to find out that Capcom has confirmed Street Fighter 5: Arcade Edition today.
Yankees To Go With Gray And Sabathia In ALDS Games 1 & 2
That could end up being in Arizona's wheelhouse since power threats such as 1B Paul Goldschmidt, 3B Mike Lamb and RF J.D. The New York Yankees (+1400) stack up well against the Minnesota Twins (+2800) in the wild-card game.
Key Decisions to Bolster Iran-Turkey Cooperation
In the same time-frame, the amount imported from Iraq dropped by 20%, as Iran replaces Iraq as the top supplier to Turkey. In the last week following the Kurdish referendum, Turkey has held joint military exercises with Iraq.
Bale out - Wales without Madrid man for final two qualifiers
Tom Lawrence insists Wales will not be fazed by the loss of talisman Gareth Bale for their final two 2018 World Cup qualifiers. The 28-year-old missed their La Liga game with Espanyol on Sunday but reported to the Wales camp the following morning.
Westbrook signs extension to stay with Thunder
Because of Westbrook's contract extension, there's at least a better chance that George and Anthony will choose do to do the same. George will hit unrestricted free agency next summer, with plenty of buzz circulating around the league about where he'll end up.
Super Nintendo mini-console is your new must-have obsession
With the release of the Super NES Classic on Friday, the videogame giant hopes to replicate the success. minus the supply issues. It comes loaded with 20 plus classic Super NES games , including versions of Super Mario, the Legend of Zelda , and Donkey Kong.
Apple Investigates iPhone 8 Plus Models 'Splitting Open'
Customers will have to recharge with a minimum of Rs 799 per month as monthly recharge on Jio's network to avail the scheme. Flipkart is offering a 52% buyback deal on iPhone 8 and 8 Plus when you will upgrade to a newer iPhone 15 months later.
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This review was presented at the symposium "Molecular and Cellular Mechanisms in Health and Disease", which took place at the Gordon Research Conference on Calcium Signalling ‐ Molecular and Cellular Mechanisms in Health and Disease in Maine, USA, 7--12 June, 2015.
AC
: adenylyl cyclase
B~2~R
: type 2 bradykinin receptor
cAMP
: cyclic adenosine monophosphate
CREB
: cAMP response element‐binding protein
EB3
: end‐binding protein 3
ER
: endoplasmic reticulum
GPCR
: G protein‐coupled receptor
IBC
: IP~3~‐binding core
IP~3~
: inositol 1,4,5‐trisphosphate
IP~3~R
: IP~3~ receptor
IRBIT
: IP~3~R‐binding protein released with IP~3~
M~1~R
: type 1 muscarinic acetylcholine receptor
PKA
: protein kinase A
PLC
: phospholipase C
SD
: suppressor domain
TMD
: transmembrane domain
Introduction {#tjp7102-sec-0020}
============
Ca^2+^ signals within cells are spatially and temporally intricate, allowing them to elicit a multitude of specific downstream effects (Berridge, [2009](#tjp7102-bib-0011){ref-type="ref"}). Inositol 1,4,5‐trisphosphate receptors (IP~3~Rs), the most widely expressed class of intracellular Ca^2+^ channel, release Ca^2+^ from intracellular stores in response to binding of IP~3~ and Ca^2+^ (Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}; Taylor & Tovey, [2010](#tjp7102-bib-0151){ref-type="ref"}). Dual regulation of IP~3~Rs by two essential stimuli, IP~3~ and Ca^2+^, is important because it endows IP~3~Rs with a capacity to propagate Ca^2+^ signals regeneratively by Ca^2+^‐induced Ca^2+^ release, as Ca^2+^ released by an active IP~3~R ignites the activity of adjacent IP~3~Rs that have bound IP~3~ (Smith & Parker, [2009](#tjp7102-bib-0136){ref-type="ref"}). This in turn plays a key role in defining the spatial organization of IP~3~‐evoked Ca^2+^ signals.
Activation of IP~3~Rs is initiated by binding of IP~3~ within a clam‐like structure, the IP~3~‐binding core (IBC) (Bosanac *et al*. [2002](#tjp7102-bib-0016){ref-type="ref"}), located near the N‐terminus of each IP~3~R subunit. Binding of IP~3~ causes a conformational change that rearranges the association of the IBC with the N‐terminal suppressor domain (SD). These changes are proposed to disrupt interactions between the N‐terminal regions of the four subunits of the IP~3~R, leading to opening of the channel. The latter is formed by transmembrane domains (TMDs) towards the C‐terminus of each IP~3~R subunit (Seo *et al*. [2012](#tjp7102-bib-0131){ref-type="ref"}) (Fig. [1](#tjp7102-fig-0001){ref-type="fig"}). It is not yet clear where binding of Ca^2+^ to the IP~3~R lies within the sequence of events linking binding of IP~3~ to channel gating. One possibility is that the conformational changes evoked by binding of IP~3~ expose a site to which Ca^2+^ must bind before the channel can open (Marchant & Taylor, [1997](#tjp7102-bib-0087){ref-type="ref"}; Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}). However, neither the structural identity of this stimulatory Ca^2+^‐binding site, nor that of the inhibitory site through which higher concentrations of Ca^2+^ inhibit IP~3~Rs have been resolved. The inhibitory site may reside on an accessory protein associated with IP~3~Rs.
{ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"}.](TJP-594-2849-g002){#tjp7102-fig-0001}
IP~3~Rs are present in almost all animal cells and some protozoa (Prole & Taylor, [2011](#tjp7102-bib-0118){ref-type="ref"}), but there are no homologous proteins in plants (Wheeler & Brownlee, [2008](#tjp7102-bib-0173){ref-type="ref"}) or fungi (Prole & Taylor, [2012](#tjp7102-bib-0119){ref-type="ref"}). The genomes of vertebrates encode three subtypes of IP~3~R subunit (IP~3~R1--3), which can form homo‐tetrameric or hetero‐tetrameric channels (Joseph *et al*. [1995](#tjp7102-bib-0065){ref-type="ref"}) with differing properties and distributions (Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}; Mikoshiba, [2007](#tjp7102-bib-0094){ref-type="ref"}). In mammalian cells, IP~3~Rs have been reported to release Ca^2+^ mainly from the endoplasmic reticulum (ER) (Streb *et al*. [1984](#tjp7102-bib-0139){ref-type="ref"}; Volpe *et al*. [1985](#tjp7102-bib-0166){ref-type="ref"}), but the Golgi apparatus (Pinton *et al*. [1998](#tjp7102-bib-0117){ref-type="ref"}) and secretory vesicles (Yoo, [2011](#tjp7102-bib-0181){ref-type="ref"}) also respond to IP~3~. Although IP~3~ initiates Ca^2+^ signals by stimulating Ca^2+^ release from intracellular stores, the signals are sustained by Ca^2+^ entry across the plasma membrane. That too is indirectly regulated by IP~3~, because store‐operated Ca^2+^ entry is stimulated by loss of Ca^2+^ from the ER (Parekh & Putney, [2005](#tjp7102-bib-0112){ref-type="ref"}; Lewis, [2012](#tjp7102-bib-0078){ref-type="ref"}). Ca^2+^ signals initiated by IP~3~Rs evoke a wide variety of cellular events, ranging from embryological development (Kume *et al*. [1997](#tjp7102-bib-0075){ref-type="ref"}; Uchida *et al*. [2010](#tjp7102-bib-0161){ref-type="ref"}) to cellular metabolism (Cardenas *et al*. [2010](#tjp7102-bib-0022){ref-type="ref"}), gluconeogenesis (Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}), exocrine secretion (Futatsugi *et al*. [2005](#tjp7102-bib-0042){ref-type="ref"}) and neuronal function (Matsumoto *et al*. [1996](#tjp7102-bib-0088){ref-type="ref"}).
Specificity within Ca^2+^ signalling pathways, or indeed any signalling pathway (Scott & Pawson, [2009](#tjp7102-bib-0130){ref-type="ref"}; Scott *et al*. [2013](#tjp7102-bib-0129){ref-type="ref"}), is achieved, in part, by the formation of macromolecular signalling complexes. Within the signalling pathways that involve phospholipase C (PLC), these complexes regulate the activity of IP~3~Rs, their distribution, and their association with both the plasma membrane receptors that evoke IP~3~ formation and the downstream targets of the Ca^2+^ released by IP~3~Rs (Konieczny *et al*. [2012](#tjp7102-bib-0073){ref-type="ref"}). The interactions of IP~3~Rs with other proteins have been reviewed previously (Choe & Ehrlich, [2006](#tjp7102-bib-0029){ref-type="ref"}; Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}; Mikoshiba, [2007](#tjp7102-bib-0094){ref-type="ref"}; Vanderheyden *et al*. [2009](#tjp7102-bib-0162){ref-type="ref"} *a*), but continued progress and the advent of high‐throughput proteomics methods (Havugimana *et al*. [2012](#tjp7102-bib-0049){ref-type="ref"}; Rolland *et al*. [2014](#tjp7102-bib-0123){ref-type="ref"}) suggest that an update is timely.
Searches of proteomic databases and published literature reveal a large number of proteins that form complexes with IP~3~Rs (Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"}). For some of these proteins, the regions within IP~3~Rs that are important for the interaction have been mapped (Fig. [1](#tjp7102-fig-0001){ref-type="fig"}). At the outset, it is worth sounding some notes of caution regarding the reported interactions. Firstly, it is often difficult to establish that two proteins interact directly, rather than via intermediate proteins. Many of these complexes may, therefore, be formed by direct or indirect interactions of IP~3~Rs with other proteins. For example, association of protein phosphatase 1 with IP~3~Rs may be mediated in part by IRBIT (IP~3~R‐binding protein released with IP~3~), which binds directly to both proteins (Ando *et al*. [2014](#tjp7102-bib-0002){ref-type="ref"}). Secondly, the interactions and their effects may depend on the cellular context, including such factors as the subtype of IP~3~R, the physiological status of the IP~3~R (e.g. phosphorylation), the cell type and the expression levels of the interacting proteins and IP~3~Rs. Thirdly, interactions that occur in cellular lysates may be precluded within intact cells. For example, the interaction of two proteins may be prevented by their physical separation within the cell or by mutually exclusive binding of other proteins or ligands. IRBIT, for example, binds to IP~3~R subunits only when they have no IP~3~ bound. Lastly, some forms of experimental evidence are more discriminating than others, and it will be necessary to verify the putative interactions indicated by methods such as yeast two‐hybrid screening and mass spectrometry.
