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This application claims the benefit of provisional application 60/600,568 filed Aug. 11, 2004 entitled “Reusable Upper Stage”.
It also references USPTO disclosure document number 548532 filed Mar. 9, 2004, entitled “Reusable Upper Stage”.
1. Field of the Invention
The present invention is related to aerospace vehicles and transport systems and, more particularly, to Earth-to-orbit aerospace vehicles used for the deployment of payloads, such as satellites, into low Earth orbits.
2. Description of Related Art
It is widely held in the Earth-to-orbit launch community that one of the single biggest keys to reducing the currently high costs of launching anything into orbit is by making the launch vehicle hardware fully reusable. This stems from the generally high cost of launch vehicle systems. Most current expendable launch vehicles cost tens of millions of dollars to build only to be tossed away after each launch. If that hardware could be recovered and reused at a low enough cost, the hardware cost per launch can be significantly reduced. Being able to reuse the hardware in many cases also provides higher reliability. Each flight vehicle could be tested and debugged before going into commercial operations much like the current practice with commercial and military aircraft.
Several prior art systems have been patents. For example:
U.S. Pat. No. 6,557,803 discloses a crewed on-orbit, returnable, and reusable space vehicle.
U.S. Pat. No. 5,927,653 discloses a two-stage reusable earth-to-orbit aerospace vehicle and transport system that employs a airbags and parachutes for reentry and landing.
U.S. Pat. No. 6,068,211 discloses a method of earth orbit space transportation and return. A reusable space craft is deployed from air and jettisoned into orbit. Upon return, the space craft flies and lands with airplane-like functionality and utility.
U.S. Pat. No. 6,557,803 discloses a crewed on-orbit, returnable, and reusable space vehicle that uses multiple reusable boosters and an airplane-like return landing.
U.S. Pat. No. 6,264,144 discloses a material assembly for an inflatable aerodynamic braking device for spacecraft deceleration and the like. Includes inflatable materials that withstand extreme temperatures.
U.S. Pat. No. 5,842,665 discloses a launch vehicle with engine mounted on a rotor that enables it to launch to orbit and return to a destination point.
However, in spite of the desirability of being able to fully reuse the launch vehicle, and in spite of the many concepts that have been proposed, to this date no fully reusable Earth-to-orbit launch vehicle has flown. In fact, there is only one currently operating example of a reusable launch vehicle, the Space Shuttle, and it in fact is only partially reusable requiring extensive refurbishment, check-out, and inspection between each launch. Of the various proposed solutions, almost all of them suffer from various drawbacks and disadvantages.
For example, one of the most commonly proposed methods for making a space vehicle reusable is to give it wings to allow for horizontal landing. The drawbacks to these options is that they generally are very volume inefficient, the wings are often massive, and there are often severe strains put on the thermal protection systems of the vehicles. While this may work fine for a suborbital vehicle, these problems can become quite severe for an orbital vehicle. When the complicated aerodynamic steering and landing equipment such as flaps and landing gear is added, the result is a fairly expensive and complicated system. To make matters worse, most rockets are vertically launched. Putting a body that can generate aerodynamic lift at the end of a long rocket causes significant steering issues for the rocket. If it is horizontally launched, it either requires a very large flying carrier vehicle, or it requires very heavy wings and landing gear to be able to handle that much weight on takeoff.
Another option frequently proposed is a capsule-style ballistic system using a parachute for landing. These also have problems. One is that parachute recovery usually requires the craft to be recovered at sea which has usually been done in the past with an aircraft carrier, which are very expensive to operate. There can also be problems with actually reusing the vehicle due to seawater corrosion. Some capsules like those used by Russia and China are recovered on land, but this requires braking rockets and such vehicles are relatively limited as to where they may land. One difficulty with a parachute descent is that it offers very little precision in the system's landing location. Parachutes also have very limited cross-range capability. There is also the risk that the retrorockets might not fire correctly or that there might be substantial impact damage if using airbags for final landing.
Several suggestions for making Single Stage to Orbit (SSTO) reusable launch vehicles have also been proposed. However, these suffer from the fact that their entire weight must be put into orbit and brought back down again. This greatly reduces there potential payload and makes them much less economically feasible even if they prove to be technically possible.
Two-Stage to Orbit (TSTO) RLVs are significantly easier to develop. For most TSTO designs, the upper stage is usually the more expensive and complicated in spite of being physically much smaller than the lower stage. However, while the prospect of reusing the upper stage is attractive financially, it is also complex to develop and test.
What is needed is a simple that can function as the top stage of a TSTO system that can safely perform a soft landing and be prepared for re-use at a minimal cost in a minimal amount of time. Its use should also avoid added complexity of the lower stage design (being a standard rocket) and avoid the complexity and cost of wings or lifting-bodies on the upper stage. It should be a minimally more complex than a non-reusable upper stage, and should be capable of a precisely located soft landing on Earth to minimize operational costs of the system by allowing it to land at the launch site.
The present invention consists of an upper stage which has the capability of making precision landings, is completely reusable, and requires a minimal amount of time for check-out, inspection, and overhaul between flights. The main embodiment consists of an upper stage that uses room temperature propellants and consists of a propulsion system, an aeroshell that protects the stage from undue heating on launch and upon reentry, a guidance system with power source, extendable legs for landing, and a system to allow the propulsion module to be shifted forward and backward during reentry. The upper stage uses its main engine for a powered precision vertical landing.
The vehicle is designed to reenter nose-first in a ballistic manner. The aeroshell is covered by a transpiration or ablative thermal protection system for the reentry. The vehicle has an internal actuation system that allows the center of gravity of the stage to be varied during the reentry process thus allowing for the transition from a nose-first reentry to a side first semi-ballistic phase (which allows for greater cross-range movement than a purely ballistic reentry), and finally to a tail-first attitude for landing. The vehicle can be kept fairly stable throughout the entire reentry process.
In one embodiment, the landing gear is a system of light-weight, inflatable, heat-resistant legs. These are lighter than metal landing gear and allow the legs to be stowed in a much smaller space than typical folding metal landing gear.
In operation, the system works as follows: The upper stage is launched as the second stage of the two stage launch system. The payload compartment is mounted on the top of the propulsion module. After the upper stage separates from the lower stage, its engines are ignited and burn sufficiently to reach the desired orbit. The propulsion module is then slid back until the payload is uncovered. The payload is released, and the propulsion module is moved forward to a position inside the aeroshell (which remains in one piece).
At the proper time, the upper stage performs a de-orbit burn to decelerate enough to drop out of orbit and back into the atmosphere. At this point, the propulsion module slides forward within the aeroshell so the center of gravity is positioned forward. During re-entry and atmospheric descent, the propulsion module can be moved forward and backward to adjust the center of gravity to control the angle of attack and the amount of drag and lift it is generating.
In one embodiment, the spacecraft has fins to control its roll which allows the spacecraft to maneuver backward and forward in order to gain more cross range capability. Cross range capability is useful because it can allow the spacecraft to re-enter from various orbits which may not cross precisely over the landing site.
After the spacecraft has slowed to below Mach 1 and is approaching the landing site, it performs a flip-over maneuver in order to be traveling tail first. This is accomplished by moving the propulsion module backward for another center-of-gravity shift thus putting the spacecraft into a high angle of attack which further reduces the speed. When the spacecraft has descended to a relatively low altitude and is moving at subsonic velocity, the propulsion module is shifted further back until the center of gravity is at the back of the vehicle so it begins to fall tail first.
Just prior to landing the main engines are ignited to reduce the vehicle's velocity from terminal velocity to a safe landing speed prior to touchdown. Thrusters may also be used to maneuver to a precise landing point.
Just before touchdown the landing gear is deployed. If the spacecraft is using inflatable landing gear, it is inflated with a gas stored on the spacecraft at this time. If it is using a mechanical landing gear, it is extended at this time.
Propulsion modules built for the upper stage are made to operate optimally in vacuum. The atmospheric pressures on a propulsion module make the thrust direction unstable under normal atmospheric conditions with a standard nozzle. The nozzle must switch from a nozzle designed for a vacuum environment to one for operation near the Earth's surface in dense atmosphere. Various methods can be employed to accomplish this. In one embodiment, a circular gas injector is attached to the propulsion nozzle to force an even separation of the gas from the nozzle wall at a point where the jet pressure is nearly equal to sea-level ambient pressure. In another embodiment, a dual bell nozzle is used, which contains an inflection point that forces even separation at near sea-level ambient pressures. Both of these embodiments prevent the flow from reattaching to the chamber wall and thus producing large unwanted side-loads on the nozzle. In another embodiment, the lower section of the nozzle is jettisoned to reduce the expansion ration of the nozzle.
One embodiment detailed in this patent can also be used for lunar and planetary landings. For operation as a lander on the moon and planets with little or no atmosphere, the aeroshell is discarded upon exiting the earth's atmosphere. The propulsion module uses thrust to orient the stage for a tail-first landing first. The inflatable landing gear is inflated before landing, as is done for earth landings.
Also, this upper stage can be configured to operate as a free-flyer orbital laboratory or manufacturing facility. In this configuration it is configured with a laboratory or manufacturing module mounted in place of the payload. The upper stage would be sent to orbit as per usual operations, and then the system would stay in orbit until the experimentation or material processing was complete, at which point it would reenter, decelerate, flip to tail first orientation, deploy landing apparatus and land.
This system of the current invention has many advantages over other proposed and existing reusable systems. The semi-ballistic trajectory allows for a degree of cross-range maneuvering during reentry. Using the propulsion module in a powered vertical landing provides much higher landing precision than is typical. This concept also delivers significant operational savings by not requiring the recovery of a stage from the sea or needing to search for a stage after it has landed. Also, by avoiding corrosive sea water, it will be easier to prepare the vehicle for its next flight in a rapid manner. Most importantly, the system is simple and much less expensive than other options. It involves a minor amount of additional hardware over that found on a typical upper stage.
FIG. 1
is a pictorial illustration of a payload launch sequence of the two stage rocket.
FIG. 2
FIG. 2
a
b
is a cross-sectional schematic of the reusable upper stage. is a cross-sectional schematic of an extended aeroshell.
FIG. 2
c
is a cross-sectional schematic of the configuration of the upper stage immediately prior to and during reentry.
FIG. 2
d
is a cross-sectional schematic showing an another embodiment of the upper stage that includes payload doors.
FIG. 2
d
is a cross-sectional schematic showing an another embodiment of the upper stage that includes payload doors.
FIG. 2
f
is a cross-sectional schematic showing the reentry configuration of payload door embodiment immediately prior to and during reentry.
FIG. 3
is a pictorial illustration of an upper stage landing sequence.
FIG. 3
a
. is an illustration of the upper stage, immediately after having released its payload into orbit.
FIG. 3
b
. is an illustration of the reentry configuration of the reusable upper stage.
FIG. 3
c
is an illustration of the upper stage during reentry.
FIG. 3
d
is an illustration of the configuration of the after it has decelerated to supersonic speeds.
FIG. 3
FIG. 3
e
f
is an illustration of the subsonic configuration of the upper stage. is an illustration of the vehicle immediately prior to touchdown.
FIG. 4
a
is a cross-sectional schematic showing the upper stage propulsion unit nozzle with side injection ports.
FIG. 4
b
is a cross-sectional schematic of another embodiment of the altitude compensation system using a dual bell nozzle.
FIG. 4
c
is a cross-sectional schematic of another embodiment of the altitude compensation system using a drop-away lower nozzle.
FIG. 5
is a schematic drawing of the inflatable landing legs of the present invention.
FIG. 5
FIG. 5
a
b
shows the location of the inflatable legs before deployment. shows the inflatable landing legs deployed.
FIG. 5
c
is a perspective view of the reusable module on the ground with landing legs deployed.
FIG. 6
shows another embodiment of the inflatable landing cushion using an inflatable toroid.
FIG. 6
FIG. 6
a
b
An illustration of the upper stage prior to deployment of the toroid. A cross-section of a deployed toroid.
FIG. 6
c
A pictorial upper view of the toroid
FIG. 6
d
A pictorial lower view of the toroid surrounding the nozzle.
FIG. 1
100
105
110
120
is a pictorial illustration of a payload launch sequence of the two stage rocket. As depicted, the two stage rocket () includes: one or more lower stages () releasably connected to an upper stage (), and a payload () that is carried on board the upper stage.
Typically two or more stages are used to send a rocket with payload into space. The rocket shown in this figure uses only two stages, however the unique aspects of this patent can also be applied to a rocket of three or more stages.
In one embodiment, the reusable upper-stage further comprises at least one releasably connected conduit configured allow the stage to be launched with partially filled propellant tanks to allow the main engine to be used to lift the stage away from the lower stage in the event of a malfunction, yet still provide enough acceleration due to the reduced mass of the stage, then allow propellant stored on the lower stage to be transferred to the upper stage prior to upper stage ignition.
In another embodiment, the upper-stage further comprises a liquid payload storage system configured to store liquid payload. In this embodiment, there is a storage system with at least one payload storage tank, a conduit to a load and unload port, and a valve to isolate the load and unload port. This is used to launch liquids such as propellant or water into space economically.
FIG. 2
a
200
215
220
225
120
230
240
250
is a cross-sectional schematic of the reusable upper stage. As depicted, the includes: a propulsion module (), some retractable railing (), an aeroshell (), a payload compartment () with a payload () inside, an inflatable landing apparatus (), a guidance and control system (), and a battery ().
200
The propulsion module () in one embodiment burns kerosene and peroxide. These room temperature storage propellants do not need to be kept at cryogenic temperatures and can be easily maintained in orbit. They also offer the advantage of being very reliable to ignite in a configuration where the peroxide is decomposed before being mixed with the kerosene.
Because of the aerodynamic loads on the engine nozzle, in the preferred embodiment it does not gimbal but achieves the required thrust vector authority by peroxide side injection in the throat of the nozzle. The nozzle must be sound enough to withstand the aerodynamic loads of the flip maneuver in the atmosphere.
200
220
120
215
The schematic shows the positioning of the propulsion module () with respect to the upper-stage aeroshell () in launch position with a payload (). The propulsion module is able to slide on the railing () which allows the stage to shift its center of gravity for different portions of the mission. During launch the propulsion module locked in place.
In another embodiment, a pressurized crew compartment is attached to the inside of the nose of the aeroshell for launching people into orbit and returning them to Earth.
FIG. 2
b
220
120
220
120
is a cross-sectional schematic of an extended aeroshell. As depicted, this includes: the extended aeroshell (), and the payload (). The aeroshell () is in position to release the payload ().
FIG. 2
c
200
220
is a cross-sectional schematic of the configuration of the upper stage immediately prior to and during reentry. As depicted, this includes the propulsion module (), and the aeroshell ().
220
200
230
During and immediately prior to reentry, the aeroshell () is fully retracted and the propulsion module () adjusted far forward into the aeroshell () to change its center of mass. This allows for good nose-first stability on reentry.
FIG. 2
d
210
120
is a cross-sectional schematic showing an another embodiment of the upper stage that includes payload doors. This embodiment includes payload doors () to enclose the payload () prior to dispensing it.
FIG. 2
e
120
210
is a cross-sectional schematic of the payload door embodiment, showing the payload being released. The payload () is being released through the open payload doors ().
FIG. 2
f
120
210
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is a cross-sectional schematic showing the reentry configuration of payload door embodiment immediately prior to and during reentry. Prior to reentry, after the payload () has been released, the payload doors () are closed, and the propulsion module () is shifted forward inside the aeroshell () to change the center of gravity for reentry.
FIG. 3
200
220
230
is a pictorial illustration of an upper stage landing sequence. The landing sequence illustration includes: the propulsion module (), the aeroshell (), and the inflatable landing apparatus ().
FIG. 3
a
. is an illustration of the upper stage, immediately after having released its payload into orbit.
FIG. 3
b
200
220
. is an illustration of the reentry configuration of the reusable upper stage. For reentry, the propulsion module () is moved forward into the nose of the aeroshell (), to move its center of gravity forward.
FIG. 3
FIG. 3
c
b
200
is an illustration of the upper stage during reentry. As in , the propulsion module () is shifted forward inside of the aeroshell. The center of mass is now ahead of the center of pressure causing it to orient itself in the direction of motion through the atmosphere.
FIG. 3
d
is an illustration of the configuration of the after it has decelerated to supersonic speeds. Here, the propulsion module is shifted to the center of the stage placing the center of mass there. The stage then rotates to fall substantially sideways to present a larger frontal area to the air. This increases the drag on the stage which further slows it. Also, in one embodiment, small aerodynamic surfaces allows the to steer itself, giving it substantial cross range.
FIG. 3
e
230
is an illustration of the subsonic configuration of the upper stage. Once the stage has reached an subsonic velocity and a low altitude around 3000 meters, the propulsion module moves back to the aft end of the stage. This urges the stage to an upright position because the drag will move the nose more than the tail causing the stage to pivot with the nose pointing away from earth. The propulsion module engine is ignited which continues to slow the stage to a speed compatible with the deployment of the landing legs ().
FIG. 3
f
230
230
is an illustration of the vehicle immediately prior to touchdown. The vehicle has slowed sufficiently that the inflatable landing legs () can then deployed and inflated before landing. The stage lands on the ground as the inflatable legs () support the stage and cushion the impact.
FIG. 4
a
is an illustration of various ways to compensate for flow separation. Without altitude compensation, flow separation could possibly occur leading to unpredictable thrust vectors and side loads on a nozzle designed for low-pressure or vacuum rather than atmospheric operation.
FIG. 4
a
405
410
420
425
430
435
440
445
is a cross-sectional schematic showing the upper stage propulsion unit nozzle with side injection ports. This propulsion unit includes: a nozzle (), side injection ports (), a flow path which the detached flow follows (), a fuel inlet (), a fuel valve (), an oxidizer inlet (), an oxidizer valve (), and the injector ().
405
410
410
405
420
In this embodiment, there are below the throat of the nozzle () several side injection ports () are located. The side injection ports () inject a propellant into the main flow at a point near the normal at sea level separation point forcing the main flow to separate from the nozzle () at this point thus performing like a smaller area ratio nozzle. The flow then follows path (). In one embodiment, the propellant injected through he side injection ports is catalytically decomposed hydrogen peroxide.
FIG. 4
b
445
450
455
450
455
is a cross-sectional schematic of another embodiment of the altitude compensation system using a dual bell nozzle. This nozzle includes: the propellant injector (), an inflection point (), and the flow path of a gas () when the ambient pressure is near sea-level. The inflection point () causes the flow to detach at the inflection point and follow path (), if the engine is operating at low-altitudes. At higher altitudes, the flow would fill the nozzle like a normal high-expansion nozzle.
FIG. 4
c
460
465
470
460
465
470
470
is a cross-sectional schematic of another embodiment of the altitude compensation system using a drop-away lower nozzle. This nozzle includes a jettisonable lower section (), a disconnect flange (), and a disconnect mechanism (). This section (), is attached to the disconnect flange () by a disconnect mechanism (), and is jettisoned prior to reentry to prevent flow separation at lower atmospheric levels. In one embodiment, the disconnect mechanism () consists of quick disconnect bolts such as those made by Starsys Corp.
FIG. 5
110
230
505
510
is a schematic drawing of the inflatable landing legs of the present invention. This schematic includes the (), the inflatable landing legs (), the landing leg compartment (), and landing leg deployment valve (). The inflatable landing legs are made of a durable, gas-impermeable material that can withstand the scuffs and heat of landing.
FIG. 5
a
shows the location of the inflatable legs before deployment.
FIG. 5
b
505
510
230
shows the inflatable landing legs deployed. Upon reaching the desired altitude and decent velocity the compartment () is opened, releasing the deflated landing legs, and valve () is opened releasing the pressurized gas to inflate the legs ().
FIG. 5
c
is a perspective view of the reusable module on the ground with landing legs deployed.
FIG. 6
610
shows another embodiment of the inflatable landing cushion using an inflatable toroid. This embodiment includes an inflatable toroid (). This embodiment provides more strength against translational forces whereas the embodiment using inflatable legs provides more cushioning between the stage and the ground.
FIG. 6
a
An illustration of the upper stage prior to deployment of the toroid.
FIG. 6
b
A cross-section of a deployed toroid.
FIG. 6
c
A pictorial upper view of the toroid.
FIG. 6
d
A pictorial lower view of the toroid surrounding the nozzle. The toroid adds some ground effect deceleration to the vehicle as it lands by capturing the pressure of the exhaust.
While the invention has been described in the specification and illustrated in the drawings with reference to a main embodiment and certain variations, it will be understood that these embodiments are merely illustrative. Thus those skilled in the art may make various substitutions for elements of these embodiments, and various other changes, without departing from the scope of the invention as defined in the claims. Therefore, it is intended that the invention not be limited to the particular embodiment illustrated by the drawings and described in the specification as the best mode presently contemplated for carrying out this invention, but that the invention will include any embodiments falling within the spirit and scope of the appended claims.
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
SHORT DESCRIPTION OF DRAWINGS
DETAILED DESCRIPTION OF INVENTION | |
This series of articles on the impacts of content moderation was commissioned from a broad selection of global academics, journalists, and civil society activists. The authors were given a relatively free hand to prioritize the issues that they saw as of primary importance, and to frame the challenges according to their own perspective. In addition to hosting the articles on our own website, they were cross-posted to several outlets, including TechDirt, Global Voices, Lawfare, Slate, and Protego Press:
- Michael Karanicolas - Moderate Globally, Impact Locally. Introducing a project to shed light on the global impacts of content moderation.
- Sergei Hovyadinov - Better Transparency Reporting Can Shed Light on Russian Internet Censorship. Transparency reporting is a critical avenue to tracking content controls, especially in repressive countries.
- Aye Min Thant - Digital technology as accelerant: Growth and Genocide in Myanmar. Facebook's role in Myanmar's digital revolution, and in the chaos that followed.
- Tomiwa Ilori - Content Moderation Is Particularly Hard in African Countries. Across Africa social media has helped to rock the status quo, and to reinforce it.
- Agustina Del Campo - Social media in Latin America, Caught between a rock and a hard place. For users in Latin America, merely understanding how the rules apply to them can be a challenge.
- Akriti Gaur - Tackling Social Media’s Hate Speech Problem in India. Platforms in India have been a vehicle for hate, they need to get serious about robust engagement and accountability.
- Andrés Calderón - Content Moderation in Social Media in Latin America: A promise to consumers. The lack of legal accountability has led social media users across Latin America to seek alternative solutions.
- Dorothy Mukasa - Internet Content Moderation in Uganda – A Taxing Situation. Authorities in Uganda view social media as a threat, the lack of public accountability reinforces this perception.
- Farieha Aziz - An internet with borders: A perspective from Pakistan. Pakistan's social media users are caught between government overreach and corporate compliance.
- Michael Karanicolas - The Countries Where Democracy Is Most Fragile Are Test Subjects for Platforms’ Content Moderation Policies. The consequences of both undermoderation and overmoderation can be dire. So how can platforms moderate content without causing damage?
New Controversies in Intermediary Liability Law – An Essay Collection (June 2019)
In Spring 2019, WIII produced and edited a collection of short, accessible essays on key issues in intermediary liability, to serve as a resource for academics, policymakers, and the general public. These essays were published on Balkinization and on the ISP website. The short essay format allowed authors to write on current, fast-moving issues. The essay collection included the following authors and topics:
- Annemarie Bridy, “Faith in Filters and the Fate of Safe Harbors”
- Jacob Rogers, “It’s Not About What You Know: An Overview of Hyperlink Law’s Troubles”
- Aleksandra Kuczerawy, “To Monitor or Not to Monitor? The Uncertain Future of Article 15 of the E-Commerce Directive”
- Anupam Chander, “A Facebook Supreme Court?”
- Eric Goldman, “Want to Kill facebook and Google? Preserving Sectio 230 Is Your Best Bet”
- Amélie Heldt, “Facebook and the EU Elections: Overzealous or Misinformed?”
- Martin Husovec, “Why Is There No Due Process Online?”
- Michael Karanicolas, “Privatizing Censorship”
- Daphne Keller, “Build Your Own Intermediary Liability Law: A Kit ofr Policy Wonks of all Ages”
- Tiffany Li, “Intermediary Liability: The Next Frontiers”
“Intermediary Liability and Private Speech Regulation: A Transatlantic Dialogue” Workshop Report (March 2019)
In September 2018, WIII hosted “Intermediary Liability and Private Speech Regulation: A Transatlantic Dialogue.” This workshop, organized with support from Stanford’s Center for Internet and Society, convened leading scholars from the United States and European Union to debate current interpretations of laws and to understand intermediary and government responsibilities for the future of online speech. Participating experts included Jack Balkin, Owen Bennett, Annemarie Bridy, Niva Elkin-Karen, Robert Hamilton, Martin Husovec, Joris van Hoboken, Daphne Keller, Aleksandra Kuczerawy, Tiffany Li, Emma Llanso, and Karmen Turk.
WIII subsequently published a report presenting findings, insights, and conclusions from the workshop discussions. The report is available on the ISP website.
“Beyond Intermediary Liability: The Future of Information Platforms” Workshop Report (February 2018)
Based on conversations from a workshop hosted by WIII, this free, publicly available report details the most critical issues necessary for understanding the role of information platforms, such as Facebook and Google, in law and society today. The report highlights insights and questions raised by experts during the event, providing an insider’s view of the top issues that influential thinkers on intermediary liability are considering in law, policy, and ethics. The report is publicly available. | https://law.yale.edu/isp/initiatives/wikimedia-initiative-intermediaries-and-information/publications |
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Langerhans cells are epidermal antigen-presenting cells that function by taking up antigens in the skin, migrating to the lymph nodes, where they are designated interdigitating cells, and triggering the immune response. The role of interdigitating cells (IDC) was investigated in a murine model of herpes simplex virus-1 infection in the skin. The number of IDC in the lymph nodes began to increase on the first day following infection and reached a peak three days p.i. Low titers of infectious virus were recovered from the fraction of lymph node cells that consisted of 60-80% IDC at one day p.i. Lymph node cells that were obtained from mice immunized with HSV-1 proliferated in vitro in response to viral antigens but did not respond to mock antigens. When mice were immunized with HSV-1 inoculated into skin that had been depleted of Langerhans cells, this in vitro proliferative response was abolished. Thus, the present results suggest that Langerhans cells function in the immune defense of the skin against HSV-1 infection by transporting the virus to the peripheral lymph nodes where an immune response is initiated. Injection of the immunomodulator OK-432 into the footpad skin caused a local increase in the number of Langerhans cells in the epidermis and led to an increased migration of dendritic cells to the lymph nodes. Under these conditions, a decrease in HSV-1 pathogenicity was noted. These observations indicate that the pathogenicity of herpes simplex virus type 1 in the skin is affected by Langerhans cell density and activity in the epidermis and the lymph nodes.
National Center for
Biotechnology Information, | https://www.ncbi.nlm.nih.gov/pubmed/2554853?dopt=Abstract |
Get latest articles and stories on India at LatestLY. Vice President M Venkaiah Naidu on Monday stressed the need for improving financial literacy among the masses and urged professionals like Chartered Accountants to work in this direction by explaining financial rules and regulations in simple and easy language for the larger benefit of the public.
Kochi, Jan 3 (PTI) Vice President M Venkaiah Naidu on Monday stressed the need for improving financial literacy among the masses and urged professionals like Chartered Accountants to work in this direction by explaining financial rules and regulations in simple and easy language for the larger benefit of the public.
"Accountancy, finance and audit are subjects in which one has to deal a lot with numbers and a maze of rules and regulations. There are many people in our society who find it difficult to understand these areas. Therefore, it's my appeal to all Chartered Accountants that you should try to explain these subjects in simple and easy language for the benefit of the people. ICAI and its members and students should also work for spreading financial literacy among the masses," Naidu said.
Naidu said the Insolvency and Bankruptcy Code has revolutionised the corporate resolution processes in the country, while the Goods and Services Tax (GST) has turned out to be a grand success as evidenced by the increasing Indirect Tax Collections.
Naidu said the post covid scenario looks bright and India could demonstrate a new saga of enterprise attracting the whole world with multiple strengths.
"Our economy today is recovering fast from the unexpected setback caused by COVID-19. FDI inflows are steadily on the increase. Once the fear of the pandemic subsides, it is expected that travel and tourism, a major Foreign Exchange earnings and a source of employment for millions in a State like yours, will also wake up with new vigour," he said.
Earlier in the day, Naidu attended an event organised to mark the 150th death anniversary of Saint Kuriakose Elias Chavara, a spiritual leader and social reformer from the Kerala Catholic community, at Mannanam near Kottayam.
The Vice President also visited the tomb of Saint Chavara at Mannanam.
Naidu returned from Lakshadweep on Sunday morning. He was accompanied by his wife Usha and other family members.
After the ICAI event, the Vice President left for New Delhi from here.
Naidu, who reached Kerala on December 31, flew to Lakshadweep the same day. He attended various programmes in the island for two days, including the inauguration of two Colleges of Arts & Sciences in Kadmat and Androth islands.
He also attended a few events in Kochi and visited the IAC Vikrant.
(This is an unedited and auto-generated story from Syndicated News feed, LatestLY Staff may not have modified or edited the content body) | |
Stakes are always high in peace operations, so decent training is vital for the various roles of peacekeepers, the implementation of the mission mandate and for ensuring operational unity, coordination and coherence. Set amid a rapidly changing backdrop, our roundtable discussed the many systemic challenges to UN peacekeeping.
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Gone are the days of peacekeepers patrolling buffer zones between two conflict parties. Instead, they face ever more complicated large-scale situations, with diverse and fragmented actors, both state and non-state, while at the same time receiving more complex multi-layered mandates Robust Peacekeeping: A Necessary Evil? The use of force in UN peacekeeping has sparked heated debates in academic and policy circles alike. Is Hybrid Peacekeeping a Model of Success? These bodies are playing more assertive roles both politically and militarily, and the most prominent recent example is the United Nations — African Union Mission in Darfur New technology isn't the cause of inequality — it's the solution.
What does the future hold for our universities? Total military and police personnel peaked around , in , up from about 12, in Recently, however, this trend has reversed.
Peacekeeping forces are down to about 92, as of January While certain countries like China have continued to step up the number of peacekeepers and dollars they contribute, the overall trend has been downsizing, which started in and accelerated in and As a result, the international community rarely meddled with the internal machinations of a given country.
Sovereignty was not to be violated and this was a system which benefited both superpowers, their allies, as well as third world governments. Now, however, with legitimacy being extended to non-state actors, as well as the opportunity for a minority to secede from a given state and form a new country there has been a dramatic shift in the international status quo. Moreover, the international community's model for conflict resolution is heavily influenced by academic thought developed in western countries. This model encourages intervening in civil wars in order to stop political violence and come to a negotiated settlement which often involves democratising efforts.
Clapham's argument is principally in relation to the situation in Rwanda leading up to the genocide , whereas Shearer focuses on the negative aspects of intervention, primarily regarding Sierra Leone , which prevents total victory by one side and results in the creation of asymmetries between belligerents which opens the door for continued bloodshed. In Rwanda, third-party attempts at a negotiated settlement between the Hutu and Tutsi afforded an opportunity for Hutu extremists to prepare for the killing of Hutu moderates and the genocide of the Tutsi.
The international community, led by regional states from the Organisation of African Unity , sought to negotiate a settlement and find a solution for the ongoing ethnic violence between Hutu and Tutsi via the Arusha Peace Process. This process lasted just over a year, included substantial international involvement, and incorporated many regional actors such as Tanzania host of the process , Burundi , Uganda and Zaire. While the Rwandan Patriotic Front RPF was a major beneficiary of the Arusha accords and was able to redress many of its grievances, many of the gains that it made could have been achieved through military action.
Arusha, according to Clapham, affected the relative power of the participants in the two following ways: a ceasefire which froze the distribution of territorial control at a particular point and secondly the importance it ascribed to the participants of the negotiations. A faction's importance was weighted not on their relative popularity or military strength, but on artificial weight assigned by the mediators.
Peacekeeping
Thus, the entire process served to undermine the RPF's position while stalling their hitherto successful military campaign, while allowing Hutu extremists to prepare for a genocide. Shearer argues that modern strategies that rely solely on consent-based negotiations are severely limited and that victory by military means should not be ignored.
He states that a shift in battlefield fortunes can often bring one belligerent to the negotiation table and will likewise moderate their demands. Consent is of great importance when it comes to negotiation and mediation. The current international system and the conflict resolution model which the international community has utilised most since the end of the Cold War puts a premium on consent. But Shearer asks that if a belligerent uses negotiations and cease-fires as a method of delay in order to allow them to reposition military forces and continue fighting, then should consent-based strategies still be pursued, regardless of the potential for lengthening a conflict and the associated human cost?
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According to the empirical analysis cited by Shearer, past civil wars with negotiated settlements have had little success. However, only 14 or 24 percent of those settled were solved by negotiation. The others 76 percent ended with military victories. Additionally, fighting resumed in seven of the 14 conflict which were initially ended by negotiation.
The overall success rate of negotiated settlements, therefore, was around 12 percent out of the internal wars that ended.
In Sierra Leone the Revolutionary United Front , led by Foday Sankoh , fought an ongoing and bloody civil war with the government from to The conflict attracted little international attention, but managed to devastate the country and destroy its economy. Neither belligerent was willing to concede or compromise on their demands, despite multiple attempts at a negotiated settlement. Sankoh would come to the table after the intervention of the private military corporation Executive Outcomes and a reversal in the RUF's battlefield fortunes. In the aftermath the RUF was a depleted threat, civilians were able to return from refugee camps and begin rebuilding their lives.
But the peace was fragile and negotiations were ongoing. The RUF was reluctant to put down their arms, concerned over potential retribution at the hands of army units and civilian militias alike. There was a planned deployment of UN peacekeepers meant to ease these concerns and help with the transition to peace, but things began to unravel.
International contributors began to shy away from further peacekeeping initiatives; such as an expensive and open-ended mission in a strategically unimportant country. As a result, the UN's intervention force was slow to come to fruition and then came to a halt completely when Sankoh argued the size of the contingent of UN peacekeepers was too large. The UN refused to engage without total consent from both parties, thus preventing the deployment of a peacekeeping force. This consent-based approach, Shearer argues, illustrates the limits the UN can play in the volatile and fragile state of affairs that exist during and after civil wars.
It also meant that Sankoh was dictating terms.
The situation was exacerbated by the fact that the newly elected President of Sierra Leone terminated the Executive Outcomes contract undermining his hard power advantage. Things were further inflamed when disaffected officers of the army overthrew the government in A small UN force of monitors was deployed to observe the security situation. However, violence would continue. Instead, with British support, an aggressive campaign was waged against the RUF.
By late and early the RUF's military strength had been severely depleted. When the British intervened militarily and substantially degraded the RUF's capability to sustain the conflict, as Executive Outcomes had done years prior, the RUF finally come to the negotiating table and allowed for the establishment of peace. Some authors question the idea of international interventions at all. Using case studies of Uganda , Eritrea , and Somalia , Weinstein demonstrates how states can develop effective institutions out of warfare.
This method has cost and benefits that must be weighed against the potential outcome of international intervention. External intervention can stop mass atrocities, but also stop institutional change.
Peacekeeping - International Relations - Oxford Bibliographies
Autonomous recovery elevates the strongest leader, but also rewards the strongest fighters who may be less inclined to share power. Furthermore, intervention depends on external influence while autonomous recovery is based on internal factors. Weinstein argues the fundamental challenge is how to incentivise good governance and assistance to rebel groups without disrupting the connection of citizens to rulers in terms of revenue collection that enables accountability.
itlauto.com/wp-includes/map17.php Although acknowledging a number of practical and moral reasons for peacekeeping operations, James Fearon and David Laitin assert that they have a tendency under some circumstances to become tangled with state-building efforts. In weak states facing successful guerrilla campaigns, peacekeepers face pressures to build state institutional and administrative capacity in order to achieve lasting peace. These pressures can lead to mission creep beyond the original purview of the peacekeeping operation; without engaging in state-building, the peacekeepers risk allowing the peacekept country to revert to violence following their exit.
Thus, Fearon and Laitin advocate for the greater integration of state-building in peacekeeping efforts through a new framework of "neotrusteeship," which would see foreign powers exercising a great deal of control over a weak state's domestic affairs in order to ensure the prevention of future violence.
A growing critique of peacekeeping is the lack of engagement between the peacekeeping officials and the local populace. Additionally, it creates a reinforcement mechanism for the peacekeeping officials, because the officials on the ground report that their plan was successfully implemented, but, in reality, it had adverse effects. If the situation on the ground turns into another outbreak of violence, the local populace will be blamed. This criticism is similar to the critic levelled at development in developing countries by authors such as James C. Scott, James Ferguson, and L.
The third-party officials-whether they are peacekeepers or agents of development-are isolated from the general populace, believing they know what is best, and refusing to gather information from a ground level. This is not out of maliciousness or imperialism, but out of a legitimate belief that they, as educated officials with access to other experts and who are well versed in development and peacekeeping literature, know what is best.
In response to criticism, particularly of the cases of sexual abuse by peacekeepers, the UN has taken steps toward reforming its operations. The Brahimi Report was the first of many steps to recap former peacekeeping missions, isolate flaws, and take steps to patch these mistakes to ensure the efficiency of future peacekeeping missions.
The UN has vowed to continue to put these practices into effect when performing peacekeeping operations in the future. The technocratic aspects of the reform process have been continued and revitalised by the DPKO in its "Peace Operations " reform agenda. This included an increase in personnel, the harmonisation of the conditions of service of field and headquarters staff, the development of guidelines and standard operating procedures, and improving the partnership arrangement between the Department of Peacekeeping Operations DPKO and the United Nations Development Programme UNDP , African Union , and European Union.
A capstone doctrine entitled "United Nations Peacekeeping Operations: Principles and Guidelines" incorporates and builds on the Brahimi analysis. One of the main issues that the Brahimi report identifies is the lack of coordination and planning of the Peacekeeping Operations. | https://bontprovvintcaf.tk/peacekeeping-and-the-international-system.php |
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References & Citations
Mathematical Physics
Title:Nonperturbative theory of power spectrum in complex systems
(Submitted on 16 Oct 2019)
Abstract: The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for complex systems whose eigenspectra -- not necessarily of the random-matrix-theory (RMT) type -- posses stationary level spacings. Motivated by potential applications in quantum chaology, we apply our formalism to calculate the power spectrum in a tuned circular ensemble of random $N \times N$ unitary matrices. In the limit of infinite-dimensional matrices, the exact solution produces a universal, parameter-free formula for the power spectrum, expressed in terms of a fifth Painlevé transcendent. The prediction is expected to hold universally, at not too low frequencies, for a variety of quantum systems with completely chaotic classical dynamics and broken time-reversal symmetry. On the mathematical side, our study brings forward a conjecture for a double integral identity involving a fifth Painlevé transcendent. | https://arxiv.org/abs/1910.07432 |
Day 1:
Our guide will pick you up upon arrival in the Zhengzhou and meet the guide for transfer to your hotel. Enjoy free time the rest of the day.
Day 2:
Breakfast. Then drive to Hebi (2 hour driving distance) visit your child's home orphanage and meet with people related to your child's adoption. If you desire, host a lunch or dinner for the orphanage director and staff. Explore the local area with your guide. If needed, locate and visit the place where your child was found or visit your child's former foster family (if applicable and pending special permission).Our guide will escort you back to your hotel.
Day 3:
Breakfast. Today you will have a full day Zhengzhou city sightseeing, visit some of the major scenic spots like Shaolin Temple, Henan Museum, Yellow River Scenic Area, etc.
Day 4:
After the breakfast, our guide will transfer you to Zhengzhou airport/railway station.
Prior to your orphanage visit application submission, please make sure you have the following documents ready:
A copy of each visitor's passports
A copy of the adoption certificate or the notarized adoption documents
An orphanage visit application letter
We all know that it is important to return to China. Apart from visiting the orphanage, children may focus more on traveling itself. Therefore, if adoptive families want to explore more tourist cities in China, please feel free to tell us. And we will customize a heritage tour of lifetime for you.
HeBi City Social Welfare Institute:
Address:Eastern Section of Qiu Jiang Road, Qi Bin District, He Bi City, He Nan Province, 458000.
General Information:The orphanage is located in Hebi Hebi City, Qibin district, about 2 hours drive from Zhengzhou, capital of Henan Province.
Some of the children living in the orphanage and other foster families in the city.Boundaries With Love has assisted in this orphanage.Hebi city has an area of 2,182 square km and a population of 1,427,700 inhabitants.
His is the Han ethnic majority .
It is rich in coal mines.
Mt. Yunmeng: Located southwest of Qixian, it is famous for beautiful mountain scenery and its ancient strategic culture.
Mt. Dapi and Mt. Fuqiu: Located in Junxian, the two mountains stand face-to-face, famous for their Taoist temples and ancient architecture.
Qi River Natural Taichi Diagram: Located northwest of the urban city, it is the biggest natural Taichi diagram in China. With many historical sites and beautiful river scenery, it has become one of the most popular tourist resorts in Hebi.
Depending on the size of the SWI and how often visitors return, a visit could can be a highly anticipated event by the staff, or a routine, minor inconvenience to the day to day running of the institution.
You will want to discuss this aspect of reality with your child and prepare her or him for what it might be like, based on what you know. It is good to talk to your child about what to expect and then what to do if things turn out differently than you expect. It is important to develop an attitude of flexibility and focus on enjoying the experience rather than to get set on things going a certain way, since things don’t always go exactly as planned on any trip or daily life experience. A small gift is always appropriate for the effort expended by the director and or staff to accommodate the visiting family.
Since it may be several years after an adoption, it’s not unusual that the orphanage moved to a new place. Remember it’s normal, natural, time will not stand still, just as your children changed dramatically from she/he was a baby when just there.
If you are interested in visit both of the orphanages, we are happy to facilitate it, you can follow the previous footprint to recall your excitement when you look at your children at first time.
We usually arrange visiting the finding site for families if have the Notarial Certificate of the finding place. The finding site usually is at the front of hospital/orphanage/government agencies, etc. Please note that there places may be changed also.
Since visiting the finding site is the most emotional part of the trip, it’s a personal decision for each family and only you can make the decision if you want to accomplish it.
We always arrange the meeting with the previous caregiver/ foster family. If you have the information of the previous caregiver, we will try our best to find her. Please do remember that it’ll be some years after your adoption, the caregiver may be moved away or be retired. If the caregiver is still working in the orphanage, the director will happy to facilitate the connection.
Also please note that the caregiver may take care of more than one hundred babies in the orphanage, so that she may not remember your child well.
If your family is interested or inclined to invite the orphanage director to lunch, it is proper to invite others in the meeting as well. This would usually be one or two of the directors' assistants. If you want to invite the caregiver or nanny, then you should extend that invitation through the director to show the proper respect that the position merits. Your guide will handle this for you, but inviting the staff through the director follows proper etiquette for the situation. Some of the orphanages offer the free lunch while the others request about USD90-USD150 for the extra charge. You may ask our trip consultant before you travel.
When visiting an orphanage, it is appropriate to prepare some gifts for the director/staff and the children. You can invite the director, the staff or the caregiver to have lunch together or prepare fruit basket for them, for their effort expended to accommodate the visiting family.
As for the gifts to kids, you can prepare some snacks, candy, books, school backpacks, toys and so on. Usually, you can buy them when arrival at the orphanage place, the guide can escort you.
If you want to donate something more valuable and not sure what is needed for the orphanage, you can first learn it from the director and then purchase them from the local market. Some SWI will issue a donation certificate to you but not every SWI will do this.
With years of experience working with children in orphanages all over China, Lead to China is uniquely qualified to offer a special homeland experience for you. You will: | https://www.leadtochina.com/travel/adoption/OrphanageTravelGuide/304 |
The CW has released a 60-seconds Preview Clip from DC’s Legends of Tomorrow episode “Blood Ties” (1.03), to be aired on Thursday, February 4 at 08:00-09:00 PM.
Nobody said saving the future would be easy.
In DC’s Legends of Tomorrow, when heroes alone are not enough… the world needs legends. Having seen the future, one he will desperately try to prevent from happening, time-traveling rogue Rip Hunter is tasked with assembling a disparate group of both heroes and villains to confront an unstoppable threat — one in which not only is the planet at stake, but all of time itself.
Based on the characters from DC Comics, DC’S LEGENDS OF TOMORROW is from Bonanza Productions Inc. in association with Berlanti Productions and Warner Bros. Television, with executive producers Greg Berlanti, Marc Guggenheim, Andrew Kreisberg and Sarah Schechter. | https://heroesvue.com/2016/02/04/the-cw-released-preview-clip-of-dcs-legends-of-tomorrow-episode-blood-ties/ |
---
abstract: 'We study the effects of ${{\cal N}}=4$ topological string amplitudes on the entropy of black holes. We analyse the leading contribution associated to six-derivative terms and find one particular operator which can correct the entropy of ${{\cal N}}=4$ black holes. This operator is BPS-like and appears in the effective action of type II string theory on $K3\times T^2$ or equivalently its heterotic dual on $T^6$. In both descriptions the leading contribution arises at one-loop, which we calculate explicitly on the heterotic side. We then consider whether this term has any consequences for the entropy of (large) ${{\cal N}}=4$ black holes and find that it makes indeed a contribution at subleading order. Repeating the computation for small black holes with vanishing horizon area at the classical level, we prove that this coupling lifts certain flat directions in the entropy function thereby being responsible for the attractor equations of some moduli fields.'
author:
- |
\
I. Antoniadis[^1] [^2] and S. Hohenegger[^3]
title: |
[CERN-PH-TH/2009-162]{}
**[${{\cal N}}=4$ Topological Amplitudes and Black Hole Entropy]{}**
---
Department of Physics, CERN - Theory Division, CH-1211 Geneva 23, Switzerland\
Institut für Theoretische Physik, ETH Zürich, CH-8093 Zürich, Switzerland\
Introduction
============
BPS-type interactions have over the years attracted a lot of attention in four-dimensional extended supergravity. These are couplings which can be written as integrals over a subspace of the full superspace thereby generalising the notion of chirality and F-terms in ${{\cal N}}=1$ supersymmetric field theories. Within the effective string theory action, such terms are believed to be always captured by topological amplitudes; the best studied case is indeed the series of the $g$-loop couplings $F_gW^{2g}$ in type II string theory compactified on a Calabi-Yau manifold [@Antoniadis:1993ze; @Bershadsky:1993cx]. Here $W$ is the chiral ${{\cal N}}=2$ supergravity multiplet and the moduli-dependent coefficient function $F_g$ was shown to be identical to the genus $g$ partition function of the ${{\cal N}}=2$ topological string, associated to the twisted Calabi-Yau $\sigma$-model.
Among many interesting properties of $F_g$’s, it was realised that they play an important role for the physics of supersymmetric black holes. In [@Lopes; @Cardoso:1998wt; @LopesCardoso:1999cv; @Lopes; @Cardoso:1999ur; @LopesCardoso:1999xn] (see also [@Mohaupt:2000mj]) higher derivative corrections to the entropy have been derived from these effective action terms, following a method first proposed in [@Wald:1993nt]. These results – at least for large values of the charges of the black hole – are in agreement with state-counting arguments in a microscopic description of the black hole as a particular configuration of branes (see e.g. [@Maldacena:1997de; @Vafa:1997gr]). Similar results have more recently been found even for particular ${{\cal N}}=4$ supersymmetric small black holes, as for example in [@Dabholkar:2004yr]. There, a D0-D4-brane setup has been studied in type II string theory compactified on $K3\times T^2$. It was shown that the only non-vanishing coupling from the series $F_{g=1}$ for the case of ${{\cal N}}=4$ supersymmetry, which is a four-derivative operator, yields the full entropy of the black hole and agrees to all orders in the large D0-D4 brane charge expansion with the expected result from microstate counting.
In [@Ooguri:2004zv] an even more direct link between $F_g$ and ${{\cal N}}=2$ black holes was established by conjecturing a relation of the form $Z_{\text{BH}}=|Z_{\text{top}}|^2$. Here $Z_{\text{BH}}$ is the “thermodynamic” partition function of the black hole in a particular mixed ensemble and $Z_{\text{top}}$ is essentially the exponential of the weighted sum over all $F_g$’s. This conjecture is understood to hold perturbatively, since a non-perturbative definition of either side of the equality is generically unclear. A somewhat deeper understanding of this relation (particularly for the square on the right hand side) was reached in [@Beasley:2006us]. Moreover, the conjecture has been tested for small supersymmetric black holes in [@Dabholkar:2005dt; @Dabholkar:2005by].
The results mentioned so far raise the question whether generalisations of $F_g$ to theories with ${{\cal N}}=4$ supersymmetry have a similar impact on the physics of four-dimensional ${{\cal N}}=4$ supersymmetric black holes. Such generalisations have first been found in [@Antoniadis:2006mr] in type II string theory compactified on $K3\times T^2$ (see also [@Berkovits:1994vy]). Explicitly, two series of higher derivative BPS couplings have been identified both of which are computed by certain correlation functions of the ${{\cal N}}=4$ topological string: $\mathcal{F}_g^{(1)}\bar{K}^2 K^{2g}$ and $\mathcal{F}_{g-1}^{(3)} K^{2g}$, where $K$ is a superdescendant of the ${{\cal N}}=4$ supergravity multiplet. Particularly the latter coupling was extensively studied in [@Antoniadis:2007cw] (see also [@Antoniadis:2007ta; @Antoniadis:2009nv]) for values $g\geq2$. In this work we will mostly be concerned with the expression for $g=1$, which corresponds to a six-derivative operator. Using string dualities, we will see that this coupling starts receiving contributions at one-loop in heterotic string theory compactified on $T^6$, which we can therefore study fairly explicitly.
We will then carry on to determine the effect of $\mathcal{F}_{g-1}^{(3)}$ with $g=1$ on the entropy of certain ${{\cal N}}=4$ supersymmetric black holes. The method we will apply is the classical entropy function formalism developed in [@Sen:2005wa; @Sen:2005iz] (for a review see e.g. [@Sen:2007qy]). This is a suitable approach to the problem as it does not necessitate the knowledge of the complete solution of the black hole in the presence of the higher derivative terms, but nevertheless it allows to extract information about the near horizon geometry and most importantly the corrected entropy of the black hole. We should also mention that our approach is ‘classical’ in the sense that non-local terms arising from integrating out massless degrees of freedom are not included. We should also point out that we have made a general analysis of dimension six operators and we found one more candidate, BPS-like on-shell involving three Riemann tensors, which however does not change the entropy of ${{\cal N}}=4$ black holes.
This paper is organised as follows. In Section \[Sect:EffectAction\] we discuss a manifestly supersymmetric formulation of the couplings $\mathcal{F}_{g-1}^{(3)}$ for $g=1$ in ${{\cal N}}=4$ harmonic superspace. After introducing our conventions we will show how to write these terms in an off-shell supersymmetric manner. We also prove that this coupling contains at the component level a term of the form $R_{(+)}^2F_{(-)}^2$ with $R_{(+)}$ the self-dual piece of the Riemann tensor and $F_{(-)}$ the anti-self-dual field strength tensor of a vector multiplet gauge field. In Section \[StringOneLoop\] we explicitly extract the leading string theory contribution to this component interaction from a one-loop amplitude in heterotic string theory compactified on $T^6$. We compute the corresponding amplitude explicitly in a particular region of the moduli space, including the integral over the modular parameter of the world-sheet torus. We also show that a similar contribution for the gauge fields replaced by graviphotons vanishes identically. This Section is accompanied by three appendices containing additional material as well as calculations which we omitted from the main body of the paper for pedagogical reasons. In Section \[Sect:EntropyBlackLarge\] we use the precise form of the one-loop expression to determine its contribution to the entropy of a particular large ${{\cal N}}=4$ supersymmetric black hole. We find a contribution of the order $-2$ in the charges. Repeating a similar analysis for certain small black holes in Section \[Sect:EntropyBlackSmall\] reveals that the entropy stemming from $R_{(+)}^2F_{(-)}^2$ is still suppressed with respect to the contributions of $R^2$ couplings. However, our six-derivative term can be shown to be responsible for the lifting of certain flat moduli directions in the entropy function, thereby providing attractor values for some scalar fields. Finally, Section \[Sect:Conclusions\] contains our conclusions.
${{\cal N}}=4$ Supersymmetric Effective Action {#Sect:EffectAction}
==============================================
In this Section we discuss a particular class of higher derivative couplings of the ${{\cal N}}=(4,4)$ type II effective action, which have first been discovered in [@Antoniadis:2006mr; @Antoniadis:2007cw]. Due to the high amount of supersymmetry, a covariant formulation of these couplings is not possible in standard superspace; for this reason we will work in harmonic superspace, for which we will first review our conventions.
${{\cal N}}=4$ Supergravity and Harmonic Superspace Description {#Sect:Superfields}
---------------------------------------------------------------
In this work we will deal with black holes in ${{\cal N}}=4$ Poincaré supergravity (SUGRA) [@Cremmer:1977tt; @Bergshoeff:1980is; @de; @Roo:1984gd] being the low energy limit of type II string theory compactified on $K3\times T^2$ or its dual heterotic string theory on $T^6$. The field content of this theory is the ${{\cal N}}=4$ supergravity multiplet coupled to $22$ ${{\cal N}}=4$ vector multiplets. The scalar fields together form the moduli space $$\begin{aligned}
\mathbb{M}=\frac{SU(1,1)}{U(1)}\times \frac{SO(6,22)}{SO(6)\times SO(22)}\,.\end{aligned}$$ The $SO(6,22)$ symmetry is linearised by introducing six additional vector multiplets that act as compensators for various (gauge-)symmetries of the theory. For example, as explained in [@Antoniadis:2007cw], the 36 scalar fields of these multiplets are eliminated by imposing the D-term constraints (20 constraints) and gauge fixing Weyl invariance (one constraint) as well as the local $SO(6)$ symmetry (15 constraints). Concerning the gauge fields there are two possibilities: Either the gauge fields of the compensating multiplets are expressed as functions of the graviphotons which sit inside the supergravity multiplet (’superstring basis’) or the relation is inverted and the graviphotons are identified with the gauge fields of the compensating multiplets; in this case, the vector bosons of the supergravity multiplet are expressed as functions of all vector multiplet gauge fields (’supergravity basis’). Throughout this paper we will consistently work in the superstring basis which is most suitable for our purpose of calculating higher derivative couplings in string theory.
A description of this theory in standard ${{\cal N}}=4$ superspace $$\begin{aligned}
\mathbb{R}^{(4|4)}=\{x^\mu,\theta^i_\alpha,\bar{\theta}_i^{\dot{\alpha}}\}\,,\label{standardSS}\end{aligned}$$ where $i=1,\ldots,4$ an index of $SU(4)$ (the automorphism group of ${{\cal N}}=4$ supersymmetry in four dimensions), turns out to be difficult. In fact it is only possible on-shell since the necessary superfields cannot be introduced in a consistent off-shell fashion. We will therefore choose a different description in four-dimensional [*harmonic superspace*]{} [@Galperin:1984av; @Galperin:1984bu; @Howe:1995md; @Hartwell:1994rp]. The latter is an enhancement of (\[standardSS\]) of the following type $$\begin{aligned}
\mathbb{HR}^{(4+4|4)}=\mathbb{R}^{(4|4)}\times \frac{SU(4)}{S(U(2)\times U(2))}=\{x^\mu,\theta^i_\alpha,\bar{\theta}_i^{\dot{\alpha}},u^{+a}_i, \, u^{-{{\dot a}}}_i\}\,.\end{aligned}$$ The coordinates which parameterise the additional coset space $\{u^{+a}_i, u^{-{{\dot a}}}_i\}$ transform as fundamentals under $SU(4)$ and carry indices $a, {{\dot a}}= 1,2$ of $SU(2)\times SU(2)$ as well as $U(1)$ charges $\pm 1$. Together with their complex conjugates ${\bar u}^i_{+a} = \overline{(u^{+a}_i)}, \, {\bar u}^i_{-{{\dot a}}} = \overline{(u^{-{{\dot a}}}_i)}$ they satisfy the unitarity conditions $$\begin{aligned}
&u^{+a}_i\, {\bar u}^i_{+b} = \delta^a_b\,, && u^{-{{\dot a}}}_i\, {\bar u}^i_{-{{\dot b}}} = \delta^{{\dot a}}_{{\dot b}}\,, && u^{+a}_i\, {\bar u}^i_{-{{\dot b}}} = u^{-{{\dot a}}}_i\, {\bar u}^i_{+b} = 0\,, &&u^{+a}_i\, {\bar u}^j_{+a} + u^{-{{\dot a}}}_i\, {\bar u}^j_{-{{\dot a}}} = \delta^j_i\,,\label{12'}\end{aligned}$$ and the unit determinant condition $$\begin{aligned}
\label{12}
{\epsilon}^{ijkl} u^{+a}_i u^{+b}_j u^{-{{\dot a}}}_k u^{-{{\dot b}}}_l = {\epsilon}^{ab}{\epsilon}^{{{\dot a}}{{\dot b}}}\,.\end{aligned}$$ It is furthermore convenient to introduce vector-like combinations of $SU(4)$ harmonics (i.e. harmonics on $SO(6)/SO(4)\times SO(2)$) of the type $u^M_{ij} = -u^M_{ji}$, with $M= (++,--, a{{\dot a}})$ (and their conjugates ${\bar u}_{M}^{ij} = \overline{u^{M}_{ij}}$) $$\begin{aligned}
& u^{++}_{ij} = u^{+a}_i {\epsilon}_{ab} u^{+b}_j\,, && u^{--}_{ij} = u^{-{{\dot a}}}_i {\epsilon}_{{{\dot a}}{{\dot b}}} u^{-{{\dot b}}}_j \,, && u^{a{{\dot a}}}_{ij} = u^{+a}_{[i} u^{-{{\dot a}}}_{j]}\ , \label{00}\end{aligned}$$ where $[ij]$ denotes weighted antisymmetrisation. The introduction of harmonic variables allows us to define “1/2-BPS short” or Grassmann (G-)analytic superfields.[^4] They depend only on half of the Grassmann variables which can be chosen to be ${\theta}^{+a}_{\alpha}= {\theta}^i_{\alpha}\, u_i^{+a}$ and ${\bar\theta}^{{\dot\alpha}}_{-{{\dot a}}} =
{\bar u}^i_{-{{\dot a}}}\,{\bar\theta}^{{\dot\alpha}}_i $. One such superfield is the linearised on-shell vector multiplet (we only display the bosonic degrees of freedom) $$\begin{aligned}
Y_A^{++}(x^\mu,{\theta}^+,{\bar\theta}_-,u) =& \phi^{ij}_A u^{++}_{ij} + {\theta}^{+a}\sigma^{{\mu}{\nu}}{\theta}^{+b}{\epsilon}_{ab}\, F_{(+),A,{\mu}{\nu}} + {\bar\theta}_{-{{\dot a}}}\bar\sigma^{{\mu}{\nu}}{\bar\theta}_{-{{\dot b}}}{\epsilon}^{{{\dot a}}{{\dot b}}}\, F_{(-),A,{\mu}{\nu}} + \ldots\ , \label{01}\end{aligned}$$ where the dots stand for additional derivative terms. Moreover, $\sigma^{\mu\nu}$ and $\bar\sigma^{{\mu}{\nu}}$ are the 4-dimensional (anti-) chiral Lorentz generators, $\phi^{ij}= \frac{1}{2}{\epsilon}^{ijkl} \bar\phi_{kl}$ are six real scalars and $F_{(\pm){\mu}{\nu}}$ is the (anti-)self-dual part of the gauge field strength. Finally, we have also included the $SO(22)$ index $A$.
Another example of a G-analytic superfield is the linearised on-shell Weyl multiplet. It is obtained from the off-shell chiral Weyl superfield [@Bergshoeff:1980is] (we only display the bosonic degrees of freedom) $$\begin{aligned}
\mathcal{W}=&\ \Phi+\theta^i_\alpha\theta^j_\beta\left(\sigma^{\alpha\beta}_{\mu\nu}T^{\mu\nu}_{(+)[ij]}+\epsilon^{\alpha\beta}S_{(ij)}\right)+\frac{1}{12}\epsilon_{ijkl}(\theta^i\sigma^{\mu\nu}\theta^j)(\theta^k\sigma^{\rho\tau}\theta^l)R_{\mu\nu\rho\tau}+\ldots\,.\label{N4SUGRA}\end{aligned}$$ Here $\Phi$ is a physical scalar (“graviscalar"), $T$ is a sixplet of graviphoton field strengths, $S_{(ij)}$ is an auxiliary field and $R_{\mu\nu\rho\tau}$ is the Riemann tensor. From $\mathcal{W}$ we can compute the following superdescendant $$\label{16}
K^{++}_{{\mu}{\nu}} = (\sigma_{{\mu}{\nu}})_{{\alpha}{\beta}}D_{-{{\dot a}}}^{\alpha}D_{-{{\dot b}}}^{\beta}{\epsilon}^{{{\dot a}}{{\dot b}}}\ \mathcal{W}=(\sigma_{{\mu}{\nu}})_{{\alpha}{\beta}}{\epsilon}^{{{\dot a}}{{\dot b}}}{\bar u}_{-{{\dot a}}}^i {\bar u}_{-{{\dot b}}}^jD^{\alpha}_i D^{\beta}_j\mathcal{W}\,,$$ which similarly to the vector superfield (\[01\]) only depends on half of the ${\theta}$ variables: $$\label{17}
K^{++}_{{\mu}{\nu}}({\theta}^+,{\bar\theta}_-,u) = T_{(+){\mu}{\nu}}^{ij} u^{++}_{ij} + {\theta}^{+a}\sigma^{{\lambda}\rho}{\theta}^{+b}{\epsilon}_{ab}\, R_{(+){\mu}{\nu}{\lambda}\rho} + {\bar\theta}_{-{{\dot a}}}\bar\sigma^{\lambda}\sigma_{{\mu}{\nu}} \sigma^\rho {\bar\theta}_{-{{\dot b}}}{\epsilon}^{{{\dot a}}{{\dot b}}}\, {\partial}_{\lambda}{\partial}_\rho \Phi + \ldots\ .$$ Repeating the same steps, but this time starting with the antichiral superfield $\bar{\mathcal{W}}({\bar\theta})$ we obtain the other half of the on-shell Weyl multiplet. It is again described by an ultrashort superfield of the same type, $$\label{18}
\bar K^{++}_{{\mu}{\nu}}({\theta}^+,{\bar\theta}_-,u) = T_{(-){\mu}{\nu}}^{ij} u^{++}_{ij} + {\bar\theta}_{-{{\dot a}}} \bar\sigma^{{\lambda}\rho}{\bar\theta}_{-{{\dot b}}}{\epsilon}^{{{\dot a}}{{\dot b}}}\, R_{(-){\mu}{\nu}{\lambda}\rho} + {\theta}^{+a}\sigma^{\lambda}\bar\sigma_{{\mu}{\nu}} \bar\sigma^\rho {\theta}^{+b}{\epsilon}_{ab} \, {\partial}_{\lambda}{\partial}_\rho \bar\Phi + \ldots\,.$$ Note that in the ${{\cal N}}=4$ G-analytic superspace there exists a special conjugation $\
\widetilde{}\ $ combining complex conjugation with a reflection on the harmonic coset, such that G-analyticity is preserved. In this sense $Y^{++} = \widetilde{Y^{++}}$ and $\bar K^{++} = \widetilde{K^{++}}$, which implies, in particular, the reality condition on the six scalars in $Y$.
We have now all ingredients to formulate higher order effective action couplings.
Higher Derivative Effective Action Term
---------------------------------------
Using the harmonic superspace approach outlined in the previous section we can construct the following higher order effective action term $$\begin{aligned}
S_g=\int d^4x \int du \int d^4 {\theta}^+\int d^4{\bar\theta}_- (D_-\cdot D_-)^2\left[\left(K_{\mu\nu}^{++} K^{++\,\mu\nu}\right)^g \mathcal{F}_g(\mathcal{W},Y_A^{++},u)\right]\,,\label{OffshellR2F2}\end{aligned}$$ where we have used the shorthand notation $(D_-\cdot D_-)_{\mu\nu}=(\sigma_{\mu\nu})_{\alpha\beta}\epsilon^{\dot{a}\dot{b}}D^\alpha_{-\dot{a}}D^\beta_{-\dot{b}}$. On shell (i.e. if $S_{(ij)}=0$ in (\[N4SUGRA\])) the only possibility to distribute the spinor derivatives is to hit two different $\mathcal{W}$ superfields inside $\mathcal{F}_g(\mathcal{W},Y_A^{++},u)$, which makes (\[OffshellR2F2\]) equivalent to $$\begin{aligned}
S_g=\int d^4x \int du \int d^4 {\theta}^+\int d^4{\bar\theta}_- \left(K_{\mu\nu}^{++} K^{++\,\mu\nu}\right)^{g+1} \mathcal{F}^{(3)}_g(\mathcal{W},Y_A^{++},u)\,,\label{OnshellR2F2}\end{aligned}$$ where we have defined $$\begin{aligned}
\mathcal{F}^{(3)}_g(\mathcal{W},Y_A^{++},u)=\frac{\partial^2 \mathcal{F}_g(\mathcal{W},Y_A^{++},u)}{\partial \mathcal{W}^2}\,.\label{N4TopDefOld}\end{aligned}$$ The effective coupling (\[OnshellR2F2\]) has first been considered in [@Antoniadis:2006mr], given as a $(g+1)$-loop component amplitude of type II string theory compactified on $K3\times T^2$, involving two Riemann tensors, two graviscalars with two derivatives each, and $2g-2$ graviphotons. In fact it was shown there that this amplitude is identical to a particular correlation function in the ${{\cal N}}=4$ topological string, which was further studied in [@Antoniadis:2007cw]. Although the works [@Antoniadis:2006mr; @Antoniadis:2007cw] focused on $g>0$ such that the above component amplitude is well defined, the case $g=0$ is also a valid contribution as can be seen from (\[OnshellR2F2\]). In fact, in a component notation it contains among others the following term $$\begin{aligned}
S_{g=0}^2&=\int d^4x\int du\int d^4\theta^+\int d^4\bar{\theta}_-(K^{++}_{\mu\nu} K^{++,\mu\nu}) Y_A^{++}Y_B^{++}\left(\frac{\partial^4\mathcal{F}_0(\mathcal{W},Y_A^{++},u)}{\partial Y_A^{++}\partial Y_B^{++}\partial \mathcal{W}^2}\right)\nonumber\\
&\simeq\int d^4x R_{(+),\mu\nu\rho\tau}R_{(+)}^{\mu\nu\rho\tau} F_{(-),A,\sigma\lambda} F_{(-),B}^{\sigma\lambda} \int du\,{\mathcal{A}^{AB}}_{\big|\theta=0}+\ldots\,.\label{A2compExp}\end{aligned}$$ In the second line we have explicitly performed the Grassmann integration. To be precise, the $\theta^+$-integral has picked $R_{(+)}$ in both of the $K^{++}_{\mu\nu}$ superfields while the $\bar{\theta}_-$-integral has extracted $F_{(-)}$ from the vector multiplets. The dots denote further terms containing fermionic fields which will be of no interest when we apply (\[A2compExp\]) to the computation of the black hole entropy. Moreover, in order to save writing we have introduced the shorthand notation $$\begin{aligned}
\mathcal{A}^{AB}(\mathcal{W},Y_A^{++},u)\equiv \left(\frac{\partial^4\mathcal{F}_0(\mathcal{W},Y_A^{++},u)}{\partial Y_A^{++}\partial Y_B^{++}\partial \mathcal{W}^2}\right)\,.\label{ShorthandCoupling}\end{aligned}$$ As we can see, this component term is of six derivative order. In the remainder of this work we will study the effective action coupling (\[A2compExp\]) in more detail in order to understand whether it yields any non-trivial corrections to the entropy of black holes.
String Theory One-Loop Amplitude {#StringOneLoop}
================================
As a first step we would like to study (\[A2compExp\]) in string theory. As already mentioned, $\mathcal{F}^{(3)}_g$ in (\[N4TopDefOld\]) has been computed as a $(g+1)$-loop string amplitude in type II theory compactified on $K3\times T^2$, via the correlator $\langle R_{(+)}^2(\partial\partial\bar{\Phi})^2T_{(+)}^{2g-2}\rangle_{g+1}$ for $g>0$. This, however, does not smoothly connect to the coupling (\[A2compExp\]), which is why ${\mathcal{A}_{AB}}$ must be computed separately. Naïve extrapolation suggests, however, that the latter starts receiving corrections at the one-loop level on the type II side. Following now the steps of reasoning as in [@Antoniadis:2006mr] the same conclusion should in fact also be true for its heterotic dual, which we will now compute explicitly.
One-Loop Gauge-Field Amplitude in Heterotic String Theory {#Sect:OneLoopHeterotic}
---------------------------------------------------------
We consider (\[A2compExp\]) as a one-loop amplitude in heterotic string theory compactified on $T^6$, which we will subsequently write as $T^4\times T^2$ (for similar computations see e.g. [@Antoniadis:1995zn; @Antoniadis:1997zt; @Lerche:1999ju]). The moduli of this theory are arranged in a $\Gamma^{(6,22)}$ Narain lattice, for which we will consider the simplest case, namely that none of the Wilson lines in the right moving (bosonic string) part are switched on.
### Vertex Operators and Contractions
The one-loop amplitude we need to compute contains two self-dual Riemann tensors and two anti-self-dual gauge field strengths. We choose a complex basis for the space-time (Euclidean) coordinates $(Z^1,\bar{Z}^1,Z^2,\bar{Z}^2)$ as well as their fermionic partners $(\chi^1,\bar{\chi}^1,\chi^2,\bar{\chi}^2)$. In this basis we pick the following kinematic structure for the vertices\
**field** **helicity** **vertex** **WS position**
------------- ------------------------------------ ------------ -----------------
graviton $R_{1212}$ $x_1$
graviton $R_{\bar{1}\bar{2}\bar{1}\bar{2}}$ $x_2$
gauge field $F_{A,\bar{1}2}$ $x_3$
gauge field $F_{B,1\bar{2}}$ $x_4$
${}$\
where the last column denotes the position on the world-sheet. The correlator which we now have to compute is $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=\langle V_{(R)}(p_1)V_{(R)}(\bar{p}_2) V^{(F)}_A(\bar{p}_1)V^{(F)}_B(\bar{p}_2)\rangle\,.\label{1LoopCorrelator}\end{aligned}$$ Counting derivatives in the effective action, it is clear that both of the graviton vertex operators have to contribute two momenta each, while each of the gauge-field vertex operators has to contribute a single momentum since the amplitude contains the field strength rather than the gauge potential. This means that only specific pieces of the above vertex operators will contribute to the contractions. First of all we see that we only need to consider contributions in the even spin-structure. The reason is that, upon writing $T^6=T^2\times T^2\times T^2$, there are six two-dimensional fermionic zero modes in the internal manifold (two for each torus) which, however, we cannot soak up all with the vertex operators we have at our disposal. Therefore, the odd-spin structure vanishes identically.
For the sum over even spin-structures to be non-vanishing, all vertex operators have to contribute the fermion bilinear part in the left moving (supersymmetric) sector. This means that the graviton vertices have to provide an additional momentum coming from the exponential factor. This results in the following correlation function $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=&\langle Z^1\bar{\partial} Z^2(x_1)\,\bar{Z}^2\bar{\partial} \bar{Z}^1(x_2)\rangle\cdot\langle\chi_1\chi_2(x_1)\,\bar{\chi}_1\bar{\chi}_2(x_2)\,\bar{\chi}_1\chi_2(x_3)\,\chi_1\bar{\chi}_2(x_4)\rangle\cdot\langle\bar{J}_A(x_3)\, \bar{J}_B(x_4)\rangle\,.\label{HetContractGauge}\end{aligned}$$ As one can see, the correlator has split into three distinct contributions, which can be computed separately in a straight-forward manner
- Space-time fermion correlator:\
Starting with the fermionic piece we have the following left-moving contribution $$\begin{aligned}
\langle\chi_1&\chi_2(x_1)\,\bar{\chi}_1\bar{\chi}_2(x_2)\,\bar{\chi}_1\chi_2(x_3)\,\chi_1\bar{\chi}_2(x_4)\rangle=\nonumber\\
&=\sum_s\frac{\vartheta_s(x_1-x_2-x_3+x_4)\vartheta_s(x_1-x_2+x_3-x_4)\vartheta^2_s(0)\eta^{12}}{\vartheta^2(x_1-x_2)\vartheta^2(x_3-x_4)}=\eta^{12}\,,\label{ResFermCorr}$$ where $\vartheta$ are Jacobi theta-functions and $\eta$ is the Dedekind eta-function. In the last step, in order to perform the sum over all even spin structures $s$ we have used the Riemann summation identity. We thus find that the result is independent of the world-sheet positions $x_{i=1,2,3,4}$.
