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Biodiversity and monitoring of colorless filamentous bacteria in sulfide aquatic systems of North Caucasus region. Bacterial mats in sulfide aquatic systems of North Caucasus are basically composed by the species of genera Thiothrix and Sphaerotilus. Additionally, several non-filamentous sulfur-oxidizing bacteria were isolated from the mats and several minor 16S rRNA phylotypes were found in clone libraries from these mats. The minor components were affiliated with Proteobacteria, Chlorobia, Cyanobacteria and Firmicutes. Even in an individual mat population heterogeneity of Thiothrix spp. was revealed by analysis of 16S rRNA gene and RAPD-PCR. Five Thiothrix isolates were described as new species Thiothrix caldifontis sp. nov. and Thiothrix lacustris sp. nov. In the Thiothrix-Sphaerotilus type of bacterial mat the proportion of dominant organisms might be influenced by sulfide concentration in the spring water. The higher sulfide concentration (more than 10 mg/l) in the spring water is more favorable for the development of bacterial mats with dominant Thiothrix organisms than for Thiothrix-Sphaerotilus type of sulfur mat.
Mamonty Yugry Mamonty Yugry (; ) is a junior ice hockey team from Khanty-Mansiysk, which contains players from the Yugra Khanty-Mansiysk school. They are members of the Junior Hockey League (MHL), the top tier of junior hockey in the country. External links Official Page Category:2011 establishments in Russia Category:HC Yugra Category:Ice hockey clubs established in 2011 Category:Ice hockey teams in Russia Category:Junior Hockey League (Russia) teams
620 So.2d 122 (1993) Bruce Wade COVINGTON v. STATE. CR 91-1580. Court of Criminal Appeals of Alabama. January 22, 1993. Rehearing Denied March 5, 1993. Certiorari Denied May 14, 1993. 123 Robert Clark and W. Lloyd Copeland, Mobile, for appellant. James H. Evans, Atty. Gen., and Gilda Williams, Asst. Atty. Gen., for appellee. Alabama Supreme Court 1920876. BOWEN, Presiding Judge. The appellant, Bruce Wade Covington, was convicted of burglary in the second degree and rape in the first degree. He was given concurrent sentences of 10 years' and 20 years' imprisonment, respectively. On this appeal from those convictions the appellant argues that he was entitled to a mistrial because "[t]he prosecutor's questions, and statements made in the presence of the jury, constituted blatant assertions that there was evidence not before the jury of an extremely damning fact: that threats made by Covington and his brother had induced [defense witness David] Smith to give false exculpatory testimony." Appellant's brief at 30. THE FACTS The victim in this case was a 20-year-old Korean female. She knew the appellant, having met him on two prior occasions, and positively identified him as her assailant. The appellant's defense was alibi. He claimed that he was at home at the time of the burglary and rape. It is undisputed 124 that shortly before the rape, the appellant was in the company of David Quinley and David Smith. The appellant also claimed that he had shaved his pubic hair at that time "in order to get rid of the crabs." R. 236. The victim testified that she saw the appellant's pubic hair at the time of the rape. Quinley was a witness for the prosecution and testified that shortly before the rape, the appellant made statements to him and Smith indicating his desire to have sexual intercourse with an oriental female. At trial, Smith testified as a defense witness that he, Quinley, and the appellant were at his sister's house prior to the rape. He testified that "sex" was not a subject of their conversation. However, Smith admitted on direct examination that he had previously told a Mobile County sheriff's detective that the appellant had made some remarks that night "about getting some oriental stuff that night." R. 289. At trial, Smith claimed that he had lied to the detective and that the appellant "did not tell [him] that. David Quinley told [him] that. And [he] told the detective that because [he] was mad because [he] thought [the appellant] had done that to Kim." R. 290. Later, on cross-examination, Smith stated, "I don't know if I believe that he did it or not. So I ain't going to sit up here and lie and that is why I'm saying this now." R. 297. Smith also testified that Quinley was "known to lie." R. 303. However, when asked, "And you are saying that David Quinley is just making this up?" Smith responded, "I ain't saying that one bit." R. 303. During her cross-examination of the appellant, the assistant district attorney sought to establish that Smith's trial testimony was false and that either the appellant or the appellant's brother had coerced or threatened Smith into giving false testimony. On cross-examination of the appellant, the following occurred in the presence and hearing of the jury: "Q. Have either you or your brother Brian made threats against David Smith or "MR. POWERS [defense counsel]: Object to the question as insulting. "THE COURT: I sustain the objection unless you are prepared to offer evidence to that effect, Ms. Murphree [assistant district attorney]. "MS. MURPHREE: I can put on David Smith's mother. "THE COURT: I mean if you tell me that you have evidence to this effect then I am going to allow the question to be asked and answered. If you tell me you do not then I will not let him answer. "MS. MURPHREE: Your Honor, I can represent to you that I do not have David Smith's mother subpoenaed but I can represent to the Court and I will do it outside the presence of the jury if you want me to, what she has personally told me regarding threats "THE COURT: If she is not a witness to testify then you can't prove it unless you represent to me that you will get her. "MS. MURPHREE: May I takeI will do my best to. If I "THE COURT: Well, then I will not allow the question. "MS. MURPHREE: She may be out in the hall. "THE COURT: All right. I will let you check on that before I will allow the question to be asked. But unless you are able to substantiate such a question then the question is an improper question." R. 250-51. The prosecutor then questioned