######
Proteins that form complexes with IP~3~Rs and enhance their activity
Protein References
--------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Effective delivery of messengers
Adenylyl cyclase 6 (AC6) Tovey *et al*. [2008](#tjp7102-bib-0156){ref-type="ref"}
Bradykinin receptor B~2~ (B~2~R) Delmas *et al*. [2002](#tjp7102-bib-0032){ref-type="ref"}; Jin *et al*. [2013](#tjp7102-bib-0063){ref-type="ref"}
Epidermal growth factor receptor (EGFR) Hur *et al*. [2005](#tjp7102-bib-0059){ref-type="ref"}
Erythropoietin receptor (EPO‐R) Tong *et al*. [2004](#tjp7102-bib-0155){ref-type="ref"}
Glyceraldehyde‐3‐phosphate dehydrogenase (GAPDH) Patterson *et al*. [2005](#tjp7102-bib-0114){ref-type="ref"}
Metabotropic glutamate receptor 1 (mGluR1;GRM1) Tu *et al*. [1998](#tjp7102-bib-0160){ref-type="ref"}
Phospholipase C‐β1 (PLCβ1) Shin *et al*. [2000](#tjp7102-bib-0132){ref-type="ref"}
Phospholipase C‐β4 (PLCβ4) Nakamura *et al*. [2004](#tjp7102-bib-0103){ref-type="ref"}
Phospholipase C‐γ1 (PLCγ1) Tong *et al*. [2004](#tjp7102-bib-0155){ref-type="ref"}; Yuan *et al*. [2005](#tjp7102-bib-0185){ref-type="ref"}
Protease‐activated receptor 2 (PAR‐2) Jin *et al*. [2013](#tjp7102-bib-0063){ref-type="ref"}
Sensitization to IP~3~/Ca^2^ ***^+^***
Bcl‐2 (B‐cell lymphoma 2)[a](#tjp7102-tbl1-note-0001){ref-type="fn"} Chen *et al*. [2004](#tjp7102-bib-0026){ref-type="ref"}; Eckenrode *et al*. [2010](#tjp7102-bib-0036){ref-type="ref"}; Monaco *et al*. [2012](#tjp7102-bib-0097){ref-type="ref"}; Chang *et al*. [2014](#tjp7102-bib-0023){ref-type="ref"}
Bcl‐X~L~ (B‐cell lymphoma extra large) White *et al*. [2005](#tjp7102-bib-0174){ref-type="ref"}; Eckenrode *et al*. [2010](#tjp7102-bib-0036){ref-type="ref"}; Monaco *et al*. [2012](#tjp7102-bib-0097){ref-type="ref"}
Chromogranin A (CGA) Yoo & Lewis, [1998](#tjp7102-bib-0182){ref-type="ref"}; Thrower *et al*. [2002](#tjp7102-bib-0153){ref-type="ref"}
Chromogranin B (CGB; secretogranin‐1) Yoo & Lewis, [2000](#tjp7102-bib-0183){ref-type="ref"}; Thrower *et al*. [2003](#tjp7102-bib-0152){ref-type="ref"}
Cyclin‐A Soghoian *et al*. [2005](#tjp7102-bib-0138){ref-type="ref"}
Cyclin‐B1 (CYB) Malathi *et al*. [2003](#tjp7102-bib-0085){ref-type="ref"}; Malathi *et al*. [2005](#tjp7102-bib-0086){ref-type="ref"}
Cyclin‐dependent kinase 1 (CDK1) Malathi *et al*. [2003](#tjp7102-bib-0085){ref-type="ref"}; Malathi *et al*. [2005](#tjp7102-bib-0086){ref-type="ref"}
Cytochrome *c* ~1~ Boehning *et al*. [2004](#tjp7102-bib-0013){ref-type="ref"}
Fyn (tyrosine‐protein kinase) Jayaraman *et al*. [1996](#tjp7102-bib-0062){ref-type="ref"}; Cui *et al*. [2004](#tjp7102-bib-0031){ref-type="ref"}
Glucosidase 2 subunit β (80K‐H) Kawaai *et al*. [2009](#tjp7102-bib-0067){ref-type="ref"}
Glycogen synthase kinase‐3β (GSK3β) Gomez *et al*. [2016](#tjp7102-bib-0045){ref-type="ref"}
Huntingtin‐associated protein 1 (HAP‐1) Tang *et al*. [2003](#tjp7102-bib-0148){ref-type="ref"} *b*
Huntingtin (HTT) (with poly‐Q expansion, HTT^exp^)[b](#tjp7102-tbl1-note-0001){ref-type="fn"} Tang *et al*. [2003](#tjp7102-bib-0148){ref-type="ref"} *b*
Lyn (tyrosine‐protein kinase) Yokoyama *et al*. [2002](#tjp7102-bib-0180){ref-type="ref"}
Mcl‐1 (myeloid cell leukemia‐1) Eckenrode *et al*. [2010](#tjp7102-bib-0036){ref-type="ref"}
mTOR (mammalian target of rapamycin) Fregeau *et al*. [2011](#tjp7102-bib-0040){ref-type="ref"}
Neuronal Ca^2+^ sensor 1 (NCS‐1) Schlecker *et al*. [2006](#tjp7102-bib-0126){ref-type="ref"}
Polo‐like kinase 1 (PLK1) Ito *et al*. [2008](#tjp7102-bib-0061){ref-type="ref"}; Vanderheyden *et al*. [2009](#tjp7102-bib-0163){ref-type="ref"} *b*
Presenilin‐1/Presenilin‐2 (PS‐1/PS‐2) Cheung *et al*. [2008](#tjp7102-bib-0028){ref-type="ref"}
Protein kinase A (PKA; cAMP‐dependent protein kinase) Ferris *et al*. [1991](#tjp7102-bib-0037){ref-type="ref"}; Bruce *et al*. [2002](#tjp7102-bib-0019){ref-type="ref"}
Receptor of activated protein kinase C1 (RACK1) Patterson *et al*. [2004](#tjp7102-bib-0113){ref-type="ref"}
Rho‐associated protein kinase (ROCK) Singleton & Bourguignon, [2002](#tjp7102-bib-0134){ref-type="ref"}
TRISK 32 (cardiac triadin TRISK 32 isoform) Olah *et al*. [2011](#tjp7102-bib-0108){ref-type="ref"}
Direct activation of IP~3~Rs
Ca^2+^‐binding protein 1 (CaBP1)[c](#tjp7102-tbl1-note-0001){ref-type="fn"} Yang *et al*. [2002](#tjp7102-bib-0179){ref-type="ref"}; Li *et al*. [2013](#tjp7102-bib-0079){ref-type="ref"}
CIB1 (Ca^2+^ and integrin‐binding protein 1; calmyrin)[c](#tjp7102-tbl1-note-0001){ref-type="fn"} White *et al*. [2006](#tjp7102-bib-0175){ref-type="ref"}
Gβγ complex Shin *et al*. [2000](#tjp7102-bib-0132){ref-type="ref"}; Zeng *et al*. [2003](#tjp7102-bib-0187){ref-type="ref"}
Other
DARPP‐32 (protein phosphatase 1 regulatory subunit 1B) Chang *et al*. [2014](#tjp7102-bib-0023){ref-type="ref"}
DHHC6 Fredericks *et al*. [2014](#tjp7102-bib-0039){ref-type="ref"}
EB3 (end‐binding protein 3) Geyer *et al*. [2015](#tjp7102-bib-0044){ref-type="ref"}
GRP‐78 (78 kDa glucose‐regulated protein; BiP) Higo *et al*. [2010](#tjp7102-bib-0052){ref-type="ref"}
Phosphatidylinositol trisphosphate 3‐phosphatase (PTEN) Bononi *et al*. [2013](#tjp7102-bib-0015){ref-type="ref"}
Selenoprotein K (SELK) Fredericks *et al*. [2014](#tjp7102-bib-0039){ref-type="ref"}
Data for Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"} were derived from manual searches of the literature, reviews (Choe & Ehrlich, [2006](#tjp7102-bib-0029){ref-type="ref"}; Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}; Mikoshiba, [2007](#tjp7102-bib-0094){ref-type="ref"}; Vanderheyden *et al*. [2009](#tjp7102-bib-0162){ref-type="ref"} *a*) and databases, including BioGRID (Chatr‐Aryamontri *et al*. [2015](#tjp7102-bib-0024){ref-type="ref"}) and IntAct (Orchard *et al*. [2013](#tjp7102-bib-0109){ref-type="ref"}). The nomenclature of proteins shown is consistent with the human homologues, although some data are derived from interactions of IP~3~Rs and proteins from other species. ^a^Some studies report sensitization of IP~3~Rs by Bcl‐2, while others report inhibition. ^b^HTT^exp^, but not wild‐type HTT, sensitizes IP~3~Rs to IP~3~/Ca^2+^. ^c^CaBP1 and CIB1 are also reported to inhibit IP~3~Rs (see Table [2](#tjp7102-tbl-0002){ref-type="table-wrap"}); direct activation seems to occur only transiently, and is controversial.
John Wiley & Sons, Ltd.
######
Proteins that form complexes with IP~3~Rs and inhibit their activity
Protein References
--------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Proteins that bind reversibly and disrupt activation by IP~3~ and/or Ca^2+^
Ankyrin‐R (ANK1) Bourguignon *et al*. [1993](#tjp7102-bib-0018){ref-type="ref"}; Joseph & Samanta, [1993](#tjp7102-bib-0066){ref-type="ref"}
Bcl‐2 (B‐cell lymphoma 2)[a](#tjp7102-tbl2-note-0001){ref-type="fn"} Chen *et al*. [2004](#tjp7102-bib-0026){ref-type="ref"}; Monaco *et al*. [2012](#tjp7102-bib-0097){ref-type="ref"}; Chang *et al*. [2014](#tjp7102-bib-0023){ref-type="ref"}
Ca^2+^‐binding protein 1 (CaBP1)[b](#tjp7102-tbl2-note-0001){ref-type="fn"} Yang *et al*. [2002](#tjp7102-bib-0179){ref-type="ref"}; Li *et al*. [2013](#tjp7102-bib-0079){ref-type="ref"}
Calmodulin (CaM) Maeda *et al*. [1991](#tjp7102-bib-0083){ref-type="ref"}; Yamada *et al*. [1995](#tjp7102-bib-0178){ref-type="ref"}
Carbonic anhydrase‐related protein (CARP; CA8) Hirota *et al*. [2003](#tjp7102-bib-0054){ref-type="ref"}
Caspase‐3 Hirota *et al*. [1999](#tjp7102-bib-0055){ref-type="ref"}
CIB1 (Ca^2+^ and integrin‐binding protein 1; calmyrin)[b](#tjp7102-tbl2-note-0001){ref-type="fn"} White *et al*. [2006](#tjp7102-bib-0175){ref-type="ref"}
DANGER (IP~3~R‐interacting protein) van Rossum *et al*. [2006](#tjp7102-bib-0164){ref-type="ref"}
ERp44 (endoplasmic reticulum resident protein 44) Higo *et al*. [2005](#tjp7102-bib-0053){ref-type="ref"}
FKBP1A (FK506‐binding protein 1A; FKBP12) Cameron *et al*. [1995](#tjp7102-bib-0021){ref-type="ref"} *b*
GIT1/GIT2 (ARF GTPase‐activating protein 1/2) Zhang *et al*. [2009](#tjp7102-bib-0188){ref-type="ref"}
IRBIT (IP~3~‐binding protein released with IP~3~) Ando *et al*. [2003](#tjp7102-bib-0003){ref-type="ref"}
K‐Ras Sung *et al*. [2013](#tjp7102-bib-0142){ref-type="ref"}
MRVI1 (IRAG; IP~3~R‐associated cGMP kinase substrate) Schlossman *et al*. [2000](#tjp7102-bib-0127){ref-type="ref"}
Nuclear protein localization protein 4 homologue (NPL4) Alzayady *et al*. [2005](#tjp7102-bib-0001){ref-type="ref"}
Polycystin‐1 (PC1; TRPP1) Li *et al*. [2005](#tjp7102-bib-0080){ref-type="ref"}
Proteins that post‐translationally modify IP~3~Rs
AKT1 (RAC‐α serine/threonine protein kinase; PKB) Khan *et al*. [2006](#tjp7102-bib-0069){ref-type="ref"}; Szado *et al*. [2008](#tjp7102-bib-0144){ref-type="ref"}
Ca^2+^/calmodulin‐dependent protein kinase II (CaMKII) Ferris *et al*. [1991](#tjp7102-bib-0037){ref-type="ref"}; Bare *et al*. [2005](#tjp7102-bib-0008){ref-type="ref"}
Calpain Μagnusson *et al*. [1993](#tjp7102-bib-0084){ref-type="ref"}; Wojcikiewicz & Oberdorf, [1996](#tjp7102-bib-0176){ref-type="ref"}
E3 ubiquitin ligase AMFR (GP78)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Pearce *et al*. [2007](#tjp7102-bib-0115){ref-type="ref"}
E3 ubiquitin ligase RNF170[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Lu *et al*. [2011](#tjp7102-bib-0081){ref-type="ref"}
Erlin‐1/Erlin‐2 (SPFH domain‐containing protein 1/2)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Pearce *et al*. [2007](#tjp7102-bib-0115){ref-type="ref"}; Pearce *et al*. [2009](#tjp7102-bib-0116){ref-type="ref"}
MAPK1/MAPK3 (mitogen‐activated protein kinase 1/3) Bai *et al*. [2006](#tjp7102-bib-0007){ref-type="ref"}
Protein phosphatase 1A (PP1A) Tang *et al*. [2003](#tjp7102-bib-0149){ref-type="ref"} *a*; Chang *et al*. [2014](#tjp7102-bib-0023){ref-type="ref"}
Transglutaminase‐2 (TGM2) Hamada *et al*. [2014](#tjp7102-bib-0047){ref-type="ref"}
Transitional endoplasmic reticulum ATPase (p97)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Alzayady *et al*. [2005](#tjp7102-bib-0001){ref-type="ref"}
Ubiquitin[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Bokkala & Joseph, [1997](#tjp7102-bib-0014){ref-type="ref"}; Oberdorf *et al*. [1999](#tjp7102-bib-0107){ref-type="ref"}
Ubiquitin‐conjugating enzyme E2 7 (UBC7)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Webster *et al*. [2003](#tjp7102-bib-0171){ref-type="ref"}
Ubiquitin conjugation factor E4A (UFD2)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Alzayady *et al*. [2005](#tjp7102-bib-0001){ref-type="ref"}
Ubiquitin fusion degradation 1 protein (UFD1)[c](#tjp7102-tbl2-note-0001){ref-type="fn"} Alzayady *et al*. [2005](#tjp7102-bib-0001){ref-type="ref"}
Bcl‐2 has also been reported to sensitize IP~3~Rs to IP~3~/Ca^2+^ (see Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}). ^b^CaBP1 and CIB1 may also cause transient activation of IP~3~Rs, although this is controversial (see Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}). ^c^Components of the proteasomal pathway.