- Space-time boson correlator:\
As we have found no $x$-dependence in (\[ResFermCorr\]), it follows that the full $x_1$ and $x_2$ dependence of ${\mathcal{A}_{AB}^{\text{het}}}$ is in the space-time bosonic correlator of (\[HetContractGauge\]). Therefore, we can immediately move on to calculate the integrated expression $$\begin{aligned}
\int d^2x_1\int d^2x_2\langle Z^1\bar{\partial} Z^2(x_1)\,\bar{Z}^2\bar{\partial} \bar{Z}^1(x_2)\rangle\,.\label{IntegBosCorr}\end{aligned}$$ Fortunately, correlators of this type have already been studied before in [@Antoniadis:1995zn]. There the following generating functional was introduced and calculated explicitly $$\begin{aligned}
G(\lambda,\tau,\bar{\tau})&=\sum_{g=1}^\infty\frac{1}{(g!)^2}\left(\frac{\lambda}{\tau_2}\right)^{2g}\langle\prod_{i=1}^g\int d^2x_i Z^1\bar{\partial}Z^2(x_i)\prod_{j=1}^{g}\int d^2y_j \bar{Z}^2\bar{\partial}\bar{Z}^1(y_j)\rangle=\nonumber\\
&=\left(\frac{2\pi i\lambda\bar{\eta}^3}{\bar{\vartheta}_1(\lambda,\bar{\tau})}\right)^2 e^{-\frac{\pi\lambda^2}{\tau_2}}\,.\label{GeneratingFunctional}\end{aligned}$$ Thus, we can easily read off the answer for (\[IntegBosCorr\]) by computing the coefficient of $\lambda^2$ in an expansion of $G(\lambda,\tau,\bar{\tau})$. To this end, following e.g. [@Marino:1998pg], we can write $$\begin{aligned}
\left(\frac{2\pi i\lambda\bar{\eta}^3}{\bar{\vartheta}_1(\lambda,\bar{\tau})}\right)^2e^{-\frac{\pi\lambda^2}{\tau_2}}=\sum_{k=0}^{\infty}\lambda^{2k}\mathcal{P}_{2k}(\hat{\bar{G}}_2,\ldots, \bar{G}^{2k})\,,\label{SpaceTimeCorrEisen}\end{aligned}$$ where $\bar{G}_{2k}$ are particular normalisations of the Eisenstein series $$\begin{aligned}
&\bar{G}_{2k}=2\zeta(2k) \bar{E}_{2k}\,,&&\text{and} &&\hat{\bar{G}}_2=2\zeta(2)\hat{\bar{E}}_2=2\zeta(2)\left(\bar{E}_2-\frac{3}{\pi\tau_2}\right)\,.\end{aligned}$$ Since Eisenstein series will be very important for our further computations we have compiled some of their properties in appendix \[App:Eisenstein\]. Moreover, $\mathcal{P}_{2k}$ is a modular function (‘almost’ modular form) of weight $(0,2k)$ $$\begin{aligned}
\mathcal{P}_{2k}(\hat{\bar{G}}_2,\ldots, &\bar{G}_{2k})=-\mathcal{S}_k\left(\hat{\bar{G}}_2,\ldots,\frac{1}{k}\bar{G}_{2k}\right)\,,&&\text{with} &&\mathcal{S}_k(x_1,\ldots,x_k)=x_k+\ldots+\frac{x_1^k}{k!}\,,\nonumber\end{aligned}$$ with $\mathcal{S}_k$ being the Schur polynomials. This particularly means $$\begin{aligned}
&{\mathcal{P}_{2}}=-\hat{\bar{G}}_2\,,&&\text{and} &&{\mathcal{P}_{4}}=-\frac{1}{2}(\hat{\bar{G}}_2^2+\bar{G}_4)\,,\end{aligned}$$ which entails for the correlator $$\begin{aligned}
\int d^2x_1\int d^2x_2\langle Z^1\bar{\partial} Z^2(x_1)\,\bar{Z}^2\bar{\partial} \bar{Z}^1(x_2)\rangle={\mathcal{P}_{2}}(\hat{\bar{G}}_2)\,.\end{aligned}$$ It is crucial to realise that although this correlator is a modular function of weight $(0,2)$ it is not an anti-holomorphic function due to the dependence of ${\mathcal{P}_{2}}$ on $\hat{\bar{E}}_2$.
- Current Correlator:\
Finally, there is still the correlator of the right moving currents in (\[HetContractGauge\]). Following [@Antoniadis:1992rq], it is given by $$\begin{aligned}
\langle\bar{J}_A(\bar{x}_3)\, \bar{J}_B(\bar{x}_4)\rangle&=P^R_AP^R_B-\frac{\delta_{AB}}{4\pi^2}\partial^2_{\bar{x}_3}\ln\bar{\vartheta}_1(\bar{x}_3-\bar{x}_4)\,,\label{RightMovingCorrelatorCurrents}\end{aligned}$$ where $P^R_A$ is a right moving vector of the $\Gamma^{(6,22)}$-Narain lattice corresponding to the toroidal compactification. Since (\[RightMovingCorrelatorCurrents\]) is the only dependence of $\mathcal{A}_{AB}^{\text{het}}$ on the insertion points $x_3$ and $x_4$, we can immediately consider the integrated version. To this end we make use of the fact that $\partial_{\bar{x}_3}\ln\bar{\vartheta}_1(\bar{x}_3-\bar{x}_4)+\frac{2\pi i}{\tau_2}\,\text{Im}(x_3-x_4)$ as a function of $x_3$ is periodic on the torus. Therefore, we can compute the integral $$\begin{aligned}
\int d^2x_3&\int d^2x_4\langle\bar{J}_A(\bar{x}_3)\, \bar{J}_B(\bar{x}_4)\rangle=\tau_2^2\left[P^R_AP^R_B-\frac{\delta_{AB}}{4\pi\tau_2}\right]\,,\label{CurrentCorrelator}\end{aligned}$$ where we have used the appropriate normalisation. In the final correlator this expression will be an insertion into the Siegel-Narain Theta-function of weight $(3,11)$, as we will see below.
### Modular Integral {#Sect:ModularIntegral}
Since from the above analysis we only found one non-vanishing contraction, we can easily reassemble the full amplitude. For this, we have to include the partition function of the space-time bosons and fermions, yielding a factor of $\eta^{-8}$, as well as the contribution of the internal CFT. The latter is a Siegel-Narain Theta-function with the insertions (\[CurrentCorrelator\]). The full expression is then of the form $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}&\simeq\int \frac{d^2\tau}{\tau_2^3\bar{\eta}^{24}}\,\tau_2^4\,{\mathcal{P}_{2}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP^R_B-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,.\label{modularintegral}\end{aligned}$$ As a simple check, we show in appendix \[App:ModInvariance\] that the integrand of this expression is indeed modular invariant.
In order to compute this integral, we recall the following property of the function ${\mathcal{P}_{2}}$ $$\begin{aligned}
\partial_\tau {\mathcal{P}_{4}}=-\frac{i\pi}{2\tau_2^2}\,{\mathcal{P}_{2}}\,.\end{aligned}$$ Performing then an integration by parts we find (including the boundary contribution) [$$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=&-\frac{3}{\pi}\int \frac{d^2\tau}{\bar{\eta}^{24}}\,\tau_2^2\,{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP^R_B-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}+\nonumber\\
&+2\int \frac{d^2\tau}{\bar{\eta}^{24}}\,\tau_2^3\,{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP^R_B-\frac{\delta_{AB}}{4\pi\tau_2}\right](P^L)^2{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}-\nonumber\\
&-\frac{\delta_{AB}}{4\pi^2}\int\frac{d^2\tau}{\bar{\eta}^{24}}\tau_2{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}+\nonumber\\
&+\frac{1}{\pi}\int_{\partial\mathcal{F}}\frac{d\tau_1}{\bar{\eta}^{24}}\tau_2^3\,{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP_B^R-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,.\end{aligned}$$]{} Introducing covariant derivatives with respect to the moduli $D_{ij,A}$, which act in the following manner on the lattice momenta (for more details see [@Antoniadis:2006mr; @Antoniadis:2007cw]) $$\begin{aligned}
&D_{ij,A}P^L_{kl}=\epsilon_{ijkl}P^R_A\,,&&\text{and} &&D_{ij,A}P^R_B=\frac{1}{2}\delta_{AB}P^L_{ij}\,,\end{aligned}$$ we can rewrite this expression as: [$$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=\left(\frac{\epsilon^{ijkl}}{16\pi^2}\,D_{ij,A}D_{kl,B}+\frac{\delta_{AB}}{2\pi^2}\right)\mathcal{I}+\mathcal{I}_{AB}^{\text{bdy}}\,,\end{aligned}$$]{} where we have introduced the following shorthand notation for the modular integrals $$\begin{aligned}
&\mathcal{I}=\int \frac{d^2\tau}{\bar{\eta}^{24}}\,\tau_2\,{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,,\label{F3ModIntegral}\\
&\mathcal{I}_{AB}^{\text{bdy}}=\frac{1}{\pi}\int_{\partial\mathcal{F}}\frac{d\tau_1}{\bar{\eta}^{24}}\tau_2^3\,{\mathcal{P}_{4}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP_B^R-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,.\label{F3ModIntegralBdy}\end{aligned}$$ As they are written, (\[F3ModIntegral\]) and (\[F3ModIntegralBdy\]) are valid for a generic toroidal compactification of the heterotic string and as such depend on the full Narain-moduli space of the $T^6$-compactification. Besides being rather tedious to compute, these integrals are also not quite what we aim to do in this work. For latter applications it will be more convenient to go to a particular region in the moduli space where we can obtain certain simplifications. To be precise our choice is the following
- Upon writing the internal $T^6=T^2\times T^4$ we will consider the limit of large $T^4$ volume $V$.
- From all the moduli of the Narain lattice, we will consider the simplest case, namely that all 16 right moving Wilson lines are vanishing.
In this case, the lattice factorises in the following manner $$\begin{aligned}
\Gamma^{(6,22)}\to \Gamma^{(2,2)}\oplus \Gamma^{(4,4)}\oplus \Gamma^{(0,16)}\,,\label{LatticeSplit}\end{aligned}$$ with the large volume limit $\Gamma^{(4,4)}\sim \frac{V}{\tau_2^2}$. The third factor in (\[LatticeSplit\]) will then just contribute the lattice sum, which is a modular form of weight $(0,8)$ and just depends on the gauge group of the heterotic string. At the one-loop level for $E_8\times E_8$ and $SO(32)$ it is explicitly given by (see e.g. [@Kiritsis:1997hj]) $\Gamma^{(0,16)}\simeq(\bar{E}_4)^2$. This moreover means that the only moduli dependence of ${\mathcal{A}_{AB}^{\text{het}}}$ stems from the $(T,U)$ moduli of the remaining $T^2$, which enters via the $\Gamma^{(2,2)}$ factor in (\[LatticeSplit\]). Putting all contributions together, we obtain the following simplified expression for $\mathcal{I}$ and $\mathcal{I}_{AB}^{\text{bdy}}$ $$\begin{aligned}
&\mathcal{I}^{\text{sim}}=\int \frac{d^2\tau}{\tau_2}\,\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}{\sum_{(P^L,P^R)\in\Gamma^{(2,2)}}}{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,,\label{modularintegralTRUNC}\\
&\mathcal{I}^{\text{bdy-sim}}_{AB}=\frac{1}{\pi}\int_{\partial\mathcal{F}} d \tau_1\tau_2\,\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}{\sum_{(P^L,P^R)\in\Gamma^{(2,2)}}}\left[P^R_AP_B^R-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}\,.\label{modularbdyTRUNC}\end{aligned}$$ We will first compute the boundary term $\mathcal{I}^{\text{bdy-sim}}_{AB}$ in (\[modularbdyTRUNC\]). To this end we realize that the only contribution comes from the limit of $\tau_2\to \infty$. In this limit, however, the integral (\[modularbdyTRUNC\]) is regularised by the presence of ${q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}$, except for the point where $P^L=P^R=0$. Therefore we obtain $$\begin{aligned}
\mathcal{I}^{\text{bdy-sim}}_{AB}&=-\frac{\delta_{AB}}{4\pi^2}\lim_{\tau_2\to\infty}\int_{-1/2}^{1/2}d\tau_1\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}=\frac{42\pi^2}{5}\,\delta_{AB}\,.\label{BdyTerm}\end{aligned}$$ Finally we are left to calculate the integral $\mathcal{I}^{\text{sim}}$. As we can see, the advantage of all previous rewriting is that $\mathcal{I}^{\text{sim}}$ is now of the form $$\begin{aligned}
\int_{\mathcal{F}}\frac{d^2\tau}{\tau_2}\,\hat{F}(\bar{\tau})\,\Theta(\tau,\bar{\tau})\,,&&\text{with} &&\hat{F}=\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}=\sum_{m\geq-1}\sum_{t=0}^2c(m,t)\bar{q}^m\tau_2^{-t}\,.\label{BorcherdsIntegral}\end{aligned}$$ Here $\Theta$ is a Siegel-Narain theta-function and $\hat{F}$ is an ‘almost’ anti-holomorphic modular function for which we have computed the first few $c(m,t)$ explicitly in appendix \[App:Eisenstein\]. Integrals of the type (\[BorcherdsIntegral\]) have been studied in [@Borcherds] (see also [@Marino:1998pg]) by developing further ideas of [@Harvey:1995fq] (for older works see also [@Dixon:1990pc]). Also in the present case the computation is along the lines of [@Marino:1998pg] and is performed in appendix \[App:ExplicitTorusIntegral\]. The result is in fact chamber-dependent, i.e. it depends on where exactly in the $(T,U)$-moduli space we are working. We have chosen to consider the region in which $T_2U_2$ becomes large, in which case we can finally give the full result[^5] $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=\left(\frac{\epsilon^{ijkl}}{16\pi^2}\,D_{ij,A}D_{kl,B}+\frac{3}{4\pi^2}\,\delta_{AB}\right)\mathcal{I}^{\text{sim}}+\mathcal{I}_{AB}^{\text{bdy-sim}}\,,\end{aligned}$$ where we have found in (\[BdyTerm\]), (\[GeneralBorcherdsInt\]) $$\begin{aligned}
&\mathcal{I}_{AB}^{\text{bdy-sim}}=\frac{42\pi^3}{5}\,\delta_{AB}\,,&&\text{and} &&\mathcal{I}^{\text{sim}}=\frac{\mathcal{I}^{\text{sim}}_{K}}{\sqrt{2z_+^2}}+\mathcal{I}^{\text{sim}}_{\lambda=0}+\mathcal{I}^{\text{sim}}_{\lambda\neq 0}\,,\end{aligned}$$ with the explicit expressions (\[ThetaTransform\]), (\[IntDegRes\]) and (\[IntNonDegRes\]) for the chamber $T_2<U_2$ $$\begin{aligned}
&\frac{\mathcal{I}^{\text{sim}}_{K}}{\sqrt{2z_+^2}}=-\frac{16\pi^5}{3}\,U_2+2T_2\sum_{t=0}^2c(0,t)\frac{t!\zeta(2t+2)}{\pi^{t+1}}\,\left(\frac{T_2}{U_2}\right)^t\,,\\
&\mathcal{I}^{\text{sim}}_{\lambda=0}=c(0,0)\left[\gamma_E-\log\left(\pi T_2U_2\right)-2\log 2\right]+c(0,1)\frac{\zeta(3)}{\pi T_2U_2}+c(0,2)\frac{3\zeta(5)}{2\pi^2 T_2^2U_2^2}\,,\\
&\mathcal{I}^{\text{sim}}_{\lambda\neq 0}=\sum_{\lambda\neq 0} \sum_{t=0}^2\sum_{s=0}^tc(\lambda^2/2,t)(T_2U_2)^{-t}\frac{\left(\text{Im}(\alpha)\right)^{t-s}}{(4\pi)^s}\,\frac{(s+t)!}{s!(t-s)!}\,\text{Li}_{1+s+t}\left(e^{2\pi i\alpha}\right)\,.\end{aligned}$$ This essentially concludes our calculation of $\mathcal{A}_{AB}^{\text{het}}$.
One-Loop Graviphoton Amplitude in Heterotic String Theory {#Sect:OneLoopHetGraviphoton}
---------------------------------------------------------
In addition to the gauge-field contribution, we can also consider whether there is a non-trivial coupling in which the gauge-fields are replaced by graviphotons. In fact, this is a non-trivial question for the following reason: As already explained in Section \[Sect:Superfields\] we are essentially considering 22+6 vector multiplets, the last six of which act as compensating multiplets. The gauge fields of the latter can – via their equations of motion – be expressed in terms of the 22 physical gauge fields as well as the graviphotons. In this way, all couplings which we can write down for the gauge fields might as well have partners containing graviphotons. To investigate this point, we can examine whether a four-point one-loop amplitude including the following vertex operators gives any non-vanishing contribution\
**field** **helicity** **vertex** **WS position**
----------- ------------------------------------ ------------ -----------------
graviton $R_{1212}$ $x_1$
graviton $R_{\bar{1}\bar{2}\bar{1}\bar{2}}$ $x_2$
graviph. $T_{\bar{1}2}$ $x_3$
graviph. $T_{1\bar{2}}$ $x_4$
${}$\
Here $X$ denotes the complex coordinate of the internal $T^2$ with $\Psi$ its supersymmetric partner. However, this amplitude is zero; to proof its vanishing it suffices to consider the fermion contribution. By inspection it is clear that the only possibility for contractions includes the fermionic correlator $$\begin{aligned}
\langle\chi_1\chi_2(x_1)\bar{\chi}_1\bar{\chi}_2(x_2)\rangle=\sum_s\frac{\vartheta_s^2(x_1-x_2)\vartheta_s^2(0)}{\vartheta^2(x_1-x_2)}=0\,.\end{aligned}$$ This establishes that there is no similar coupling involving graviphotons at one-loop. This result ties in with the expression for the higher-derivative couplings which we have obtained from harmonic superspace. Recalling the explicit component form (\[A2compExp\]) we can see that the coupling only involves gauge fields from vector multiplets, but no graviphotons. Notice, however, that this analysis does not exclude such couplings appearing at higher loops (or non-perturbatively) in string theory. However, for this to happen, the corresponding harmonic superspace interaction will have to contain the dilaton in a non-trivial manner as we will discuss now.
Duality
-------
Before applying the results we have obtained so far to the study of entropy corrections in ${{\cal N}}=4$ black holes, we would like to pause for a moment and discuss some aspects of duality covariance of the newly found higher derivative term (\[A2compExp\]). The fact that this interaction only involves the $SO(22)$ gauge-fields $F_{A}^{\mu\nu}$ might lead to the suspicion that it breaks $SO(6,22)$ covariance. However, one way to see that this is not the case is to reformulate (\[A2compExp\]) in the supergravity basis instead of the superstring basis (recall the discussion of section \[Sect:Superfields\]). In this basis, at the component level, we will find $$\begin{aligned}
S_{g=0}^{2,\text{SUGRA}}&\simeq\int d^4x R_{(+),\mu\nu\rho\tau}R_{(+)}^{\mu\nu\rho\tau} F_{(-),I,\sigma\lambda} F_{(-),J}^{\sigma\lambda} \int du\,{\mathcal{A}^{IJ}}_{\big|\theta=0}\,,\label{DualSUGRAframe}\end{aligned}$$ with $I,J$ indices of $SO(6,22)$ and $\mathcal{A}^{IJ}$ an expression similar to (\[ShorthandCoupling\]), which is a tensor-valued modular function of $SO(6,22)$. The expression (\[DualSUGRAframe\]) is therefore manifestly $SO(6,22)$ covariant.
Switching to the superstring basis (which we have been using so far and which we will also use in the later sections) entails to replace the $SO(6)$ gauge fields $F^{\mu\nu}_{I=1,\ldots,6}$ by the graviphotons $T^{\mu\nu}_{ij}$. As for example explained in [@Antoniadis:1993ze], this change of basis will involve the tree-level gauge-kinetic terms of the superstring action and therefore will also involve the heterotic dilaton. Thus, while the contribution of the $SO(22)$ gauge fields becomes precisely the term (\[A2compExp\]), the corresponding contributions of the graviphotons will receive an extra dilaton dependence. These couplings will therefore not appear at the one-loop level in the superstring frame, but will only receive higher-loop or non-perturbative contributions. Notice that this is in perfect agreement with our explicit computation in section \[Sect:OneLoopHetGraviphoton\]. Only if these additional contributions are included, $SO(6,22)$ covariance will be restored in the superstring frame.
Entropy Corrections for Large Black Holes {#Sect:EntropyBlackLarge}
=========================================
After having studied the higher derivative couplings (\[A2compExp\]) both from a superspace point of view and calculated them explicitly as heterotic string amplitudes, we now study whether they have any effect on the physics of (large) ${{\cal N}}=4$ supersymmetric black holes.
Spectrum and Charge Setup {#Sect:ChargeSetup}
-------------------------
So far we have been discussing an ${{\cal N}}=4$ theory of $22$ physical vector multiplets coupled to the ${{\cal N}}=4$ SUGRA multiplet. For computing the entropy of black holes, it will, however, be more useful to describe the theory in an ${{\cal N}}=2$ language. In this case the ${{\cal N}}=4$ SUGRA multiplet decomposes in the following manner $$\begin{aligned}
[(2),4(3/2),6(1),4(1/2),(0)]&\longrightarrow[(2),2(3/2),(1)]\oplus2[(3/2),(1),(1/2)]\oplus[(1),2(1/2),(0)]\,.\label{SUGRAdecompose}\end{aligned}$$ The right hand side corresponds to the ${{\cal N}}=2$ SUGRA multiplet, two spin–$3/2$ multiplets and an ${{\cal N}}=2$ vector multiplet. We recall that the scalar in this decomposition (i.e. the graviscalar in ${{\cal N}}=4$) is identified with the heterotic dilaton in string theory. Each of the ${{\cal N}}=4$ vector multiplets on the other hand side is decomposed as follows $$\begin{aligned}
[(1),4(1/2),(0)]\longrightarrow[(1),2(1/2),(0)]\oplus[2(1/2),(0)]\,,\label{VectorDecompose}\end{aligned}$$ where the right hand side corresponds to an ${{\cal N}}=2$ vector and a hypermultiplet.
The first step to describe a particular black hole in supergravity is to choose a particular setup of charges which it will carry. This means that we have to choose the black hole to be charged under some of the gauge fields inside the ${{\cal N}}=2$ multiplets on the right hand side of (\[SUGRAdecompose\]) and (\[VectorDecompose\]) while the remaining multiplets will be truncated. Starting with the fields coming from the ${{\cal N}}=4$ SUGRA multiplet in (\[SUGRAdecompose\]), we choose the black hole to carry electric charges $q_1$ and $q_3$ with respect to the ${{\cal N}}=2$ SUGRA (graviphoton) and the vector multiplet respectively and completely truncate the spin–$3/2$ multiplets. For the ${{\cal N}}=4$ vector multiplets, we first recall that in the computation of the heterotic one-loop amplitude in Section \[Sect:ModularIntegral\] we have considered the limit of large $T^4$ volume. In this limit 20 of the ${{\cal N}}=4$ physical vector multiplets get truncated and we are only left with those containing the $T$ and $U$ modulus of the remaining $T^2$ of the internal theory. From these – under the decomposition (\[VectorDecompose\]) – we will keep the ${{\cal N}}=2$ vector multiplets by choosing the black hole to carry magnetic charges $p_2$ and $p_4$ under the corresponding gauge fields while we will completely truncate the hypermultiplets.
This choice of charges together with the large volume limit of $T^4$ makes it possible for us to make contact with the work of e.g. [@Sen:2005iz], where black holes in heterotic string theory compactified on $\mathcal{M}\times S^1_{(1)}\times S^1_{(2)}$, with large volume of $\mathcal{M}$ (which is either $K3$ or $T^4$ or some orbifold thereof) were considered. As explained in [@Sen:2005iz], in string theory the electric charges of the graviphotons can be interpreted as winding and momentum along the direction $S^1_{(1)}$ while the magnetic charges of the gauge fields correspond to Kaluza-Klein and H-monopole charge associated with $S^1_{(2)}$. In fact, to obtain the real physical quantum numbers $(n,w,N,W)$ (which are also quantised) the following redefinition is necessary $$\begin{aligned}
&q_1=\frac{n}{2}\,,&&q_3=\frac{w}{2}\,,&&p_2=4\pi N\,,&&p_4=4\pi W\,.\label{ChargeRescaling}\end{aligned}$$ In most of our calculations we will stick to the set $(q_1,q_3,p_2,p_4)$. Moreover, to match the assumptions we have made during the explicit computation of the one-loop amplitude and to guarantee a weakly coupled theory, we will have to impose the following hierarchy of charges $$\begin{aligned}
q_1\gg q_3\gg p_2\gg p_4\ggg1\,.\label{chargeHier}\end{aligned}$$ For completeness, let us also mention that the dual setup in type II string theory compactified on $K3\times T^2$ corresponds to a D0-D4-D4-D4 brane configuration (see e.g. [@Dabholkar:2005dt]). There, the electric charges stem from D0-branes as well as a stack of D4-branes wrapping $K3$, while the magnetic charges correspond to the remaining two stacks of D4-branes which wrap $T^2\times \gamma_{1,2}$, where $\gamma_{1,2}$ are two 2-cycles inside $K3$.
Entropy Function {#Sect:SecondDerEntrop}
----------------
We will now compute the entropy function [@Sen:2005wa; @Sen:2005iz] for the black hole setup outlined in the previous subsection. We will work iteratively order by order in a derivative expansion of the effective action, starting with the tree-level one and assume large charges throughout.
### Ansatz for the Fields {#Sect:AnsatzFields}
Before considering the action, we have to make an ansatz for all fields of the theory in the vicinity of the horizon of the black hole. Starting with the metric we assume (following [@Sen:2005wa; @Sen:2005iz]) that the near-horizon geometry is of the form $AdS_2\times S^2$ for which we make the ansatz $$\begin{aligned}
ds^2=G_{\mu\nu}dx^\mu dx^\nu=v_1\left(-r^2dt^2+\frac{dr^2}{r^2}\right)+v_2(d\theta^2+\sin^2\theta d\varphi^2)\,.\label{metric}\end{aligned}$$ Here $v_1$ and $v_2$ are two constants parameterising the radii of $AdS_2$ and $S^2$ respectively. We will determine both of them in the following. Concerning the scalar fields, after the truncation outlined in Section \[Sect:ChargeSetup\] we still have to deal with three of them: the heterotic dilaton (inside the ${{\cal N}}=2$ SUGRA multiplet) and the $(T,U)$-moduli of $T^2$ (inside the two vector multiplets). We will make the following ansatz for them $$\begin{aligned}
&e^{-2\Phi}=s\,,&&R_1=T_2U_2=r_1\,,&&R_2=\frac{T_2}{U_2}=r_2\,,\end{aligned}$$ with $s$, $r_1$ and $r_2$ constants which need to be determined explicitly. Here we have chosen to follow [@Sen:2005iz] and consider the limit in which $T^2$ factorises into $S^1_{(1)}\times S^1_{(2)}$ with radii $R_1$ and $R_2$ respectively.
Finally for the gauge field strength tensors, following our outline of the charge setup in Section \[Sect:ChargeSetup\] we make the following ansatz [$$\begin{aligned}
&F_{\mu\nu}^{(1)}=
\left(
\begin{array}{cccc}
0 & e_1 & 0 & 0 \\
-e_1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{array}
\right)\,,&& &&F_{\mu\nu}^{(2)}= \left(
\begin{array}{cccc}
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & \frac{p_2 \sin\theta}{4 \pi } \\
0 & 0 & -\frac{p_2 \sin\theta}{4 \pi } & 0
\end{array}
\right),\label{field1}\\
&\nonumber\\
&F_{\mu\nu}^{(3)}= \left(
\begin{array}{cccc}
0 & e_3 & 0 & 0 \\
-e_3 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{array}
\right)\,, && &&F_{\mu\nu}^{(4)}= \left(
\begin{array}{cccc}
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & \frac{p_4 \sin\theta}{4 \pi } \\
0 & 0 & -\frac{p_4 \sin\theta}{4 \pi } & 0
\end{array}
\right)\,,\label{field4}\end{aligned}$$]{} where $(p_2,p_4)$ are the magnetic charges respectively and $(e_1,e_3)$ are essentially the Legendre transforms of the electric charges $(q_1,q_3)$.
### Two Derivative Entropy Function
We start by determining the entropy and near horizon geometry for a large black hole characterised by the charges $(q_1,q_3,p_2,p_4)$ in the classical limit. To this end, we consider the classical tree-level action given by (see [@Sen:2005iz]) $$\begin{aligned}
S^{\text{tree}}=\frac{1}{32\pi}\int d^4x&\sqrt{-G} e^{-2\phi} \bigg[R+4\partial_\mu\phi\partial^\mu\phi -r_1^{-2}\partial_\mu r_1\partial^\mu r_1-r_2^{-2}\partial_\mu r_2\partial^\mu r_2-\nonumber\\
-&r_1^2F^{(1)}_{\mu\nu}F^{(1),\mu\nu}-r_2^2F^{(2)}_{\mu\nu}F^{(2),\mu\nu}-r_1^{-2}F^{(3)}_{\mu\nu}F^{(3),\mu\nu}-r_2^{-2}F^{(4)}_{\mu\nu}F^{(4),\mu\nu}\bigg],\label{TreeLevelAction}\end{aligned}$$ where $R$ is the Ricci scalar computed from the space-time metric $G_{\mu\nu}$ with determinant $G$. This action gives rise to the following entropy function $$\begin{aligned}
\mathcal{E}_{(2)}=2\pi (e_1q_1+e_3q_3)-\frac{\pi s (v_1-v_2)}{2}-\frac{\pi sv_2}{2v_1}\left( e_1^2r_1^2+\frac{e_3^2}{r_1^2}\right)+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)\,,\label{TreeLevelEntropyFunction}\end{aligned}$$ whose extremum with respect to the parameters $(v_1,v_2,s,r_1,r_2)$ is the leading order entropy.[^6] A quick computation reveals that the extremum is situated at $$\begin{aligned}
&v_1=v_2=\frac{p_2p_4}{4\pi^2}\,,&& &&s=\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\,,&& &&r_1=\sqrt{\frac{q_1}{q_3}}\,,\label{nearhorsol1}\\
&r_2=\sqrt{\frac{p_4}{p_2}}\,,&& &&e_1=\frac{q_3\sqrt{p_2p_4}}{4\pi\sqrt{q_1q_3}}\,,&& &&e_3=\frac{q_1\sqrt{p_2p_4}}{4\pi\sqrt{q_1q_3}}\,,\label{nearhorsol2}\end{aligned}$$ from which the entropy follows to be $$\begin{aligned}
\mathcal{S}_{(2)}=\sqrt{q_1q_3p_2p_4}=2\pi\sqrt{nwNW}\,.\label{BHentropyLARGE}\end{aligned}$$ This result has already been obtained in [@Sen:2005iz]. We will now consider corrections to this result due to the 4th-order higher derivative terms, similar to [@Sen:2005iz].
### Four Derivative Entropy Function {#Sect:FourthDerEntrop}
The first correction to the entropy will stem from four derivative terms in the effective action. The full tree-level contribution to these terms in heterotic string theory is given by the dimensional reduction of a manifestly covariant term in six dimensions [@Metsaev:1987zx; @Hull:1987pc] together with the gravitational Chern-Simons term. However, it was proven in [@Sahoo:2006pm] that the contribution of these terms to the black hole entropy is the same with the one obtained from the four-dimensional Gauss-Bonnet term. Since the computations are much simpler in this case, we will simply follow [@Sen:2005iz] and add the Gauss-Bonnet term to the tree-level action (\[TreeLevelAction\]) (for related computations in a non-supersymmetric setup see [@Olea:2005gb]): $$\begin{aligned}
\Delta S_{GB}=-\frac{3}{16\pi^2}\int d^4x \ln\left(2s |\eta(a+is)|^4\right) \left(R_{\mu\nu\rho\tau}R^{\mu\nu\rho\tau}-4R_{\mu\nu}R^{\mu\nu}+R^2\right)\,,\label{GaussBonnet}\end{aligned}$$ where $a$ is the axion field. Using the same ansatz as in Section \[Sect:SecondDerEntrop\] we can write the modified entropy function in a straight-forward manner $$\begin{aligned}
\mathcal{E}_{(4)}=&2 \pi (e_1 q_1+e_3 q_3)-\frac{\pi s (v_1-v_2)}{2}-\frac{\pi sv_2}{2v_1}\left( e_1^2r_1^2+\frac{e_3^2}{r_1^2}\right)+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)-\nonumber\\
&-\frac{3}{8\pi} \ln\left(2s|\eta(a+is)|^4\right)\,.\end{aligned}$$ The extremum with respect to the axion is fixed by $$\begin{aligned}
\frac{\partial \mathcal{E}_{(4)}}{\partial a}=-\frac{3}{4\pi}\left(\frac{\eta'(a+is)}{\eta(a+is)}-\frac{\eta'(-a+is)}{\eta(-a+is)}\right)=0\,,\end{aligned}$$ which has a solution at $a=0$. Introducing the shorthand notation $$\begin{aligned}
\zeta(s):=-\frac{3}{32\pi^2}\ln\left(2s|\eta(is)|^4\right)\,,\label{ZetaDef}\end{aligned}$$ the entropy function takes the form $$\begin{aligned}
\mathcal{E}_{(4)}=&2 \pi (e_1 q_1+e_3 q_3)-\frac{\pi s (v_1-v_2)}{2}-\frac{\pi sv_2}{2v_1}\left( e_1^2r_1^2+\frac{e_3^2}{r_1^2}\right)+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)+4\pi\zeta(s)\,.\label{RedEntropR2}\end{aligned}$$ Extremising this function with respect to $(v_1,v_2,r_1,r_2)$ is straight-forward, as it only requires solving polynomial equations. The answer (in terms of the remaining variable $s$) is given by $$\begin{aligned}
&v_1=v_2=\frac{p_2p_4}{8\pi^2}+\frac{8q_1q_3}{s^2}\,,&&\text{and} &&r_1=\sqrt{\frac{q_1}{q_3}}\,,&&\text{and}&&r_2=\sqrt{\frac{p_4}{p_2}}\,.\label{nearhorsolR2pre}\end{aligned}$$ As we can see, using relation (\[chargeHier\]) it follows that $T_2U_2\gg 1$ and $T_2\ll U_2$ which matches our assumptions of appendix \[App:ExplicitTorusIntegral\]. The solution for the Legendre transformed electric charges is given by $$\begin{aligned}
&e_1=\frac{2q_3}{s}\,,&&\text{and} &&e_3=\frac{2q_1}{s}\,.\end{aligned}$$ However, extremising the entropy function (\[RedEntropR2\]) also with respect to the dilaton $s$ is more involved, due to the presence of the non-trivial function $\zeta(s)$ (see (\[ZetaDef\])). We therefore need to find a way of approximating the equation. To this end, we make the following ansatz for $s$ based on (\[nearhorsol1\]) $$\begin{aligned}
s=\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}+x_s\,,\end{aligned}$$ with $x_s$ a function of the charges of order $\mathcal{O}(q^{-2},p^{-2})$. With this ansatz, we have to solve $$\begin{aligned}
\frac{\sqrt{p_2^3p_4^3}}{64\pi^2\sqrt{q_1q_3}}\,x_s+4\pi\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-2},p^{-2})=0\,,\end{aligned}$$ which has the solution $$\begin{aligned}
x_s=-\frac{256\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-4},p^{-4})\,.\end{aligned}$$ Therefore, the final result to leading order in the charges is given by $$\begin{aligned}
&v_1=v_2=\frac{p_2p_4}{4\pi^2}+8\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-2},p^{-2})\label{SolR21}\,,\\
&s=\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}-\frac{256\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-4},p^{-4})\,,\\
&e_1=\frac{q_3\sqrt{p_2p_4}}{4\pi\sqrt{q_1q_3}}+\frac{64q_3\pi^2}{p_2p_4}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-3},p^{-3})\,,\\
&e_3=\frac{q_1\sqrt{p_2p_4}}{4\pi\sqrt{q_1q_3}}+\frac{64q_1\pi^2}{p_2p_4}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-3},p^{-3})\,,\end{aligned}$$ while the moduli $r_1$ and $r_2$ remain the same as in (\[nearhorsol1\]) and (\[nearhorsol2\]) $$\begin{aligned}
&r_1=\sqrt{\frac{q_1}{q_3}}+\mathcal{O}(q^{-4},p^{-4})\,,&&\text{and} &&r_2=\sqrt{\frac{p_4}{p_2}}+\mathcal{O}(q^{-4},p^{-4})\,.\label{SolR25}\end{aligned}$$ Inserting this result into (\[RedEntropR2\]), we get the following expression for the black hole entropy $$\begin{aligned}
\mathcal{S}_{(4)}&=\sqrt{q_1q_3p_2p_4}+4\pi\zeta\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\mathcal{O}(q^{-2},p^{-2})=\nonumber\\
&=2\pi\sqrt{nwNW}+4\pi\zeta\left(\sqrt{\frac{nw}{NW}}\right)+\mathcal{O}(n^{-2},w^{-2},N^{-2},W^{-2})\,.\label{BHentropyR2}\end{aligned}$$ With this result we are now ready to include the effect of the six-derivative terms.
### Six Derivative Entropy Function
In order to reduce writing to a minimum, we use the following shorthand notation for the effective coupling ${\mathcal{A}_{AB}^{\text{het}}}$ of (\[ShorthandCoupling\]) $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}=\xi_{AB}(r_1,r_2)\,.\end{aligned}$$ The precise moduli dependence has been computed in Section \[Sect:OneLoopHeterotic\]. Notice, since ${\mathcal{A}_{AB}^{\text{het}}}$ is a one-loop amplitude, $\xi$ is independent of the dilaton $s$. With this and using the same ansatz for the fields in the near horizon area of the black hole as in Section \[Sect:AnsatzFields\], the contribution of the six-derivative term (\[A2compExp\]) reads $$\begin{aligned}
\mathcal{E}_{(6)}=&\,2 \pi (e_1 q_1+e_3 q_3)-\frac{\pi s (v_1-v_2)}{2}-\frac{\pi sv_2}{2v_1}\left( e_1^2r_1^2+\frac{e_3^2}{r_1^2}\right)+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)+\nonumber\\
&+4\pi \zeta(s)-\frac{4 (v_1^2+v_2^2)}{v_1 v_2^3}\,(\xi_{AB} (r_1,r_2)p^Ap^B)\,.\label{Entrop62}\end{aligned}$$ Here we have combined the two magnetic charges into a vector of the form $$\begin{aligned}
p^A=\left(\begin{array}{c}p_2 \\ p_4\end{array}\right)\,.\label{VectCharge}\end{aligned}$$ Extremisation of (\[Entrop62\]) with respect to $(e_1,e_3)$ can be performed analytically yielding $$\begin{aligned}
&e_1=\frac{2q_1v_1}{sr_1^2v_2}\,,&&\text{and}&&e_3=\frac{2q_3r_1^2v_1}{s2v_2}\,.\end{aligned}$$ For the remaining parameters $(v_1,v_2,s,r_1,r_2)$ an analytic solution for the full entropy function turns out to be quite difficult to obtain, mostly due to the complicated functions $\zeta(s)$ and $\xi(r_1,r_2)$. We therefore again proceed by searching for an approximated solution. To this end, we make the following ansatz based on (\[SolR21\])–(\[SolR25\]) $$\begin{aligned}
&v_1=\frac{p_2p_4}{4\pi^2}+8\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+x_1\,,&&v_2=\frac{p_2p_4}{4\pi^2}+8\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+x_2\,,\label{HigherOrderAnsatzv1}\end{aligned}$$ $$\begin{aligned}
s=\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}-\frac{256\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+x_s\,,\label{HigherOrderAnsatzs}\end{aligned}$$ $$\begin{aligned}
&r_1=\sqrt{\frac{q_1}{q_3}}+x_{r_1}\,,&&r_2=\sqrt{\frac{p_4}{p_2}}+x_{r_2}\,,\label{ansatzSOL2}\end{aligned}$$ where $(x_{1},x_{2})$ are assumed to be of order $\mathcal{O}(q^{-2},p^{-2})$ and $(x_s,x_{r_1},x_{r_2})$ of order $\mathcal{O}(q^{-4},p^{-4})$ in the charges.
With this ansatz, we can extremise the entropy function (\[Entrop62\]) to leading order, finally obtaining the following result [$$\begin{aligned}
v_1=&\frac{p_2p_4}{4\pi^2}+8\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)-\frac{2048\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\,\zeta''\!\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\,,\label{SOLR2full1}\\
&\nonumber\\
v_2=&\frac{p_2p_4}{4\pi^2}+8\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)-\frac{2048\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\,\zeta''\!\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)-\nonumber\\*
&-\frac{64\pi^2p^Ap^B}{\sqrt{q_1q_3}\sqrt{p_2^3p_4^3}}\,\xi_{AB}\!\left(\sqrt{\frac{q_1}{q_3}},\sqrt{\frac{p_4}{p_2}}\right)\,,\\
&\nonumber\\
s=&\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}-\frac{256\pi^3\sqrt{q_1q_3}}{\sqrt{p_2^3p_4^3}}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\frac{2048\pi^5p^Ap^B}{p_2^3p_4^3}\,\xi_{AB}\!\left(\sqrt{\frac{q_1}{q_3}},\sqrt{\frac{p_4}{p_2}}\right)+\nonumber\\*
&+\frac{12288\pi^5\sqrt{q_1q_3}}{\sqrt{p_2^5p_4^5}}\,\left(\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\right)^2+\frac{65536\pi^6q_1q_3}{p_2^3p_4^3}\,\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\,\zeta''\!\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)+\nonumber\\
&+\mathcal{O}(q^{-6},p^{-6})\,,\\
&\nonumber\\
r_1=&\sqrt{\frac{q_1}{q_3}}+\mathcal{O}(q^{-6},p^{-6})\,,\hspace{2cm}\text{and} \hspace{2cm}
r_2=\sqrt{\frac{p_4}{p_2}}+\mathcal{O}(q^{-6},p^{-6})\,.\label{SOLR2full5}\end{aligned}$$]{} Inserting this into (\[Entrop62\]), we find for the entropy $$\begin{aligned}
\mathcal{S}_{(6)}=&\sqrt{q_1q_3p_2p_4}+4\pi\zeta\left(\frac{8\pi\sqrt{q_1q_2}}{\sqrt{p_2p_4}}\right)-\frac{512\pi^4\sqrt{q_1q_2}}{\sqrt{p_2^3p_4^3}}\left(\zeta'\left(\frac{8\pi\sqrt{q_1q_3}}{\sqrt{p_2p_4}}\right)\right)^2-\nonumber\\
&-\frac{128\pi^4p^Ap^B}{p_2^2p_4^2}\,\xi_{AB}\!\left(\sqrt{\frac{q_1}{q_3}},\sqrt{\frac{p_4}{p_2}}\right)+\mathcal{O}(q^{-4},p^{-4})\,.\label{BHentropyR2full}\end{aligned}$$ With the physical quantum numbers (\[ChargeRescaling\]) this becomes $$\begin{aligned}
\mathcal{S}_{(6)}=&2\pi\sqrt{nwNW}+4\pi\zeta\left(\sqrt{\frac{nw}{NW}}\right)-\frac{4\pi\sqrt{nw}}{\sqrt{N^3W^3}}\left(\zeta'\left(\sqrt{\frac{nw}{NW}}\right)\right)^2-\nonumber\\
&-\frac{8\pi^2N^AN^B}{N^2W^2}\,\xi_{AB}\!\left(\sqrt{\frac{n}{w}},\sqrt{\frac{W}{N}}\right)+\mathcal{O}(n^{-4},w^{-4},N^{-4},W^{-4})\,.\end{aligned}$$ Here we have also combined $(N,W)$ into $N^A$ in a similar fashion as in (\[VectCharge\]). Notice that this correction is precisely of the expected order in the charges. Moreover, we see that there are in fact two correction terms. The first one, which depends on $\zeta$, is just the higher order correction from the Gauss-Bonnet term (\[GaussBonnet\]). The last term, on the other hand, is proportional to $\xi$ and therefore is a contribution stemming from the six-derivative term (\[A2compExp\]).
Entropy Corrections for Small Black Holes {#Sect:EntropyBlackSmall}
=========================================
As we have seen in the previous section, in the case of large black holes, i.e. those which already classically have a non-vanishing horizon, the topological terms (\[A2compExp\]) give only a subleading contribution to the entropy. One can now ask what the situation is in the case of small black holes for which a non-vanishing horizon is only provided by higher derivative terms in the effective supergravity action. In particular, it would be interesting to understand whether there are black holes for which the first non-trivial contribution to the entropy is provided by (\[A2compExp\]). In this Section we would like to take a first step into this direction by considering two special cases.
Charge Setup
------------
We wish to consider particular limits of the charge setup discussed in Section \[Sect:ChargeSetup\], namely we want to calculate the entropy in the case that we set to zero two out of the four charges $(q_1,q_3,p_2,p_4)$. Obviously we cannot simply apply this limit to the final result (\[BHentropyR2full\]) since we have assumed throughout the computation in Section \[Sect:SecondDerEntrop\] that all charges are very large and we therefore have to perform the computations from scratch. To be more precise, with respect to the four charges $(q_1,q_3,p_2,p_4)$ there are two possible limits which we are interested in, namely vanishing magnetic charges $p_2=p_4=0$ and vanishing electric charges $q_1=q_3=0$.
The first option has already been studied in [@Dabholkar:2004yr] on the type II side. As higher derivative correction terms the topological $R^2$ interaction for a $K3\times T^2$ compactification was added.[^7] It was proven explicitly that this term is not only responsible for the black hole to obtain a finite-size horizon but that the entropy calculated for this setup matches the result of the microstate counting to all orders in the large charge expansion. Put it differently, the $R^2$-interaction already captures the complete entropy of the black hole. It is therefore an interesting check for the consistency of our computations to see that the six derivative topological term (\[A2compExp\]) does not modify this result. That this is indeed the case is quick to see. According to our discussion in Section \[Sect:ChargeSetup\] the two remaining gauge fields in this setting correspond to two graviphotons. However, in this case, as explicitly calculated in Section \[Sect:OneLoopHetGraviphoton\], there is no contribution of the type (\[A2compExp\]) and the result of [@Dabholkar:2004yr] is not modified.
One is therefore left to consider the second option, namely setting $q_1=q_3=0$. For this case we will now compute the entropy function including the fourth derivative Gauss-Bonnet term (\[GaussBonnet\]) as well as the sixth-derivative coupling (\[A2compExp\]).
Entropy Function {#entropy-function}
----------------
### Four Derivative Entropy Function {#four-derivative-entropy-function}
We will use the same ansatz for the fields in the near-horizon region of the black hole as in Section \[Sect:AnsatzFields\], however, with $q_1$ and $q_3$ set to zero. In this case extremisation of the tree-level entropy function yields a vanishing entropy. We therefore immediately proceed to include the Gauss-Bonnet term (\[GaussBonnet\]). To be explicit, we will use (\[ProdRepDedekind\]) to expand the function $\zeta(s)$ introduced in (\[ZetaDef\]) in powers of $s$ in the following manner $$\begin{aligned}
\zeta(s):=-\frac{3}{32\pi^2}\ln\left(2s|\eta(is)|^4\right)=\frac{s}{32\pi}-\frac{3}{32\pi^2}\,\log(2s)+\ldots\,.\label{ZetaExpand}\end{aligned}$$ Here the dots stand for exponentially suppressed terms, whose contributions we are not interested in. With this explicit expression, the fourth-derivative entropy function takes the form $$\begin{aligned}
\mathcal{E}_{(4)}^{\text{small}}=-\frac{\pi s(v_1-v_2)}{2}+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)+\frac{s}{8}-\frac{3}{8\pi}\,\log(2s)\,.\label{EntrFct4DerSmall}\end{aligned}$$ The extremum of this function is at the point $$\begin{aligned}
&v_1=v_2=\frac{p_2p_4}{8\pi^2}\,,&&\text{and}&&r_2=\sqrt{\frac{p_4}{p_2}}\,,&&\text{and} &&s=\frac{6}{p_2p_4+2\pi}=\frac{6}{p_2p_4}-\frac{12\pi}{p_2^2p_4^2}+\mathcal{O}(p^{-6})\,.\label{Solution4DerSmall}\end{aligned}$$ Note that since $\mathcal{E}_{(4)}^{\text{small}}$ is independent of the modulus $r_1$ its extremisation does not provide a value for it. Therefore, to this order in the charges, the entropy function formalism does not provide an attractor equation for $r_1$. Nevertheless, inserting (\[Solution4DerSmall\]) into (\[EntrFct4DerSmall\]), we obtain the entropy of the small black hole $$\begin{aligned}
\mathcal{S}_{(4)}^{\text{small}}&=\frac{3}{8\pi}\log\left(\frac{p_2p_4+2\pi}{12}\right)+\frac{3}{8\pi}=\frac{3}{8\pi}\log\left(\frac{p_2p_4}{12}\right)+\frac{3}{8\pi}+\mathcal{O}(p^{-2})=\nonumber\\
&=\frac{3}{8\pi}\log\left(\frac{4\pi^2 NW}{3}\right)+\frac{3}{8\pi}+\mathcal{O}(N^{-2},W^{-2})\,.\end{aligned}$$ As we can see, the entropy depends logarithmically on the charges. The reason for this is that the first non-trivial contribution essentially comes from the second (logarithmic) term in (\[ZetaExpand\]), while the first term taken alone would still give a vanishing entropy.
### Six Derivative Entropy Function
We now want to include also the sixth derivative topological terms (\[A2compExp\]) for a twofold reason. On the one hand, we want to see whether it also contributes to the entropy of this black hole (although maybe in a subdominant way) and on the other hand, we want to check whether it allows to fix the value of the remaining modulus $r_1$. The modified entropy function is given by the expression $$\begin{aligned}
\mathcal{E}_{(6)}^{\text{small}}=&-\frac{\pi s(v_1-v_2)}{2}+\frac{sv_1}{32\pi v_2}\left(p_2^2r_2^2+\frac{p_4^2}{r_2^2}\right)+\frac{s}{8}-\frac{3}{8\pi}\,\log(2s)-\nonumber\\
&-\frac{4(v_1^2+v_2^2)p^Ap^B}{v_1v_2^3}\,\xi_{AB}(r_1,r_2)\,.\label{EntrFct6DerSmall}\end{aligned}$$ Extremizing this expression is rather difficult due to the presence of the complicated function $\xi_{AB}(r_1,r_2)$. We will therefore apply the same strategy as in Section \[Sect:SecondDerEntrop\] and linearise the equations around the solution (\[Solution4DerSmall\]) by making the ansatz $$\begin{aligned}
&v_1=\frac{p_2p_4}{8\pi^2}+x_1\,,&&v_2=\frac{p_2p_4}{8\pi^2}+x_2\,,&&s=\frac{6}{p_2p_4}-\frac{12\pi}{p_2^2p_4^2}+x_s\,,&&r_2=\sqrt{\frac{p_4}{p_2}}+x_{r_2}\,.\end{aligned}$$ Here we assume the following scaling behaviour of the corrections $$\begin{aligned}
&x_1\sim x_2=\mathcal{O}(p^0)\,, &&x_s=\mathcal{O}(p^{-4})\,,&&r_1=\mathcal{O}(p^0)\,,&&x_{r_2}=\mathcal{O}(p^{-2})\,.\end{aligned}$$ Extremizing (\[EntrFct6DerSmall\]) to leading order in the charges amounts for $r_1$ to solve $$\begin{aligned}
\frac{\partial}{\partial r_1}\left[p^Ap^B\xi_{AB}\left(r_1,\sqrt{\frac{p_4}{p_2}}\right)\right]=0\,,\end{aligned}$$ whose solution $r_1^{(0)}$ therefore corresponds to the attractor value. Extremizing then $\mathcal{E}_{(6)}^{\text{small}}$ for the remaining quantities $(x_1,x_2,x_s,x_{r_2})$ yields the following next-to-leading order solution $$\begin{aligned}
&v_1=\frac{p_2p_4}{8\pi^2}+\frac{1024\pi^2p^Ap^B}{3p_2p_4}\,\xi_{AB}\left(r_1^{(0)},\sqrt{\frac{p_4}{p_2}}\right)+\mathcal{O}(p^{-2})\,,\\
&v_2=\frac{p_2p_4}{8\pi^2}+\mathcal{O}(p^{-2})\,,\\
&s=\frac{6}{p_2p_4}-\frac{12\pi}{p_2^2p_4^2}+\mathcal{O}(p^{-6})\,,\\
&r_2=\sqrt{\frac{p_4}{p_2}}+\frac{1024\pi^5p^Ap^B}{3p_2^3p_4}\,\xi_{AB}^{(0,1)}\left(r_1^{(0)},\sqrt{\frac{p_4}{p_2}}\right)+\mathcal{O}(p^{-4})\,.\end{aligned}$$ Here $\xi_{AB}^{(0,1)}$ denotes the first derivative of $\xi_{AB}$ with respect to the second argument. Reinserting this solution into (\[EntrFct6DerSmall\]) we obtain the corrected entropy $$\begin{aligned}
\mathcal{S}_{(6)}^{\text{small}}&=\frac{3}{8\pi}\log\left(\frac{p_2p_4}{12}\right)+\frac{3}{8\pi}+\frac{3}{4p_2p_4}-\frac{2048\pi^4p^Ap^B}{4p_2^2p_4^2}\,\xi_{AB}\left(r_1^{(0)},\sqrt{\frac{p_4}{p_2}}\right)+\mathcal{O}(p^{-4})=\nonumber\\
&=\frac{3}{8\pi}\log\left(\frac{4\pi^2 NW}{3}\right)+\frac{3}{8\pi}+\frac{3}{64\pi^2 NW}-\frac{32\pi^2N^AN^B}{N^2W^2}\,\xi_{AB}\left(r_{1}^{(0)},\sqrt{\frac{W}{N}}\right)+\nonumber\\
&\hspace{1cm}+\mathcal{O}(N^{-4},W^{-4})\,.\end{aligned}$$ Since this result depends on $\xi_{AB}$, it follows that the sixth-derivative terms (\[A2compExp\]) indeed yield a non-trivial contribution to the entropy. However, looking more precisely, this contribution is in fact subdominant with respect to the contribution coming from the Gauss-Bonnet term (\[GaussBonnet\]).
Conclusions {#Sect:Conclusions}
===========
In this work we have studied the effects of a particular topological six-derivative term on the entropy of black holes. We have explicitly calculated this term as a one-loop contribution in the effective heterotic string action, performing also the integral over the modular parameter of the world-sheet torus.
In the case of large black holes, this term yields a non-vanishing correction to the entropy of the order $\mathcal{O}(p^{-2},q^{-2})$. For small black holes, we have studied two different setups: Black holes carrying only charges with respect to two graviphotons do not receive any corrections at all. This is in perfect agreement with the literature (see e.g. [@Dabholkar:2004yr]) where it has been shown that the entropy of such black holes is already captured by the topological fourth-derivative $R^2$ effective action coupling.
On the other hand, for small black holes which are only charged with respect to two physical gauge fields, the leading contribution to the entropy also comes from $R^2$ terms (e.g. the Gauss-Bonnet combination), however not from the tree-level expression but rather from higher logarithmic corrections. In this setup the topological sixth-derivative corrections are still suppressed being of order $\mathcal{O}(p^{-2},q^{-2})$. However, they are responsible for lifting certain flat directions in the moduli space of the entropy function, thereby providing attractor values for some of the scalar fields involved.
It would be very interesting to compare our macroscopic results with some results obtained from state-counting. This would allow us to obtain a microscopic interpretation of the entropy in the setup we considered. Microscopic computations up to order $-2$ in the charges have recently been performed in [@Banerjee:2008ky]. There, it was speculated about the nature of higher derivative terms in the effective action which would be responsible for these entropy corrections on the macroscopic side. In this spirit, the term we have discussed in this paper seems to be a good candidate for this task. However, as far as we can see, in order to be able to make a precise comparison between our macroscopic calculations and the microscopic results of [@Banerjee:2008ky] it seems necessary to taken into account non-local terms in the effective action which arise upon integrating out massless degrees of freedom. We leave this study for further work.
Acknowledgements {#acknowledgements .unnumbered}
================
It is a pleasure to thank Atish Dabholkar, Sergio Ferrara, Finn Larsen, Boris Pioline, Frank Saueressig, Ashoke Sen and Emery Sokatchev for enlightening discussions. S.H. would like to thank the Laboratoire de Physique Théorique et Hautes Energies (LPTHE) in Paris for kind hospitality during the initial stage of this work. The work of I.A. was supported in part by the European Commission under the ERC Advanced Grant 226371 and the contract PITN-GA-2009-237920 and in part by the CNRS grant GRC APIC PICS 3747. The research of S.H. was supported by the Swiss National Science Foundation.
Modular Functions and Eisenstein Series {#App:Eisenstein}
=======================================
Since they play a major role throughout the heterotic one-loop computation in Section \[Sect:OneLoopHeterotic\], we will compile some useful identities and formulas for Eisenstein series in this appendix.
The functions $G_{2k}$ appearing in the generating functional (\[SpaceTimeCorrEisen\]) are the canonically defined Eisenstein series $$\begin{aligned}
G_{2k}(\tau)=\sum_{\text{\tiny $\begin{array}{c}m,n=-\infty \\ mn\neq 0\end{array}$}}^{\infty}(m\tau+n)^{-2k}\,.\end{aligned}$$ In this work we will also use a different normalisation of the Eisenstein series $$\begin{aligned}
E_{2k}(q)=\frac{G_{2k}(\tau)}{2\zeta(2k)}=1+c_{2k}\sum_{n=1}^\infty\sigma_{2k-1}(n)q^n\,,\end{aligned}$$ where $q=e^{2i\pi\tau}$, $\sigma_{k}(n)$ is the divisor function (i.e. the sum of the $k$-th powers of the integer divisors of $n$), and $$\begin{aligned}
c_{2k}=\frac{(2\pi i)^{2k}}{(2k-1)!\zeta(2k)}\,.\end{aligned}$$ For latter use we give the explicit $q$-expansion of the first few $E_{2k}$ $$\begin{aligned}
&E_{2}(q)=1-24q-72q^2-96q^3-168q^4-144q^5+\ldots\,,\\
&E_{4}(q)=1+240q+2160q^2+6720q^3+17520q^4+30240q^5+\ldots\,,\\
&E_{6}(q)=1-504q-16632q^2-122976q^3-532728q^4-1575504q^5+\ldots\,,\\
&E_{8}(q)=1+480q+61920q^2+1050240q^3+7926240q^4+37500480q^5+\ldots\,.\end{aligned}$$ For $k>1$, $G_{2k}$ (and $E_{2k}$) are modular functions of weight $2k$. However, $G_2$ picks up an additional shift term under modular transformations, instead of which we introduce $$\begin{aligned}
\hat{G}_2=2\zeta(2)\hat{E}_2=2\zeta(2)\left(E_2-\frac{3}{\pi\tau_2}\right)\,.\end{aligned}$$ The additional term cancels precisely the shift rendering $\hat{G}_2$ a modular function of weight two, however, at the expense of being no longer purely holomorphic.
Using moreover the expansion of the Dedekind function $$\begin{aligned}
\eta(\tau)&=q^{\frac{1}{24}}\left[1+\sum_{n=1}^{\infty}(-1)^n\left(q^{n(3n-1)/2}+q^{n(3n+1)/2}\right)\right]=q^{\frac{1}{24}}\left(1-q-q^2+q^5+q^7+\ldots\right)=\nonumber\\
&=q^{\frac{1}{24}}\prod_k^\infty\left(1-q^k\right)\,,\label{ProdRepDedekind}\end{aligned}$$ we are finally in a position to determine the first few expansion coefficients $c(m,t)$ in (\[BorcherdsIntegral\]). They are given by $$\begin{aligned}
&c(-1,0)=-\frac{\pi^4}{15}\,,&&c(-1,1)=\frac{\pi^3}{3}\,,&&c(-1,2)=-\frac{\pi^2}{2}\,,\\
&c(0,0)=-\frac{168\pi^4}{5}\,,&&c(0,1)=160\pi^3\,,&&c(0,2)=-252\pi^2\,,\\
&c(1,0)=-\frac{24828\pi^4}{5}\,,&&c(1,1)=20532\pi^3\,,&&c(1,2)=-36882\pi^2\,,\\
&c(2,0)=-\frac{612352\pi^4}{3}\,,&&c(2,1)=-\frac{888320\pi^3}{3}\,,&&c(2,2)=-1347520\pi^2\,,\\
&c(3,0)=-7320798\pi^4\,,&&c(2,1)=-5094930\pi^3\,,&&c(2,2)=-27377865\pi^2\,,\\
&c(4,0)=-\frac{1002596352\pi^4}{5}\,,&&c(3,1)=-245568768\pi^3\,,&&c(3,2)=-389320128\pi^2\,.\end{aligned}$$
Modular Invariance {#App:ModInvariance}
==================
In this appendix we check modular invariance of the integrand of (\[modularintegral\]). To this end, we will separately check invariance under the two generators of the modular group $\tau\to\tau+1$ and $\tau\to-\frac{1}{\tau}$. Indeed, the first one can be checked in a straight-forward manner. Using the fact that $\hat{\bar{E}}_2$ and $\bar{\eta}^{24}$ are respectively invariant under the shift, we find that under $\tau\to\tau+1$ $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}\to\int \frac{d^2\tau}{\bar{\eta}^{24}}\,\tau_2\,\hat{\bar{E}}_2{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP^R_B-\frac{\delta_{AB}}{4\pi\tau_2}\right]{q^{\frac{1}{2}(P^L)^2}\bar{q}^{\frac{1}{2}(P^R)^2}}e^{\pi i\left[(P^L)^2-(P^R)^2\right]}\,.\end{aligned}$$ However, since $\Gamma^{(6,22)}$ is a self-dual lattice, the additional phase in the lattice sum is in fact one. We are therefore left to consider the transformation $\tau\to-\frac{1}{\tau}$. Using that the Dedekind functions transforms as $\bar{\eta}^2\to\bar{\tau}\bar{\eta}^2$ we find for ${\mathcal{A}_{AB}^{\text{het}}}$ $$\begin{aligned}
{\mathcal{A}_{AB}^{\text{het}}}\to \tilde{\mathcal{A}}_{AB}^{\text{het}}=\int \frac{d^2\tau}{\bar{\eta}^{24}}\,\frac{\tau_2\hat{\bar{E}}_2}{\tau^3\bar{\tau}^{13}}{\sum_{(P^L,P^R)\in\Gamma^{(6,22)}}}\left[P^R_AP^R_B-\frac{\delta_{AB}\tau\bar{\tau}}{4\pi\tau_2}\right]e^{-\frac{\pi i}{\tau}(P^L)^2}e^{\frac{\pi i}{\bar{\tau}}(P^R)^2}\,.\end{aligned}$$ For this expression we now perform a Poisson resummation $$\begin{aligned}
\tilde{\mathcal{A}}_{AB}^{\text{het}}=\int \frac{d^2\tau}{\bar{\eta}^{24}}&\,\frac{\tau_2\hat{\bar{E}}_2}{\tau^3\bar{\tau}^{13}}\sum_{(X^L,X^R)\in\Gamma^{(6,22)}}\int d^6P^L\int d^{22}P^R\left[P^R_AP^R_B-\frac{\delta_{AB}\tau\bar{\tau}}{4\pi\tau_2}\right]e^{-\frac{\pi i}{\tau}(P^L)^2}e^{\frac{\pi i}{\bar{\tau}}(P^R)^2}\cdot\nonumber\\
&\cdot e^{2\pi i(X^L\cdot P^L)}e^{-2\pi i(X^R\cdot P^R)}\,.\nonumber\end{aligned}$$ Transforming to new coordinates $Y^L_{ij}=(P^L_{ij}-\tau X^L_{ij})$ and $Y^R_A=(P^R_A-\bar{\tau}X^R_A)$ and evaluating explicitly the Gaussian integrals we obtain the expressions: $$\begin{aligned}
\tilde{\mathcal{A}}_{AB}^{\text{het}}=\int \frac{d^2\tau}{\bar{\eta}^{24}}&\,\frac{\tau_2\hat{\bar{E}}_2}{\tau^3\bar{\tau}^{13}}\sum_{(X^L,X^R)\in\Gamma^{(6,22)}}\left[\tau^3\bar{\tau}^{13}X^R_AX^R_B-\frac{\delta_{AB}\tau^3\bar{\tau}^{13}}{4\pi\tau_2}\right]q^{\frac{1}{2}(X^L)^2}\bar{q}^{\frac{1}{2}(X^R)^2}\,.\end{aligned}$$ This amounts to $\tilde{\mathcal{A}}_{AB}^{\text{het}}={\mathcal{A}_{AB}^{\text{het}}}$ which finishes the proof of modular invariance of (\[modularintegral\]).
Torus Integral via Lattice Reduction {#App:ExplicitTorusIntegral}
====================================
In this appendix we explicitly compute the modular integral $\mathcal{I}^{\text{sim}}$ of (\[modularintegralTRUNC\]), where we will mainly follow [@Marino:1998pg; @Borcherds]. The first step is to reduce the $\Gamma^{(2,2)}$ unimodular lattice to a $\Gamma^{(1,1)}$ sublattice. For this, we start by writing $\Gamma^{(2,2)}$ in the form[^8] $$\begin{aligned}
\Gamma^{(2,2)}=H(-1)\oplus H(1)=\langle {\bf e_1},{\bf f_1}\rangle_{\mathbb{Z}}\oplus\langle {\bf e_2},{\bf f_2}\rangle_{\mathbb{Z}}\,, \end{aligned}$$ with $({\bf e_1},{\bf f_1})=-({\bf e_2},{\bf f_2})=-1$ the only non-vanishing inner products. In addition to the lattice we also have an isometry $P:\,\Gamma^{(2,2)}\otimes \mathbb{R}\longrightarrow \mathbb{R}^{2,2}$, whose projection to $\mathbb{R}^{2,0}$ and $\mathbb{R}^{0,2}$ will be called $P_\pm$ respectively. Explicitly, for a given vector ${\mathbf{\lambda}}$, we have $$\begin{aligned}
&P^L=P_-({\bf \lambda})=\frac{1}{\sqrt{2T_2U_2}} \left(n_1+n_2\bar{T}+m_2U+m_1\bar{T}U\right)\,,\\
&P^R=P_+({\bf \lambda})=\frac{1}{\sqrt{2T_2U_2}}\left(n_1+n_2T+m_2U+m_1TU\right)\,.\end{aligned}$$ In order now to perform a lattice reduction, we pick a primitive null-vector ${\bf z}$ inside $\Gamma^{(2,2)}$ alongside with another vector ${\bf z'}$, such that $({\bf z},{\bf z'})=1$. A natural choice for this is to pick ${\bf z}={\bf e_1}$ and ${\bf z'}=-{\bf f_1}$. With this vector we can define a new lattice $$\begin{aligned}
K=\left(\Gamma^{(2,2)}\cap {\bf z^\perp}\right)/\mathbb{Z}{\bf z}\,,\end{aligned}$$ which is of signature $(1,1)$. Here $\mathbb{Z}{\bf z}$ stands for all integer multiples of the null-vector ${\bf z}$. In $K$ we will define new projections $\tilde{P}_\pm$. To this end, we denote the projections of ${\bf z}$ in the old lattice as ${\bf z_\pm}=P_\pm({\bf z})$, for which we find explicitly $$\begin{aligned}
z_+^2=|{\bf z_+}|^2=\frac{1}{2T_2U_2}\,.\label{FirstLattRedVector}\end{aligned}$$ In fact, in order for the lattice reduction to be valid, this expression needs to be small (see [@Borcherds]), which entails that we need to restrict to a region in moduli space, where $T_2U_2\gg 1$.
With ${\bf z_\pm}$ we can decompose $$\begin{aligned}
&\mathbb{R}^{2,0}=\langle {\bf z_+}\rangle\oplus\langle {\bf z_+}\rangle^\perp\,,&&\text{and} &&\mathbb{R}^{0,2}=\langle {\bf z_-}\rangle\oplus\langle {\bf z_-}\rangle^\perp\,.\end{aligned}$$ The reduced projections $\tilde{P}_\pm$ will then be the projections onto the orthogonal complement $\langle {\bf z_+}\rangle^\perp$ and $\langle {\bf z_-}\rangle^\perp$, respectively. They are given in terms of the old projections $P_\pm$ in the following manner $$\begin{aligned}
\tilde{P}_\pm({\bf \lambda})=P_\pm({\bf \lambda})-\frac{(P_\pm({\bf\lambda}),{\bf z_\pm})}{z_\pm^2}\,{\bf z_\pm}\,.\end{aligned}$$ With this, the lattice momenta in the new lattice are given by $$\begin{aligned}
&\tilde{P}^L=\frac{1}{\sqrt{2T_2U_2}}\left(n_2\bar{T}+m_2U\right)\,,&&\text{and} &&\tilde{P}^R=\frac{1}{\sqrt{2T_2U_2}}\left(n_2T+m_2U\right)\,.\end{aligned}$$ Following [@Marino:1998pg], it particularly follows for a vector $\lambda\in K$ $$\begin{aligned}
&\tilde{P}_+(\lambda)=\text{Im}(\tilde{P}^R)\,&&\text{and} &&\tilde{P}_-(\lambda)=\text{Im}(\tilde{P}^L)\,.\label{ProjRedLatt}\end{aligned}$$ For latter use, let us also introduce the following vector in $K\otimes \mathbb{R}$ $$\begin{aligned}
\mu=-{\bf z'}+\frac{{\bf z_+}}{2z_+^2}+\frac{{\bf z_-}}{2z_-^2}\,.\end{aligned}$$ At this point we can use the final result of [@Borcherds; @Marino:1998pg]: The theta-transform $\mathcal{I}^{\text{sim}}$ is given as a sum of three terms $$\begin{aligned}
&\mathcal{I}^{\text{sim}}=\frac{\mathcal{I}^{\text{sim}}_{K}}{\sqrt{2z_+^2}}+\mathcal{I}^{\text{sim}}_{\lambda=0}+\mathcal{I}^{\text{sim}}_{\lambda\neq0}\,.\label{GeneralBorcherdsInt}\end{aligned}$$ Here $\mathcal{I}^{\text{sim}}_{K}$ is another theta-transform, however, in the reduced lattice $K$. Moreover, the remaining two contributions are given by $$\begin{aligned}
&\mathcal{I}_{\lambda=0}^{\text{sim}}=\sqrt{\frac{2}{z_+^2}}\sum_{n>0}\sum_tc(0,t)\left(\frac{\pi n^2}{2z_+^2}\right)^{-\epsilon-t-1/2}\Gamma\left(t+\frac{1}{2}+\epsilon\right)_{\big|\epsilon=0}\,, \label{BorchDeg}\\
&\mathcal{I}_{\lambda\neq0}^{\text{sim}}=\sqrt{\frac{2}{z_+^2}}{\sum_{\lambda\in K}}'\sum_{n>0}e^{(n\lambda,\mu)}\sum_t2c(\lambda^2/2,t)\left(\frac{n}{2|z_+||\tilde{P}_+(\lambda)|}\right)^{-t-1/2}\!\mathcal{K}_{-t-1/2}\left(\frac{2\pi n|\tilde{P}_+(\lambda)|}{|z_+|}\right) \label{BorchNonDeg}\end{aligned}$$ where the prime on the sum over $\lambda$ in (\[BorchNonDeg\]) means that the zero-vector is excluded and $\mathcal{K}_{-t-1/2}$ is a modified Bessel function of second kind. Equation (\[BorchDeg\]) must be understood as the constant piece of an analytic Laurent expansion in $\epsilon$.
In the following we discuss all three contributions in detail.