the appellant about another matter and established that the appellant did intend to call Smith as a defense witness. R. 255 On cross-examination of defense witness Smith, the following occurred: "Q. [by the prosecutor]: Mr. Smith, isn't it a fact that shortly after this happened you told the truth when you talked to David Hill and you have talked to Bruce [the appellant] since then haven't you? "A. On and off. ". . . . "Q. Okay. Have you talked to Bruce [the appellant] about your testimony in this case? 125 "A. No, I haven't. "Q. Has Bruce threatened you? "A. No, he hasn't. "Q. Has his brother Brian threatened you? "A. No, he hasn't. "Q. Are you aware that your mother called me last night to tell me "MR. POWERS: I am going to object to that your Honor. "THE COURT: I have already sustained the objection "MS. MURPHREE: He had indicated that he could get his mother to Court. "THE COURT: I have already sustained the objection previously unless you make the proper representation to this Court. "MS. MURPHREE: The representation I am making is that he said he could get his mother to Court.[1] "Q. Is that correct Mr. Smith? "THE COURT: No, that's not your question though, is it, Ms. Murphree? "MS. MURHPREE: It is now. "THE COURT: I am not going to allow you to go into that matter unless you can show the Court that you can go ahead and back up any question that you ask this witness. Not whether or not you can get his mother to Court but whether or not you can back up anything that is said. "MR. POWERS: Your Honor, I move for a mistrial. "THE COURT: Only proper evidence. "MR. POWERS: I move for a mistrial. "THE COURT: The Court will deny the motion. Go ahead Ms. Murphree. "Q. David Smith, i[s] your mother available to come to Court today? "MR. POWERS: Your Honor, I am going to object to this line of questioning. It's getting back to what Your Honor has already ruled on. "THE COURT: I will let him answer that question if he knows the answer. "A. No, she is not available today. "Q. Do you see that lady sitting back there in the back of the Court? Stand up for me. Did you initially tell her when I sent her out to "THE COURT: Ms. Murphree, you are beating a dead horse. I have already ruled on that issue. "MS. MURPHREE: I'm sorry then, Your Honor. I am missing your point. "THE COURT: Proceed to another matter. "MS. MURPHREE: If I can "THE COURT: Proceed to another matter. "MS. MURPHREE: May I just ask one other "THE COURT: Proceed to another matter. Well, we will take a recess. May I see the lawyers in my office?" R. 297-300 (footnote added). There is no record of what occurred in the judge's office. When the trial resumed, the following occurred: "MR. POWERS: I renew at this time my motion for a mistrial. "THE COURT: I deny the motion. You may proceed Ms. Murphree." R. 300. Shortly after this exchange, the defense rested its case. The prosecution presented no rebuttal. THE IMPROPRIETY OF THE PROSECUTOR'S COMMENTS We find the prosecutor's conduct highly improper. Statements made by the prosecution that imply or suggest that there exists additional evidence, which has not been introduced and which could prove the defendant's guilt are "intolerable" and highly prejudicial. Ex parte Washington, 507 So.2d 1360, 1362 (Ala.1986). "It has long been the rule in Alabama that, although counsel should be given considerable latitude in drawing reasonable inferences from the evidence, they may not argue as a fact that which is not 126 supported by the evidence.... This has been the rule since it was first stated in McAdory v. State, 62 Ala. 154[, 163] (1878): "`[C]ounsel should not be permitted to comment upon facts not proved before the jury as true, and not legally competent and admissible as evidence. However reluctant an appellate court may be to interfere with the discretion of a primary court in regulating the trial of cases, if it should appear that it had refused, to the prejudice of a party, to compel counsel to confine their arguments and comments to the jury, to the law and evidence of the case under considerationif it had permitted them to refer to and comment upon facts not in evidence, or which would not be admissible as evidence, it would be a fatal error....'" Washington, 507 So.2d at 1361-62. See also King v. State, 518 So.2d 191, 194 ((Ala.Cr.App.1987). "[F]or the state's attorney to ask a question which implies the existence of a factual predicate which the examiner knows he [or she] cannot support by the evidence is unprofessional conduct." Daniel v. State, 534 So.2d 1122, 1126 (Ala. Cr.App.1988). "The alleged prosecutorial misconduct consisted of making prejudicial allegations without being able to prove them by lawful evidence. The `lawful evidence' standard applies in Alabama and the good faith of [the] prosecutor or lack thereof is not the test. ". . . . "`Laying prejudicial allegations before the jury "by dint of cross-examination without being prepared to prove them is generally regarded as reversible error." United States v. Brown, 519 F.2d 1368, 1370 (6th Cir.1975). It is improper for the prosecutor "to ask a question which implies a factual predicate which the examiner knows he cannot support by evidence or for which he has no reason to believe that there is a foundation of truth." United States v. Harris, 542 F.2d 1283, 1307 (7th Cir.1976).'" Daniel v. State, 534 So.2d 1122, 1126 (Ala. Cr.App.1988). See also Hooper v. State, 585 So.2d 142, 151 (Ala.Cr.App.1991), cert. denied, ___ U.S. ___, 112 S.Ct. 1295, 117 L.Ed.2d 517 (1992); Gillespie v. State, 549 So.2d 640, 645 (Ala.Cr.App.1989). In Ex parte Peagler, 516 So.2d 1369, 1371 (Ala. 1987), the Alabama Supreme Court held that in attempting to impeach a hostile witness by questioning the witness about a prior conviction, a prosecutor must be prepared to rebut a negative answer with proper proof of the prior conviction: "`When a witness denies that he has been convicted of the crime, it becomes incumbent upon the impeaching party to prove the conviction.'" Here, the comments of the prosecutor imply that the prosecutor had personal knowledge of the incriminating evidence, which she could not prove because of a missing