John Wiley & Sons, Ltd.
######
Proteins that form complexes with IP~3~Rs and act as downstream effectors
Protein References
---------------------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Anoctamin‐1 (ANO1, Ca^2+^‐activated Cl^−^ channel) Jin *et al*. [2013](#tjp7102-bib-0063){ref-type="ref"}
Calcineurin (CN; protein phosphatase 2B) Cameron *et al*. [1995](#tjp7102-bib-0020){ref-type="ref"} *a*; Chang *et al*. [2014](#tjp7102-bib-0023){ref-type="ref"}
CASK (Ca^2+^/calmodulin‐dependent serine protein kinase) Maximov *et al*. [2003](#tjp7102-bib-0091){ref-type="ref"}
CRTC2 (CREB‐regulated transcription coactivator 2) Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}
IRBIT (IP~3~‐binding protein released with IP~3~)[a](#tjp7102-tbl3-note-0001){ref-type="fn"} Ando *et al*. [2003](#tjp7102-bib-0003){ref-type="ref"}
KCa1.1 (BK~Ca~; large conductance Ca^2+^‐activated K^+^ channel) Zhao *et al*. [2010](#tjp7102-bib-0190){ref-type="ref"}; Mound *et al*. [2013](#tjp7102-bib-0098){ref-type="ref"}
Na^+^/Ca^2+^ exchanger 1 (NCX1) Lencesova *et al*. [2004](#tjp7102-bib-0077){ref-type="ref"}; Mohler *et al*. [2005](#tjp7102-bib-0095){ref-type="ref"}
Orai‐1 (Ca^2+^ release‐activated Ca^2+^ channel 1) Woodard *et al*. [2010](#tjp7102-bib-0177){ref-type="ref"}; Lur *et al*. [2011](#tjp7102-bib-0082){ref-type="ref"}
Plasma membrane Ca^2+^ ATPase (PMCA) Shin *et al*. [2000](#tjp7102-bib-0132){ref-type="ref"}; Huang *et al*. [2006](#tjp7102-bib-0058){ref-type="ref"}
Protein kinase C (PKC) Ferris *et al*. [1991](#tjp7102-bib-0037){ref-type="ref"}; Rex *et al*. [2010](#tjp7102-bib-0122){ref-type="ref"}
SERCA 2B/3 (sarco/endoplasmic reticulum Ca^2+^‐ATPase) Redondo *et al*. [2008](#tjp7102-bib-0121){ref-type="ref"}
STIM1 (stromal interaction molecule 1) Santoso *et al*. [2011](#tjp7102-bib-0124){ref-type="ref"}
TRPC1‐7 (transient receptor potential canonical channels) Boulay *et al*. [1999](#tjp7102-bib-0017){ref-type="ref"}; Mery *et al*. [2001](#tjp7102-bib-0093){ref-type="ref"}; Tang *et al*. [2001](#tjp7102-bib-0147){ref-type="ref"}; Yuan *et al*. [2003](#tjp7102-bib-0184){ref-type="ref"}; Tong *et al*. [2004](#tjp7102-bib-0155){ref-type="ref"}
VDAC1 (voltage‐dependent anion channel 1) Szabadkai *et al*. [2006](#tjp7102-bib-0143){ref-type="ref"}
IRBIT also inhibits IP~3~Rs by occluding the IP~3~‐binding site (Table [2](#tjp7102-tbl-0002){ref-type="table-wrap"}).
John Wiley & Sons, Ltd.
######
Other proteins that form complexes with IP~3~Rs
Protein References
-------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Cytoskeletal, scaffolding and adaptor proteins
14‐3‐3 protein zeta/delta (PKC inhibitor protein 1) Angrand *et al*. [2006](#tjp7102-bib-0004){ref-type="ref"}
α‐Actin Sugiyama *et al*. [2000](#tjp7102-bib-0140){ref-type="ref"}
Ankyrin‐B (ANK2) Hayashi & Su, [2001](#tjp7102-bib-0050){ref-type="ref"}; Mohler *et al*. [2004](#tjp7102-bib-0096){ref-type="ref"}; Kline *et al*. [2008](#tjp7102-bib-0070){ref-type="ref"}
AKAP9 (A‐kinase anchor protein 9; Yotiao) Tu *et al*. [2004](#tjp7102-bib-0159){ref-type="ref"}
BANK1 (B‐cell scaffold protein with ankyrin repeats) Yokoyama *et al*. [2002](#tjp7102-bib-0180){ref-type="ref"}
Caveolin‐1 Murata *et al*. [2007](#tjp7102-bib-0100){ref-type="ref"}; Sundivakkam *et al*. [2009](#tjp7102-bib-0141){ref-type="ref"}; Jin *et al*. [2013](#tjp7102-bib-0063){ref-type="ref"}
Coiled‐coil domain‐containing protein 8 Hanson *et al*. [2014](#tjp7102-bib-0048){ref-type="ref"}
Homer 1/2/3 Tu *et al*. [1998](#tjp7102-bib-0160){ref-type="ref"}
EB1 / EB3 (end‐binding protein 1/3)[a](#tjp7102-tbl4-note-0002){ref-type="fn"} Geyer *et al*. [2015](#tjp7102-bib-0044){ref-type="ref"}
KRAP (K‐Ras‐induced actin‐interacting protein) Fujimoto *et al*. [2011](#tjp7102-bib-0041){ref-type="ref"}
LAT (linker of activated T‐cells) deSouza *et al*. [2007](#tjp7102-bib-0034){ref-type="ref"}
Myosin‐2A Walker *et al*. [2002](#tjp7102-bib-0168){ref-type="ref"}; Hours & Mery, [2010](#tjp7102-bib-0057){ref-type="ref"}
Obscurin‐like protein 1 Hanson *et al*. [2014](#tjp7102-bib-0048){ref-type="ref"}
Protein 4.1N (band 4.1‐like protein 1) Maximov *et al*. [2003](#tjp7102-bib-0091){ref-type="ref"}
SEC8 (exocyst complex component) Shin *et al*. [2000](#tjp7102-bib-0132){ref-type="ref"}
SNAP‐29 (synaptosomal‐associated protein 29) Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
α‐Spectrin/β‐spectrin (α/β‐fodrin) Lencesova *et al*. [2004](#tjp7102-bib-0077){ref-type="ref"}
Syntaxin 1B Tanaka *et al*. [2011](#tjp7102-bib-0146){ref-type="ref"}
Talin Sugiyama *et al*. [2000](#tjp7102-bib-0140){ref-type="ref"}
Vimentin Dingli *et al*. [2012](#tjp7102-bib-0035){ref-type="ref"}
Vinculin Sugiyama *et al*. [2000](#tjp7102-bib-0140){ref-type="ref"}
Other proteins
Anaplastic lymphoma kinase (ALK) Crockett *et al*. [2004](#tjp7102-bib-0030){ref-type="ref"}
ARHGAP1 (Rho GTPase‐activating protein 1) Nagaraja & Kandpal, [2004](#tjp7102-bib-0102){ref-type="ref"}
γ‐BBH (γ‐butyrobetaine dioxygenase) Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
Beclin‐1 Vicencio *et al*. [2009](#tjp7102-bib-0165){ref-type="ref"}
BOK (Bcl‐2‐related ovarian killer protein) Schulman *et al*. [2013](#tjp7102-bib-0128){ref-type="ref"}
Calnexin Joseph *et al*. [1999](#tjp7102-bib-0064){ref-type="ref"}
CD44 antigen (heparin sulphate proteoglycan) Singleton & Bourguignon, [2004](#tjp7102-bib-0135){ref-type="ref"}
CEMIP (cell migration‐inducing and hyaluronan‐binding protein) Tiwari *et al*. [2013](#tjp7102-bib-0154){ref-type="ref"}
Cyclophilin D (peptidyl‐prolyl cis‐trans isomerase F) Paillard *et al*. [2013](#tjp7102-bib-0111){ref-type="ref"}
FAM19A4 (chemokine‐like protein TAFA‐4) Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
F‐box and leucine‐rich repeat protein 14 Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
FGL2 (fibrinogen‐like 2) Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
FERM domain‐containing 1 Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
GluRδ2 (ionotropic glutamate receptor δ2) Nakamura *et al*. [2004](#tjp7102-bib-0103){ref-type="ref"}
Golgi anti‐apoptotic protein (GAAP; Lifeguard 4; TMBIM4) de Mattia *et al*. [2009](#tjp7102-bib-0033){ref-type="ref"}
GRP‐75 (glucose‐regulated protein 75; stress‐70 protein) Szabadkai *et al*. [2006](#tjp7102-bib-0143){ref-type="ref"}
Heat shock protein 90 (HSP90) Nguyen *et al*. [2009](#tjp7102-bib-0106){ref-type="ref"}
Junctate Treves *et al*. [2004](#tjp7102-bib-0157){ref-type="ref"}
Lethal(3)malignant brain tumor‐like protein 2 Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
Lymphoid‐restricted membrane protein (LRMP; JAW1) Shindo *et al*. [2010](#tjp7102-bib-0133){ref-type="ref"}
Na^+^/K^+^‐transporting ATPase Mohler *et al*. [2005](#tjp7102-bib-0095){ref-type="ref"}; Yuan *et al*. [2005](#tjp7102-bib-0185){ref-type="ref"}
Neuronal acetylcholine receptor α3 Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
PASK (PAS domain‐containing protein kinase) Schlafli *et al*. [2011](#tjp7102-bib-0125){ref-type="ref"}
Phospholamban Koller *et al*. [2003](#tjp7102-bib-0071){ref-type="ref"}
Polycystin‐2 (PC2; TRPP2) Li *et al*. [2005](#tjp7102-bib-0080){ref-type="ref"}
Protein kinase G1 (PKG1; cGMP‐dependent protein kinase 1) Schlossman *et al*. [2000](#tjp7102-bib-0127){ref-type="ref"}
PTPα (protein tyrosine phosphatase‐α) Wang *et al*. [2009](#tjp7102-bib-0169){ref-type="ref"}
Rab29 (Ras‐related protein Rab7L1) Huttlin *et al*. [2013](#tjp7102-bib-0060){ref-type="ref"}
Rac1 (Ras‐related C3 botulinum toxin substrate 1; TC25) Natsvlishvili *et al*. [2015](#tjp7102-bib-0105){ref-type="ref"}
RhoA Mehta *et al*. [2003](#tjp7102-bib-0092){ref-type="ref"}
Sigma 1 receptor (σ1R) Hayashi & Su, [2001](#tjp7102-bib-0050){ref-type="ref"}; Natsvlishvili *et al*. [2015](#tjp7102-bib-0105){ref-type="ref"}
Sirtuin‐7 Tsai *et al*. [2012](#tjp7102-bib-0158){ref-type="ref"}
c‐Src (proto‐oncogene tyrosine‐protein kinase Src) Jayaraman *et al*. [1996](#tjp7102-bib-0062){ref-type="ref"}; Wang *et al*. [2009](#tjp7102-bib-0169){ref-type="ref"}
STARD13 (StAR‐related lipid transfer protein 13; RhoGAP) Nagaraja & Kandpal, [2004](#tjp7102-bib-0102){ref-type="ref"}
Syndecan‐1 (SYND1; CD138) Maximov *et al*. [2003](#tjp7102-bib-0091){ref-type="ref"}
TESPA1 (thymocyte‐expressed positive selection‐associated protein 1) Matsuzaki *et al*. [2012](#tjp7102-bib-0089){ref-type="ref"}
Both EB1 and EB3 associate with IP~3~Rs, but only EB3 has been shown to be required for effective Ca^2+^ signalling in endothelial cells (Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}) (Geyer *et al*. [2015](#tjp7102-bib-0044){ref-type="ref"}).