- Reduced theta-transform (degenerate orbit)\
In order to compute the left-over theta-transform, we perform another lattice reduction to arrive at the trivial lattice. For this, we pick the vectors ${\bf \tilde{z}}={\bf e_2}$ and ${\bf \tilde{z}'}={\bf f_2}$ which particularly yields $$\begin{aligned}
\tilde{z}_+^2=|{\bf \tilde{z}_+}|^2=\frac{T_2}{2U_2}\,.\end{aligned}$$ Notice that with this choice we are working in the patch $T_2<U_2$. Exchanging ${\bf \tilde{z}}$ and ${\bf \tilde{z}'}$ will bring us to the patch $T_2>U_2$. All results will be exactly the same upon the exchange $T_2\longleftrightarrow U_2$. With this reduction, we are left with two contributions $$\begin{aligned}
\frac{\mathcal{I}^{\text{sim}}_{K}}{\sqrt{2z_+^2}}=&\frac{1}{2\sqrt{z_+^2\tilde{z}_+^2}}\int_{\mathcal{F}}\frac{d^2\tau}{\tau_2^2}\,\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}+\nonumber\\
&+\frac{1}{\sqrt{z_+^2\tilde{z}_+^2}}\sum_{t=0}^2c(0,t)\frac{2^{t+1}\Gamma(t+1)}{\pi^{t+1}}\,(\tilde{z}_+^2)^{t+1}\zeta(2t+2)\,.\label{FullRedThetaTransform}\end{aligned}$$ The first term is an integral over the fundamental domain, which can nevertheless be evaluated directly $$\begin{aligned}
\int_{\mathcal{F}}\frac{d^2\tau}{\tau_2^2}\,\frac{{\mathcal{P}_{4}}(\bar{E}_4)^2}{\bar{\eta}^{24}}&=-\frac{1}{2}\int_{\mathcal{F}}\frac{d^2\tau}{\tau_2^2}\left[\frac{\bar{\hat{G}}_2^2(\bar{E}_4^2)}{\bar{\eta}^{24}}+\frac{\bar{G}_4(\bar{E}_4^2)}{\bar{\eta}^{24}}\right]=-\frac{16\pi^5}{3}\,,$$ where we have used [@Lerche:1988np] (see also [@Marino:1998pg]) $$\begin{aligned}
\int_{\mathcal{F}}\frac{d^2\tau}{\tau_2^2}\left(\hat{G}_2(\tau)\right)^n F(\tau)=\frac{1}{\pi(n+1)}\left[(G_2(\tau))^{n+1}F(\tau)\right]_{q^0}\,.\end{aligned}$$ Inserting this expression into (\[FullRedThetaTransform\]) we obtain $$\begin{aligned}
\frac{\mathcal{I}^{\text{sim}}_{K}}{\sqrt{2z_+^2}}=-\frac{16\pi^5}{3}\,U_2+2T_2\sum_{t=0}^2c(0,t)\frac{t!\zeta(2t+2)}{\pi^{t+1}}\,\left(\frac{T_2}{U_2}\right)^t\,.\label{ThetaTransform}\end{aligned}$$
- $\lambda=0$ contribution to the non-degenerate orbit\
Next we will discuss the contribution to the non-degenerate orbit given in (\[BorchDeg\]). First of all, following [@Marino:1998pg], the sum over $n$ can be analytically continued into a Riemann zeta-function, leaving $$\begin{aligned}
\mathcal{I}_{\lambda=0}^{\text{sim}}=\sqrt{\frac{2}{z_+^2}}\sum_tc(0,t)\left(\frac{\pi }{2z_+^2}\right)^{-\epsilon-t-1/2}\zeta(1+2t+2\epsilon)\Gamma\left(t+\frac{1}{2}+\epsilon\right)_{\big|\epsilon=0}\,.\end{aligned}$$ Extraction of the constant piece in the $\epsilon$-expansion can be done in a straight-forward way yielding $$\begin{aligned}
\mathcal{I}^{\text{sim}}_{\lambda=0}&=c(0,0)\left[\gamma_E-\log\left(\pi T_2U_2\right)-2\log 2\right]+c(0,1)\frac{\zeta(3)}{\pi T_2U_2}+c(0,2)\frac{3\zeta(5)}{2\pi^2 T_2^2U_2^2}\,,\label{IntDegRes}\end{aligned}$$ where $\gamma_E$ is the Euler-Mascheroni constant.
- $\lambda\neq0$ contribution to the non-degenerate orbit\
Finally, we are left to deal with the contribution (\[BorchNonDeg\]) which we compute following a very similar computation in [@Marino:1998pg]. To this end, we choose a parameterisation of the vector $\lambda\in K$ of the form $\lambda=n_2 {\bf e_2}+m_2 {\bf f_2}$. In addition, we introduce the following shorthand notation $$\begin{aligned}
\alpha=\frac{1}{2}\text{Re}(n_2T+m_2U)+i|\text{Im}(n_2T+m_2U)|\,,\end{aligned}$$ upon which we find $$\begin{aligned}
|\tilde{P}_+(\lambda)|=\text{Im}(\tilde{P}^R)=\frac{1}{\sqrt{2T_2U_2}}|\text{Im}(n_2T+m_2U)|=\frac{\text{Im}(\alpha)}{\sqrt{2T_2U_2}}\,.\end{aligned}$$ Using moreover the relation $({\bf z_+},\lambda)=\sqrt{z_+^2}\,\text{Re}(\tilde{P}^R)$ for $\lambda\in K$ we derive the following expression $$\begin{aligned}
\mathcal{I}^{\text{sim}}_{\lambda\neq0}&=\sqrt{\frac{2}{z_+^2}}\sum_{\lambda\neq 0}\sum_{n=1}^\infty \sum_{t=0}^22c(\lambda^2/2,t)\left(\frac{nT_2U_2}{\text{Im}(\alpha)}\right)^{-t-\frac{1}{2}}\,e^{2\pi in\text{Re}(\alpha)}\, \mathcal{K}_{-t-\frac{1}{2}}(2\pi n\text{Im}(\alpha))\,.\nonumber\end{aligned}$$ Using $\mathcal{K}_{-s}=\mathcal{K}_{s}$ together with its precise definition we can also write $$\begin{aligned}
\mathcal{I}^{\text{sim}}_{\lambda\neq0}&=\sum_{\lambda\neq 0} \sum_{t=0}^2\sum_{s=0}^tc(\lambda^2/2,t)(T_2U_2)^{-t}\frac{\left(\text{Im}(\alpha)\right)^{t-s}}{(4\pi)^s}\,\frac{(s+t)!}{s!(t-s)!}\,\text{Li}_{1+s+t}\left(e^{2\pi i\alpha}\right)\,,\label{IntNonDegRes}\end{aligned}$$ where $\text{Li}_{1+s+t}\left(e^{2\pi\alpha}\right)$ denotes the polylogarithm.
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[^1]: [email protected]
[^2]: On leave from CPHT (UMR CNRS 7644) Ecole Polytechnique, F-91128 Palaiseau
[^3]: [[email protected]]{}
[^4]: For more details on their construction see e.g. [@Antoniadis:2007cw].
[^5]: Notice that due to our simplifications the derivatives will be all anti-symmetrised combinations of $(T_1,T_2,U_1,U_2)$.
[^6]: For a pedagogical outline of the entropy-function formalism see e.g. [@Sen:2007qy]. Notice moreover that in some cases in the literature (e.g.[@Sen:2007qy; @Sen:2005iz]) it has been shown to be useful to perform a suitable $SO(6,22)$-rotation of the charges such that a number of gauge fields will decouple at the attractor point. We have chosen not to perform such a rotation in the following but we will directly extremize the entropy function thereby directly obtaining the attractor values of all fields.
[^7]: This is the first term of the series of the topological $R^2T^{2g-2}$ couplings [@Antoniadis:1993ze]. However, in backgrounds with ${{\cal N}}=4$ supersymmetry, only the term for $g=1$ yields a non-zero contribution.
[^8]: We will use bold-face letters to denote lattice vectors.
| |
Q:
How to stack n divs vertically to n width?
I have been given a design with a number of variable height items stacked vertically in a fixed height container, with a variable width. So the idea is that the items can scroll off screen (will be in a wrapper) so that they can be scrolled horizontally onto screen.
I'm having trouble coming up with a solid way of organising the divs so that they stack reliably. Here is what I'm trying to achieve.
A:
Try this - DEMO
HTML
<section>
<div style="height: 100px;"> 1 </div>
<div style="height: 50px;"> 2 </div>
<div style="height: 150px;"> 3 </div>
<div style="height: 300px;"> 4 </div>
<div style="height: 50px;"> 5 </div>
<div style="height: 100px;"> 6 </div>
<div style="height: 100px;"> 7 </div>
<div style="height: 70px;"> 8 </div>
</section>
CSS
section {
-webkit-column-count: 3;
-moz-column-count: 3;
column-count: 3;
height: 400px;
background: beige;
}
div {
width: 200px;
margin: 0 10px 10px;
background: orange;
display: inline-table;
}
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23 comments:
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In Castlebay, North Wales, Dick Merrill is on trial, accused of murdering his wife by administering a lethal dose of arsenic. Merrill, good-looking and attractive, is fatally in love with Margot Stone, who's herself already married. Philip Vane, a lawyer whose career was mysteriously ruined, finds himself similarly infatuated with Margot when he becomes personally involved in Merrill's sensational murder trial. A shadowy figure, Vane's participation in the trial is twisted and erratic--will the outcome be as unpredictable? A classic thrilling courtroom drama filled with unexpected twists and turns! | https://www.recordedbooks.com/title-details/9781434442895 |
NILES -- Four seconds seperated victory from defeat Wednesday night in Niles' Big 16 Conference West Division showdown with Dowagiac.
With four seconds left on the clock in the final matc of the night, Niles senior George Nelson, trailing 2-1, took down Dowagiac freshman Mike Kasper to secure a victory for the Vikings against their arch rivals.
Nelson's victory gave Niles a 33-28 win over the Chieftains, its second victory over Dowagiac this season. Niles edged Dowagiac 36-35 at the Big 16 Conference Tournament back in January.
The win sent Niles coach Bob Galvin sprinting across the mat with his arms raised in triumph.
Charles Nelson had a chance to put the match away with the Vikings (24-3, 3-1) leading 30-25.
But three warnings for stalling and a technical violation earlier in his match with Austin Lawrence, awarded the Dowagiac grappler two penalty points at the end of regulation which tied the bout at 5-5.
Austin scored a takedown in overtime to set up the dramatics between Kasper and George Nelson.
The match started at 140 due to the fact that several Niles wrestlers were involved in a SAT workshop.
Rodney Leneway opened up the match with a 13-5 win over Justin Desjardin.
Dowagiac picked up an 11-3 win at 145 as Jeromy Northrop defeated Robert Cinninger.
Kyle Isabel then stuck Dowagiac's Elijah Caldwell in 3:46 at 152-pounds to get the Niles fans revved up.
From there the match went back and forth.
Dowagiac (23-7, 1-3) picked up victories at 160, 189, 275 and 112. Niles earned victories at 171, 215 and 103.
Back-to-back wins at 119 by Derek Purcell and 125 by Mason Stephenson gave the Vikings a 30-25 advantage. | https://www.leaderpub.com/2004/02/05/nelson-clinches-victory-for-niles/ |
Address: 1600-212 Olive Chapel Road, Apex, North Carolina, USA.
TRUgaming was founded in 2014 as a gaming community. As TRUgaming grew we found a need for dedicated voice and gaming servers. After using several different companies, we decided that we were tired of overpriced services, poor customer service, and poor service quality; It was time for a change.
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Copyrights © 2021 Walldirectory.com. All rights reserved. | https://walldirectory.com/listing/technology-trugaming-gaming-servers |
A rule defines a filter and an action to perform on the incoming requests that match the filter. The rule filter expression defines the scope of the rule and the rule action defines what happens when there is a match for the expression. Rule filter expressions are defined using the Rules language.
For example, consider the following ruleset with four rules (R1, R2, R3, and R4). For a given incoming request, the expression of the first two rules matches the request properties. Therefore, the action for these rules runs (Execute and Log, respectively). The action of the first rule executes a managed ruleset, which means that every rule in the managed ruleset is evaluated. The action of the second rule logs an event associated with the current phase. There is no match for the expressions of rules 3 and 4, so their actions do not run. Since no rule blocks the request, it proceeds to the next phase.
Rules can have additional features through specific Cloudflare products. You may have more fields available for rule expressions, perform different actions, or configure additional behavior in a given phase.
Rule evaluation and field values
While evaluating rules for a given request/response, the values of all request and response fields are immutable within each phase. However, field values may change between phases.
For example:
- If a Rewrite URL Rule #1 updates the URI path or the query string of a request, Rewrite URL Rule #2 will not take these earlier changes into consideration.
- If a HTTP Request Header Modification Rule #1 sets the value of a request header, HTTP Request Header Modification Rule #2 will not be able to read or evaluate this new value.
- If a Rewrite URL Rule updates the URI path or query string of a request, the
http.request.uri,
http.request.uri.*, and
http.request.full_urifields will have a different value in phases after the
http_request_transformphase (where Rewrite URL Rules are executed). | https://developers.cloudflare.com/ruleset-engine/about/rules/ |
You first arrive at the Bangalore airport, where you will be received by the representative. Then, you head towards Mysore, it takes about 3 hours drive to reach. Once you are there, you check- in at the hotel. Later, you visit the beautiful Brindavan Garden and return back to the hotel for dinner and an overnight stay.
Day 2 : Mysore - Ooty
You check - out of the hotel in the morning, after your breakfast. You go out for a sightseeing tour in Mysore; visit the Chamundi Hills and the Bull Temple. Lastly, you visit the Mysore Palace and proceed to Ooty. On the way you stop to see the Pykara Lake, which offers a great view. Once you reach Ooty, you check- in at the hotel, enjoy your dinner, and later retire for the night.
Day 3 : Ooty
Your day is planned out for Ooty sightseeing, so to do that you leave right away after breakfast. You visit Doddabetta Peak, Botanical Garden and later visit Charing Cross, You can indulge in shopping and a nice lunch in the town. Next, you visit the Tea Museum and the Ooty lake where you can enjoy the boat ride. Later, in the evening, you return to the hotel for an overnight stay.
Day 4 : Ooty - Kodaikanal
You check out of the hotel in the morning after breakfast and head towards Coonoor. There is also a toy train ride that takes you to Coonoor, you can opt for that. After the exciting train journey, you visit the Sim’s park, dolphin’s nose and lamb’s rock. You further drive to Kodaikanal, and on reaching there you check in at the hotel where dinner will be served and you can retire for the night.
Day 5 : Kodaikanal
After breakfast, you go out for kodaikanal sightseeing, the place is covered in greenery and the view it offers is spectacular. Visit the Pillar Rock and the Coakers Walk. Later you can enjoy boating at the Kodai lake and then, return to the hotel. Have dinner and stay overnight.
Day 6 : Departure
The trip comes to an end with your return to the airport for your journey later.
Payment Terms & Methods :
* Some Advance Percentage of total booking amount
* Airfare/Transport fare to be paid full at one time in advance.
Cancellation & Refund Policy :
* Upon cancellation, refund will be made after deducting the Retention Amount.
* Retention Amount varies as per the number of days left before your package start date.
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Reviewed: Sep 18, 2018
As a travel agent, this company provides amazing packages in the tourism industry. The packages it offers are truly amazing. Anyone who want package from luxury to budget can contact it. I had an amazing experience of booking my travel package with them. So, you should also give it a try.
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My decision to put my faith in this company for longer period turns out to be the best decision I have ever made. I am enjoying their services from very long and thus, I can confidently state that they provide the best deals for any travel requirement. Thank you for turning me into a loyal client of yours.
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Reviewed: Sep 01, 2018
I was reaching out to hundreds of travel agents in the past one year to get exclusive travel deals. I came in contact with this agent through my relative. And surprisingly, they offered me the best travel package including complete itinerary and other additional facilities such as car transfer, sightseeing, accommodation, and others. | https://www.tourtravelworld.com/packages/mesmerizing-western-ghats-with-mysore-tour-74998.html |
One of Carly Sachan’s dogs being attacked in the front yard of their home when they were let out by a dog sitter.
An Okanagan resident says her neighbourhood is living in fear due to an aggressive pack of coyotes.
“Pretty scary. We’ve been doing this for a few weeks,” said Carly Sachan.
Sachan shared with Castanet a video of one of her dogs being attacked in the front yard of their home when they were let out by a dog sitter.
“Thank god, he’s about 35 pounds, so it wasn’t able to lift it off the ground,” Sachan says.
The pug only suffered superficial wounds, but Sachan says she went out and bought both her dogs protective vests. “We call him my little battle pug.”
Sachan says she has contacted the BC Conservation Officer Service and “was told if I walked the dogs and walk with a stick or something, I’ll be fine.”
She says there have been other recent run-ins with coyotes in the neighbourhood while dog owners are walking their dogs on leash, while another neighbour’s cat was killed and left in pieces on her lawn.
Sachan says she believes the coyotes are living nearby, “we can hear them howling at night.”
Sachan says she and her neighbours feel like they are under siege and her video cameras seem to indicate the coyotes are very active in the area, “we are picking up the same coyote (on video) coming and going on the same path across our lawn and down the street now almost hourly.”
With this attack on video being the second this week, Sachan says the neighbourhood is starting to get frustrated.
According to the provincial website, If a wolf or coyote approaches you:
- Make yourself look as large as possible – if sitting, stand for example.
- Wave your arms and throw objects at the wolf or coyote.
- Shout at the wolf or coyote in a loud aggressive voice.
- If the wolf or coyote continues to approach don’t run or turn your back. Continue to exaggerate the above gestures and slowly move to safety. | https://pawchi.com/coyote-attack-on-pug-caught-on-surveillance-video-in-kelowna-6/ |
The Ringmaster Time Forgot
Murmurs circle the dark from hushed mouths waiting for the show to begin. They’ve waited seven years for this show to arrive, and now that it’s here—as it’s always on time—they can’t wait any longer.
But they will wait, and Lyra Lane knows it—waiting makes the show that much better.
From behind the curtains, with her eyes closed, she can feel their energy. It’s their delicious energy that makes the magic. She waits for the perfect moment, the crest between excitement and agitation, before she takes a deep breath and steps out into the darkness. In this space, before the audience is aware she’s there, as she’s standing invisible before them but fully present, she remembers how long she’s been doing this. Far longer than any of their first memories, an age more than she’d admit to, hiding from Time and beneath Death’s nose.
The lights go on, a spiral of yellow and gold speckles her dark skin. She is the universe, stars and all. The pre-recorded introduction captured on old Earth technology jolts on and issues words from a friend, a mentor, lost to time but not from her memories, shake her from her reverie. The deepness of the voice always resonates in her bones. The tenor of feeling in the words. The secret stories behind the words and the love embedded in them. “Welcome to the Infinite Circus! It’s my great pleasure to introduce you to your story navigator tonight, Ringmaster Lyra Lane!”
Cheers erupt from the stands, and as their energy swells Lyra breathes it into her lungs and roars with a might few on this side of the galaxy have seen—
“Welcome Friends! Fiends! Folks of Atmos 5, the best station on Ceres, to the most spectacular show in the universe!”
As she takes her next breath, swelling with energy and magic, she looks out to the crowd and searches for them. No one she has ever met, but people she knows intimately. Those who look to the stars to find their stories. Those who are waiting to be swept up and lost in a tide of tales. People like her.
The crowd roars in response, and Lyra looks for the one who will one day take her place. The timeless one who is her mirror—they are also the universe, stars and all.
The Eye of the Universe
Before Flora knows about the world, before she understands loss, before she’s plucked up and out of reality to swim in magic with the finest acrobats in the universe, her eyes meet the Ringmaster’s. She squeezes her mom’s hand as a feeling—like the moment before a great adventure or the twinkling of a possibility—courses through her.
Her mom’s smile radiates back at her, illuminated by speckles of stars that are swirling around them. She leans down, her bangs falling into her eyes, and squeezes her hand back.
“This is just how I remember it when I was a kid. And Lyra looks exactly the same!” The excitement in her mom’s face, her voice, the warmth of her hand, is a moment. A snapshot. Flora tucks it away, filed between clips of sour school days, soundtracks of the rumble of the quarry and weary of the workers, and stills of her mother’s illness.
“Thank you for bringing me,” Flora says in her softest voice, for the audience is hushed.
Her mom puts her arm around her. “There’s no where I’d rather be and no one I’d rather be with. Being with you is the greatest magic.”
As Flora’s voice catches in her throat, she suddenly feels weightless. She gives her mom a panicked glance and grabs her hand.
Smiling, her mom only says, “It’s beginning.”
Flora, her mom, and all of the audience of Atmos 5 all begin to float, and their stadium seats seem to disappear into an endless sea of space. Flora clutches her mom’s hand for minutes before letting go, wondering what it’s like to actually fly.
And they do. The audience floats, circling the main stage like a school of human space fish, swirling around gently as the acrobats in the center twist and turn and spin. As they dance, a blue light radiates from their center.
Magic. Flora knows that’s the only way this could possibly exist.
The spectators float gently around the acrobats, the weightlessness a strange sensation even though they live on a space station. Flora watches a story unfold that tells a tale about a mysterious wanderer who meets Fate.
Flora lets the momentum of the crowd pull her like a calm and gentle tide, and seeing her mom’s joy, wonders what it would be like to live forever. She’s not sure how or why, but she thinks the Ringmaster could know.
When they leave the Infinite Circus, after the Eye of the Universe, after cotton candy, after holographic animals, after face painting, Flora’s mind flutters with wistful thoughts.
Over the years, Flora will forget many things unworthy of remembering and willfully ignore impolite memories that intrude on her feelings.
But not the Infinite Circus. She’ll always remember the smell of the Old Earth popcorn, the calm in her mom’s eyes, and the feeling of being transported into a tale infinitely more beautiful than reality—especially when that reality, eventually, no longer includes her mother.
The Mysterious Wayfarer
Before Lyra Lane takes a bow in front of the Atmos 5 audience, before she dazzles them with her parting smile, before she steps onto the gigantic robotic leviathan ship, she feels something amiss.
The hunger from the audience seemed greater, and she wonders if she’s accomplished what she set out to do—provide them a magical escape—when she can still feel their gnawing appetite at her back. Seven years ago they were vibrant. What could change so much in that small amount of time?
She is more exhausted than she can ever remember, and she thinks maybe Time has seen her and has mentioned her presence to Death. As she pats the metallic leviathan, fondly named Echo, in circus tradition, she tries to leave all of her worries outside the traveling space train.
Despite her attempt, a small shadow climbs aboard with her, full of its own worry and wonder.
It isn’t until hours later when she’s taking a stroll in the dome of Echo and marveling at how much space there is and how, even after centuries, it still takes her breath away, she encounters the girl, a small thing full of worry and wonder.
“You’re a long way from home now,” Lyra says to the girl who seems older in memories and younger in spirit. “Won’t Atmos 5 miss you?” Lyra knows the answer already, but sometimes when you know something inside of you, it still helps to hear it spoken aloud.
“I don’t think so. I don’t have any family there anymore.” The girl looks up at the stars, and Lyra wonders if the girl feels like the universe could swallow her at any moment too.
“Won’t you miss Atmos 5? It’s your home.” Lyra crouches and sits beside the girl who seems more at home on Echo than Lyra has ever felt.
“Yes.” It’s all she says.
“Did you see the show?” Lyra asks.
The girl shakes her head. “No… not this time. I saw it when you were here last, though, with my mom. It was wonderful.”
Lyra smiles. “Thank you. I suppose you were too busy figuring out how to sneak on our caravan to see the show?”
The girl grins. “I saw the beginning. When you welcomed everyone. It’s my favorite part.”
This surprises Lyra. “Really? Not The Eye of the Universe where you’re floating in the air like stardust?” She gestures widely with her arms as though she is announcing in the stadium. “Or Geraldine’s Magical Animal Menagerie?” She conjures her top hat and tips it with a wink. “Or Captain Ocean’s Voyage?” She leans forward to look at the girl squarely. “Why?”
“Those are all good shows, but the beginning is the best part. It’s the furthest from the end of the show.” The girl paused. “Like when you love a story and you read it and you have all that adventure ahead of you? Even when you’re at a good part in the story, you know it’ll be over one day. But the beginning? That’s the moment you know you’re okay. That’s the moment when you have all of the possibilities ahead of you.” The girl sighed. “That’s when you don’t have to go back to real life.”
They sit in silence for a little while, universe-gazing, and Lyra can’t help but wonder about the girl. They are the same. Both of them a blazing fire burning over deep layers of grief.
“What’s your name?” Lyra asks and takes her hat off.
“Flora.”
“Well, Flora, I hope you’re ready for a new beginning. As much as I’d like to tell you that I can turn this beast around and take you back, that ship has sailed.”
Flora nods.
They sit in silence for a while longer, before Flora speaks.
“Will I be okay?” This isn’t the fire speaking, it’s the grief, and Lyra reaches for her own.
“Yeah. You’re good.” Lyra gently puts her top hat on Flora’s head.
Lyra doesn’t tell Flora about being timeless and wandering the stars and creating more voids by chasing memories she couldn’t possibly fill. In that moment, she’s just grateful for the quiet company, and finally, the absence of hunger and worry.
The Ghost of Ceres
Nothing has changed on Atmos 5 since Flora left seven years ago. Not the way the air purifier smells gently of flowers Flora has never actually seen. Not the way its inhabitants seem gaunt emotionally. Not the way the stars seem to yell from the distance—“We’re out here! There’s more! Don’t lose hope!”
The Infinite Circus arrives a few days before the show, at Flora’s request, but she feels like a stranger in a place where no one remembers a small, sad girl who disappeared seven years ago.
Flora visits all of the places that remind her of her mother and even though she imagined she’d feel haunted by the memories, wandering here and there with little to no interaction with anyone makes her feel like the specter. The Ghost of Ceres.
She passes through the bustling diner where she learned about pancakes, the shopping square where she coveted things she couldn’t afford, and the edges of the building where her mother taught before she was too sick. She couldn’t bring herself to go in. She just hovered and watched and felt.
When Flora arrives back at the caravan, she feels a void. Sad? She had wondered—worried—whether she’d suddenly be transported back to fifteen, and if she’d feel as unmoored and empty as the day she left. But she feels largely unchanged, and for some reason, that bothers her, and continues to bother her until she waits for the show to begin.
Flora steps into the darkness.
“Welcome to the Infinite Circus! It’s my great pleasure to introduce you to your story navigator tonight, Ringmaster Flora Future!” Lyra’s recorded voice permeates the audience and Flora’s heart.
“Will you be okay?” Lyra asks, knowing that loss is never easy. “It’s my time.”
“Yeah, I’m good.” Flora knows that loss is difficult, but life could be infinite in stories—in memories.
“This is really just the beginning,” Lyra says, her eyes filled with starlight. “You’re going to be a great Ringmaster.”
“Welcome Friends! Fiends! Folks of Atmos 5, the best station on Ceres, to the most spectacular show in the universe!” Flora steps into the dazzling light. She will help the audience escape, weave stories from her memories, and transport them to worlds they could never dream of. Together, they’ll create a new beginning. | https://lunastationquarterly.com/story/the-infinite-circus/ |
How old is Daniel Middleton?
Daniel Middleton was born on 8 November 1991.
Daniel Middleton is 31 years old.
How old is Daniel Middleton in days now?
Daniel Middleton is 31 years 26 days old.
Total 11,349 days old now.
When is the next birthday of Daniel Middleton?
Daniel Middleton's next birthday is in 11 months 4 days.
What is the zodiac sign of Daniel Middleton?
Zodiac sign of Daniel Middleton is Scorpio.
Known as DanTDM, Daniel Middleton is an iconic gamer of the modern times. He was born in November 1991 in the UK. Since his childhood, he has been a big fan of Minecraft game and, together with his elder brother, they have been promoting the idea of popularizing this game via their social media accounts. Daniel opened his first YouTube account in 2012 and the number of his fans started immediately increasing. Dan loves the character of Doctor Trayaurus and other fictional characters, so he frequently adds those to his videos. As of the late 2021, there are over 25 million followers on his YouTube account. Jemma Middleton, his wife, is also a famous media star and Minecraft game fan. The couple has a son who came to this world in the early 2020. | https://www.myagecalculator.com/how-old-is-daniel-middleton |
The invention relates to the technical field of industrial cleaners, in particular to a water-based metal heavy oil stain cleaner, which comprises the following components in percentage by weight: (1) 0.5-3% of ethylene diamine tetraacetic acid tetrasodium salt, (2) 0.5-2% of sodium metasilicate, (3) 0.3-1.2% of sodium carbonate, (4) 4-12% of fatty alcohol-polyoxyethylene (9) ether, (5) 2-6% of fatty alcohol-polyoxyethylene ether sodium sulfate; (6) 4-6% of glycol amide of coconut oil; (7) 1-7% of triethanolamine and (8) the balance of water. The water-based metal heavy oil stain cleaner has the advantages of energy saving, using safety, reduced environmental pollution, improved labor conditions, lowered the cleaning cost, good cleaning effect, convenience for use and the like. Meanwhile, the water-based metal heavy oil stain cleaner provided by the invention has extremely wide application scope and can be applied to precise cleaning of various machining parts and surface cleaning of large mechanical devices, in particular cleaning of internal and external walls of industrial pipelines with heavy oil stain, thereby filling the blank in the field of pipeline cleaning. | |
CHARLOTTETOWN, P.E.I. — P.E.I. is freezing the cost of monthly transit passes until the end of March 2023.
In June, the cost of a monthly transit pass was set to $20 for adults and $10 for seniors and post-secondary students. In a release Thursday, the province announced those rates will remain until March 31, 2023.
All transit routes in Prince Edward Island are free for children and K-12 students.
Previously, pass prices were $45 for adults and $35 for seniors and post-secondary students.
Monthly transit passes can be purchased at Shoppers Drug Mart and Murphy’s Pharmacy locations in the Charlottetown area.
Passes can also be bought at the T3/Maritime Bus Terminal, the Holland College bookstore, the town and city halls in Stratford, Cornwall and Charlottetown and through the HotSpot mobile app. They can also be purchased through bus drivers.
Transportation and Infrastructure Minister Cory Deagle said Islanders have been hit by cost of living increases, including unpredictable fuel prices. He said improving the public transit system keeps transportation options open for Islanders.
"Reliable, accessible and affordable public transit Island-wide is helping reduce Islander’s dependence on personal use vehicles and helping relieve some of the financial pressure on families," said Deagle. | https://www.saltwire.com/atlantic-canada/news/pei-monthly-transit-pass-price-freezing-until-end-of-march-2023-100788158/ |
Most Likely Spots In Utah For Speeding Tickets
SALT LAKE CITY, Utah – A glimpse in the rear-view mirror. The flashing lights behind you. The realization that you’re going too fast. We all know how it feels to be busted for speeding.
Last year alone, Utah officers wrote more than 160,000 speeding tickets across the state.
How can you avoid getting a ticket? The obvious answer is not to speed. The KSL Investigators wanted to find out which agencies wrote the most speeding tickets. They also analyzed tens of thousands of speeding tickets to learn when you’re most likely to get one.
Our data comes from the Utah State Courts and includes 163,272 speeding tickets from 138 cities and counties across Utah during 2018.
Top Cities/Counties Based On Ticket Volume In 2018
- Salt Lake City: 10,846 tickets
- Sandy: 9,958 tickets
- Washington County: 6,021 tickets
- Iron County: 5,385 tickets
- Orem: 5,125 tickets
Officer Zack Young is a traffic cop with Unified Police Department. He doesn’t work in Salt Lake City, but says the high number in the state’s capital makes sense.
“I think it all has to do with not so much as how many violators are in your area, but how many officers you have looking for those violators,” said Young.
Top Cities/Counties Based On Per Capita Population In 2018
But what about those towns that don’t have a lot of officers, which are sometimes accused of running speed traps? The KSL Investigators dug a little deeper to find out which cities and counties give out the most tickets per capita. In no particular order, they include:
- Mantua
- Wellington
- Big Water
- Monticello
- Emery County
- Garfield County
- Juab County
Based on the data, Mantua gives out the most tickets based on population. It was the only area to hand out more tickets (1,283) in 2018 than it has people living there (822).
Time Of The Month
Most drivers KSL talked to believe speeding tickets are most often given out at the end of the month.
“I always assume that at the end of the month they’re trying to fill a quota,” said Damon.
“Probably more towards the end of the month,” said Ken.
“We always used to hear that at the end of the month cops would be out a lot more,” said Rafael.
However, out of the 13,346 tickets KSL Investigators checked from February 2018, more tickets were actually filed in the first week of the month and it gradually went down from there.
- 1st week: 3,747
- 2nd week: 3,695
- 3rd week: 3,110
- 4th week: 2,794
Day Of The Week
As for the biggest day of the week, KSL did a deep dive into nearly 3,000 speeding tickets from this same week last year and data shows Saturday was the most popular day for tickets.
Time of The Year
Most drivers believe the summer months are when you’re most likely to get a speeding ticket.
“I would say the summer months because I feel like people are more reckless then,” said Noel.
Traffic cops, like Officer Young, agree.
“I don’t know what it is about summer, but it’s a crazy time for drivers,” said Young. “So that’s when we’re going to be out there stepping up our enforcement.”
However, when KSL broke down those tens of thousands of tickets, the busiest month in 2018 was not actually in the summer. It was in the spring, with March having the highest number of speeding tickets given.
- January: 14,416
- February: 13,364
- March: 16,572
- April: 14,892
- May: 15,233
- June: 14,540
- July: 13,268
- August: 13,169
- September: 12,243
- October: 11,895
- November: 12,915
- December: 10,782
KSL also asked Officer Young a question almost every driver wants to know: Is there a speed you can go above the limit without getting a ticket? There’s good news and bad news. Young says he has a buffer zone but every officer is different.
“Me personally, I’m looking for 13 over,” said Young.
For him, it’s not so much about the driver’s apparent need for speed, it more about the need for safety.
“Speed in and of itself may not contribute to the number of incidents of crashes, but it certainly contributes to whether or not that crash is fatal,” said Young. “My end goal is to change people’s driving behavior.”
Leading to driving behaviors that keep all of us safe on the roads.
Young has a Facebook page called “Zack the Traffic Cop” that he uses as a platform to promote safe driving. | https://ksltv.com/408855/likely-get-speeding-ticket-ksl-investigators-analyze-160000-tickets/ |
The thrombopenic effect of ellagic acid in the rat. Another model of platelet stimulation "in vivo".
In the rat, intravenous injection of large doses (30 mg/Kg) of ellagic acid (EA) induced a decrease in the plasma level of fibrinogen and in the blood platelet content and an increase of the activated partial thromboplastin time. The long-lasting thrombocytopenia was inhibited by heparin (4 mg/Kg), defibrase (20 U/Kg), clocoumarol (4 mg/Kg) and CCI 17810 (120 mg/Kg). It was not inhibited by aspirin (90 mg/Kg), indomethacin (8 mg/Kg), ketoprofen (4-10 mg/Kg), epsilon-aminocaproic acid (150 mg/Kg), methysergide (4 mg/Kg), chlorpromazine (10 mg/Kg) and promethazine (4 mg/Kg). On the contrary, the small doses of indomethacin (4 mg/Kg) and of ketoprofen (0.5-2 mg/Kg) increased the thrombopenic effect of EA. EA induced the accumulation of Cr51-labelled platelets into the lungs and the liver, accompanied by a 64% fall in Cr51 blood radioactivity. The platelet stimulating effect of EA would depend on an intravascular coagulation which occurs in the whole cardiovascular system. It is suggested that the pro-aggregating derivatives of arachidonic acid had a minor role in this stimulation. The intravascular coagulation induced by EA was accompanied by a swelling of the lymph nodes and of the spleen. In immune platelet depleted rats, EA induced only the swelling of lymph nodes.
| |
Baman Chakawa Population
Baman Chakawa is a Village in Chandauli district of Uttar Pradesh, India. It falls under Sakaldiha Tehsil. Baman Chakawa population in 2019/2020 is between 38 and 47 and total households residing are 4.
The Baman Chakawa Village located in Sakaldiha Tehsil, 39 People are living in this Village, 15 are males and 24 are females as per 2011 census. Expected Baman Chakawa population 2019/2020 is between 38 and 47. Literate people are 17 out of 11 are male and 6 are female. People living in Baman Chakawa depend on multiple skills, total workers are 7 out of which men are 7 and women are 0. Total 3 Cultivators are depended on agriculture farming out of 3 are cultivated by men and 0 are women. 4 people works in agricultural land as a labour in Baman Chakawa, men are 4 and 0 are women.
39
30
20
10
0
Total
Male
Female
Population
Literacy
Workers
Cultivators
Labour
Households
Baman Chakawa barchart on population, literacy, workers & households
Population of Baman Chakawa(2011 Census)
|Population||Males||Females||Households|
|39||15||24||4|
Every Indian Village got a Story, Share with every one if you know anything about Baman Chakawa Wiki
Articles
- Which is the smallest state of india?
- Which is the Largest State of India? | http://www.indiagrowing.com/Uttar_Pradesh/Chandauli/Sakaldiha/Baman_Chakawa |
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abstract: 'We consider all perturbative radiative corrections to the total $e{^+}e{^-}$ annihilation cross section $R_{e{^+}e{^-}}$ showing how the renormalization group (RG) equation associated with the radiatively induced mass scale $\mu$ can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log (LL), next-to-leading-log (NLL) etc. contributions to $R_{e{^+}e{^-}}$ using in turn the one-loop, two-loop, etc. contributions to the RG function $\beta$. A second summation shows how all logarithmic corrections to $R_{e{^+}e{^-}}$ can be expressed entirely in terms of the log-independent contributions when one employs the full $\beta$-function. Next, using Stevenson’s characterization of any choice of renormalization scheme by use of the contributions to the $\beta$-function arising beyond two-loop order, we examine the RG scheme dependence in $R_{e{^+}e{^-}}$ when using the second way of summing logarithms. The renormalization scheme invariants that arise are then related to the renormalization scheme invariants found by Stevenson. We next consider two choices of renormalization scheme, one which can be used to express $R_{e{^+}e{^-}}$ solely in terms of two powers of a running coupling, the second which can be used to express $R_{e{^+}e{^-}}$ as an infinite series in the two-loop running coupling (i.e., a Lambert $W$-function). In both cases, $R_{e{^+}e{^-}}$ is expressed solely in terms of renormalization scheme invariant parameters that are to be computed by a perturbative evaluation of $R_{e{^+}e{^-}}$. We then establish how in general the coupling constant arising in one renormalization scheme can be expressed as a power series of the coupling arising in any other scheme. We then establish how by using a different renormalization mass scale at each order of perturbation theory, all renormalization scheme dependence can be absorbed into these mass scales when one uses the second way of summing logarithmic corrections to $R_{e{^+}e{^-}}$. We then employ the approach to renormalization scheme dependency that we have applied to $R_{e{^+}e{^-}}$ to a RG summed expression for the Coleman-Weinberg effective potential $V$ in a massless scalar model with quartic self coupling, showing that the previously derived result that $V$ is independent of the background field $\phi$ if $V^\prime(\phi \neq 0) = 0$ is renormalization scheme independent. The way in which Stevenson’s “principle of minimal sensitivity” (PMS) can be applied to the RG summed form of $R_{e{^+}e{^-}}$ is then discussed. The significance of our results is considered in a concluding section.'
author:
- 'D.G.C. McKeon [^1]'
title: |
Renormalization Scheme Dependence\
with Renormalization Group Summation
---
10.0in 9.0in -0.60in
Key Words: Renormalization Scheme Dependence, Log summation\
PACS No.: 11.10Hi
Introduction
============
Soon after it was established that divergences found present in quantum field theory calculations could be removed through the process of renormalization, it was realized that ambiguities arose at any finite order of perturbation theory. Requiring that physical quantities be independent of parameters characterizing these ambiguities has led to the RG equations \[1-3\]. The parameter most usually considered is $\mu$, the mass scale introduced in the course of renormalization (for an interesting perspective on this see ref. \[4\]) but the additional ambiguities that arise in quantum chromodynamics (QCD), when using mass-independent renormalization \[5,6\], have been shown by Stevenson \[7\] to be parameterized by the coefficients $c_i(i \geq 2)$ of the expansion of the $\beta$-function associated with $\mu$ beyond two-loop order. The RG functions $\beta_i$ associated with these parameters $c_i$ can be expressed in terms of the $\beta$-function itself; certain linear combinations of renormalization scheme dependent parameters were shown to be renormalization scheme independent \[7,8\].
Various approaches have been considered to mitigate the dependence of physical quantities at finite order in perturbation theory on the parameters characterizing the renormalization scheme used \[7, 9-20\]. The total cross section for $e^+e^-$ annihilation into hadrons provides a convenient example for testing the efficacy of these approaches \[7, 21-23\].
It has been shown that variation of physical quantities with changes in the scale parameter $\mu$ is reduced by using the RG equation associated with $\mu$ to sum so-called leading-log (LL), next-to-leading-log (NLL) etc. corrections that arise at arbitrarily high order of perturbation theory. This was originally suggested by Maxwell \[24\], and has been carried out in various physical processes \[25,26\], as well as in the effective action for instantons \[27\], thermal field theory \[28\], and the Coleman-Weinberg potential \[29-36\]. (This summation procedure has also been used to show that when using the MS renormalization scheme to relate the bare and renormalized coupling in dimensional regularization \[38\], the bare coupling vanishes rather than diverges when the dimensionality of space-time approaches four \[39\].)
Instead of using the RG equation to sum all LL, NLL etc. contributions to a physical process, it is also possible to perform a sum of all logarithmic contributions to a physical process, leading to an expression in which only the log-independent parts explicitly contribute, along with an auxiliary “running coupling” that contains all log-dependent contributions and whose behaviour is governed by the usual RG function $\beta$. This summation has been useful in considering the effective action \[27\] as well as the Coleman-Weinberg potential \[33-37\].
In this paper, we will consider application of the RG equations associated with the parameters $c_i$ to the RG summed expression for $R_{e{^+}e{^-}}$, using the second approach to summation. The RG functions $\beta_i$ in this case depend not only on the couplant $a$ but also on the parameters $c_i$ themselves. This prevents one from integrating these RG equations even formally; this is unlike the situation for the RG equation associated with the mass scale $\mu$ as the $\beta$-function associated with $\mu$ depends solely on the couplant $a$ and is independent of $\mu$ itself. However, it is possible to determine how the log independent contributions to $R_{e{^+}e{^-}}$ depend on $c_i$, which in turn fixes the dependence of the log dependent contribution to $R_{e{^+}e{^-}}$ on these parameters.
In the course of determining how $R_{e{^+}e{^-}}$ depends on the parameters $c_i$, renormalization scheme invariants $\tau_i$ arise. We show how these $\tau_i$ are related to the renormalization scheme invariants $\rho_i$ found by Stevenson \[7,8\].
We now consider two different choices of renormalization scheme; that is, we consider two different ways of selecting the parameters $c_i$. First, we can eliminate all dependence of $R_{e{^+}e{^-}}$ on effects beyond two-loop order, save for the dependence of the running coupling on the renormalization scheme independent parameters $\tau_i$. Secondly, we can set all $c_i$ equal to zero, allowing one to expand $R_{e{^+}e{^-}}$ in powers of the two-loop running coupling (which is given by the Lambert $W$-function \[28, 40, 41\]) with coefficients dependent solely on the $\tau_i$. In both cases, $R_{e{^+}e{^-}}$ is independent of the scheme dependent parameters $c_i$. Upon comparing these two ways of expanding $R_{e{^+}e{^-}}$ with a general expression relating the running coupling in two different renormalization schemes; we find consistency between these two renormalization schemes used to compute $R_{e{^+}e{^-}}$.
Next we show how within a given renormalization scheme, the running coupling at one mass scale can be expanded in powers of the running coupling at a different mass scale. Upon using this result in conjunction with the expansion of the RG summed form of $R_{e{^+}e{^-}}$ we show how the mass scale at each order of the running coupling can be chosen to absorb all renormalization scheme dependency of $R_{e{^+}e{^-}}$.
This is in keeping with the approach known as the “principle of maximum conformality” \[13-20\] (PMC), though this way of handling renormalization scheme ambiguities was originally applied to a perturbative expansion of $R_{e{^+}e{^-}}$ in which RG summation had not been used.
The summation of all logarithmic corrections to the Coleman-Weinberg effective potential $V$ by use of the RG equation has led to the interesting result that $V$ is independent of the constant background field $\phi$ when the condition $V^\prime (\phi) = 0$ at $\phi = v$ is applied, provided $v \neq 0$. This has been demonstrated in a number of models \[33-37\]; here we consider the simplest of these (a massless $\phi^4$ model in four dimensions) and show that the resulting expression for $V(\phi)$ is renormalization scheme independent.
We then consider how Stevenson’s PMS approach to choosing the parameters ($\mu$, $c_i$) that characterize a renormalization scheme can be applied to $R_{e{^+}e{^-}}$ after performing each of the two RG summations that have been considered.
Renormalization Group Summation
===============================
To illustrate how renormalization scheme dependence occurs after employing RG summation, we will consider the usual example of the total cross section for $e^+e^-$ annihilation into hadrons, ignoring the threshold effects of heavy quarks and complications due to gauge choice, after normalizing it by the cross section for $e^+e^-$ annihilating into $\mu^+\mu^-$. If this quantity $R_{e{^+}e{^-}}$ is written as \[7\] $$R_{e{^+}e{^-}} = \left(3 \sum_i q_i^2\right) (1 + R)$$ then $R$ can be expanded in powers of the couplant $a$ $$R = \sum_{n=0}^\infty r_n a^{n+1} \quad (r_0 = 1)$$ where $r_n$ contains the $n$ loop contribution to $R$. By considering the Feynman diagrams that contribute to $R$ one can see that $r_n$ is given by $$r_n = \sum_{m=0}^n T_{nm} L^m$$ where $T_{00} = 1$ and $L \equiv b\log(\mu/Q)$ where $Q$ is the centre of mass energy for $R_{e{^+}e{^-}}$. As $R$ is independent of the renormalization mass scale $\mu$, we have the RG equation $$\mu \frac{d}{d\mu}R = \left( \frac{\partial}{\partial \mu} + \beta(a) \frac{\partial}{\partial a} \right) R = 0$$ where $$\beta (a) = \mu \frac{\partial a}{\partial \mu} = - b a^2 \left(1 + c a + c_2 a^2 + c_3 a^3 + \ldots \right).$$ In ref. \[7\] it is shown that $c_2, c_3, \ldots$ characterize the renormalization scheme ambiguities that reside in $R$ when it is computed to finite order in perturbation theory when using mass independent renormalization. To show that $b$ and $c$ in eq. (5) are renormalization scheme independent, one considers the couplings $a$ and $\overline{a}$ associated with two different schemes so that $$\overline{a} = a + x_2 a^2 + x_3 a^3 + \ldots .$$ If
$$\begin{aligned}
\overline{\beta}(\overline{a}) = \mu \frac{\partial \overline{a}}{\partial\mu}\\
\intertext{then together eqs. (5, 6, 7a) show that}
\overline{\beta}(\overline{a}) &= - \overline{b} \overline{a}^2 ( 1 + \overline{c}\;
\overline{a} + \overline{c}_2\overline{a}^2 + \ldots )\nonumber \\
&= (1 +2x_2 a + 3x_3 a^3 + \ldots ) (-ba^2) (1 + ca+c_2 a^2 + \cdots)
\end{aligned}$$
which are compatible if $b = \overline{b}$, $c = \overline{c}$ while $c_2 = \overline{c}_2 + cx_2 + x^2_2 - x_3$ etc.
Relations between $T_{nm}$
--------------------------
We now will consider eq. (4) in more detail, and show how it can be used to fix $T_{nm}(1 \leq m \leq n)$ in terms of $T_{n0}$. We can write eq. (4) as $$\begin{aligned}
\left( \mu \frac{\partial}{\partial \mu} - ba^2(1 + ca + c_2 a^2 + \ldots )\frac{\partial}{\partial a}\right) \sum_{n=0}^\infty \sum_{m=0}^n a^{n+1} T_{nm}L^m\nonumber \\
\qquad = \sum_{n=0}^\infty \sum_{m=0}^n \big[ m\,a^{n+1} T_{nm} L^{m-1} - a^2 (1 + ca + c_2a^2 + \ldots )\nonumber \\
\left( (n+1) T_{nm} a^n L^m \right)\big] = 0.\end{aligned}$$ By considering individual terms of order $a^pL^q$ in eq. (8), relations such as
$$\begin{aligned}
T_{ii} &= T_{i-1,i-1} \\
T_{21} &= (c + 2 T_{10})\\
2T_{32}& = (2cT_{11} + 3T_{21})\\
\intertext{and}
T_{31} &= c_2 + 3T_{20} + 2cT_{10}\end{aligned}$$
follow.
Leading-log etc. Summation
--------------------------
We now can systematically sum contributions to $R$ using the RG eq. of eq. (4). We first define, as in ref. \[25, 26, 37\] functions $$S_n = \sum_{k=0}^\infty T_{n+k,k} (aL)^k$$ so that eq. (2) becomes $$R = R_\Sigma = \sum_{n=0}^\infty a^{n+1} S_n(aL)$$ by eq. (3). $S_0$ is the leading-log (LL) contribution to $R$, $S_1$ the next-to-leading-log (NLL) contribution to $R$, $S_p$ the N$^p$LL contribution etc. Substitution of eq. (11) into eq. (4) leads to
$$\begin{aligned}
&S_0^\prime - (S_0 + u S_0^\prime) = 0\\
&S_1^\prime - (2S_1 + u S_1^\prime) - c (S_0 +uS_0^\prime) = 0\\
&S_2^\prime - (3 S_2 + uS_2^\prime) - c(2S_1 + u S_1^\prime) - c_2 (S_0 + u S_0^\prime) = 0\\
& \mathrm{etc.}\nonumber\end{aligned}$$
Solving these equations sequentially leads to \[25, 26\]
$$\begin{aligned}
&S_0 = \frac{T_{00}}{w} \quad (w = 1 - u)\\
&S_1 = \frac{T_{10} - c T_{00} \ln |w|}{w^2}\\
&S_2 = \frac{T_{20} - (2c T_{10} + c^2 T_{00})\ln |w| + (c^2 - c_2) T_{00} (w-1) + c^2T_{00} \ln^2 |w|}{w^3}\\
& \mathrm{etc.}\nonumber\end{aligned}$$
This shows how $T_{n+k,k}(k = 1, 2 \ldots)$ is determined by $T_{n0}$ in addition to $b, c, c_2 \ldots c_n$. In ref. \[26\] it is demonstrated how
$$\begin{aligned}
R^{[M]} = \sum_{n=0}^M a^{n+1} r_n\\
\intertext{varies more widely with changes in $\mu$ than does}\nonumber \\
R^{[M]}_{\sum} = \sum_{n=0}^M a^{n+1} S_n (aL).\end{aligned}$$
This is to be expected as $R$ itself is independent of $\mu$, and so $R_{\sum}^{[M]}$ is necessarily a closer approximation to the exact expression for $R$ than $R^{[M]}$, containing as it does more terms in the expansions of eqs. (2,3).
Summation of All Logarithms
---------------------------
In place of the groupings of eq. (10), we consider a second grouping \[27\] $$A_n = \sum_{m=0}^\infty T_{n+m,n} a^{n+m+1}$$ so that $$R = R_A = \sum_{n=0}^\infty A_n(a)L^n.$$ Substitution of eq. (16) into eq. (4) now leads to $$\sum_{n=0}^\infty \left( b\,n A_n(a)L^{n-1} + \beta(a) A^\prime_n (a) L^n \right) = 0.$$ This is satisfied at order $L^{n-1}$ provided $$A_n(a) = - \frac{\beta(a)}{bn} \frac{d}{da} A_{ n-1}(a) .$$ If now a parameter $\eta$ is introduced, $$\eta \equiv \int_{a_{I}}^{a(\eta)} \frac{dx}{\beta(x)} \quad (a_I = \mathrm{const.})$$ then $$\beta(a) \frac{d}{da} = \frac{d}{d\eta}$$ and so eq. (18) becomes $$A_n(a) = \frac{-1}{bn}\frac{d}{d\eta} A_{n-1} (a(\eta)) = \frac{1}{n!}\left( - \frac{1}{b}\frac{d}{d\eta}\right)^n A_0 (a(\eta)).$$ From eq. (16) then $$R_A = \sum_{n=0}^\infty \frac{1}{n!} \left( - \frac{L}{b}\right)^n \frac{d^n}{d\eta^n} A_0 (a(\eta))$$ $$= A_0 \left( a\left( \eta - \frac{1}{b} L\right)\right).$$ This further demonstrates how $R$ depends on $T_{nm} (1 \leq m \leq n)$ only indirectly as $T_{nm} (1 \leq m \leq n)$ is fixed in terms of $T_{n0}$. We note that dependence of $R$ on $\eta$ in eq. (23) can be absorbed into dependence on $\mu$ as $$\eta - \frac{1}{b} L = -\frac{1}{b} L^\prime \equiv -\frac{1}{b} \log \left( \frac{\mu^\prime}{Q}\right)$$ where $\mu^\prime =e^{ -\eta b}\mu$.
The function $a(\eta)$ introduced in eq. (19) satisfies $$\frac{d a(\eta)}{d\eta} = \beta (a (\eta))$$ but it is distinct from the “running couplant” $a$ originally appearing in eq. (2). The $a$ in eq. (2), as it also appears in the RG equation (4), satisfies $$\mu \frac{da(\mu)}{d\mu} = \beta (a(\mu))$$ and has a boundary condition \[7, 4\] that involves a scale parameter $\Lambda$. It is suggested in ref. \[7\] that the solution to eq. (26) is taken to be $$\ln \left( \frac{\mu}{\Lambda}\right) = \int_0^a \frac{dx}{\beta(x)} + \int_0^\infty \frac{dx}{bx^2(1+c x)},$$ which is convergent for $a \neq 0$. It is apparent that the $a(\eta)$ appearing in eqs. (19, 25) is distinct from $a(\mu)$ appearing in eqs. (26,27) even though they satisfy differential equations that have the same form. To distinguish the two, we will henceforth denote $a(\eta)$ appearing in eqs. (19, 25) by $\alpha(\eta)$ so that eq. (23) becomes $$R = R_A = A_0 \left( \alpha \left( - \frac{1}{b}L^\prime\right)\right).$$ The $a_I$ appearing in eq. (19) as an integration constant to the differential equation of eq. (25) can be seen by setting $Q = \mu^\prime$ in eqs. (2, 3, 28) to be just function $a(\mu)$ appearing in eqs. (26, 27). Thus when we use $R_A$ to compute the $e^+e^-$ annihilation cross section, the value of $\Lambda$ is not in itself relevant; rather we should concern ourselves with the value of $a(\mu)$ which is the boundary value of $\alpha$ when $Q = \mu^\prime$ (using the renormalization scheme parameterized by $c_i$).
From now on we will drop the prime on $\mu^\prime$ and $L^\prime$.
Renormalization Scheme Dependence
=================================
As has been shown above, in the expansion of $\beta(\alpha)$ given by eq. (5), $b$ and $c$ are independent of the renormalization scheme used; in ref. \[7\] Stevenson has demonstrated that the constants $c_i$ provide a complete set of parameters characterizing any renormalization scheme in massless QCD provided it is a mass independent scheme. We will now show explicitly how $A_0\left(\alpha (-\frac{1}{b} L)\right)$ in eq. (28) depends on $c_i$.
If the RG function $\beta_i(\alpha , c_i)$ is defined by $$\beta_i (\alpha, c_j) = \frac{\partial \alpha}{\partial c_i}$$ then as $$\left( \frac{\partial^2}{\partial \eta\partial c_i} - \frac{\partial^2}{\partial c_i \partial\eta}\right) \alpha = 0$$ it follows from eqs. (25, 29) that \[7, 42\] $$\begin{aligned}
\beta_i (\alpha, c_j) &= -b \beta(\alpha) \int_0^\alpha \frac{dx\, x^{i+2}}{\beta^2(x)}\\
&= \frac{\alpha^{i+1}}{i-1} \sum_{n=0}^\infty W_n^i \alpha^n\end{aligned}$$ where $W_0^i = 1$ and $$W_j^i = \left\vert
\begin{array}{cccl}
-(-2|0)c & +(-3|1)c_2 & -(-4|2)c_3\ldots & (-1)^j(-j-1|j-1)c_j \\
1 & -(-1|1)c & +(-2|2)c_2 \ldots &(-1)^{j+1} (-j+1|j-1)c_{j-1} \\
& 1 & -(0|2)c \ldots &(-1)^j (-j+3|j-1)c_{j-2}\\
\dots & \ldots & \ldots & \ldots \\
& & 1 & -(j-3|j-1) c
\end{array}
\right\vert$$ with $$(m|n) \equiv (i + m)/(i+n).$$ The first few terms contributing to eq. (32) are $$\begin{aligned}
\beta_j (\alpha , c_i)& = \frac{\alpha^{j+1}}{j-1}\bigg[ 1 + \frac{(-j+2)c}{j} \alpha + \frac{(j^2-3j+2)c^2+(-j^2+3j)c_2}{(j+1)j} \alpha^2 \\
&+ \frac{c_3(-j^3 + 3j^2 +4j)+cc_2(2j^3-6j^2+4)+c^3(-j^3+3j^2-2j)}{(j+2)(j+1)j} \alpha^3 + \ldots \bigg]. \nonumber\end{aligned}$$
We now have the requirement that $$\frac{d}{dc_i} R = \left( \frac{\partial}{\partial c_i} + \beta_i (\alpha , c_j)\frac{\partial}{\partial\alpha}\right) R_A = 0$$ which by eqs. (15, 28, 32) becomes (with $T_n \equiv T_{n0}$) $$\left( \frac{\partial}{\partial c_i} + \frac{\alpha^{i+1}}{i-1} \sum_{j=0}^\infty W_j^i \alpha^j \frac{\partial}{\partial \alpha}\right)
\left[ \sum_{n=0}^\infty T_n \alpha^{n+1} \right] = 0.$$ By considering terms of order $\alpha^{i+j}$ in eq. (37) we find that $$\begin{aligned}
\frac{\partial T_{i+j}}{\partial c_i} + \frac{1}{i-1} \big[ (1) W_j^i T_0 + (2) W_{j-1}^i T_1 + (3) W_{j-2}^i T_2\\
+ \ldots +(j+1) W_0^i T_j \big] = 0\nonumber\end{aligned}$$ with $W_j^i$ given by eq. (33).
From eq. (38), we find that $$\frac{\partial T_2}{\partial c_2} + 1 = 0$$ which shows that $$T_2 = -c_2 + \tau_2$$ where $\tau_2$ is a constant of integration for eq. (39). It then follows from eq. (38) that
$$\begin{aligned}
\frac{\partial T_3}{\partial c_2} + 2\tau_1 = 0 \\
\intertext{and}
\frac{\partial T_3}{\partial c_3} + \frac{1}{2} = 0 \end{aligned}$$
and so $$T_3 = -2c_2 \tau_1 -\frac{1}{2} c_3 + \tau_3 ;$$ similarly
$$\begin{aligned}
&\frac{\partial T_4}{\partial c_2}+ \frac{1}{3} c_2 + 3T_2 = 0 \\
&\frac{\partial T_4}{\partial c_3} + \frac{1}{2}\left(- \frac{1}{3} c + 2 T_1\right) = 0 \\
&\frac{\partial T_4}{\partial c_4} + \frac{1}{3} = 0 \end{aligned}$$
show that $$T_4 = - \frac{1}{3} c_4 -\frac{c_3}{2}\left(-\frac{1}{3} c + 2 \tau_1\right) +
\frac{4}{3} c_2^2 - 3 c_2 \tau_2 + \tau_4$$ and
$$\begin{aligned}
&\frac{\partial T_5}{\partial c_2} + \left( -\frac{1}{6} c_2 c + \frac{1}{2} c_3\right) + 2 \left(+ \frac{1}{3} c_2 \right) T_1 + 4 T_3 = 0\\
&\frac{\partial T_5}{\partial c_3} + \frac{1}{2} \left[ \frac{1}{6} c^2 + 2 \left(+ \frac{1}{3} c\right) T_1 + 3 T_2\right] = 0\\
&\frac{\partial T_5}{\partial c_4} + \frac{1}{3}\left[ \left( - \frac{1}{2} c\right) + 2 T_1 \right]= 0\\
&\frac{\partial T_5}{\partial c_5} + \frac{1}{4} = 0\end{aligned}$$
lead to $$\begin{aligned}
T_5 &= \left[ \frac{1}{3} c c_2^2 + \frac{3}{2} c_2 c_3 + \frac{11}{3} c_2^2 \tau_1 - 4 c_2 \tau_3 \right]\nonumber \\
&- \frac{1}{2} \left[ \frac{1}{6} c^2c_3 - \frac{2}{3} c_3 c \tau_1 + 3 c_3 \tau_2 \right]\nonumber \\
&-\frac{1}{3} \left[ -\frac{1}{2} c_4 c + \frac{1}{2} c_4 \tau_1\right] - \frac{1}{4} c_5 + \tau_5 . \end{aligned}$$ In eqs. (40, 42, 44, 46) $\tau_i$ are all constants of integration associated with the differential equations for $T_i$; they are renormalization scheme invariants as they are independent of $\mu$ and $c_i$. To evaluate them, one must compute the Feynman diagrams associated with $R$ to the appropriate order in perturbation theory using the same renormalization scheme that has been used to determine the $c_i$; knowing $T_i$ and $c_i$ one can then solve for the $\tau_i$.
It is of interest to see how the renormalization invariants $\rho_i$ \[7,8\] are related to the $\tau_i$. We first consider the invariant $$\begin{aligned}
\rho_2 &= L - r_1\nonumber \\
& = T_{00} L - (T_{10} + T_{11} L).\end{aligned}$$ The term in eq. (35) dependent on $L$ is satisfied by virtue of eq. (9a); the term independent of $L$ results in $$\rho_2 = -\tau_1.$$ Next, the invariant $\rho_3$ is given by $$\rho_3 = c_3 + 2r_3 -2c_2 r_1 - 6r_2r_1 + c r_1^2 + 4 r_1^3$$ which, using eq. (3) becomes $$\begin{aligned}
\rho_3 &= c_3 + 2 (T_{30} + T_{31} L + T_{32} L^2 + T_{33} L^3) - 2 c_2 (T_{10} + T_{11} L)\nonumber \\
& \quad -6 (T_{20} + T_{21} L + T_{22} L^2) (T_{10} + T_{11} L)\nonumber \\
&\qquad + c (T_{10} + T_{11} L)^2 + 4 (T_{10} + T_{11} L)^3.\end{aligned}$$ From eqs. (9a-d) one finds that eq. (50) is satisfied due to eq. (4) at orders $L$, $L^2$ and $L^3$; from the terms independent of $L$ we find from eq. (50) that $\rho_3$ can be expressed in terms of $\tau_1$, $\tau_2$, $\tau_3$, and $c$ using eqs. (40, 42). It is independent of $c_2$ and $c_3$, as it should, as these parameters are scheme dependent. This pattern should persist for all $\rho_n$.
We now consider two special values for the parameters $c_i$ which characterize our choice of renormalization scheme. First of all, the $c_i$ can be expressed in terms of the $\tau_j$ so that $T_n = 0$ for all $n \geq 2$. From eqs. (40, 42, 44, 46) this means that
$$\begin{aligned}
c_2 &= \tau_2\\
c_3 &= 2(-2 c_2 \tau_1 + \tau_3)\nonumber \\
&= -4 \tau_2\tau_1 + 2\tau_3\\
c_4 &= 3 \bigg[ - \frac{c_3}{2}\left( - \frac{1}{3} c + 2 \tau_1 \right) + \frac{4}{3} c_2^2 \nonumber\\
&\quad- 3 c_2\tau_2 + \tau_4 \bigg]\nonumber \\
&\quad= c(\tau_3 - 2 \tau_1\tau_2) + 12 \tau_1^2 \tau_2 - 6 \tau_1\tau_3 - 5 \tau_2^2 + 3\tau_4 \\
\intertext{and}
c_5 &= 4 \bigg\{ \left[ \frac{1}{3} cc_2^2 + \frac{3}{2} c_2c_3 + \frac{11}{3}c_2^2 \tau_1 - 4c_2\tau_3 \right]\nonumber \\
&\qquad-\frac{1}{2}\left[ \frac{1}{6} c^2c_3 - \frac{2}{3}c_3 c \tau_1 +3 c_3\tau_2 \right]\nonumber \\
&\qquad-\frac{1}{3}\left[- \frac{1}{2} c_4c + \frac{1}{2}c_4 \tau_1\right] +\tau_5\bigg\}\nonumber\\
&= \left[ \frac{4}{3} c\tau_2^2 + \frac{44}{3} \tau_2^2\tau_1 - 16 \tau_2\tau_3 \right]\nonumber \\
&\quad+ \left[2\tau_3- 4 \tau_1\tau_2 \right]
\left[ 6\tau_2 - \frac{1}{3} c^2 + \frac{4}{3} c\tau_1 - 6 \tau_2 \right]\nonumber\\
&\quad +\left[c(\tau_3 - 2 \tau_1\tau_2) + 12 \tau_1^2\tau_2 - 6 \tau_1\tau_3 - 5 \tau_2^2 + 3\tau_4 \right]\left[ \frac{2}{3} (c - \tau_1)\right] + 4\tau_5
\end{aligned}$$
with $c_6$, $c_7$ etc. being computed in a similar fashion. This leads to complicated expressions for the $c_i$ in terms of the renormalization scheme invariants $\tau_i$, but the full expression for $R$ collapses down to just two terms $$R = R_A^{(1)} = \alpha_{(1)} \left( - \frac{1}{b} L\right) + \tau_1 \alpha_{(1)}^2 \left( - \frac{1}{b} L\right)$$ by eq. (28). ($\alpha_{(1)}$ denotes the running couplant $\alpha$ with this first choice of $c_i$.)
A second choice for the $c_i$ is to simply set $c_i = 0$ \[43\]. In this case, $T_n = \tau_n$ and we have the running couplant given exactly by (from eq. (19)) $$\eta = \int_a^{\alpha_{(2)}(\eta)} \frac{dx}{-bx^2(1+c x)} ,$$ from which we obtain \[28, 40, 41\] $$\left(-1-\frac{1}{c\alpha_{(2)}}\right) e^{-1-\frac{1}{c\alpha_{(2)}}} = e^{-\frac{b\eta}{c}} \left(-1-\frac{1}{ca}\right)e^{-1-\frac{1}{ca}}$$ showing that with this second choice for $c_i$, the running coupling $\alpha_{(2)}(\eta)$ can be expressed in terms of the Lambert function $W(x)$ (i.e., $x = W(x)e^{W(x)}$ \[41\]). With all $c_i = 0$, then $T_i = \tau_i$ and so now $$R = R_A^{(2)} = \alpha_{(2)} + \tau_1 \alpha_{(2)}^2 + \tau_2 \alpha_{(2)}^3 + \tau_3 \alpha_{(2)}^4 + \ldots\, .$$ Unlike the expression for $R_A^{(1)}$ given in eq. (52), this expression for $R_A^{(2)}$ involves an infinite series, though $R_A^{(2)}$ does have the advantage that the couplant $\alpha_{(2)}$ is known exactly. Both $R_A^{(1)}$ and $R_A^{(2)}$ depend exclusively on the renormalization scheme invariants $b$, $c$, $\tau_i$ which are to be determined through the evaluation of Feynman diagrams.
We now will derive a general relationship between couplants $\alpha_{(c)}$ and $\alpha_{(d)}$ evaluated using different renormalization schemes characterized by the parameters $c_i$ and $d_i$ respectively. To do this, we make an expansion $$\alpha_{(c)} = \alpha_{(\alpha)} + \lambda_2 (c_i, d_i) \alpha^2_{(d)} + \lambda_3 (c_i, d_i) \alpha_{(d)}^3 + \ldots$$ Since $\alpha_{(c)}$ is independent of $d_j$, then $$\frac{d}{dd_j} \alpha_{(c)} = \left( \frac{\partial}{\partial d_j} + \beta_j (d_i)
\frac{\partial}{\partial\alpha_{(d)}} \right) \sum_{N=1}^\infty \lambda_N (c_i, d_i) \alpha^N_{(d)} = 0$$ where $\beta_j(d_i)$ is given by eqs. (32-35). Eqs. (35) and (57) together show that $$\frac{\partial\lambda_2}{\partial d_2} = 0, \quad
\frac{\partial\lambda_3}{\partial d_2} + 1 = 0, \quad
\frac{\partial\lambda_4}{\partial d_2} + 2\lambda_2 = 0, \quad
\frac{\partial\lambda_5}{\partial d_2} + \frac{d_2}{3} +3\lambda_3 = 0 \eqno(58a-d)$$ $$\frac{\partial\lambda_2}{\partial d_3} = 0, \quad
\frac{\partial\lambda_3}{\partial d_3} = 0, \quad
\frac{\partial\lambda_4}{\partial d_3} + \frac{1}{2} = 0, \quad
\frac{\partial\lambda_5}{\partial d_3} + \frac{1}{2}\left( - \frac{c}{3} + 2\lambda_2 \right) = 0 \eqno(59a-d)$$ $$\hspace{-5cm} \frac{\partial\lambda_2}{\partial d_4} = 0, \quad
\frac{\partial\lambda_3}{\partial d_4} = 0, \quad
\frac{\partial\lambda_4}{\partial d_4} = 0, \quad
\frac{\partial\lambda_5}{\partial d_4} + \frac{1}{3} = 0 \eqno(60a-d)$$ etc. (We see that $\lambda_{N-1}$ can depend on $d_2 \ldots d_N$.) Solving eqs. (58-60) subject to the boundary condition $$\lambda_N (c_i,c_i) = 0 \eqno(61)$$ leads to $$\alpha_{(c)} = \alpha_{(d)} - (d_2 - c_2) a^3_{(d)} - \frac{1}{2} (d_3 - c_3) \alpha^4_{(d)}\nonumber$$ $$+ \bigg[ - \frac{1}{6} \left( d_2^2 - c_2^2\right) + \frac{3}{2} \left(d_2 - c_2\right)^2 + \frac{c}{6} \left(d_3 - c_3 \right)\nonumber$$ $$- \frac{1}{3} \left(d_4 - c_4 \right) \bigg] \alpha^5_{(d)} + \ldots . \eqno(62)$$ If eq. (62) is used to expand $\alpha_{(d)}$ in terms of $\alpha_{(e)}$ and then $\alpha_{(d)}$ is eliminated in eq. (62), then the resulting expansion of $\alpha_{(c)}$ in terms of $\alpha_{(e)}$ is also of the form of eq. (62). This is a useful consistency check.
If in eq. (62) we were to $d_i = 0$ and chose $c_i$ so that $T_n = 0\;\, (n = 2,3 \ldots)$ (i.e., $c_2 \ldots c_5$ are given by eq. (31)) then we have an expansion for $\alpha_{(1)}$ in terms of $\alpha_{(2)}$. but since the expansions for $R$ given in eqs. (52) and (55) can be equated, we also have $$\alpha_{(1)} + \tau_1 \alpha_{(1)}^2 = \alpha_{(2)} + \tau_1 \alpha_{(2)}^2 + \tau_2 \alpha_{(2)}^3 + \tau_3 \alpha_{(2)}^4 + \ldots \eqno(63)$$ It can be shown that eqs. (62) and (63) are compatible upon identifying $\alpha_{(c)}$ and $\alpha_{(d)}$ in eq. (62) with $\alpha_{(1)}$ and $\alpha_{(2)}$ respectively in eq. (63), demonstrating the two renormalization schemes used to compute $R$ are consistent.
Varying of Mass Scales and RG Summation
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It has been suggested that in the standard perturbative expansion, such as the one for $R$ in eq. (2), the mass scale $\mu$ chosen at each order of perturbation theory could be different and that by an appropriate selection of mass scales, all dependency on the renormalization scheme parameters can be absorbed into these mass scales. We now will examine how this approach can be applied to the RG summed form of $R$ given by $R_A$ in eq. (28).
To begin with, we note how $\alpha_0 \equiv \alpha \left( - \frac{1}{b} \log \frac{\mu}{Q}\right)$ appearing in eq. (28) can be expanded in terms of $\alpha_i \equiv \alpha \left( - \frac{1}{b} \log \frac{\nu_i}{Q}\right)$ associated with the mass scale $\nu_i$ in the following way \[27, 18, 44\] $$\alpha_0 = \alpha_i + \left(\sigma_{21} \ell_{0i} \right) \alpha_i^2 + \left(\sigma_{31} \ell_{0i} + \sigma_{32} \ell_{0i}^2 \right)\alpha_i^3\eqno(64)$$ $$+ \left(\sigma_{41} \ell_{0i} + \sigma_{42} \ell_{0i}^2 +\sigma_{43} \ell_{0i}^3 \right) \alpha_i^4 + \ldots \nonumber$$ where $ \ell_{0i} \equiv \ln \left( \frac{\nu_i}{\mu}\right)$. The coefficients $\sigma_{mn}$ can be fixed by noting that $\alpha_0$ is independent of $\nu_i$ so that $$\nu_i \frac{d}{d\nu_i} \alpha_0 = \left[ \nu_i \frac{\partial}{\partial \nu_i}- \frac{1}{b} \beta (\alpha_i) \frac{\partial}{\partial \alpha_i} \right] \sum^\infty_{m=1} \sum_{n=0}^{m-1} \sigma_{mn} \ell_{0i}^n a^m_i \quad \left(\sigma_{m0} = \delta_{m0}\right) =0. \eqno(65)$$ From eq. (65) we find that $$\alpha_0 = \alpha_i - \ell_{0i} \alpha_i^2 + \left( -c \;\ell_{0i} + \ell_{0i}^2 \right) \alpha_i^3 +
\left( -c_2\ell_{0i} + \frac{5}{2} c\; \ell_{0i}^2 - \ell_{0i}^3 \right) \alpha_i^4\nonumber$$ $$+ \left( -c_3 \ell_{0i} + \left( 3c_2 + \frac{3}{2} c^2\right) \ell_{0i}^2 - \frac{13}{3} c \;\ell_{0i}^3 + \ell_{0i}^4\right) \alpha_i^5 \nonumber$$ $$+ \bigg( -c_4 \ell_{0i} + \frac{7}{2}\left( c_3 +c_2c\right)\ell_{0i}^2 - \left(6c_2 + \frac{35}{6} c^2\right) \ell_{0i}^3 \nonumber$$ $$+ \frac{77}{12} c \;\ell_{0i}^4 - \ell_{0i}^5\bigg) \alpha_i^6 + \ldots \;. \eqno(66)$$
Similarly , $\alpha_i$ can be expanded in terms of $\alpha_j$ with $\ell_{0i}$ in eq. (66) being replaced by $\ell_{ij} = \ln \left(\frac{\nu_j}{\nu_i}\right)$. If eq. (66) is used to expand $\alpha_0$ in terms of $\alpha_i$ and then into this expansion we substitute the expansion of $\alpha_i$ in terms of $\alpha_j$, we obtain an expansion of $\alpha_0$ in terms of $\alpha_j$ which has the form of eq. (66) upon using $\ell_{ij} = \ell_{0j} - \ell_{0i}$ (as expected).