witness. The prosecutor, through her comments, attempted to assume the role of a witness. See Waldrop v. State, 424 So.2d 1345, 1347-48 (Ala.Cr.App.1982). THE MOTION FOR MISTRIAL The general rule is stated in Ex parte Marek, 556 So.2d 375, 379 (Ala.1989): "If a litigant points out an alleged error and asks for such drastic relief as a mistrial, then the litigant is certainly `objecting' to the question or line of questioning made the basis of the motion for the mistrial.... "... [W]hen a litigant makes a motion for a mistrial immediately after the question or questions are asked that are the grounds made the basis of the motion for the mistrial, and the grounds for the motion are clear and definite, then the motion for mistrial will preserve for review lesser prayers for relief, such as an objection or motion to strike. We make this holding because, as we stated earlier, a litigant who requests such drastic relief as a mistrial implicitly requests lesser relief that is proper, in case the greater relief is denied or is found to be improper." "Marek indicates that a motion for mistrial compensates for the lack of an objection or 127 motion to strike as long as the motion for mistrial follows immediately after the offending question." Robinson v. State, 584 So.2d 533, 538 (Ala.Cr.App.) (emphasis in original), cert. quashed, 584 So.2d 542 (Ala. 1991). There is no requirement that in making a motion for a mistrial, defense counsel include a request for instructions to disregard. "Furthermore, it should be noted that a requirement that the defendant requests the Court to instruct the jury to disregard the prosecutor's statement could be construed to constitute a waiver of his motion for a mistrial because of the antithesis of the two conflicting requests. The motion for a mistrial proceeds on the premise of the ineradicable nature of the remarks. A request for instructions, on the other hand, concedes that the trial [c]ourt, by appropriate charge, may disabuse the jurors' minds of any prejudicial effect of such statements and allow the defendant to receive a fair trial. It is at least arguable that unless alternatively made, or so separated by time as to constitute separate motions, a request for the latter (instruction to disregard) could be said to waive the former (motion for mistrial)." Stennett v. State, 340 So.2d 65, 67 (Ala. 1976). However, here defense counsel made only two objections and two requests for a mistrial. Defense counsel's only grounds of objection were that the "question [was] insulting" and that the assistant district attorney was "getting back to what Your Honor has already ruled on." Defense counsel never stated any ground for his motion for a mistrial. Defense counsel never stated a ground for his requests for a mistrial. Although defense counsel never stated the ground of objection raised on appeal, it is obvious that the trial court perceived the impropriety of the comments of the prosecutor. Indeed, it was the trial court that initially and repeatedly informed the prosecutor that she must confine her questions to matters that she could prove. "`Specific objection or motions are generally necessary before the ruling of the trial judge is subject to review, unless the ground is so obvious that the trial court's failure to act constitutes prejudicial error.'" Ex parte Purser, 607 So.2d 301 (Ala.1992). "An objection, of course, should fairly and specifically point out the particular grounds on which an alleged error occurred in order to inform the trial judge of the legal basis of the objection, thereby affording the trial judge an opportunity to reevaluate his or her initial ruling in light of the grounds alleged and to change it, if deemed necessary." Ex parte Webb, 586 So.2d 954, 957 (Ala.1991). It is clear that the trial court understood the basis for the objection. See Felder v. State, 593 So.2d 121, 122-23 (Ala.Cr.App. 1991); Marshall v. State, 570 So.2d 832, 834 (Ala.Cr.App.1990). "[T]he record clearly shows that the trial judge was aware of the objection and the reason counsel was requesting it." Ex parte McCall, 594 So.2d 628, 631 (Ala.1991). See also Ex parte Pettway, 594 So.2d 1196, 1200 (Ala. 1991) ("[i]t is apparent from the colloquy between Pettway's counsel and the court that the court was aware of the substance of the instructions that counsel was requesting, and the reasons why such instructions should be given under the particular facts of his case"). In this case, it was the trial court who aggressively confined the prosecutor to questions for which she could properly establish a factual basis. The trial court sustained defense counsel objections to the prosecutor's improper comments, although it denied the two general motions for mistrial. Defense counsel never requested any curative action. We do not think that the comments of the prosecutor mandated the granting of a mistrial because the remarks of the prosecutor could have been eradicated by the prompt action of the trial court. "`A motion for a mistrial should not be granted where the prejudicial qualities of the comment can be eradicated by action of the trial court.'" Henry v. State, 468 So.2d 896, 901 (Ala.Cr.App.1984), cert. denied, 128 468 So.2d 902 (Ala.1985). Even an improper comment on a defendant's exercise of the right against self-incrimination does not warrant a mistrial "if the trial court sustains an objection to improper remarks and promptly and appropriately instructs the jury of the impropriety of those remarks." Ex parte Wilson, 571 So.2d 1251, 1265 (Ala.1990) (emphasis in original). "[A] motion [for a mistrial] is addressed to the sound discretion of the trial court, and its ruling will not be reversed in the absence of a clear showing of abuse of discretion." Ex parte Jefferson, 473 So.2d 1110, 1114 (Ala.1985), cert. denied, 479 U.S. 922, 107 S.Ct. 328, 93 L.Ed.2d 300 (1986). "A trial judge is allowed the exercise of broad discretion in deciding whether th[e] high degree of necessity [for the granting of a mistrial] is present." Woods v. State, 367 So.2d 982, 984 (Ala.1978). Here, defense counsel never requested curative instructions. Defense counsel