John Wiley & Sons, Ltd.
Although we focus on the ability of IP~3~Rs to release Ca^2+^ from intracellular stores, IP~3~Rs have additional roles. For example, binding of IP~3~ is proposed to release IRBIT from the IP~3~‐binding site, freeing IRBIT to regulate additional targets that include ion channels, transporters and the enzyme ribonucleotide reductase (Ando *et al*. [2014](#tjp7102-bib-0002){ref-type="ref"}; Arnaoutov & Dasso, [2014](#tjp7102-bib-0005){ref-type="ref"}). IP~3~Rs may also regulate associated proteins independently of their ability to release Ca^2+^. For example, a direct interaction between IP~3~Rs and TRPC (transient receptor potential canonical) channels is proposed to stimulate opening of the latter (Zhang *et al*. [2001](#tjp7102-bib-0189){ref-type="ref"}). Hence, when reviewing the effects of proteins associated with IP~3~Rs, we should look beyond the effects of IP~3~ on cytosolic Ca^2+^ signals, to consider also consequences within the ER lumen, effects on Ca^2+^ entry, and effects unrelated to Ca^2+^ signalling. That scope is too ambitious for this short review. Instead we provide a comprehensive summary of proteins suggested to interact with IP~3~Rs (Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"}, within which we provide most references) and then explore a few selected examples to illustrate some general features.
Signalling complexes containing IP~3~Rs span entire signalling pathways {#tjp7102-sec-0030}
=======================================================================
The sheer number of proteins reported to form complexes with IP~3~Rs is striking and so too is their diversity, in terms of both cellular geography and function (Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"}). IP~3~Rs form complexes with many of the proteins that link extracellular stimuli to formation of IP~3~, including G protein‐coupled receptors (GPCRs), the epidermal growth factor receptor (EGFR), the erythropoietin receptor, the Gβγ complexes of G proteins, and some forms of PLC. IP~3~Rs also associate with other signalling proteins linked to PLC signalling, including protein kinase C (PKC), RACK1 (receptor of activated PKC) and the phosphoinositide phosphatase PTEN. The interactions extend also to proteins from other signalling pathways, including adenylyl cyclase (AC), the small G protein K‐Ras, and the protein kinases AKT1 (RAC‐α serine/threonine protein kinase), mTOR (mammalian target of rapamycin), c‐Src and MAPK1/MAPK3 (mitogen‐activated protein kinase 1/3) (Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"}, [2](#tjp7102-tbl-0002){ref-type="table-wrap"}, [3](#tjp7102-tbl-0003){ref-type="table-wrap"}, [4](#tjp7102-tbl-0004){ref-type="table-wrap"} and Fig. [1](#tjp7102-fig-0001){ref-type="fig"}). Proteins that respond to the Ca^2+^ released by IP~3~Rs also form complexes with IP~3~Rs. These include ion channels, exchangers and pumps within the plasma membrane. It is clear that IP~3~Rs reside within macromolecular complexes that both span entire signalling pathways from cell‐surface receptors to the effectors that respond to Ca^2+^, and include proteins that integrate signals from other signalling pathways.
The advantages of these signalling complexes are clear. They allow information to be directed selectively from specific extracellular stimuli to specific intracellular targets through conserved signalling pathways. Furthermore, associated proteins can integrate signals from different signalling pathways and so modulate traffic through the complex. Hence, protein complexes confer both specificity and plasticity. A third advantage is speed. Signalling pathways must be able to turn on and off quickly. Fast activation benefits from high concentrations of reactants and fast on‐rates (*k* ~1~) for association of messengers with their targets. Rapid de‐activation requires rapid destruction or dissipation of the messenger and a fast dissociation rate (*k* ~−1~). By facilitating delivery of messengers at high local concentrations to their targets (e.g. IP~3~ to IP~3~Rs), signalling complexes contribute to both rapid activation and de‐activation, the latter because diffusion of messengers away from the site of delivery may be sufficient to allow their concentration to fall below that required for activation as soon as synthesis of the messenger ceases. Secondly, targets can have fast off‐rates (*k* ~−1~) with a corresponding loss of affinity (equilibrium association constant, *K* ~A~ = *k* ~1~/*k* ~−1~) that does not compromise their capacity to respond to high local concentrations of messenger. We suggest, then, that assembly of proteins around IP~3~Rs contributes to fast and specific signalling, while providing opportunities for signal integration and plasticity.
For convenience, we consider the proteins that associate with IP~3~Rs under four somewhat arbitrary (and overlapping) headings: proteins that enhance or inhibit the activity of IP~3~Rs (Tables [1](#tjp7102-tbl-0001){ref-type="table-wrap"} and [2](#tjp7102-tbl-0002){ref-type="table-wrap"}); proteins that respond to Ca^2+^ released by IP~3~Rs (Table [3](#tjp7102-tbl-0003){ref-type="table-wrap"}); and proteins with more general roles, including those associated with movement of IP~3~Rs (Table [4](#tjp7102-tbl-0004){ref-type="table-wrap"}).
Proteins that enhance the function of IP~3~Rs {#tjp7102-sec-0040}
=============================================
Usually, IP~3~Rs open only when they have bound both IP~3~ and Ca^2+^ (Foskett *et al*. [2007](#tjp7102-bib-0038){ref-type="ref"}; Taylor & Tovey, [2010](#tjp7102-bib-0151){ref-type="ref"}). Unsurprisingly, therefore, most of the proteins that associate with IP~3~Rs and enhance their activity do so either by allowing more effective delivery of IP~3~ and/or Ca^2+^ to IP~3~Rs, or by enhancing the responsiveness of IP~3~Rs to IP~3~ and/or Ca^2+^ (Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}).
The association of IP~3~Rs with GPCRs, EGFR and erythropoietin receptors, with the βγ subunits of G proteins, with some isoforms of PLC, and with scaffold proteins, like Homer 1 that tethers IP~3~Rs to metabotropic glutamate receptors and PLC (Tu *et al*. [1998](#tjp7102-bib-0160){ref-type="ref"}), suggest mechanisms by which receptors may effectively deliver IP~3~ to specific IP~3~Rs. This targeted delivery of IP~3~ provides two advantages: it allows rapid responses and it may allow spatially organized Ca^2+^ signals to retain an 'imprint' of the stimulus that evoked them. Bradykinin B~2~ receptors (B~2~Rs) are a well‐defined example. In sympathetic neurons, both muscarinic M~1~ receptors (M~1~Rs) and B~2~Rs activate PLC, but only activation of B~2~Rs evokes Ca^2+^ release through IP~3~Rs (Delmas *et al*. [2002](#tjp7102-bib-0032){ref-type="ref"}). This selectivity arises because B~2~Rs, but not M~1~Rs, form complexes with IP~3~Rs. Rapid generation of IP~3~ in response to activation of B~2~Rs thereby generates relatively high concentrations of IP~3~ in the vicinity of IP~3~Rs, which are not achieved by the more distant M~1~Rs. In this case, selective coupling between plasma membrane receptors and IP~3~Rs may allow sympathetic neurons to generate different intracellular responses to pro‐inflammatory and cholinergic inputs.
Rather than enhancing the delivery of IP~3~ to IP~3~Rs, many other proteins sensitize IP~3~Rs to prevailing concentrations of IP~3~ and/or Ca^2+^ (Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}). An example, which may play an important role in human disease, is the sensitization of IP~3~Rs by mutant forms of presenilins (Cheung *et al*. [2008](#tjp7102-bib-0028){ref-type="ref"}). Mutations in presenilin‐1 (PS1) and presenilin‐2 (PS2) are major causes of familial Alzheimer\'s disease. Although both wild‐type and mutant presenilins associate with IP~3~Rs, only the disease‐causing mutant forms of PS1 and PS2 enhance the activity of IP~3~Rs in response to IP~3~ and Ca^2+^. The mechanism involved may be a change in the modal gating of IP~3~Rs (Cheung *et al*. [2010](#tjp7102-bib-0027){ref-type="ref"}). This increased activity of IP~3~Rs results in enhanced release of Ca^2+^, which may lead to aberrant processing of β‐amyloid (Cheung *et al*. [2008](#tjp7102-bib-0028){ref-type="ref"}), constitutive activation of cyclic AMP response element binding protein (CREB)‐mediated transcription (Muller *et al*. [2011](#tjp7102-bib-0099){ref-type="ref"}), synaptic dysfunction and neuronal degeneration (Mattson, [2010](#tjp7102-bib-0090){ref-type="ref"}).
Although activation of IP~3~Rs normally requires binding of IP~3~ and Ca^2+^, a few proteins have been reported to cause reversible activation of IP~3~Rs directly, without the coincident presence of IP~3~ and Ca^2+^ (Table [1](#tjp7102-tbl-0001){ref-type="table-wrap"}). These include Gβγ (Zeng *et al*. [2003](#tjp7102-bib-0187){ref-type="ref"}), CIB1 (White *et al*. [2006](#tjp7102-bib-0175){ref-type="ref"}) and, more controversially, CaBP1 (Yang *et al*. [2002](#tjp7102-bib-0179){ref-type="ref"}). The initial report on the actions of CaBP1 described an activation of *Xenopus* IP~3~Rs in the absence of IP~3~ *in vitro*. However, subsequent studies have demonstrated that CaBP1 inhibits Ca^2+^ release via mammalian and *Xenopus* IP~3~Rs by stabilizing an inactive state of the IP~3~R (Haynes *et al*. [2004](#tjp7102-bib-0051){ref-type="ref"}; Nadif Kasri *et al*. [2004](#tjp7102-bib-0101){ref-type="ref"}; White *et al*. [2006](#tjp7102-bib-0175){ref-type="ref"}; Li *et al*. [2013](#tjp7102-bib-0079){ref-type="ref"}). Similarly, CIB1 was reported to activate IP~3~Rs in *Xenopus* oocytes and Sf9 insect cells in the absence of IP~3~, but it too inhibits Ca^2+^ release via mammalian IP~3~Rs (White *et al*. [2006](#tjp7102-bib-0175){ref-type="ref"}). Uniquely, an irreversible activation of IP~3~Rs appears to occur after proteolytic cleavage by caspase‐3 (Assefa *et al*. [2004](#tjp7102-bib-0006){ref-type="ref"}; Nakayama *et al*. [2004](#tjp7102-bib-0104){ref-type="ref"}), a process that may play a prominent role in apoptosis.
Proteins that inhibit the function of IP~3~Rs {#tjp7102-sec-0050}
=============================================
Many proteins that interact with IP~3~Rs inhibit their function (Table [2](#tjp7102-tbl-0002){ref-type="table-wrap"}). These interactions may enable rapid feedback regulation of Ca^2+^ release and provide long‐term attenuation of IP~3~R activity by promoting degradation or irreversible inhibition of IP~3~Rs. These mechanisms contribute to the tight regulation of IP~3~R activity needed to achieve spatial and temporal organization of Ca^2+^ signals (Konieczny *et al*. [2012](#tjp7102-bib-0073){ref-type="ref"}). They also provide protection from the damaging consequences of excessive increases in cytosolic free Ca^2+^ concentration (Orrenius *et al*. [2015](#tjp7102-bib-0110){ref-type="ref"}) and disturbance of the other essential roles of the ER while it fulfils its role in Ca^2+^ signalling (Berridge, [2002](#tjp7102-bib-0010){ref-type="ref"}). Proteins that inhibit IP~3~Rs in a Ca^2+^‐dependent manner, like calmodulin, CaBP1, calcineurin, CaMKII and the unidentified protein(s) that may mediate the universal inhibition of IP~3~Rs by Ca^2+^, are prime candidates for mediating this negative feedback. Proteins that inhibit IP~3~Rs fall into two broad categories: those that bind reversibly to interfere with binding of IP~3~ and/or Ca^2+^ or their links to gating; and those that cause post‐translational modifications of the IP~3~R (Table [2](#tjp7102-tbl-0002){ref-type="table-wrap"}).