We also note that summations of terms in eq. (66) similar to those in eqs. (11) and (23) is possible \[27\].
The expansion of $R$ in eq. (28), upon using eqs. (40,42,44,46) can be written as $$\hspace{-1cm} R = \alpha_0 + \tau_1 \alpha_0^2 + (-c_2 + \tau_2) \alpha_0^3 + \left( -2c_2 \tau_1 - \frac{1}{2} c_3 + \tau_3\right) \alpha_0^4\eqno(67)$$ $$\qquad + \left[ -\frac{1}{3} c_4 - \frac{c_3}{2} \left(- \frac{1}{3} c + 2 \tau_1\right) + \frac{4}{3} c_2^2 - 3 c_2 \tau_2 +\tau_4\right] \alpha_0^5\nonumber$$ $$\hspace{2cm} + \bigg[ \left(\frac{1}{3} cc_2^2 + \frac{3}{2} c_2c_3 + \frac{11}{3} c_2^2 \tau_1 - 4 c_2\tau_3 \right) - \frac{1}{2} \bigg( \frac{1}{6} c^2 c_3 - \frac{2}{3} c_3 c \tau_1 \nonumber$$ $$\hspace{2cm}+ 3c_3\tau_2 \bigg) - \frac{1}{3} \left( - \frac{1}{2} c_4 c + \frac{1}{2} c_4\tau_1\right) - \frac{1}{4} c_5 + \tau_5 \bigg] \alpha_0^6 + \ldots \,.\nonumber$$
We now use eq. (66) to re-express $(\alpha_0)^N$ wherever it occurs in eq. (67) as $(\alpha_N )^N$. For example, we can have $$\alpha_0 = \alpha_1 - \ell_{01} \alpha_1^2 + (-c\; \ell_{01} + \ell_{01}^2) \alpha_1^3 + (-c_2 \ell_{01} + \frac{5}{2} c \;\ell_{01}^2 - \ell_{01}^3) \alpha_1^4 + \ldots\nonumber$$ $$\hspace{-1.5cm}= \alpha_1 - \ell_{01} \left[ \alpha_2 - \ell_{12} \alpha_2^2 +( -c \;\ell_{12} + \ell_{12}^2) \alpha_2^3 + \ldots\right]^2\eqno(68)$$ $$\hspace{-1.5cm} + (-c \;\ell_{01} + \ell_{01}^2) \left[ \alpha_3 - \ell_{13} \alpha_3^2 + \ldots \right]^3\nonumber$$ $$+ \left( -c_2 \ell_{01} + \frac{5}{2} c \ell_{01}^2 - \ell_{01}^3 \right) \left[ \alpha_4 + \ldots \right]^4 + \ldots .\nonumber$$ Repeating this procedure we eventually find $$\hspace{-1cm} \alpha_0 = \alpha_1 - \ell_{01} \alpha_2^2 + \left[2\ell_{01} \ell_{12} + (-c\; \ell_{01} + \ell_{01}^2)\right] \alpha_3^3 \eqno(69a)$$ $$+\bigg[ -6 \ell_{01}\ell_{12}\ell_{23}
- \ell_{01} \left( \ell_{12}^2 + 2 (-c \;\ell_{12}
+ \ell_{12}^2)\right)\nonumber$$ $$\hspace{1cm} - 3 \ell_{13} ( - c \;\ell_{01} + \ell_{01}^2) + \left( -c_2 \ell_{01} + \frac{5}{2} c\; \ell_{01}^2 - \ell_{01}^3 \right)\bigg] \alpha_4^4 + \ldots \nonumber$$ as well as $$\alpha_0^2 = \alpha_2^2 - 2\ell_{02} \alpha_3^3 + \left[6\ell_{02} \ell_{23} + \ell_{02}^2 +
2 (-c\; \ell_{02} + \ell_{02}^2)\right] \alpha_4^4 + \ldots \eqno(69b)$$ $$\hspace{-6.5cm} \alpha_0^3 = \alpha_3^3 - 3\ell_{03} \alpha_4^4 + \cdots \eqno(69c)$$ $$\hspace{-7.7cm} \alpha_0^4 = \alpha_4^4 + \ldots .\eqno(69d)$$ (We keep only terms to order $\alpha^4$.)
Together, eqs. (67) and (69) result in $$R = \alpha_1 + \alpha_2^2 \left(- \ell_{01} + \tau_1\right) + \alpha_3^3 \bigg\lbrace 2\ell_{02} (\ell_{01} - \tau_1) - (c\; \ell_{01} + \ell_{01}^2)\eqno(70)$$ $$+ (-c_2 + \tau_2)\bigg\rbrace + \alpha_4^4 \bigg\lbrace 3\ell_{03} \bigg[ 2\ell_{02} (-\ell_{01} + \tau_1) + \ell_{01}(\ell_{01} + c)\nonumber$$ $$- (-c_2 + \tau_2) \bigg] + \bigg[ 3\ell_{02}^2 (\ell_{01} - \tau_1) +2c \;\ell_{02} (\ell_{01} - \tau_1) - \ell_{01}^3 \nonumber$$ $$- \frac{5}{2} c\;\ell_{01}^2 - c_2\ell_{01} + \left(-2 c_2 \tau_1 - \frac{1}{2} c_3 + \tau_3\right)\bigg]\bigg\rbrace + \ldots .\nonumber$$ (Again, we have used $\ell_{ij} = \ell_{0j} - \ell_{0i}$.)
In the PMC approach, the ambiguities in inherent in the parameters $c_i$ are absorbed into the mass scalars $\nu_i$. It is easily seen how this can be done upon examining eq. (B.7). At order $\alpha_1$ and $\alpha_2^2$, $R$ is independent of any $c_i$ and hence is unambiguous; however at order $\alpha_3^3$ the parameter $c_2$ explicitly occurs but it can be removed by choosing $\nu_2$ so that $$2 \ell_{02} (\ell_{01} - \tau_1) - (c \;\ell_{01} + \ell_{01}^2 ) + (-c_2) = 0 \eqno(71)$$ leaving the coefficient to $\alpha_3^3$ being the renormalization scheme invariant $\tau_2$. Next, by choosing $\nu_3$ so that $$\hspace{-2cm} 3\ell_{03} \left[ 2\ell_{02} (-\ell_{01} + \tau_1) + \ell_{01} (\ell_{01} + c) - (-c_2 + \tau_2)\right]\eqno(72)$$ $$+ \bigg[ 3\ell_{02}^2 (\ell_{01} - \tau_1) + 2c\;\ell_{02} (\ell_{01} - \tau_1) - \ell_{01}^3 - \frac{5}{2} c \;\ell_{01}^2 - c_2 \ell_{01}\nonumber$$ $$+ (-2 c_2 \tau_1 - \frac{1}{2} c_3) \bigg] = 0\nonumber$$ we eliminate all scheme dependence in the coefficient of $\alpha_4^4$ leaving solely the contribution coming from the renormalization scheme invariant quantity $\tau_3$. This procedure can be applied at each order of $\alpha$ in the expansion of $R$; $\nu_j (j = 2,3 \ldots)$ can be selected to eliminate the dependence of the term of order $\alpha_{j+1}^{j+1}$ in the expansion of eq. (70) on $c_2, c_3 \ldots c_j$ leaving us solely with $\tau_j a_{j+1}^{j+1}$. This should be possible for all $j$ as $\ell_{0j}$ enters the term of order $a_{j+1}^{j+1}$ only linearly. We are left with $$R = \alpha_1 + (-\ell_{01} + \tau_1) \alpha_2^2 + \tau_2 \alpha_3^3 + \tau_4 \alpha_4^4 + \ldots \eqno(73)$$ which is reminiscent of eq. (55). We note though that in eq. (73) the mass scales $\nu_j$ which enter $\alpha_j^j$ are scheme dependent as their value depends on the values of $c_2, c_3 \ldots c_j$. In addition, $\alpha_1$, $\alpha_2$ etc. are necessarily dependent on the values of the $c_i$. Thus unlike $R$ given by eq. (55), $R$ in eq. (73) retains an indirect renormalization scheme dependence.
The possibility of choosing $\nu_j$ so that the coefficient of $\alpha_{j+1}^{j+1}$ disappears completely for all $j$ should be considered. However, this is not feasible (nor should we expect it to be, as $R$ would then reduce to being simply $\alpha_1$). To see what happens if we attempt this, we note from eq. (70) that if we choose $\ell_{01}$ to eliminate the coefficient of $\alpha_2^2$, then the term of order $\alpha_3^3$ loses its dependence on $\ell_{02}$. Similarly, if $\ell_{02}$ is chosen to eliminate the term of order $\alpha_3^3$ (with $\ell_{01} \neq \tau_1$) then the coefficient of $\ell_{03}$ in the term of order $\alpha_4^4$ vanishes, making it impossible to select $\ell_{03}$ so that the term of order $\alpha_4^4$ vanishes. This pattern should repeat itself at each term of order $\alpha_j^j$.
An interesting consistency check is to use eq. (62) to replace $\alpha\left( - \frac{1}{b} \log \frac{\nu_i}{Q}, c_j\right)$ by $\alpha\left( - \frac{1}{b} \log \frac{\nu_i}{Q}, d_j\right)$ in eq. (70); we find that eq. (70) is recovered with $d_j$ replacing $c_j$ and $\alpha\left( - \frac{1}{b} \log \frac{\nu_i}{Q}, d_j\right)$ replacing $\alpha\left( - \frac{1}{b} \log \frac{\nu_i}{Q}, c_j\right)$.
Renormalization Scheme Ambiguities in the Effective Potential
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We will now examine renormalization scheme dependence in the Coleman-Weinberg effective action $V$ as considered in refs. \[33-36\]. Our attention will be restricted to a simple model in which a massless scalar field $\phi$ has a quartic self interaction so that the classical action is $$S = \int d^4x \left[\frac{1}{2}\left( \partial_\mu \phi \right)^2 - \frac{a}{4!} \phi^4\right].
\eqno(74)$$ The form that $V$ takes is $$V = \sum_{n=0}^\infty \sum_{m=0}^n T_{nm} a^{n+1} L^m \phi^4 \eqno(75)$$ with $L = \log \left(\frac{\phi}{\mu}\right)$ where now $\phi$ is the constant background field and $\mu$ is again the radiatively induced mass scale. The $RG$ equation is $$\left( \mu \frac{\partial}{\partial \mu} + \beta(a) \frac{\partial}{\partial a} + \gamma (a) \frac{\partial}{\partial \phi} \right) V = 0\eqno(76)$$ when using a mass-independent renormalization scheme \[5,6\]. The $RG$ function $\beta (a)$ again has the form of eq. (5), while $$\gamma (a) = \frac{\mu}{\phi} \frac{\partial\phi}{\partial\mu} = fa \left(1 + g_1a + g_2a^2 + \ldots\right).\eqno(77)$$ Under the finite renormalizations of eq. (6) and $$\overline{\phi} = \phi\left(1 + y_1a + y_2a^2 + \ldots\right)\eqno(78)$$ it is apparent that $b$, $c$, $f$ are unaltered while $c_2, c_3 \ldots, g_1, g_2 \ldots$ are all altered. Following refs. \[7, 42\] (as well as ref. \[45\] for the case in which there is a mass to be renormalized) we characterize the renormalization scheme dependency by $c_2, c_3 \ldots$ and $g_1, g_2 \ldots$. It is evident that $a$ is independent of $g_i$, while its dependency on $c_i$ is again given by eqs. (31-35); furthermore $$\frac{\partial \phi}{\partial c_i} = \phi \gamma_i^c \eqno(79a)$$ and $$\frac{\partial \phi}{\partial g_i} = \phi \gamma_i^g .\eqno(79b)$$ Just as one can find $\beta_i$ from eq. (30), it follows from $$\left( \frac{\partial^2}{\partial\mu\partial c_i} -
\frac{\partial^2}{\partial c_i\partial\mu}\right) \phi = \left( \frac{\partial^2}{\partial g_i\partial c_j} - \frac{\partial^2}{\partial c_j\partial g_i}\right) \phi = \left( \frac{\partial^2}{\partial\mu\partial g_i} - \frac{\partial^2}{\partial g_i\partial\mu}\right) \phi = 0 \eqno(80)$$ that $$\gamma_i^g = \int_0^a dx \frac{fx^{x+1}}{\beta(x)} \eqno(81a)$$ and $$\gamma_i^c = \frac{\gamma(a)\beta_i(a)}{\beta(c)} + b \int_0^a dx \frac{x^{i+2}\gamma(x)}{\beta^2(x)} .\eqno(81b)$$
One can regroup the sum in eq. (75) as in eq. (10). We will follow refs. \[33, 37\] and regroup the sum in eq. (75) as in eq. (15) so that $$V = \sum_{n=0}^\infty A_n (a) L^n \phi^4 \eqno(82)$$ with $$A_n(a) = \sum_{m=n}^\infty T_{mn} a^{m+1}.\eqno(83)$$ Eq. (36) now leads to $$\hat{A}_{n+1} (a(\eta)) = \frac{1}{(n+1)} \frac{d}{d\eta} \hat{A}_n(a(\eta)) = \frac{1}{(n+1)!}\; \frac{d^{n+1}}{d\eta^{n+1}} \hat{A}_0(a(\eta))\eqno(84)$$ where $$\eta = \int_{a_{I}}^{a(\eta)} \frac{dx}{\hat{\beta}(x)} \qquad (a (\eta = 0) \equiv a_I)\eqno(85)$$ and $$\hat{A}_n (a) = A_n(a) \exp \left( 4 \int_{a_{I}}^a \frac{\hat{\gamma}(x)}{\hat{\beta}(x)} dx \right) \eqno(86)$$ where $\hat{\beta} = \beta / (1-\gamma)$ and $\hat{\gamma} = \gamma / (1-\gamma)$. Together, eqs. (82) and (86) lead to $$V = A_0 (a(\eta + L)) \exp \left( 4 \int_{a(\eta)}^{a(\eta + L)}
\frac{\hat{\gamma}(x)}{\hat{\beta}(x)} dx \right) \phi^4 . \eqno(87)$$ By eq. (82), $$\frac{dV}{d\phi} = \sum_{n=0}^\infty\left[ (n+1) A_{n+1} (a) + 4A_n(a)\right]L^n\phi^3; \eqno(88)$$ this vanishes at order $L^0$ when $\phi = v$ provided either $v = 0$ or $$A_1(a) + 4 A_0 (a)= 0.\eqno(89)$$
Together, eq. (84) when $n = 0$ and eq. (89) result in $$\left[ \hat{\beta}\frac{d}{da} + 4(1 + \hat{\gamma})\right] A_0(a) = 0 \eqno(90)$$ and $$A_0 (a) = A_0 (a_I) \exp \left( -4 \int_{a_{I}}^a \frac{dx}{\beta(x)}\right).\eqno(91)$$ Together eqs. (87) and (91) result in $$V = A_0 (a_I) \exp \left( -4 \int_{a_{I}}^a \frac{dx}{\beta(x)}\right) \mu^4 .\eqno(92)$$ Thus $V$ is independent of $\phi$ if $v \neq 0$. It is immediately obvious that the $RG$ equation of eq. (76) is satisfied by $V$.
We now can examine the scheme dependence of eq. (92). As $a$ is independent of $g_i$ and $V$ is independent of $\phi$, the equation $$\left( \frac{\partial}{\partial g_i} + \phi \gamma_i^g \frac{\partial}{\partial \phi} \right) V = 0 \eqno(93)$$ is automatically satisfied. It is also clear that the equation $$\left( \frac{\partial}{\partial c_i} + \beta_i \frac{\partial}{\partial a} + \phi \gamma_i^c \frac{\partial}{\partial \phi} \right) V = 0 \eqno(94)$$ is satisfied on account of eq. (31). Since eq. (92) satisfies eqs. (76), (93) and (94) it is wholly independent of all parameters that characterize the renormalization scheme being used. We anticipate that this scheme independence also holds for the effective potential in more complicated models that have been considered such as a massive $\phi_4^4$ model \[34-35\], massless scalar electrodynamics \[33\] and the Standard Model with a single Higgs doublet of scalars \[36\]. In each of these models, $V$ has been shown to be independent of the background scalar field by using the appropriate versions of eqs. (76) and (88).
The Principle of Minimal Sensitivity and RG Summation
=====================================================
Stevenson in ref. \[7\] has proposed not only use of $(\mu , c_i)$ to characterize one’s choice of renormalization scheme in massless QCD when using mass independent renormalization, but also has argued that a “principle of minimal sensitivity” (PMS) be used to fix dependence of finite order perturbative results on these parameters. When this approach has been applied to computations of $R_{e{^+}e{^-}}$ \[21-23\], the perturbative form of eq. (2) has been considered. We will now see how PMS can be used with the RG summed form of $R$ given by eqs. (11) and (28) when only a finite number of terms contribute to these sums.
The cross section $R_{e{^+}e{^-}}$ has already been considered using the expansion of eq. (11) (as have the calculation of a number of physical quantities) \[26\]. It has been shown that variation of $R$ with changes of the scale parameter $\mu$ within a given renormalization scheme is considerably reduced when this RG summed form of $R$ is used instead of the perturbative result of eq. (2). This is not unexpected, as the exact expression for $R$ must be independent of $\mu$ (and $c_i$), and since both RG summations include more contributions to $R$ than comes from an approximation arising from a truncated form of eq. (2), we should anticipate that the RG summed expressions have less dependency on $\mu$.
To consider this application of PMS more explicitly, let us examine the approximation $$R_\Sigma^{(3)} = a S_0 (aL)+ a^2S_1 (aL) + a^3 S_2 (aL) \eqno(95)$$ to $R_\Sigma$ in eq. (11). In more detail, by eqs. (13, 40) result in $$R_\Sigma^{(3)} = \frac{a}{w} + a^2 \left(\frac{\tau_1 - c \ln |w|}{w^2}\right) \eqno(96)$$ $$+ a^3 \left( \frac{-c_2+\tau_2 - \left(2c\tau_1 + c^2\right) \ln |w| + \left(c^2-c_2\right) (w-1) + c^2 \ln^2 |w|}{w^3}\right) \nonumber$$ where $w = 1 - ab\log (\mu/Q)$ and to the order we are working by eqs. (27, 31) $$\ln \left( \frac{\mu}{\Lambda}\right) = \int_0^a \frac{dx}{-bx^2(1+cx+c_2x^2)} + \int_0^\infty \frac{dx}{bx^2(1+cx)} \eqno(97a)$$ and $$\frac{\partial a}{\partial c_2} = a^2 (1 + ca + c_2 a^2) \int_0^a \frac{dx}{(1+cx+c_2x^2)^2}. \eqno(97b)$$ In principle, the PMS criterion applied to $R_\Sigma^{(3)}$ involves applying the criterion $$\frac{\partial R_\Sigma^{(3)}}{\partial\mu}= \frac{\partial R_\Sigma^{(3)}}{\partial c_2} = 0 \eqno(98)$$ in order to optimize the values of $\mu$ and $c_2$ in eq. (96). Applying analyticly eq. (98) to $R_\Sigma^{(3)}$ in eq. (96) is clearly more difficult than applying the PMS criterion to the approximation $$R^{(3)} = a + r_1 a^2 + r_2 a^3 \eqno(99)$$ which follows from eq. (2) as was done in refs. \[7, 21-23\].
If in place of $R_\Sigma$ in eq. (11) one we to consider the RG sum of $R_A$ in eq. (28), then the approximation $$R_A^{(3)} = \sum_{n=0}^3 T_n \alpha^n \left( - \frac{1}{b} L\right)\eqno(100)$$ is of the same order as $R_\Sigma^{(3)}$ in eq. (95). However, $R_\Sigma^{(3)}$ and $R_A^{(3)}$ are distinct quantities, having been derived using different RG summations. More explicitly, using eqs. (40, 19, 31) we obtain $$R_A^{(3)} = \alpha \left( \ln \frac{Q}{\mu}\right) + \tau_1 \alpha^2 \left( \ln \frac{Q}{\mu}\right) + (-c_2 + \tau_2)\alpha^3 \left( \ln \frac{Q}{\mu}\right)\eqno(101)$$ where $$\ln\left( \frac{Q}{\mu}\right) = \int_a^\alpha \frac{dx}{-bx^2(1 + cx + c_2x^2)}, \eqno(102)$$ $\frac{\partial\alpha}{\partial c_2}$ is given by eq. (97b) with $a$ being replaced by $\alpha$, and the dependence of $a$ in eq. (102) on $\mu$ and $c_2$ itself being subject to eqs. (97a,b).
As with $R_\Sigma^{(3)}$, applying the PMS criterion $$\frac{\partial R_A^{(3)}}{\partial \mu} = \frac{\partial R_A^{(3)}}{\partial c_2} = 0 \eqno(103)$$ analyticly is more involved than applying it to $R^{(3)}$ in (99).
Discussion
==========
In this paper we have outlined two ways of performing RG summation of logarithmic contributions to the cross section $R_{e{^+}e{^-}}$; the final result in both cases involves simply the log-independent contribution to $R_{e{^+}e{^-}}$ and the RG function $\beta$. Even though portions of $R_{e{^+}e{^-}}$ to arbitrarily high order in perturbation theory are incorporated by using these RG sums, the final result in both cases is not exact and consequently has explicit dependence on the parameters $\mu$ and $c_i$ that characterize the renormalization scheme used. We have shown how these RG summed expressions for $R_{e{^+}e{^-}}$ depend on these parameters to any finite order in perturbation theory. (We have also shown that the exact expression for $V$ in eq. (92) is renormalization scheme independent.) In principle the PMS criterion can be applied to select “optimal” values of $\mu$ and $c_i$ but to do this would be non-trivial.
Of special interest are the two choices of the parameters $c_i$ that lead to the expansion $R_A^{(1)}$ and $R_A^{(2)}$ of eqs. (52) and (55) for $R$. In both of these expansions, only the renormalization scheme invariants $b$, $c$ and $\tau_i$ appear; there is no dependency on $c_i$ either implicit or explicit. All dependency on the physical moment $Q$ is in the argument of the auxiliary function $\alpha\left(\log \frac{Q}{\mu}\right)$; this function arises in the course of summing all of the logarithms appearing in eqs. (2) and (3). The mass scale parameter $\mu$ only explicitly occurs in the ratio $Q/\mu$ and hence only serves to calibrate the magnitude of $Q$. The couplant $a$ appearing in the expansion of eq. (2) is a boundary value for $\alpha(\eta)$ in eq. (25) and so all that is needed when considering $R_A^{(1)}$ and $R_A^{(2)}$ is the value of $a$ for some choice of $\mu$. It is not necessary to consider how $a$ depends on $\mu$ through eq. (27) and the value of $\Lambda$ only reflects the value of $a$ at the value of $\mu$ chosen to calibrate the magnitude of $Q$.
The choice of $c_i$ that leads to $R_A^{(1)}$ in eq. (52) is appealing as $R$ then involves merely two terms; all $Q$ dependence of $R$ resides in the argument of $\alpha_{(1)}(\log Q/\mu)$ and its square. This function has its behaviour dictated by the relation between the expansion constant $c_i$ and the renormalization scheme invariants $\tau_i$ (typified by eqs. (51a-d)).
A second choice for the $c_i$ is $c_i = 0$ \[43\] (though the feasibility of making this choice has been questioned in ref. \[46\]). The auxiliary function $\alpha_{(2)} (\log Q/\mu)$ is now given in closed form (see. eq. (54)); the $\tau_i$ are now the expansion coefficients in the infinite series of eq. (55). The simplicity of this result is again quite appealing.
We note that upon setting $Q = \mu$, so that by eq. (19) $$\alpha (Q = \mu) = a_I \eqno(104)$$ it follows by eqs. (52,55) $$R_\Sigma^{(1)} (Q = \mu) = a_{(1)} + \tau_1 a_{(1)}^2 \eqno(105a)$$ and $$R_I^{(2)} (Q = \mu) = a_{(2)} + \tau_1 a_{(2)}^2 + \tau_2 a_{(2)}^3 + \ldots\;. \eqno(105b)$$ Thus it is quite straight forward to determine $a_{(1)}$ (the value of $\alpha_{(1)}$ when $Q = \mu$) as it involves solving the quadratic in eq. (105a). The value of $a_{(2)}$ is determined from eq. (105b); $a_{(1)}$ and $a_{(2)}$ are related due to eq. (63).
Clearly much can now be done. The ideas presented should be applied to a full quantitative analysis of the cross section $R_{e{^+}e{^-}}$. It would also be of interest to extend this approach to renormalization scheme dependency to processes in which there are non-trivial masses and/or multiple couplings in the classical action. The scheme dependency occurring in the $\beta$-function of $N = 1$ supersymmetry \[47, 48\] and the effective action for an external gauge field \[49\] or instantons \[27\] might also be considered. These questions are currently being examined.
Acknowledgements {#acknowledgements .unnumbered}
================
R. Macleod had useful input.
[99]{} E.C.G. Stueckelberg and A. Peterman, *Hel. Phys. Acta* **26**, 499 (1953). N.N. Bogoliubov and D.V,. Shirkov, *Introduction to the theory of quantized fields*, Interscience, NY (1959). M. Gell-Mann and F. Low, *Phys. Rev.* **95**, 1300 (1954). P.M. Stevenson, *Ann. of Phys.* **132**, 383 (1981). G. ’t Hooft, *Nucl. Phys.* **B61**, 455 (1973). S. Weinberg, *Phys. Rev.* **D8**, 3497 (1973). P.M. Stevenson, *Phys. Rev.* **D23**, 2916 (1981). P.M. Stevenson, *Phys. Rev.* **D33**, 3130 (1986). G. Grunberg, *Phys. Lett.* **95B**, 70 (1980); *Phys. Rev.* **D29**, 2315 (1984). A. Dhar and V. Gupta, *Phys. Rev.* **D29**, 2822 (1984). S.J. Maximov and V.I. Vovk, *Phys. Lett.* **199B**, 443 (1987). C.J. Maxwell, *Phys. Rev.* **D29**, 2884 (1984). S.J. Brodsky, P. Lepage and P.B. Mackenzie, *Phys. Rev.* **D28**, 228 (1983). S.J. Brodsky and H.J. Lu, *Phys. Rev.* **D51**, 3652 (1995). M. Mojaza, S.J. Brodsky and X.G. Wu, *Phys. Rev. Lett.* **110**, 192001 (2013). S.J. Brodsky and S.G. Wu, *Phys. Rev.* **D86**, 034038 (2012) (Erratum: ibid. **86**, 079903 (2012)). S.J. Brodsky, M. Mojaza and X.G. Wu, *Phys. Rev.* **D89**, 014027 (2014). X.G. Wu, S.J. Brodsky and M. Mojaza, *Prog. Part. Nucl. Phys.* **72**, 44 (2013). H.M. Ma, X.G. Wu, Y. Ma, S.J. Brodsky and M. Mojaza, *Phys. Rev.* **D91**, 094028 (2015). X.G. Wu, Y. Ma, S.Q. Wang, H.B. Fu, H.H. Ma, S.J. Brodsky and M. Mojaza, hep-ph 1405.3196. J. Chyla, A. Kataev and S. Larin, *Phys. Lett.* **267B**, 269 (1991). A.C. Mattingly and P.M. Stevenson, *Phys. Rev.* **D49**, 437 (1994). P.M. Stevenson, *Nucl. Phys.* **B868**, 38 (2013). C.J. Maxwell, *Nucl. Phys. B (Proc. Suppl.)* **86**, 74 (2000). M.R. Ahmady, F.A. Chishtie, V. Elias, A.H. Fariborz, N. Fattahi, D.G.C. McKeon, T.N. Sherry and T.G. Steele, *Phys. Rev.* **D66**, 014010 (2002). M.R. Ahmady, F.A. Chishtie, V. Elias, A.H. Fariborz, D.G.C. McKeon, A. Squires and T.G. Steele, *Phys. Rev.* **D67**, 034017 (2003). M.R. Ahmady, V. Elias, D.G.C. McKeon, A. Squires and T.G. Steele, *Nuvl. Phys.* **B655**, 221 (2003). D.G.C. McKeon and A. Rebhan, *Phys. Rev.* **D67**, 027701 (2003). V. Elias, R.B. Mann, D.G.C. McKeon and T.G. Steele, *Phys. Rev. Lett.* **91**, 251601 (2003). V. Elias, R.B. Mann, D.G.C. McKeon and T.G. Steele, *Nucl. Phys.* **B678**, 147 (2004) (Erratum: **B703**, 413 (2004). F.A. Chishtie, T. Hanif, J. Jia, R.B. Mann, D.G.C. McKeon, T.N. Sherry and T.G. Steele, *Phys. Rev.* **D83**, 105009 (2011). T.G. Steele and Z.W. Wang, *Phys. Rev. Lett.* **110**, 151601 (2013). F.T. Brandt, F.A. Chishtie and D.G.C. McKeon, *Mod. Phys. Lett.* **A20**, 2215 (2005). F.T. Brandt, F.A. Chishtie and D.G.C. McKeon, *Int. J. Mod. Phys.* **A22**, 1 (2007). F.A. Chishtie, T. Hanif, J. Jia, D.G.C. McKeon and T.N. Sherry, *Int. J. Mod. Phys.* **A25**, 5711 (2010). F.T. Brandt, F.A. Chishtie and D.G.C. McKeon, hep-th 1409.2820. D.G.C. McKeon, hep-th 1112.4201. G. ’t Hooft and M. Veltman, *Nucl. Phys.* **B44**, 189 (1972). V. Elias and D.G.C. McKeon, *Int. J. Mod. Phys.* **A18**, 2395 (2003). E. Gardi, G. Grunberg and M. Karliner, *JHEP* **9807:007**, (1998). R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey and D.E. Knuth, *Adv. Comput. Math.* **5**, 329 (1996). H.J. Lu and S.J. Brodsky, *Phys. Rev.* **D48**, 3310 (1993). G. ’t Hooft, *The whys of subnuclear physics*, Erice 1977, ed. A. Zichichi, Plenum Press N.Y. (1979). J.M. Chung and B.K. Chung, *Phys. Rev.* **D60**, 105001 (1999). D.G.C. McKeon, *Can. J. Phys.* **61**, 564 (1983); ibid **59**, 1327 (1981). I.M. Suslov, hep-ph 0605115. V. Novikov, V. Shifman, A. Vainshtein and V. Zakharov, *Nucl. Phys.* **B229**, 381 (1983). D.R.T. Jones, *Phys. Lett.* **123B**, 45 (1983). G.V. Dunne, H. Gies and C. Schubert, *JHEP* **0211**, 032 (2002).
[^1]: [email protected]
| |
EAS100 Lecture Notes - Lecture 19: Pressure Gradient, Coriolis Force, Polar Front
For unlimited access to Class Notes, a Class+ subscription is required.
October 27 2014
EAS 3 - 27
Atmosphere
Wind Direction: parallel to isobars (lines of equal pressure)
Geostropic flow
"geostropic" means 'earth turning'
Arises from the rotation of the earth.
Newtons laws:
1) A body at rest stays at rest while a body in motion
stays in motion,
travelling at a constant speed and in a straight
line, until acted upon
by a net outside force.
"Inertia"
2) F = ma
"Momentum"
Vector and addition of forces
Velocity is a vector, direction and speed.
F_a + F_b = F_ab
Geostropic: Pressure gradient force + Coriolis force = 0
F_PG + F_c = 0
F_C is proportional to velocity
F_C points 90 deg to right of motion (in north hemisphere)
Occurs when at high enough altitude that surface friction
is negligible
See associated images.
Near-surface flow
Pressure gradient force + Coriolis force + Ground friction
force = 0
Faster winds where isobars are closely spaced
Jet Stream
Located above polar front, steep pressure gradients form.
Speeds up to 460 km/h have been measured. | https://oneclass.com/class-notes/ca/u-of-alberta/eas/eas100/432947-19-atmospheretxt.en.html |
It is no mystery that at 2 Seas Agency we are passionate about translation, and we know we are not the only ones. Since its foundation in 2001, Literature Across Frontiers has been at the forefront in promoting literary exchange throughout the world; most recently, in April 2015, LAF launched a much awaited report unveiling the current situation of literature in translation in the UK and Ireland from 2000 to 2012 (download the study here).
In order to find out more about LAF’s mission and future plans, we spoke to director Alexandra Büchler.
Giulia: What are LAF’s main activities?
Alexandra: Broadly speaking, LAF fosters international literary exchange and encourages diversity in literary publishing and programming of live literary events by working with a range of partners across Europe and in other regions. We also monitor our field and engage in research into the publishing of translated literature and support for literary translation in order to contribute to an on-going policy debate. The outcomes are published electronically on our website where you can also find our information resources.
While working with the book sector is at the heart of what we do, our activities are also about creating opportunities for cross-cultural collaboration among writers and translators, particularly emerging ones. This is done mainly through residential workshops in which writers explore each other’s work through direct or bridge-language translation. To date, we have organised over eighty such workshops in some sixteen countries with writers working in over fifty languages. The same principle is applied in our larger-scale projects based on exchange residencies. An element of collaboration and reciprocity is always central to these projects: Sealines involved twenty writers and six bilingual European port cities, Metropoetica was a project focusing on women’s poetry about inhabiting urban spaces, Word Express involved over sixty young writers from the entire region of South East Europe, and Tramlines paired authors who explored each other’s cites by navigating them through the tram system. The last one inspired the creation of a short story application Lit Nav which is available for free from Apple app store.
Giulia: Do you feel that the status of translated literature in the Anglophone world has changed since LAF was founded in 2001?
Alexandra: Yes, I believe it has. Most importantly, literary translation has become a widely discussed topic with a visible professional community – translators, of course, writers, publishers, literary programmers. The setting up of the Literary Translation Centre at the London Book Fair in 2010 was landmark occasion which gave this community a home at a leading industry event. Today, the LTC is one of the liveliest spots in the book fair with a fantastic programme and big audiences. In other words, translation has been given unprecedented visibility and a support infrastructure with a number of organisations playing a role, many of which have found a permanent home in the Free Word Centre in London – a literature hub and another significant landmark in a relatively recent development which would not have happened without targeted strategic financial support from public and private funders.
The question is whether this “buzz” around translation is evident also in publishing. Our research shows that the number of translated titles has grown by 69% over the past twelve years and the publishing scene is one of great diversity with a number of innovative small independents focusing on translated literature and gathering a steady following. But this is a growth which shadows the steadily growing volume of British publishing, the least receptive to writing from other cultures which still represents only around 4% of books published every year. This outlook is then reflected in the way books are promoted – for example writing can come from outside the English-speaking world is rarely reviewed, British literary festivals can still be quite mono-cultural in their programming and translated literature is not part and parcel of most people’s reading habit.
The general scene has changed from what it was ten or twenty years ago and there is a greater acceptance of diversity, but we still have a lot of catching up to do and this is occasionally acknowledged by respected commentators: this year’s International Man Booker Prize judge and renowned author and scholar, Marina Warner, describes the British outlook on word literature as “oddly provincial” while the veteran publisher of translated literature Christopher MacLehose spoke of the “abject incuriosity” of the British in a public debate at last year’s Frankfurt Book Fair. So, although there has been a change, we still have a long way to go if we want to catch up with the rest of Europe on this front. European readers grow up with literature in translation, it is part of the literary canon. This is emphatically not the case in the English-speaking world and will probably never be, but here has been some progress and more diversity in the publication and reception of translated literature.
Giulia: What would you say is the main reasons for this change?
Alexandra: There are many factors which come together and sometimes it is difficult to decide which are the predominant ones, but it seems that changes in arts policy have led to an increasing emphasis on international as an important part of the cultural landscape, and access to international writing is seen as a cultural right. Another factor that has contributed to a wider acceptance or even growing popularity of translated fiction is genre writing and particularly the success of Scandinavian crime or Nordic noir both in print and on the small screen. British TV is not known for screening foreign films, drama or documentary, and having a subtitled series on prime time television is a new phenomenon. But even these dramas and films have had US remakes.
Giulia: What factors have the biggest influence on the translation policies adopted by publishers? In short, why some languages and literatures are so underrepresented in translation?
Alexandra: Each publisher has a different focus and the diversity we are witnessing is due to the work of small independent publishers many of whom started publishing relatively recently and whose outlook is decidedly non-commercial, such as Istros Books, focusing on writing from South East Europe, Peirene Press with their eclectic list of beautiful book objects, Pushkin Press which launched a list of translations for children and young readers, or And Other Stories whose list is based on recommendations of reading groups. The Wales-based Parthian Books and Seren can also be quite adventurous and take a gamble on a Slovak or Basque author. And it is these publishers who fill the gaps: Ismail Kadare may be the International Booker Prize winner but how many other Albanian authors have been translated? Without And Other Stories and Istros Books there would be none. Ultimately, publishers do what they have to do, what they feel passionate about. If you publish a book you don’t believe in, you won’t convince readers it is worth buying and reading.
Another factor has been the impact of national bodies promoting literature and supporting translations, and probably also the growing influence of a new category of literary agents who represent an international array of authors, and, last but not least, translators play a role too, assisted by funding available for sample translations which makes it easier for them to pitch titles to publishers.
Giulia: What are LAF’s future projects?
Alexandra: We work on regular projects with partners abroad and in the UK, literary organisations, festivals and book fairs. We are planning a multi-year project focusing on writing and multilingualism in Turkey where there is a very interesting Kurdish literary scene we know very little about in Europe, and especially in English-speaking countries. Another large project we are planning will examine shared cultural heritage between India and some European countries, and we also have been working increasingly with Indian literary festivals on promotion of European writing. In China, our partner is the Bookworm Literary Festival, and we hope to be able to take more European authors there next year. Of course all these plans depend on available funding and sponsorship.
On home ground we would like to focus on touring of international authors in the UK, especially outside London, and on developing a programme of writers’ and translators’ residencies in Wales. Providing residential opportunities for international authors is a crucial aspect of the kind of dialogue we aim to stimulate. Unfortunately, compared to other European countries, this is another area where the UK lags behind. I wish we had an equivalent of the DAAD programme they have in Berlin or an apartment which hosts writers on a monthly basis like the one managed by Passa Porta Literature House in Brussels. Even tiny and not particularly wealthy countries such as Georgia, Latvia or Slovenia have such facilities and I can’t see why we should not be able to set up something similar in Wales, our home base. | https://2seasagency.com/literature-in-translation-fostered-by-literature-across-frontiers/ |
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The Board will assist with funding up front costs to a maximum of $1,000 in recognition of the promotion of safety and well-being of the students brought about by the LC Senior All-Nighter. The assistance provided by way of up-front funding of LC All-Nighter expenses shall be considered an advance with the expectation that the same will be repaid by the LC All-Nighter Committee, funds permitting.
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The Board will consider requests for funds for extraordinary items not specifically set for the above based upon the recommendation of the members or parent representative. In considering such requests, the board shall consider its corporate charter, goals, and guidelines set forth herein. The approval of any such extraordinary request shall be solely in the discretion of the Board.
v. The urgent need for the request.
The Board prefers to consider activity requests prior to the purchase of equipment, supplies, travel or extraordinary items. Requests made for Booster Club funds after purchases have occurred will not be presumed to be reimbursed but will be considered according to the above-mentioned criteria and will not take priority or have preference over other requests.
The decision to make approve a disbursement shall be made by a majority of members present at the principal place for meetings.
h. Attendance. The parent representative requesting funding (or his or her proxy) must be present at the meeting in which funds are being requested.
In order to submit this form please verify that you have read and agree to the Policy on Disbursement above.
List items requested and associated cost (at this time) in order of highest priority. Whenever possible, research at least two bids for each item and identify the preferred supplier. Not necessary if Nike items from BSN are being purchased. | https://www.lcboosters.org/booster-club-allocation-request/ |
Fort Wayne Philharmonic Cancels Holiday Shows Amid Failed Union Negotiations
The Fort Wayne Philharmonic canceled its holiday concerts scheduled for this weekend. The cancellation comes after out-of-town guest musicians asked to be let out of their contracts.
The Philharmonic said the request came because the union asked the replacement musicians not to work with the orchestra. Last month, the Fort Wayne Philharmonic was placed on The American Federation of Musicians International "Unfair List." The list is meant to discourage other musicians from working with orchestras on the list.
The Fort Wayne Philharmonic Players Association released its Position Paper Thursday, detailing the paper details the Philharmonic Management’s “unfair negotiating tactics, destructive and harmful proposals to musicians, and the impact such actions could have on our orchestra, the quality of life in our community, and economic development in Northeast Indiana.”
The Philharmonic said the negotiating team has offered several options for musicians, but that the musicians have not returned to the table since Sept. 28. The Association called the latest offer “radical and destructive.” The offer included reducing the number of full-time musicians from 63 to 15. The Philharmonic said this was "in order to allow the institution more flexibility to respond to the realities of the marketplace while expanding programs and performance opportunities."
The Association said the Philharmonic is using "the pretect of the COVID-19 pandemic" to un-lawfully furlough musicians without pay. They also say the Philharmonic "does not lack money at this time" due to a recent capital campaign that raised nearly $10 million and an endowment.
At the Philharmonic's board meeting on Tuesday, the Board of Directors voted to extend paying 99% of musician health premiums through Jan. 31. After that date, the musicians would be responsible for 30% of their health insurance premiums.
The Philharmonic said musicians "have failed to respond to repeated requests to return to the bargaining table." In the past few months, the Philharmonic has been charged with two Unfair Labor Practices. | https://www.wboi.org/news/2020-12-03/fort-wayne-philharmonic-cancels-holiday-shows-amid-failed-union-negotiations |
Plurals of English Nouns
Most nouns do their many by simply including –s to the end (e.g. Cat/cats, book/books, journey/journeys). Some do readjust their endings, though. The main varieties of noun that carry out this are:
Nouns finishing in -y
If the noun ends v a consonant to add -y, make the plural by an altering -y come -ies:
|singular||plural|
|berry||berries|
|activity||activities|
|daisy||daisies|
If the noun ends through -ch, -s, -sh, -x, or -z, add -es to kind the plural:
|singular||plural|
|church||churches|
|bus||buses|
|fox||foxes|
There’s one exemption to this rule. If the -ch finishing is pronounced with a ‘k’ sound, you add -s quite than -es:
|singular||plural|
|stomach||stomachs|
|epoch||epochs|
Nouns ending in -f or -fe
With nouns that finish in a consonant or a single vowel add to -f or -fe, adjust the -f or -fe to -ves:
|singular||plural|
|knife||knives|
|half||halves|
|scarf||scarves|
Nouns which finish in two vowels to add -f usually form plurals in the regular way, with just an -s
|singular||plural|
|chief||chiefs|
|spoof||spoofs|
Nouns finishing in -o
Nouns finishing in -o can add either -s or -es in the plural, and also some have the right to be spelled one of two people way.
You are watching: Most nouns form their plurals by adding
|singular||plural|
|solo||solos|
|zero||zeros|
|avocado||avocados|
|singular||plural|
|studio||studios|
|zoo||zoos|
|embryo||embryos|
|singular||plural|
|buffalo||buffaloes|
|domino||dominoes|
|echo||echoes|
|embargo||embargoes|
|hero||heroes|
|mosquito||mosquitoes|
|potato||potatoes|
|tomato||tomatoes|
|torpedo||torpedoes|
|veto||vetoes|
|singular||plural|
|banjo||banjos or banjoes|
|cargo||cargos or cargoes|
|flamingo||flamingos or flamingoes|
|fresco||frescos or frescoes|
|ghetto||ghettos or ghettoes|
|halo||halos or haloes|
|mango||mangos or mangoes|
|memento||mementos or mementoes|
|motto||mottos or mottoes|
|tornado||tornados or tornadoes|
|tuxedo||tuxedos or tuxedoes|
|volcano||volcanos or volcanoes|
Plurals of international nouns
The many of words which have actually come into English from a international language such as Latin or Greek frequently have two feasible spellings: the foreign plural spelling and an English one. For example, you deserve to spell the plural of aquarium (from Latin) as either aquaria (the Latin plural) or aquariums (the English plural).
Words of Latin origin
Here’s a perform of part words that came into English from Latin i m sorry can kind their many in 2 ways:
|Word||Latin plural||English plural|
|antenna||antennae||antennas|
|appendix||appendices||appendixes|
|cactus||cacti||cactuses|
|curriculum||curricula||curriculums|
|formula||formulae||formulas|
|index||indices||indexes|
|millennium||millennia||millenniums|
|referendum||referenda||referendums|
|stadium||stadia||stadiums|
|terminus||termini||terminuses|
|thesaurus||thesauri||thesauruses|
|vortex||vortices||vortexes|
Note that there space a couple of nouns which have come into English indigenous Latin which must always form their many in the Latin way. Most of these are scientific or technical terms. The most common ones are:
|singular||plural|
|alga||algae|
|alumnus||alumni|
|larva||larvae|
Remember too, that the plural form of octopus should constantly be octopuses and never octopi. This is due to the fact that the word came into English from Greek, not Latin, and also so the usual rules because that Latin plurals don"t apply.
Words of Greek origin
Nouns which finish in -is normally come from Greek. Their plurals are made by changing the -is to -es:
|singular||plural|
|crisis||crises|
|analysis||analyses|
|neurosis||neuroses|
Words that French origin
Certain native which have come into English native French have actually two feasible plural forms: the original French plural and an English one. This words end in the letters -eau, for example:
|Word||French plural||English plural|
|bureau||bureaux||bureaus|
|chateau||chateaux||chateaus|
|gateau||gateaux||gateaus|
|trousseau||trousseaux||trousseaus|
Words the Italian origin
Most native which have come into English native Italian type their plurals with an -s, as if they were English words. Because that example, the Italian plural of cappuccino is cappuccini, yet when words is provided in English, that plural kind is cappuccinos. Right here are some an ext examples:
|Word||Italian plural||English plural|
|espresso||espressi||espressos|
|pizza||pizze||pizzas|
|risotto||risotti||risottos|
|fresco||freschi||frescos or frescoes|
A notable exception to this is words paparazzo, which keeps the Italian plural type paparazzi in English.
There"s additionally a team of Italian words i m sorry have gone into English in their plural creates – these are commonly the name for various kinds the pasta. For example:
spaghetti; tagliatelle; tortellini; cannelloni; lasagne.
Although this words are already in their Italian plural forms, they deserve to take one -s to kind English plurals in specific contexts. For example:
They ordered three spaghettis and two cannellonis.
Here, the meaning is ‘a dish or serving of spaghetti’ quite than ‘a sort of pasta’.
Note that in british English, you have to spell lasagne v an e in ~ the end. In American English it"s spelled through an -a in ~ the end, i.e. lasagna (which is the Italian singular form, though this is rarely if ever used in Italian itself).
See more: Tác Dụng Đá Thạch Anh Màu Hồng " Giá Tốt Tháng 10, 2021, Hợp Mệnh Nào
Words that have come into English from international languages are well-known as loanwords. Several of these loanwords have occurred plural (or singular) develops in English that are concerned as grammatically incorrect since they go against the grammar the the initial language. | https://betterworld2016.org/most-nouns-form-their-plurals-by-adding/ |
The city of Denver has only one school where architecture faculty can find employment. The trends in Denver's architecture academic community can be evaluated by looking at the statistics and graphs below, which includes architecture training at the following levels:
Statistics
Professional Trends
Denver Vs. Colorado Architecture Employment
|Denver||3,300|
|Colorado||5,360|
Exactly 3,300 of the 5,360 architecture professionals employed in Colorado, work in Denver. Between 2006 and 2010, in Denver, there has been a 25% decline in the number of architecture professionals. As the employment for architecture professionals in Denver has decreased, overall employment in Denver has increased.
Denver Vs. Colorado Architecture employment growth
|7,030||7,270||7,570||6,420||5,360|
|4,410||4,560||4,880||4,010||3,300|
|2006||2007||2008||2009||2010|
- Grey: Colorado
- Dark Yellow: Denver
Architecture VS. All professions salaries in Denver
|$58,080||$58,877||$61,247||$65,297||$69,383|
|$43,990||$45,610||$47,150||$48,560||$49,440|
|2006||2007||2008||2009||2010|
- Light Blue: Architecture in Denver
- Dark Yellow: All Professions in Denver
In Denver, salaries for architecture professionals have increased. In 2010 an average salary of $69,383 per year was earned by architecture professionals in Denver. Four years earlier in 2006, the average salary for architecture professionals in Denver was $58,080 per year. The growth in the salary of architecture professionals in Denver is faster than the salary trend for all careers in the city.
Salary percentiles for Architecture professionals in Denver
|
|
10th percentile
|$40,440|
|
|
25th percentile
|$48,860|
|
|
50th percentile
|$65,307|
|
|
75th percentile
|$89,753|
|
|
90th percentile
|$105,953|
Architecture professionals in Denver earn a median salary of $65,307 per year. The 10% of architecture professionals in the lowest pay bracket earn less than $40,440 per year, while those in the highest pay bracket earn approximately $105,953 per year.
Average Salaries for Architecture professionals and related professions in Denver
|
|
Design
|$49,873|
|
|
Drafting
|$55,303|
|
|
Civil Engineering
|$60,147|
|
|
Architecture
|$69,383|
On average architecture professionals in Denver earn salaries that are higher than the salaries earned by other professionals in Denver.
Educational Trends
Architecture schools in Denver
Many of Denver's architecture professionals are graduates of the only accredited architecture school in the city.
Architecture Programs Offered In Denver
|
|
associate
|0|
|
|
bachelor
|0|
|
|
master
|3|
|
|
doctor
|1|
|
|
Certificate
|0|
|Total||4|
There are a total of 4 degree and certificate programs in architecture offered by Denver's architecture schools.
Student Completed Architecture Degrees In Denver
|
|
associate
|0|
|
|
bachelor
|0|
|
|
master
|185|
|
|
doctor
|2|
|
|
Certificate
|0|
|Total||187|
In 2010 approximately 187 students completed architecture courses. | https://www.educationnews.org/career-index/architecture-schools-in-denver-co/ |
There is a game called Labyrinth that consists of a square box with a platform inside. On the platform is a maze punctuated by little holes. The object is to move a ball from one end of the maze to the other without letting it fall into one of the holes. Knobs on the outside let you guide the ball by rotating the platform in any direction.
A simple game, but difficult in practice! The slightest miscalculation, and the ball goes down. If you lean the platform too far in one direction, you lose control. If you try to compensate, you lose control in the other direction. The only strategy that works is a patient shepherding of the ball along the path as you maintain a balance of movement and force in all directions.
I see in Labyrinth a metaphor for our navigation along the pathway of life. We travel from birth to death negotiating around the "holes" by continually balancing our approaches. We maintain steady progress forward by making countless life adjustments -first here, then there. Our actions offset each other in a dance that is sometimes delightful, often challenging.
The key is always balance. To achieve balance, we must know how to express all the energies available to us. Personal balance is never static. It comes from the ability to choose dynamically the option that will work in any given moment.
A tarot reading is a map of all the counterbalancing tendencies that are or could be operating in your life at one time. To read this map, you must understand the Law of Opposition - that any quality, once identified, implies its opposite. This is a basic principle of the material universe. The Fool discovers this principle at the very beginning of his journey when he meets the Magician and the High Priestess. These two show him that nothing can be defined in isolation, only as one pole of a balancing pair.
At the deepest level, opposition does not exist. There is just Oneness, but, in physical life, we perceive Oneness as broken up into countless different energies. These are the forces we navigate in our search for balance.
One way to discover your balance issues is by looking for two cards in a reading that oppose each other. One meaning of the Eight of Swords is restriction - being trapped in an oppressive or limiting situation. If you ponder this meaning for awhile, you realize that simply by acknowledging the idea of restriction, you imply the opposing idea of freedom - the breaking out of bonds and limitations. This quality is represented by the Four of Wands.
In a reading, these two cards could be showing you the importance of the restriction/freedom issue in your life. They define the extreme ends of a continuum of experience from which you choose the best balance point for yourself. There are three types of card pairs.
Certain cards form clear and obvious permanent opposites. The Eight of Swords and Four of Wands are this type of pair. The Magician and the High Priestess are another. The Magician represents action and conscious awareness; the High Priestess, nonaction and unconscious awareness.
You can create a pair between any two court cards or two Aces. These pairs reflect the balance patterns that emerge when you contrast two suits or ranks.
The King of Pentacles acts outwardly (King) in an enterprising, adept way based on his interest in the material world (Pentacles). The Queen of Cups has an inner focus (Queen) that is emotional and intuitive based on her concern with feelings (Cups).
In a reading, this pair could represent a conflict between two people - a can-do type who wants to get the job done, and a dreamer who first wants to see how everyone feels. This pair could also represent a dual approach within you - perhaps a need to focus on worldly concerns vs. a desire to concentrate on the spiritual. There are many possibilities, all based on the dynamic between these two styles. Check the court card and suit pair charts for some ideas on how the suits and ranks interact. | https://www.tarotjournal.us/learning/card-pairs.html |
A Look at Basic Service Design
The five previous posts in this series have all been mostly concerned with physical spaces. Now let’s take a quick look at basic service design.
The Design Thinking For Libraries website states:
|
|
Any kind of service can be transformed and made better. Let’s take one example: the core service of identifying, finding, and checking out a book or other resource.
How do your users identify an item they want to borrow?
- Word of mouth recommendation
- School booklist
- Saw an ad on the media
- Browsing
- Reader’s advisory
- Online catalog search
Imagine each of these possibilities from the patron’s AND the staff’s point of view. Use personas and think about what the customer wants. Are they a grab-it-and-go kind of person? Or do they want a chat and personalized service? Do they need an in-depth reference interview to determine what they’re really looking for? Are they a digital native who likes chat-based reference, or do they want to get up-close and personal?
Once the item is located, what check-out options are available? Is your e-book and e-audio service user-friendly? Can a person in a hurry grab their DVD from the hold shelf, use the nearby self-check station, and be on their way? What happens when the book they want isn’t on the shelf – or in the collection at all?
All of these scenarios require a different approach and series of steps to implement. In public libraries, we are blessed and cursed with the full gamut of personalities, ages, and skill levels. The ability to read a patron and tailor services to their needs is something that most people are not born with, it takes practice.
A few simple places to start:
- Ask how much time the user has up front – this can help set the tone of the interaction
- Ask the user if s/he wants you to look something up for them, or would rather you show them how to use search techniques themselves
- If they want a particular item, or books on a particular subject, offer to walk them to the area in the shelves if at all possible
- If self-check is a new service, make sure a staff person is nearby at all times to help newbies through the process, and always offer at least one traditional checkout station for those who prefer it
Try to remember that most people using the library are not well-versed in classification systems, and don’t keep detailed knowledge of your materials and procedures in their head. Things that you can do in your sleep are brand new concepts to many. The point is to make collections and services accessible. That’s what libraries are for. | http://publiclibrariesonline.org/2017/01/a-look-at-basic-service-design/ |
Due to COVID-19, this place may be closed or inaccessible.
Parking lot day/night
München, 26 Fritz-Schäffer-Straße
München, 26 Fritz-Schäffer-Straße
Parking on parallel track at the national, not too noisy even on working days in the morning. Very quiet at night. Shopping center and metro about 500m.
Id : 113917 - Créé le 13 03 2019 par dl3el
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Information about Le Fanal Hotel
This hotel and restaurant sits just 4 km from the town centre of Argelès-sur-Mer, 500 metres from the port and 50 metres from the beach. Free public parking is available nearby. Le Fanal offers air-conditioned, en suite rooms with flat-screen TV. The Double Room with Terrace offers a furnished terrace with a sea view. The restaurant serves local and regional cuisine with a number of seafood dishes, wines and desserts. The on-site bar has baby-foot and a pool table available for a supplement. Wi-Fi internet access is free of charge throughout the entire hotel and the hotel provides guests access to a computer with internet and printing facilities.
Please inform Le Fanal in advance of your expected arrival time. You can use the Special Requests box when booking, or contact the property directly with the contact details provided in your confirmation. If you plan on arriving after 20:00, please notify the property in advance. Contacts can be found on the booking confirmation.
Services of Le Fanal Hotel
- Beachfront
- Physical distancing in dining areas
- Air conditioning
- Terrace
- Board games/puzzles
- Water sport facilities on site
- Shared stationery such as printed menus, magazines, pens, and paper removed
- Kid meals
- Smoke alarms
- Breakfast in the room
- Express check-in/check-out
- Internet services
- Fax/photocopying
- Bar
- Physical distancing rules followed
- WiFi
- Non-smoking rooms
- Snack bar
- Breakfast takeaway containers
- Cashless payment available
- Guest accommodation is disinfected between stays
- First aid kit available
- WiFi available in all areas
- Linens, towels and laundry washed in accordance with local authority guidelines
- Concierge service
- CCTV in common areas
- Use of cleaning chemicals that are effective against Coronavirus
- Outdoor furniture
- 24-hour security
- Heating
- Billiards
- Security alarm
- Wine/champagne
- Daily housekeeping
- Free WiFi
- Walking tours
- Coffee house on site
- Safety deposit box
- Beach
- Restaurant
- Family rooms
- Luggage storage
- Staff follow all safety protocols as directed by local authorities
- Fire extinguishers
- Sun terrace
- Soundproof rooms
- All plates, cutlery, glasses and other tableware have been sanitized
- Hand sanitizer in guest accommodation and key areas
- Non-smoking throughout
- Sun loungers or beach chairs
Address
50 Avenue Torre d'en Sorra
Hotel badges
- Beach Hotel
Similar hotels to Le Fanal Hotel
Near Anse du Portell
Near Parc Venitien
Frequently asked questions
Why should I buy my travel on lastminute.com?We sell over 284,000 hotel bookings per year online to our customers since 1998, being one of the firsts in the sector.
What services can I add to my booking?During the booking process you will be offered all the services you can add:
- Our support packs
- Our service Check-in NoProblem
- Additional luggage
- Car rental
- Parking at the airport
- Transfers
At what time can I have my room? And what time do I have to leave?Check-in and check-out times vary according to the property. However, the schedules are usually as follows:
- Hours of arrival ( check-in ) from 14:00.
- Departure times ( check-out ) at 11:00.
What is the price match guarantee?If you book a hotel or city break (Flight + Hotel/ Eurostar + Hotel) on lastminute.com and you find the same product or package for less on another website within 24 hours of booking, we'll give you the difference! Subject to terms & conditions. | https://www.lastminute.com/hotels/france/argeles-sur-mer/le-fanal-hotel |
Popcorn is one of the things that popup (pun unintended) in many folk’s minds when they go to see a movie at the cinema. For a long time, it has been the typical food served at cinemas because it is easy to prepare, appealing, and not messy.
However, what happens when you actually want to see a movie in your home and still want to enjoy a popcorn snack along with it? This post details an easy honey popcorn recipe that you can try out in the comfort of your home.
READ ALSO: #NIGERIAN RECIPE: How To Make Porridge Yam With Vegetables
Contrary to popular belief, Popcorn is actually one of the easiest snacks to prepare.
Find the honey popcorn recipe below:
Ingredients:
Unpopped Corn Kernels
Vegetable Oil
Honey
Method:
Step 1:
Pour about 4 tablespoons vegetable oil into a pot – just enough to cover the whole bottom of the pot – and leave it heat up for about 2 minutes minute. Ensure the heat is minimal.
Step 2:
Add about 5 to 6 tablespoon corn kernels into the pot and stir until virtually all the corns are coated with the oil. Cover the pot and allow the heat do its magic.
Step 3:
Shake the pot from time to time to prevent the corn kernels from burning and watch out for the popping sound.
Step 4:
Once you start hearing a popping sound from the pot, it means the popcorn will soon be done.
Step 5:
Keep shaking the pot occasionally to prevent burning and wait till you can’t hear any popping sound anymore, which signifies that all the kernels have popped.
Step 6.
Allow the popped corns to cool down for about five minutes before you add the honey.
Step 7:
Add about 4 tablespoons of honey to the popped corn,shake the mixture.
Step 8:
Transfer your popcorn into a serving dish and treat yourself to a nice movie as you munch it.
If you liked this popcorn recipe and you’d like to see another beautiful recipe, drop your suggestions in the comment section below. | https://reterdeen.com/learn-how-to-make-sweet-honey-popcorn-with-this-super-easy-recipe/ |
Groundskeepers maintain private and publicly owned property. This includes mowing lawns, pruning trees and shrubs, planting flowers and gardens, fertilizing and watering green spaces, and clearing property grounds of debris. Groundskeepers have a high school diploma or equivalent, a valid driver’s license plus related experience. To work as a groundskeeper you need to be able to use hand and power tools, lift heavy objects, crouch, climb, stand for long periods of time, follow instructions and be available for overtime.
A good resume is well-written and concise. It should be neat and easy to read, listing previous experience in a logical order.
Our resume samples will provide you with multiple examples of what you can include when writing your resume.
Contents
The Best Groundskeeper Resume Samples
These are some examples of accomplishments we have handpicked from real Groundskeeper resumes for your reference.
Groundskeeper
- Clean and maintain parks, playgrounds, and surrounding areas to provide a safe environment.
- Provided park patrons with directions and answer questions regarding parks activities.
- Checked playground equipment for damage; report needed repairs to supervisor.
- Flag hazardous material, sweep, rake, and collect leaves and debris for pick up.
- Inspected, repaired, and maintained all vehicles and equipment used by the maintenance department.
Groundskeeper
- Responsible for daily upkeep of property, buildings, and grounds which include, cleaning and removal of trash and bulk garbage.
- Responsible for the care, maintenance and inventory of all supplies and equipment owned by the property and/or the management company.
- Responsible for removing downed branches as well as shrubs and trees for safety of the guests/pedestrians and buildings.
- Safe and proper use of commercial motorized power tools, such as back pack blowers, lawn mowers, weed whackers.
- Researched, taught, acquired knowledge of equipment to install and maintain in the repair shop.
Groundskeeper
- Performing grounds keeping duties in accordance with state and local government regulations.
- Worked within a team environment to ensure the timely completion of assigned projects and tasks.
- Communicated directly with supervisory and management staff to report arising issues and brainstorm action plans for resolution.
- Assisted with orientation and training of any new employees to the work site.
- Managed a crew of 14 and the grounds of a local college campus, providing permanent landscaping and maintenance services.
Groundskeeper
- Manually pick-up of litter and debris from apartment complex, and deposit refuse in on-site central dumpster.
- Maintain appearance of all parking, roadway, swimming pool, and patio areas on property.
- Clean interior of apartment buildings and leasing office including all surfaces, floors, furniture and restrooms.
- Maintained a great eye for any and all maintenance needs for the maintenance garage/shop as well as assigned areas around campus.
- Maintained and repaired lawns, walkways, driveways, and fences.
Groundskeeper
- Operate zero turn mowers, walk behind mowers, tractors, trencher, vehicles and equipment.
- Utilized a variety of hand and power tools in park landscape maintenance work.
- Operate a weed eater, mower, backpack blower and loader or other equipment as necessary.
- Initiated city-wide tree planting program with volunteer help built a website to manage volunteers.
- Designed and managed a landscape project for the State of South Dakota Department of Transportation; designed and constructed a 40-foot arbor over a parking lot.
Groundskeeper
- Maintain park upkeep and cleanliness, ensuring all public areas are free of hazardous material and debris.
- Report any damaged equipment in or around park facilities, conducting routine checks and inspection throughout park grounds.
- Performing pruning and weed whacking task ensuring that all dead branches and leaf’s are removed daily.
- Designed, installed, and maintained a city-owned ornamental garden located in downtown Sioux Falls, SD; trained new horticulturists.
- Responsible for the management of several commercial properties featuring water features, fountains, lakefront landscaping, and hardscape.
Groundskeeper
- Clean parks, playgrounds, and surrounding areas and sweep, rake, and collect leaves and debris.
- Paint and remove graffiti from benches, walls, playground equipment, and comfort stations.
- Prepared debris for removal; flag hazardous material for pick up and report all safety hazards directly to supervisor.
- Invested in land development by purchasing gift cards to purchase tools necessary to develop acreage into usable spaces; increased value three-fold after seven months.
- Maintained a $20 million dollar, 42-hectare facility including turf, irrigation, and irrigation systems, trees and plants, buildings, fencing, decorative infrastructure, and grounds.
Groundskeeper
- Performed general cleaning and upkeep of housing parks, parking lots, housing office (ex; sweeping, mopping, dusting, shrubbery/ hedge trimming, etc.).
- Ensure that housing grounds were kept clean, safe, and hazard-free for children, elderly, etc.
- Assisted in floor moves, merchandising, display maintenance, and housekeeping.
- Worked independently to plan work schedule.
- Installed over 500 meters of fencing; tracked expenses for personal equipment and materials; completed purchase requisitions for additional equipment.
Groundskeeper
- Maintain the athletic fields, greens, parks and other grounds by cutting grass, watering, fertilizing, and checking for disease or insect damage.
- Regulate valves, check for leaks, and adjust pressure hands and water as needed.
- Operate a variety of standard power tools and equipment during grounds maintenance and repair.
- Carried out assigned duties and responsibilities in the planning, organization, maintenance, and repair of grounds.
- Provided technical support to the business by ensuring the safety of the facility by inspecting grounds and providing preventative maintenance tasks.
Groundskeeper
- Utilized various machinery such as lawnmowers and weed eaters, in addition to hand tools such as hedgers, trimmers, shovels and rakes.
- Attended to broken headstones and deal with any issues of vandalism.
- Removal of dead flowers that were left after a funeral and take away plant containers that held flowers at a grave site.
- As groundskeeper, I was in charge of correcting anything that’s unsightly in order to give the visitors a feeling of peace.
- Cared for the campus grounds, maintaining vegetation, and pruning, transplanting, and fertilizing trees, shrubs, and flowers.
Groundskeeper
- Performed operator maintenance on grounds equipment and vehicles as needed.
- Assisted in areas outside of normal duties such as washing sidewalks, mulching flowerbeds, pest control, and watering.
- Provided training and supervision to onboarding employees to ensure all duties are performed in a safe and professional manner.
- Ensured the safety of both students and faculty by properly maintaining the campus grounds.
- Trained maintenance personnel in standard maintenance practices.
Groundskeeper
- Performed different landscaping and maintenance jobs on the city’s parks and public areas.
- Maintain all city property such as landscaping, mowing, trimming trees, edging and trash pickup throughout the city.
- Load equipment into assigned company vehicle and drove crew members to assigned work location.
- Maintained the front and back yards, landscaping, walkways, and roads at an apartment complex.
- Started and managed a crew of 5 to maintain over 20 acres of land which included; mowing grass, deadheading shrubs, maintaining the lawn and trees for maintenance.
Wrap Up
You need to make sure your resume stands out amongst the other candidates. It is the first impression that employers have of your work experience and skills. Use the samples above to put together a resume that best suits your needs and helps you get the job you want. | https://realresumetemplate.com/groundskeeper-resume-sample/ |
Last weekend I got a little literary on myself, and before I went to work on Saturday, I walked down to Hart House and went to the Stories That Bind Festival, a free event celebrating multicultural writing, dancing, and performance art.
I got there in time to hear Priscila Uppal, and Dae Tong Huh read some of their fiction and poetry, and to hear Al Moritz read a short story. It was refreshing to sit down amidst a crowd of people and listen to the authors read, but to not have to jot down notes at top speed. A bit like being read bedtime stories as a kid: totally recreational, and all you need to do is sit, relax, and ingest.
It’s been a long time since I’ve gone to a literary reading, and it sort of reminded me of Trampoline Hall, a monthly event held both in Toronto and New York where non-professionals give speeches about specific topics. Some past speeches that I’ve seen included topics like War Craft, Amazonian Exploration Mishaps, and Fungus. They’re a real lark, and surprisingly informative too.
Between the readings at Stories That Bind, several groups of dancers of all ages performed a number of colourful Korean Ham Mam dances. One of the dances involved about a dozen girls, whose dresses were adorned with sleeves that flowed down in streams of silk to about the bottom of their dresses, instead of ending at the wrist. When any one of them moved their arms, the sleeves replicated colourful wings or flags, flowing around the dancer. It made quiet the impression when they all moved in syncronocity. In another set the young dancers, all in layers of dyed silks, drummed along with the music while dancing around.
The event that got the most attention was a magic show put on by Jason McConnie. A lively crowd of both kids and adults sat around the room while he mysteriously put into play a number of tricks involving knives, boxes, and human heads, and all other sorts of fun.
Some of the other performances between readings included Axe Caporeia, Slovenian folk dance, two storytellers, and some music by the Sandy MacIntyre Trio.
I learned about The Stories That Bind Festival from the Open Book Toronto website, an organization that features and publicizes Toronto and Canadian writers. The idea behind Open Book Toronto seems to be to keep Toronto’s literary scene accessible through the promotion of readings and literary events, which can be found here. It puts a strong emphasis on independent authors and publishers, and on showing a wide range of authors. It also has a new writer-in-residence, Linda Rogers, who has a blog of her own (oh wow!), where you can ask questions pertaining to writing and get back personal responses. Events aren’t only literary, either. Although you find a lot about various reading series and book launches, the site also includes dancing nights, film festival showings, and art exhibits. | https://blogs.studentlife.utoronto.ca/lifeatuoft/2008/12/01/636/ |
Welcome back to Medieval Monday! Our “First Kiss” theme continues, and this week, I’m featuring Daryl Devoré’s The Last Dragon. Such a cool cover!
If you’re following my excerpt from Return of the Raven, you can find Snippet #4 on Daryl’s blog. Remember, you’ll find links to all the participating authors’ snippets at Medieval Romance Lovers on Facebook. (#MedMonSpring21)
Now, let’s enjoy Daryl’s fourth snippet:
“Do ye…” Derry’s words stuck in her throat. What if her powers scared Hawkyns? No. He did not scare easily. He fought and slayed dragons. But, what if her powers caused a question within him? No. He showed no sign of that. She’d healed him. He said he enjoyed being with her. He spoke true words.
Stop being a foolish one.
Hawkyns pulled his horse to a stop. “Do I what?”
She lowered her eyes and refused to meet his gaze. The gaze that already gave her the answer to her unasked question. And still she was too afraid to ask. Doubt clouded her senses.
See last week’s snippet on Sherry Ewin’s blog – https://www.sherryewing.com/blog
Follow along next week on Jenna Jaxon’s blog – https://jennajaxon.wordpress.com/
More about The Last Dragon:
What do dragons, knights and romance have in common? Grab a copy of multi-published author Daryl Devore’s medieval fantasy romance – The Last Dragon and discover the answer.
A sorcerer craving dominance merged with a dragon, the power overwhelmed him causing him to split into three dragons. Demora ruled thought, but was lost in time. Yidithe offered protection, shining like the light of the sun. Ayrradex craved chaos, revelling in destroying souls.
Many knights died, attempting to slay the devil beast. One knight, Prince Hawkyns, did not fear death. He’d lost everything. Away on a mission when Ayrradex attacked his father’s kingdom, Penrythe, Hawkyns returned to find his noble father – feeble and defeated. His wise mother – crazed. His beautiful wife and unborn child – dead. Only a pile of ashes remained for him to bury. He knelt before his King and vowed to slay the devil-beast or be slain.
Derry was born with powers that terrified her parents. They delivered her to a nunnery to be raised in secret. Jathe, a wise sorceress, discovered the young girl and trained her to one day use the secret hidden in her soul.
Legends spoken around campfires hinted the sole way to destroy Ayrradex was when the hearts of a knight and a golden dragon became one. But after a vicious battle with Ayrradex, the golden dragon was thought to be dead.
Can Prince Hawkyns’s bravery and Derry’s powers end the reign of the devil-beast’s terror?
Buy the book: | https://judithmarshallauthor.com/2021/03/01/medieval-monday-the-last-dragon/?replytocom=12341 |
Last night, like every night before it these last few weeks, was one of the most glorious of my life. It was midnight, and I was walking through the woods, alone. The trees blocked most of the moonlight and starlight, but above and below and all around me, I was surrounded by fireflies.