never made a motion to exclude or a motion to strike the prosecutor's improper remarks. Even on this appeal it is not argued that the trial court committed reversible error in failing to give curative instructions. The appellant takes an "all or nothing" approach; he was entitled to a mistrial and nothing less. Indeed, had the trial court instructed the jury to disregard the prosecutor's remarks and denied the requested mistrial, the argument on appeal, in all probability, would be that in giving those instructions to disregard the trial court only exacerbated and emphasized the prejudicial effect of the prosecutor's comments. In this case, the real question is not whether the trial court erred in denying the motion for a mistrial, but whether the trial court erred in failing, on its own and without request, to instruct the jury to disregard the improper statements of the prosecutor after sustaining the appellant's objection but denying the request for a mistrial. Without question, instructions to disregard would have been the better practice and are highly encouraged by this Court. "In considering a motion for a mistrial, the trial judge has much discretion. On review, this Court will not reverse the trial court's denial of a motion for a mistrial based on a party's improper statements `unless it affirmatively appears from the entire record that the statements involved were probably prejudicial to the [complaining party]...." Georgia Cas. and Sur. Co. v. White, 582 So.2d 487, 495 (Ala.1991) (emphasis in original). Under the circumstances of this case, the appellant's conviction is not due to be reversed because the trial court, in denying the request for a mistrial, did not, on its own motion, give curative instructions to the jury to disregard the comments of the prosecutor. The trial court sustained the appellant's objections and actively intervened during the course of the trial to prevent the prosecutor from commenting on facts which she could not prove. Although we affirm the judgment of the circuit court we find applicable the comments of the Alabama Supreme Court in Ex parte Farley, 406 So.2d 1050, 1051 (Ala. 1981): "Trial courts are possessed of ample powers to deal with conduct of attorneys who fail to conduct themselves according to high standards of courteous and correct behavior in the trial of cases; the trial courts should not hesitate, in proper instances, to exercise those powers." The judgment of the circuit court is affirmed. AFFIRMED. All Judges concur. NOTES [1] On cross-examination, the appellant testified that he intended to call Smith as a defense witness. There is no indication in the record, other than this statement of the prosecutor, that Smith ever testified that he "could get his mother to Court."
Identification of the gene(s) and protein product(s) responsible for Golgi casein kinase activity. Phosphorylation is an important and ubiquitous way for cells to regulate a multitude of functions. The protein Golgi casein kinase (GCK) has been implicated in the phosphorylation of numerous secreted proteins at S-X- E/pS motifs but yet, the gene or genes that give origin to this enzyme is(are) not known. It is speculated that this enzyme is important for the phosphorylation of several enamel extracellular matrix (ECM) proteins such as amelogenin (AMEL), enamelin (ENAM), and ameloblastin (AMBN) which all contain this unique SXE motif. Mutations in these proteins, with the exception of ameloblastin, have been shown to cause amelogenesis imperfecta (AI), or malformation of the enamel. To date only about 50% of the known AI cases have a confirmed genetic cause. This study may demonstrate that GCK is another causative gene of AI, which would increase our understanding of this genetic disease and the formation of dental enamel in general. To date, GCK has only been characterized biochemically. Therefore, the purpose of this study is to identify the primary protein sequence(s) and gene(s) responsible for GCK. This study will also try to determine whether GCK activity preferentially correlates with Golgi membrane or its soluble components as this will affect how the protein could function. Therefore, I hypothesized that GCK activity is localized to the Golgi membrane and that it is responsible for phosphorylating amelogenin. To study this hypothesis the study has two aims: 1) to identify the primary protein sequence(s) and gene(s) responsible for GCK and 2) to determine if GCK activity is membrane associated or a content enzyme activity. This study plans to use rat liver homogenates to purify Golgi fractions using an ultracentrifuge technique and solutions of variable sucrose density. These fractions will be further separated into the Golgi membrane portion and soluble components, which will be analyzed separately. The Golgi fractions will be further purified using high performance liquid chromatography (HPLC) and positive fractions containing GCK will be identified using a radiolabeling assay with 32P and short custom peptides that only GCK can phosphorylate. Active peaks from HPLC will be further fractionated using a PF2D fractionation system and each resulting fraction will be tested phosphorylative capability. Active fractions will be subjected to 2D-gel analysis and resulting spots will be isolated and sequenced. Sequences will be checked using BLAST to identify similar protein and nucleotide sequences among various species, and then the percent sequence identity will be determined. Protein functional domain analyses will be conducted and the GCK unique sequence will be used to generate two anti-peptide antibodies. These antibodies will be used for immunohistochemistry to determine GCK expression patterns in liver sections.