IRBIT inhibits all three IP~3~R subtypes by competing with IP~3~ for binding to the IBC (Ando *et al*. [2003](#tjp7102-bib-0003){ref-type="ref"}). IRBIT binds only when it is phosphorylated at several sites, probably because the phosphorylated residues mimic the essential phosphate groups of IP~3~ (Fig. [2](#tjp7102-fig-0002){ref-type="fig"} *A*). Residue S68 is the 'master' phosphorylation site. When it is phosphorylated by a Ca^2+^‐dependent kinase, perhaps a Ca^2+^/calmodulin‐dependent protein kinase (CaMK), it allows casein kinase I‐mediated phosphorylation of the two residues (S71 and S74, residue numbering relates to mouse IP~3~R1) that are critical for binding of IRBIT to IP~3~Rs (and its other targets) (Ando *et al*. [2014](#tjp7102-bib-0002){ref-type="ref"}). Dephosphorylation of S68 is catalysed by protein phosphatase 1 (PP1), which also associates with IRBIT. The competition between phospho‐IRBIT and IP~3~ for occupancy of the IBC through which IP~3~ initiates activation of IP~3~Rs allows IRBIT to tune the sensitivity of IP~3~Rs to IP~3~. Hence, inhibiting expression of IRBIT, or expression of a dominant negative form (IRBIT‐S68A), allows Ca^2+^ release at lower concentrations of IP~3~ (Ando *et al*. [2014](#tjp7102-bib-0002){ref-type="ref"}). This tuning of IP~3~R sensitivity has been demonstrated in sympathetic neurons where, as discussed earlier, M~1~Rs do not associate with IP~3~Rs and do not normally generate sufficient IP~3~ to activate more distant IP~3~Rs (Delmas *et al*. [2002](#tjp7102-bib-0032){ref-type="ref"}). However, expression of the dominant negative IRBIT allows M~1~Rs to evoke Ca^2+^ release through IP~3~Rs (Zaika *et al*. [2011](#tjp7102-bib-0186){ref-type="ref"}). Although the details are not fully resolved, the interplay between Ca^2+^ and the activation of IRBIT is intriguing because it suggests potential feedback loops that might control the sensitivity of IP~3~Rs to IP~3~ (Ando *et al*. [2014](#tjp7102-bib-0002){ref-type="ref"}). The phosphorylation (of S68) that initiates activation of IRBIT is Ca^2+^ sensitive, deactivation of IRBIT by proteolytic cleavage within its N‐terminal may be mediated by Ca^2+^‐sensitive calpain, and IRBIT itself inhibits Ca^2+^/calmodulin‐dependent protein kinase IIα (CaMKIIα) (Kawaai *et al*. [2015](#tjp7102-bib-0068){ref-type="ref"}) (Fig. [2](#tjp7102-fig-0002){ref-type="fig"} *B*).
{#tjp7102-fig-0002}
Post‐translational modification of IP~3~Rs by associated proteins may be reversible (e.g. phosphorylation) (Betzenhauser & Yule, [2010](#tjp7102-bib-0012){ref-type="ref"}) or irreversible (e.g. proteolysis and some covalent modifications). An example of the latter is the Ca^2+^‐dependent enzyme transglutaminase type 2 (TGM2). By covalently modifying a glutamine residue within the C‐terminal tail of IP~3~R1, TGM2 causes irreversible cross‐linking of adjacent IP~3~R subunits via a lysine residue and the modified glutamine. This prevents the conformational changes required for activation of IP~3~Rs, and so inhibits IP~3~‐evoked Ca^2+^ release (Hamada *et al*. [2014](#tjp7102-bib-0047){ref-type="ref"}). The Ca^2+^ sensitivity of TGM2 may allow it to contribute to feedback control of Ca^2+^ release and to disruption of IP~3~R function when dysregulation of Ca^2+^ signalling occurs in pathological conditions such as Huntington\'s disease (Hamada *et al*. [2014](#tjp7102-bib-0047){ref-type="ref"}). Activation of IP~3~Rs and the ensuing release of Ca^2+^ also trigger ubiquitination and proteasomal degradation of IP~3~Rs (Pearce *et al*. [2009](#tjp7102-bib-0116){ref-type="ref"}) and their cleavage by calpains (Μagnusson *et al*. [1993](#tjp7102-bib-0084){ref-type="ref"}; Wojcikiewicz & Oberdorf, [1996](#tjp7102-bib-0176){ref-type="ref"}). Hence, proteins that associate with IP~3~Rs provide mechanisms that allow both acute and long‐term feedback regulation of IP~3~R activity.
Downstream effectors {#tjp7102-sec-0060}
====================
IP~3~Rs also form complexes with proteins that are downstream effectors of IP~3~R activation; most of these respond to the Ca^2+^ released by IP~3~Rs (Table [3](#tjp7102-tbl-0003){ref-type="table-wrap"}). Many of these proteins are cytosolic, but others reside within membranes that allow IP~3~Rs within the ER to communicate with other intracellular organelles or the plasma membrane. The importance of this communication between organelles, mediated by junctional complexes between them, is increasingly recognized (Lam & Galione, [2013](#tjp7102-bib-0076){ref-type="ref"}).
Hepatic gluconeogenesis, which is likely to play an important role in diabetes and obesity, is stimulated by glucagon released by the pancreas during fasting, and inhibited by insulin released when the plasma glucose concentration increases. A complex containing IP~3~Rs, the Ca^2+^‐regulated protein phosphatase calcineurin, the transcriptional co‐activator of CREB‐regulated transcription CRTC2 (CREB‐coactivator C2), PKA and AKT1 coordinates gluconeogenesis (Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}) (Fig. [3](#tjp7102-fig-0003){ref-type="fig"}). De‐phosphorylated CRTC2 binds to nuclear CREB and up‐regulates genes that promote gluconeogenesis. This is repressed by SIK2, a kinase that phosphorylates CRTC2. IP~3~‐evoked Ca^2+^ release activates calcineurin, which de‐phosphorylates CRTC2. Glucagon receptors stimulate production of both cAMP and IP~3~ (Wakelam *et al*. [1986](#tjp7102-bib-0167){ref-type="ref"}; Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}). The cAMP activates PKA, which phosphorylates, and thereby inhibits, SIK2; and it phosphorylates IP~3~Rs, sensitizing them to activation by IP~3~ and Ca^2+^. IP~3~Rs are also directly sensitized by cAMP (Tovey *et al*. [2008](#tjp7102-bib-0156){ref-type="ref"}). Increased release of Ca^2+^ via IP~3~Rs activates calcineurin, which dephosphorylates CRTC2 (Vanderheyden *et al*. [2009](#tjp7102-bib-0162){ref-type="ref"} *a*; Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}). Hence glucagon both inhibits the kinase (SIK2) and stimulates the phosphatase (calcineurin) that control phosphorylation of CRTC2. Glucagon also reduces binding of CRTC2 to IP~3~Rs (Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}), further enhancing the nuclear translocation of dephosphorylated CRTC2. The signals evoked by insulin receptors also feed into this IP~3~R complex. Insulin stimulates phosphatidylinositol 3‐kinase (PI3K) and thereby AKT1. The latter phosphorylates IP~3~Rs and attenuates their activity. Hence insulin, by inhibiting IP~3~Rs, opposes the actions of glucagon by restraining the activation of calcineurin and so maintains CRTC2 in its inactive phosphorylated state (Wang *et al*. [2012](#tjp7102-bib-0170){ref-type="ref"}). This example illustrates some of the intricate interactions that the assembly of proteins around IP~3~Rs can allow: signals from a GPCR and a receptor tyrosine kinase converge at IP~3~Rs, which then integrate the inputs and transduce them into a regulation of gene expression (Fig. [3](#tjp7102-fig-0003){ref-type="fig"}).
{#tjp7102-fig-0003}
Proteins that determine the distribution of IP~3~Rs {#tjp7102-sec-0070}
===================================================
The subcellular distribution of IP~3~Rs is an important influence on their behaviour, not least because it defines the sites at which they will release Ca^2+^, and whether they will be exposed to effective concentrations of the stimuli that activate them, IP~3~ and Ca^2+^. Assembly of IP~3~Rs with components of the PLC signalling pathway (see above) can ensure targeted delivery of IP~3~, but Ca^2+^ is most often provided by neighbouring IP~3~Rs. An important interaction, therefore, is that between IP~3~Rs themselves, because their proximity to neighbours dictates whether Ca^2+^ released by an active IP~3~R can ignite the activity of other IP~3~Rs. Considerable evidence suggests that clustering of IP~3~Rs within the plane of the ER membrane is dynamically regulated by IP~3~ and/or Ca^2+^ (Tateishi *et al*. [2005](#tjp7102-bib-0150){ref-type="ref"}; Rahman *et al*. [2009](#tjp7102-bib-0120){ref-type="ref"}; and see references in Geyer *et al*. [2015](#tjp7102-bib-0044){ref-type="ref"}), although the role of this process in shaping Ca^2+^ signals remains controversial (Smith *et al*. [2014](#tjp7102-bib-0137){ref-type="ref"}). We have suggested that IP~3~‐evoked clustering of IP~3~Rs may contribute to the coordinated openings of IP~3~Rs that underlie the small Ca^2+^ signals ('Ca^2+^ puffs') evoked by low stimulus intensities, by both bringing IP~3~Rs together and retuning their Ca^2+^ sensitivity (Rahman *et al*. [2009](#tjp7102-bib-0120){ref-type="ref"}). Head‐to‐head interactions of IP~3~Rs have also been observed in electron micrographs of purified IP~3~Rs (Hamada *et al*. [2003](#tjp7102-bib-0046){ref-type="ref"}), between opposing ER membranes within cells (Takei *et al*. [1994](#tjp7102-bib-0145){ref-type="ref"}) and between the isolated N‐terminal domains of IP~3~Rs (Chavda *et al*. [2013](#tjp7102-bib-0025){ref-type="ref"}). The functional significance of these interactions has not been established.
A recent study of the Ca^2+^ signals evoked by thrombin‐mediated stimulation of the protease‐activated receptor PAR‐1 in endothelial cells provides evidence that microtubules may guide IP~3~Rs into the clusters within which Ca^2+^ release can most effectively recruit neighbouring IP~3~Rs (Geyer *et al*. [2015](#tjp7102-bib-0044){ref-type="ref"}). In lung microvascular endothelial cells, thrombin, which activates PAR‐1 by cleaving its N‐terminal, stimulates PLC and thereby evokes Ca^2+^ release through IP~3~Rs. The resulting increase in cytosolic Ca^2+^ concentration contributes to disassembly of the adherens junctions that maintain the integrity of the endothelium (Komarova & Malik, [2010](#tjp7102-bib-0072){ref-type="ref"}). These effects are attenuated when the interaction between type 3 IP~3~Rs (IP~3~R3) and end‐binding protein 3 (EB3) are disrupted. EB3 belongs to a family of proteins that bind to the plus‐end of growing microtubules and recruit other proteins, often via an S/TxIP motif (where x denotes any residue) (Honnappa *et al*. [2009](#tjp7102-bib-0056){ref-type="ref"}). Mutation of the TxIP motif within the regulatory domain of IP~3~R3 prevents its binding to EB3, attenuates thrombin‐evoked Ca^2+^ signals, and reduces both the basal clustering of IP~3~R3 and the enhanced clustering evoked by thrombin. Hence, in endothelial cells, the association of IP~3~R3 with EB3 and microtubules is required for both clustering of IP~3~Rs and effective Ca^2+^ signalling. This suggests that clustering allows IP~3~Rs to deliver Ca^2+^ more effectively to other IP~3~Rs and so allows the amplification provided by Ca^2+^‐induced Ca^2+^ release (Fig. [4](#tjp7102-fig-0004){ref-type="fig"}). We conclude that association of IP~3~Rs with other proteins, components of the PLC signalling pathway or EB3, contributes to effective delivery of the two essential regulators of IP~3~Rs, IP~3~ and Ca^2+^, respectively.