All at once, I felt secluded in nature, and like I was scuba diving, and like I was riding Space Mountain, and like I was on some kind of drug that just makes you love everything around more than you thought possible.
One of the most important lessons I've learned as a dog owner (other than, "Keep the Christmas truffles on the highest possible shelf," "Don't assume they won't knowingly jump off a balcony chasing a squirrel," and, "Leave the tent door unzipped or else!") is that many of the health changes we assume are natural parts of aging... are actually symptoms of something totally treatable.
Social Distancing is the MOST IMPORTANT TIME EVER to Perfect *This* Social Skill
3/31/2020
When people ask me what my blog is about, I want to tell them, "Playfulness." Playfulness is why I started this blog. It's on my About page; it's discussed on some of my most popular posts...
Yet one recurring theme has been assertiveness. Assertiveness seems at odds with playfulness... but, in fact, I've found assertiveness to be a crucial skill that enables my playfulness.
And it's probably one of the most important possible social skills you can learn and use during the current lockdown/quarantine/social distancing protocols.
Your Best Shot at Finding Mr. Right... May Be Saying "Yes" to a Dance With Mr. Wrong
1/23/2020
I recently had the good fortune of meeting Rich Gosse, chairman of The Society of Single Professionals and author of The Donald Trump Syndrome: Why Women Choose the Wrong Men to Love.
He told me something none of you millennials are going to believe:
"Even though I founded the second ever online dating site back in the 1990s, I still think meeting face-to-face is best.”
And I agree.
You know I have a thick skin -- I love making fun of virtue signaling, regressive feminism, whiny little babies, and social justice warriors.
But I canNOT stand the disgusting rape song that is "Baby, It's Cold Outside." When it comes on, I literally wait outside until the song is over.
Last Saturday, as I was writing my review of Broadway by the Bay's Into the Woods, an episode of Malcolm Gladwell's Revisionist History began playing. Within seconds, I was able to summarize the entire episode in a few sentences:
"They're going to say that Olympic silver medalists feel worse than bronze medalists, because silver medalists upward social compare ('I could have been the best in the world, but I'm not,') and bronze medalists downward social compare ('I'm so happy I got a medal!')."
Let me start by saying that I love you. I love that you want to be there for me. I love that you're showing concern for my health and recovery. It means so much.
But can I just, real quick, tell you what my mornings have been like since my injury?
"All disease," some antivaxxing dumbass who, apparently, is writing a book about his amazing perspective and incredible life experiences, "comes from a toxic mindset and bad lifestyle choices."
"Right," I replied. "And the woman who runs marathons and does yoga every day and eats kale who still gets cancer...?"
"There is something wrong in her mind. Maybe she has a bad marriage or something."
Yesterday, I wrote about how there's a difference between helping a depressed friend and enabling an abuser. My intention was to inform those whose friends suffer from mental illness to be compassionate... but remember to think critically about your actions and the effects they may have on your friend and his/her partner.
Today, I'm writing a quick reminder to those who are, or may be, affected by mental illness:
Your partner is not your emotional slave.
There is a difference between helping a depressed friend and enabling an abuser.
1/12/2019
My background is in psychology -- but not abnormal or relationship psychology. (I studied adult playfulness!) I want to acknowledge that before I start, because this is far from my area of expertise.
But I just saw some of THE MOST FUCKED UP SHIT on Facebook, and it prompted an important realization:
There is a difference between helping a depressed friend and enabling an abuser.
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About the Author
Eva is a content specialist with a passion for play, travel... and a little bit of girl power. Read more >
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A tropical climbing or trailing vine that doesn't require much attention.
Botanical name: Syngonium Neon Robusta
Common name: /
Dimensions*
You can find the dimensions in the title above.
∅ = diameter plastic pot
h = height plant [starting from the bottom]
Care instructions
- Light: Bright filtered light with no direct sun.
- Watering: Water regularly, but let the soil dry out in between drinks. Provide proper drainage. The Syngonium wendlandii plant will not tolerate wet soil at all. At the same time, under-watering will cause the lower leaves to dry out and turn brown.
- Temperature: Min. 15 °C.
- Humidity: Spray regularly to wipe dust from the leaves.
- Extra care info: This plant is a great air purifier.
Shipping info
This item can be delivered in Brussels by bike or collected in-store.
See shipping details. Free delivery from €100.
Plants & pots are sold separately.
The actual plant may vary in shape or appearance from the one shown in the picture.
*When looking for a pot, always add at least 2 cm to the size of the plastic plant pot.
If your plastic pot has a diameter of 10 cm or smaller, you can use the same diameter for the pot. | https://webshop.gruun.brussels/en/syngonium-neon-robusta-7-h15.html |
The branch of theology that studies what the Bible teaches about humanity.
- One key biblical passage for the study of anthropology:
Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.” So God created man in his own image, in the image of God he created him; male and female he created them. And God blessed them. And God said to them, “Be fruitful and multiply and fill the earth and subdue it, and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth.” (Genesis 1:26-28 ESV)
- From the Belgic Confession:
- From Systematic Theology by Louis Berkhof, The Origin of Man:
Chapter 14 We believe that God created man from the dust of the earth and made and formed him in his image and likeness— good, just, and holy; able by his own will to conform in all things to the will of God.
But when he was in honor he did not understand it and did not recognize his excellence. But he subjected himself willingly to sin and consequently to death and the curse, lending his ear to the word of the devil.
For he transgressed the commandment of life, which he had received, and by his sin he separated himself from God, who was his true life, having corrupted his entire nature.
So he made himself guilty and subject to physical and spiritual death, having become wicked, perverse, and corrupt in all his ways. He lost all his excellent gifts which he had received from God, and he retained none of them except for small traces which are enough to make him inexcusable.
Moreover, all the light in us is turned to darkness, as the Scripture teaches us: “The light shone in the darkness, and the darkness did not receive it.” Here John calls men “darkness.”
Therefore we reject everything taught to the contrary concerning man’s free will, since man is nothing but the slave of sin and cannot do a thing unless it is “given him from heaven.”
For who can boast of being able to do anything good by himself, since Christ says, “No one can come to me unless my Father who sent me draws him”?
Who can glory in his own will when he understands that “the mind of the flesh is enmity against God”? Who can speak of his own knowledge in view of the fact that “the natural man does not understand the things of the Spirit of God”?
In short, who can produce a single thought, since he knows that we are “not able to think a thing” about ourselves, by ourselves, but that “our ability is from God”?
And therefore, what the apostle says ought rightly to stand fixed and firm: “God works within us both to will and to do according to his good pleasure.”
For there is no understanding nor will conforming to God’s understanding and will apart from Christ’s involvement, as he teaches us when he says, “Without me you can do nothing.”
1. MAN’S CREATION WAS PRECEDED BY A SOLEMN DIVINE COUNSEL. Before the inspired writer records the creation of man, he leads us back, as it were, into the council of God, acquainting us with the divine decree in the words, “Let us make man in our image, after our likeness,” Gen. 1:26. The Church has generally interpreted the plural “us” on the basis of the trinitarian existence of God. Some scholars, however, regard it as a plural of majesty; others, as a plural of communication, in which God includes the angels with Himself; and still others, as a plural of self-exhortation. Of these three suggestions the first is very unlikely, since the plural of majesty originated at a much later date; the second is impossible, because it would imply that the angels were co-creators with God, and that man is also created in the image of the angels, which is an un-Scriptural idea; and the third is an entirely gratuitous assumption, for which no reason can be assigned. Why should such a self-exhortation be in the plural, except for the reason that there is a plurality in God.
2. THE CREATION OF MAN WAS IN THE STRICTEST SENSE OF THE WORD AN IMMEDIATE ACT OF GOD. Some of the expressions used in the narrative preceding that of the creation of man indicate mediate creation in some sense of the word. Notice the following expressions: “And God said, Let the earth put forth grass, herbs, yielding seed, and fruit-trees bearing fruit after their kind” — “Let the waters swarm with swarms of living creatures” … and, “Let the earth bring forth living creatures after their kind”; and compare these with the simple statement, “And God created man.” Whatever indication of mediacy in the work of creation is contained in the former expressions, is entirely wanting in the latter. Evidently the work of God in the creation of man was not mediated in any sense of the word. He did make use of pre-existent material in forming the body of man, but even this was excluded in the creation of the soul.
3. IN DISTINCTION FROM THE LOWER CREATURES MAN WAS CREATED AFTER A DIVINE TYPE. With respect to fishes, birds, and beasts we read that God created them after their kind, that is, on a typical form of their own. Man, however, was not so created and much less after the type of an inferior creature. With respect to him God said, “Let us make man in our image, after our likeness.” We shall see what this implies, when we discuss the original condition of man, and merely call attention to it here, in order to bring out the fact that in the narrative of creation the creation of man stands out as something distinctive.
4. THE TWO DIFFERENT ELEMENTS OF HUMAN NATURE ARE CLEARLY DISTINGUISHED. In Gen. 2:7 a clear distinction is made between the origin of the body and that of the soul. The body was formed out of the dust of the ground; in the production of it God made use of pre-existing material. In the creation of the soul, however, there was no fashioning of pre-existing materials, but the production of a new substance. The soul of man was a new production of God in the strict sense of the word. Jehovah “breathed into his (man’s) nostrils the breath of life; and man became a living soul.” In these simple words the twofold nature of man is clearly asserted, and their teaching is corroborated by other passages of Scripture, such as, Eccl. 12:7; Matt. 10:28; Luke 8:55; II Cor. 5:1-8; Phil. 1:22-24; Heb. 12:9. The two elements are the body and the breath or spirit of life breathed into it by God, and by the combination of the two man became “a living soul,” which means in this connection simply “a living being.”
5. MAN IS AT ONCE PLACED IN AN EXALTED POSITION. Man is represented as standing at the apex of all the created orders. He is crowned as king of the lower creation, and is given dominion over all the inferior creatures. As such it was his duty and privilege to make all nature and all the created beings that were placed under his rule, subservient to his will and purpose, in order that he and his whole glorious dominion might magnify the almighty Creator and Lord of the universe, Gen. 1:28; Ps. 8:4-9.
Learn more:
- GotQuestions.org: What is Christian Anthropology?
- Nathan Pitchford: Knowing Ourselves
- Stanford Murrell: Anthropology: The Study of Man
- James White: The Doctrine of Man
- Bruce Ware: Humanity and Sin
- Greg Herrick: Anthropology and Harmartiology: Man and Sin
- S. Lewis Johnson: Lectures on Anthropology (audio)
Related terms:
- cultural mandate
- fall (of man)
- federal head
- free agency
- image of God
- imago Dei
- inability
- noetic effects of sin
- original sin
- sensus divinitatus
- sin
- total depravity
- vocation
Filed under Theological Categories
Do you have a a theological term you’d like to see featured here as a Theological Term of the Week? If you email it to me, I’ll seriously consider using it, giving you credit for the suggestion and linking back to your blog when I do.
Clicking on Theological Terms in the navigation bar above will take you to a list of all the previous theological terms in alphabetical order. | http://www.rebecca-writes.com/rebeccawrites/2015/1/20/theological-term-of-the-week.html |
By now, the Internet has reached basically all corners of the Earth — and not just its surface. Being online onboard an airplane is already old hat, and even the International Space Station has a connection to the Web. Space exploration agencies are getting ready to move on and get other planets in our solar system connected. The space Web is not all about work, either; it helps people far away from mother Earth keep in touch with their homes. This post is about how it works now and how it will develop.
WWW on the ISS
The International Space Station crew accessed the Web for the first time back in 2010. The access service was provided by NASA. The astronauts use a satellite link to connect to a computer in Houston in remote desktop mode, and get online from there. It is safer that way: even if a malicious link or file is opened by an ISS crew member, only the ground computer will be compromised.
NASA astronaut T.J. Creamer honored the arrival of the Web on the ISS by posting the first ever unassisted tweet from space:
Hello Twitterverse! We r now LIVE tweeting from the International Space Station — the 1st live tweet from Space! 🙂 More soon, send your ?s
— TJ Creamer (@Astro_TJ) January 22, 2010
Russian space Internet
It seems the ISS will soon have more than one Internet provider: Russia plans on getting its segment of the station hooked up soon enough, too. The task will be implemented using a network of Luch relay satellites, which is currently undergoing an upgrade.
Last year, cosmonauts Alexander Misurkin and Anton Shkaplerov made an upgrade to the ISS antenna so it could receive large volumes of satellite data, while at the same time setting a Russian record for extravehicular work duration — 8 hours and 12 minutes.
According to Sergey Krikalev, cosmonaut and Roscosmos spokesperson, the new equipment has already been tested, so the ISS will soon get online through Luch satellites.
Satellite hitches
Of course, the Internet they have on the ISS is not nearly as fast and delay-free as what you have at home. Satellite communications have advantages over wired technologies — such as being available in places where cables cannot be used, obviously — but also challenges.
High ping, low speed
Even though the ISS is orbiting at an elevation of some 400 km (about 250 miles), the data covers a much longer distance to reach Earth. First, the ISS sends the signal upward, to a relay satellite flying as high as 35,786 km (22,000 miles) above the ground. Only from there can it go downward to a ground space communication station.
So, the total distance covered by data from onboard the ISS and the response signal sent back to it is just short of 150,000 kilometers, or close to 100,000 miles. That takes time. According to a NASA employee, data exchange with the ISS has a transmission latency of about half a second — about 20 times that of the average cable connection.
In addition to that, astronauts need the satellite link available to them for more than just the Web. They also use it to stream lots of scientific data and video content (which their colleagues on the ground broadcast to the Internet for users to follow life onboard the ISS and the views from it) to the mission control center. The same satellite link enables audio and video conferencing with Earth for the ISS residents.
As a result, only a small fraction of the bandwidth can be used for tweets and browsing. Moreover, although the satellite’s downlink is as broad as 300 mbps, the uplink is limited to 25 mbps. In terms of speed, the connection available to the ISS is comparable to that of ancient modems.
On top of that, the station leaves the satellite coverage zone at intervals. For every 1.5 hours it takes the ISS to circle Earth, it may have no coverage at all for up to 15 minutes.
Limited fuel
Satellites maintain continuous contact with Earth, going around exactly as fast as our planet itself rotates to remain over the same spot at all times. Yet the orbit has to be adjusted from time to time, otherwise satellites risk falling out of it and becoming unreachable. Maneuvers are accomplished using propellant. But satellites are not cars or planes, either — they cannot simply fly back to Earth for refueling.
To solve this problem, companies around the globe are searching for ways to refuel satellites directly in space. Systems that aim to deliver propellant into orbit are being tested in the US segment of the ISS, by the Canadian MDA Corporation, and by the British–Israeli Effective Space Solutions. And the European Space Agency (ESA) has developed an engine that can use molecules of air from the upper layers of Earth’s atmosphere for fuel.
Electric power shortage
The propellant problem can be solved in part using electricity, which can reduce fuel consumption and is renewable through solar panels. Electricity is also required to communicate with Earth and other spacecraft. But satellites are shielded from the Sun by our planet some of the time, so they work on batteries, which are of limited capacity.
Russian scientists have proposed a solution that involves several dozen orbiting robots that would recharge satellites that have run out of power. The robots will draw electricity from both solar emission and radio transmissions from Earth. The technology can extend spacecraft life spans 1.5 times, while also making them lighter by dumping excess batteries and solar panels.
Overheating
Space repeaters or relay satellites, which always work at full capacity, face the problem of overheating. Orbit space being airless, fans used to cool computers on the ground would be useless. So even though it is much colder out in space than on the planet’s surface, heat dissipation is actually a much more challenging problem there.
Spacecraft use large radiators — units transforming heat into radiated emission — to keep from overheating. The more powerful the satellite, the larger the radiator it needs for cooling. Thus, to provide cooling for the new-generation 25 kW communication satellites, researchers created a radiator — a large one, 4 × 1 m.
Cosmic rays
Another problem is cosmic rays, which disrupt everything electronic. Here on the ground, protection comes from the magnetic field and atmosphere of the planet. But no such protection exists in orbit, so the electronic components used in spacecraft are built to withstand radiation — yet radiation continues to be a key problem for satellites.
According to cosmonaut Pavel Vinogradov, laptops go out of service very quickly on the ISS, even though the ISS modules are protected quite well. Cameras suffer, too: images quickly get strewn with dead pixels. In addition, radiation grossly interferes with signals transmitted by satellites and may damage individual segments of memory in onboard devices.
Radiation versus cryptography
Radiation is one of the reasons information between Earth and many spacecraft is exchanged without encryption. Should radiation damage the storage area used for the encryption key, communication will be disrupted.
The problem is not so acute for the relay satellites through which the ISS crew gets online — those are more or less protected. That, however, is not the case with most of the other spacecraft in Earth’s orbit.
Lack of encryption is a sore subject, because satellites, just like ground computers, are potential targets for attack. The European Space Agency recently launched an experiment meant to remedy the situation. Researchers are testing two approaches to maintaining robust encrypted communication with satellites at a reasonable price.
- A secondary fallback base key wired into the hardware. Should the main key be compromised, the system will generate a new one based on the secondary key. However, only a limited number of such keys can be created.
- A number of identical microprocessor cores. If one core fails, another one can step in at any moment while the faulty core reloads its configuration, thereby repairing itself.
The device to test these methods was flown to the ISS in April, 2019, and it is expected to run continuously for at least a year. It is based on a standard Raspberry Pi Zero minicomputer, which makes it a relatively low-cost solution.
Communication with satellites cannot be expected to become safe in the years to come, however; there is no easy way to upgrade the systems already launched into space.
Martian Internet
While some researchers are busy improving satellite protection and bandwidth, others are thinking about creating an interplanetary Internet. In many respects, the problems to be solved for that are similar to those faced by the ISS crew, although on a completely different scale.
For example, it takes 3 to 22 minutes for a signal to reach Mars, depending on the red planet’s position relative to Earth. That’s not nearly as good as the half-second delay on the ISS. In addition to that, direct communication between Mars and Earth is interrupted for two weeks every two years, when the Sun is positioned between the two planets and blocks signals.
Space Internet also has some unique features. All nodes of the network are in constant motion. With terrestrial Internet technologies useless in such conditions, scientists develop alternative arrangements to enable communication between Earth, its moon, Mars, and other planets. These may rely on:
- Data transfer protocols, such as NASA’s Delay/Disruption Tolerant Networking (DTN) data transfer solution, made to cope with long delays, substantially high error rates, and frequent inaccessibility of nodes. According to this model, intermediate nodes (e.g., satellites) store data until they are able to transmit it to the next ones.
- Abandoning current radio-based satellite communications in favor of optical (e.g., laser) data transfer technologies. Firstly, optical communications offer many times the bandwidth. Secondly, optical transmitters and receivers are more compact and require less power — critical resources on any relay satellite.
- Satellite arrangements able to transmit signal around the Sun, even if Earth and Mars (or other planets on the space Net) are on opposite sides of the star.
The future is closer than it appears
As you see, social networking or even video conferencing with residents of Mars or Moon is not as fantastic as it used to appear. Of course, the humankind has a long way to go to take the Internet to deep space, but the first steps have already been taken. | https://www.kaspersky.co.uk/blog/internet-in-space/16690/ |
BACKGROUND OF THE INVENTION
Field of the Invention
Related Background Art
SUMMARY OF THE INVENTION
BRIEF DESCRIPTION OF THE DRAWING
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Embodiment 1
Embodiment 2
Embodiment 3
Embodiment 4
Embodiment 5
Embodiment 6
This invention relates to a magneto-optical recording medium suitable for use in an information memory system such as the outside memory of a computer or an image file.
9
A magneto-optical recording medium using a rare earth-iron group amorphous alloy thin film is not sufficient in its durability, and suffers from problems such as selective oxidation of rare earth elements, surface oxidation of magnetic film and erosion, and various improving methods have been proposed in this respect. One of them is the addition of elements intending to improve the durability of the magnetic film itself (for example, the Journal of Japan Applied Magnetic Association (1985) 93). The elements added include Cr, Al, Ti, Ni, Co, Pt, etc.
Also, the magneto-optical recording medium using a rare earth-iron group amorphous alloy thin film is not sufficient in its reading-out characteristic and various propositions have been made as to a method of improving this. One of them is, as proposed, for example, in U.S. Patent No. 4,799,114, an exchange-coupled two-layer magnetic film comprising a film having a good recording characteristic (a recording layer) and a film having a good reading-out characteristic (a reading-out layer). In the conventional exchange-coupled two-layer magnetic film, Tb-Fe, Dy-Fe, Tb-Fe-Co or Dy-Fe-Co has been used for the recording layer, and Gd-Fe, Gd-Co, Gd-Fe-Co or Tb-Fe-Co has been used for the reading-out layer.
Considering the addition of an element for the improvement indurability, Cr is best if only its effect is taken into account, but this has posed the problem that the curie temperature falls and the magneto-optical effect is reduced. If the curie temperature falls, the recording sensitivity will become higher, but the stability of recording information for a temperature rise will become smaller and therefore, unnecessary fall of the curie temperature is not preferable. Also, a reduction in the magneto-optical effect reduces the reading-out characteristic and therefore, this is neither preferable.
Co is another element for improving the durability, but is inferior to Cr in the effect of improving the durability. Also, the addition of Co increases the magneto-optical effect, but this involves the rise of the curie temperature with a result that the recording sensitivity is reduced.
Considering the addition of the two elements, Cr and Co, the reduction in the curie temperature caused by the addition of Cr can be prevented by the addition of Co, but even if an attempt is made so that the curie temperature may not change, the magneto-optical effect will still be reduced.
Accordingly, to suppress the reduction in the magneto-optical effect to such a degree that there is no problem in practice, Cr could not be much added and thus, an improvement in the durability could not be sufficiently achieved.
Now, with regard to the rare earth-iron group amorphous alloy thin film, it is known that the more content of Co as an iron group element results in the greater improvement in the durability (particularly the prevention of pit erosion). In the exchange-coupled two-layer magnetic film, the reading-out layer thereof may have any high curie temperature and therefore, use can be made of Tb-Fe-Co containing a great deal of Co, and an improvement in the reading-out characteristic as well as an improvement in the durability can be accomplished to a certain degree. However, Tb-Fe or Dy-Fe is used in the recording layer, and the addition of Co thereto, even in a small amount, has led to the problem that the curie temperature rises considerably and the recording sensitivity becomes worse.
It is the object of the present invention to solve the above-noted problems peculiar to the prior art and to provide a magneto-optical recording medium having good information recording and reading-out characteristics and excellent in durability.
The above object of the present invention is achieved by a magneto-optical recording medium comprising a first magnetic layer consisting of an R₁-Fe-Co-Cr amorphous alloy when R₁ is at least one element of Tb and Dy, and a second magnetic layer having a higher curie temperature than said first magnetic layer and a low coercive force at room temperature and exchange-coupled to said first magnetic layer, said second magnetic layer consisting of an R₂-Fe-Co amorphous alloy when R₂ is at least one element of Tb, Dy and Gd, wherein the composition ratio of Co in said first magnetic layer being smaller than the composition ratio of Co in said second magnetic layer.
Figure 1 is a schematic cross-sectional view showing an embodiment of the magneto-optical recording medium of the present invention.
Referring to Figure 1 which is a schematic cross-sectional view showing the construction of an embodiment of the magneto-optical recording medium of the present invention, the reference numeral 1 designates a transparent substrate formed of glass or plastic. On this substrate 1, there is provided an underlining layer 2 for providing the interference effect and the corrosion preventing effect formed of a dielectric material such as Si₃N₄. Further, on this underlining layer 2, there are formed a second magnetic layer 3 which is a reading-out layer, and a first magnetic layer 4 which is a recording layer having a higher coercive force at room temperature and a lower curie temperature than said second magnetic layer 3. These magnetic layers are continuously made as films without breaking vacuum during the making of the medium, and are exchange-coupled to each other. Also, on the first magnetic layer 4, there is formed a protective layer 5 formed of a dielectric material such as Si₃N₄ to prevent the corrosion of these magnetic layers.
In the exchange-coupled two-layer film as described above, the recording layer need be suitably low in its curie temperature, but has nothing to do with reading-out and therefore, however low its magneto-optical effect may be. On the other hand, the reading-out layer need be great in its magneto-optical effect, but has nothing to do with recording and therefore, however high its curie temperature may be.
In the present invention, paying attention to this respect, a small amount of Co and a great amount of Cr are added in the recording layer, whereby a great effect of durability is obtained in such a manner that its magneto-optical effect is reduced but its curie temperature is not changed. This reduction in the magneto-optical effect does not affect the reading-out characteristic.
On the other hand, in the reading-out layer, Co alone is added in a great amount, whereby a great effect of durability is obtained in such a manner that its curie temperature becomes higher but its magneto-optical effect is not reduced. This rise of the curie temperature does not affect the recording sensitivity.
1-x
x
z
1-y
y
1-z
w
The material of the recording layer may preferably be R-Fe-Co-Cr (R being Tb and/or Dy). The composition of the material, when expressed as
{(TbDy)(FeCo)} 1-wCr
in terms of the element ratio, may preferably be in the range of 0 < x ≦ 1, 0 < y ≦ 0.5, 0.1 ≦ z ≦ 0.4 and 0.01 < w ≦ 0.3. The film thickness may preferably be of the order of 100 - 2000 Å. Among the curie temperature Tc of this recording layer, the element number ratio x of Dy, the element number ratio y of Co and the element number ratio w of Cr, there has been substantially obtained the relation that
Tc = 130(1-x) + 70x + (400-600)y - 500w(°C).
Accordingly, the values of x, y and w can be suitably chosen so that the curie temperature of the recording layer may be a desired value.
In a magneto-optical memory, information is recorded by the utilization of the heat action of laser light and therefore, the lower is the curie temperature of its magnetic film, the higher becomes the recording sensitivity. What determines the recording sensitivity in an exchange-coupled two-layer magnetic film is the curie temperature of the recording layer thereof and therefore, if the curie temperature of the recording layer is lowered, the recording sensitivity becomes higher. However, taking the stability of recording information into consideration, the curie temperature of the recording layer cannot be lowered so much. When the stability of the recording information is taken into consideration, the stability not only at room temperature but also at a tempreature somewhat higher than room temperature need also be taken into consideration. This is because various heat generation sources are present in the drive device of a magneto-optical memory and therefore the interior thereof sometimes rises to a temperature of the order of 50 - 60 °C and further in the reading-out of information, a weak laser light of such a degree that will not record information is applied to the medium to thereby accomplish reading-out, but nevertheless a certain degree of temperature rise of the medium is unavoidable, and also because for the convenience of the operation of the drive device, there is a case where reading-out must be effected with a bias magnetic field for recording and erasing being applied to the medium. Accordingly, even when in the drive device of the order of 50 - 60 °C, the temperature of the medium further rises due to the reading-out light under the application of a bias magnetic field, it is necessary that the recording information be stable. Taking all these into consideration, the curie temperature of the recording layer may desirably be of the order of 150 - 200 °C.
2z
1-y
y
1-z
x
z
1-y
y
1-z
As a material suitable for use as the readingout layer, mention may be made of R₂-Fe-Co (R₂ being at least one element of Gd, Tb and Dy). However, as the composition of this material,
R(FeCo)
and particularly, (Tb1-xDy)(FeCo)
is preferable in terms of the element number ratio. Here, a material which is in the range of 0 ≦ x ≦ 1, 0.1 ≦ y ≦ 1 and 0.1 ≦ z ≦ 0.4 and in which the composition ratio of Co in the recording layer is smaller than the composition ratio of Co in the reading-out layer is preferable. The film thickness may preferably be of the order of 100 - 2000 Å.
The magneto-optical effect of the rare earth-iron group amorphous alloy thin film in the wavelength of a visible range depends chiefly on the magneto-optical effect of the iron group element, and the iron group magnetic moment in the vicinity of room temperature becomes greatest for a composition of the order of Fe.70 Co.30, and if Co is less than that, the iron group magnetic moment decreases considerably, and if Co is more than that, the iron group magnetic moment decreases somewhat. Accordingly, the composition of Co may preferably be about 30 atom.% or more for Fe.
By the use of the ordinary magnetron sputtering method, a conventional disk-like magneto-optical recording medium and the disk-like magneto-optical recording medium of the present invention having a diameter of 130 mm were made, and experiment was carried out about the recording sensitivity, the reading-out characteristic and the durability thereof. The Ar gas pressure was about 0.15 Pa. As a protective film, SiN was provided to 700 Å on the both sides of each recording medium. In the conventional medium, the reading-out layer was Gd.22 (Fe.70Co.30).78 and had a film thickness of 200 Å, and the recording layer was Tb.22 (Fe.92Co.08).78 and had a film thickness of 600 Å, and in the present invention, the reading-out layer was Tb.18 (Fe.70Co.30).82 and had a film thickness of 200 Å, and the recording layer was (Tb.22 (Fe.85Co.15).78).93 Cr.07 and had a film thickness of 600 Å. Polycarbonate was used for the substrate. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.9 mW was necessary for recording on the conventional medium and the medium of the present invention could accomplish recording at laser power of 4.7 mW and no difference was found in the recording characteristic thereof. Also, the reading-out CN ratio at 3.08 MHz was 49dB in the conventional medium, and 48dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin-holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
Experiment was carried out under the same conditions as Embodiment 1 with the exception that in the conventional medium, the recording layer was Dy.21 (Fe.82Co.18).79 and had a film thickness of 600 Å and in the medium of the present invention, the recording layer was (Dy.21(Fe.75Co.25).79).93 Cr.07 and had a film thickness of 600 Å and the reading-out layer was Dy.18 (Fe.70Co.30).82, and had a film thickness of 200 Å. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.8 mW was necessary for recording on the conventional medium, and the medium of the present invention could accomplish recording at laser power of 4.9 mW, and no difference was found in the recording characteristic. Also, the reading-out CN ratio at 3.08 MHz was 48dB in the conventional medium, and also 48dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin-holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
Experiment was carried out under the same conditions as the above-described embodiments with the exception that in the conventional medium, the recording layer was (Tb.50Dy.50).22 (Fe.87Co.13).78 and had a film thickness of 600 A and in the medium of the present invention, the recording layer was ((Tb.50Dy).22 (Fe.80Co.20).78).93 Cr.07 and had a film thickness of 600 Å and the reading-out layer was (Tb.60Dy.40).18 (Fe.70Co.30).82 and had a film thickness of 200 Å. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.8 mW was necessary for recording on the conventional medium, and the medium of the present invention could accomplish recording at laser power of 4.9 mW, and no difference was found in the recording characteristic. Also, the reading-out CN ratio at 3.08 MHz was 47dB in the conventional mcdium, and 48dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin-holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
1-x
x
z
1-y
y
1-z
In the above-described embodiments, R-Fe-Co (R being Tb and/or Dy) is used as the reading-out layer, but likewise Gd-R-Fe-Co (R being Tb and/or Dy) can be suitably used. The composition, when expressed as
(GdR) (FeCo),
is 0.1 ≦ x ≦ 0.9, 0.1 < y < 1 and 0.1 ≦ z ≦ 0.4. Examples of this will be shown below.
By the use of the ordinary magnetron sputtering method, a conventional disk-like magneto-optical recording medium and the disk-like magneto-optical recording medium of the present invention having a diameter of 130 mm were made, and experiment was carried out about the recording sensitivity, the reading-out characteristic and the durability thereof. The Ar gas pressure was about 0.15 Pa. As a protective film, SiN was provided to 700 Å on the both sides of each recording medium. In the conventional medium, the reading-out layer was Gd.22 (Fe.70Co.30).78 and had a film thickness of 300 Å, and the recording layer was Tb.22 (Fe.92Co.08).78 and had a film thickness of 500 Å, and in the medium of the present invention, the reading-out layer was (Gd.50Tb.50).20 (Fe.70Co.30).80 and had a film thickness of 300 Å, and the recording layer was (Tb.22(Fe.85Co.15).78).93 Cr.07 and had a film thickness of 500 Å. Polycarbonate was used for the substrate. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.7 mW was necessary for recording on the conventional medium, and the medium of the present invention could accomplish recording at laser power of 4.9 mW and no difference was found in the recording characteristic. Also, the reading-out CN ratio at 3.08 MHz was 49dB in the conventional medium, and 50dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin-holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
Further, in a magnetic field of 600 Oe, the maximum reproducing power for which the recording information is not deteriorated was as low as about 1.4 mW in the conventional medium, but was as high as about 1.9 mW in the medium of the present invention.
Experiment was carried out under the same conditions as the above Embodiment with the exception that in the conventional medium, the recording layer was Dy.21 (Fe.82Co.18).79 and had a film thickness of 500 Å and in the medium of the present invention, the recording layer was (Dy.21(Fe.75Co.25).79).93 Cr.07 and had a film thickness of 500 Å and the reading-out layer was (Gd.50Dy.50).20 (Fe.70Co.30).80 and had a film thickness of 300 Å. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.6 mW was necessary for recording on the conventional medium, and the medium of the present invention could accomplish recording at laser power of 4.6 mW and no difference was found in the recording characteristic. Also, the reading-out CN ratio at 3.08 MHz was 48dB in the conventional medium, and 49dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin-holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
Further, in a magnetic field of 600 Oe, the maximum reproducing power for which the recording information is not deteriorated was as low as about 1.3 mW in the conventional medium, but was as high as 1.9 mW in the medium of the present invention.
Experiment was carried out under the same condition as the above-described embodiments with the exception that in the conventional medium, the recording layer was (Tb.50Dy.50).22 (Fe.87Co.13).78 and had a film thickness of 500 Å and in the medium of the present invention, the recording layer was ((Tb.50Dy.50).19(Fe.80Co.20).81).93 Cr.07 and had a film thickness of 500 Å and the reading-out layer was (Gd.34Tb.33Dy.33).22 (Fe.70Co.30).78 and had a film thickness of 300 Å. The curie temperature of the recording layer was about 170 °C in both of the conventional medium and the medium of the present invention.
For the number of revolutions 1500 rpm and a radius of 35 mm, under a bias magnetic field 200 Oe, laser power of 4.9 mW was necessary for recording on the conventional medium, and the medium of the present invention could accomplish recording at laser power of 5.1 mW and no difference was found in the recording characteristic. Also, the reading-out CN ratio at 3.08 MHz was 48dB in the conventional medium, and 59dB in the medium of the present invention, and no difference was found in the reading-out characteristic.
Also, in the test of durability using NaCl water solution of 1 N, considerable pin holes were observed in the conventional medium after it was immersed in the solution for 15 minutes, while no pin-hole was observed in the medium of the present invention.
Further, in a magnetic field of 600 Oe, the maximum reproducing power for which the recording information is not deteriorated was as low as about 1.4 mW in the conventional medium, but was as high as 2.0 mW in the medium of the present invention.
The present invention permits various applications besides the above-described embodiments. The present invention covers all such applications without departing from the scope of the invention as defined in the appended claims. | |
The site permitting deadlock which has trapped around 100 wind and other renewable energy projects in Britain's troublesome planning system is to be eased. The government will now allow developers to transfer projects with power purchase contracts won under the Non Fossil Fuel Obligation (NFFO) from sites that failed to secure consents to alternative locations.
Stalled projects such as National Wind Power's proposed £12 million 15 MW High Moor wind farm in County Durham might now proceed elsewhere. Until now the site-specific terms of NFFO contracts have prevented developers from negotiating more acceptable sites with planners or from trying again in a different local authority area.
Developers will be able to seek alternative sites anywhere in England and Wales. But any move is conditional on them having sought and been refused planning permission for the old site and obtaining consents for the new site. The Department of Trade and Industry will effect the change through secondary legislation.
Unless the renewables build rate dramatically improves, the government will fail to meet its targets of 5% of UK electricity from renewables by 2003 (requiring some 1500 MW of declared net capacity) and 10% by 2010. Of a total 3638 MW DNC of NFFO contracts awarded in the UK, just 855 MW had been commissioned by September 2000.
Energy minister Peter Hain is optimistic, however. "New freedom for NFFO projects, combined with the introduction of regional strategies and targets ensures that renewables projects can be brought on stream more rapidly while still paying closer attention to local concerns." | https://www.windpowermonthly.com/article/961400/government-eases-deadlock |
What is Visual Acuity?/
In basic terms, visual acuity is a measurement of the eye’s ability to distinguish small letters, symbols or shapes.
20/20, 20/40, 20/80 or 6/6, 6/12, 6/24. What do all these fractions mean? The top number refers to the distance at which your vision is being tested and is usually measured in feet (ie 20 feet). However, Some Canadian and British optometrists will also use metric measurements (ie 6 meters). The bottom number refers to the distance from which an average person’s eye should be able see the same size letter. So if your visual acuity is 20/20, we say that you have perfect vision. But if your visual acuity is 20/40, that means that you can only see something at 20 feet that an average person can see from 40 feet away. Therefore your visual acuity is reduced.
It’s important to know however that even patients with perfect 20/20 vision can have other vision related problems or eye health conditions. As such, everyone should have an annual eye examination by an optometrist.
Book your next eye examination with a StoneWire Optometrist today.
Book your annual eye exam with a Doctor of Optometry at
Stonewire Optometry in Kingsway Mall Today. | https://www.stonewire.ca/blog/2014/1/31/what-is-visual-acuity |
Is AAR useless when looking at investment performance?
My apologies for the somewhat clickbait-y title of this question, but I've never understood Quicken's fascination with reporting AAR in its investment reports and am hoping someone can explain to me why it's useful. When I look at my investment portfolios, one of the primary questions I want answered is performance: how are my investments performing year-to-date, quarter-to-date, or some arbitrary date range. I think the metric that best answers that question is ROI-percentage, and the only place I've found in Quicken that reports ROI is the Investments "portfolio" view. All the reports (specifically the investment performance report) show AAR.
Investment advisers don't use AAR when talking to their clients, people don't use AAR when talking about investments with each other, so why does Quicken insist on using it? What am I missing? Thanks for any feedback!
You are right that IRR (AKA AAR) is not useful for periods of less than one year, unless you are looking at a fixed price investment like a money market fund.
However for multi year performance it is more useful than other measures, because it takes compounding into account.
It is also the measure that mutual funds use to show their long term performance.
One way to use the ARR for a YTD report is to set the end date of the report to 12/31.
Thanks Jim, that makes sense - so for an account with a mix of investments (stocks, equity mutual funds, bonds) is AAR still a reasonable way to look at performance, assuming the time period is greater than 1 year?
Also, and I guess this is a related question, if I had an account with only non-dividend paying stocks, would AAR look about the same as ROI since there is no compounding to take into consideration?
If there are no transactions during the year, I think the 12 month ROI and IRR will be the same. The ROI is not annualized, so for any other period ,the results will be different.
"You are right that IRR (AKA AAR) is not useful for periods of less than one year, unless you are looking at a fixed price investment like a money market fund. "
I completely disagree. There's no "magic" about "a year" that somehow makes the IRR a nonsensical number for shorter periods. The IRR is what it is: a percentage figure, typically expressed as an "annual rate", though other periods could be used, of a security's or an account's performance and it's perfectly valid to compare the number to other securities or accounts or "the market" for the same period.
If I have a stock that's gone up by 50% in half a year, resulting in an IRR of something on the order of 126%, where "the market" has gone up by 25% in the same period for an IRR of around 57%, which one has performed better over that time? The IRR here is purely a backward-looking metric and provides a very clear picture of relative performance.
Conversely, if I have a stock that's gone up 50% in 364 days, for an IRR of about 50%, (you can figure out that one in your head), how is that not useful? Barring some disaster or earth-shaking even on the 365th day, I know the IRR for the year is going to be 50%. Was that a good investment, or not? I can't say "yes" or "no" on day 364 but I can on day 365?
@Tom Young, perhaps I misspoke when I said IRR is not useful for periods of less than one year.
Really you just need to understand what it is telling you. For a period of less than one year, an IRR calculation assumes that the performance will continue at the same rate for the rest of the year. Is that a good assumption? It depends on the investment.
Also published investment performance data typically shows raw percentage changes for quarterly and YTD periods matching Quicken's ROI data, but annualized numbers matching the IRR for annual and longer periods.
"For a period of less than one year, an IRR calculation assumes that the performance will continue at the same rate for the rest of the year."
Yes, that's the "annual rate" aspect of the calculation and I think that's what befuddles people. But as a measure of performance it's perfectly valid. And even pure backwards-looking calculations assume that cash flows can actually be invested at the IRR rate, which probably also isn't accurate. It's no a "perfect" metric; the better metric would be to use your own cost of capital, but nobody, really, knows that.
Yes, that's the "annual rate" aspect of the calculation and I think that's what befuddles people. But as a measure of performance it's perfectly valid.
Except that typically people compare their performance against an index. If the S&P is up 4.8% so far this year and I said, "that's nothing, my portfolio IRR is actually up 78%" I'd be labeled a fool. I'd also be a fool to assume that I'm going to get the same return for the next 9 months. That's why Quicken's Investment performance reports are basically useless for me, unless I'm looking at a long time period I guess. I'm not suggesting the number is not mathematically correct, I'm saying it's not helpful, and I can't for the life of me understand why those reports don't at least also include ROI.
Can't you use the Investment Performance report with date range set to Yearly and Current Year? That's what I use.
I agree Quicken is very confusing. I never use the Investing Portfolio tab anymore. The ROI calculation there is useless if you are buying/selling shares throughout the year as its calculation is just the change in share price * current share balance.
Yes, setting the date range to yearly and current year does produce a useful YTD value in the investing performance report. The underlying assumption is that the return will be flat for the rest of the year. This may or may not be valid for your investment.
I think if you take a closer look at the ROI(%) calculation, you will find that it does include purchase and sales.
Wow, that was the trick - thank you both! Setting the date range to yearly seems to be the magic bullet that makes the AAR not "annualize" the gain/loss. I can't believe I've been a Quicken user for this many years and have not been able to get those reports to do what I want. | https://community.quicken.com/discussion/7848510/is-aar-useless-when-looking-at-investment-performance |
A Mary Immaculate College (MIC) student has been awarded the Gold Gaisce medal by President Michael D Higgins at a special event at Áras an Uachtaráin. Second year Bachelor of Education in Education & Psychology student Sarah Ryan Purcell was one of 79 people from across Ireland to be presented with the prestigious award by the President in recognition of their commitment to volunteering and personal development.
To achieve the award, Sarah, who is from Blackrock in Cork, completed 52 weeks of piano, 52 weeks of the role of cantor in her local church, 78 weeks of tennis, a four-day hike along the Ballyhoura Way and a summer internship at the University of California Santa Cruz, where she participated in research in child psychology.
Sarah had previously been awarded the Gaisce Bronze Award during her Transition Year at Scoil Mhuire in Cork and jumped straight to Gold medal, which meant completing an additional 26 hours of a challenge area – in Sarah’s case, tennis – in lieu of completing her Silver award. | https://www.mic.ul.ie/news/2022/gold-gaisce-for-mic-student |
Cinderella and the Power of Kindness
I have to admit, I’m a girl who loves princess movies. As a kid I saw every Disney princess movie ever made. But I think the recent release of Disney’s live action Cinderella is one of my favorites, because it illustrates the power in kindness, courage, work and forgiveness in this fairy tale. The simplicity in these virtues often causes them to be overlooked and underappreciated in the world today. But they brought out the best in Cinderella and helped her to stay strong and true to who she was even when those around her were lost in their grief and sorrows.
These virtues aren’t just powerful in the movies—they are superpowers in the real world, too. The scriptures as well as modern prophets and Apostles of The Church of Jesus Christ of Latter-day Saints provide excellent examples of these virtues in action. But at the end of the day, do we really understand how powerful these virtues are in our own lives?
Kindness—Not Just for Cinderella
Cinderella is famous for her friendships with the mice in her house and other animals around her. She is kind to everyone, even when that kindness is not reciprocated. Cinderella’s mother, on her deathbed, told Cinderella that kindness is a power that few people truly understand. The late Elder Joseph B. Wirthlin agreed. He said:
Kindness is the essence of greatness and the fundamental characteristic of the noblest men and women I have known. Kindness is a passport that opens doors and fashions friends. It softens hearts and molds relationships that can last lifetimes.
Kind words not only lift our spirits in the moment they are given, but they can linger with us over the years. … Kindness should permeate all of our words and actions at work, at school, at church, and especially in our homes.
Jesus Christ set the example of kindness for us. Elder Wirthlin said:
Ad
Jesus, our Savior, was the epitome of kindness and compassion. He healed the sick. He spent much of His time ministering to the one or many. He spoke compassionately to the Samaritan woman who was looked down upon by many. He instructed His disciples to allow the little children to come unto Him. He was kind to all who had sinned, condemning only the sin, not the sinner.
The love the Savior described is an active love. It is not manifested through large and heroic deeds but rather through simple acts of kindness and service. There are myriad ways and circumstances in which we can serve and love others.
… In this long eternal quest to be more like our Savior, may we try to be “perfect” men and women in at least this one way now—by offending not in word, or more positively put, by speaking with a new tongue, the tongue of angels. Our words, like our deeds, should be filled with faith and hope and charity, the three great Christian imperatives so desperately needed in the world today.
Another way that we show kindness is in the way we treat others. Elder Wirthlin said:
Each one of us will travel a different road during this life. Each progresses at a different rate. Temptations that trouble your brother may not challenge you at all. Strengths that you possess may seem impossible to another.
Never look down on those who are less perfect than you. Don’t be upset because someone can’t sew as well as you, can’t throw as well as you, can’t row or hoe as well as you.
We are all children of our Heavenly Father. And we are here with the same purpose: to learn to love Him with all our heart, soul, mind, and strength, and to love our neighbor as ourselves.
The Courage of a Queen
The other piece of advice that Cinderella’s mother gave her as she lay dying was to have courage no matter what. Courage is another virtue that carries a lot of power. Elder Lynn G. Robbins said:
Courage is not just one of the cardinal virtues, but as C. S. Lewis observed: “Courage is … the form of every virtue at the testing point. … Pilate was merciful till it became risky.” King Herod was sorrowful at the request to behead John the Baptist but wanted to please “them which sat with him at meat” (Matthew 14:9). … Many of the New Testament chief rulers “believed on [the Lord]; but because of the Pharisees they did not confess him, lest they should be put out of the synagogue: for they loved the praise of men more than the praise of God” (John 12:42–43). The scriptures are full of such examples.
The scriptures are also full of examples of those who showed great courage in the face of adversity, such as Queen Esther in the Old Testament. Esther was raised by her cousin Mordecai, who worked for the king, after her parents passed away. She pleased the king, and he made her his queen. (See Esther 2:17.) She never disclosed that she was Jewish, per Mordecai’s instructions. Not long afterward, Mordecai angered Haman, one of the leader’s in the king’s court, by refusing to kneel before him. In retaliation, Haman plotted to destroy not only Mordecai but all of the Jewish people.
Realizing the grave danger which loomed over his people, Mordecai pled with Esther to seek help from the king: “For if thou altogether holdest thy peace at this time, then shall there enlargement and deliverance arise to the Jews from another place; but thou and thy father’s house shall be destroyed: and who knoweth whether thou art come to the kingdom for such a time as this?” (Esther 4:14).
Consider Esther’s dilemma: It was against the law to approach the king without being summoned. Such an act was punishable by death. If she were to remain quiet, she would likely enjoy a life of luxury and ease. She could live the life of a queen or risk her life to save her family and her people. She counted the cost and chose to heed the longings of her people and of her heart.
Esther asked Mordecai and the Jews to fast for three days, and she and her handmaids did the same. She declared:
… So will I go into unto the king, which is not according to law: and if I perish, I perish. (Esther 4:16).
Esther had gathered her courage and would stand firm and immovable for that which was right.
Physically, emotionally, and spiritually prepared, Esther stood in the inner court of the king’s house. When the king saw her, he held out his golden scepter, telling her that he would grant whatever request she had. She invited the king to a feast she had arranged, and during the feast she revealed that she was a Jew. She also exposed Haman’s underhanded plot to exterminate all of the Jews in the kingdom. Esther’s plea to save herself and her people was granted.
Esther, through fasting, faith, and courage, had saved a nation.
Esther could truly be described as a scriptural Cinderella (minus the wicked relatives). Raised as the daughter of someone who worked for the king, she found favor with the king and was chosen to be his queen. But her greatness came not in being elevated to the status of royalty but in being willing to sacrifice her status to help save a nation—her people—from destruction. President Monson said:
The call for courage comes constantly to each of us. Every day of our lives courage is needed—not just for the momentous events but more often as we make decisions or respond to circumstances around us. Said Scottish poet and novelist Robert Louis Stevenson: “Everyday courage has few witnesses. But yours is no less noble because no drum beats for you and no crowds shout your name.”
The Magic of Work
Cinderella’s stepmother put her to work in the house, saying that it would help keep her mind off of her sorrow. Ironically, Cinderella’s stepmother was absolutely right. I have to wonder how differently Cinderella’s stepfamily would have turned out had they heeded their own advice. Bishop H. David Burton said:
Today, many have forgotten the value of work. Some falsely believe that the highest goal in life is to achieve a condition in which one no longer needs to work. President David O. McKay (1873–1970) was fond of saying, “Let us realize that the privilege to work is a gift, that power to work is a blessing, that love of work is success.”
Work is not a matter of economic need alone; it is a spiritual necessity. … To work—honestly and productively—brings contentment and a sense of self-worth.
Work is not just doing things for ourselves but also reaching out to help others. This is another example that Jesus Christ set for us. Elder James B. Martino said:
Christ was the epitome of service. His life was filled with examples of helping and serving others, and His greatest gift of all was what He did for us. … When we serve others, we forget our own problems, and by working to relieve the pain or discomfort of others, we strengthen ourselves.
God has designed this mortal existence to require nearly constant exertion. I recall the Prophet Joseph Smith’s simple statement: “By continuous labor [we] were enabled to get a comfortable maintenance” (Joseph Smith—History 1:55). By work we sustain and enrich life. It enables us to survive the disappointments and tragedies of the mortal experience. Hard-earned achievement brings a sense of self-worth. Work builds and refines character, creates beauty, and is the instrument of our service to one another and to God. A consecrated life is filled with work, sometimes repetitive, sometimes menial, sometimes unappreciated but always work that improves, orders, sustains, lifts, ministers, aspires.
Cinderella benefitted from the magic of work while her stepmother and stepsisters languished in vanity, misery and spiritual poverty. She lost herself in the work of serving others, and thus in so doing rose above her circumstances.
Forgiveness is Freeing
Through the love of the Savior, Jesus Christ, we can find the strength to forgive those who have trespassed against us.
In the end, Cinderella frankly forgave her stepmother and stepsisters of their trespasses. She didn’t want to be burdened by the weight of animosity and bitterness that beset her stepfamily. They were ravaged by resentment, disappointment, grief and pride. Unable to see beyond their own circumstances, they sought to elevate themselves by destroying Cinderella. In the end, they did just the opposite. This is true in our own lives as well. If we seek to elevate ourselves by ruining another, we will only succeed in destroying ourselves.
President Boyd K. Packer told the story of a man who lost his wife after the birth of their first child due to the negligence of the traveling country doctor. The man was grief-stricken and angry at the doctor. President Packer continued:
A grieving, heartbroken young man went to see his spiritual leader. … The counsel from this wise servant was simply: “John, leave it alone. Nothing you do about it will bring her back. Anything you do will make it worse. John, leave it alone.”
My friend told me then that this had been his trial, his Gethsemane. How could he leave it alone? Right was right! A terrible wrong had been committed, and somebody must pay for it.
However, the man finally decided to get hold of himself and follow the counsel that he had been given. President Packer said:
Then [the man] told me, “I was an old man before I finally understood. It was not until I was an old man that I could finally see a poor country doctor—overworked, underpaid, run ragged from patient to patient, with little proper medicine, no hospital, few instruments. He struggled to save lives, and succeeded for the most part.
“He had come in a moment of crisis when two lives hung in the balance and had acted without delay.
“I was an old man,” he repeated, “before finally I understood. I would have ruined my life,” he said, “and the lives of others.”
… And that is my counsel to you. If you have festering sores, a grudge, some bitterness, disappointment, or jealousy, get hold of yourself. You may not be able to control things out there with others, but you can control things here, inside of you.
In life it is easy to see things from our own points of view, but we can’t always see the whole picture. However, our Heavenly Father and His Son, Jesus Christ can. It is for this reason that the Savior said, “I, the Lord, will forgive whom I will forgive, but of you it is required to forgive all men” (Doctrine & Covenants 64:10). Elder David E. Sorenson said:
This is not to say that forgiveness is easy. When someone has hurt us or those we care about, that pain can almost be overwhelming. It can feel as if … we have no choice but to seek vengeance. But Christ, the Prince of Peace, teaches us a better way. It can be very difficult to forgive someone the harm they’ve done us, but when we do, we open ourselves up to a better future. No longer does someone else’s wrongdoing control our course. When we forgive others, it frees us to choose how we will live our own lives. Forgiveness means that problems of the past no longer dictate our destinies, and we can focus on the future with God’s love in our hearts.
This is the beauty and miracle of forgiveness. And it is found only in and through the example and Atonement of Jesus Christ. President Dieter F. Uchtdorf said:
The pure love of Christ can remove the scales of resentment and wrath from our eyes, allowing us to see others the way our Heavenly Father sees us: as flawed and imperfect mortals who have potential and worth far beyond our capacity to imagine. Because God loves us so much, we too must love and forgive each other.
Our Choices Define Who We Are
At the end of the day, our choices define who we are. Like Cinderella’s wicked stepfamily, we can choose to be miserable in our circumstances. Or we can choose to be happy, as did Cinderella. Into each life, some rain will come. But it’s how we choose to deal with the rain and mud that defines our character. Elder L. Tom Perry said:
Those of us who have been around a while … have recognized certain patterns in life’s test. There are cycles of good and bad times, ups and downs, periods of joy and sadness, and times of plenty as well as scarcity. When our lives turn in an unanticipated and undesirable direction, sometimes we experience stress and anxiety. One of the challenges of this mortal experience is to not allow the stresses and strains of life to get the better of us—to endure the varied seasons of life while remaining positive, even optimistic. Perhaps when difficulties and challenges strike, we should have these hopeful words of Robert Browning etched in our minds: “The best is yet to be” (“Rabbi Ben Ezra,” in Charles W. Eliot, ed., The Harvard Classics, 50 vols. [1909–10], 42:1103).
Each of us has a little bit of Cinderella in us—and some of her stepfamily, too. But ultimately, it’s up to each one of us to decide how our fairy tales will end. As President Monson said:
It has been said … that history turns on small hinges, and so do people’s lives. Our lives will depend upon the decisions which we make—for decisions determine destiny.
This website is not owned by or affiliated with The Church of Jesus Christ of Latter-day Saints (sometimes called the Mormon or LDS Church). The views expressed herein do not necessarily represent the position of the Church. The views expressed by individual users are the responsibility of those users and do not necessarily represent the position of the Church. For the official Church websites, please visit LDS.org or Mormon.org.
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Conservation of Marine Megafauna [CRN 83300]304:
Whales, sharks, squids, sea turtles, albatrosses… oh my! FW 304 will be an engaging introduction to marine megafauna, ecology, and conservation. We will first examine the physical dimensions of the world’s ocean and describe ocean zones based on the ecosystems found within them. We will then explore the evolution of life in the oceans and how large marine animals have adapted to the challenges of a cold, dark, and deep ocean. Throughout the class we will highlight how scientists study the oceans and the large animals that live in them, providing glimpses of new technologies that boost our understanding of marine ecology. The course will also cover challenges we face in sustaining and conserving healthy oceans for the future. For example, we will learn how issues such as bycatch and climate change are affecting ocean species and how we can better conserve out charismatic marine megafauna. What better place to take such a class than on a ship?!
Field ClassCountry: Spain
Day: 3
Date: October 1, 2019
From the port of Cadiz, we will travel to Tarifa on Spain’s southern tip and board a whale-watching vessel. During the 2-hour cruise in the Strait of Gibraltar, we may see ocean sunfish,,common and bottlenose dolphins, pilot whales, killer whales, and possible larger whale species (e.g., sperm, fin whales). On board, we will be instructed by either a professional naturalist provided by the vessel operator or a marine biologist from CIRCE, an NGO dedicated to the study of cetaceans in the Strait of Gibraltar and the Gulf of Cadiz. A CIRCE marine biologist will discuss her research on the cetaceans we observe and will also discuss both current and historical methods and issues with major fisheries in the area, including the tuna fishery. On the way back from Tarifa, we will stop off for a visit to the Ruins of Baelo Claudia, an ancient Roman town that thrived 2000 years ago near the current seaside town of Belonia. Baelo Claudia derived its wealth from the tuna fishing industry, from which they produced garum, a fish paste that was a sought-after delicacy throughout the Roman Empire. In addition to the impressive temple, forum, and basilica, the ruins of the large fish-salting factory are the perfect backdrop for a discussion of the importance of the tuna fishery both today and in ancient times, and to review current tuna fishing techniques and fishery issues.
Learning Objectives:
1. Gain firsthand appreciation of, and identification skills for, marine megafauna (specifically whales, dolphins, tuna) in southern Spain as well as their adaptations for living in a marine environment.
2. Compare the importance of tuna fisheries over two millennia and review modern fishery and conservation issues.
3. Comprehend current conservation challenges for cetaceans and tuna such as those relating to mortality due to fisheries interactions, ship strikes, disease, pollution.
4. Discuss/present possible solutions to these problems. | https://www.semesteratsea.org/courses/conservation-marine-megafauna/ |
With a $26.5 million opening weekend, it is safe to say that “Happy Death Day” continues the trend of low budget horror movies gaining major critical acclaim. It’s not the average superficial horror film, it’s better. Audience members will be left in the theater trying to process everything going on. Once viewers think they have figured it out, a new plot twist emerges.
The film, released on Oct. 13 by Blumhouse Productions, features a cast of unknown actors such as Jessica Rothe, who plays the main character Tree Gelbrman. It also includes Ruby Modine, who is Tree’s roommate, and Israel Broussard, who plays Carter. Although most of the plot focuses on Tree, she doesn’t steal the show from her talented co-stars.
The plot starts when Tree is woken up by a birthday ringtone. She questions her unfamiliar surroundings and assumes she must have had a crazy night. The scene continues with the camera following her as she walks back to her sorority house. Along the way we find out that Tree isn’t as sweet as her beautiful face lets on, she’s a total butthole. While Tree’s day goes on, the viewers get to form their own impression of her. Some understand where her mean demeanor comes from and others don’t. Right when the audience forms an opinion about her, she’s killed violently. Suddenly the day starts all over again.
After first freaking out that she’s still alive and reliving the same day repeatedly, she decides to find her killer. She also realizes what a rude person she had become. The college girl, after her deaths, slowly becomes nicer each time she dies. As she corrects her flaws, she narrows her suspect list and starts spreading positivity to those she was once mean to.
The audience goes through multiple changes of heart, from wishing she was still dead to cheering her on while she is trying to find her killer. The viewers experience an emotional journey while they contemplate who the murderer could be. They are continuously proven wrong and are sometimes ready to give up, but the answer of who the killer is remains boldly in their face.
Happy Death Day is a must see this October. Its unique combination of comedic jokes, hand clinching horror and mysterious plot gives the audience a thrilling experience worth more than the $10. Years from now, while sitting in the dorm lounge of your college campus, Happy Death Day will pop into your head and have you wondering, who is plotting against you? | https://thsoutlook.com/entertainment/2017/10/17/happy-death-day-worth-more-admission/ |
This recipe is by Great British Bake Off Winner, Martha Collison on behalf of Waitrose.
If you love lemon, then this fresh cake will be a sure winner for you. This easy bake delivers slightly more than a standard lemon drizzle cake. The lemon curd and mascarpone filling give an extra kick and make it slightly indulgent, yet still fresh. It’s a great afternoon tea cake or can even act as a dessert.
The recipe gives really thick, light and fluffy sponge layers, the poppy seeds offer a slight crunch and the filling is refreshing. The fact that this cakes uses mascarpone cheese means that it doesn’t keep fresh for too long. It needs to be kept in the fridge and eaten within three days, which is never a problem in our house!
Ingredients
225g (8oz) softened butter
225g (8oz) self-raising flour
225g (8oz) caster sugar
1 teaspoon of baking powder
4 large eggs
2 tablespoon poppy seeds
2 lemons, zested
2 tablespoons milk
For the filling
100ml double cream
150g (5oz) mascarpone cheese
50g (2oz) icing sugar, plus extra for dusting
Juice of half a lemon
3 tablespoons lemon curd
- Preheat the oven to 180°C/gas mark 4 and grease and line two 20cm sandwich cake tins with baking parchment.
- Cream the butter and sugar together using a handheld or electric whisk, until they become light and fluffy. Add the eggs one at a time, whisking after each addition.
- In a small bowl, combine the flour, baking powder and poppy seeds. Slowly add these dry ingredients into the butter, sugar and egg mixture a few tablespoons at a time, and continue to mix until a smooth batter forms. Add the lemon zest and milk, and mix again.
- Divide the mixture between the two sandwich tins and smooth over the top. Bake for 25-30 minutes or until golden and well risen. Insert a knife in the centre of the cake, which should come out clean if the cake is baked. Allow to cool for a few minutes in the tins before turning onto a wire rack to cool completely.
- For the filling beat together the mascarpone, double cream, lemon juice and icing sugar until smooth. Spread the mascarpone on to the flat side of the bottom sponge layer, then spread the lemon curd on top, place the other layer on top and dust with icing sugar to serve.
Keep in the fridge for up to five days.
If you decide to give this recipe a go, please share a picture of your Lemon and Poppy Seed Cake via my social media pages or contact me. | https://achetobake.co.uk/2020/06/02/martha-collisons-lemon-and-poppy-seed-cake/ |
Go to the documentation of this file.
21 * The heuristic applies multiple NLP local searches to a mixed-integer nonlinear program with, probably nonconvex,
22 * constraints of the form \f$g_j(x) \le 0\f$. The algorithm tries to identify clusters which approximate the boundary
23 * of the feasible set of the continuous relaxation by sampling and improving randomly generated points. For each
24 * cluster we use a local search heuristic to find feasible solutions. The algorithm consists of the following four
29 * Sample random points \f$ x^1, \ldots, x^n \f$ in the box \f$ [\ell,u] \f$. For an unbounded variable \f$ x_i \f$
30 * we consider \f$ [\ell_i,\ell_i + \alpha], [u_i - \alpha,u_i], \f$ or \f$ [-\alpha / 2, \alpha / 2]\f$ for an \f$
35 * For each point \f$ x^i \f$ we use a gradient descent method to reduce the maximum infeasibility. We first compute
47 * where \f$ n_j \f$ is the number of strictly positive \f$ d_j \f$. The algorithm is called Constraint Consensus
53 * We use a greedy algorithm to all of the resulting points of step 3. to find clusters which (hopefully) approximate
58 * Depending on the current setting, we solve a sub-problem for each identified cluster. The default strategy is to
59 * compute a starting point for the sub-NLP heuristic (see @ref heur_subnlp.h) by using a linear combination of the
66 * Since the sub-NLP heuristic requires a starting point which is integer feasible we round each fractional
71 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
76 #include "scip/def.h"
77 #include "scip/type_retcode.h"
78 #include "scip/type_scip.h" | https://scipopt.org/doc-6.0.2/html/heur__multistart_8h_source.php |
School of Saint Mary Profile
The School of St. Mary is a fully accredited preK through 8th grade school affiliated with the Roman Catholic Church of St. Mary in Tulsa, Oklahoma. Saint Mary emphasizes academics in a Christian environment with Spanish, art, music and physical education. An after school care program is available.
Top Administrator: Maureen Clements, (K-8)
Carla Lechner, Preschool Director
Address/Location: 1365 E. 49th Pl.
Tulsa, OK 74105
1 ½ blocks east of Peoria on the south side of 49th Pl. – parking and school entrance are on the north side of the building.
Phone: School – 918-749-9361
Phone: Preschool – 918-743-4030
Fax: 918-712-9604
Hours/Days: K-8: M-F 8:00-3:00
Preschool: M/W/F, T/Th/F or T/Th, 9:30-2:30
Grades: 2 yrs. through 8th grade
Student/teacher ratio: 15:1 (K-8) with a total student population of 335.
Entrance age requirements: Students must be 2 by September 1st to enroll in the 2 yr. old program and students must be 5 prior to September 1st of the kindergarten year.
Fees:
Entrance test fee:
$30.00 for placement test in grades 1-8
$30.00 for placement test for entry into kindergarten
$25.00 (Preschool)
Book fee:
$85.00 per student (k-8)
Enrollment fee:
$150.00 (k-8)
$50.00 (Preschool)
Home and School Association fee:
$45.00 per family
Tuition 2019-2020 school year:
K-8 tuition: parishioner – $5,559(a multi-child discount is available)
K-8 tuition: nonparishioner – $6,942.00
Preschool: Please contact the Preschool Director, Carla Lechner, at 918-743-4030 for the current preschool tuition.
Scholarships/financial assistance: subject to acceptance and availability for students in K-8 who are Catholic.
Uniform required: yes (K-8)
Comments: The School of St. Mary strives to provide an atmosphere within which students can aspire to excellence in academics, foreign language, music, art, and athletics. It is our hope that our students aspire to excellence in the pursuit of wisdom and knowledge, in the search for understanding of values, and in the discovery of their talents in an atmosphere of love, affirmation, faith, prayer, and service that is Catholic education. | https://schoolofsaintmary.com/profile/ |
Natural disasters affect structural health of buildings, thus directly impacting public safety. Continuous structural monitoring can be achieved by deploying an internet of things (IoT) network of distributed sensors in buildings to capture floor movement. These sensors can be used to compute the displacements of each floor, which can then be employed to assess building damage after a seismic event. The peak relative floor displacement is computed, which is directly related to damage level according to government standards. With this information, the building inventory can be classified into immediate occupancy (IO), life safety (LS) or collapse prevention (CP) categories. In this work, we propose a zero velocity update (ZUPT) technique to minimize displacement estimation error. Theoretical derivation and experimental validation are presented. In addition, we investigate modeling sensor error and interstory drift ratio (IDR) distribution. Moreover, we discuss the impact of sensor error on the achieved building classification accuracy.
Keywords— earthquakes; structural health monitoring; ZUPT; IDR; sensors; sensor networks.
I Introduction
Monitoring the structural health of buildings during and after natural disasters, such as earthquakes provides the public and policy makers with a clear view of the state of critical infrastructure that affects the safety and well being of the population. Previous research on building damage assessment generally falls into one of two main categories: remote sensing techniques and sensor-based technology. In the former, optical images are captured using spacecraft or aircraft, then before and after image comparisons are performed to assess the damage. This technique is effective in detecting partial to complete collapse of buildings, however it cannot reliably detect incipient collapse because the resolution is too low [image09]. On the other hand, sensor based technology uses an IoT network of pre-installed sensors to capture the movement of a building during an event, enabling distributed, accurate and instantaneous monitoring of structures [sensor06].
Measuring relative displacement of floors within a given building is used to calculate the IDRs for the building using (1). Documents released by government agencies and civil engineering societies such as Federal Emergency Management Agency (FEMA) and American Society of Civil Engineers (ASCE) relate IDR values to building damage level. Basically, these documents define two main critical thresholds of relative floor displacement of a given building, such that the building can be classified into one of three categories: immediate occupancy (IO), life safety (LS) or collapse prevention (CP), which indicate that the building is either safe, needs further inspection or unsafe respectively. In other words, measuring the instantaneous relative floor displacement of a given building during an earthquake event is a good indicator of the structure state [fema273, american2007seismic].
|(1)|
Sensors are typically accelerometers, that are used to measure acceleration and consequently displacement. The cost of an accelerometer depends on several parameters such as dynamic range, linearity, bandwidth, output data rate, output noise and output type, i.e. analog or digital. Based on those specifications, cost ranges from a few dollars to a few thousand dollars. According to [cambridge_inertial], sensor output noise is a major contributor to displacement measurement error, which is accentuated by double integration required to calculate displacement from acceleration. Hence, to minimize the system cost without sacrificing the accuracy, noise cancellation methodologies are adopted so that a cheaper less accurate device can be used instead of an expensive, highly accurate one.
While other technologies such as global positioning system (GPS) are widely used for localization and position estimation, accuracy becomes a major limiting factor in their suitability for structural health monitoring. As will be discussed later in the paper, to be useful, IDR values need to be estimated with an accuracy that is within a few centimeters from ground truth. This degree of accuracy is not possible using GPS alone, unless high-end GPS receiver is used, which is much more expensive than a standard GPS receiver [GPS02, gpsGov]. Furthermore, GPS signals are not available indoors, which mandates outdoor installation for the sensing devices. Another approach to estimate position is to use vision based displacement estimation techniques as mentioned in [cameras01]. Although this approach does not suffer from error accumulation, it faces other challenges such as, measurement error due to heat haze and ground motion, in addition to errors due to dim lighting and optical noise.
Therefore, in this paper, we focused on studying the limits of using accelerometers to estimate structural displacement for a number of reasons: 1) earthquake event time is relatively short (20-30 seconds) which results in bounded accumulated error that can be quantified, 2) accelerometers can work indoors which is not the case of GPS, and 3) accelerometers are not affected by ambient light conditions as compared to cameras.
As mentioned earlier, accelerometer inherent noise is one of the main challenges in displacement estimation. However, noise cancellation can be achieved by depending on the fact that a disaster vibration intensity fades gradually and eventually stops at zero velocity and acceleration. In this case, the measured velocity at the end of shaking (EOS) reflects the accumulated error in the preceding samples, which can be used to minimize the estimation error. This technique is known as ZUPT [zupt10, zupt12].
The main contributions of this work can be summarized as follows:
-
Derive how ZUPT can be applied to minimize displacement estimation error; a theoretical derivation is presented and validated by shake table experiments.
-
Study how displacement measurement error affects the accuracy of building damage classification based on its maximum IDRs.
-
Present how different system parameters such as sensor noise and IDR can be accurately modeled.
-
Apply the derived methodology on a number of commercially available sensors to relate the probability of error versus duration of observation.
The rest of the paper is organized as follows. In section II, ZUPT algorithm is derived. Section III describes the classification methodology and derives the probability of classification error, in addition to accelerometer noise and IDR distribution modeling. System overall probability of error and sensor selection charts are presented in section IV. Finally, the conclusions are drawn in section V.
Ii Noise Cancellation
An earthquake signal is characterized by stopping at zero acceleration and zero velocity. The EOS instant can be detected when the absolute acceleration is below a certain threshold within a specified window of time as illustrated in figure 1. The selection of is arbitrary, whereas is dependent on the sensor noise. If the sensor noise standard deviation (STD) is , then we believe selecting is a reasonable assumption, which indicates that the noise is below that threshold most of the time, In this region, the sensor has true zero velocity. Any non-zero velocity measured at this time is due to the sensor noise, and is correlated with the noise at shaking time. As mentioned before, using such characteristic in noise cancellation is known in the literature as ZUPT [zupt10, zupt12].
ZUPT has been used in inertial navigation systems, specifically pedestrian ones [zupt11]. In such systems, navigation devices are mounted on a pedestrian’s foot, which is known to be stationary on the ground once every step. The goal of applying ZUPT in that case is to reset the velocity and prevent further error accumulation, which in turn reduces the error in upcoming velocity samples and consequently reduces the error in displacement estimation as well. However, in this work, we are only concerned in correcting displacement estimation for the time window prior to the EOS instant, since that window contains the peak relative displacement which reflects the damage state.
Ii-a Noise cancellation using Zupt
In this work, we are concerned with measuring floors’ horizontal displacement. Hence, we assume that accelerometers will be oriented to measure only horizontal motion, i.e. gravity will not affect the reading. However, to account for miss-orientation, we consider a fraction of the gravity will couple into the measurement. Assuming linear motion, is constant throughout the motion, hence this constant can be removed with the sensor constant bias using long term averaging while the device is at rest. In general, in case of curvilinear motion, is not constant, and removing the gravity component in this case is more complex and can be addressed by using techniques described in [gravity01]. Curvilinear motion is out of the scope of this paper and will be investigated in future work.