Country's second 'electropreneur' park to come up in Bhubaneswar The Software Technology Parks of India (STPI) has entered into a pact with India Electronics and Semiconductor Association (IESA), the premier trade body representing the Indian electronic system design and manufacturing (ESDM) sector and International Institute of Information Technology, Bhubaneswar for setting up an electropreneur park in Bhubaneswar. Related Stories No Related Stories Found Widgets Magazine The park, akin to the electropreneur park which has come up in Delhi University, will incubate startups in the ESDM space. The incubation centre will be set up within the premises of STPI's new facility in Bhubaneswar. It aims at achieving the objectives of the ESDM vision outlined in the National Policy on Electronics and other policies. “The park will incubate about 40 start-ups in the ESDM space and will see an investment of Rs 22 crore equally shared by the state and the Centre. STPI is the nodal agency for implementing the project", said an official. A memorandum of understanding (MoU) for the new park was signed by Omkar Rai, director general at STPI, Gopal Krishna Nayak, Director of IIIT, Bhubaneswar and Jitendra Chaddah, vice president of IESA. “This is the second of its kind in the country after the first electropreneur park in University of Delhi. The electropreneur park is aimed at creating products in ESDM sector to meet the requirement indigenously and create products for further exports. With a view to create synergy between both the electrorpeneur parks , we have decided that both the parks will work in a complimentary manner. They will capitalize on the smart lab that we have in Bangalore and another we are going to establish in Bhubaneswar itself", said Rai. Start-ups under verticals- energy, education and industrial automation and process control will be given focus at the centre. To promote the successful startups or incubatees of the proposed ESDM incubation centre, it is envisaged to offer preferential allotment in Electronic Manufacturing Cluster on the outskirts of Bhubaneswar. The Odisha government has taken a host of measures- preparation of road map for the hardware industry and characterization lab for chip testing to attract investments in the ESDM sector. The ESDM sector, as per a strategic roadmap, is poised to generate cumulative revenue of Rs 18,800 crore in Odisha by 2024. The report said, investments of Rs 7,340 crore need to be pumped into the sector in three phases to realise the projected revenue and employment generation for around 60,000 people. Khurda, Rayagada, Sundergarh, Balasore and Ganjam districts are identified as the potential areas for setting up of ESDM projects. In addition, the Information and Communication Technology Policy-2014, promises sops for the promotion of ESDM units.
Robert W. MacVicar Robert William MacVicar (1918–1998) was a professor of chemistry, the chancellor of Southern Illinois University, and the president of Oregon State University between 1970 and 1984. Biography Early years Robert W. MacVicar was born in Princeton, Minnesota, on September 28, 1918. Academic career MacVicar was a student of chemistry at the University of Wyoming, graduating from there in 1939. Upon graduation, MacVicar was awarded a Rhodes scholarship, but it proved impossible for him to attend due to the outbreak of World War II in Europe. Instead, MacVicar enrolled and Oklahoma State University in Stillwater, Oklahoma, where he continued his chemistry studies. MacVicar obtained his Master of Science in 1940 from Oklahoma State, authoring a thesis entitled "The Effect of Adrenaline Injections on the Chloride and Phosphorus Distribution of the Blood" en route to obtaining his degree. MacVicar spent the duration of the war as an officer in the United States Army. He left military service as a colonel in the U.S. Army Air Corps. Following the conclusion of the war, MacVicar moved to Madison to attend the University of Wisconsin–Madison, from which he obtained a PhD in biochemistry in 1946. MacVicar's dissertation was entitled "The Boron Metabolism of Plants" and included material which he had been able to publish in the American Potato Journal and Botanical Gazette. With degree in hand, MacVicar returned to Stillwater to take a position as an assistant professor of agricultural chemistry research and chemistry, later gaining promotion to a full professorship. He remained at Oklahoma State until 1964. Administrative career Concurrently with his professorship at Oklahoma State, MacVicar became involved in school administration, taking on the role of dean of the graduate school in 1953. He continued to serve in that capacity until his departure from Stillwater in 1964. From 1957 he also served as vice president for academic affairs. In 1968, MacVicar was named chancellor of Southern Illinois University, located in the town of Carbondale in the state's downstate coal mining country. MacVicar remained there until 1970, when he came west to Corvallis, Oregon, to assume a post as the 15th president of Oregon State University. MacVicar remained as head of Oregon State until his retirement in 1984, during which time the campus was expanded with the addition of 23 new buildings. Under MacVicar's watch the total number of faculty at OSU expanded from 1,766 to 2,247, while the school's budget tripled. After his retirement, he was named professor emeritus of chemistry and president emeritus, special assistant to the chancellor. He also served as acting president of the College of Ganado, a small college in Arizona, for seven months in 1985. Death and legacy Following his retirement, MacVicar was awarded the title professor emeritus of chemistry as well as president emeritus and special assistant to the chancellor. MacVicar remained active in the Corvallis community and put his networking skills to use establishing a fund-raising program on behalf of the College of Ganado, located on a Navajo reservation in northeastern Arizona. MacVicar died on December 26, 1998. He was 80 years old at the time of his death. Over the course of his career, MacVicar published over 135 papers, reports and articles. His papers are held by Oregon State University Archives in Corvallis. Footnotes Works Feeding Trials with Mineral and Protein Supplements for Two-and Three-Year-Old Steers Wintering on Dry Grass. With Oscar Burr Ross and D.F. Stephens. Stillwater, OK: Oklahoma Agricultural Experiment Station, 1950. Science is Everybody's Business. Oklahoma City, OK: United Founders Life Insurance Co., n.d. [1960]. Vitamin A Studies with Beef Cattle: A Summary of Experimental Studies Conducted at Oklahoma State University, 1946–1959. With L.S. Pope and Frank H. Baker. Stillwater, OK: Oklahoma Agricultural Experiment Station, 1961. External links "Guide to the Robert W. MacVicar Papers 1942-1995," Oregon State University Archives, Valley Library, Corvallis, OR. "Guide to the President's Office Photographs, 1923-1998," Oregon State University Archives, Valley Library, Corvallis, OR. Category:1918 births Category:1998 deaths Category:University of Wyoming alumni Category:Oklahoma State University alumni Category:University of Wisconsin–Madison alumni Category:Southern Illinois University Carbondale faculty Category:Presidents of Oregon State University Category:People from Princeton, Minnesota