{ref-type="ref"}) suggests that the EB3‐mediated interaction of IP~3~R3 with microtubules is essential for the clustering of IP~3~Rs that allows the Ca^2+^ released by one IP~3~R to be amplified by recruitment of neighbouring IP~3~Rs.](TJP-594-2849-g005){#tjp7102-fig-0004}
Conclusions {#tjp7102-sec-0080}
===========
IP~3~Rs and the Ca^2+^ they release are called upon to specifically regulate many physiological processes (Berridge, [2009](#tjp7102-bib-0011){ref-type="ref"}), while neither perturbing the other essential roles of the ER (Berridge, [2002](#tjp7102-bib-0010){ref-type="ref"}) nor subjecting the cell to the deleterious consequences of excessive increases in cytosolic Ca^2+^ concentration (Orrenius *et al*. [2015](#tjp7102-bib-0110){ref-type="ref"}). These demands impose a need for complex regulation of IP~3~Rs, much of which is achieved by assembling proteins around IP~3~Rs to form signalling complexes (Konieczny *et al*. [2012](#tjp7102-bib-0073){ref-type="ref"}). These complexes allow signals to be directed through conserved signalling pathways and endow the pathways with speed, integrative capacity and plasticity. The very large size of IP~3~Rs relative to most other ion channels might be viewed as an evolutionary adaptation to meet this need for them to function as signalling hubs.
Advances in genomics, proteomics, antibody technologies and bioinformatics have transformed analyses of protein--protein interactions. It is now possible to interrogate these interactions on a whole‐proteome scale (Havugimana *et al*. [2012](#tjp7102-bib-0049){ref-type="ref"}; Rolland *et al*. [2014](#tjp7102-bib-0123){ref-type="ref"}). Bioinformatic methods can predict protein--protein interactions (Baughman *et al*. [2011](#tjp7102-bib-0009){ref-type="ref"}; Kotlyar *et al*. [2015](#tjp7102-bib-0074){ref-type="ref"}) and even the regions of the proteins that are involved (Gavenonis *et al*. [2014](#tjp7102-bib-0043){ref-type="ref"}). These powerful technologies, and the opportunities they provide to design new therapies (Wells & McClendon, [2007](#tjp7102-bib-0172){ref-type="ref"}), cannot displace the need for direct confirmation of the interactions and their functional significance. Together, these approaches pave the way to defining the properties and functional importance of IP~3~R signalling hubs in normal physiology and disease.
Additional information {#tjp7102-sec-0090}
======================
Competing interests {#tjp7102-sec-0100}
-------------------
None declared.
Author contributions {#tjp7102-sec-0110}
--------------------
All authors have approved the final version of the manuscript and agree to be accountable for all aspects of the work. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.
Funding {#tjp7102-sec-0120}
-------
This work was supported by the Biotechnology and Biological Sciences Research Council (L0000075) and the Wellcome Trust (101844).
**David Prole** studied Natural Sciences at the University of Cambridge before exploring the structure and function of K^+^ channels during his PhD with Neil Marrion at the University of Bristol and HCN pacemaker channels during postdoctoral training with Gary Yellen at Harvard Medical School. After moving back to the University of Cambridge to work with Colin Taylor he held a Meres Research Associateship from St John\'s College and now explores the roles of ion channels in cell signalling.
{#nlm-graphic-1}
**Colin Taylor** began his career as an insect physiologist with Mike Berridge, before moving into phosphoinositide and Ca^2+^ signalling during a postdoc with Jim Putney in Virginia. He is presently Professor of Cellular Pharmacology and a Wellcome Trust Senior Investigator in the Department of Pharmacology in Cambridge, where he continues to explore the workings of IP~3~ receptors.
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Q:
Prove that $[a]_X \subseteq [a]_Y$ .
Let $X,Y$ be two equivalence relations defined on a set $A.$ Show that $X \cup Y$ be the equivalence relation iff $[a]_X \subseteq [a]_Y$ (or $[a]_Y \subseteq [a]_X$). Here $[a]_{X(Y)}$ denotes the eqiuvalence class of elemenent $a \in A.$ My idea was consider an element $b \in [a]_X \setminus [a]_Y]$ and verify the intersection:
$$
[a]_{X \, \cup \, Y} \cap [b]_{X \, \cup \, Y}.
$$
Since $[a]_{X \, \cup \, Y}=[a]_{X } \cup [a]_{ Y}$ we get
\begin{gather*}
[a]_{X \, \cup \, Y} \cap [b]_{X \, \cup \, Y}=([a]_{X } \cup [a]_{ Y}) \cap ([b]_{X} \cup [b]_{ Y})=\\ \\=([a]_{X } \cap [b]_{ X}) \cup ([a]_{X } \cap [b]_{ Y}) \cup ([a]_{Y } \cap [b]_{ X}) \cup ([a]_{Y } \cap [b]_{ Y}).
\end{gather*}
Since $b \in [a]_X$ then $[b]_X=[a]_X$ and $[a]_{X } \cap [b]_{ X}=[a]_X$. Thus
$[a]_{X \, \cup \, Y} \cap [b]_{X \, \cup \, Y}$ is not empty set. It follows that
$[a]_{X \, \cup \, Y} = [b]_{X \, \cup \, Y}.$
Is this enougth?
A:
I’m afraid that I can’t follow your reasoning: the fact that $[a]_{X\cup Y}\cap[b]_{X\cup Y}\ne\varnothing$ does not imply that $[a]_{X\cup Y}=[b]_{X\cup Y}$. Moreover, the statement that you’re to prove is an iff statement, so you have two implications to prove, not just one:
if $[a]_X\subseteq[a]_Y$ for each $a\in A$, then $X\cup Y$ is an equivalence relation; and
if $X\cup Y$ is an equivalence relation, then either $[a]_X\subseteq[a]_Y$ for each $a\in A$, or $[a]_Y\subseteq[a]_X$ for each $a\in A$.
I would start by observing that $X\cup Y$ is reflexive: if $a\in A$, then $\langle a,a\rangle\in X\subseteq X\cup Y$. Moreover, $X\cup Y$ is symmetric: if $\langle a,b\rangle\in X\cup Y$, then either $\langle a,b\rangle\in X$ or $\langle a,b\rangle\in Y$. In the first case $\langle b,a\rangle\in X\subseteq X\cup Y$, and in the second case $\langle b,a\rangle\in Y\subseteq X\cup Y$, so $\langle b,a\rangle\in X\cup Y$. Thus, $X\cup Y$ is an equivalence relation iff it’s transitive. I’ll get you started on both parts; see if you can finish them.
Suppose that $[a]_X\subseteq[a]_Y$ for each $a\in A$. We want to show that $X\cup Y$ is transitive, so suppose that $\langle a,b\rangle,\langle b,c\rangle\in X\cup Y$. Then $b\in[a]_X\cup[a]_Y=[a]_Y$, and ...
Now suppose that there is some $a\in A$ such that $[a]_X\nsubseteq[a]_Y$ and $[a]_Y\nsubseteq[a]_X$; we want to show that $X\cup Y$ is not transitive. Let $b\in[a]_X\setminus[a]_Y$ and $c\in[a]_Y\setminus[a]_X$. Then $\langle b,a\rangle\in X\cup Y$ and $\langle a,c\rangle\in X\cup Y$; why? Now show that $\langle b,c\rangle\notin X\cup Y$.
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Three people are facing charges for the vicious brawl at Disneyland’s Toontown that occurred on July 5.
Video of the fight at the theme park quickly went viral, showing the feuding family yelling and punching each other. The main aggressor, identified as Avery Desmond-Edwinn Robinson, is seen punching a woman, identified as his sister, 40-year-old Andrea Nicole Robinson, and her husband, 44-year-old Daman Petrie. Avery is also seen knocking his girlfriend to the ground and then repeatedly punching her and dragging her by her hair.
DISNEY WORLD GUEST REPORTEDLY PUNCHES TOWER OF TERROR CASTMEMBER, STARTS PUSHING RIDE'S BUTTONS
Avery, 35, has been charged with five felonies and nine misdemeanors, “for attacking his sister, brother-in-law and girlfriend, endangering his child and three other children who were at Disneyland with the family, and threatening to kill members of his family as he drove out of a Disneyland parking structure,” according to a press release from the District Attorney’s office.
Avery has also been accused of assaulting a Disneyland employee with his car while he was leaving the park.
CLICK HERE TO GET THE FOX NEWS APP
He has been charged with felony domestic battery with corporal injury and one felony count of assault with force likely to produce great bodily injury, assault with a deadly weapon and two felony counts of criminal threats. He also faces misdemeanor battery and child abuse and endangerment charges.
The man is facing a maximum of seven years and four months in state prison if convicted on all charges.
His sister Andrea is facing five misdemeanor charges – including battery for attacking her brother, his girlfriend and a Disneyland employee; and one assault charge. She faces up to two years and six months in jail.
Her husband faces up to six months in jail if convicted of one misdemeanor battery charge.
“The Orange County District Attorney’s Office does not tolerate domestic violence or child endangerment anywhere,” Orange County District Attorney Todd Spitzer said in the press release.
CLICK HERE TO SIGN UP FOR OUR LIFESTYLE NEWSLETTER
Before the video went viral, the family initially denied that the fight had taken place. Police claim the group was uncooperative and did not pursue felony charges until after the video was shared on YouTube.
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KABUL (Reuters) - Afghan President Ashraf Ghani rejected on Sunday a Taliban demand for the release of 5,000 prisoners as a condition for talks with Afghanistan’s government and civilians - included in a deal between the United States and the Islamist militants.
Afghanistan's President Ashraf Ghani speaks during a news conference in Kabul, Afghanistan March 1, 2020. REUTERS/Omar Sobhani
“The government of Afghanistan has made no commitment to free 5,000 Taliban prisoners,” Ghani told reporters in Kabul, a day after the deal was signed in Qatar to start a political settlement aimed at ending the United States’ longest war.
U.S. Secretary of State Mike Pompeo told CBS’s “Face the Nation” program there had been prisoner releases from both sides in the past, and voiced hope that negotiations would begin in the coming days between the Afghan government and the Taliban.
“It’s going to be rocky and bumpy,” Pompeo said. “No one is under any false illusion that this won’t be a difficult conversation.”
Western diplomats see challenges ahead for U.S. negotiators as they shepherd negotiations between Ghani’s government and the Taliban, who ruled Afghanistan from 1996 to 2001 and imposed many restrictions on women and activities deemed “un-Islamic”.
Under the accord, the United States and the Taliban are committed to work expeditiously to release combat and political prisoners as a confidence-building measure, with the coordination and approval of all relevant sides. The agreement calls for up to 5,000 jailed Taliban prisoners to be released in exchange for up to 1,000 Afghan government captives by March 10.
On the issue of the prisoner swap, Ghani said, “It is not in the authority of United States to decide, they are only a facilitator.”
Ghani told CNN on Sunday that U.S. President Donald Trump had not asked for the release of the prisoners and that the issue of prisoner releases should be discussed as part of a comprehensive peace deal. The political consensus needed for such a major step does not currently exist, Ghani said.
Ghani said key issues need to be discussed first including the Taliban’s ties with Pakistan and other countries that had offered it sanctuary, its ties with what he called terrorist groups and drug cartels, and the place of Afghanistan’s security forces and its civil administration.
“The people of Afghanistan need to believe that we’ve gone from war to peace, and not that the agreement will be either a Trojan horse or the beginning of a much worse phase of conflict,” Ghani added.
Ghani said verifiable mechanisms were needed to ensure commitments made are actually delivered.
The accord was signed on Saturday by U.S. special envoy Zalmay Khalilzad and Taliban political chief Mullah Abdul Ghani Baradar, witnessed by Pompeo.
After the ceremony, Baradar met foreign ministers from Norway, Turkey and Uzbekistan in Doha along with diplomats from Russia, Indonesia and neighboring nations, the Taliban said, a move that signaled the group’s determination to secure international legitimacy.
“The dignitaries who met Mullah Baradar expressed their commitments toward Afghanistan’s reconstruction and development. ... the U.S.-Taliban agreement is historical,” said Taliban spokesman Zabiullah Mujahid.
Trump rejected criticism around the deal and said he would meet Taliban leaders in the near future.
Pompeo said Trump would be actively engaged in the process, but gave no date for a possible meeting with Taliban leaders.