True velocity is expressed by (2), where is the ground truth horizontal acceleration sample. True displacement is obtained by (3)-(5), where is the true acceleration vector and .
|(2)|
|(3)|
|(4)|
|(5)|
Measurement noise is considered additive with zero mean, since constant bias is estimated by long term averaging and then subtracted from the measurement [cambridge_inertial]. Hence, measured acceleration is expressed by (6). Consequently, measured displacement is shown by (7)-(9). As a result, displacement error is shown by (10)-(12), where is the noise vector.
|(6)|
|(7)|
|(8)|
|(9)|
|(10)|
|(11)|
|(12)|
Let the shaking window length be samples, i.e., is the measured velocity at the EOS instant, which is equal to the accumulated noise since the true velocity at that instant is zero. As shown by (13), ZUPT is applied at any given sample , by multiplying by certain coefficient and then adding the result to the displacement measurement. Thus, the modified displacement error is calculated by (14), where is an vector of ones.
|(13)|
|(14)|
Let and be the mean squared error in displacement at sample without and with applying ZUPT respectively as shown by (15) and (16).
|(15)|
|(16)|
where denotes the expectation operator and the noise covariance and are given by (17) and (18) respectively. The value of is calculated such that is minimized as shown by (19) and (20).
|(17)|
|(18)|
|(19)|
|(20)|
Assuming that the noise can be modeled as a stationary process as will be illustrated in section III-A1, then , where is calculated by (21). Hence, equation (20) can be simplified as shown by (22). The resulting mean squared error is expressed by (23).
|(21)|
|(22)|
|(23)|
It is clear that the resulting mean squared error is a function of which depends on the noise characteristics. For example, in case of white noise, and , where is the identity matrix and is the noise variance. By substituting in (15), the mean squared error without applying ZUPT is calculated by (24) and can be simplified by (28) for sufficiently large .
|(24)|
|(25)|
|(26)|
|(27)|
|(28)|
Similarly, by substituting in (23), the mean squared error with applying ZUPT is calculated by (29), where is an matrix of zeros. For sufficiently large , (29) can be simplified as shown by (30)-(34).
|(29)|
|(30)|
|(31)|
|(32)|
|(33)|
|(34)|
At the EOS instant, i.e., at , the mean squared error without and with applying ZUPT are expressed by (35) and (36) respectively. Comparing both equations, it is concluded that using ZUPT reduces the mean squared error by 75% at the EOS instant. For the rest of the paper we will refer to as .
|(35)|
|(36)|
Ii-B Experimental Validation
In order to validate the developed algorithm, shake table experiments have been performed. We have used different amplitudes of sinusoidal, triangular and random vibration profiles for a duration of 20 seconds. The sensing device is a smart phone that captures acceleration using its internal accelerometer and transmits the data to a PC. The phone internal accelerometer chip is Invensense MPU6500 which is a 6-axis inertial module that contains 3 accelerometers and 3 gyroscopes sensors, and is widely used in commercial devices [MPU6500]. Figure 2 shows the experimental setup.
The motion starts and ends by zero velocity to mimic a seismic event. Figure 3 shows the STD of theoretical and measured error in displacement . It is clear that the measured error follows the theoretical one with and without applying the ZUPT algorithm, and that applying ZUPT decreases by more than 75%. It is worth noting that the reduction is greater than the one calculated in section II-A, which is expected since in this experiment other noise sources were taken into account when modeling the sensor noise such as: bias instability (BI) and rate random walk (RRW) rather than just white noise.
Measured error is slightly higher than the modeled one, due to the contribution of other sources of error, such as nonlinearity and sampling time jitter.
Iii Building Classification
According to government documents, buildings are classified according to their damage state as IO, LS or CP buildings. For instance, table I lists the IDR limits for steel moment frame buildings which are stated in [fema273, american2007seismic], and the corresponding physical tag used to signal the buildings’ post-event condition. Hence, a building’s performance can be assessed by comparing its peak IDR to the predefined thresholds. Knowing the floor height, which is 4m in typical US construction, thresholds in IDR corresponds to certain thresholds in relative floor displacement that we denote by and .
Let the true displacement of the two floors be denoted as and , then the relative displacement is expressed by equation (37). Since each displacement measurement has its own error, then the measured relative displacement is calculated by (38), where and are the measurement error for and respectively.
|(37)|
|(38)|
|(39)|
let then
|(40)|
and knowing that the errors in both measurements are not correlated, then the mean squared error in relative displacement measurement is expressed by (41). If identical sensors are used, then and (41) reduces to (42).
|(41)|
|(42)|
To evaluate classification accuracy, let and be the building’s estimated and true states respectively. Equation (40) shows the measured relative displacement of two consecutive floors. The accuracy of the true classification of a building is obtained by evaluating the conditional probability as shown by (43).
|(43)|
where and are expressed by (44) and (45).
|(44)|
|(45)|
where is the joint probability density function (PDF) of and , and is the marginal PDF of . The integral in (44) is done over the area shown in figure 4. Besides, limits of the integral in (45) is given by table II.
The measurement error only depends on the accelerometer itself and its inherent sources of noise, which is not related to the excitation signal. Hence, noise distribution is considered independent of IDR distribution. As a result, the joint PDF of and is expressed by (46).
|(46)|
where is the marginal PDF of . We will illustrate below how and can be modeled.
Iii-a Modeling
Iii-A1 Sensor Noise
Acceleration measured by an accelerometer sensor is contaminated by several sources of noise, which can be modeled as: constant bias, angle random walk (ARW) (or velocity random walk), BI, and RRW (or acceleration random walk), where each of these is considered an independent Gaussian noise source with certain power spectral density. Since we are only concerned with relatively short durations, higher order noise sources such as drift rate ramp (DRR) are ignored and removed with the constant bias.
According to [noise01], different noise sources can be modeled as white Gaussian noise shaped with a shaping finite impulse response (FIR) function . Since the input of the FIR filter is white Gaussian noise, i.e., wide sense stationary (WSS) noise process, then the generated noise is also WSS.
Case Study: For instance, consider the Invensense MPU6500, which is a 6-axis inertial module that utilizes 3 accelerometer and 3 gyroscope sensors. MPU6500 is widely used in commercial devices such as smartphones. To characterize the noise profile of the sensor, the output of the chip was recorded for 12 hours without motion. Using methods described in [modeling03], noise can be modeled as ARW, BI and RRW, and the overall noise covariance matrix is calculated. Figure 5 shows the real (measured) and modeled noise density of MPU6500 accelerometer sensor. It is clear that the noise model matches the real one at low frequency, whereas there is some discrepancy at high frequency, this is due to the fact that the sensor has a low pass filter in the output. However, since in our application the data is double integrated, the low frequency content is the main contributer to the displacement error. Therefore, the discrepancy at high frequency is irrelevant.
In order to provide a reference for comparison, we selected a number of sensors with different noise characteristics as summarized in table III. Figure 6 shows the noise spectral density of the selected sensors based on their data sheets. From the figure, it is clear that some of the sensors noise can be approximated as white flat noise such as MTI100 and AXO215 sensors, whereas for other sensors higher order noise sources as BI and ARW should be considered.
Iii-A2 Idr Distribution
Simulation of building response is conducted in order to model the IDR distribution as a result of earthquake excitation. We consider four and eight-story buildings designed by NIST [nist] in Seattle to be representative of steel frame buildings. The buildings have 42.7 m x 30.5 m plans as shown in figure (a)a. Three-bay perimeter steel special moment frames (SMFs) on each side of the building are used for the lateral load resisting system. The SMFs are designed with reduced beam sections (RBS). With respect to the type of soil, we consider site class which includes mixtures of dense clays, silts, and sands, which is the most common site class throughout the United States [siteclass01]. The seismic design category is , i.e., structures are expected to suffer from considerable rotational loads during strong earthquakes [siteclass02]. As shown in figure (b)b, finite element models of the SMFs are created using HyperMesh [hypermesh] and analyzed using the commercial code LS-DYNA [livermore]. The steel is ASTM-A992 and its engineering stress-strain properties are converted into true stress-strain data then assigned to the finite elements as done in [momentframe01]. Gravity loads from the tributary area shown in figure (a)a are directly applied to the frame and the remainder of the gravity loads are applied to a leaning column connected to the SMF by truss members. Mass weighted damping of 2.5% is assumed at the first mode period of the SMFs. Additional modeling details can be found in [momentframe01].
The distributions of peak relative displacement are computed for three seismic hazard levels: 2% probability of exceedance in 50 years, 10% in 50 years, and 50% in 50 years. Eleven seismic records are selected from the Far-Field ground motion record set in FEMA [fema695] and scaled to the three specified hazard levels at the first period of each building, resulting in 33 records for each building. The first period spectral accelerations corresponding to the three hazard levels are 0.55g, 0.26g, and 0.07g for the four-story building and 0.41g, 0.17g, and 0.04g for the eight-story building, respectively. Each building is then subjected to the scaled seismic records for each hazard level and the peak relative displacement is computed. The histogram of peak relative displacement is shown in figures (a)a through (c)c. The distribution can be approximated as Gaussian with mean and variance that depend on the hazard level, with slight variation depending on the building type.
Iii-A3 Earthquake Strong Motion Duration
Damage prone buildings will suffer damage during the strong shaking part of the seismic event. As mentioned in [quakes01], there are several definitions for the strong motion duration, which is calculated based on acceleration magnitude or cumulative energy obtained by integrating squared acceleration. In [quakes01], strong motion duration of 140 earthquake records were evaluated, and figure 14 shows the cumulative density function (CDF) of strong motion duration.
Iii-B Probability of Classification Error
As mentioned in section III-A, relative displacement measurement error can be modeled as zero mean Gaussian of variance , and relative displacement distribution can be modeled as Gaussian of mean and variance which varies according to the hazard level. As a result, substituting into (46), the joint probability distribution can be expressed by (47).
|(47)|
where is a Gaussian distribution with mean and variance . Figure 15 shows a sketch of Gaussian peak relative displacement distribution. Classification boundaries are highlighted, where error is expected to occur.
Substituting (47) in (43) and (44), conditional probabilities can be calculated. For instance, for IO buildings, the probability of correct classification is defined as , whereas probability of error is defined as , i.e. . Similarly, for LS buildings, the probability of correct classification is defined as , whereas the probability of error is defined as , and with respect to CP buildings, the probability of correct classification is defined as , whereas the probability of error is defined as . The probability of error of the system is calculated by (48), and will be used later in section IV for sensor selection.
|(48)|
Iv Sensor Selection
In section III we showed that the probability of classification error is a function of displacement measurement accuracy, hazard level and strong motion duration. In this section, we demonstrate how a sensor can be selected based on the acceptable probability of error which is calculated by (48). The probability of classification error is calculated for each of the sensors mentioned in section III-A1.
Figure 16 shows the probability of error in buildings classification as a function of strong motion duration in case of 50% in 50 years hazard level. As expected, it is clear that the high accuracy seismic sensors such as Mistras1030 and KB12VD have very small probability of error, and the probability of error increases as sensor accuracy decreases. In the same figure, we also compare between the simple white noise model, and the more complex model that takes into account other noise components. It is worth noting that for high accuracy sensors, using white noise model results in negligible probability of error which is not plotted in the figure. Hence, only the more complex noise model is plotted for the two high accuracy sensors Mistras 1030 and KB12VD. However, for MTI-100 and AXO215, using only the simple white noise model results in probability of error slightly smaller but comparable to the complex model. With respect to MPU6500, there is a larger discrepancy between white noise model and complex noise model results. Intuitively, that result was expected, as mentioned in section III-A1 by comparing the noise density curves shown earlier in figure 6, it is clear that only MTI-100 and AXO215 noise can be approximated as flat white noise. Similarly, figures 17 and 18 show the probability of error in case of 10% in 50 years and 2% in 50 years hazard levels respectively. Depending on the acceptable probability of error, the curves presented in figures 16 to 18 can be used to evaluate the maximum accepted noise density, hence an appropriate sensor can be selected.
V Conclusion
Monitoring structural health of buildings during and after natural disasters is crucial, and directly impacts public safety. Buildings can be added to an IoT network by deploying inertial sensors in civil infrastructure, which facilitates post disaster identification of structurally unsound buildings. In this work, we illustrated how accelerometer sensors can be employed to identify buildings damage state. We presented a theoretical derivation of a ZUPT algorithm that is used to increase displacement measurement accuracy, and consequently increase buildings classification accuracy. The developed algorithm has been validated experimentally using shake table experiments. We investigated the effect of sensors inherent noise on the overall building classification accuracy. The probability of error was calculated as a function of sensor noise density, earthquake duration time and IDR distribution.
While the focus of this paper is accelerometers, we believe that hybrid systems that combine multiple modalities (e.g. accelerometers + GPS + Camera) will provide enhanced accuracy over a single modality. The trade-offs involved in these systems will be the subject of future work. | https://www.groundai.com/project/effect-of-sensor-error-on-the-assessment-of-seismic-building-damage/ |
1.. Introduction {#s1}
================
One of the primary areas of investigation in comparative genomics is the identification and characterization of homologous regions in closely related genomes. The subjects of these investigations range in scale from multi-megabase syntenic regions covering most of a chromosome to small loci containing just a few genes. Studying the syntenic regions can uncover large-scale events in the evolutionary history of a genome, such as segmental duplications or polyploidization; however, these regions in different species can differ significantly. Such variation results from a large number of genomic alterations occurring over time while maintaining sufficient collinearity to define regions of synteny. On the other hand, comparative analysis of small loci can produce detailed evolutionary histories of groups of neighboring genes and provide examples of the types of changes possible in a genome. However, it is difficult to expand these studies to a genome-wide scale due to the number of genes involved and the problem of generalizing these types of changes to allow their quantification.
In this study, we conduct an intermediate form of comparative analysis. By examining pairs of adjacent genes, we can detect changes at the level of single genes and still observe relationships between genes. Owing to the simplicity and small scale of our subjects, all changes can be assigned to a manageable number of classes, thereby producing results that are easily interpreted in genome-wide studies of this type. Our previous investigation compared gene pairs^[@DSQ022C1]^ in three plant species (rice, *Arabidopsis*, and *Populus*) which diverged 130--200 million years ago (mya).^[@DSQ022C2]--[@DSQ022C4]^ This study, on the other hand, compares four members of the Poaceae family (rice, sorghum, maize, and *Brachypodium*) whose last common ancestor dates to 50--70 mya.^[@DSQ022C2],[@DSQ022C5]^ Genomes of the four grass species used in this study have been sequenced.^[@DSQ022C6]--[@DSQ022C9]^ The shorter evolutionary distances separating these species simplifies the interpretation of any observed genomic rearrangements, due to the reduced probability of multiple independent events affecting the same region. However, many small rearrangements have been identified in earlier comparative studies of Poaceae genomes,^[@DSQ022C10],[@DSQ022C11]^ providing sufficient variation among genomes to identify any trends regarding selection for or against disruption of ancestral gene pairs. It has been hypothesized that gene order is not entirely random, but rather is connected to gene function and regulation,^[@DSQ022C12]^ and that genomic rearrangements can alter the function of genes or even lead to the creation of new gene families. Thus, gene order possibly contributes to phenotypic differences between species, even when individual genes are conserved.^[@DSQ022C13]^
We previously reported^[@DSQ022C1]^ that their strand-wise arrangement has a significant influence on many characteristics of gene pairs. For this study, we classified all pairs of adjacent genes as convergent (→ ←), divergent (← →), or tandem (→ → or ← ←), we identified homologous genes in other species and determined the status of each pair (conserved, inverted, moved, or missing homologs). We also estimated the effect of correlated expression on these types of gene-pair rearrangements. To gain an understanding of the evolutionary timing of the rearrangements we observed, a putative evolutionary history was created for each gene pair, based on its status in each of the four species. Overall, this study provides an overview of the frequencies and types of genomic rearrangements within a subset of the Poaceae, as well as many other properties of the genomes being studied.
2.. Materials and methods {#s2}
=========================
2.1.. Identification of gene pairs {#s2a}
----------------------------------
Genome sequence and annotation data were downloaded for rice (*Oryza sativa* subsp. *japonica*; <http://rice.plantbiology.msu.edu>, MSU rice pseudomolecules release 6), sorghum (*Sorghum bicolor*; <http://www.phytozome.net/sorghum>, sequence assembly v1.0, gene set v1.4), maize (*Zea mays*; <http://www.maizesequence.org>, release 3a.50), and *Brachypodium* (*Brachypodium distachyon*; <http://www.brachypodium.org>, 8X coverage release). A second set of rice sequence and annotation data was obtained from the Rice Annotation Project (RAP; <http://rapdb.dna.affrc.go.jp/>, sequence build 5) for comparison with the MSU rice gene set and was processed and analyzed using the same methods as the MSU rice and sorghum gene sets. Annotated genes in the rice and sorghum genomes were sorted by chromosome and position and then, based on which strand the gene is transcribed from, all pairs of adjacent genes were classified as either convergent (→ ←), divergent (← →), or tandem (→ → or ← ←) pairs. Pairs containing hypothetical- or transposon-related genes, as determined by annotation and RepeatMasker ([www.repeatmasker.org](www.repeatmasker.org); 50% or greater transposon content of unspliced sequence), were excluded from all analyses.
2.2.. Comparative sequence analysis {#s2b}
-----------------------------------
The coding region sequences of all rice and sorghum gene pairs were aligned with the genome assemblies of the other three species using BLASTN. For each gene, individual hits (presumably corresponding to single exons) with *e*-values of 0.00001 or less were grouped with other nearby hits on the same strand and contig to produce a putative homolog. The locations of each pair\'s homologs were then used to determine the pair\'s status in that species. Pairs were considered 'conserved\' if both genes had homologs in the original strand-wise arrangement (convergent, divergent, or tandem) within 50 kb of each other and had no other genes inserted between them. Fifty kilobases were chosen to allow for insertions of repetitive DNA such as nested retrotransposons. 'Inverted\' pairs also possessed homologs within the cutoff distance, but had different strand-wise arrangements than the original pair. Pairs were considered 'rearranged\' if homologs for both genes were found but were \>50 kb apart, separated by other genes, or located on different contigs. Those pairs in which one or both genes were missing homologs in a given species were also identified. In addition to 50 kb, genes residing within 20 and 75 kb were used to perform the above analysis.
2.3.. Expression analysis {#s2c}
-------------------------
Two types of quantitative expression data were collected for all rice genes (MSU data): microarray and massively parallel signature sequencing (MPSS). First, MPSS^[@DSQ022C14]^ data were downloaded from the Rice MPSS Database (<http://mpss.udel.edu/rice/>). Only 17-bp signatures of classes 1, 2, 5, and 7 that mapped to a single gene were used, and abundance values \<5 were ignored as background interference. When multiple signatures had significant abundance values in the same library, their average abundance was used. Correlated expression between genes in convergent, divergent, and tandem pairs was examined by calculating the Pearson correlation coefficient using each gene\'s average abundance values across 72 libraries.
Microarray data were downloaded from the Yale rice project (<http://bioinformatics.med.yale.edu/rc/overview.jspx>) for a total of 446 hybridizations. Correlated expression was again tested with the Pearson correlation coefficient, this time pairing data points for each gene from the same hybridization and channel, where data were available for both genes for that hybridization and channel.
Correlation coefficients were calculated separately for each expression data type. Thus, if expression data were present for both genes in both sets, a gene pair would have both an MPSS-derived and microarray-derived correlation coefficient. For those pairs with both coefficients, the pair was considered strongly correlated if at least one was greater than the cut-off value.
The fraction of strongly correlated gene pairs falling into each of the four categories (conserved, inverted, rearranged, or missing homologs) was then compared with the fractions of uncorrelated or weakly correlated pairs in those same categories. The statistical significance of their differences was evaluated using the normal approximation of the binomial test, with a significance level of *P* \< 0.05 (*Z* \> 1.6449). Two definitions of 'strong\' correlation were used: the first one using a correlation coefficient cut-off of 0.5 used in other studies,^[@DSQ022C1],[@DSQ022C15]^ and the second one based on a *P* \< 0.05 significance level for a normal distribution with a mean of 0.187 and a standard deviation of 0.247, the sample statistics from the set of all calculated correlation coefficients, giving a minimum 'strong\' correlation of 0.594.
2.4.. Evolutionary analysis of gene pairs {#s2d}
-----------------------------------------
The evolutionary history of each gene pair was constructed by comparing the status of the pair in each of the four species in this study. The likelihood of a given scenario was based on the number of gene rearrangements, deletions, and conservation using the fewest possible changes to the homologous regions of the last common ancestor to arrive at the present state. Gene pairs were then assigned to one of 14 groups based on their putative histories that could produce the observed results of the comparative analysis. Rice MSU data were used for this analysis.
3.. Results and discussion {#s3}
==========================
3.1.. Conservation and rearrangements {#s3a}
-------------------------------------
Convergent, divergent, and tandem gene pairs in the rice and sorghum genomes were identified as described in methods. Four thousand and eight hundred convergent pairs, 3711 divergent pairs, and 9428 tandem pairs from the MSU rice gene set and 5059 convergent, 4913 divergent, and 11847 tandem pairs from the sorghum gene set were identified.
The primary goal of this analysis was to determine how frequently the exact arrangement of a pair of adjacent genes is conserved in the genomes of other grass species and what changes have taken place when the pair is not conserved. Out of the four grass species selected for this study, rice and sorghum were chosen as starting points for comparisons because their sequence and annotation data sets were considerably better than those of maize and *Brachypodium*. Our comparative sequence analysis placed each rice or sorghum gene pair into one of four categories based on the presence or the absence of homologous genes and their locations in the genome. A pair of adjacent genes in rice/sorghum was considered to be conserved in other genomes when both the individual sequences of genes and the strand-wise arrangement of the pair were conserved. If a pair\'s homologs were found to be still adjacent but with a different strand-wise arrangement, then the pair was designated 'inverted\'. Homologs falling on different contigs, separated by other genes, or \>50 kb apart were considered 'rearranged\'. Finally, one or both genes in the original pair may be lacking homologs because they were deleted in that species' lineage or they arose in the ancestors of rice or sorghum after diverging from their last common ancestor. Together, these categories include all the major events of genomic evolution at this scale, and the relative frequencies of these events provide insight into the importance of proximity and strand-wise arrangement to proper gene function and regulation. To estimate the statistical significance of the variation observed among pair types, we compared the fraction of pairs of each type that fell into each category with the corresponding fraction of all pairs in that category.
Conservation rates for both rice and sorghum gene pairs (Figs [1](#DSQ022F1){ref-type="fig"} and [2](#DSQ022F2){ref-type="fig"}, [Supplementary Tables S1 and S2](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1)) followed quite similar patterns. In every comparison, divergent gene pairs were conserved least often, with conservation frequencies significantly below the all pair average. Similarly, convergent pairs were conserved significantly more often than the all pair average. Tandem pair conservation rates were generally close to the all pair average. The conservation frequency differed a great deal among pair types in maize, where divergent pairs are conserved at rates close to half that of convergent or tandem pairs. Further, in *Brachypodium*, rice gene pairs are more frequently conserved than sorghum pairs. Although *Brachypodium* appears to be closer to rice than sorghum based on the divergence times of 40--53 Myr for *Brachypodium*--rice and 45--60 Myr for *Brachypodium*--sorghum based on synonymous substitution rates (Ks) of orthologous gene pairs,^[@DSQ022C9]^ these evolutionary relationships are not well resolved. Likewise, maize is more closely related to sorghum than to rice^[@DSQ022C11],[@DSQ022C16]^; thus, sorghum pairs have higher rates of conservation in maize than do rice pairs. Figure 1.Conservation and rearrangement of rice gene pairs (MSU data) in sorghum, maize, and *Brachypodium*. A '+\' or '−\' at the base of a column indicates that pairs in that class are significantly (*P* \< 0.01) overrepresented or underrepresented, respectively, compared with the general population of gene pairs using *Z*-test. Figure 2.Conservation and rearrangement of sorghum gene pairs in rice (MSU data), maize, and *Brachypodium*. A '+\' or '−\' at the base of a column indicates that pairs in that class are significantly (*P* \< 0.01) overrepresented or underrepresented, respectively, compared with the general population of gene pairs using *Z*-test.
Inversion of one or both genes was quite a rare phenomenon, ranging from 0.5% of sorghum tandem pairs inverted in rice (Fig. [1](#DSQ022F1){ref-type="fig"}A) to 2% of sorghum divergent pairs in maize (Fig. [2](#DSQ022F2){ref-type="fig"}B). We observed some variation among different pair types and comparison species, but the variation was not statistically significant.
Among rearranged pairs, rice and sorghum gene pairs differ more than conserved and inverted pairs. Overall, sorghum pairs are more likely to be rearranged than rice pairs, with the rearrangement rates of sorghum pairs being ∼10--20% higher than those of rice pairs (Figs [1](#DSQ022F1){ref-type="fig"} and [2](#DSQ022F2){ref-type="fig"}). For both rice and sorghum pairs, rearrangement is most common in maize (Figs [1](#DSQ022F1){ref-type="fig"}B and [2](#DSQ022F2){ref-type="fig"}B) by a substantial margin and is least common in *Brachypodium* (Figs [1](#DSQ022F1){ref-type="fig"}C and [2](#DSQ022F2){ref-type="fig"}C). Divergent pairs are consistently the most commonly rearranged type, whereas convergent and tandem pairs are generally rearranged with similar frequencies in all comparison species.
Considerable differences between rice and sorghum were also noted among gene pairs lacking homologs for one or both genes. Rice pairs missing homologs in sorghum are roughly one-half more common than sorghum pairs missing homologs in rice (15.7% versus 9.9%). In maize, rice genes are missing homologs more than twice as often as sorghum genes (22.7% versus 10%). The fractions of rice and sorghum pairs without homologs in *Brachypodium* are almost equal. Pair type does not seem to affect the presence or the absence of homologs because none of the pair types in any comparison species deviated significantly from the all pair average.
Conservation and rearrangement rates differ between maize and the other comparison species most likely as a result of three primary sources. First, the genomic sequence of maize used in our study is in the form of individual BAC sequences, most of which are shorter than ∼250 kb, rather than in the form of assembled sequences of near-chromosome length. Smaller sequences are, of course, less likely to contain complete gene pairs, especially if their intergenic regions have accumulated other genes or transposons over time. Second, transposons make up a much larger fraction of the maize genome than that of rice, sorghum, or *Brachypodium* genomes. In addition to physically disrupting the region into which they insert themselves, transposons can also increase the likelihood of recombinations, deletions, and other alterations in any area they inhabit. Third, the ancestors of maize quite likely suffered large-scale gene loss.^[@DSQ022C16]^ If the first gene in a pair is deleted from one copy and the second gene was deleted in the other copy of the pair, both genes would still exist in the genome, but would no longer be paired. This type of occurrence would explain why more rice and sorghum gene pairs had more physically distant homologs in maize than in any other comparison species. All these factors would reduce the frequency of gene-pair conservation and correspondingly increase rearranged pairs, as we observed.
In addition to 50 kb, genes residing within 20 and 75 kb were used to perform the above analysis. Although the number of gene pairs varied, the results showed same trends that were observed with 50 kb limit ([Supplementary Tables S3 and S4](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1)).
Comparative analysis was performed using a second set of rice genome annotation data, from the RAP (<http://rapdb.dna.affrc.go.jp)>,^[@DSQ022C17]^ to evaluate the effect of different methods of genome annotation on our results. We found that the analysis of the MSU rice gene set as well as the RAP gene set exhibited similar major trends regarding differences among the three pair types and comparison species. Although many of the same conclusions about conservation and rearrangement of gene pairs could be inferred from both the MSU and RAP results, significant differences exist between the two data sets (Table [1](#DSQ022TB1){ref-type="table"} and [Supplementary Table S5](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1)). In sorghum, gene pairs identified using the RAP annotation data were conserved significantly less frequently than the MSU rice gene pairs, whereas the fractions of rearranged pairs were significantly higher among all pair types in sorghum and *Brachypodium*, and among tandem gene pairs in maize. Last, pairs missing homologs were less common overall when using the RAP annotation data, with the largest differences being found in maize and *Brachypodium*. However, comparing Fig. [1](#DSQ022F1){ref-type="fig"}, [Supplementary Table S1](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1), and Table [1](#DSQ022TB1){ref-type="table"}, nine statistically significant comparisons of conserved and rearranged gene pairs were common when MSU and RAP gene sets were used as starting points. The remaining two statistically significant comparisons (rice convergent pairs conserved and rearranged in *Brachypodium*) using the MSU gene set were close to being significant using the RAP gene set. These variations are most likely due to differences in RAP and MSU annotations. The MSU gene set contains considerably more genes than the RAP set (57 840 versus 34 780), a distinction that remains even after excluding hypothetical- and transposon-related genes (29 686 versus 22 308). Therefore, it is likely that either the MSU set contains a large number of incorrectly predicted genes or the RAP set is missing a similar number of real genes. The lower rates of missing homologs among the RAP set suggests that at least some of the genes found only in the MSU set are either false positives or unique to rice. These unique genes could also be low copy number transposable elements which are transcribed but not annotated as transposable elements.^[@DSQ022C18]^ Table 1.RAP rice gene-pair conservation and rearrangementPairsConserved*Z*-valueInverted*Z*-valueRearranged*Z*-valueMissing homologs*Z*-valueRice versus sorghum Convergent36411169 (32.1%)**4.91**112 (3.1%)0.781875 (51.5%)−**6.50**485 (13.3%)−0.31 Divergent3376648 (19.2%)−**4.01**119 (3.5%)1.022160 (64.0%)**4.82**449 (13.3%)−0.31 Tandem75821887 (24.9%)−0.5139 (0.5%)−1.124580 (60.4%)1.951076 (14.2%)0.37 Total14 5993704 (25.4%)270 (1.8%)8615 (59.0%)2010 (13.8%)Rice versus maize Convergent3641987 (27.1%)**3.96**103 (2.8%)0.321880 (51.6%)−**4.92**671 (18.4%)−0.31 Divergent3376472 (14.0%)−**4.71**146 (4.3%)1.202137 (63.3%)**5.75**621 (18.4%)−0.33 Tandem75821678 (22.1%)0.6292 (1.2%)−0.954347 (57.3%)0.041465 (19.3%)0.41 Total14 5993137 (21.5%)341 (2.3%)8364 (57.3%)2757 (18.9%)Rice versus *Brachypodium* Convergent36411429 (39.2%)1.82117 (3.2%)0.501569 (43.1%)−2.25526 (14.4%)−0.23 Divergent33761128 (33.4%)−**2.48**154 (4.6%)1.291587 (47.0%)0.88507 (15.0%)0.14 Tandem75822830 (37.3%)0.4781 (1.1%)−1.173541 (46.7%)0.961130 (14.9%)0.10 Total14 5995387 (36.9%)352 (2.4%)6697 (45.9%)2163 (14.8%)[^2]
3.2.. Effects of correlated expression on rearrangements {#s3b}
--------------------------------------------------------
The Pearson correlation coefficient of all rice gene pairs was calculated using microarray and MPSS expression data. Those pairs with coefficients of 0.5 or greater were considered significantly correlated as described earlier.^[@DSQ022C1]^ The full set of rice gene pairs (MSU data set) was divided into correlated and uncorrelated sets, and difference in the frequencies of each type of rearrangement within these sets was tested for significance using the binomial test. The purpose of this test was to determine whether gene pairs with correlated expression levels were subject to any of the various types of rearrangements at a significantly different rate than uncorrelated pairs.
Correlated divergent and tandem gene pairs were more common among conserved pairs in all three species (Table [2](#DSQ022TB2){ref-type="table"}), although the increase in conservation was statistically significant only for tandem pairs in sorghum and for divergent and tandem pairs in *Brachypodium*. The difference in the conservation rates between correlated and uncorrelated pairs was highest for tandem pairs, followed closely by divergent pairs, whereas the effect of correlation on convergent pairs was considerably weaker. Conservation of coexpressed tandem gene pairs could be due to tandemly duplicated genes which are likely to have similar expression patterns. Conservation of coexpressed divergent gene pairs could be due to bidirectional promoters regulating these gene pairs.^[@DSQ022C19]^ Table 2.Conservation and rearrangement of correlated rice gene pairs with *r* \> 0.5TotalConservedInvertedRearrangedMissing homologsNumberPercentage*Z*-valueNumberPercentageZ-valueNumberPercentageZ-valueNumberPercentageZ-valueRice versus sorghum ConvergentCorrelated32915346.51.6172.11.9113541.0−0.423410.3−**2.21**Uncorrelated4471188342.1471.1188642.265514.6 DivergentCorrelated2969732.81.2841.40.8015351.7−0.534214.2−1.07Uncorrelated3415100329.4310.9181853.256316.5 TandemCorrelated65127642.4**2.98**40.60.2326340.4−**3.21**10816.60.40Uncorrelated8777322736.8480.5409646.7140616.0Rice versus maize ConvergentCorrelated32910130.70.9451.50.5617152.00.925215.8−**2.32**Uncorrelated4471126828.4531.2221049.494021.0 DivergentCorrelated2964214.21.3441.4−0.8518161.1−0.856923.30.23Uncorrelated341539911.7702.0216963.577722.8 TandemCorrelated65116625.51.9060.9−0.5231648.5−**2.22**16325.00.87Uncorrelated8777196622.41001.1464152.9207023.6Rice versus Brachypodium ConvergentCorrelated32914142.90.3541.2−0.4812437.70.066018.2−0.37Uncorrelated4471187341.9691.5167837.585119.0 DivergentCorrelated29611237.8**1.98**51.70.1911839.9−1.416120.6−0.61Uncorrelated3415110832.4531.6150043.975422.1 TandemCorrelated65126640.9**2.23**81.20.4524737.9−**2.28**13020.00.01Uncorrelated8777321736.7921.0371742.3175119.9[^3]
The small sample size used in the examination of the effect of correlated expression on gene-pair inversion reduced the effectiveness of the binomial test. In contrast, correlated expression in rice gene pairs appears to select against the disruption of a gene pair\'s physical arrangement in the other three grass genomes, with tandem pairs being significantly underrepresented in all three comparison species among pairs whose homologs are physically distant (Table [2](#DSQ022TB2){ref-type="table"}). Divergent pairs showing correlated expression are also underrepresented in all three species, although the difference is not statistically significant. Correlated convergent pairs showed no significant difference compared with non-correlated pairs.
Rice-correlated convergent pairs were strongly underrepresented among pairs lacking homologs in sorghum and maize.
A second analysis was performed, this time using a statistically significant (see 'Materials and methods\' section for details) cut-off value for 'strong\' correlation of *R* \> 0.594 ([Supplementary Table S6](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1)). The greatest difference between this analysis and the first one using a cut-off of *R* \> 0.5 is the number of strongly correlated pairs. The reduced sample size substantially affects the ability of the binomial test in determining significant variation between correlated and non-correlated pairs. As a result, statistical significance was observed only in convergent gene pairs missing homologs in maize, which were significantly underrepresented among strongly correlated pairs. Otherwise, most trends noted in the first analysis were also observed in the second analysis, with modest increases in conservation and inversion frequency and decreases in rearrangement frequency. The fractions of pairs missing homologs, either unchanged or reduced with the *R* \> 0.5 definition of strong correlation, were more often increased with the alternative definition. These differences most likely result from the smaller sample size and its effect on the statistical test rather than any real biological differences between the set of gene pairs with *R* \> 0.5 and those with *R* \> 0.594.
Rice gene pairs displaying strongly correlated expression levels were more likely to be conserved in sorghum, maize, and *Brachypodium*. These results lend further support to the hypothesis that the strand-wise arrangement of pairs of adjacent genes may be essential to the regulatory schemes of some strongly correlated gene pairs, such that rearrangements disturbing the pair would be selected against. Correlated expression levels have also been found to increase the likelihood of conservation among fungi.^[@DSQ022C20]^ The largest increases in the frequency of conservation as a result of correlated expression was observed among divergent and tandem pairs, a pattern that has been observed before in a comparison of human, mouse, and chicken gene clusters.^[@DSQ022C21],[@DSQ022C22]^ Therefore, correlated expression levels increasing the likelihood of conservation appears to be a universal phenomenon in eukaryotes including plant genomes.
3.3.. Evolutionary history of gene pairs {#s3c}
----------------------------------------
The estimated evolutionary history of each rice or sorghum gene pair was arrived at by examining the status of each gene pair in its three comparison species. For this analysis, a pair could be in one of three states in each species: conserved, rearranged (physically distant homologs, any inversion, and insertions), or deleted (one or both homologs nonexistent). On the basis of the possible combinations of these states, 14 categories of evolutionary history were devised. The putative evolutionary tree for the four species consisted of two branches, one with rice and *Brachypodium*, the other with sorghum and maize. Similarities within branches, as well as differences between them, served as the basis for many of the 14 categories.
The first category consisted of those pairs whose exact arrangement was shared in all four species (Table [3](#DSQ022TB3){ref-type="table"}, four species, and Fig. [3](#DSQ022F3){ref-type="fig"}A). Results varied little between the rice- and sorghum-based analyses. Convergent pairs were the most common in this class, with over 18% of pairs falling into this category, followed by tandem pairs (∼10%) and divergent pairs (∼6%). Table 3.Evolutionary history of rice and sorghum gene pairsRiceSorghumConvergentDivergentTandemConvergentDivergentTandemPair with conserved orientation in four species874 (18.2%)207 (5.6%)934 (9.9%)921 (18.2%)258 (5.3%)1222 (10.3%)Pair with conserved orientation in three species One rearrangement878 (18.3%)591 (15.9%)1827 (19.4%)932 (18.4%)800 (16.3%)2245 (18.9%) One deletion64 (1.3%)33 (0.9%)151 (1.6%)56 (1.1%)28 (0.6%)158 (1.3%)Pair with conserved orientation in two species Branch-specific pairs Others rearranged396 (8.3%)434 (11.7%)945 (10.0%)408 (8.1%)215 (4.4%)840 (7.1%) Others deleted53 (1.1%)30 (0.8%)129 (1.4%)20 (0.4%)14 (0.3%)101 (0.9%) One deletion, one rearrangement32 (0.7%)25 (0.7%)78 (0.8%)45 (0.9%)24 (0.5%)110 (0.9%) Cross-branch conserved pairs Others rearranged340 (7.1%)346 (9.3%)974 (10.3%)438 (8.7%)718 (14.6%)1481 (12.5%) Others deleted24 (0.5%)12 (0.3%)71 (0.8%)10 (0.2%)4 (0.1%)51 (0.4%) One deletion, one rearrangement68 (1.4%)45 (1.2%)163 (1.7%)55 (1.1%)57 (1.2%)225 (1.9%)Pair with unique orientation in one species Species-specific gene(s)505 (10.5%)475 (12.8%)1130 (12.0%)197 (3.9%)218 (4.4%)529 (4.5%) Common genes, species-specific pair1037 (21.6%)1047 (28.2%)2038 (21.6%)1293 (25.6%)1730 (35.2%)3189 (26.9%) Branch-specific genes, species-specific pair73 (1.5%)51 (1.4%)170 (1.8%)158 (3.1%)219 (4.5%)457 (3.9%) Two rearrangements, one deletion, mixed299 (6.2%)278 (7.5%)530 (5.6%)395 (7.8%)460 (9.4%)913 (7.7%) One rearrangement, two deletions, mixed157 (3.3%)137 (3.7%)288 (3.1%)131 (2.6%)168 (3.4%)326 (2.8%) Figure 3.Categories of gene-pair evolution. Each image is a representative of the many specific scenarios that may be found in that category. The bottom branch of each tree represents the species in which the pair was first identified (i.e. either rice or sorghum), and the two genes in question are shown in a divergent pair in these examples. Rearrangements are represented by the inversion of one gene, inversion of both genes, insertions within the pair, or translocation to other regions or chromosomes. Likewise, deletions may involve one gene, as shown, or both genes in the pair. In some of the scenarios where the pair is conserved in two species (D, E, G, and H), the rearranged or deleted states are just as likely to be the ancestral state as the divergent pair shown. In scenario L, it is also possible that both genes existed in the common ancestor and a deletion took place in the top branch rather than new gene(s) being created.
Pairs conserved in two of their three comparison species most likely underwent a single species-specific rearrangement or deletion (Table [3](#DSQ022TB3){ref-type="table"} three species, and Fig. [3](#DSQ022F3){ref-type="fig"}B and C). The former event was by far the most common, comprising 16--19% of all pairs, compared with the ∼1% or less of pairs with one or both homologs deleted in a single species. Rice and sorghum results differed by less than one percentage point across all pair types.
The six categories comprise pairs conserved in only one other species were divided into two groups (Table [3](#DSQ022TB3){ref-type="table"}, two species), those in which the pair was conserved within one branch of the evolutionary tree (i.e. a rice pair conserved in *Brachypodium*), referred to here as a 'branch-specific\' pair (Fig. [3](#DSQ022F3){ref-type="fig"}D--F), and those in which the pair was conserved in one species in each branch, a state referred to as 'cross-branch conservation\' (Fig. [3](#DSQ022F3){ref-type="fig"}G--I). Among both branch-specific and cross-branch conserved pairs, it was far more common (7--12% of pairs in rice and 4--15% in sorghum) for the pair to be rearranged in the other two species than for it to be deleted in one (0.5--1.9%) or both species (0.1--1.4%). In rice, branch-specific pairs were slightly more common than cross-branch conserved pairs; in sorghum, the opposite was true. There were only two sets of genes in which rice and sorghum differed substantially. The first was branch-specific divergent pairs with the pair being rearranged in the other two species, including 11.7% of rice divergent pairs but only 4.4% of sorghum pairs (Table [3](#DSQ022TB3){ref-type="table"}, two species). The opposite situation was observed among cross-branch conserved divergent pairs, again with two rearrangements. These pairs made up 9.3% of rice divergent pairs, compared with 14.6% of sorghum pairs.
The last five categories consist of pairs with unique orientation in only one species (Table [3](#DSQ022TB3){ref-type="table"}, one species). Pairs whose genes exist in all four species but whose pair-wise arrangement is found in a single species (Fig. [3](#DSQ022F3){ref-type="fig"}K) were the most common category in both species (25--35% in sorghum and 21--28% in rice). Divergent pairs fell into this category substantially more often than convergent or tandem pairs in both rice and sorghum. In rice, the second most common category (10--12% of all pairs) is those pairs containing one or more genes unique to that species (Fig. [3](#DSQ022F3){ref-type="fig"}J); in sorghum, this category is approximately one-third that of rice. These observations are most likely due to differences in the gene annotation methods used by the two genome projects and/or a larger number of genes unique to rice than to sorghum reflecting their biology. This conclusion is supported by RAP data which identified 56, 28, and 172 species-specific genes that are part of convergent, divergent, and tandem gene pairs, respectively, in rice but not the other three grass genomes, respectively, compared with 505, 475, and 1130 species-specific rice genes in MSU data that are part of convergent, divergent, and tandem gene pairs, respectively. A few other studies have also identified several genes and gene families specific to rice and sorghum.^[@DSQ022C7],[@DSQ022C23]^ The third category (Fig. [3](#DSQ022F3){ref-type="fig"}L) for all pair types were more than 2-fold in sorghum compared with rice (Table [3](#DSQ022TB3){ref-type="table"}, one species). The distribution of pairs among the remaining two categories (Fig. [3](#DSQ022F3){ref-type="fig"}M and N) showed little variation both between rice and sorghum and between pair types.
Overall, our study provides valuable insights into conservation and rearrangement of gene pairs during the evolution of the grasses serving as basis for future investigations on functional interactions between adjacent genes.
Supplementary data {#s4}
==================
[Supplementary data are available at www.dnaresearch.oxfordjournals.org](http://dnaresearch.oxfordjournals.org/cgi/content/full/dsq022/DC1).
Funding {#s5}
=======
This work was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service (2007-35301-18036).
Supplementary Material
======================
###### Supplementary Data
[^1]: Edited by Satoshi Tabata
[^2]: Test used is the binomial test (normal approximation) with cutoff of *P* \< 0.01 (*Z* \< 2.3267) shown in bold.
[^3]: Values in the '*Z*\' columns are test statistics of the binomial test. Values in bold denote significant differences (*P* \< 0.05) in the frequency of strongly correlated pairs in each category compared with the frequency of uncorrelated pairs.
| |
Vanderbilt Commencement is todayMay. 10, 2019, 8:45 AM
An expected 1,701 undergraduates and 2,125 graduate students will receive degrees from Vanderbilt University today at ceremonies held across campus.
Watch a livestream of the ceremony on Alumni Lawn. >>
The main Commencement ceremony will begin at 9 a.m. on Alumni Lawn, with Chancellor Nicholas S. Zeppos addressing Class of 2019 graduates, their friends and family members. It will be Zeppos’ final Commencement as chancellor, having announced earlier this year that he will step down Aug. 15 and take a yearlong sabbatical before returning to the faculty as a law professor.
As part of its sustainability initiative, Vanderbilt will distribute 2,000 reusable water bottles and offer hydration stations for guests to fill their own reusable containers at the main Commencement ceremony, reducing thousands of single-use plastic water bottles at the event.
Undergraduates and their families are invited to join faculty, classmates and others at 12:15 p.m. for strawberries and champagne on Library Lawn. Near the strawberries and champagne tent, Barnes & Noble will host a pop-up shop. All in attendance are encouraged to stop by and view the selection of Vanderbilt University merchandise and apparel available for purchase.
Students and families are encouraged to share their Commencement excitement on social media using the hashtag #VU2019. | https://news.vanderbilt.edu/2019/05/10/vanderbilt-commencement-is-today/ |
Two 10-week-old puppies that had been helping an autistic boy to express emotion have gone missing from the back yard of a beauty salon in Stanwell.
Hong Duong, known as 'Julie Le' to her friends and customers, runs Pinky J nail, hair and beauty salon in Clare Road, where the puppies were being kept during the day. She believes they were stolen as CCTV footage from nearby businesses appeared to show two men carrying the puppies shortly after they disappeared.
The 42-year-old bought the male jack russell terrier puppies, named Dragon and Hunter, just 10 days before they went missing, on Saturday, June 22 at about 6.30pm.
Ms Duong has been left devastated and desperately wants to be reunited with her "two handsome newborn babies".
"I'm heartbroken," she said. "I have two boys – they really loved my dogs. I wanted to train them before I gave one to my mum and dad. They are really ill and having a puppy has really helped them a lot.
"My first son has autism and struggles to speak, but as soon as he saw the puppies, he started showing some expression and talking. It brought out a lot of nice things for the family."
Ms Duong would take the puppies to work, where they had their own space in the back yard with a cage, blankets, food and water.
Her customers loved visiting and playing with the puppies, and she said it was "beautiful" to watch the two of them cuddling outside on the blankets.
Despite being surrounded by a six-foot wall, it is thought someone jumped over the wall and took them while Ms Duong was painting one of her client's nails. She went back outside and saw they were missing.
"My heart just dropped," she said. "There were so many things going round my head – How? When? Who did it? I kept thinking – is it my fault? Is it my staff?"
Ms Duong, her clients, friends and the local community rallied together to search the surrounding area, but couldn't find them.
She claims CCTV footage from local businesses shows two shirtless men carrying the puppies away from her property.
She said: "If they can take things that easily, and steal without asking, they will do it again and again. They will bully, bully, bully and we can't let that happen.
"I don't want this to continue. I do not want to see this happening to them or for my kids to see this happening. I want them to feel free and safe.
"They better bring back the puppies fast."
Surrey Police has filed the case, saying if more information comes to light, it will be reopened.
A spokesman said: "The puppies are 10 weeks old, both are male and are microchipped – Dragon (981000010721021) and Hunter (981000010731506). One of the puppies was wearing a red collar with paw prints on, and one was wearing a plain blue collar.
"Officers have carried out lines of enquiry, including reviewing CCTV and liaising with local partners and agencies, so should these dogs be located they can be returned to their rightful owner. The case has been filed but will be reviewed pending any new information coming to light."
Anyone with information is asked to contact Surrey Police on 101 quoting reference number PR/45190065289.
Alternatively, contact Ms Duong on 07404 734445. | https://www.getsurrey.co.uk/news/surrey-news/woman-heartbroken-after-10-week-16496467 |
The dance team was arranging seats for its performance. They expected 225 people to attend, and they wants to arrange the seats in fewer than 10 equal rows. How many rows and seats per row could they set up for the performance?
1 answers
Answered May 18Accounting
Verified
Husain MukadamMake Learning Fun Again! MSc | BSc | 4yrs+ exp. | DBS Certified✔️423 students helped
If you have 22 seats per row, you'll end up with 10 equal rows but 5 extra seats left (for an 11th row). With 23 seats per row, you'll end up with 9 equal rows, plus a 10th row with 18 seats.
Ask questions
Get an answer in 5 minutes from expert tutors at Oxford, Cambridge, Imperial and more. | https://scoodle.co.uk/questions/in/accounting/the-dance-team-was-arranging-seats-for-its-performance-they-expected-225-people-to-attend-and-they-wants-to-arrange-the-seats-in-fewer-than-10-equal-rows-how-many-rows-and-seats-per-row-could-they-set-up-for-the-performance |
Beyond the Books
Talking with the experts who solve the world's biggest problems.
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We are two biomedical engineering students at the University of Waterloo who love to learn new things. Join us as we interview experts conducting research into COVID-19, happiness, blackholes and everything in between. We know that research can be very confusing, but we're here to help you understand, learn, and most importantly, have fun!
Latest Episode - Beyond Earth with Col. Chris Hadfield
We're beyond thrilled for this episode with Canadian legend Chris Hadfield! The former commander of the International Space Station drops by Beyond the Books to discuss life in space, his work on the ISS, and more! What is 0G like? What does food taste like in outer space? How does he feel about the portrayal of astronauts in popular media? We talk about his upcoming book, The Apollo Murders, and see if he can tell whether some famous quotes are from real astronauts or characters from movies/TV!
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On a beautiful Saturday evening, I sat on my balcony, relaxing my tired body from the week’s work. I was glad I had no wedding or any ceremony to attend. It was just me having a good time in my own way. Thankful to God, the breeze was cool, so soothing it was to my tired head that I was beginning to doze off when I suddenly heard a shrill voice downstairs. It was the wailing of a child, I wanted to ignore it and just keep enjoying myself but the cry wouldn’t stop. So I bent over the handrails to shush the child but I just stood there watching, as the drama unfolded before me.
I saw the weeping child rolling on the floor, throwing tantrums and crying nonstop, I managed to listen to her words, she was shouting “give me my candy, give me my candy”. There was another older child trying to placate her while the oldest was inspecting the so called candy. Obviously the oldest child had snatched the candy from the youngest child now wailing. The older child was confused, while trying to placate the youngest child he was staring angrily at the oldest. All I wanted was to make them stop so I can get back to my relaxation but the drama hadn’t finished.
The oldest child shouted “David come here” the older child didn’t answer, he didn’t want to leave the wailing child. But the oldest called again, “David, are you deaf? I say come here now”! Still, he didn’t respond to the call. But as he saw him coming, he ran towards him and angrily mumbled ‘Yes’. The oldest looked him over, he even wanted to slap him but didn’t carry out his threat. All the while the wailing child didn’t stop, the oldest child drew David by his ears, reprimanding him sternly “Are you blind? Can’t you see that there is a hole in the candy you bought for our Daniella? Didn’t you hear when Mum told us to always check the things we buy very well before we leave the shop? Again, I can see an opening on the wrap, which means a sugar ant had gained access.” David was now remorseful, he saw that the fault was from him. So he bowed his head, avoiding the eyes of his brother “Now what are you going to do? The oldest child fired back “I will go and change it”. David said silently.
David took the candy from his elder brother and ran out of the compound, when the wailing child saw David taking the candy away, she increased her wailing again. The drama was interesting, I could not go back to my chair. While David was away, the oldest child looked away from the wailing child. The child looked at him judgingly but he stood there with his back turned to her. David ran into the compound with another piece of candy, he was elated as he ran towards his elder brother. The brother inspected the piece of candy over and over and certified it okay. “Now go and give your sister, he ordered”. The child rose silently as he saw David coming towards her, David gave her the candy and helped wiped her tears. The child stopped crying immediately and took the candy joyfully. The Oldest child smiled with satisfaction and walked inside while the girl started practicing some dance steps. Everything looked peaceful again.
I went back to my seat as I smiled to myself “what an episode!” I was Relaxed again and wanted to keep dozing off when the Holy Spirit started giving me some insights into the story.
When you ask God for something and he does not give you, it means it’s not right or good for you. When the candy was collected, it seemed the oldest child hated the youngest, but that was love. When she wailed and wailed, it seemed he didn’t care as he turned his back but he shared in that pain too. He didn’t want anything bad to happen to her by eating a seemingly infected candy. When God delays your request, he is only making sure that what he is giving you is the best and nothing but the best. And while God is at it, making sure that you have the best, no matter how hard you wail, roll on the floor, go without eating for days or even refuse to talk to him, he won’t pity you and give you the bad choice. Though your wailing is great, he will wait till all things are ready and are in their best condition so that your joy may be full indeed. So, some times when it seems God is delaying your answers, be grateful because he is working it out to give you the best and when you don’t seem to get what you want from God, be grateful for the things he didn’t give you. He has your best interests at heart and he won’t do anything to hurt you. Most Importantly, Remember that those times when it seems the pressure is unbearable and it seems you cannot take it any longer, please hang in there because your answer is only a step away. God is faithful, he will never forsake any of his own. | https://www.onomewrites.com/be-grateful-for-the-things-god-didnt-give-you/ |
For good reason, the covered-call strategy is one of the first option strategies that new traders start trading, explains Markus Heitkoetter of Rockwell Trading.
This is an effective strategy that options traders often use to provide income on stocks they already own.
Questions to Be Considered in This Article:
- What is a covered call?
- Should you trade it?
- Specific example
- Can you do it in a retirement account, e.g., IRA?
What Is a Covered Call?
A covered call is an options strategy used by traders to produce income on long stocks held in their portfolio. This strategy is used by traders who believe that stock prices are unlikely to rise in the short term. A covered-call strategy is defined as holding a long position in stock while simultaneously selling a call option on that same asset.
This strategy can provide income to a trader who is long-term bullish on stocks, but doesn’t believe there will be a significant increase in price immediately. A covered call will limit a trader’s potential upside profit if there is a significant move in the price of the stock upwards. This strategy provides little to no protection if the asset price moves downwards.
Covered-Call Example
For the specific example that we’re going to cover today, we’ll take a look at JP Morgan (JPM). If you were holding JPM stock in your portfolio before the pandemic, chances are that you are currently underwater.
As of writing this article, JP Morgan’s stock price is 96.46
DISCLAIMER
***For the purpose of full transparency, I do not own or hold any JPM stocks*** I typically only hold stocks between five and 25 days.
Stock Price Movement Recap
For this example, we’re going to assume that I own 100 shares of JPM. If I were to purchase 100 shares for $96 it would mean that the capital requirement for this position is $9,600. You’re probably familiar with the way profits move in relation to stock prices…but just to be safe:
Price action of bare stocks with no calls.
When the stock increased to $106, or $10, I would earn $1,000.
If the stock increased to $116, or $20, I would earn $2,000.
When the stock decreased to $86, or -$10, I would lose $-1000.
How Does a Covered Call Work?
- Sell one call option contract for every 100 shares of the underlying stock in your portfolio.
- The contract selected would ideally have a short expiration date of seven days.
- You would choose an “out of the money” call at a higher strike than the current price of the stock. When choosing this strike price, you would typically choose a price at least one standard deviation away from the current strike price. In other words, choosing a strike price that you do not believe the current strike price will exceed before the date of expiration.
What’s the Benefit of Having a Covered Call for the Stocks in my Portfolio?
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It’s simple really. When you sell a call option contract, you will receive a premium. This strategy generates income when you don’t expect to profit from the movement of the underlying stock price.
JPM showing no signs of significant moves in the near future. In this example with JPM, I received a premium of $55 for selling a call option contract at the price of $116. Provided that the underlying strike price does not move above $116, the contract will expire worthless and I will keep the premium I collected by selling the options contract.
Let’s take a look at how a covered call will affect your portfolio with the same stock movements.
Price movement with the covered-call strategy.
If the stock increased to $106, or moves $10, I would earn $1,000 plus the $55.
If the stock increased to $116, or moves $20, I would earn $2,000 plus the 55.
If the stock decreased to $86, or moves -$10, I would lose $-1000 but keep the $55 for a total loss of -$945.
Why Does This Work?
If you take the entire amount of premium you received and divide it by the number of days between now and contract expiration, you come up with a number like this: $55 dollars in 7 = $8(ish) per day.
This covered-call contract is paying us $8 dollars per day.
If you take the $8 dollars, divide that by your total capital investment of $9,600 it equals 0.08%.
This may not sound too incredible, but…If we do some basic arithmetic and take 0.08% and multiply that by 360 trading days per year, you end up with a return of over 30%. This is in addition to what you earned from the growth of the stock. On some stocks, it’s possible to earn upwards of $20 per day. This could increase annual returns in excess of 40% to 50%.
Does this sound a little more exciting? YES! Should you trade it? ABSOLUTELY!
BUT…there is a risk associated with this strategy. If there is a large movement of the underlying stock price that surpasses the strike price of your call option contract, you will be forced to sell your shares at this price. This would limit your upside potential to the difference between the current stock price and the price of the call option contract.
Example: If the price of the stock went up to $117 (past the $116 call option) and the options contract expires, your stocks will be sold $117.
This means you would earn $1,100 + $55, or $1,155. In other words, you would lose $100 for every $1 the strike priced moved above your call option contract.
The silver lining is that you can probably buy your stock back the next day if you wanted to hold them long term. This type of trade can be taken inside of your retirement account such as an IRA, which provides you with another way to grow your account conservatively.
Learn more about Markus Heitkoetter at Rockwell Trading. | https://www.moneyshow.com/articles/tebiwkly08-55926/covered-call-for-beginners/ |
The utility model discloses a self-elevating safety protection flexible platform for a building, and relates to the technical field of building devices. The device comprises a main beam, a secondary beam, a guide rail, a flexible protective cover, a steel wire rope, a sliding sleeve and a power device, the guide rail vertically penetrates through a floor, the main beam is transversely fixed to thetop of the guide rail, and the secondary beam is longitudinally fixed to the main beam; the steel wire rope transversely spans between the two sections of secondary beams, a plurality of nodes are arranged on the flexible protective cover, each node is fixedly connected with a sliding sleeve, and the sliding sleeves penetrate through the steel wire rope and slide along the steel wire rope; the sliding sleeve at one end of the flexible protective cover is fixedly connected with one of the secondary beams, and the sliding sleeve at the other end of the flexible protective cover is fixedly connected to the steel wire rope; one side of each of the two secondary beams is provided with a power device, and the power devices are used for driving the steel wire ropes to pull the flexible protective cover to move between the two secondary beams, so that the flexible protective cover is opened or closed; the utility model has the beneficial effects that the door can be automatically stretched orcontracted to be opened or closed, and the structure is attractive. | |
'Talk for Writing'
We use an approach to writing called 'Talk for Writing', developed by Pie Corbett. Talk for Writing is powerful because it enables children to imitate the language they need for a particular topic orally before reading and analysing it and then writing their own version. It builds on 3 key stages:
Stage 1: Imitation
Stage 2: Innovation
Stage 3: Independent application
Stage1:Imitation
Once the teacher has established a creative context and an engaging start, a typical Talk-for-Writing unit would begin with some engaging activities warming up the tune of the text, as well as the topic focused on, to help children internalise the pattern of the language required. This is often followed by talking an exemplar text, supported visually by a text map and physical movements to help the children recall the story or non-fiction piece.
In this way the children hear the text, say it for themselves and enjoy it before seeing it written down. Once they have internalised the language of the text, they are in a position to read the text and start to think about the key ingredients that help to make it work.
This stage could include a range of reading as-a-reader and as-a-writer activities. Understanding the structure of the text is easy if you use the boxing-up technique and then help the children to analyse the features that have helped to make the text work. In this way the class starts to co-construct a toolkit for this type of text so that they can talk about the ingredients themselves – a key stage in internalising the toolkit in their heads.
Stage 2: Innovation
Once the children have internalised the text, they are then ready to start innovating on the pattern of the text. This could begin with more advanced activities to warm up the key words and phrases of the type of text focused on so the children can magpie ideas. Younger children and less confident writers alter their text maps and orally rehearse what they want to say, creating their own version. The key activity in this stage is shared writing, helping the children to write their own by “doing one together” first. This could begin with using a boxed-up grid (innovating on the exemplar plan) to show how to plan the text and then turning the plan into writing. This allows the children to see how you can innovate on the exemplar text and select words and phrases that really work.
Demonstrating how to regularly read your work aloud to see if it works is important here. This process enables the children to write their own versions through developing their ability to generate good words and phrases and also, hopefully, develops the inner judge when they start to decide why one word or phrase is best. If, during this process a teaching assistant (or in KS2 an able child) flip-charts up words and phrases suggested, these can be put on the washing line alongside the shared writing so when the children come to write they have models and words and phrases to support them.
Throughout the shared writing, the children should be strengthening the toolkit so they start to understand the type of ingredients that may help. Once they have finished their own paragraph/s children should be encouraged to swap their work with a response partner. Then the whole class can also discuss some of the more successful work. Time now needs to be found to enable the children to give their own work a polish in the light of these discussions and perhaps to begin the dialogue about what works by writing their own comment on their work for the teacher to comment on.
Stage 3: Moving from innovation to independent application
The teacher now has the opportunity to assess the children’s work and to adapt their planning in the light of what the children can actually do. This stage could begin with some activities focused on helping the children understand aspects that they were having difficulty with and should include time for the children to have a go at altering their work in the light of what they have just learnt so that they start to make progress. This stage will continue to focus on the next steps needed to support progress so the children can become independent speakers and writers of this type of text. Perhaps some more examples of the text are compared followed by more shared writing on a related topic and then the children can have a go themselves on a related topic of their own choosing. Typically, teachers work with the children to set ‘tickable targets’ which focus on aspects that they need to attend to. Again this section will end with response partner and whole class discussion about what features really worked, followed by an opportunity to polish your work. This process also helps the children internalise the toolkit for such writing so that it becomes a practical flexible toolkit in the head rather than a list to be looked at and blindly followed. At the end of the unit, the children’s work should be published or displayed. The teacher will now have a good picture of what features to focus on in the next unit to move the children forward.
Handwriting:
Here at Al-ikhlaas we have extremely high expectations of presentation. From the earliest age we foster the correct posture, seating positions and pencil grips. We use hand and finger strengthening activities to promote fine motor development.
In early years and Year 1 children are taught correct letter shapes and formations.
From Year 2 onwards, we begin to explicitly teach correct joins and a stronger awareness of ascenders and descenders. These skills are developed through weekly handwriting lessons and practise as well as ongoing application in all of their writing. It is closely monitored and additional support is given to those that require it. | https://www.al-ikhlaas.org.uk/curriculum/core-subjects/writing |
Frequency Distribution Tables A frequency distribution table is a table that shows how often a data point or a group of data points appears in a given data set. To make a frequency distribution table, first divide the numbers over which the data ranges into intervals of equal length.... Creating a Histogram using FREQUENCY Function If you want to create a histogram that is dynamic (i.e., updates when you change the data), you need to resort to formulas . In this section, you’ll learn how to use the FREQUENCY function to create a dynamic histogram in Excel.
Simply using the freq=FALSE argument does not give a histogram with percentages, it normalizes the histogram so the total area equals 1. To get a histogram of percentages of some data set, say x, do: how to make a jewelry holder for the wall Frequency Distribution Tables A frequency distribution table is a table that shows how often a data point or a group of data points appears in a given data set. To make a frequency distribution table, first divide the numbers over which the data ranges into intervals of equal length.
A graph that uses vertical columns to show frequencies (how many times each score occurs). And no gaps between the bars. | http://kelownaautosport.com/australian-capital-territory/how-to-make-a-relative-frequency-histogram.php |
Thursday December 17 2020
Summary
While driving recently, I noticed a huge cloud of smoke in my rear-view mirror and realised it was coming from my car. There was no check engine light or overheating and the engine was running fine. I pulled over and checked the exhaust and noticed what seemed to be a mixture of water and oil. I checked my oil dipstick and no oil was present, although I had just changed the oil. What could this be? Agnes
Hello Agnes, your car is burning engine oil. That explains the loss of oil and bellowing blue smoke from the exhaust as you drive. A car will burn oil when the engine piston rings are damaged. Piston rings are metallic seals between the piston and engine cylinder walls designed to prevent oil intrusion into the combustion chamber as the pistons compress the fuel air mixture for ignition by the spark to achieve combustion.
Piston rings can get damaged due to poor lubrication and buildup of oil sludge (caused by delayed engine oil change, use of counterfeit or substandard oils and filters). Damaged piston rings allow oil to leak into the combustion chamber, where it is burnt together with the fuel air mixture. This reduces engine performance and fuel efficiency, and harms the environment.
An inspection of the engine with an engine compression test will quickly confirm piston ring damage without dismantling it. When you decide to repair the engine, it can be dismantled to determine the extent of damage and parts required to repair it. | |
Championship gets underway at the at the five star M?venpick Hotel in Cairo,
Egypt, from October 19 - November 2.
This year's Championship will be very special in that one side of the venue
will overlook the Pyramids of Giza, which under floodlight will give all
visitors an awe inspiring view and feeling of an ancient time in history.
Follow the progress of a record eighty-eight competitors from forty-three
countries around the world on the SnookerUSA.com website, as we provide a
comprehensive results and reports service from the Championship.
Tom Kollins, the most experienced international snooker player from the
United States, will be the United States representative at the Championship
as the current holder of the U.S. National Snooker Championship - a title he
has won on five occasions.
Tom has been drawn in Group C where he will have to face the sensational
15-year-old Ding Junhui from China - the current IBSF World Under-21 Snooker
Champion and Asian Games Individual Snooker Gold Medalist.
Regards.
Alan Morris.
SnookerUSA.com - the Official Website of the United States Snooker
Association. | http://sporttoday.org/12_14ead8d3c5ac1de2_1.htm |
When I think of lemon and blueberry together I think of fresh flavors and the Spring/Summer season. Two very different flavors that come together perfectly.
Bake it in the summer when fresh blueberries are in season!
In Indiana, blueberries are in season the end of July/August. I have fun memories growing up going to the local blueberry patch and picking, and picking, and picking until we got a good amount to bring home for fresh blueberries and to put some up in the freezer. I have enjoyed taking my kids as well!
The blueberries provide a nice moistness to the cake with bursts of flavor, while the lemon and lemon zest give a nice zingy, lemony flavor, but not over powering. An added hint of sweetness is in the light icing.
Ingredients:
2 3/4 cups flour
1 1/2 tsp Clabber Girl Baking Powder
1/4 tsp Clabber Girl Baking Soda
1/4 tsp salt
1 cup butter, softened
1 3/4 cups sugar
4 eggs
4 Tbsp lemon juice, freshly squeezed
lemon zest from the lemons
1 tsp vanilla extract
1 cup milk
2 1/2 cups blueberries
For the icing:
1 cup powdered sugar
2 Tbsp lemon juice, freshly squeezed
lemon zest
Directions:
In a mixing bowl, add the flour, baking powder, baking soda, and salt and mix until combined and set aside. In another bowl, beat together the butter and sugar until well blended. Add the eggs and use a hand mixer and blend in one at a time. Add the lemon juice, zest, vanilla, and milk and beat together until just combined together. Add the flour mixture to the wet ingredient mixture and mix together well with a hand mixer. Add the blueberries and gently fold them in with a rubber spatula until incorporated. Grease a large bundt pan. Pour the prepared batter in the bundt pan. Bake for 50 to 60 minutes or until toothpick comes out clean. Cool for 20 minutes and run a thin knife around the edges to loosen the cake. Cool turned over and cool completely, then remove from pan.
For the icing, mix together all icing ingredients until smooth. Drizzle over cooled cake. It will seep into the cake.
PRINTABLE RECIPE HERE
Not only is this cake delicious, but its also definitely looks stunningly delicious too! Perfect for carry-ins, family holidays, breakfast, brunch, or dessert. So many options to make this pleasant lemon blueberry bundt cake.
You can't help but smile when enjoying this cake!
Enjoy! | http://www.thebackroadlife.com/2017/04/lemon-blueberry-bundt-cake.html |
Jordan's Abdelkareem Mohmmad Ahmad Khattab secured his first-ever Powerlifting World Cup title as he won the men's up to 80 kilograms competition in Dubai today.
Khattab topped the podium after he cleared 210kg, with Syria’s Shadi Issa the only lifter in the category to complete three lifts at the Dubai Club for the Disabled.
Issa managed 188kg to take home the silver medal, while Michael Yule of Britain's lift of 185kg was enough for the bronze.
Khattab had attempted to go five kilograms higher with his third attempt but fell short with the title already secure.
It was Jordan's third gold medal of the event following victories for Mohammad Tarbash and Omar Qaradeh in the up 59kg and up to 49kg categories respectively.
Rasool Mohsin of Iran, silver medallist at last year's Paralympic Games in Rio de Janeiro, dominated the men's up to 72kg competition and comfortably claimed the gold medal with a best lift of 210kg.
The world record holder needed just one good lift at the weight for victory, with Turkmenistan’s Sergey Meladze earning silver on 185kg.
Thailand’s Thongsa Marasri lifted the same total as Meladze but was pushed down to third spot by virtue of a heavier body weight.
Tetyana Shyrokolava added to Ukraine's haul from the event in Dubai as she proved too strong in the women's up to 61kg competition.
Following team-mate Mariana Shevchuk returning to the scene of her doping controversy last year to claim the gold medal in the up to 55kg event yesterday, Shyrokolava continued the impressive display from the nation with a lift of 100kg.
It ensured she retained the Dubai Powerlifting World Cup title she sealed last year.
Fatema Alhasan lifted 91kg in her opening attempt to take the silver medal, while Egypt’s Fatma Korany registred 82kg to earn bronze with her last effort.
The event in Dubai is due to continue tomorrow with with the men’s up to 88kg and up to 97kg and the women’s up to 73kg competitions. | https://web3.insidethegames.biz/articles/1047605/jordan-win-third-gold-medal-at-dubai-powerlifting-world-cup |
Q:
Different behavior with different types of arrays
i have tested two different varianat of similary code ,suppose i have char array
char x[]="snow comes in winter ";
then following code
#include <iostream>
#include <string.h>
using namespace std;
int main(){
char x[]="snow comes in winter ";
int k=0;
int n=3;
cout<<x+n-k+1<<endl;
system("PAUSE");
return EXIT_SUCCESS;
}
prints "comes in winter "
while following
int a[]={12,3,2,4,5,6,7};
int k=0;
int n=3;
cout<<a+n-k+1<<endl;
return 0;
}
prints 0xbffd293c
if we change it a bit
}
prints number 5.
so my question is why we can access in case of char array so easily?what is main reason of it?i am very curiousy and please could anybody explain me?
A:
why we can access in case of char array so easily?
Because there's a convention that C strings are represented by char*, people assume char* are actually strings. The iostreams follow that and overload output for char* to print the string, whereas for an int* (in your second example), they print the representation of the address.
BTW there is a similar overload for input, which is most unfortunate, since you can't control that to prevent buffer overflows. ie. don't do this:
char x[10];
std::cin >> x;
| |
Defense Advanced Research Projects Agency (DARPA, p.2017 ,
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Multimodal Explanations: Justifying Decisions and Pointing to the Evidence, 2018. ,
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Understanding Black-box Predictions via Influence Functions, 2017. ,
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, Towards a Rigorous Science of Interpretable Machine Learning, 2017.
The structure and function of explanations, Trends in Cognitive Science, vol.10, issue.10, 2006. ,
What makes an explanation a good explanation? : adult learners' criteria for acceptance of a good explanation, 1999. ,
Towards explainable NPCs: A relational exploration learning agent, Extraction from Games: Papers from the AAAI Workshop, 2018. ,
Why Should I Trust You?": Explaining the Predictions of Any Classifier, 2016. ,
Explainable Agency for Intelligent Autonomous Systems, 2017. ,
Interpretable Matrix Factorization with Stochasticity Constrained Nonnegative DEDICOM, 2017. ,
Interpreting Black-Box Classifiers Using Instance-Level Visual Explanations, Proceedings of the 2nd Workshop on Human-In-the-Loop Data Analytics, 2017. ,
Interpretability of machine learning models and representations: An introduction, 2016. ,
An Exploratory Study on the Benefits of using Natural Language for Explaining Fuzzy Rule-based Systems, IEEE International Conference on Fuzzy Systems, 2017. ,
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Looking for a Fuzzy System Interpretability Index: An Experimental Approach, International Journal of Approximate Reasoning, 2009. ,
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Interpretability of Fuzzy Rule-based Systems: An Overview of Interpretability Measures, Information Sciences, 2011. ,
UCI Machine Learning Repository, 2017. , | https://hal.inria.fr/hal-02060044v1/html_references |
More than 1 in 100 individuals are diagnosed with Autism Spectrum Disorder (ASD), with profound impacts on the quality of life of those who are affected and their families. Many parents of children with ASD identify concerns as early at 12-18 months of age, yet the average age of diagnosis remains around four years. Children who receive an early diagnosis of ASD can benefit from a growing array of evidence-based interventions. There is also evidence that diagnosing and treating autism earlier leads to better long-term outcomes for children and families, and reduces ultimate societal costs related to treatment.
Over the past decade, studies of highrisk infants - younger siblings of children with ASD - have revolutionized the field, bringing us to the threshold of earlier diagnosis and treatment. The members of this international team are made up of researchers from Canada, UK and Israel who have been at the forefront of research on this high-risk cohort of “baby sibs” and for this particular project they are expanding on previous research on the early development of ASD.