Background {#Sec1} ========== Along with high proportions of other fatty acids from plants, polyunsaturated fatty acids (PUFAs) such as cis-9,12-octadecadienoic acid (linoleic acid; LA) and cis-9,12,15-octadecatrienoic acid (α-linolenic acid; ALA) are essential to human health. These PUFAs are used to produce cis-6,9,12-octadecatrienoic acid (γ-linolenic acid; GLA) and cis-6,9,12,15-octadecatrienoic acid (stearidonic acid; SDA), which are health-promoting molecules as well as serving as precursors for the very long chain polyunsaturated fatty acids (VLCPUFAs) found in algae, fungi and vertebrates, including fish and human. GLA is an omega-6 fatty acid that acts as an anti-inflammatory agent and relieves skin problems, such as atopy \[[@CR1], [@CR2]\]. SDA is an omega-3 fatty acid that serves a precursor for other omega-3 fatty acids such as cis-5,8,11,14,17-eicosapentaenoic acid (EPA) and cis-4,7,10,13,16,19-docosahexaenoic acid (DHA), a representative ω-3 VLCPUFAs. In humans, dietary SDA is more efficiently converted to EPA compared to ALA \[[@CR3]\], and SDA therefore provides similar health benefits to humans as ω-3 VLCPUFAs \[[@CR4]\]. In addition, SDA has been characterized as a potent inhibitor of cancer cell growth and an effective molecule against skin inflammation and atopic dermatitis that also prevents hypertriglyceridemia \[[@CR5]\]. As humans can synthesize DHA from either ALA or SDA, it may be beneficial for humans to take in high levels of ALA and/or SDA through their diet. GLA and/or SDA are present in the seed oils of several plant species, such as evening primrose (Oenothera biennis) \[[@CR6]\], blackcurrant (Ribes nigrum) \[[@CR7]\], Primula spp. \[[@CR8]\], Echium spp. \[[@CR9]\], hemp (Cannabis sativa) \[[@CR10]\] and Boraginaceae plants \[[@CR11]\], including borage (Borago officinalis). However, these wild plants do not produce large amounts of oil, and they produce only low levels of GLA and SDA. Consequentially, GLA- and SDA-containing health foods are rather expensive. GLA and SDA are converted from LA and ALA, respectively, through desaturation at the sixth carbon, a process catalyzed by Δ6 desaturase (D6DES). Fungal D6DES can also convert oleic acid to C18:2Δ^6,9^ \[[@CR12], [@CR13]\], and ALA-specific D6DES from Primula spp. synthesizes only SDA \[[@CR14], [@CR15]\]. The D6DES gene, which was first identified in a cyanobacterium \[[@CR16]\], encodes a divergent form of the sphingolipid Δ8-desaturase \[[@CR17]\]. Subsequently, D6DES genes have been identified in bacteria, algae, fungi, mosses, vertebrates and several plant species \[[@CR18]\]. Fatty acid desaturases involved in the synthesis of VLCPUFA, including D6DES, are "front-end" desaturases that contain a cytochrome b5 (cyb5) domain at their N-termini, which is essential for fatty acid desaturation \[[@CR19]--[@CR21]\]. Perilla (Perilla frutescens var. frutescens) is an annual herbaceous plant belonging to the mint family, Lamiaceae. Perilla has been widely cultivated as an oilseed crop and leaf vegetable in East Asia. Perilla seed oil is used as both an edible and an industrial crop in products such as paint, varnish and ink \[[@CR22]\]. Perilla seeds comprise 35--45% oil and accumulate one of the highest proportions of ALA (54--64%) in the plant kingdom \[[@CR22]\]. The mechanism underlying the production of high levels of ALA is of interest, and thus, transcriptome analysis has been performed to identify perilla genes involved in ALA bisoynthesis and accumulation \[[@CR23]\]. PUFAs represent approximately 80% of the total fatty acid composition in perilla seeds, which could confer health benefits for humans \[[@CR24]\]. We therefore hypothesized that if perilla were transformed with the D6DES gene, it would produce high amounts of GLA and/or SDA and serve as a feasible resource for large-scale GLA and/or SDA production. Furthermore, the seeds from these transgenic crops could potentially be used for effective, large-scale production of EPA or DHA. In this study, we confirmed that D6DES from the fungus Phytophthora citrophthora synthesizes GLA and SDA from LA and ALA, respectively, in budding yeast. We further revealed that transgenic perilla seeds expressing PcD6DES produced very high levels of GLA and SDA, with each accounting for over 20% of the seed oil content. Our results indicate that PcD6DES and perilla are an effective gene and host combination that could be utilized to efficiently produce GLA and SDA. Methods {#Sec2} ======= Plant material {#Sec3} -------------- Perilla frutescens var. frutescens cv. Yeobsil was grown in a greenhouse and the seeds were harvested for transformation. The seeds were surface sterilized in 70% (v/v) ethanol for 1 min, followed by 4-fold diluted commercial bleach for 20 min, washed three times with sterile distilled water and immersed in sterile distilled water for 2 h at room temperature. After brief drying on sterile filter paper, the seeds were placed on Murashige and Skoog (MS) basal medium \[[@CR25]\] supplemented with 30 g/L sucrose and 0.4% (w/v) Phytagel (Sigma, USA) with the pH adjusted to 5.8 before autoclaving. Surface sterilized seeds were germinated in a culture room at 28 °C under a 16 h:8 h (light: dark) photoperiod. Gene cloning {#Sec4} ------------ The D6DES gene was cloned from P. citrophthora (KACC 40188), which was obtained from the National Agrobiodiversity