Ghani’s aides said Trump’s decision to meet the Taliban could pose a challenge to Afghanistan’s government at a time when the U.S. troop withdrawal becomes imminent.
Slideshow ( 4 images )
‘NO LEGAL STANDING’
Iran on Sunday dismissed the agreement as a pretext to legitimize the presence of U.S. troops in Afghanistan.
“The United States has no legal standing to sign a peace agreement or to determine the future of Afghanistan,” Iran’s Foreign Ministry said in a statement reported by state media.
Under the agreement, the United States is committed to reducing the number of its troops in Afghanistan to 8,600 from 13,000 within 135 days of signing. It also is committed under the accord to work with allies to proportionally reduce the number of coalition forces in Afghanistan over that period, if the Taliban forces adhere to their security guarantees and ceasefire.
A full withdrawal of all U.S. and coalition forces would occur within 14 months, a joint statement said. The withdrawal depends on security guarantees by the Taliban.
After being ousted from power in 2001 in a U.S.-led invasion following the Sept. 11 attacks on the United States engineered by al Qaeda forces harbored by the Taliban, Taliban forces have led a violent insurgency. The Afghan war has been a stalemate for more than 18 years, with Taliban forces controlling or contesting more territory yet unable to capture and hold major urban centers.
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A Startup is Using Blockchain to Help Restore Power in Puerto Rico
The country of Puerto Rico has been suffering from a power crisis for nearly eight (8) months now after Hurricane Maria battered the island and destroyed a lot of its infrastructure, including its electrical grid.
Power Ledger, an Australian startup, will be using blockchain technology to help bring back stable power to the island that has been suffering continuous power outages as a result of the damage. Power Ledger was reported to have already hired a grid resiliency and security expert to lead this cause.
First, companies or even home owners should have access to micro-grid resources such as solar panels. Power Ledger, by the use of blockchain tech, will allow the trade of the power from these micro-grid resources among each other. Through this, those who are in need of power can just easily buy any surplus power generated by another company or home with cash, cryptocurrencies, or even with just labor.
The Puerto Rican government is also looking to blockchain startups to help boost its economy and recover from the effects of hurricane Maria. The tax incentives Puerto Rico has offered these companies have paid off as more than 800 companies have relocated to the island country to do business.
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Q:
Qt QGraphicsScene origin point
Whenever I add a new item to a QGraphicsScene, the origin of the QGraphicsScene seem to change for the position of the item I have just added.
How to make the QGraphicsScene origin fixed?
Do I need to add the item first in the QGraphicsScene and then specify a position for the item?
A:
Well, by default the content of the scene will be centered in the QGraphicsView. The origin of the graphics scene does not change randomly.
You might want to use setSceneRect() to define the size of the scene, so that the QGraphicsView always centers the scene in the view in a fixed manner. (If you don't set it manually, the rect will be calculated based on the items in the scene, which changes if you add more.)
A:
I answered a related question about a year ago that may be helpful:
How to draw a point (on mouseclick) on a QGraphicsScene?
Ditto to what badcat.
There are a lot of controls for adjusting or manipulating your viewport(s) that you have pointing at your scene. The scene sets what is on the stage. The view is how you look at it. Be sure to set the sceneRect or set it indirectly using centerOn or fitInView or scale or translate from the QGraphicsView class.
http://qt-project.org/doc/qt-4.8/graphicsview.html
http://qt-project.org/doc/qt-4.8/qgraphicsview.html
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311 F.Supp. 967 (1970)
William J. CARROLL, and Carroll Amusements, Inc., a Florida corporation, Plaintiffs,
v.
CITY OF ORLANDO, a Municipal corporation, and Carl T. Langford, Bill C. Ankney, J. Douglas Barnes, Donald L. Crenshaw, and W. M. Sanderlin, City Commissioners; and Robert Chewning, Chief of Police of the City of Orlando,[1] Defendants.
Civ. No. 69-255-Orl.
United States District Court, M. D. Florida, Orlando Division.
February 18, 1970.
Robert G. Petree, Bornstein, Petree & Gluckman, Orlando, Fla., for plaintiff.
Egerton K. van den Berg, van den Berg, Gay, Burke & Dyer, Tom Capelle (Police Dept.), Joseph X. DuMond, Jr., Orlando, Fla., for defendants.
C. Andrew Coomes, Orlando, Fla., for City of Orlando and Robert J. Chewning.
Before SIMPSON, Circuit Judge, and McRAE, and YOUNG, District Judges.
SIMPSON, Circuit Judge:
This action arises from the seizure of a single print of the motion picture film, "The Secret Sex Lives of Romeo and Juliet", and the arrest by police of the City of Orlando of the owner and operator of the theatre in which the film was exhibited. The basis of the seizure and arrest was the alleged obscenity of the film under the provisions of City Ordinance Sec. 43.56-1 of the City of Orlando and Florida Statutes, Sections 847.011 and 847.03, F.S.A. adopted in haec verba and in toto by the city ordinance. We do not reach the issue of obscenity.
Plaintiffs sought judgment declaring Sections 847.011 and 846.03 of the Florida Statutes, F.S.A. unconstitutional on their face; an order suppressing the seizure of the film, and its return; and temporary and permanent injunctions against further prosecution of the plaintiffs in the Municipal Court of the City of Orlando. A three-judge court has been convened pursuant to Title 28, U.S. C., Section 2284.[2] Motion for temporary restraining order was denied by Judge Young of this court. The parties have stipulated to all the relevant facts [see Appendix] and submitted the case for *968 final decision under the facts as stipulated.
We must determine whether an arrest and seizure[3] made without a prior adversary judicial determination of the claimed obscene character of the seized film is constitutionally permissible.
The general proposition that a prior adversary judicial determination must be made before obscene material may be seized is settled by the weight of authority and is an essential safeguard to protect the evanescent guarantee of freedom of speech. Marcus v. Search Warrants of Property, 1961, 367 U.S. 717, 81 S.Ct. 1708, 6 L.Ed.2d 1127; A Quantity of Copies of Books v. Kansas, 1964, 378 U.S. 205, 84 S.Ct. 1723, 12 L.Ed.2d 809; Bethview Amusement Corp. v. Cahn, 2 Cir. 1969, 416 F.2d 410; Tyrone, Inc. v. Wilkinson, 4 Cir. 1969, 410 F.2d 639, cert. denied 396 U.S. 985, 90 S.Ct. 478, 24 L.Ed.2d 449 (1969); Metzger v. Pearcy, 7 Cir. 1968, 393 F.2d 202; City News Center, Inc. v. Carson, M.D.Fla. 1969, 298 F.Supp. 706; Morrison v. Wilson, 307 F.Supp. 196 [N.D.Fla. Dec. 5, 1969] (three-judge court); May v. Harper, 306 F.Supp. 1222 [N.D.Fla. Nov. 28, 1969]; HMH Publishing Co. v. Oldham, 306 F.Supp. 495 [M.D.Fla. Oct. 15, 1969]; Entertainment Ventures, Inc. v. Brewer, M.D.Ala. Sept. 30, 1969, 306 F.Supp. 802; Masters v. Russell, 308 F.Supp. 306 [M.D.Fla. Sept. 1969]; Gable v. Jenkins, 309 F.Supp. 998 [N.D. Ga. Oct. 1969] (three-judge court); Carter v. Gautier, 305 F.Supp. 1098 [M.D.Ga. September 15, 1969] (three-judge court); Mandell v. Carson, 309 F.Supp. 326 [M.D.Fla. Oct. 8, 1969]; Central Agency, Inc. v. Brown, 306 F. Supp. 502 [N.D.Ga. Aug. 26, 1969]; Delta Book Distributors, Inc. v. Cronvich, E.D.La.1969, 304 F.Supp. 662 (three-judge court); Sokolic v. Ryan, S.D.Ga.1969, 304 F.Supp. 213; Fontaine v. Dial, W.D.Tex.1969, 303 F.Supp. 436; Grove Press, Inc. v. City of Philadelphia, E.D.Pa.1969, 300 F.Supp. 281; Cambist Films, Inc. v. Tribell, E.D.Ky.1968, 293 F.Supp. 407; Cambist Films, Inc. v. Illinois, N.D.Ill. 1968, 292 F.Supp. 185; United States v. Brown, S.D.N.Y.1967, 274 F.Supp. 561; Felton v. City of Pensacola, Fla.App.1967, 200 So.2d 842, rev'd on other grounds, 1968, 390 U.S. 340, 88 S.Ct. 1098, 19 L.Ed.2d 1220; Contra, Milky Way Productions, Inc. v. Leary, S.D.N.Y.1969, 305 F.Supp. 288; Schackman v. Arnebergh, C.D.Calif. 1966, 258 F.Supp. 983; Pinkus v. Arnebergh, C.D.Calif.1966, 258 F.Supp. 966.
The real question posed is whether law enforcement officers may for the purpose of obtaining evidence for use in a criminal prosecution seize a single print of film (as opposed to cases involving mass seizure of books, e. g. A Quantity of Books v. Kansas, supra) without having an adversary judicial hearing prior to the seizure. On this issue, the authorities are split. Compare Bethview Amusement, supra;[4] Tyrone v. Wilkinson, supra; Metzger v. Pearcy, supra; Carter v. Gautier, supra; Delta Book Distributors, Inc. v. Cronvich, supra; with United States v. Wild, 2 Cir. 1969, 422 F.2d 34 [October 29, 1969]; Bazzell v. Gibbens, E.D.La.1969, 306 F.Supp. 1057; United States v. Appell, D.C.Md.1968, 259 F.Supp. 156; Rage Books, Inc. v. Leary, S.D.N.Y.1969, 301 F.Supp. 546 (appeal pending). We adopt the reasoning expressed in Bethview, supra, 416 F.2d at 412:
"Appellants argue that there is a difference between the seizure of a large number of books and the seizure of a single print of a motion picture film. We do not agree that the difference is legally significant. We are told that the Bethview Theater has 300 seats. Assuming half of them to be occupied for four showings of a film *969 each day for a week, over 4000 individuals would see the film. Preventing so large a group in the community from access to a film is no different, in the light of first amendment rights, from preventing a similarly large number of books from being circulated.
"We are supported in our view that the rule of the Kansas case is equally applicable to seizure of films by the recent decisions of sister circuits in Metzger v. Pearcy, 393 F.2d 202 (7th Cir. 1968) and Tyrone, Inc. v. Wilkinson, 410 F.2d 639 (4th Cir. 1969). In Metzger the court said at p. 204:
`This analysis [of the Supreme Court cases] requires this court to hold unconstitutional the seizure of the film "I, a Woman" since there must be an adversary hearing on the issue of obscenity before a movie can be constitutionally seized.'
"The appellants contend that a print of the motion picture is needed for purposes of prosecution. There are a number of ways in which this can be accomplished without seizure of the film. The court can direct that a print be made reasonably available to the prosecution; a subpoena duces tecum can be used.
"Finally it is suggested that unless the police or other local authorities have actual possession of the film pending the required adversary proceeding, the distributor may take advantage of the delay, for example, by shipping the film out of the jurisdiction or by cutting out the offending scenes. If there is a real threat of such activity it can be controlled by an ex parte restraining order."
We hold therefore that the seizure and arrest were unlawful because there was no prior judicially superintended adversary determination of the obscenity of the moving picture film in question. The seizure of the film must be suppressed and the film accordingly returned to the plaintiffs.
Plaintiffs seek to enjoin the defendant from proceeding with prosecutions against them, as well as from enforcing Section 847.03 of the Florida Statutes, F.S.A. with respect to "The Secret Sex Lives of Romeo and Juliet" in the future. We decline to grant such permanent injunctive relief against future prosecutions.
In view of our holding that the arrest and seizure are invalid for want of a prior adversary judicial determination of obscenity, which holding requires suppression of the seizure and return of the film, this prosecution, for practical purposes, is terminated. We have no reason to question that the defendant will, in good faith, abide by our requirement of a prior adversary hearing as to pending or future prosecutions or future arrests and seizures. If our holding is complied with, no injunctions are necessary. We retain jurisdiction for the purposes of hereafter entering any orders necessary to enforce the views expressed herein. Delta Book Distributors, Inc. v. Cronvich, supra.