They are looking at how at-risk infants direct their attention and regulate their emotions, and how this relates to their ability to communicate and interact with others. They believe these relationships may help in understanding the earliest expression of ASD. Their research project consists of two related projects.
In the first project (involving the Canadian and Israeli teams) they will examine how flexibly infants shift their attention from one interesting object to another, and how this influences their responses to situations that elicit positive or negative emotion. Infants who have difficulty shifting their visual attention may also get ‘stuck’ on intense emotions, and that may impair both their ability to interact and communicate with others, leading to increased risk of ASD. In the second project, they will test whether teaching infants to become more flexible in shifting their attention (using computer games developed by their UK team) helps them benefit further from other interventions developed by the Canadian and UK teams. The team has just completed the first year of their grant.
Progress has mainly focused on preparing the research team trialing new technologies for the home-based intervention trial, working with international partners to learn the novel intervention approaches that they believe will further optimize benefits to infants with early signs of ASD, and engaging with community partners to begin the process of ensuring that findings from their research will ultimately be incorporated into clinical practice.
They have also begun data collection activities for their early detection study, as well as the intervention trial. The next steps involve accelerating recruitment into both studies to achieve their ultimate goal of mapping early developmental pathways of ASD risk and understanding how these pathways can be targeted to improve on interventions for children with early signs of ASD. Based on findings from this research, they will train health professionals to better identify the earliest signs of ASD, and work with community partners to implement new interventions to help these children reach their potential. | https://braincanada.ca/research-stories/diagnosing-autism-in-the-youngest-of-patients/ |
The Spotfin Frogfish (Antennatus Nummifer), also known as Coin-Bearing Frogfish, Dark-Spotted Frogfish, Spotfin Anglerfish, Spotfin Angler, Whitefinger Anglerfish, or Whitefinger Frogfish, can be found on sheltered reefs and on sandy bottoms with rich sponge growth along them. They are widespread across the Indo-Pacific region.
The Yellow Angler Fish or Spotfin Frogfish is found in all subtropical oceans to depths of 300 meters. It grows to 5.1″ inches in total length. The species varies in color to match their surroundings. They are known for their ability to camouflage and get lost in their surroundings to avoid predators. Yellow Angler Fish or Spotfin Frogfish are able to lure in their prey with a stalk found between their eyes that imitates the movements of their prey; its mouth can be opened and expanded to the same width as its body to catch and swallow prey. They feed on small fish, crustaceans, and worms.
Additional information
|Weight||8 lbs|
|Dimensions||N/A|
Reviews
There are no reviews yet.
Only logged in customers who have purchased this product may leave a review. | https://petesaquariums.com/shop/saltwater-aquarium-fish/anglerfish/yellow-angler-fish-or-spotfin-frogfish/ |
6/21/2022. The Board of Trustees (the “Board”) of Collaborative Investment Series Trust (the “Trust”) has determined that it is in the best interests of shareholders to liquidate the NextGen Trend and Defend ETF (a “Fund”), and a series of the Trust, following a recommendation by the Funds’ investment adviser, NextGen ETFs, LLC. The Board has determined to liquidate the Fund with the liquidation payment to shareholders expected to take place on or about June 29, 2022 (“Liquidation Date”).
After the close of business on June 23, 2022, each Fund no longer will accept creation orders. The last day of trading on the CBOE BZX Exchange, will be June 23, 2022. Shareholders should be aware that while a Fund is preparing to liquidate, it will not be pursuing its stated investment objective or engaging in any business activities except for the purposes of winding up its business and affairs, preserving the value of their assets, paying its liabilities, and distributing its remaining assets to shareholders.
Shareholders may sell their holdings of a Fund on its Exchange until market close on June 23, 2022 and may incur typical transaction fees from their broker-dealer. The Fund’s shares will no longer trade on its Exchange after market close on June 23, 2022, and the shares will be subsequently delisted. Shareholders who do not sell their shares of the Fund before market close on June 23, 2022 will receive cash equal to the amount of the net asset value of their shares, which will include any capital gains and dividends, in the cash portion of their brokerage accounts, on or about the Liquidation Date.
Shareholders generally will recognize a capital gain or loss equal to the amount received for their shares over their adjusted basis in such shares. You may wish to consult your tax advisor about your particular situation. If you have questions or need assistance, please contact your financial advisor directly or a
Fund at (866) 505-1107. This Supplement and the Prospectus dated June 17, 2022, provide relevant information for all shareholders and should be retained for future reference. Both the Prospectus and the Statement of Additional Information have been filed with the Securities and Exchange Commission and are incorporated by reference and can be obtained without charge by calling the Fund at (866) 904-0406.
Distributor: Foreside Fund Services, LLC
Source: Collaborative Investment Series Trust
For further information: Chuck Brokop at [email protected]
TRDF
Liquid Alternative Long/Short ETF
Strategy Characteristics
Predictable Correlation
Predictable Correlation
Our signals are centered around price movements on the S&P 500 Index. Because of this, when large cap price levels are declining TRDF shorts the index and offers a negative 1.0 correlation to the S&P 500 index…Read More
This can lead to predictable inverse correlations during tail risk events and periods of heightened volatility by investing into liquid inverse S&P 500 ETFs when our signals are bearish. Historically, portfolio diversification includes spreading risk across a basket of asset classes with mathematically lower correlations than 1.0. The problem is this does not capture the empirical evidence that correlations among asset classes increase during tail risk events, right when you need that diversification most.
Tail Risk Protection
Tail Risk Protection
Most Trend Following and “defensive” strategies rotate into safe-haven assets during a market downturn. TRDF becomes defensive during these periods of modest market corrections as well, however, when the empirical evidence indicates the market downtrend should persist and worsen, we then rotate the portfolio into our short position.Read More
Our ability to short the index when other strategies invest in treasury bills or cash has the potential to generate outsized positive returns during market selloffs (Crisis Alpha). Rotating to cash doesn’t offer negative correlation in tail-risk events, but being short the index mathematically offers near perfect negative correlation.
Lower Fee Structure
Lower Fee Structure
Traditional hedge funds charge 2.0% in management fees, and 20% in performance fees. In the early years of hedge funds markets were not as efficient and prices did not reflect new information almost instantaneously as they do now as technology continues to evolve the industry…Read More
Managers could use skill to gain an edge in markets and create alpha for their investors, justifying the fees. As more managers came into the space, this led to the inevitable degradation of alpha. With time, what was once alpha became beta due to innovation and competition. What has resulted is advisors pay 2% and 20% for essentially low volatility beta exposures, which can be quantitatively replicated at much lower fees given innovation in technology and fund structures. At substantially lower fee structures, this has the potential to create alpha above traditional hedge funds, net of fees.
Potential Tax Advantage
Potential Tax Advantage
ETFs offer tax benefits relative to limited partnerships for some investors. In traditional hedge funds, the buying and selling of individual securities may trigger capital gains taxes passed through to the investor on their K-1.Read More
Thanks to a long-standing ETF rule, these taxes can potentially be avoided or significantly reduced through “basket trading” giving the ETF structure a potential leg-up on traditional hedge fund structures for investors that focus on net, after-tax return characteristics of an asset class.
Liquidity Preference
Liquidity Preference
TRDF is an actively traded ETF providing investors on-demand liquidity. This can benefit investors seeking the diversification benefit of alternatives such as hedge funds, but are averse to holding illiquid assets and locking up capital for multi-year periods.
TRDF is an actively traded ETF providing investors on-demand liquidity. This can benefit investors seeking the diversification benefit of alternatives such as hedge funds, but are averse to holding illiquid assets and locking up capital for multi-year periods.
Behavioral Alpha
Behavioral AlphaLoss Aversion
Research conducted by Daniel Kahneman and Amos Tversky (Kahneman & Tversky 1979) proved that the bad feeling of a financial loss is twice as powerful as the positive feeling of a financial gain. When our trend following strategy shorts the market during tail risk events, it offers investors positive returns during a period where they’d traditionally be panicking.Classic Retail Mistake 🡪 Read More
When people don't have a pre-determined plan for various market events, they can make poor decisions as emotion and panic overrides the logical brain. This typically results in selling their portfolio when markets have already lost substantial value. The subsequent action is to avoid re-investing until the regret of missing out on the recovery overrides their fear of losses which typically occurs after markets have reached substantially higher levels. This is captured quite well in the capital destruction process diagram, which can be found by clicking here
How It Works
Portfolio Positioning
When we are Short
Trend is Negative
Volatility is Rising
When we are Long
Trend is Positive
Volatility is Declining
TRDF Characteristics
Negative Downside Capture
Systematic
Liquid Alternative
Positive Upside Capture
Imperfect
Not "Low Vol"
Portfolio Positioning
When we are Short
When we are Long
Trend is Negative
Trend is Positive
Volatility is Rising
Volatility is Declining
TRDF Characteristics
Negative Downside Capture
Positive Upside Capture
Systematic
Imperfect
Liquid Alternative
Not "Low Vol"
US Stock Market Crash Coming?! | https://www.nextgen-funds.com/ |
The media in Africa have a role to play in the attainment of Sustainable Development Goals (SDGs) by building awareness, setting the public agenda, and influencing and holding to account political leaders. In this chapter, we examine the problematic context of a commercialised and privatised media system playing a significant role in debates about development and in development education and advocacy—topics which are not necessarily profitable. Media can play a role as public information channels, engagement platforms, watchdogs and advocates for policy improvement—all crucial to the successful implementation of the SDGs—but media do not necessarily fulfil these obligations. With advances in technology, the power of the media to open new opportunities to drive social change and to transform development in Africa is unsurpassed. We explore how the contemporary political economy of Kenyan media challenges or supports such objectives. We also examine how information gaps concerning SDG goals, such as climate information in rural communities, pose a challenge to the realisation of the SDGs. We conduct an investigation into the form of analysis of media coverage of climate change and action in Kenya, but draw primarily from existing research concerning Kenyan media. Our findings show that the Kenyan media are ill-equipped to specifically support SDG 13 on climate change and action in the country. | https://eprints.whiterose.ac.uk/163435/ |
HLA supertype variation across populations: new insights into the role of natural selection in the evolution of HLA-A and HLA-B polymorphisms.
Dos Santos Francisco R, Buhler S, Nunes JM, Bitarello BD, França GS, Meyer D, Sanchez-Mazas A. Immunogenetics 2015 Nov;67(11-12):651-63. 10.1007/s00251-015-0875-9. 10.1007/s00251-015-0875-9. PMC4636516.
Supertypes are groups of human leukocyte antigen (HLA) alleles which bind overlapping sets of peptides due to sharing specific residues at the anchor positions-the B and F pockets-of the peptide-binding region (PBR). HLA alleles within the same supertype are expected to be functionally similar, while those from different supertypes are expected to be functionally distinct, presenting different sets of peptides. In this study, we applied the supertype classification to the HLA-A and HLA-B data of 55 worldwide populations in order to investigate the effect of natural selection on supertype rather than allelic variation at these loci. We compared the nucleotide diversity of the B and F pockets with that of the other PBR regions through a resampling procedure and compared the patterns of within-population heterozygosity (He) and between-population differentiation (G ST) observed when using the supertype definition to those estimated when using randomized groups of alleles. At HLA-A, low levels of variation are observed at B and F pockets and randomized He and G ST do not differ from the observed data. By contrast, HLA-B concentrates most of the differences between supertypes, the B pocket showing a particularly high level of variation. Moreover, at HLA-B, the reassignment of alleles into random groups does not reproduce the patterns of population differentiation observed with supertypes. We thus conclude that differently from HLA-A, for which supertype and allelic variation show similar patterns of nucleotide diversity within and between populations, HLA-B has likely evolved through specific adaptations of its B pocket to local pathogens. | https://genev.unige.ch/publication/2543 |
“In fourteen hundred and ninety-two, Columbus sailed the ocean blue.” True enough. However, the story of European exploration is much greater and begins centuries earlier than Christopher Columbus.
Throughout the Middle Ages, Europeans traveled extensively throughout North Africa and Asia. Niccolo and Maffeo Polo, not to mention Niccolo’s slightly more famous son Marco Polo (1255-1324), traveled all the way to China and even spent time in the court of the legendary Kublai Khan. Before the Polo expeditions, the pope sent emissaries to the Mongol capital of Karakorum.
Those who traveled abroad brought back many fantastic stories of fascinating far-off places. Polo, in his book Travels, told of his difficult journey to China and back and of his time in such places as Sri Lanka and Sumatra. More fantastic tales were spread in a book titled The Travels of Sir John Mandeville written in the early fourteenth century. Its author tells of finding giants, headless humans, and more in his travels to the Far East. These stories stayed with Europeans and eventually helped spark some interest in what else might be found abroad. These travelers weren’t traveling just for the sake of traveling, though. They were trading, and trade was good for quite a while.
Would You Believe?
Although Marco Polo is famous for his travels to China, as chronicled in his book Travels, some historians doubt the authenticity of his stories. Furthermore, some historians doubt he even made it all the way to China!
Especially while the Mongols controlled the lands between Europe and China, profitable trade routes existed as far east as India and even into parts of China. The Crusades opened up many trade routes in North Africa for Europeans who demanded silks, spices, mirrors, and other luxury items crusaders took back to Europe. Both during and after the Crusades, European traders profited greatly from these trade routes.
For the most part, these trade routes were over land. Very little sea travel occurred at this time, for a few reasons. Shipbuilding and cartography had hardly reached zeniths during the Middle Ages, so traders tended to be land lovers. With the rise of the Islamic Ottoman Turks in southwest Asia and the decline of the Mongol Empire, Europeans, not known for their friendly relations with the Muslims, found it more and more difficult and dangerous to trade in Ottoman-controlled lands. It was thanks to the Ottomans, then, that Europeans started looking for safer and more profitable trade routes.
Define Your Terms
Cartography is the science of mapmaking. | https://erenow.net/common/europeanhistory/29.php |
The programme is dealt with very much from a strategic point of view, examining the factors that businesses have to consider constantly. The effects of inflation, interest rates and currency movements will be a thread, as will the influence of financial markets, legislation and political events in addition to particular market places.
The programme will ensure a high degree of participation throughout so that delegates are able to put their point of view and absorb and examine the topics covered in the day.
AIMS AND OBJECTIVES
This programme aims to ensure that the participants on the programme will:
- Gain a clearer understanding of the financial impact of strategic decisions
- Identify and appreciate what makes good financial stewardship
- Recognise what impacts upon financial performance and identify appropriate strategies
- Understand how financial institutions assess organisations
- Have an appreciation of how companies are valued
NB: Participants should already have a grasp of basic financial information, and be familiar withy the common ratios used by most business, although the basics are briefly reviewed during the introductory module. | https://anthonyparmiter.com/business-finance-for-senior/ |
Cancer arises from the accumulation within a single cell of a defined set of genetic alterations that ultimately lead to the loss or gain of crucial functions that regulate cellular division and cell death. The exponential increase in our knowledge concerning the molecular mechanisms that underlie tumorigenesis combined with the deciphering of the human genome has dramatically changed our vision of cancer, and is bound to have a major impact in prevention, diagnosis and drug development.
Hereditary genetic variants are linked to an increased predisposition for specific tumors. Cancer-predisposing variants, such as those of the BRCA genes that are associated to hereditary breast cancers, can confer up to 40-fold increase in the risk of developing a specific type of tumor in the course of the individual’s lifespan. Their identification and classification is one of the most promising approaches for the development of programs aimed at preventing disease onset.
Acquired genetic abnormalities that arise in the course of an individual’s life span are linked to the pathogenesis of specific tumors, and confer distinctive clinical characteristics. Consequently, their detection plays a major role in diagnostic settings. In the case of hematologic tumors, such as acute leukemias, for example, the identification of specific genetic abnormalities serves for correct diagnosis and has a direct impact in the clinical management of patients and choice of therapeutic regimens.
One of the main objectives in cancer research is the discovery of specific biomarkers that correlate with the natural history of the disease (prognostic markers) and/or with the likelihood of response to a treatment (predictive markers). These can be exploited, alongside other clinical information for the personalized choice of therapeutic regimens, with the aim of avoiding unnecessarily aggressive treatment of tumors with favorable biological characteristics. Finally, the discovery of genetic alterations resulting in specific functional abnormalities in cancer cells has led to the development of a new generation of targeted drugs that bear the promise of higher efficacy and lower toxicity. | http://www.thefutureofscience.org/speakerdetail/fifth-world-conference-on-the-future-of-science-the-dna-revolution-veronesi-umberto-250 |
3. Adagio - 6:02 4. Menuetto/Trio - 2:44. Instrumentation. Full Score Oboe I-II Bassoon I-II Bb Clarinet I-II Eb Contra-alto Clarinet Horn in F I-II. Errata. None discovered thus far. Program Notes. Mozart’s ability to seamlessly juxtapose operatic lyricism with endearing folk melodies is brought to life in his Serenade No. Sep 13, 2010 · 50 videos Play all Mix - Mozart - Serenade for wind instruments in E flat K375 V Finale Allegro YouTube Mozart / Serenade for Winds in E-flat major, K. 375 Paavo Järvi - Duration: 23:43. The Serenade No. 6 for Orchestra in D major K. 239, Serenata notturna, was written by Wolfgang Amadeus Mozart in Salzburg, in 1776.Mozart's father, Leopold Mozart, wrote the title and a January 1776 date on the original manuscript. It has three movements:. Marcia maestoso Minuetto.
In both works here – the so-called Gran partita for 12 wind instruments plus double bass, and the E flat Serenade K375 – the princely Berlin Philharmonic Wind Ensemble achieve this beautifully. The players respond exuberantly to the rustic elements of K375 – the two jaunty minuets and the bubbly finale, with its gleeful exchanges between. View credits, reviews, tracks and shop for the 1984 Vinyl release of Wind Serenades In E Flat K.375 / In C Minor K.388 on Discogs. Sep 26, 2015 · The Serenade in E-flat major, K. 375, exists today in two versions: a sextet of two clarinets, two bassoons, and two horns, and an octet that adds two oboes. The sextet came first, finished in October 1781 and premiered on the 15th at the home of Viennese court painter Joseph Hickel. Wolfgang Amadeus Mozart: Serenade In E-Flat Major K.375: Ensemble: Study Score Barenreiter a 6 et a 8-The Serenade in E-flat K.375 exists in two versions one for two clarinets two horns and two bassoons and another for the same forces plus two oboes forming an octet.From Mozart himself we know a fair amount about. Get this from a library! Serenade in E flat major, for wind instruments: Op. 7. [Richard Strauss].
The "Serenade" for 13 wind instruments enjoys a special position among the works of Richard Strauss's youth and suggests that this period was coming to an end: it is the work that brought recognition to Strauss as a composer outside his n. It was scored for the usual sextet of instruments, two each of a treble instrument in this instance clarinets, horns, and bassoons. By mid-October, the Serenade in E flat was completed, and on the 15th given its first performance at Heckel's home. Nov 08, 2014 · Provided to YouTube by The Orchard Enterprises Serenade No. 11 for Wind Instruments in E-Flat Major, K. 375: III. Adagio · Everest Woodwind Octet · Wolfgang Amadeus Mozart · Newell Jenkins. OCLC Number: 2667160: Notes: For 2 flutes, 2 oboes, 2 clarinets, 4 horns, 2 bassoons, and contrabassoon or bass tuba. Pl. no.: 519. Description: 1 study score 22.
Discover releases, reviews, track listings, recommendations, and more about Wolfgang Amadeus Mozart, Otto Klemperer, The London Wind Quintet And Ensemble - Serenade For 13 Wind Instruments at Discogs. Complete your Wolfgang Amadeus Mozart, Otto Klemperer, The London Wind Quintet And Ensemble collection. SERENADE in Eb major KV 375 study. Composer: Mozart, Wolfgang. SERENADE No.11 in Eb K375 score Composer: Mozart, Wolfgang Amadeus 1756-1791 Instrumentation: 2ob. 2cl. 2bn. 2hn. We offer a truly comprehensive selection of wind music online, with well over 65,000 titles listed, most of which are in stock and ready for immediate. Serenade no. 11 in E-flat major, K375 Full Score - Full Score Sheet Music Woodwind Ensemble Paperback – January 1, 1782 by Wolfgang Amadeus Mozart Author See all formats and editions Hide other formats and editions. Price New from Used from Kindle.
Serenade no. 11 in E-flat major, K375 Full Score - Kindle edition by Wolfgang Amadeus Mozart. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Serenade no. 11 in E-flat major, K375 Full Score. Apr 28, 2018 · The serenades are multi-movement, short in length, and feature descriptive titles the movements of the Serenade No. 11 are entitled Pastoral, Humoreske, Nocturne, Intermezzo, and Capriccio. Other Persichetti works for band include Symphony No. 6, Divertimento, Pageant, Three Chorale Preludes, and Celebrations for Chorus and Wind Ensemble. The Serenade for 13 Wind Instruments, Op. 7, from 1881, is the first work of the German composer Richard Strauss to have survived in the concert hall. Although a youthful work, its charm, vivacity, and technical assurance makes it a worthy successor of Mozart's Gran Partita, upon which it is clearly modeled. Scored for the standard double winds plus four horns and contrabassoon, the Serenade. Check out Mozart: Serenade for 13 Wind Instruments/Serenade K.375 etc by Sir Neville Marriner & Holliger Wind Ensemble & Academy of St. Martin in the Fields on Amazon Music. Stream ad-free or purchase CD's and MP3s now on Amazon. | http://kelloggchurch.org/serenade-no-6-in-e-major-for-6-wind-instruments-k375-stsc-study-score |
Graphene on silicon carbide substrate wafer with 2 inches diameter and 330 µm thickness
Graphene is present in the circle with a diameter around 3 mm smaller than the size of the SiC wafer. Properties of graphene are given after choosing a specific number of layers.
Properties of graphene regardless of the number of layers:
- Phase: monocrystal on the whole sample
- Method of production: partly reversible graphitisation of SiC (0001) under silicon atoms’ flux
- Electrical properties: doped, type n, electric charge neutral point (Dirac point) around 0.35 eV below Fermi level
Properties of a substrate:
- Material: silicon carbide (SiC)
- Phase: monocrystal
- Thickness: 330 µm (±25 µm)
- Surface orientation: <0001> (±0.5 °)
- The concentration of micropipe-type defects (MPD): 15 cm-2
- Resistivity: 1E5 Ω cm
- Band gap: 3.23 eV
- TTV / Bow / Warp: 15 µm / 25 µm / 25 µm
- Thermal conductivity along a axis in 298 K: 4.9 W/cm K
- Thermal conductivity along c axis in 298 K: 3.9 W/cm K
Characterisation:
Results of characterisation techniques such as ARPES, XPS, spectrophotometry, Raman spectrometry, and AFM are available upon request. | https://beegraphene.com/2-inch-wafer/ |
Our Geography provision will aim to inspire in pupils a curiosity and fascination about the world and its people. We want to equip pupils with knowledge about diverse places, people, resources and natural and human environments. Local geography will also be important so that children can compare and contrast with other locations. Our aim is for our pupils to have a secure understanding of local, national and international geographical issues and be able to discuss this confidently using key vocabulary accurately. Our whole school curriculum vision supports and drives our intent for Geography at Far Forest Primary.
Our intent is to teach content in small, manageable steps to reduce cognitive load. The geography curriculum will ensure that children have the pre-requisite knowledge required in order to access new learning and concepts are revisited to ensure that children build on and retain what they have been taught in previous years. Retrieval practice will be used to support children transferring ideas from their working memory into their long term memory. Children will be given regular opportunities to retrieve through;
More detail about how we will achieve our intent is outlined in our Curriculum Statement for Geography below.
Implementation
Planning
At Far Forest Primary we strongly believe in children knowing more and remembering more. The key skills and knowledge for each topic covered across the school has been carefully tailored to meet the needs of our pupils. This is achieved by ensuring that planning not only introduces children to new learning but also reinforces and builds on prior learning. Furthermore, the vocabulary that the children are exposed to over the years is clearly outlined on plans so our pupils are encouraged to speak like e.g a historian, scientist etc.. This is modelled by all staff and training has provided teachers and TA's with the tools to create a vocabulary rich classroom that supports pupils.
Our curriculum is enquiry based with a key question driving the learning. Our tailored plans support our intent and provide opportunities for children to become critical thinkers, explore ideas, make connections and ask their own questions. See sample medium term plans below which outline how we plan and also how prior learning is not only embedded but developed. All plans are linked to our school drivers of 'Resilience, Diversity and Possibilities'. | https://www.farforestlea.worcs.sch.uk/geography-3/ |
This study investigates a method of detecting and tracking damage in an offshore platform located in the North Sea under the excitation of a typical sea storm by performing a finite element simulation. A modal analysis and nodal displacement results from Finite Element (FE) simulation are adopted for analysing the dynamic characteristics of this platform. For this purpose, the JONSWAP spectrum and Morison equation are applied to simulate the typical wave force in the North Sea using Matlab and Simulink programmes. The associated mode shape vector obtained in modal analysis was correlated with the sea force vector which was the forcing function (force per unit length) to the structure. The determination of the dynamic response with realization to the real scenario was established by introducing some reduction of material stiffness in one of the diagonal member in stages. The results in time-displacement domain obtained from FE simulation were converted into time-acceleration domain before they were analysed in frequency spectrum using Power Spectrum Density in Matlab. The frequency analysis showed that there was a significant shift in peak frequency between the intact and damaged structure response with 30% stiffness reduction, provided that the sea force applied is in the direction of the damaged beam member orientation. This suggested that the shift in the natural frequencies of the dynamic response can provide a useful tool in monitoring the dynamic response and tracking the progression of fatigue failure of the structure.
Science Alert
INTRODUCTION
As offshore oil and gas exploration enter into deeper waters, there is a significant increase in research and investigation into methods of examining vibration characteristics in monitoring structural integrity. This great need for the monitoring and evaluation of mechanical structures is attributed to the safety requirements for the structures themselves and also the people involved.
Technological advancements in computational processing, sensors and finite
element methods presently contribute to the improvement in damage detection
using a vibration-based method which has been developed since the early 70s
(Smityh, 1988). The main purpose of this method is to
establish an alternative inspection to traditional options like the Visual Inspection
Method which is costly and difficult to implement especially when offshore structures
are located in deep water and often susceptible to the unpredictable nature
of sea conditions.
Offshore structures are more likely to experience structural damage than other
civil engineering structures as they are continuously exposed to sea waves,
currents, seismatic actions and marine growth. The damage will reduce the stiffness
and alter the modal properties of the structure such as the natural frequency,
damping ratios and mode shapes. The changes in these properties are the fundamental
concepts when inspecting the vibration characteristics of the structure (Brincker
et al., 1995). As offshore structures are regularly acted upon by
hydrodynamic forces like sea waves which are variable with time, it is necessary
to examine the effects of the sea wave on the dynamic response of the structure.
The important aspect in examining the dynamic characteristics is to ensure the
fundamental natural frequency of the designed platform is well separated from
the frequency at which the peak energy of the wave occurs (Harnett
et al., 1997).
Fundamental natural frequencies and mode shapes of the structure under free
excitation is significantly important when examining the dynamic characteristics
of the structure. In this study, the first mode shape of the platform is utilized
in developing the sea force before applying on the nodes on the platform. In
reality, the measurement of the platforms natural frequency is achieved
by analyzing the signal from the accelerometers; however mode shape determination
is not feasible.
A modal simulation is carried out in the study to estimate the mode shapes of the platform which is utilized in developing the sea force. The modal analysis is also applied to build the top platform mass by tuning on the first natural frequency of the platform between 0.6 and 0.7 Hz.
The aim of this study is to investigate the dynamic response of an offshore structure subjected to sea wave forces and explore the frequency spectrum technique for detecting damage in the structure. The nodal displacement results obtained from FE dynamic analysis simulation is first converted into acceleration and finally into frequency response using Fast Fourier Transform (FFT) which is very useful in determine the peak frequencies of the structures response.
The sea force which is the only forcing input for the platform is developed using Morison equation and JONSWAP frequency spectrum in Matlab. Some properties of the platform like area and volume of lumped mass and mode shape are described in the sea force model in Simulink. The frequency of the sea wave at which the peak energy occurs is also identified and compared with the fundamental natural frequency of the platform.
The key aspect in the Study is to perform the dynamic simulation which acquires input from the sea force data at various heights and angles. The dynamic response of the platform is analyzed based on the sea force applied in various directions named X, Z and 45° diagonal to X and Y directions. The dynamic response of the platform is then investigated by inspecting the shift in natural frequencies as the material stiffness in the diagonal member is reduced in stages. This study will determine whether the shift in natural frequency in the response is able to indicate a substantial damage in the structure as experienced in real life.
FORMULATION OF A WAVE LOADING
The sea force incident on the structure is normally random in nature and very complex to generate. However, they can be best formulated using the Morison sea force equation as described below.
When analyzing the offshore structures, it is essential to include the effects of surface waves on the structure. The JONSWAP spectrum is used to describe the spectrum frequencies of irregular ocean waves in the North Sea for a usual 100 year storm which is given as:
where, Hs = 7 m is the significant wave height, ωp = 0.1 Hz is the peak frequency, γ = 3.3 and γβ is a frequency-dependant factor which determines the peak sharpness and is given by:
where, τ = 0.07 (ω≤ωp), τ = 0.09 (ω>ωp)
By using Morisons equation, the wave force per unit length in single directions such as in x-direction at a height y from the seabed can be determined for an offshore structure as shown below. The velocity of the structure relative to the wave particle is neglected as the structure is considered to be initially at rest. The force per unit length for the structure is given as:
where, xw is the wave particle horizontal displacement at height, y and time, t. D is the structures equivalent diameter, ρ is the density of the sea water, CD = 1 is drag co-efficients and CI = 2 is inertia co-efficients.
The total wave force acting on the submerged platform is calculated using the integral of the force per unit length over the submerged platform:
where, φ (z) is the mode shape vector (Hillis, 2009).
FINITE ELEMENT METHOD
This model of the platform is created in ANSYS using key points which define the co-ordinates in the working plane. The model is also created based on element types where different element types have a different number of nodes and degrees of freedom.
BEAM189 element type which is used in this model of the structure is based on quadratic polynomials. This element type only supports nodal concentrated force besides surface loads and does not offset a distributed load. Therefore, in this study, the sea force is applied directly to the points where the nodes are defined (Fig. 1). BEAM 189 is computationally efficient and has excellent convergence capability with respect to mesh refinement which is as accurate as a Hermitian element as described in the Formulating Beam Element. Specifically element BEAM189 is described as:
In this model, the simplest and by far most common application of linearly elastic and isotropic model has been used. It means when the load is removed from the structure, all the deformation is recovered because of the linear relationship between force and deflection. This assumption also implies that the displacement of the structure compared to its overall dimensions is small due to the non yielding load.
A beam element subjected to a uniform distributed load: The beam elements
used in this study are subjected to nodal force and the theoretical concept
shown below is relevant to this study. A uniform distributed load acting on
a 2D beam of length L and its equivalent nodal loading can be presented here
as shown in the Fig. 2 and 3 (ANSYS,
2000).
In this study, the sea force vector which is force per unit length and the associated height is applied to the selected nodes on the beam. The distribution force obtained from Simulink model is applied as nodal force on the specific nodes by multiplying the force per unit length with the distance between the selected nodes. This action will simulate a distribution load between the selected nodes.
The displacement in FE: In this study, displacement response is considered as one of the main parameter to detect the dynamic behaviour of the structure. The structure displaced states are wholly defined by translational displacements at the nodes. The displacement parameters are defined at three degrees of freedom at the nodes of the structural elements. For structural analysis, the degree of freedom consists of translation and rotational in X, Y and Z-direction. Thus, the displacement results are analyzed according to the number of degrees of freedom in the structure.
The interpolation of the node displacement under the action of external load can be written in the form:
Where:
In this notation, u represents the displacement components at a point in the
element. Ne is a shape matrix which determines the element shape and de is a
vector which has the nodal displacements. The displacement in element BEAM 189
is calculated based on the Timoshenko theory and its element is shown in Fig.
4 (ANSYS, 2000).
MODEL ANALYSIS
Model analysis relates to free vibration analysis where the system is free from external forces. The analysis will determine the natural frequency of a dynamic system which is subjected to a dynamic load. This is an important analysis to ensure the structures will not vibrate to its natural frequency value. This is to avoid resonance which can lead to catastrophic failure in the structure.
In finite element method, for a structure that undergoes free vibration, the system equation for an individual element can be represented as:
The solution of the free vibration system can be written as:
where, φ is the amplitude of the nodal displacement, ω is the frequency of the free vibration, t is the time, M and K are the mass and stiffness of the element, respectively.
By substituting Eq. 7 into Eq. 6, an eigenvalue equation is obtained:
By substituting ω2 = λ, the following equation can be derived:
where, λi is the eigenvalues corresponding to the systems
natural frequency and φi corresponds to a vibration mode of
the i th mode of the vibrating structure as illustrated in Fig.
5 (Smityh, 1988).
DYNAMIC (TRANSIENT) ANALYSIS
In ANSYS, a dynamic analysis is also called as a transient analysis (sometimes called time-history analysis). It is a technique used to determine the dynamic response of a structure under the action of any general time-dependent loads.
The linear dynamic behaviour of a structure depends on Eq. 9. The dynamic response is obtained by solving the following equation of motion:
Figure 6 shows a free body diagram of the internal forces accounted in the structure and its correspondence to a finite element model.
SIMULATION RESULTS
Finite element analysis is an efficient technique of analyzing the dynamic
performance of most structures because it can reduce the time in design process,
optimize the budget in the construction process and increase the safety of the
structure.
A model analysis is carried out using FE simulation to determine the mode shapes of the intact structure before assigning the normalised mode shape vector into the sea force mode shape function parameter. The magnitude of the sea force is associated with the mode shape of the intact platform, thus the displacement of the structure is the determining factor for the magnitude of the sea force (the sea force magnitude increases as the displacement increases). The displacement increases significantly starting from the height of 35 m to the top of platform.
The mode shapes contour plots produced in ANSYS present the displacement
in X-direction of the entire structure in good detail. The structure legs in
mode 1 are found to be straighter than those in modes 2 and 3. These results
are found to be consistent with the findings of Harnett
et al. (1997).
The change in response signatures for the first mode of the intact platform is shown in Fig. 8.
Figure 7a-c describe the three main mode
shapes of the intact platform under free excitation. The first three modes of
the modal analysis have an associated natural frequency of 0.604, 0.671 and
0.741 Hz, respectively. The mode shapes show that the largest displacement occurs
at the top (red contour plot) which are consistent for the three main modes.
The structure of mode 1 has the least displacement throughout the structure
jackets as compared to mode 2 and mode 3 as displayed by the dark blue plot
(mode 1) in comparison to light green plot for modes 2 and 3. It is worth mentioning
that mode shape 1 is utilised in the sea force mode shape function parameter
in developing the sea wave force acting dynamically on the platform.
DYNAMIC ANALYSIS OF SEA WAVE
The sea force plot converted from time domain to frequency spectrum (Fig. 9) provides better approximation of the peak frequencies of the sea wave. The sea force magnitude increases significantly at the height of 40m, corresponding to the mode shape function of the platform (higher displacement approaching the top).
The peak frequency of the sea force is about 0.12 Hz, similar to the JONSWAP frequency spectrum for typical North Sea Storm conditions. This signifies that the sea force developed for this specific platform provides a good approximation of a typical storm in the North Sea which is one of the key objectives of this study.
Figure 10 shows the position of the selected nodes along the legs of the main structure and the directions of the respective sea wave forces applied on the nodes. The arrows represent the sea forces which act on the selected nodes.
DYNAMIC ANALYSIS OF THE PLATFORMS
FE dynamic simulation establishes the effects of material stiffness reduction on the structure acceleration response. A data conversion from time trace into frequency domain in Power Spectral Density (PSD) describes the effects of material stiffness reduction on the peak frequency response of the structure.
Primarily, this study investigated the influence of the reduction of material
stiffness on the natural motion of the platform subjected to sea force in X,
Z and at 45° angle diagonal to X and Y-directions. Detecting the dynamic
response using frequency spectrum analysis is a deterministic method which adequately
estimates the natural frequencies, comparable to a real situation on a platform.
This is possible by converting the structural acceleration response obtained
through mounted accelerometers into frequency domain (Harnett
et al., 1997).
The material stiffness of one of the upper diagonal beam members of the platform (Fig. 10) was reduced by 10, 30, 50 and 90% for each of the sea wave directions. The structure with zero material stiffness reduction was recognised as an intact platform. The details are listed in Table 1.
As the stiffness was reduced, the peak frequencies for all intact and damaged
platforms were identified, giving the approximate values of the natural frequencies.
This result is in agreement with the study of Mangal et
al. (2001) who reported that natural frequencies of a platform are identified
by performing a Fast Fourier Transform (FFT) on the data.
The change of material stiffness from 30 to 90% had the greatest influence
on the shift in peak or resonance frequencies when the sea force is excited
in the X-direction and at 45° diagonal to XY as shown in Fig.
11 and 12 in relative to Z-direction (Fig.
13, 14). The shift in resonance frequencies is less apparent
for damage induced by reduction in material stiffness by 30% or less.
The energy excitation for damaged platform IV (with 90% stiffness reduction)
is almost eight times higher as compared to the intact platform. This significant
excitation is primarily due to the large displacement of the platform when the
diagonal member is almost totally damaged and the platform integrity is affected.
This also indicates a lower damping ratio for the damaged platform as compared
to the intact platform. The rotational acceleration of the platform (Fig.
15, 16) gives relatively less effect on the natural frequency
shift as compared to the linear acceleration.
The magnitude of the rotation has a relatively insignificant effect on the
platforms dynamic behaviour.
The sea force incident in the Z-direction has no influence on the shift of
natural frequencies following the reduction in the member stiffness (Fig.
14, 17). This is due to the fact that the damaged beam
member geometry is located in the X-plane and thus gives no effect on the structural
integrity as the dynamic force is applied in the Z-direction. Applying this
understanding, the location of the damaged beam member either in parallel or
perpendicular to the X or Z-axis in the structure global co-ordinates can be
identified if the direction of sea force is known.
The natural or resonance frequency shifts is apparent on the dynamic response of the platform when the sea force is excited at an angle of 45° diagonal to X and Z-directions (Fig. 12). As expected, by considering the vector sea force in X-direction, the peak frequency shift is more significant as the damage is induced by 50 to 90% reduction in material stiffness. There is little effect on the natural frequency shift for the intact and damaged platforms of 10 and 30% stiffness reduction in the diagonal member. However, the effects of frequency shift in the 10 and 30% are still detectable. Considering that the damage only occurs in one of the diagonal members of the platform, the detection of the damaged platform can be performed by examining the natural frequency shift in the dynamic response.
When the sea force is applied in the Z-direction, there is no effect on the resonance frequency shift. However, the energy excitation by a damaged platform with 90% stiffness reduction in the diagonal member is relatively much higher as compared to platforms with 50% or less stiffness reduction. It is not possible to consider the effects of frequency change in the Z-direction as the decrease in the natural frequencies are not consistent with the decrease in material stiffness. This is contributed by the fact that the location of the damaged beam is perpendicular to the sea force direction, thus the effect of the sea force is insignificant to the structure response.
The rotational acceleration about y-axis due to sea force at an angle of 45°
diagonal to X and Z-directions is found to be in agreement with the rotational
acceleration excited by sea force in the X-direction. There is apparent resonance
frequency shift as the stiffness is reduced from 10 to 90%. However, the magnitude
of the response is less significant as compared to the translational acceleration.
It is also found that the sea force at 45° angle produces a slightly larger
resonance frequency shift as compared to the sea force in X-direction. This
is contributed by the fact that the sea force at 45° angle consists of sum
vectors of sea force in X and Z-directions.
The structures with 30 and 50% stiffness reduction in the diagonal member show a detectable shift in resonance frequency and that with 90% stiffness reduction shows a very evident shift in resonance frequency. In reality, it is desirable to inspect and take appropriate measures on the weakened member before the stiffness is reduced up to 90%. Therefore, values at 30 and 50% stiffness reduction are more reliable when taking necessary action for the structure rehabilitation process. By measuring the structure acceleration via the mounted accelerometers on the platform, the time response should be converted into frequency spectra to determine the shift in natural frequency. By observing the shift in the peak frequencies, it indicates whether damage may have occurred in the structure beam.
CONCLUSION
This study presents the dynamic characteristics of an offshore structure due to sea wave excitation in the North Sea. It outlines some key procedures in performing the dynamic analysis of the platform under sea force action using finite element simulation. From the analysis carried out, it was shown that there was a detectable shift in resonance or natural frequencies of the platform according to the changes of the material stiffness in the structure. The shift in natural frequencies is only significant if the damaged member is in the same direction as the sea force and the member stiffness is reduced by more than 10%. The result of the dynamic analysis is considered reliable as only one diagonal beam is modelled as a damaged member with reduced material stiffness. Therefore, it can be concluded that the shift in the natural frequencies can be utilized as an indicator tool to monitor structural dynamic behaviour that are altered due to material stiffness reduction in the structural member while the platform is in service. By monitoring the structural response obtained using fixed accelerometers on the platform and converting them into frequency spectra, structural engineers should be able to identify any possibility of structure weakening due to corrosion or fatigue by detecting any shift in the peak frequencies response before further detailed inspection on the platform is carried out. This method of examining the shift in natural frequency offers an economical and convenient way in tracking the progression of damage in the structure. | https://scialert.net/fulltext/?doi=jas.2011.1688.1697&org=11 |
Cardiovascular disease describes all forms of heart and circulatory disease, including coronary heart disease (CHD), heart failure, stroke and peripheral artery disease. Diet reduces the risk and slows the progression of many of these conditions. Dietary advice used to be related to reduction of fat, rather than categorising fat as good or bad. However, fat intake must be looked at in the context of the diet as a whole.
Replacing saturated fat with unsaturated fat is beneficial, but not if it is replaced by refined carbohydrate.
Not all carbohydrates are the same. Fruits, pulses, vegetables and whole grains are carbohydrates with a beneficial effect. White starchy carbohydrates and free sugars should be avoided. Reducing salt intake is also important because this reduces blood pressure and therefore the risk of stroke and CHD.
Obesity is a risk factor for coronary vascular disease and type 2 diabetes. However, cardiac patients should ensure that when lowering their energy intake, this is not at the cost of the balance of good food groups. The whole-diet approach promotes whole foods with higher intakes of fruits and vegetables, legumes, wholegrain cereals, poultry and fish.
This results in higher intake of fibre, vitamins, antioxidants, minerals and unsaturated fats and lowering of glycaemic load, salt and saturated and trans fats. People should focus on changing more than one part of their diet. Different foods interact to provide health benefits, so a combination of healthy foods is more important than any single element.
Parker T, Taylor V (2018) Cardioprotective whole-diet advice in cardiac rehabilitation. British Journal of Cardiac Nursing. 13, 9, 428-435. | https://rcni.com/nursing-older-people/newsroom/journal-scan/whole-diet-approach-important-to-reduce-cardiovascular-disease-risk-140461 |
Researchers suggest that dog owners who don’t clean up after their pets in parks are likely to harm the environment and wildlife. Dog feces and urine contain significant amounts of phosphorus and nitrogen, according to a new study. Left in conservation areas, these excess chemicals can lead to over-fertilization of the soil.
This can adversely affect a wide range of plant and animal species and interactions between species.
The scientists called for a ban on dogs from parks or walking dogs on a leash in sensitive areas.
They also suggested alternative “nearby off-leash dog parks” and stressed the need for dog owners to fetch after their pets.
They said: “Dogs bring significant amounts of nutrients into ecosystems, but this disruption and the associated impacts on biodiversity have often been neglected.”
The study, published in the journal Ecological Solutions and Evidence, states, “Dogs appear to be a non-negligible, essential and underappreciated source of nutrients for peri-urban ecosystems.”
It goes on to say: “It is clear that the canine fertilization levels estimated here may have potential negative impacts on the biodiversity and ecosystem functions of species-rich vegetation that are often tracked in forest and nature management.
“Higher nutrient levels lead to increased plant growth, mainly by a limited number of nutrient-demanding species that will outperform specialists, particularly by taking away available light, resulting in a loss of plant species.”
READ MORE: Vet lists dog breeds at risk of ban amid bulldogs in Norway
For this study, the scientists counted 1,629 dogs over the course of 18 months in peri-urban forests and nature reserves near Ghent, Belgium.
They found the dogs left an estimated annual average of 11kg of nitrogen and 5kg of phosphorus per hectare, which they described as “considerable”.
The researchers said: “Based on our findings, we suggest land managers, particularly in ecosystems with species adapted to nutrient-poor soils, to take action to encourage visitors to remove solid feces (the main source of phosphorus) by reducing fertilization.” emphasize the impact of their dogs on top of other well-known negative impacts, such as on wildlife.”
They also suggested that local governments and park officials “enforce leash use more strictly, establish more off-leash dog parks, and more frequently consider total dog bans in oligotrophic ecosystems.”
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The scientists warned that exposure to dog feces could lead to the spread of disease.
They continued: “Furthermore, removing dog feces prevents infection of grazing animals with zoonotic diseases such as Neospora caninum.
“Dogs are the definitive hosts of this obligate intracellular parasite, but many other animal species can become infected.
“In wild ruminants such as deer, but especially domesticated grazing animals such as cattle and sheep, infection with Neospora is a major cause of miscarriage.”
They also stated that the usual “stick and flick” strategy used by the Forestry Commission in the UK to reduce nuisance from stepping on dog waste “should be avoided”. | https://dogdoright.com/dog-news-pooches-will-be-banned-from-parks-over-environmental-damage-from-feces-and-urine-science-messages/ |
# Radio City (album)
Radio City is the second album by the American rock group Big Star. Released in 1974, Radio City was recorded during 1973 at Memphis' Ardent Studios. Though not a commercial success at the time, it is now recognized as a milestone album in the history of power pop music. Critically acclaimed upon its release, the record sold poorly, partly due to a lack of promotion and the distribution problems of the band's struggling record label, Ardent Records. The album included "September Gurls" and "Back of a Car", which remain among the most famous Big Star songs; both the Searchers and the Bangles have covered "September Gurls".
The original Ardent Records LP featured record-jacket photographs by noted photographer William Eggleston, including The Red Ceiling on the cover. Eggleston was a close friend of band member Alex Chilton.
Some of the outtakes from the album include "I Got Kinda Lost", "Gone with the Light", "Motel Blues", and "There Was a Life" (an early version of "There Was a Light" from Chris Bell's I Am the Cosmos CD). The singles released from the album were "O My Soul" and "September Gurls".
Radio City's reputation has grown since its release, with many critics and listeners of the opinion that it is not only the definitive power pop album but one of the finest rock-music albums. As writer Richard Meltzer told an interviewer, "Big Star...is the means through which most bands today who are influenced by the Beatles get their dose of the British Invasion."
It was voted number 319 in the third edition of Colin Larkin's All Time Top 1000 Albums (2000). In 2003 and 2012, the album was ranked number 405 on Rolling Stone magazine's list of the 500 greatest albums of all time, and at number 359 in the 2020 edition. Rolling Stone magazine also ranked the song "September Gurls" as number 178 on its 500 Greatest Songs of All Time. Sound & Vision ranked it number 43 on its Top 50 Albums of All Time list.
## Composition and recording
In late 1972, following the release of the debut album, #1 Record, founding member Chris Bell left the group and the band became inactive for four months. Bell had already contributed to the music and lyrics of "O My Soul" and "Back of a Car"—songs which Alex Chilton recalls were written "by committee"— but receives no official credit. Chilton, aided by drummer Richard Rosebrough and at times by bassist Danny Jones, completed the recording of "Mod Lang", "She's a Mover", and "What's Going Ahn" without Jody Stephens or Andy Hummel. After performing at the Rock Writers Convention in 1973, the band returned to the studio to start work on Radio City.
## Reception
On its release in February 1974, Radio City met with general acclaim. Record World judged the musicianship "superb"; Billboard described the album as "a highly commercial set", and Cashbox called it "a collection of excellent material". However, sales were thwarted by an inability to make the album available in stores. Stax Records, primary distributor for the band's Ardent Records label, had recently placed distribution of its catalog in the hands of the much larger Columbia Records; Radio City's release coincided with a disagreement between Stax and Columbia, which left Columbia refusing to distribute the catalog. As a result, the album achieved only minimal sales of around 20,000 copies at the time.
Giving an "A" rating, Robert Christgau calls the album "Brilliant, addictive", observing meanwhile that "The harmonies sound like the lead sheets are upside down and backwards, the guitar solos sound like screwball readymade pastiches, and the lyrics sound like love is strange," concluding his review with, "Can an album be catchy and twisted at the same time?" AllMusic's William Ruhlmann considers that the band's follow-up to #1 Record "lacked something of the pop sweetness (especially the harmonies)" of the debut but captured "Alex Chilton's urgency (sometimes desperation) on songs that made his case as a genuine rock & roll eccentric. If #1 Record had a certain pop perfection that brought everything together, Radio City was the sound of everything falling apart, which proved at least as compelling."
## Track listing
Side one
"O My Soul" (Alex Chilton) – 5:40 "Life Is White" (Chilton, Andy Hummel) – 3:19 "Way Out West" (Hummel) – 2:50 "What's Going Ahn" (Chilton, Hummel) – 2:40 "You Get What You Deserve" (Chilton) – 3:08
Side two
"Mod Lang" (Chilton, Richard Rosebrough) – 2:45 "Back of a Car" (Chilton, Hummel) – 2:46 "Daisy Glaze" (Chilton, Hummel, Jody Stephens) – 3:49 "She's a Mover" (Chilton) – 3:12 "September Gurls" (Chilton) – 2:49 "Morpha Too" (Chilton) – 1:27 "I'm in Love with a Girl" (Chilton) – 1:48
## Personnel
Big Star
Alex Chilton – guitar, vocals Andy Hummel – bass guitar Jody Stephens – drums, vocals
Additional musicians
Danny Jones – bass guitar ("Mod Lang", "She's a Mover", "What's Going Ahn") Richard Rosebrough – drums ("Mod Lang", "She's a Mover", "What's Going Ahn")
## Cover versions
In 1981, the Searchers covered "September Gurls" on their album Love's Melodies, thus bringing full circle the influence that British Invasion bands had had on Big Star's sound. In 1986, The Bangles covered "September Gurls" on their album Different Light. The Gin Blossoms released a cover of "Back of a Car" on the 2002 deluxe edition of their album New Miserable Experience. In 2011, Chris Carrabba of Dashboard Confessional covered "I'm in Love with a Girl" on his album Covered in the Flood. In 2015, Lucero included "I'm in Love with a Girl" on their LP All a Man Should Do. Jody Stephens sang back up vocals and the title also comes from the song. Lucero recorded the album at Ardent studios with Jody Stephens frequently "popping in". | https://en.wikipedia.org/wiki/Radio_City_(album) |
The Lagos State Government on Friday vowed to strengthen its enforcement mechanism and collaboration with experts to check the collapse of buildings in the state.
The newly appointed Commissioner for Physical Planning and Urban Development, Mr Omotayo Bamgbose-Martins, said this during a roundtable discussion with stakeholders, in Ikeja, on ending building collapse.
The gathering looked at “The role of profesionals in effective monitoring and stage inspection- a solution to building collapse”.
He said that the government was determined to confront all issues boldly, towards taming the menace, which had become an embarrassment.
Bamgbose-Martins said the kind of prayers offered by notable stakeholders for him upon assumption of office revealed the enormity of complications in the regulation of the Lagos built environment.
“This deployment is an assignment for me,” the commissioner said, vowing to tackle the problem headlong.
He said that building collapse and the attendant loss of lives adversely affected the global reputation of the ministry and the state.
The commissioner said he was beginning immediate implementation of reforms in partnership with construction experts.
He urged staff of the ministry to turn a new leaf and shun bad practices during the implementation of regulations.
This, he said, was necessary, towards achieving the state government’s zero tolerance for building collapse.
“We have to clean our house, and we will clean our house,” he said.
He assured that he would not sack staff but ensure they change their attitude while improving their capacities and competencies through retraining.
The commissioner reassured Lagos residents that they would see changes in reforms to end building collapse and safeguard lives and investments.
He called on developers, individuals and built environment professionals to join hands in tackling the problem.
“There has to be an attitudinal change in order to stop the collapse of buildings,” he said.
He said he would adopt partnerships and collaboration with the built environment experts, strengthen and enforce regulations, and ensure the indemnity of constructions.
The commissioner gave an assurance that the government would engage with built environment professionals and regulate developers.
He said that quality control through the Lagos State Materials Testing Laboratory was important and would be sustained.
Bamgbose-Martins vowed that drastic actions would be taken against changing of building designs from the originally approved ones.
While taking questions from journalists, Bamgbose-Martins said the governor had given approval for a team of 60 policemen to back up the building control enforcement officials during visits to construction sites.
Earlier, General Manager, Lagos State Building Control Agency (LASBCA), Mr Gbolahan Oki, aligned with construction experts, noting that an existing committee working on domestication of the National Building Code was expected to submit its report within two weeks.
Oki said the agency would embark on mass enlightenment campaigns across the state towards curbing the menace of building collapse.
“We all must come together to form consortiums,” Oki said.
The General Manager, Lagos State Materials Testing Laboratory (LSMTL), Mr Olufunsho Elulade, said from inception of any project, testing should be seen as key.
He said that sanctions were being made stiffer, for deterrence.
Elulade said the state was updating its tests, urging residents and developers to always engage the right professionals.
The Permanent Secretary, Lagos State Ministry of Physical Planning and Urban Development, Mrs Abiola Kosegbe, said government had been engaging experts on codes and regulations.
She said that collaboration would ensure proactive steps were taken against infractions and building collapse.
Kosegbe said stakeholders’ engagements started over two months ago and would continue until permanent solutions were achieved.
On his part, the Special Adviser to Governor Babajide Sanwo-Olu on E-GIS, Dr Babatunde Olabode, urged the built environment professionals to profer solutions and not resort to blame game.
Olabode said this was important to prevent further calamities and deaths.
He said the office of E-GIS and planning had several programmes and cited a technology tagged “capture Lagos” which would use an app to monitor building development across the state.
The special adviser said another scheme targeted 6,000 smart phones for effective monitoring of construction sites while there was a technology to digitise all planning approvals, as well as use of satellite imagery.
“All planning process will soon become transparent when we use technology,” he said.
The seven built environment profesional associations, their affiliates and regulatory bodies took turns to offer technical advice.
Associations in attendance inlcuded Nigerian Institute of Architects, Nigerian Institute of Building, Nigerian Institute of Town Planners, Nigerian Society of Engineers, Council for the Regulation of Engineering in Nigeria, and Nigerian Institute of Mining and Geosciences.
A former commissioner of the Lagos State Ministry of Physical Planning and Urban Development, Mr Toyin Ayinde, as well as the first Commissioner of the ministry, Mr Kayode Anibaba, alongside other top officials offered valid suggestions. | https://brandpowerng.com/building-collapse-lagos-govt-reads-riot-act-partners-experts-to-check-trend/ |
By Nicholas von Wettberg
According to a recent follow-up telephone survey of 400 likely Davis voters, over half of those polled were in support of a $960 parcel tax for improvements in Davis Joint Unified School District (DJUSD) schools.
While the overall numbers from the research reflected positively on the district-wide school climate, the amount of potential interest, however, fell well short of the required two-thirds vote for such a measure.
As a result, EMC Research will recommend to school board members at Thursday’s meeting that the dollar amount originally proposed for the measure appear on the November ballot.
Trustees requested the follow-up survey after they were given results from the firm’s initial study, in which 71-percent of 400 likely Davis voters responded that they would support a school parcel tax at a proposed $620 for 8 years.
The board could be called aspirational in its decision to further explore voter support for an increase in the funding of district programming, especially with a sampled 41-percent voter base unaware of a current parcel tax, but the difference in tax amount would raise approximately $5 million more per year for Davis schools.
Much of that additional funding would go toward one of the district’s current priorities: closing the achievement/opportunity gap, in the form of “providing more support for struggling students, high-quality teachers, additional literacy and math specialists, innovative science programs and improved art and music.”
In the follow-up survey, conducted from May 15-22, the tenth question presented was, “If the election were held today, would you vote yes to approve this measure ($960 for 8 years) or no to reject it?”
Fifty-five percent of the voters responded with a solid yes to the question, which amounted to a 16-percent drop compared to answers from the study in April.
In both of the EMC interviews, there was a plus/minus Margin of Error of 4.9 percentage points.
One key finding was that, similar to the previous survey, subgroups including older voters and high-propensity voters were less in favor of supporting an increase “than the overall support level.”
The follow-up survey also revealed that district parents had some trouble supporting the increase, with 57 percent of parents of a DJUSD student voting a solid yes – a 14-percent decrease when compared to the findings from the first study.
If Davis renters and others were the only subgroup to cast a vote in the General Election, there might be a chance for an increased amount to be placed on that ballot.
A sizable 71 percent of that category (enough to surpass the threshold) replied with a solid yes to the support for the $960 amount. The same could be said for voters, ages 18-49, whose responses recorded a similar percentage.
Voting homeowners, on the other hand, were not so receptive to a boost in yet another tax, as successful and important as the extra funding has been to Davis education for the past 32 years.
Only 47 percent of homeowners responded with a solid yes, which was down 19 percent from the previous survey.
Component-wise, the study confirmed that voters are concerned about issues like retaining high-quality teachers, providing outstanding academic programs and providing more support for struggling students.
As for the term, “support for struggling students,” there was a marked difference in importance level between how it was worded in each survey.
In the proposal for a $620 measure, it read, “Providing support for struggling students,” which garnered a reply of very important from 58 percent of likely Davis voters.
Comparatively, only 46 percent of voters gave a very important reply to the phrase, ”Closing the achievement gap by providing more support for struggling students.”
Other language tested in the polls showed favorable ratings (an increase of 17 percent) when a word like “maintaining” was used instead of “improving,” or through the omission of the word “additional.”
Questions 21 through 27 in the survey gauged the support level of voters when presented with reasons for backing the measure.
Respondents were asked, “Now I’m going to read you some additional information about the proposed school parcel tax measure for Davis Joint Unified School District. After hearing each statement, please tell me if it makes you much more likely to support the measure, somewhat more likely to support it, or if it makes no difference to you.”
The statement voters supported the most was, “This measure will prevent the district from having to lay off over 100 teachers.”
Just over half those polled (51 percent) answered that they would be much more likely to support the measure for that reason.
The second highest percentage (44 percent) of voter support came after being read the statement, “All of the revenue from this measure will be spent here in our local schools and cannot be taken away by the state.”
Conversely, when posed with statements that opposed the proposed increase, over half of the reported voters were less likely (25 percent much less and 28 percent somewhat less) to support the measure, not only because of the overall amount involved but also because the increase comes at too fast a rate.
The statement read to voters was, “$960/parcel is just too expensive and it represents an 80% increase above what we currently pay for Davis schools.”
It seems clear that after hearing the results of the follow-up survey the board will reject an increase in the amount for a school parcel tax, sticking instead to the original plan for a measure of $620 for 8 years (raising approximately $9.5 million per year for programming). | https://www.davisvanguard.org/2016/06/board-hear-recommendation-parcel-tax/ |
The PADI Drift Diver Specialty Course teaches you how to enjoy going with the flow as you scuba dive down rivers and use ocean currents to glide along. It feels like flying – except that you’re underwater using scuba equipment. Drift diving can be relaxing and exhilarating at the same time.
What will you learn?
Along with drift diving techniques and procedures, you’ll:
- Receive an introduction to drift diving equipment – floats, lines and reels.
- Get an overview of aquatic currents – causes and effects.
- Practice with buoyancy control, navigation and communication during two drift dives.
- Learn techniques for staying close to a buddy or together as a group as you float with the current.
How can you start learning now?
Get a PADI Drift Diver Manual and the video to start learning immediately. Along with your basic scuba equipment, you’ll learn to use various surface marker buoys and floats with lines and reels. Ask your PADI Instructor or local dive centre staff about other equipment you may need to get the most of your drift dives.
Prerequisites: | https://pdldivers.net/drift-diver-specialty-course/ |
Comparative genomics is the analysis and comparison of genomes from different species. This area of research is driven by the large number of sequenced genomes and heavily relies on efficient algorithms and software to perform pairwise and multiple genome comparisons.
Results
Most of the software tools available are tailored for one specific task. In contrast, we have developed a novel system CoCoNUT (C omputational C omparative geN omics U tility T oolkit) that allows solving several different tasks in a unified framework: (1) finding regions of high similarity among multiple genomic sequences and aligning them, (2) comparing two draft or multi-chromosomal genomes, (3) locating large segmental duplications in large genomic sequences, and (4) mapping cDNA/EST to genomic sequences.
Conclusion
CoCoNUT is competitive with other software tools w.r.t. the quality of the results. The use of state of the art algorithms and data structures allows CoCoNUT to solve comparative genomics tasks more efficiently than previous tools. With the improved user interface (including an interactive visualization component), CoCoNUT provides a unified, versatile, and easy-to-use software tool for large scale studies in comparative genomics. | https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-9-476 |
As Nigeria intensifies preparation for Rio 2016 Olympic, Mr President, Muhammadu Buhari, Tuesday, tells members of Nigeria Olympic Committee (NOC) whose presence in Brazil will be ineffective to remain in the country or be responsible for the cost.
The president further warned the members of the Nigerian contingent to the Rio 2016 Olympics to do away with drugs and other acts that could bring disrepute to the country.
Buhari while speaking before he handed over Team Nigeria to the NOC at the Old Banquet Hall, State House, Abuja, said, “We are all aware of our nation’s dwindling revenue and the current global economic challenges. It is, therefore, imperative that funds provided for the Games are utilized judiciously.
“In this regard, any official who has no business at the Games should stay at home to cheer the team from here and if they must travel to the Olympics, they should do so at their own expense.”
The president, who was decorated by the Olympic body as the NOC Grand Patron, charged all athletes and team officials going to the Olympic Games to be worthy ambassadors of the country, both on the field of play and outside the sporting arena, noting that the eyes of the global community would be on them and as such, they should desist from acts that could dent Nigeria’s image.
He said, “The menace of drug use in sports is threatening the core foundation of sports and has led to embarrassing situations as well as sanctions of some great sporting nations. I, therefore, urge you to keep the integrity of our nation intact by competing clean and fair at the Olympic Games.
“Please bring as many medals back home as a result of your efforts and endeavour. But remember it is more important to compete and acquit your country as a fair sporting nation than to bring a pack of medals as a result of bending the rules and denying the Games of fair competition.”
He added: “Aside the sports that we have qualified for the Olympic Games, I have equally been informed that our athletes have qualified athletes for the Paralympic Games, which comes up immediately after the Olympic Games in Brazil.”
He assured that the Federal Government was fully committed to the delegation’s successful participation in the Rio Olympic Games and will ensure that funds budgeted for the Games were released without further delay.
Sports and Youths Development Minister, Solomon Dalung, thanked the President for his unwavering commitment to sports development in the country. He cited the N2.9 billion the President approved for the Ministry on the heels of the last African Games, while assuring the president that “members of the team are competing on merit… they have trained sufficiently and they are still training. 86 athletes will be carrying Nigerian banners in nine different sports.”
This year Olympic, which will be hosted in Rio De Janeiro, Brazil from 5th to 21st August, has over 10,500 athletes from 206 participating nations with 306 events, 37 venues and 42 sport disciplines. | http://www.newsofthepeople-ng.com/buhari-tells-noc-stay-home-if-you-have-no-business-in-brazil/ |
The Department of Defense executes Global Health Engagement or "GHE" activities to establish and improve the capabilities of Partner Nations' military or civilian health sectors, or those of the DoD.
DoD's GHE activities advance operational readiness and protect our troops, build interoperability so we can work more effectively with the armed forces of our partner nations, and enhance security cooperation so DoD can establish and maintain strong relationships around the world. A key enabler to regional stability and security for DoD's combatant commands, GHE reduces risks to U.S. armed forces while fostering mission capability of partner nations' forces so that together, we can continue working effectively to defend global interests.
Read more about the DoD's policy for Global Health Engagement.
Global Health Engagement
Global Emerging Infections Surveillance
HIV/AIDS Prevention and Treatment
Global Health Security Agenda
Medical professionals and leaders from across the Department of Defense engaged with partner nation colleagues while participating in the Asia Pacific Military Health Exchange 17 (APMHE) in Singapore May 23-26.
Recommended Content:
A growing partnership of more than 60 nations is working to build countries’ capacity to help create a world safe and secure from infectious disease threats and elevate global health security
Department of Defense and other senior U.S. government leaders travel to the Netherlands to attend a summit on the Global Health Security Agenda
For nearly two decades, the Military Health System has supported global public health surveillance to protect its forces and allies
DHA Address: 7700 Arlington Boulevard | Suite 5101 | Falls Church, VA | 22042-5101
The appearance of hyperlinks does not constitute endorsement by the Defense Health Agency of non-U.S. Government sites or the information, products, or services contained therein. Although the Defense Health Agency may or may not use these sites as additional distribution channels for Department of Defense information, it does not exercise editorial control over all of the information that you may find at these locations. Such links are provided consistent with the stated purpose of this website. | https://www.health.mil/News/In-the-Spotlight/Global-Health-Engagement?type=Articles&page=4 |
Virginia Chapter Sections
Sections are geographic areas of the Commonwealth where members share common geographies, interests and challenges. The Chapter established the sections to encourage interaction among members at the local and regional levels. The sections promote networking, education, and professional development through local events and interactions. Once a year, the sections hold a statewide symposium, which functions as a day-long conference that focuses on a specific topic. The symposium themes may include coastal or rural planning, economic development, downtown revitalization or other popular topics.
APA Virginia established 9 sections that serve our members throughout the state. These sections include the Northern Virginia, Hampton Roads, Central, Chesapeake, Piedmont, Shenandoah Valley, Roanoke/New River Valley, Southwest and Southside. The exact boundaries for each are largely based on the borders of the Virginia's Planning District Commissions (PDCs). Each section elects one or more members into leadership positions and are referred to as Section Directors. These leaders serve as representatives that connect the Chapter's members and the Board, raising concerns and sharing ideas from their regions. Primarily, Section Directors serve to organize events and provide personalized service our members.
Sections encourage interaction among members at the local and regional level.
Virginia Sections
Updated section info & contact info coming soon
Frequently Asked Questions
HOW AM I ASSIGNED TO A SECTION?
All Chapter members are also members of a section. APA Virginia assigns sections to members based on the information from their APA profiles. When members from APA sign up to be a member or edit their accounts, this information goes directly to the state-level chapters. Some people use their homes addresses on their APA profile, while others enter their office address. The chapter uses these addresses to assign members to a section.
I CHANGED JOBS OR MOVED BUT KEEP GETTING EMAILS FROM MY OLD SECTION. HOW DO I GET SIGN-UP TO MY CURRENT SECTION?
Section membership is based on profiles from the APA National records. If you moved or changed jobs, please go to the American Planning Association website and update your profile. Once those records are updated, the Chapter will soon have your current information and you will be included into a new section.
CAN I ATTEND EVENTS IN A DIFFERENT SECTION?
Yes. APA and APA Virginia members can attend any section events, statewide. Each section sends out event notifications and updates to their section members. Even if you do not belong to a particular section, you can view section information on this website.
HOW DO I BECOME A SECTION DIRECTOR?
The sections only have one official officer, the section director. Some sections have multiple co-section directors, to share responsibilities when their regular job gets busy. If you are interested in being a section director, or co-director, please contact the VP of Sections, at [email protected]. We will keep a record of your interest. If the Section Director position opens, then we will contact you and confirm if you are still interested.
WHAT IS THE TIME COMMITMENT FOR BEING A SECTION DIRECTOR?
Section leadership positions allow members to take initiative and ownership in building their sections. Each section is asked to hold at least one event per year, and encouraged to hold quarterly events. As volunteer positions, the Chapter recognizes that an individual's first priority is to his or her fulltime job. There is flexibility, in terms of time commitments, but section directors should be prepared to dedicate a few hours per month on these responsibilities. With a co-section director, leadership can share the workload when time is more limited.
HOW CAN I BECOME MORE INVOLVED IN MY SECTION?
The Section Directors have the ability to designate unofficial officers, to assist with events and other services. Contact your section director to inquire about these opportunities.
WHERE DO I FIND OUT ABOUT SECTION EVENTS?
The sections occasionally send out notices to their members about activities and events. Contact your Section Director to confirm that you are on the mailing list. APA Virginia also provides information via a digital newsletter, and this website also provides updates on events, such as networking and training opportunities.
CAN THE SECTION BOUNDARIES CHANGE?
Yes, the Chapter can change the section boundaries, per the APA Virginia bylaws. The Board can establish a new section or modify existing sections by a two-thirds vote.
DO SECTIONS FUNCTION AS SMALL CHAPTERS?
No, but sections can develop a structure that is similar to a full organization. A section can adopt Bylaws to govern section affairs, but those bylaws must be consistent with the APA Virginia bylaws or the Articles of Incorporation. Each section must also follow the financial policies established by the Board. | https://virginia.planning.org/connect-apa-virginia/sections/ |
The Organization for Economic Cooperation and Development (OECD) has issued the following publications in its Series on the Safety of Manufactured Nanomaterials:
- No. 55 — Harmonized Tiered Approach to Measure and Assess the Potential Exposure to Airborne Emissions of Engineered Nano-Objects and their Agglomerates and Aggregates at Workplaces: The primary goal of this publication is to describe a reliable formal methodology for conducting consistent exposure related measurements and assessments of aerosols containing engineered nano-objects and their agglomerates and aggregates in workplace operations. This publication presents a harmonized tiered approach that is “systematic, consistent, practical, and flexible for conducting field-based, real-time workplace release and exposure measurement and assessment” to airborne nano-objects and their agglomerates and aggregates and off-line analyses of measurement samples.
- No. 56 — Analysis of the Survey on Available Methods and Models for Assessing Exposure to Manufactured Nanomaterials: The OECD Working Party for Manufactured Nanomaterials (WPMN) Steering Group 8 agreed to conduct an informal survey as an initial step in compiling information regarding methods and models for assessing exposure to manufactured nanomaterials. The results were intended to develop an inventory of available methods and models used to assess human and environmental exposure to manufactured nanomaterials. The survey gathered information on a variety of types of methods and models, including those used to set priorities, screen nanomaterials, develop detailed assessments of exposure, and other types of methods or models.
- No. 57 — Guidance Manual Towards the Integration of Risk Assessment into Life Cycle Assessment of Nano-Enabled Applications: Based on the conclusions of a 2011 workshop on “Environmentally Sustainable Use of Manufactured Nanomaterials,” the OECD WPMN Steering Group 9 Project on the Environmentally Sustainable Use of Manufactured Nanomaterials developed this guidance manual intended to support decision making in various situations; including research, innovation, product development, scaling-up of production, marketing, and end-of-life, as well as regulatory decisions. This publication aims to incorporate knowledge of risk analyses of the environmental impact in life cycle assessment studies as decision-making tools during both upstream (research and development) and downstream (industrialization, usage, re-use, end-of-life management: recycling, recovery, destruction) phases of a nanostructured product. | https://nanotech.lawbc.com/2015/07/oecd-issues-new-publications-in-series-on-the-safety-of-manufactured-nanomaterials/ |
1. Introduction {#sec1-metabolites-05-00794}
===============
Carotenoids represent a subcategory of tetraterpenoid pigmented lipid compounds made by plants and various fungi and bacteria \[[@B1-metabolites-05-00794]\]. Majorly exemplified by ß-carotene, lycopene, astaxanthin, zeaxanthin, fucoxanthin, ß-cryptoxanthin, canthaxanthin, lutein, and crocetin, compounds of the carotenoids family handle a diversity of bright colors such as yellow, red, purple, and orange \[[@B2-metabolites-05-00794],[@B3-metabolites-05-00794]\]. Lycopene is a bioactive phytochemical of this vast family of carotenoids that has gained much concerns these recent years because of its commercial attributes and due to its biofunctionality \[[@B4-metabolites-05-00794]\]. Exclusively synthesized on one hand, by plants like tomato, watermelon, guava, papaya, apricots, pink grapefruits, and red oranges and on the other hand by carotenogenic microorganisms, lycopene is essential for the human body given that it can only be provided through its ingestion under multiple forms such as food or drugs. Lycopene promotes good health owing to its therapeutic, prophylactic, and nutraceutical functions. Increasing scientific evidence displays its implications in carcinogenic cell apoptosis and cell cycle arrest of diverse types of human cancers \[[@B5-metabolites-05-00794],[@B6-metabolites-05-00794],[@B7-metabolites-05-00794],[@B8-metabolites-05-00794]\]. Lycopene is also recognized as a strong cancer chemo-preventive agent \[[@B9-metabolites-05-00794],[@B10-metabolites-05-00794]\] and has been found to have cardio-protective, antioxidant, and anti-inflammatory effects \[[@B11-metabolites-05-00794]\]. In view of the above, the large scale production of lycopene is of fundamental necessity. However, the current manufacture of lycopene from plant sources faces food competition, environment, high production cost, long processing time, and low yield problems. Besides, microbial fermentation using carotenogenic microorganism is scarce and fails to produce sizable titers of lycopene. Big efforts have been made to engineer non-carotenogenic hosts for lycopene production; but the fermentation process still constitutes the foremost impediment for generating great amounts of lycopene. *Yarrowia lipolytica*, categorized as GRAS (Generally Recognized As Safe), has been established as a promising fermentation platform. Recently, a complete procedure for engineering *Y. lipolytica* for lycopene production was developed. Nonetheless, apart from the culture medium and genetic manipulation procedure provided \[[@B12-metabolites-05-00794]\], no deep investigation of cultural conditions was communicated. In addition, a fed-batch process for lycopene production from this species was established, but authors did not focus on the improvement of the bioprocess route \[[@B13-metabolites-05-00794]\]. Furthermore, up to now, only one patent has reported lycopene production from engineered strains of *Y. lipolytica* under lipid accumulation conditions \[[@B14-metabolites-05-00794]\]. Therefore, endeavors need to be made for building complete innovative, cost-effective, and competitive bioprocesses for lycopene production from genetically engineered strains of *Y. lipolytica*. One of the most efficient tools for yielding high titers of carotenoids in engineered strains is based on knock-out or overexpression of specific genes coupled with computational approaches \[[@B15-metabolites-05-00794],[@B16-metabolites-05-00794],[@B17-metabolites-05-00794]\]. Moreover, whole-genome sequencing and high-throughput omics as well as the detailed biochemical and enzymatic documentation on microbial metabolism have promoted prosperous genome-scale metabolic network (GSMN) reconstruction \[[@B18-metabolites-05-00794],[@B19-metabolites-05-00794]\].