Center, National Institute of Agricultural Science, RDA, Republic of Korea. Total RNA was extracted from P. citrophthora for D6DES gene cloning. First-strand cDNA was synthesized from total RNA using a PrimeScript™ 1st strand cDNA Synthesis Kit (Takara, Japan) following the manufacturer's protocol. Degenerate PCR and 5′−/3′-RACE PCR were used for cloning. Primer sequences for degenerate PCR were designed based on consensus sequences of D6DES from the fungus Mucor circinelloides and Rhizopus stolonifera var. stolonifer. Degenerate PCR was performed at 94 °C for 5 min, followed by 30 cycles of 94 °C for 20 s, 54 °C for 30 s and 72 °C for 1 min, with an additional extension at 72 °C for 5 min. PCR amplification was performed with the degenerate primers using Ex Taq polymerase (Takara, Japan). RACE PCR was performed using a SMART RACE cDNA Amplification Kit (Clontech, USA) following the manufacturer's protocol. The D6DES gene from P. citrophthora (PcD6DES) was registered in GenBank NCBI under Accession No. DQ836059. Primers used in these procedures are listed in Additional file [1](#MOESM1){ref-type="media"}: Table S1. Vector construction {#Sec5} ------------------- To confirm the function of PcD6DES in budding yeast (Saccharomyces cerevisiae), the PcD6DES gene was subcloned in between the HindIII and BamHI sites of the pYES2/CT vector (Invitrogen, USA) harboring the galactose-inducible GAL1 promoter and URA3 gene. The complete vector was named pYES2-PcD6DES. The process used to transform and express the PcD6DES gene in perilla was as follows: the pVicOCS vector containing the seed-specific vicilin promoter and octopine synthase III (OCSIII) terminator was digested with BamHI and HindIII, and the ORF of PcD6DES was inserted between the vicilin promoter and OCSIII terminator. The vicilin promoter-PcD6DES-OCSIII terminator cassette was inserted into the multiple cloning site of pCAMBIA3300. The complete vector was named pCAMBIA-PcD6DES. The destination vectors used in this study are shown in Additional file [2](#MOESM2){ref-type="media"}: Figure S1. Phylogenetic and transmembrane domain analysis {#Sec6} ---------------------------------------------- The sequences of D6DES genes registered in GenBank were collected by carrying out BLASTN with the PcD6DES gene sequence as a query. The phylogenetic relationship of these D6DES genes was analyzed using DNASTAR MegAlign (Ver. 7.2.1) via the ClustalW method. A phylogenetic tree was constructed from the alignment data using TreeView (Ver. 1.6.6). The transmembrane domain was predicted with TOPCONS (<http://topcons.cbr.su.se/>). Yeast transformation and culture {#Sec7} -------------------------------- Saccharomyces cerevisiae INVSc1 (Invitrogen, USA) was used for the expression of PcD6DES and subsequent production of GLA and SDA. Yeast transformation was carried out in accordance with the manufacturer's protocol. Yeast culture and induction of PcD6DES were performed as follows: Yeast cells containing pYES2-PcD6DES were cultured in uracil-deficient medium containing with 2% raffinose and 1% Tergitol NP-40 at 30 °C. At O.D~600~ = 0.5--0.6, 0.5 mM of the substrates LA and ALA with 2% galactose as an inducer were added to the culture, followed incubation for 3 days at 20 °C. Perilla transformation {#Sec8} ---------------------- Perilla transformation was performed as described by Kim et al. \[[@CR26]\] with slight modifications. Agrobacterium tumefaciens strain EHA105 harboring pCAMBIA-PcD6DES was inoculated in Luria Bertani broth containing 50 mg/L kanamycin and 50 mg/L rifampicin and cultured at 28 °C overnight. The cells were harvested and resuspended in liquid MS basal medium. Hypocotyl pieces 0.5 to 1 cm in length were excised from in vitro-grown seedlings and inoculated with Agrobacterium solution for 1 h. After brief blotting with sterile filter paper, the explants were transferred to MS basal medium supplemented with 30 g/L sucrose and 0.4% Phytagel and co-cultured for 2 days at 26 °C in the dark. After co-culture, the explants were transferred to fresh MS medium supplemented with 30 g/L sucrose, 3.0 mg/L benzyladenine, 0.01 mg/L naphthaleneacetic acid, 2 mg/L phosphinothricin, 400 mg/L carbenicillin and 0.4% Phytagel. The explants were subcultured every two weeks for 8 weeks. The shoots that regenerated on the explants were excised and transferred to fresh selective MS basal medium for shoot elongation. The elongated shoots were transferred to half-strength MS basal medium for rooting. When whole plants had formed, they were acclimated on commercial soil in an airtight container for 1 week and transferred to the greenhouse. Fatty acid composition analysis and the determination of seed oil content {#Sec9} ------------------------------------------------------------------------- Fatty acid extraction and FAME preparation in yeast cells were followed slightly modified version of method by Kim et al. \[[@CR27]\]. Yeast cells were centrifuged, resuspended in 1 volume of distilled water to remove residual fatty acids (LA and ALA), harvested and lyophilized for 48 h. Lipids of freeze-dried yeast cells with 0.5 mg pentadecanoic acid were extracted with 5 mL extraction solution (chloroform: methanol = 2:1, v/v) via sonication at room temperature. Five milliliters of 0.58% NaCl solution was added to the mixture and centrifuged at 2000 rpm for 10 min. The supernatant was discarded and the lower phase was dried under a flow of nitrogen. Toluene (0.5 mL) and 0.5 N NaOH in methanol were added to the dried samples, and the transmethylation mixture was reacted in boiling water for 3 min. After cooling, 2 N BF~3~ in methanol was added to the mixture, which was reacted once more for 5 min. Ten milliliters of distilled water and 10 mL petroleum ether were added to the sample, followed by centrifugation. The supernatant containing fatty acid methyl esters (FAMEs) was collected for gas chromatography (GC) analysis performed on a HP 5890 (Agilent, USA) with flame ionization detector (FID) and 25 m × 0.2 mm (inner diameter) HP 20 M from 180 °C to 200 °C at 1 °C/min. Perilla seeds were weighed and crushed with a metal stick in a glass tube. A mixture of