We decline to pass on the constitutionality of Florida Statutes, Sections 847.011 and 847.03, F.S.A. The same challenges are raised in another case, Meyer v. Austin, M.D.Fla. No. 69-678-Civ-J., argued before this same panel on the same day as the present case. They do not need to be reached to dispose of this case. However, we do grant a temporary injunction against further proceedings, if any, arising at issue here, pending this panel's decision in Meyer v. Austin, supra.
Judgment will be entered in accordance with this opinion.
JUDGMENT
For reasons assigned in Judge Simpson's opinion for the majority of this court filed herein this day (Judge Young dissenting by separate opinion), it is ordered:
1. That all individual defendants other than Robert Chewning, Chief of Police of the City of *970 Orlando, be dismissed from this suit;
2. That the motion picture film, "The Secret Sex Lives of Romeo and Juliet", seized from the plaintiffs on October 29, 1969, by Sgt. Van-Scoyoc of the Orlando Police Department, be returned, instanter, to the plaintiffs by the defendant Chewning, upon taking proper receipt therefor;
3. That use of said motion picture film is suppressed as evidence in any pending or future prosecutions based upon the seizure here involved;
4. That the preliminary and permanent injunctions prayed for are denied;
5. That the declaratory judgments prayed for are denied;
6. That defendant, his agents, employees or attorneys; are hereby temporarily restrained from seizing prints of the movie film, "The Secret Sex Lives of Romeo and Juliet", in the custody of plaintiffs, or from engaging in any conduct related to prosecution for exhibition on or before October 30, 1969, until this court has ruled in Meyer v. Austin, No. 69-678-Civ-J (M.D.Fla.) (three-judge court); and
7. That jurisdiction is retained herein for the issuance of such further orders as may be necessary and proper.
GEORGE C. YOUNG, District Judge (dissenting).
The majority opinion recognizes that the real question posed in this case is whether law enforcement officers may for the purpose of obtaining evidence for use in a criminal prosecution, seize a single print of film (as opposed to cases involving mass seizure of books) without having an adversary judicial hearing prior to the seizure. The majority opinion also recognizes that on this issue the authorities are split. The majority adopted the reasoning of Bethview Amusement Corp. v. Cahn, 2 Cir. 1969, 416 F.2d 410, which held that an adversary hearing on the issue of obscenity must be had before a movie film can be constitutionally seized.
However, in United States v. Wild, 2nd Cir., 422 F.2d 34 (Oct. 29, 1969), the Second Circuit speaking through its Chief Judge Lumbard, in an opinion rendered subsequent to Bethview, supra, had this to say:
"In conjunction with the specific claim that the items seized should have been suppressed, appellants present a broader argument that seizures in an obscenity case without a prior adversary hearing on the issue of obscenity are unconstitutional under Quantity of Books v. Kansas, 378 U.S. 205, 84 S.Ct. 1723, 12 L.Ed.2d 809 (1964), and Marcus v. Search Warrants, 367 U.S. 717, 81 S.Ct. 1708, 6 L.Ed.2d 1127 (1961). These cases are inapposite since they involved massive seizures of books under state statutes which authorized warrants for the seizure of obscene materials as a first step in civil proceedings seeking their destruction. The seizures in this case were of instrumentalities and evidence of the crime for which appellants were indicted and lawfully arrested. We do not believe Marcus and Quantity of Books can be read to proscribe the application of the ordinary methods of initiating criminal prosecution to obscenity cases."
A study of this entire subject causes me to believe that the Wild decision, supra, is the more reasonable and should be the one followed by this Court. If we did so, the prayer for the return of the film and its suppression as evidence would be denied.
But even if the reasoning of Bethview be adopted, the theater should make available a copy of the film for the purpose of the criminal prosecution which should be permitted to proceed. That was the procedure adopted in Tyrone, *971 Inc. v. Wilkinson, 4th Cir. 1969, 410 F.2d 639, which is a case relied upon by the majority opinion in its adoption of the Bethview reasoning. In Tyrone, supra, it was held by the Fourth Circuit that the film must be returned to the theater because it had been seized without a prior adversary hearing but that the criminal prosecution could continue and the theater would have to make available a copy of the seized film for the preparation and trial of the criminal case. If such procedure were followed here, the city prosecution could continue instead of being terminated as required by the majority opinion.
For the foregoing reasons I respectfully dissent.
APPENDIX
UNITED STATES DISTRICT COURT
MIDDLE DISTRICT OF FLORIDA
ORLANDO DIVISION
WILLIAM J. CARROLL, and
CARROLL AMUSEMENTS, INC.,
a Florida corporation,
Plaintiffs,
vs. No. 69-255 Orl. Civ.
CITY OF ORLANDO, a Municipal
corporation, et al.,
Defendants.
STIPULATION
Come now the Plaintiffs and Defendants, by and through their undersigned counsel, and stipulate that the following facts and documents may be received in evidence in the above-styled cause for all purposes relevant and material to all matters before the Three-Judge Panel sitting in this case.
1. That WILLIAM J. CARROLL is a resident of Orange County, Florida, and President of CARROLL AMUSEMENTS, INC., a Florida corporation; that Plaintiffs operate the Vogue Theater, having a seating capacity of 625 persons, in Orlando, Florida, showing numerous films of various interest to the general public.
2. That ROBERT CHEWNING is the Chief of Police of Orlando, Florida, and the other named Defendants are the individual elected members of the City Council of said City.
3. That on or about the 30th day of October, 1969, a police officer of the City of Orlando, Florida, delivered his affidavit, a proposed arrest warrant and search warrant to the Judge of the Municipal Court of the City of Orlando at his private law office. After approximately five to ten minutes, during which said warrant and affidavits were read, said search and arrest warrants were then and there executed by said Judge and returned to said officer, thereby concluding the entire judicial proceedings in connection with the issuance of said warrants. A copy of said officer's affidavit in support of said warrants and search warrant are attached hereto as Exhibit "A". No prior adversary hearing on the question of the obscenity of the matter sought to be seized was ever held. Plaintiffs' film had been exhibited to approximately 3,009 persons in Plaintiffs' theater at the time it was seized.
*972 4. That on or about 30 October 1969, police officers of the City of Orlando, Florida, confiscated Plaintiffs' film, as alleged in Paragraph 4 of the complaint herein, and refuse to return the same to Plaintiffs who have made demand therefor.
5. That the City of Orlando accomplished the aforesaid confiscation under the authority of Municipal Ordinance No. 43-56-1, of the City of Orlando, and F.S. 847.011, as alleged in paragraph 5 of Plaintiffs' complaint, copies of which ordinance and statute are attached hereto as Exhibit "B". The Petitioner, WILLIAM J. CARROLL, was arrested and taken into custody on or about the 30th day of October, 1969, pursuant to the warrant of arrest, which warrant for arrest is attached as Plaintiffs' Exhibit "C", and charged with violation of Chapter 847 of the Florida Statutes, all as particularly alleged in paragraph 6 of Plaintiffs' complaint.
6. That the Plaintiff, WILLIAM J. CARROLL, has sought and been denied, a writ of prohibition in the Circuit Court of the Ninth Judicial Circuit, in and for Orange County, Florida, seeking to restrain the Municipal Court of the City of Orlando from exercising jurisdiction in this matter on the grounds of its denial of the said WILLIAM J. CARROLL's constitutional rights under the First and Fourteenth Amendments of the United States Constitution and upon the ground of the denial of his Petition for trial by jury; that the Municipal Court of the City of Orlando has denied the Defendant, WILLIAM J. CARROLL's motion to quash the search warrant and suppress the evidence, to-wit: the rolls of film taken into custody pursuant to search warrant above described, notwithstanding the said WILLIAM J. CARROLL's assertion therein that said film was illegally seized by the Police Officers without regard to due process of law as guaranteed by the First and Fourteenth Amendments to the United States Constitution, in that said seizure was carried out without any prior adversary hearing on the question of obscenity, and other matters which are set forth in a copy of the motion to quash the warrant and suppress evidence, which is attached hereto as Exhibit "D"; Defendant's motion in the municipal court for the return of his property, to-wit, the motion picture film on the grounds the same was illegally confiscated, a copy of which is attached hereto as Exhibit "E", was denied by the Order of the Court dated December 9, 1969, a copy of which Order is attached hereto as Exhibit "F"; Defendant's motion for continuance of trial pending resolution of the federal constitutional issues before this federal panel, dated 26 November 1969, was also denied, a copy thereof is attached hereto as Plaintiff's Exhibit "G"; that the Plaintiff has accordingly exhausted all of his remedies in the Municipal Court in the City of Orlando in an effort to obtain suppression of the illegally seized evidence under doctrines of due process of law guaranteed to him by the Constitution of the United States, and all such efforts have been denied.
7. That on the 9th day of January, 1970, the Plaintiff, WILLIAM J. CARROLL, pleaded not guilty to the charges described hereinabove and prosecution of Plaintiff was commenced. The trial of said cause was recessed on 9 January 1970 prior to the closing of the Prosecution's case and pending reconvening of said trial court at some future date compatible with the Court's schedule.
8. That Plaintiff's film has not been placed in evidence in the Municipal Court and no conviction of Plaintiff has occurred.
9. That each of the parties hereinabove stipulate that the Exhibits attached to the stipulation may be taken and considered by the Court in evidence without further proof or production of originals or certified copies.
10. That the Plaintiffs and Defendants stipulate that other than the arrest described hereinabove, there have been no prior or subsequent arrests of the Plaintiff, and that Defendants have not *973 harassed the Plaintiffs, other than as hereinabove described.
Dated this 14th day of January, 1970, at Orlando, Florida.
____________________________
ROBERT G. PETREE, of
BORNSTEIN, PETREE &
GLUCKMAN,
125 S. Court Ave., Orlando,
Florida, 32801
____________________________
THOMAS A. CAPELLE,
16 S. Magnolia Ave., Orlando,
Florida, 32801
ATTORNEY FOR DEFENDANTS
NOTES
[1] The City's unopposed motion to dismiss the suit as to all individual defendants except Robert Chewning, Chief of Police, is granted.
[2] This court has jurisdiction under several statutes including Title 28, U.S.C., Section 1343(3) and (4) and Title 42, U.S.C., Section 1983. The case is properly heard by a three-judge court. Title 28, U.S.C., Sec. 2281 et seq.
[3] Although the matter is unclear from the stipulation [see Appendix], we were informed on oral argument that the arrest and search warrants were issued simultaneously.
[4] Bethview was decided on October 9, 1969. On October 29, 1969, another Second Circuit panel reached a seemingly opposite result in United States v. Wild, supra, without reference to Bethview.
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Q:
Cannot set Alpha channel to 0 in OpenGL + SDL2
I am trying to save OpenGL rendered screen to PNG image with transparent background. But all I am getting in the 4th channel is all 255 values.
Even before drawing anything on screen and just clearing does not help.
What I have done in OpenGL for initialization to get the transparent background is roughly the following:
gWindow = SDL_CreateWindow("View", SDL_WINDOWPOS_UNDEFINED,
SDL_WINDOWPOS_UNDEFINED, width, height,
SDL_WINDOW_OPENGL|SDL_WINDOW_SHOWN|SDL_WINDOW_RESIZABLE);
gContext = SDL_GL_CreateContext(gWindow);
GLfloat clear_col[4] = {0.0, 0.0, 0.0, 0.0};
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(fov, width/(float)height, nearplane, farplane);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
glClearColor(clear_col[0], clear_col[1], clear_col[2], clear_col[3]);
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LESS);
glShadeModel(GL_FLAT);
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
pixels = (unsigned char*) malloc(width*height*4);
glReadPixels(0, 0, width, height, GL_RGBA, GL_UNSIGNED_BYTE, pixels);
// checking the values
FILE*ffp = fopen("saved.bin", "wb");
fwrite(pixels, width*height*4, 1, ffp);
fclose(ffp);
Thanks in advance.
A:
By default, SDL will not explictely request a framebuffer with an alpha channel. You'll have to call
SDL_GL_SetAttribute(SDL_GL_ALPHA_SIZE, 1);
before you create the window to make sure that you actually get an alpha buffer. Note that this conceptually requests at least 1 bit alpha. Usually, GL implementations provide pixel formats/visuals with either 0 or 8 bits of alpha per pixel. If you want to make sure to get at least 8 bits, you could also request that explicitely.
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