*In silico* models are valuable for comprehending the biochemical aptitudes of an organism and to foresee the influence of genetic and/or medium perturbations on growth and metabolic fluxes \[[@B20-metabolites-05-00794],[@B21-metabolites-05-00794]\]. Flux balance analysis (FBA) has been materialized as an operational *in silico* channel for scrutinizing biological networks in a quantitative approach. Contrary to mechanistic simulations that rely on precise kinetic information, FBA is based on the stoichiometric matrix and a biologically important objective function for identifying optimal reaction flux distributions which are subsequently used to unravel the metabolic capabilities of the studied system \[[@B22-metabolites-05-00794]\].
The present-day FBA is in a wide way to guide designs of experiments. In a previous study, we constructed a genome scale metabolic model of *Y. lipolytica* for lipid production and predicted a minimal culture medium for lipids biosynthesis. Afterward, we have updated this model for generating model information for terpenoids production. The updated model is apt to provide reliable information when farnesyl diphosphate (FPP), one of the key precursors of terpenoids backbone in *Y. lipolytica*, is resolved as the objective metabolite. We hypothesized that such a metabolic network model can support the prediction of culture media for ameliorating the yield of lycopene in biotechnological applications.
Statistical design methods, especially the Plackett-Burman design, are commonly employed for optimization of fermentation media. The Plackett-Burman designs are usually resolution III, highly efficient two level fractional factorial screening designs for studying N-1 variables using N runs, where N is a multiple of 4. They use the minimum number of runs to quickly identify the factors with a significant effect on the response. However, the choice of the initial set of chemical compounds is laborious since these compounds are generally randomly selected. In addition, though GSMN can predict the nutritional requirements for a given biological system, the accuracy of the amount of a single predicted compound to be added is difficult to determine because *in silico* data rarely match with the in vivo metabolic behavior. However, by combining GSMN (FBA) results and statistical methods such as Plackett-Burman design, it is possible to develop an efficient culture medium for the production of valuable objective products.
Therefore, in this paper, we run FBA by means of COBRA Toolbox 2.0 \[[@B23-metabolites-05-00794]\] to foresee environmental conditions contributing to FPP overproduction that may well redirect the carbon flux toward lycopene biosynthesis in an engineered strain of *Y. lipolytica* harboring only *crtE*, *crtB*, and *crtI* genes. As model predictions do not correctly reflect the in vivo situation, we combined modelling data with Plackett-Burman factorial design of experiments for optimizing cultivation media. Furthermore, we compared lycopene production in modeling suggested media with other media designed based on compounds usually reported in the literature through fermentation scale up experiments.
2. Results {#sec2-metabolites-05-00794}
==========
2.1. Media Designing for Bioprocess Improvement {#sec2dot1-metabolites-05-00794}
-----------------------------------------------
### FBA-Independent Screening of Medium Components
Up to date, no deep investigation for development of fermentation media for lycopene production from *Y. lipolytica* has been realized. In order to establish a reference medium for evaluation of the FBA efficiency, we first selected a set of 23 factors in the light of preliminary experiments and literature review for the designing of FBA-independent cultivation medium. Bioprocess improvement experiments were carried out using the engineered strain Po1f-1312E-1269IB. In a first step, we screened a set of chemicals without considering the flux balance analysis (FBA). The matrix of the Plackett-Burman design used in regard of this achievement is reported in [Table 1](#metabolites-05-00794-t001){ref-type="table"}. According to the Plackett-Burman principle, data transformation is required if the ratio max/min is greater than 10. For this reason, we used Log~10~ or the root square (Sqrt) for data transformation. Subsequently, the Pareto chart was used for analyzing the effects of different components and selecting those to be included in the model. There are two different *t* limits plotted on the graph based on the Bonferroni or family-wise corrected *t* and a standard *t* for individual effects tested. Effects above the Bonferroni Limit were added to the model as certainly significant factors. Effects above the *t*-value Limit were possibly significant and added if they make sense. Effects below the *t*-value limit were likely insignificant. Pareto charts of all experimental data are reported in [Supplementary File 1](#metabolites-05-00794-s001){ref-type="supplementary-material"}.
The results showed that biomass production was significantly (effects above the Bonferroni Limit) improved by the effects of KNO~3~, MgSO~4~·7H~2~O, FeCl~3~·6H~2~O, FeSO~4~·7H~2~O, yeast extract, fructose, BaCl~2~·2H~2~O, NiCl~2~·6H~2~O, KH~2~PO~4~ and vitamin B~1~ in this decreasing order. The effect of MnCl~2~·4H~2~O, Na~2~MoO~4~·2H~2~O and KI were also positively significant (*t*-value \< effects \< Bonferroni Limit) while the positive effect of K~2~HPO~4~ was not significant. The set of factors including CuCl~2~·2H~2~O, NiSO~4~·6H~2~O, CoCl~2~·6H~2~O, H~3~BO~3~, ZnCl~2~, MnSO~4~·7H~2~0, NaCl, Glucose, (NH~4~)~2~SO~4~ were found as inhibitors of biomass production. The highest biomass concentration obtained was 16.14 g/L with max/min value of 25.22. The final equation in term of coded factors was: Sqrt (Biomass) = 2.24 − 0.38 × A − 0.18 × B − 0.043 × C + 0.29 × D + 0.15 × E − 0.13 × G − 0.095 × H + 0.072 × J + 0.089 × K + 0.28 × L + 0.082 × M + 0.29 × N + 0.37 × O − 0.095 × Q +0.22 × R + 0.25 × S − 0.20 × T + 0.14 × U + 0.020 × V + 0.12 × W + 0.19 × X.
For lycopene production, MgSO~4~·7H~2~O, FeCl~3~·6H~2~O, fructose, KNO~3~, NiCl~2~·6H~2~O, vitamin B1 and KH~2~PO~4~ had significant positive effects. The maximum lycopene concentration obtained in flasks was 9.18 mg/L. The final equation in terms of coded factors was: Sqrt (Lycopene)= 0.75 − 0.52 × A − 0.12 × B − 0.2 × C + 0.32 × D + 0.18 × E + 0.059 × G + 0.074 × H + 0.081 × J + 0.052 × K + 0.049 × L + 0.049 × M + 0.3 × N + 0.26 × O − 0.064 × P − 0.071 × Q + 0.28 × R − 0.15 × T + 0.11 × U − 0.17 × V + 0.14 × W + 0.072 × X.
The maximal lycopene content obtained from the 24 runs was 1.11 mg/g dry cell weight (DCW). Lycopene content was positively promoted by the effects of MgSO~4~·7H~2~O, NiCl~2~·6H~2~O, ZnCl~2~, MnSO~4~·7H~2~0, KI, MnCl~2~·4H~2~O, FeCl~3~·6H~2~O, KNO~3~, fructose, KH~2~PO~4~, vitamin B1, BaCl~2~·2H~2~O. Other components had negative effects.
The post-optimization experiments conducted to the optimized medium (PM medium) with the following composition (g/L): MgSO~4~·7H~2~O (14.74), NiCl~2~·6H~2~O (0.097), H~3~BO~3~ (0.099), ZnCl~2~ (0.15), MnSO~4~·7H~2~0 (0.4), KI (0.012), MnCl~2~·4H~2~O (0.2), Na~2~MoO~4~·2H~2~O (0.1), FeCl~3~·6H~2~O (2.87), KNO~3~ (0.05), Glucose (19.9), fructose (20), yeast extract (0.96), (NH~4~)~2~SO~4~ (0.51), KH~2~PO~4~ (10) and vitamin B1 (1.00E-02).
metabolites-05-00794-t001_Table 1
######
Matrix of Plackett-Burman screening of medium components selected independently from the FBA.
Std Run A:CuCl~2~·2H~2~O B:NiSO~4~·6H~2~O C:CoCl~2~·6H~2~O D:MgSO~4~·7H~2~O E:NiCl~2~·6H~2~O F:H~3~BO~3~ G:ZnCl~2~ H:MnSO~4~·7H~2~0 J:KI K:MnCl~2~·4H~2~O L:FeSO~4~·7H~2~O M:Na~2~MoO~4~·2H~2~O N:FeCl~3~·6H~2~O O:KNO~3~ P:NaCl Q:Glucose R:Fructose S:Yeast extract T:(NH~4~)~2~SO~4~ U:KH~2~PO~4~ V:K~2~HPO~4~ W:Vitamine B1 X:BaCl~2~·2H~2~O Biomass Lycopene Lycopene content
-------- ----- ------------------ ------------------ ------------------ ------------------ ------------------ ------------- ----------- ------------------ ------ ------------------ ------------------ ---------------------- ------------------ ---------- -------- ----------- ------------ ----------------- ------------------- -------------- -------------- --------------- ------------------ --------- ---------- ------------------
**10** 1 0.03 1 0.4 1.5 0.1 0.01 0.01 0.02 0.01 0.2 2.5 0.1 3 0.2 0.01 20 0 10 10 0.01 0 0.01 1 14.26 1.76 0.12
**22** 2 0.3 3 0.4 1.5 0.1 0.01 0.15 0.4 0.01 0.01 2.5 0.1 0.02 0.01 1 10 20 0.5 0.5 0.01 0 0.01 1 1.52 0 0
**12** 3 0.3 3 0.02 1.5 0.1 0.01 0.15 0.02 0.01 0.01 0.1 0.1 3 0.2 1 20 0 10 0.5 10 3.5 0 0.01 3.38 0 0
**2** 4 0.03 3 0.4 15 0.1 0.1 0.01 0.4 0.01 0.2 2.5 0.01 0.02 0.2 1 10 0 10 0.5 10 0 0 0.01 11.06 1.82 0.16
**7** 5 0.03 3 0.02 1.5 0.05 0.01 0.15 0.4 0.1 0.2 2.5 0.01 3 0.01 1 20 0 0.5 10 10 0 0 1 2.36 0.6 0.26
**13** 6 0.03 3 0.4 1.5 0.05 0.1 0.01 0.4 0.01 0.01 0.1 0.01 3 0.2 1 20 20 0.5 10 0.01 3.5 0.01 0.01 2.66 0.37 0.14
**1** 7 0.3 3 0.4 15 0.1 0.01 0.15 0.02 0.1 0.2 0.1 0.01 3 0.2 0.01 10 20 0.5 10 0.01 0 0 0.01 3.46 1.17 0.34
**16** 8 0.3 3 0.02 1.5 0.1 0.1 0.01 0.02 0.1 0.01 2.5 0.01 0.02 0.01 0.01 20 20 10 10 10 0 0.01 0.01 2.38 0 0
**3** 9 0.03 1 0.4 15 0.1 0.1 0.15 0.02 0.1 0.01 2.5 0.1 0.02 0.01 1 20 0 0.5 10 0.01 3.5 0 0.01 2.74 0.04 0.02
**15** 10 0.3 1 0.02 15 0.1 0.01 0.01 0.4 0.01 0.2 0.1 0.01 0.02 0.01 1 20 20 10 10 0.01 3.5 0 1 2.82 0 0
**14** 11 0.03 1 0.4 15 0.05 0.01 0.15 0.02 0.1 0.01 0.1 0.01 0.02 0.2 1 20 20 10 0.5 10 0 0.01 1 12.84 3.82 0.3
**21** 12 0.3 3 0.02 15 0.05 0.1 0.15 0.02 0.01 0.2 2.5 0.01 0.02 0.2 0.01 20 0 0.5 0.5 0.01 3.5 0.01 1 3.76 0.04 0.01
**24** 13 0.03 1 0.02 1.5 0.05 0.01 0.01 0.02 0.01 0.01 0.1 0.01 0.02 0.01 0.01 10 0 0.5 0.5 0.01 0 0 0.01 0.64 0 0
**18** 14 0.3 1 0.4 15 0.05 0.01 0.15 0.4 0.01 0.01 2.5 0.01 3 0.01 0.01 10 0 10 10 10 3.5 0.01 0.01 3.52 0 0
**19** 15 0.03 3 0.02 15 0.1 0.01 0.01 0.4 0.1 0.01 0.1 0.1 0.02 0.2 0.01 10 0 0.5 10 10 3.5 0.01 1 7.36 2.82 0.38
**6** 16 0.3 1 0.02 1.5 0.05 0.1 0.15 0.4 0.1 0.2 0.1 0.1 0.02 0.2 1 10 0 10 10 0.01 0 0.01 0.01 1.38 0 0
**23** 17 0.3 3 0.4 15 0.05 0.1 0.01 0.4 0.1 0.01 0.1 0.1 3 0.01 0.01 20 0 10 0.5 0.01 0 0 1 2.4 0 0
**5** 18 0.03 1 0.02 1.5 0.1 0.1 0.15 0.4 0.1 0.01 2.5 0.01 3 0.2 0.01 10 20 10 0.5 0.01 3.5 0 1 16.14 5.76 0.36
**8** 19 0.3 1 0.4 1.5 0.05 0.01 0.01 0.4 0.1 0.2 2.5 0.1 0.02 0.2 0.01 20 20 0.5 0.5 10 3.5 0 0.01 4.44 0 0
**17** 20 0.03 3 0.4 1.5 0.05 0.1 0.15 0.02 0.01 0.2 0.1 0.1 0.02 0.01 0.01 10 20 10 10 10 3.5 0 1 2.76 0 0
**4** 21 0.03 1 0.02 15 0.1 0.1 0.15 0.4 0.01 0.2 0.1 0.1 3 0.01 0.01 20 20 0.5 0.5 10 0 0.01 0.01 8.3 9.18 1.11
**11** 22 0.3 1 0.02 15 0.05 0.1 0.01 0.02 0.01 0.01 2.5 0.1 3 0.2 1 10 20 0.5 10 10 0 0 1 11.26 2.17 0.19
**9** 23 0.03 3 0.02 15 0.05 0.01 0.01 0.02 0.1 0.2 2.5 0.1 3 0.01 1 10 20 10 0.5 0.01 3.5 0.01 0.01 15.16 3.27 0.22
**20** 24 0.3 1 0.4 1.5 0.1 0.1 0.01 0.02 0.1 0.2 0.1 0.01 3 0.01 1 10 0 0.5 0.5 10 3.5 0.01 1 4.36 0 0
2.2. Combination of Flux Balance Analysis and Plackett-Burman Design for Media Designing {#sec2dot2-metabolites-05-00794}
----------------------------------------------------------------------------------------
### 2.2.1. Flux Balance Analysis and Prediction of Media Components {#sec2dot2dot1-metabolites-05-00794}
In this study, the flux balance analysis (FBA) was implemented to determine metabolic flux distribution with the genome-scale metabolic network model of *Y. lipolytica* (yli v1.7) that was updated from model iYL619_PCP by correcting topological network and parameters of model (model yli v1.7 is available at <http://www.echaoceshi.com/ECLOSB/CN/Default.aspx>). In model yli v1.7, R0763 is the only reaction, in which farnesyl diphosphate (FPP) is produced; R2000 is the reaction of growth (biomass formation reaction). Besides, the maximum flux of R2000 (specific growth rate) is 0.0350 h^−1^ in the glucose minimal media. The model yli v1.7 and iYL619_PCP predicted the equal glucose minimal media. The composition of minimal media in the experiment is as follows: glucose (20 g/L), NH~4~SO~4~ (3 g/L), KH~2~PO~4~ (2 g/L), in which the maximum specific growth rate is 0.0352 h^−1^. This indicates that model yli v1.7 predicted the maximum specific growth rate more accurately ([Supplementary File 2](#metabolites-05-00794-s001){ref-type="supplementary-material"}).
The fluxes of exchange reactions of the updated model were generated through FBA. Exchange reactions with negative fluxes indicated compounds that needed to be consumed when targeting a maximized production of FPP and the addition of those components into the culture medium was of crucial requirement. To predict the potential benefit of supplementing the minimal media with of amino acids or several cofactors in terms of FPP production based on FBA metabolic flux distributions, we relaxed the exchange reactions of model yli v1.7. The list of exchange reactions with negative fluxes and their fluxes when glucose, fructose, or both carbohydrates were selected as carbon sources is summarized in [Supplementary File 3 (Table S1 of Supplementary File 3)](#metabolites-05-00794-s001){ref-type="supplementary-material"}. The most prevailing class of exchange reactions included exchange reactions involving amino acids such as [l]{.smallcaps}-isoleucine, [l]{.smallcaps}-leucine, [l]{.smallcaps}-valine, [l]{.smallcaps}-asparagine, [l]{.smallcaps}-histidine, [l]{.smallcaps}-methionine, [l]{.smallcaps}-tryptophan, guanine, and [l]{.smallcaps}-lysine. The additional exchange reactions were those of O~2~, thiamine diphosphate, succinate, phosphate, ammonia, 4-aminobutanoate, ergosterol, ethanolamine, [d]{.smallcaps}-fructose, urea, [d]{.smallcaps}-glucose, hypoxanthine, and (R)-pantothenate. The number of negative exchange reactions and fluxes varied widely with the nature of the carbon source opted for. Putting aside the fact that FBA only gives one possible random solution instead of looking at all the possibilities (like Flux Variability Analysis would do, for example), it seems that the only "non-zero" values in this table are those corresponding to O~2~ exchange, [d]{.smallcaps}-fructose exchange and [d]{.smallcaps}-glucose exchange. All other values from −8.05e-35 to −1.46e-13 are most probably rounding errors of the LP solver, and so all those values could be considered as zeros. However, in order to predict the potential benefit of supplementing the minimal media with of above amino acids or several cofactors in terms of FPP production based on FBA metabolic flux distributions, we relaxed the exchange reactions of model yli v1.7. We first tested effects of 18 amino acids (only 18 amino acid can be utilized in model yli v1.7) on FPP production in a definite specific growth rate (90% of the maximum specific growth rate), and found that all the 18 amino acids facilitated FPP production in different degrees ([Table 2](#metabolites-05-00794-t002){ref-type="table"}). However, only eight amino acids ([l]{.smallcaps}-isoleucine, [l]{.smallcaps}-leucine, [l]{.smallcaps}-valine, [l]{.smallcaps}-asparagine, [l]{.smallcaps}-histidine, [l]{.smallcaps}-methionine, [l]{.smallcaps}-lysine, [l]{.smallcaps}-tryptophan) were found as amino acids that could be supplemented to the minimal medium owing to the guarantee of C/N ratio more than 10. Additionally, we also tested effects of 10 factors on FPP production in a definite specific growth rate ([Table 3](#metabolites-05-00794-t003){ref-type="table"}). We found that a certain number of factors had significant effect on FPP production. Furthermore, all 10 factors were chosen and supplemented to the minimal medium to verify their effects on FPP production ([Supplementary File 3](#metabolites-05-00794-s001){ref-type="supplementary-material"}).
metabolites-05-00794-t002_Table 2
######
Fluxes (mmol/g DCW/h) of 18 exchange reactions of amino acids and their respective effects on FPP production.
ID Reaction Name Biomass FPP Flux
------- ---------------------------------------- ------------- -------- ---------
R1202 [l]{.smallcaps}-isoleucine exchange 0.0315 ^\#^ 0.4342 −0.0042
R1203 [l]{.smallcaps}-leucine exchange 0.0315 0.4352 −0.0085
R1205 [l]{.smallcaps}-valine exchange 0.0315 0.4350 −0.0104
R1226 [l]{.smallcaps}-glutamate exchange 0.0315 0.4763 −2 ^\$^
R1241 [l]{.smallcaps}-alanine exchange 0.0315 0.5871 −2
R1244 [l]{.smallcaps}-arginine exchange 0.0315 0.5159 −2
R1245 [l]{.smallcaps}-asparagine exchange 0.0315 0.4344 −0.0052
R1248 [l]{.smallcaps}-cysteine exchange 0.0315 0.5878 −2
R1268 [l]{.smallcaps}-histidine exchange 0.0315 0.4347 −0.0030
R1273 [l]{.smallcaps}-methionine exchange 0.0315 0.4352 −0.0072
R1275 [l]{.smallcaps}-lysine exchange 0.0315 0.4353 −0.0067
R1280 [l]{.smallcaps}-serine exchange 0.0315 0.6640 −2
R1283 [l]{.smallcaps}-threonine exchange 0.0315 0.7025 −2
R1285 [l]{.smallcaps}-tryptophan exchange 0.0315 0.4339 −0.0010
R1298 [l]{.smallcaps}-aspartate exchange 0.0315 0.6640 −2
R1300 [l]{.smallcaps}-phenylalanine exchange 0.0315 0.6215 −2
R1301 [l]{.smallcaps}-proline exchange 0.0315 0.5150 −2
R1303 [l]{.smallcaps}-tyrosine exchange 0.0315 0.5650 −1.6980
^\#^ we set a definite specific growth rate of 0.0315 h^−1^ at the 90% of the maximum specific growth rate; ^\$^ we respectively set the lower bounds of amino acids exchange reaction to −2 mmol/g DCW/h.
metabolites-05-00794-t003_Table 3
######
Fluxes (mmol/g DCW/h) of 10 exchange reactions of factors used to test effects on FPP production.
ID Reaction name Biomass FPP Flux
------- ------------------------------- ------------- -------- ---------
R1207 Thiamine diphosphate exchange 0.0315 ^\#^ 0.4332 0.0000
R1239 4-aminobutanoate exchange 0.0315 0.4525 −1 ^\$^
R1251 Ergosterol exchange 0.0315 0.4333 −0.0002
R1258 Ethanolamine exchange 0.0315 0.4392 −0.0769
R1267 Guanine exchange 0.0315 0.4345 −1
R1278 (R)Pantothenate exchange 0.0315 0.4332 0.0000
R1281 Sulfite exchange 0.0315 0.4332 0
R1287 Urea exchange 0.0315 0.4332 0
R1296 Hypoxanthine exchange 0.0315 0.4353 −0.0049
R1306 Pyridoxine exchange 0.0315 0.4332 0
^\#^ we set a definite specific growth rate of 0.0315 h^−1^ at the 90% of the maximum specific growth rate; ^\$^ we respectively set the lower bounds of factors exchange reaction to −1 mmol/g DCW/h.
### 2.2.2. Plackett-Burman Design Screening of FBA-Predicted Components {#sec2dot2dot2-metabolites-05-00794}
Taking into account the results of the above simulations, we applied the Plackett-Burman design for experimental validation of FBA-predicted factors. The design matrix and responses obtained for biomass, lycopene and lipid production in Plackett-Burman design screening of FBA-predicted factors are correspondingly reported in [Table 4](#metabolites-05-00794-t004){ref-type="table"}. The results showed that biomass production ranged from 9.075 to 35.5 g/L (ratio max/min = 3.91) while the produced lycopene and lipid concentrations ranged from 1.77 to 41.23 mg/L (ratio max/min = 23.29) and 0.82 to 2.65 g/L (ratio max/min = 3.23), respectively. The highest lycopene and lipid contents were respectively 2.9 mg/g (ratio max/min = 29.48) and 12.01% (ratio max/min = 4.48). On media corresponding to run 7 and run 8, the engineered strain of *Y. lipolytica* produced consistent amount of lycopene (41.23 and 40.54 mg/L, respectively) with average biomass production of 14.23 and 16.53 g/L leading to lycopene content of 2.90 and 2.45 mg/g. Approximately equal quantities of lipids (1.55 and 1.53 g/L) were yielded on both media and corresponded to lipid contents of 10.90% and 9.23%.
The analysis of the effects of FBA-predicted factors on the biomass production showed that thiamine pyrophosphate, nicotinate, KH~2~PO~4~, ethanolamine, guanine, [l]{.smallcaps}-methionine, [l]{.smallcaps}-tryptophan, [l]{.smallcaps}-valine, [l]{.smallcaps}-asparagine, [d]{.smallcaps}-glucose, and [d]{.smallcaps}-fructose had positive effects on biomass production. Fructose was the most significant terms (effect above the Bonferroni Limit) followed by KH~2~PO~4~, [l]{.smallcaps}-valine, ethanolamine, nicotinate, [l]{.smallcaps}-asparagine, guanine, [l]{.smallcaps}-tryptophan, and glucose. The list of compounds composed of pyridoxine hydrochloride, succinate, 4-aminobutyric acid, Na~2~SO~3~, hypoxanthine, [l]{.smallcaps}-histidine, [l]{.smallcaps}-isoleucine, and [l]{.smallcaps}-leucine had negative effects on biomass production. The negative effects of 4-aminobutyric acid, [l]{.smallcaps}-histidine, and [l]{.smallcaps}-leucine were not significant. The effects of thiamine pyrophosphate and [l]{.smallcaps}-methionine were not significant for biomass production. The final equation of biomass production obtained after ANOVA analysis in terms of coded factors was:
Biomass = 1761.61 +1.00 × A − 1.16 × B + 1158.95 × C − 1.25 × D − 0.77 × E +2.70 × F − 1.70 × J + 1.57 × L − 1.18 × M + 1.51 × N − 0.71 × O + 0.63 × P + 1.41 × R + 1.75 × S + 1.52 × T − 1.85 × U − 0.66 × V + 1.14 × W + 3.28 × X.
Six factors were found to have significant positive effects on lycopene production. The most significant factors were [l]{.smallcaps}-tryptophan, [l]{.smallcaps}-isoleucine, ergosterol, and thiamine pyrophosphate (effect above the Bonferroni Limit) followed by ethanolamine and (NH~4~)~2~SO~4~ (effects above the *t*-value Limit). Although [l]{.smallcaps}-asparagine had a positive effect, this effect was not significant. All other compounds had an inhibitory effect on lycopene production. The final equation in terms of coded factors was:
Log~10~ (Lycopene) = 1.10 + 0.055 × A − 0.049 × B − 0.14 × D − 0.056 × E − 0.046 × F + 0.026 × G − 0.15 × J + 0.080 × K + 0.049 × L − 0.11 × M − 0.010 × N − 0.085 × P + 5.397e-004 × Q + 0.14 × R − 0.027 × S + 8.320e-003 × T + 0.095 × U − 0.14 × V − 0.053 × W − 0.077 × X.
[l]{.smallcaps}-isoleucine was found as the most significant factor having positive effect on lycopene content, followed by [l]{.smallcaps}-tryptophan, ergosterol, thiamine pyrophosphate, and [l]{.smallcaps}-histidine. Ethanolamine and (NH~4~)~2~SO~4~ had negligible positive effects on lycopene content. The large number of factors negatively influenced the lycopene content.
metabolites-05-00794-t004_Table 4
######
Matrix of Plackett-Burman design of FBA predicted medium components.
Std Run A:Thiamine pyrophosphate B:Pyridoxine, hydrocloride C:Succinate D:(R) Pantothenate E:4-Aminobutyric acid F:KH~2~PO~4~ G:(NH~4~)~2~SO~4~ H:Urea J:Sulfite Na~2~SO~3~ K:Ergosterol L:Ethanolamine M:Hypoxanthine N:Guanine O:[l]{.smallcaps}-histidine P:[l]{.smallcaps}-methionine Q:[l]{.smallcaps}-lysine R:[l]{.smallcaps}-tryptophan S:[l]{.smallcaps}-valine T:[l]{.smallcaps}-asparagine U:[l]{.smallcaps}-isoleucine V:[l]{.smallcaps}-leucine W:[d]{.smallcaps}-glucose X:[d]{.smallcaps}-fructose Lycopene Biomass Lycopene content Lipid Lipid content
----- ----- -------------------------- ---------------------------- ------------- -------------------- ----------------------- -------------- ------------------- -------- ---------------------- -------------- ---------------- ---------------- ----------- ----------------------------- ------------------------------ -------------------------- ------------------------------ -------------------------- ------------------------------ ------------------------------ --------------------------- --------------------------- ---------------------------- ---------- --------- ------------------ ------- ---------------
12 1 0.006 0.006 1 1 5 6 2 0.5 0.1 0.01 0.05 5 5 5 5 5 1 5 1 10 10 20 20 9.99 13.35 0.75 1.27 9.51
16 2 0.006 0.006 1 1 5 12 0.5 0.5 2 0.01 0.3 1 1 1 1 5 5 5 10 10 1 60 20 34.51 26.73 1.29 2.41 9.02
4 3 0.0006 0.0006 1 5 5 12 2 2 0.1 0.1 0.05 5 5 1 1 5 5 1 1 10 1 60 20 27.87 19.48 1.43 2.2 11.3
6 4 0.006 0.0006 1 1 1 12 2 2 2 0.1 0.05 5 1 5 5 1 1 5 10 1 1 60 20 9.85 27.4 0.36 1.57 5.73
20 5 0.006 0.0006 5 1 5 12 0.5 0.5 2 0.1 0.05 1 5 1 5 1 1 1 1 10 10 60 60 6.69 30.88 0.22 1.6 5.18
22 6 0.006 0.006 5 1 5 6 2 2 0.1 0.01 0.3 5 1 1 5 1 5 1 1 1 1 60 60 18.47 31.45 0.59 1.02 3.24
8 7 0.006 0.0006 5 1 1 6 0.5 2 2 0.1 0.3 5 1 5 1 5 5 1 1 10 10 20 20 41.23 14.23 2.9 1.55 10.9
24 8 0.0006 0.0006 1 1 1 6 0.5 0.5 0.1 0.01 0.05 1 1 1 1 1 1 1 1 1 1 20 20 40.54 16.53 2.45 1.53 9.23
18 9 0.006 0.0006 5 5 1 6 2 2 0.1 0.01 0.3 1 5 1 1 1 1 5 10 10 10 60 20 19.95 29.05 0.69 1.63 5.61
13 10 0.0006 0.006 5 1 1 12 0.5 2 0.1 0.01 0.05 1 5 5 5 5 5 1 10 1 10 60 20 12.41 30.58 0.41 0.82 2.68
3 11 0.0006 0.0006 5 5 5 12 2 0.5 2 0.01 0.3 5 1 1 5 5 1 1 10 1 10 20 20 2.07 21.05 0.1 1.45 6.86
5 12 0.0006 0.0006 1 1 5 12 2 2 2 0.01 0.3 1 5 5 1 1 5 5 1 1 10 20 60 9.8 33.23 0.3 1.4 4.21
7 13 0.0006 0.006 1 1 1 6 2 2 2 0.1 0.3 1 5 1 5 5 1 1 10 10 1 20 60 23.58 23.65 1 1.62 6.85
2 14 0.0006 0.006 5 5 5 12 0.5 2 0.1 0.1 0.3 1 1 5 5 1 1 5 1 10 1 20 20 16.44 21.33 0.77 0.88 4.13
19 15 0.0006 0.006 1 5 5 6 0.5 2 2 0.01 0.05 5 1 5 1 1 1 1 10 10 10 60 60 1.77 9.08 0.2 1.09 12.01
9 16 0.0006 0.006 1 5 1 6 0.5 0.5 2 0.1 0.3 5 5 1 5 1 5 5 1 1 10 60 20 4.09 21.3 0.19 1.56 7.3
15 17 0.006 0.0006 1 5 5 6 0.5 2 0.1 0.1 0.05 1 1 1 5 5 5 5 10 1 10 20 60 12.36 29.13 0.42 1.44 4.93
14 18 0.0006 0.0006 5 5 1 6 2 0.5 2 0.01 0.05 1 1 5 5 5 5 5 1 10 1 60 60 11.14 24.75 0.45 1.56 6.3
10 19 0.0006 0.0006 5 1 5 6 0.5 0.5 0.1 0.1 0.3 5 5 5 1 5 1 5 10 1 1 60 60 16.32 35.5 0.46 1.89 5.32
1 20 0.006 0.006 5 5 5 6 2 0.5 2 0.1 0.05 1 5 5 1 1 5 1 10 1 1 20 20 24.84 20.73 1.2 2 9.65
21 21 0.006 0.006 1 5 1 12 2 0.5 0.1 0.1 0.3 1 1 5 1 5 1 1 1 1 10 60 60 9.99 28.65 0.35 2.65 9.23
17 22 0.0006 0.006 5 1 1 12 2 0.5 0.1 0.1 0.05 5 1 1 1 1 5 5 10 10 10 20 60 24.79 32.63 0.76 2.22 6.8
11 23 0.006 0.0006 1 5 1 12 0.5 0.5 0.1 0.01 0.3 5 5 5 5 1 5 1 10 10 1 20 60 22.7 33.83 0.67 1.19 3.52
23 24 0.006 0.006 5 5 1 12 0.5 2 2 0.01 0.05 5 5 1 1 5 1 5 1 1 1 20 60 3.07 27.73 0.11 1.62 5.83
The final equation for lycopene content in terms of coded factors was:
Log~10~ (Lycopene content) = −42.56 + 0.033 × A − 0.025 × B − 28.22 × C − 0.12 × D − 0.035 × E − 0.10 × F + 0.012 × G − 0.12 × J + 0.067 × K + 0.015 × L − 0.073 × M − 0.041 × N + 0.020 × O − 0.10 × P + 0.10 × R − 0.065 × S − 0.017 × T + 0.14 × U − 0.12 × V − 0.072 × W − 0.13 × X.
For lipid production, ergosterol, (NH~4~)~2~SO~4~, and [l]{.smallcaps}-lysine had significant positive effects. The effects of KH~2~PO~4~, glucose, and thiamine pyrophosphate were also moderately significantly positive. [l]{.smallcaps}-methionine, urea, [l]{.smallcaps}-histidine, nicotinate, and hypoxanthine significantly inhibited lipid production. The effects of other components were not significant. The final equation for lycopene content in terms of coded factors was:
Lipid = −76.10 + 0.072 × A − 51.85 × C − 0.036 × E + 0.077 × F + 0.13 × G − 0.19 × H + 0.029 × J + 0.17 × K − 0.038 × M − 0.023 × N − 0.10 × O − 0.26 × P + 0.12 × Q + 0.024 × R + 0.030 × S + 0.021 × T − 0.034 × V + 0.077 × W.
Lipid content was positively affected by [l]{.smallcaps}-isoleucine, Na~2~SO~3~, [l]{.smallcaps}-lysine, hypoxanthine, ergosterol, succinate, pyridoxine hydrochloride, 4-aminobutyric acid, (NH~4~)~2~SO~4~, and [l]{.smallcaps}-leucine. [l]{.smallcaps}-histidine had no significant positive effect. The rest of predicted components strongly repressed lipid accumulation.
Based on the above observations and multiple post-optimization experiments, the optimization process gave MP medium constituted of 1 g/L asparagine, 6 g/L KH~2~PO~4~, 0.5 g/L (NH~4~)~2~SO~4~, 0.1 g/L ergosterol, 0.3 g/L ethanolamine, 5 g/L lysine, 5 g/L tryptophan, 10 g/L isoleucine, 20 g/L fructose, and 10 g/L glucose.
### 2.2.3. Analysis of the Correlation between Lipid Content and Lycopene Content {#sec2dot2dot3-metabolites-05-00794}
The correlation analysis was carried out using the Pearson correlation analysis method with a two-tailed test of significance. The correlation analysis was applied to the data obtained from the Plackett-Burman design responses obtained with the FBA-predicted factors. We obtained a Pearson correlation of 0.49 with a significance of 0.01. The correlation between both variable was significant at the 0.05 level. Furthermore, we found commonness between both variables when positive factors were taken into account. Specifically, lycopene content and lipid content were both significantly stimulated by [l]{.smallcaps}-isoleucine, ergosterol and (NH~4~)~2~SO~4~. This suggested the positive correlation between lipid accumulation and lycopene biosynthesis. This relationship between both pathways may be influenced by the composition of the culture medium since we found diverse discrete distribution of the concentration of these compounds in the different culture media. In addition, high lipid content did not necessarily imply high lycopene content.
### 2.2.4. Analysis of the Effect of FBA Predicted Factors on the Expression of Genes of the Terpenoids Backbone {#sec2dot2dot4-metabolites-05-00794}
Following the first Plackett-Burman design (PBD), we conducted another PBD ([Supplementary File 4](#metabolites-05-00794-s001){ref-type="supplementary-material"}) in order to adjust the culture medium components to optimized conditions and determine the effect of above selected positive factors on the terpenoids backbone genes through the determination of their expression levels. The PBD design responses demonstrated that biomass production was significantly improved by the effects of lysine, fructose, [l]{.smallcaps}-tryptophan, (NH~4~)~2~SO~4~, KH~2~PO~4~, thiamine, and [l]{.smallcaps}-isoleucine in this decreasing order. The rest of the components including glucose, [l]{.smallcaps}-asparagine, and ethanolamine had moderate negative effects on biomass production. The highest biomass production of 33.58 g/L was obtained with run 10. The elimination of factors with negative effects in the first PBD driven on the FBA predicted components did not significantly affect biomass production, showing that their elimination was not due to errors. Similarly, KH~2~PO~4~, fructose, ergosterol, (NH~4~)~2~SO~4~, and [l]{.smallcaps}-tryptophan promoted lycopene accumulation. A lycopene production of 4.35 mg/g DCW (76.62 mg/L) was achieved under the coordinated effect of these compounds in shake flasks. Only KH~2~PO~4~ had positive effect on lycopene content.
This second tour PBD suggested that the selected components were further optimizable for biomass and lycopene concentration but did not really impact on lycopene content. Furthermore, some of components with positive effects in the first round of screening were found inhibiting lycopene production. This could be explained by the fact that the scale of choice of these components was reduced.
In order to get insights into the effect of selected factors on genes of the terpenoids backbone, we realized quantitative RT-PCR experiments to explore expression levels of these genes. No significant effect was found for *YALI0B16126g* which is annotated as protein farnesyltransferase/geranylgeranyltransferase type-1 subunit alpha. On the contrary, significant effects were recorded for *YALI0C18755g*, the gene encoding for (2E,6E)-farnesyl pyrophosphate (FPP) specific hexaprenyl-diphosphate synthase. This gene was significantly stimulated by the effects of [l]{.smallcaps}-tryptophan, [l]{.smallcaps}-lysine, [l]{.smallcaps}-isoleucine, [l]{.smallcaps}-asparagine, KH~2~PO~4~, and fructose. The high number of positive factorial effects corroborated with the fact that FPP was set as the target metabolite in the FBA simulation. Only ergosterol, thiamine, and glucose had inhibitory effects on this gene. In addition, the ditrans, polycis-polyprenyl diphosphate synthase (also specific to (2E,6E)-farnesyl diphosphate) gene *YALI0C18799g* was activated by [l]{.smallcaps}-tryptophan, ergosterol, [l]{.smallcaps}-asparagine, and to some extent KH~2~PO~4~ while other components displayed negative effects. *YALI0D17556g*, another gene responsible for (2E,6E)-FPP specific ditrans, polycis-polyprenyl diphosphate synthase, was significantly stimulated by ethanolamine but repressed by [l]{.smallcaps}-tryptophan. The expression of the gene in charge of protein farnesyltransferase subunit beta, *YALI0D14762g*, was similarly triggered by [l]{.smallcaps}-lysine, [l]{.smallcaps}-asparagine, fructose, KH2PO4, and [l]{.smallcaps}-tryptophan and to a minor extent by glucose. Only [l]{.smallcaps}-tryptophan had a positive effect on *YALI0D17050g* (geranylgeranyl diphosphate synthase). The rate-limiting gene of the mevalonate pathway governing the expression of hydroxymethylglutaryl-CoA reductase (HMGCR), *YALI0E04807g*, was significantly activated by factors including [l]{.smallcaps}-lysine, [l]{.smallcaps}-asparagine, [l]{.smallcaps}-tryptophan, KH~2~PO~4~, and fructose but significantly inhibited by ergosterol and thiamine. The activation of this gene was necessary for converting HMG-CoA into mevalonic acid and subsequent metabolites of the terpenoids biosynthesis backbone. *YALI0E05753g* ((2E,6E)-farnesyl diphosphate synthase) was significantly stimulated by [l]{.smallcaps}-tryptophan, KH~2~PO~4~ and to a minor extent by L-asparagine. However, the lycopene biosynthesis genes introduced into the engineered strains, although highly expressed, were activated by numerous positive factors. However, the number of positive effects was not as significant as expected. This could be explained by the fact that the FBA was targeted towards FPP synthesis. Specifically, the expression of the *crtE*, *crtB*, and *crtI* genes were all promoted by ethanolamine (significant effect) and [l]{.smallcaps}-lysine, [l]{.smallcaps}-isoleucine, glucose, (NH~4~)~2~SO~4~, ergosterol, and glucose to a trivial degree.
Overall, the results showed that FBA-predicted and PBD screened factors differentially affected genes of the terpenoids backbone, *zwf* and *crt* genes. [Figure 1](#metabolites-05-00794-f001){ref-type="fig"} is the heat map of the hierarchical clustering of genes relative expression levels obtained from the PBD experiments. We found that genes of the terpenoids backbone ([Supplementary Figure S1](#metabolites-05-00794-s001){ref-type="supplementary-material"}) were downregulated after seven days of cultivation compared to the housekeeping gene *ACT1* while all heterologous genes were upregulated. The upregulation of heterologous genes implied that the carbon metabolism was efficiently directed to FPP biosynthesis and subsequently permitted lycopene production. Nevertheless, different amounts of biomass and lycopene yielded on different runs of culture media could be explained by divergences in expression patterns as depicted in [Figure 1](#metabolites-05-00794-f001){ref-type="fig"}.
{#metabolites-05-00794-f001}
Indeed, though some heterologous genes were highly expressed in certain media, the level of produced lycopene did not match with expression levels. We found that some media components were inhibiting genes of the terpenoids backbone at different levels but the inhibition did not necessarily imply low production of lycopene. Each gene of the terpenoids backbone was activated by specific selected factors whose coordinated actions allowed high lycopene production.
2.3. Fed-Batch Fermentation of Y. lipolytica for Lycopene Production on Designed Media {#sec2dot3-metabolites-05-00794}
--------------------------------------------------------------------------------------
Designed media were initially used for lycopene production in a 1.5 L fermenter with a working volume of 1 L in batch. The fed-batch operation started at 24 h and consisted in the supplementation of a feeding solution containing 200 g/L glucose and 200 g/L of fructose. The feeding (50 mL) was executed every 24 h. The pH was initially controlled at 5.5 and then controlled at 3 after 48 h when the color began to appear. The results of biomass and lycopene production on different media over the fermentation course are depicted in [Figure 2](#metabolites-05-00794-f002){ref-type="fig"}.
{#metabolites-05-00794-f002}
After 10 days of fermentation, we found a maximum biomass production of 40.2 g/L with a lycopene concentration of 126 mg/L from the medium designed without taking into account the FBA predictions (PM) ([Figure 2](#metabolites-05-00794-f002){ref-type="fig"}a). Lycopene production increased progressively to reach a maximum value of 126 mg/L. In the medium obtained by combination of FBA and Plackett-Burman design (MP), a biomass of 61.08 g/L and a lycopene concentration of 242 mg/L were obtained after 10 days of fermentation ([Figure 2](#metabolites-05-00794-f002){ref-type="fig"}b). Lycopene production in the designed using both methods (MP) was about two-fold that obtained in the PM medium. The maximum lycopene content of 4.02 mg/g DCW was obtained on this medium.
3. Discussion {#sec3-metabolites-05-00794}
=============
Relative to other yeasts, *Y. lipolytica*, as an oleaginous yeast, is able to accumulate significant quantities of lipid bodies under certain growth conditions. This property provides a reliable storehouse for carotenoids biosynthesis and, consequently, the heterologous production of carotenoids using *Y. lipolytica* may constitute a promising asset for large-scale operations. The heterologous synthesis of lycopene in *Y. lipolytica* requires the introduction of the biosynthetic genes (*crtE*, *crtB* and *crtI*) even if the expression of *crtE* is not necessary in various heterologous hosts including *Y. lipolytica*, and bioengineering approaches for integrating these genes in *Y. lipolytica* have been described previously \[[@B24-metabolites-05-00794]\]. *CrtE* is a geranylgeranyl diphosphate synthase that catalyzes the conversion of FPP and IPP to GGPP and *CrtB* is a phytoene synthase that can condense two molecules of the C~20~ precursor, GGPP, to yield the first C~40~ hydrocarbon, the phytoene. This is followed by a series of sequential desaturations of phytoene to produce ζ-carotene, neurosporene, and, finally, lycopene \[[@B25-metabolites-05-00794]\]. This process is catalyzed by the phytoene desaturase (*CrtI*). The most advanced lycopene production using *Y. lipolytica* is the recent publication of Matthäus, Ketelhot, Gatter, and Barth \[[@B13-metabolites-05-00794]\] in which the codon-optimized genes *crtB* and *crtI* of *Pantoea ananatis* were expressed in *Y. lipolytica* under the control of the TEF1 promoter of *Y. lipolytica*. Moreover, these authors undertook the modifications of native metabolic pathways in *Y. lipolytica* via the overexpression of bottleneck genes in the isoprenoid pathway (GGS1 and HMG1) and the knock-out of *POX1* to *POX6* as well as *GUT2* genes and successfully enhanced lycopene production (16 mg/g DCW). In a previous study, taking into account the fact that the use of expression vectors pINA1269 and pINA1312, carotenoid genes *crtE*, *crtB*, and *crtI* can be successively integrated into the yeast chromosome with improved strain stability, we synchronically introduced combinations of these plasmids carrying lycopene biosynthesis genes and spawned lycopene producing strains. Further characterization of these engineered strains showed discrepancies in terms of lycopene and biomass production among engineered strains and suggested the impact of engineering tactics on lycopene biosynthesis in engineered strains.
In the present study, we aimed to establish an effective fermentation platform for lycopene production from the most robust engineered strain (Po1f-1312E + 1269IB) using statistical and GSMN modeling tools for screening chemical compounds and designing culture media. Efficient media were employed for fed-batch cultivation. The improvement of cultivation conditions (media and scale-up) led to lycopene production of 242 mg/L of lycopene using the medium designed based on the variables screened from the FBA-predicted factors. This concentration of lycopene was approximately the double of that obtained in the medium designed based on the literature. The above results demonstrated the usefulness of FBA and modelling tools for improved production of lycopene in consistency with previous investigations showing that FBA simulations can be efficiently applied for experimental validation and improvement of the production of objectives production or biological processes \[[@B26-metabolites-05-00794],[@B27-metabolites-05-00794],[@B28-metabolites-05-00794]\]. The lycopene content obtained in shake flasks was three-fold that achieved by Matthäus, Ketelhot, Gatter, and Barth \[[@B13-metabolites-05-00794]\] but the lycopene content in fed-batch cultivation mode was lower compared to their results. This could be explained by the fact that these authors carried out supplementary genetic modifications in their experiments or because of the source of lycopene biosynthesis genes. As a matter of fact, the lycopene production obtained from the present study was higher than the concentration these authors obtained with their basic strain (H222 Δ BI). In view of the above, we believe that the FBA-driven designed medium will contribute largely in the improvement of lycopene production. This could be applicable to a wide range of engineered strains of *Y. lipolytica* and other yeast species for lycopene and other terpenoids molecules. Additionally, our study gave insights into the comprehension of the effects of some external factors on genes of the terpenoids pathway. Correct monitoring of these factors for media designing, coupled with adequate metabolic engineering tactics, will contribute to the fundamental research and the efficient production of lycopene even at the industrial level.
4. Material and Methods {#sec4-metabolites-05-00794}
=======================
4.1. Description of the Engineered Lycopene Producing Y. Lipolytica Strain {#sec4dot1-metabolites-05-00794}
--------------------------------------------------------------------------
Prior to cultivation improvement experiments, we first proceeded to the bioengineering of *Y. lipolytica* in order to obtain a dependable lycopene producing strain. The bioengineering work has been published in a local Chinese journal. The strain designated as Po1f-1312E + 1269IB, representing the recombinant strain obtained from the introduction of plasmid pINA1312 (carrying gene *crtE*) and pINA1269 (carrying genes *crtI* and *crtB*) into the host strain *Y. lipolytica* Po1f, was used in this study given that it displayed noteworthy growth and lycopene production behavior.
4.2. Modeling Platform {#sec4dot2-metabolites-05-00794}
----------------------
Flux balance analysis (FBA) is the paramount method for estimating flux distributions and assumes that organisms utilize substrates adequately to maximize a fixed objective of model (biomass or a particular reaction of production). The FBA method can be used to reproduce environmental conditions necessary for achieving the maximization of the objective function of the model and is an integrated element of the COBRA 2.0 Toolbox in Matlab. The FBA was carried out using Matlab R2011a (Mathworks, Natick, MA, USA) and the COBRA 2.0 toolbox. We used an *in silico Y. lipolytica* terpenoids biosynthesis genome-scale metabolic model (GSM) yli v1.7 updated from our previous publication \[[@B29-metabolites-05-00794]\]. The updated GSM yli v1.7 was composed of 718 genes, 1293 reactions, and 986 metabolites. The solvers used to optimize problems included "glpk" (version 4.35) and Tomlab/CPLEX (version 7.9). All the calculations were implemented on a personal computer with 3.40 GHz Intel (R) Core (TM) i7-2600k and 16.0 GB RAM. The implementation consisted in the computation of flux distributions with farnesyl pyrophosphate (FPP), a key terpenoids biosynthesis precursor, as the objective metabolite. Medium components were predicted by screening exchange reactions with negative fluxes.
4.3. Plackett-Burman Design and Shake Flasks Cultivation {#sec4dot3-metabolites-05-00794}
--------------------------------------------------------
To identify the vital factors that affect biomass and lycopene production in the engineered strain and make breakthrough improvements, a saturated screening design based on the Plackett-Burman structures incorporated into Design expert software (version 8) was adopted. The total number of trials to be implemented according to Plackett-Burman was (*n*+1) runs, wherein *n* represents the number of modules to be screened. Each component was assigned two levels of concentrations (high concentration and low concentration). Firstly, a set of 23 factors selected in light of the preliminary experiments and literature review (data not shown), were combined in 24 trials for the designing of FBA-independent cultivation media. Following this, the FBA-driven predicted factors (*n* = 23) were used for conducting a Plackett-Burman design of 24 runs. Numerous post-optimization experiments were equally carried out on the basis of Plackett-Burman design.
The cultivation conditions were as follows. Primarily, the metabolically engineered *Y. lipolytica* harboring carotenogenic plasmids were inoculated into 50 mL of S2 medium for 24 h at 30 °C with a shaking speed of 200 rpm. These pre-cultures were then transferred to a 250 mL shake flask containing 50 mL of each designed medium and grown for another seven days under the same fermentation temperature and agitation speed.
4.4. Bioreactor Scale-up {#sec4dot4-metabolites-05-00794}
------------------------
The optimized designed media were directly used for aerobic fermentation of the transgenic *Y. lipolytica* strain Po1f-1312E + 1269IB for lycopene production. The fermentation process was run in fed-batch mode in a 1.5 L stirred-tank fermenter (Baoxing Co., Shanghai, China) with a working volume of 1 L at 30 °C. The aeration rate was fixed at 1 vvm (volume air per volume per minute) and the agitation rate was set to automatically respond to the dissolved oxygen (DO) concentration so as to maintain it at 50%. Sterile air filters with 0.2 µm pores were used for air transfer into bioreactor. The DO concentration in the culture broth was measured using a pO~2~ electrode. Silicone was periodically added as an antifoam agent. The fed-batch operation started at 24 h and consisted in the supplementation of a feeding solution containing 200 g/L glucose and 200 g/L of fructose. The feeding (50 mL) was executed every 24 h. The pH was initially controlled at 5.5 and then controlled at 3 after 48 h following the appearance of color.
4.5. Determination of Glucose Concentration, Dry Cell Weight, and Lipids {#sec4dot5-metabolites-05-00794}
------------------------------------------------------------------------
After cultivation, 5 mL of cell broth was harvested, centrifuged at 12,000 rpm for 5 min, washed twice with distilled water and dried at 105 °C for 48 h. The dry cell weight (DCW) was determined by gravimetrically measuring the weight of the dry cell pellets. Glucose measurement was monitored by a spectrophotometric procedure by means of a Glucose Reagent Kit (Kexin Biotech Co., Ltd., Shanghai, China) following the vendor's guidelines. Lipid extraction protocol was as described in our previous publication \[[@B30-metabolites-05-00794]\].
4.6. Lycopene Extraction and HPLC Analysis {#sec4dot6-metabolites-05-00794}
------------------------------------------
Following the cultivation end time, precise volumes of homogenous culture broth were harvested, centrifuged at 12,000 rpm for 10 min at 4 °C and washed twice with deionized water. The supernatant was discarded and the pellet was used for lycopene extraction. Prior to lycopene extraction, pellets were dissolved in 500 μL of dimethyl sulfoxide (DMSO), pre-warmed at 55 °C for 30 min, shook strongly for 30 s, and then maintained for an extra 30 min without shaking. After that, 500 μL of acetone was added to the DMSO extract and homogenized by vortexing for 30 s, followed by incubation at 55 °C for 15 min with intermittent shaking. The mixture was subsequently centrifuged at 12,000 rpm for 10 min, and the colored mixed supernatants were transferred into a new tube. The extraction step was repeated until all visible pigments in the residual cell pellet and supernatant were extracted. The obtained colored supernatants were pooled together and used for lycopene quantification via high-performance liquid chromatography (HPLC) analysis. All operations occurred on ice under dim light to prevent photodegradation, isomerizations, and structural changes of the carotenoids.
The lycopene concentration of each extract was quantified by HPLC analysis which was performed on a Shimadzu LC-20A HPLC instrument equipped with a LC solution software program, LC-20AD pump, and a detector with a UV-Vis lamp. Specifically, it was carried out by injecting 10 μL of the crude carotenoid extract into a Zorbax SB-Aq C18-reverse-phase column (4.6 mm × 250 mm, 5 μm; Agilent Technologies, Palo Alto, CA, USA). The extract was eluted under isocratic condition with a mobile phase containing 80% acetonitrile, 15% methanol and 5% isopropanol at a flow rate of 1 mL/min at 30 °C. Quantitative analysis was accomplished using a calibration curve obtained with a lycopene standard and final lycopene concentrations were obtained by normalization to the total initial volumes used during extraction.
4.7. Quantitative Reverse Transcription-PCR (qRT-PCR) Studies {#sec4dot7-metabolites-05-00794}
-------------------------------------------------------------
The cells were pelleted and total RNA was extracted as previously described \[[@B31-metabolites-05-00794]\]. To keep comparable content of starting materials, the total RNA was prudently determined with a DU 800 spectrophotometer (Beckman-Coulter, Fullerton, CA, USA). The chromosomal DNA was degraded by treatment with DNase I according to the manufacturer's instructions. Next, 1000 ng of RNA from each sample was used for the reverse transcription with ReverTra Ace qPCR RT Master Mix instrument (Toyobo Co., Ltd., Osaka, Japan). Subsequently, 1 μL sample from each reaction mixture was used to perform quantitative PCRs (qPCRs) (in triplicate) with SYBR Green Realtime PCR Master Mix (Toyobo) using specific primers, with a non-template control. The primers used are presented in [Supplementary File 5](#metabolites-05-00794-s001){ref-type="supplementary-material"}. The reactions were performed in a CFX Fast real-time PCR system (Bio-Rad Laboratories, Inc., Hercules, CA, USA).
To prevent the variation of starting materials amounts, *ACT1* was utilized as a housekeeping gene. The results were expressed as fractions of gene expression between the target gene and the housekeeping gene, *ACT1* \[[@B32-metabolites-05-00794]\].
5. Conclusions {#sec5-metabolites-05-00794}
==============
The FBA and Plackett--Burman screening investigational design empowered the bringing about of significant variables for lycopene production from *Y. lipolytica*. The findings of the present study could have implications for improved production of lycopene using *Y. lipolytica* as a fermentation platform and promote terpenoids production at the industrial scale. [Supplementary material](#metabolites-05-00794-s001){ref-type="supplementary-material"} in relation to Pareto charts of Plackett-Burman design and the Plackett-Burman design regarding terpenoids backbone genes expression levels is available on the journal website.
This study was financially supported by National Basic Research Program of China (973 Program) (2012CB721101) and National Natural Science Foundation of China (21576089).
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Komi Nambou, Qiang Hua, Xingxing Jian, Xinkai Zhang, Liujing Wei conceived and designed the experiments; Komi Nambou, Xingxing Jian, Xinkai Zhang. performed the simulation and experiments, Komi Nambou, Xinkai Zhang, Qiang Hua. analyzed the data; Jiajia Lou, Catherine Madzak contributed reagents and materials; Komi Nambou wrote the manuscript under supervision of Qiang Hua.
The authors declare no conflict of interest.
[^1]: These authors contributed equally to this work.
[^2]: Present address: INRA, UMR782 GMPA, AgroParisTech Campus, CBAI, F-78850 Thiverval-Grignon, France
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- Reinventing Indonesia by Ginandjar Kartasasmita and Joseph J. Stern
Reinventing Indonesia charts the development of Indonesia’s political economy and path to democracy since the country achieved independence in 1945. Since the downfall of Suharto’s authoritarian regime in May 1998, Indonesia has been regarded as one of the most successful examples of democratization in the world. This co-authored book offers insightful views on the history of Indonesia’s political economy, some of the key challenges it faced and how the government dealt with them.
The authors, Ginandjar Kartasasmita and Joseph J. Stern, begin their book by briefly charting Indonesia’s sixty-year journey from independence to democracy. They summarize the country’s regime changes from President Sukarno to President B.J. Habibie. They also explain how the 1997–98 Asian Financial Crisis buckled the economy and how the government eventually managed to overcome the crisis and kick start economic growth. Kartasasmita, who served as the Coordinating Minister of Economy, Finance and Industry (1998–99) and had previously been the head of the National Development Planning Agency (1993–98), provides valuable insights into that period of crisis and reform. Stern, the Project Coordinator for the Harvard Institute for International Development, has had extensive professional experience in assisting Indonesian decision-makers. The authors’ expertise and familiarity with the country’s major political and economic issues accords them in a unique position to analyze Indonesia’s democratization and economic development.
The organization of this book allows readers to easily understand the changes to Indonesia’s political economy in chronological order. In each chapter, Kartasasmita and Stern describe in detail the country’s political changes, the policies adopted by governments and the impact those policies had on Indonesia’s economic and political development. Taking note of how Suharto maintained power for thirty-two years, Kartasasmita and Stern explain that the New Order regime relied on three political forces — the military, the Golkar party and the civil service — to retain power, and initiated three major economic reforms — the balanced budget rule, the removal of all restrictions on capital inflows and outflows, and the unification of multiple exchange rates to help maintain the real value of the currency. The Suharto regime also undertook economic reforms that [End Page 226] laid the foundation for the country’s financial and banking system, tax system, trade and investment.
With regard to the sources of its political legitimacy, the authors argue that the New Order was successful in maintaining political stability, economic growth and equity for over three decades. Here, the military’s dual-function played a crucial role in ensuring national stability. However, the 1997–98 financial crisis and subsequent civil unrest eventually led to the collapse of the New Order regime in 1998. This book provides a detailed analysis of the three key factors that plunged the largest Southeast Asian country into an economic crisis; namely the vulnerability of Indonesia’s financial institutions, the regime’s slow response towards recommendations made by the International Monetary Fund and the World Bank, as well as the lack of well-functioning institutions including an impartial judicial system to effectively deal with conflicts that arose.
Explaining the country’s democratic transition and economic recovery, the authors focus on political-economic developments during the Habibie administration. On taking over from Suharto, Habibie undertook five key economic reforms: restoring macro-economic stability, restructuring the banking system, eliminating corporate debts, stimulating market demand and reducing the impact of the economic crisis on the poor. By the end of his administration, Indonesia was well on its way to recovery from the financial crisis. In addition to restoring the economic prospects of the country, President Habibie also laid the foundations for a democratic political system by separating the powers of the legislative, executive and judicial branches, as well as promoting freedom of expression, decentralization and multi-party politics. Unlike conventional democratic transitions in other countries, the authors argue that the authoritarian regime played a decisive role in bringing democracy to Indonesia.
Referring to Huntington’s democratization theory, Kartasasmita and Stern analyze key political events in... | https://muse.jhu.edu/article/657991/pdf |
Criminal Defense F.A.Q.
Answers from an Orange County Criminal Defense Attorney
Can a person be punished for attempting to commit a crime?
Many jurisdictions have either a general "attempt" crime or individual statutes that make attempted murder or attempted robbery or the like a crime. The purpose of these statutes is to punish an individual who has shown himself or herself to be dangerously inclined to commit a crime without waiting until the criminal act is actually completed. In order to convict a person for an attempted crime, the government must prove beyond a reasonable doubt that the person had the intent to do an act or bring about certain consequences that would amount to a crime, and that he or she took some step beyond mere preparation towards that goal.
What is a "grand jury"?
A grand jury is a group of people called together by the prosecutor to gather information about suspected criminal activity by listening to testimony from witnesses and examining documents and other evidence. The prosecutor acts as legal advisor to the grand jury and directs the flow of witnesses and evidence. At the end of the proceeding, the grand jury decides whether there is enough evidence to put the defendant on trial for the crime.
Why do I need a lawyer if I intend to plead guilty?
Even if you intend to plead guilty to the crime you are charged with, representing yourself in court is rarely a good idea. An experienced criminal defense lawyer can try to negotiate a lighter sentence or lesser charge on your behalf. People who attempt to act as their own lawyer typically end up with harsher punishments than those who have good legal representation.
Do I need a lawyer to represent me even if I am innocent?
Every criminal defendant needs a criminal defense lawyer. Innocent defendants are perhaps in even greater need of zealous representation throughout the criminal process to ensure that their rights are protected and that the truth prevails. Even innocent people end up in jail, so the best way to prevent that miscarriage of justice is to employ the services of a seasoned veteran of criminal defense law.
Who is the "prosecutor"?
Prosecution refers to the government's role in the criminal justice system. When criminal activity is suspected, it is up to the government to investigate, arrest, charge and bring the alleged offender to trial. Prosecutors are the lawyers who work for the government and who are responsible for presenting the government's case against a defendant. Prosecutors may be called county attorneys, city attorneys, or district attorneys.
How does the prosecutor decide which cases to pursue?/h3>
The first thing the prosecutor looks for is a legally sound case, or one without any obvious defects that will get it thrown out of court, such as violations of the defendant's constitutional rights or destruction of evidence crucial to the defense. The prosecutor next decides if there is enough evidence, with regard to both the quantity and the quality thereof, to make conviction probable. Finally, the prosecutor decides if prosecuting the case fits in with the office's policy objectives, or whether a more informal disposition such as pre-trial diversion may be in order.
What is the difference between parole and probation?
Parole and probation are employed in the punishment phase of the criminal justice process. Parole comes into play after a person has been imprisoned and is released subject to supervision by an officer of the court. Probation, by contrast, refers to a criminal sentence separate and distinct from incarceration. Probation is the most frequent sentence imposed for less serious or first offenses and typically involves releasing the convicted offender into the community subject to a list of terms and conditions.
What is "restitution"?
Restitution involves ordering the defendant to pay the victim a sum of money designed to compensate the victim for the monetary costs of the crime, such as medical bills, property damage, and lost wages. By federal law, under the Mandatory Victims' Restitution Act of 1996, restitution is required when a violent crime has been committed and for certain other, limited, offenses. Many state and federal laws also require a criminal offender to make restitution to the victim, and the court will order restitution under those laws when the offender is sentenced.
What is "white collar crime"?
White collar crime is a term originally used to describe criminal activity by members of the upper classes in connection with their professions. Today, the most common definition of white collar crime no longer focuses on the social status of the offender but rather on the type of conduct involved: illegal acts using deceit and concealment to obtain money, property, or services, or to secure a business or professional advantage. White collar crimes are usually less violent than other crimes, but their effects can be just as devastating, such as in the recent Enron case.
Are children charged with committing crimes prosecuted in the same manner as adults?
Children are subject to a separate judicial system called the juvenile court system. Generally, the focus of the juvenile court system is more on rehabilitation than on punishment. In some cases, however, older juveniles who commit more serious crimes will be charged as adults and tried in the regular criminal courts. In such cases, their sentence, too, will be more in accord with adult punishment, whereas in juvenile court any incarceration is usually in a more rehabilitative setting and generally ends when the juvenile attains the age of majority. | http://ccgomezlaw.com/criminal-defense-frequently-asked-questions.html |
"In diversity there is beauty and there is strength."
-Maya Angelou
A few weeks ago, I had the privilege of photographing the lovely Susan. I grew up in a household full of love for all kinds of music and so when I found out she loved The Beatles, I almost high-fived her for being so cool. Her friendly demeanor and smile was nothing short of awesome to work with and I am honored to be able to share with you not only these photos from her recent photo shoot with me but also a little bit more about the person behind that friendly smile.
A special thanks to stylist Julianne Chai of Prettyologie for Susan's hair & make up!
Happy Tuesday!
Give us a little snapshot of who you are...
I am a mom of two wonderful individuals, and the wife of a handsome Swede. I like baths, England, chocolate cake, databases, champagne, philosophical conversations, before and afters, wackiness, sleeping in, rainy weather, flying business class, The Beatles, Apple, Cary Grant, a clean house, coffee, giving compliments, and my German shepherd, Duchess. I don't like hot tuna or grape leaves, the words "yummy" or "tasty", debt, figuring out what to cook for dinner, busywork, Bruno Mars, and self-centered, negative, or phony people.
Who or what 3 things have helped shape you to be the woman you are today?
1. Being a part of a hilarious, kind, non-hysteria-prone family with incredible parents. Growing up, our house was full of friends and family with lots of laughs, music, and the sound of rolling dice!
2. The Beatles! Love for the Beatles launched my interest in England, travel, and learning about all different cultures.
3. College. I loved learning new ideas and ways of looking at things outside of the pre-fabricated education that came before then. I am still delighted when I learn something totally new, especially discovering a new way of looking at something I'd thought I knew everything about.
Don't worry, everything will fall into place. My dad actually said that to me around that age, but if I could have really understood it and believed it then, I could have done a lot less fretting.
What leadership qualities do you most admire?
Patience, humor, compassion, and a clear vision that includes the big and small picture.
What are you most passionate about?
My kids and family. I used to feel passionate about pursuing and obtaining "happiness" but as I've gotten older I've shifted that focus to "satisfaction." Not in the Mick Jagger way, but in feeling that I'm accomplishing something worthwhile. That could be making someone else a little bit happier or better off, making progress on a project at work, or seeing my kids turn into kind, funny, wise people and knowing that I had a part in that.
What is your personal motto or mission statement?
"This too shall pass." Such a profound and powerful thing to remember during bad and good times.
If you could share a message about beauty, self-esteem, or self-worth to other women (whether older or younger), what would that be?
Each time you blame someone else for making you unhappy, you give away y our own power. Take responsibility for your own happiness and fulfillment in life. Don't waste time comparing yourself to others, instead compare yourself to the person you were yesterday. | https://www.heartbox-photography.com/blog/artbox-photographyblog.com/2013/12/susan-2013-bay-area-glamour-photo.html |
In the stock market, the questions that flash through every trader’s mind when the S&P 500 has a bearish week go something like this:
“What if this is it?”
“What if this is the end of the bullish rally?”
“What if the bears are waking up and taking control?”
Those questions flashed through the minds of many traders at the end of last week when the S&P 500 fell for the fourth time in a week and dipped below 3,700 for the first time since early January (see Fig. 1 below).
However, we think those worries are premature. Sure, there was some profit taking last week, but the index is already starting to rebound.
Just as Punxsutawney Phil saw his shadow yesterday and predicted six more weeks of winter, we are expecting the bears on Wall Street to keep on hibernating.
The CBOE Volatility Index (VIX)
So, why do we think last week’s pullback was just bullish profit taking instead of the beginning of a bearish pullback?
Well, because Wall Street isn’t nearly nervous enough.
If Wall Street was really worried the bears were ready to start driving the trend, the CBOE Volatility Index (VIX) would be rising to new highs, not falling back to support (see Fig. 2 below).
The VIX jumped last week as stocks were falling, but it failed to break 40, which is the level the index breached when it shot higher in late October 2020.
Seeing the VIX form a lower high and then drop right back down toward support at 20 is a great sign that traders aren’t forecasting long-term volatility.
Corporate Earnings in the Stock Market
So, why isn’t Wall Street worried?
Traders have been reassured that companies were growing their profits through the end of 2020 and will likely be able to continue growing their profits in 2021 as the U.S. economy continues to recover from the novel coronavirus pandemic.
Let’s start by looking at how companies are currently doing.
As you can see in Fig. 3 below, out of the nearly 40% of S&P 500 companies that have reported their Q4 2020 earnings, 82% of them have beaten earnings expectations.
Seeing earnings growth like this across the stock market — with information technology, healthcare and financial stocks leading the way — has shown Wall Street that even though coronavirus cases started spiking in late 2020, Corporate America was able to weather the storm.
This strong Q4 performance is increasing traders’ confidence in the Federal Reserve’s median projection that the U.S. economy is going to grow by 4.2% during 2021 (see Fig. 4 below).
You can tell that traders across the board are confident in the economic outlook for the United States because it is not just stock prices that are rallying.
Treasury Yields
Bond traders are pushing Treasury yields higher once again in anticipation of stronger economic growth spurring increased inflationary pressure in the United States. You can see this in the 10-year Treasury Yield (TNX) chart in Fig. 5 below.
After breaking up through 1% on Jan. 6, the TNX dropped back to test this former resistance level and see if it would hold up as a new support level. As you can see by the rally on Jan. 28, support at 1% held nicely, and yields are continuing to climb.
Commodity traders are also pushing crude oil prices higher in anticipation of increased economic activity during 2021, driving up demand for gasoline and other oil-based fuels. You can see this in the crude oil futures chart in Fig. 6 below.
After consolidating in a bullish wedge continuation pattern for the past few weeks, crude oil prices have broken out higher and could easily be headed toward $60 per barrel.
We wouldn’t be surprised to see the S&P 500 consolidate for a bit between 3,700 and 3,875, but ultimately, we are looking for the index to once again break up to new highs.
On the date of publication, John Jagerson & Wade Hansen did not hold (either directly or indirectly) any positions in the securities mentioned in this article.
John Jagerson & Wade Hansen are just two guys with a passion for helping investors gain confidence — and make bigger profits with options. In just 15 months, John & Wade achieved an amazing feat: 100 straight winners — making money on every single trade. If that sounds like a good strategy, go here to find out how they did it. | https://investorplace.com/2021/02/the-bears-are-still-hibernating-stock-market/ |
I Need You by The Kid Laroi Ft. Don Toliver Mp3 Download
Australian rapper and singer The Kid Laroi has released his new single, “I Need You”, featuring rapper Don Toliver.
The Kid Laroi originally gained recognition from his association and friendship with American rapper, Juice Wrld while he was on tour in Australia. He gained a local following before joining a partnership agreement with Lil Bibby’s Grade A Productions and Columbia Records and attained further popularity in 2020 with his collaboration with Juice Wrld on “Go”, which peaked at number 52 on the Billboard Hot 100.
The Kid Laroi’s debut mixtape, F*ck Love (2020), peaked at number one on the Australian ARIA Charts, making him the youngest Australian solo artist ever to reach the top of the chart, and also reached number one on the US Billboard 200.
The Kid Laroi is the recipient of various accolades, including an APRA Award, an iHeartRadio Music Award, two ARIA Awards, a National Indigenous Music Award, and nominations for two Grammy Awards, two American Music Awards, three MTV Video Music Awards, and four People’s Choice Awards.
Stream & Download I Need You Mp3 by The Kid LAROI Ft. Don Toliver Below: | https://hiphopget.com/music/the-kid-laroi-ft-don-toliver-i-need-you/ |
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