LA (Sigma, St. Louis, MO, USA), GLA (Matreya, PA, USA), ALA (Sigma, St. Louis, MO, USA) and SDA (Santa Cruz Biotechnology, CA, USA) was used as an external standard. Seed samples and the external standard were transmethylated at 85 °C for 90 min in 0.3 mL of toluene and 1 mL of 5% H~2~SO~4~ (v/v) in methanol. Pentadecanoic acid (100 μg) was added to each sample as an internal standard. After transmethylation, 1.5 mL of 0.9% NaCl solution was added to the sample and the FAMEs were transferred to a new tube after extracting the sample three times with 1.5 mL of n-hexane. The FAMEs were analyzed by GC-2010 plus (Shimadzu, Japan) GC with FID and a 30 m × 0.25 mm (inner diameter) HP-FFAP column (Agilent, USA) while increasing the oven temperature from 190 °C to 230 °C at 3 °C/min. Nitrogen was used as the carrier gas in both cases for fatty acid analysis. Seed oil contents were determined based on the results by fatty acid analyses. The formula for seed oil content is as follows. Seed oil content = (Total peak area of all seed fatty acids except internal standard)\(mass of internal standard)/(peak area of internal standard). GC-TOF MS analysis {#Sec10} ------------------ Each FAME sample (1 μL) was injected into the Agilent 7890A GC with an Agilent 7683B autosampler (Agilent, Atlanta, GA, USA) with a split ratio of 25 and separated in a 30 m × 0.25 mm I.D. fused-silica capillary column coated with 0.25 μm CP-SIL 8 CB Low Bleed (Varian Inc., Palo Alto, CA, USA). The injector temperature was 230 °C. The helium gas flow rate through the column was 1.0 mL/min. The temperature program was as follows: starting temperature 80 °C, maintained for 2 min, followed by an increase to 320 °C at 15 °C/min and a 10 min hold at 320 °C. The transfer line and ion-source temperatures were 250 and 200 °C, respectively. The scanned mass range was 85--600 m/z, and the detector voltage was set at 1700 V. Thin layer chromatography (TLC) {#Sec11} ------------------------------- Lipid extraction and TLC were performed based on Kim et al. \[[@CR28]\]. Briefly, lipids were extracted with extraction solution (chloroform: methanol = 2:1, v/v) from ground perilla seeds and spotted onto silica gel G60 plates (Merck Millipore, USA). Lipid samples were separated using developing solvent (hexane: diethylether: acetic acid = 70:30:1, v/v/v) in a TLC developing tank for 50 min at room temperature. The silica gel plate was removed from the TLC developing tank and sprayed with 0.1% primuline (Sigma, St. Louis, MO, USA) in 80% acetone. Lipid spots were visualized on an ultraviolet transilluminator. A large spot at the top (TAG), two small spots in the middle (diacylglycerol) and two small spots around the baseline (polar lipids) were scraped off the TLC plate with a scalpel and subjected to fatty acid analysis. RT-PCR and quantitative RT-PCR {#Sec12} ------------------------------ Total RNAs of yeast cells and perilla tissues were extracted with RNeasy Mini kit and RNeasy Plant Mini kit (Qiagen, USA), respectively. First-strand cDNA was synthesized using RNA to cDNA EcoDry Premix (Clontech, USA) following the manufacturer's protocol. RT-PCR was carried out using ExTaq DNA polymerase (Takara, Japan) and 1 μg first-strand cDNA from yeast RNA as a template. The PCR conditions were as follows: 94 °C for 3 min, 30 cycles of 94 °C for 20 s, 55 °C for 20 s and 72 °C for 80 s, and additional extension at 72 °C for 5 min. Quantitative RT-PCR was carried out with SYBR premix Ex Taq II (Tli RNaseH plus; Takara, Japan), and first-strand cDNA diluted 20-fold was used as template for PCR on a StepOnePlus Real-Time PCR System (Applied Biosystems, USA). The PCR conditions were as follows: 94 °C for 30 s, 40 cycles of 94 °C for 5 s, 55 °C for 20 s and 72 °C for 20 s, and an additional cycle of 94 °C for 15 s, 55 °C for 1 min, and finally, after increasing the temperature at 0.5 °C/min, 94 °C for 15 s. Quantitation was performed using StepOne software ver. 2.3 (Applied Biosystems, USA), employing perilla β-actin* as a reference gene. Primers were designed with the GenScript website for real-time PCR primer design to generate approximately 200 bp amplicons with a 55 °C melting temperature (<https://www.genscript.com/ssl-bin/app/primer>). Primers for qRT-PCR are listed in Additional file [1](#MOESM1){ref-type="media"}: Table S1. Results {#Sec13} ======= PcD6DES gene cloning and sequence analysis {#Sec14} -------------------------------------------- We began by cloning the full-length PcD6DES mRNA, which was 1529 bp with a 1371 bp sequence encoding 456 aa. Residues 11 to 81 were predicted to form a cyb5 domain, which is characteristic of front-end desaturases (Fig. [1](#Fig1){ref-type="fig"}) \[[@CR20]\]. In addition to the cyb5 domain, fatty acid desaturases contain the heme-binding motif HPGG-X~8~-G-X~6~-F-X~3--6~-H known as HPGG \[[@CR19]\]. PcD6DES encodes a protein with an HPGG motif at 42--45 aa, with the sequence HPGG-X~7~-G-X~6~-F-X~3~-H, in the cyb5 domain. In addition, PcD6DES has three histidine boxes (His boxes): HDVLHH, HNFHH and QIEHH. His boxes are the most important characteristics of fatty acid desaturases, as they determine their desaturase function \[[@CR29], [@CR30]\]. The His boxes of common fatty acid desaturases have the sequences HXXXH, HXXHH and HXXHH. Importantly, the third His box of the front end desaturase has the sequence QXXHH, and it appears that the Q residue mediates desaturase function \[[@CR30]\]. The sequences of the His boxes of PcD6DES (HDVLHH, HNFHH and QIEHH) are consistent with the conserved His box motifs HXXXH, HXXHH and QXXHH of D6DES (Fig. [1](#Fig1){ref-type="fig"}) \[[@CR30]\]. Finally, most membrane-bound fatty acid desaturases have four to six transmembrane domains (TMs) \[[@CR31]--[@CR33]\], and PcD6DES was predicted to have six TM domains (Fig. [1](#Fig1){ref-type="fig"}, Additional file [2](#MOESM2){ref-type="media"}: Figure S2). TM1 to TM6 were predicted to be located sequentially at 128--148 aa, 153--173 aa, 191--211 aa, 267--287 aa, 305--325 aa and 328--348 aa (Fig. [1](#Fig1){ref-type="fig"}, Additional file [2](#MOESM2){ref-type="media"}: Figure S2).The TMs patterns of of PcD6DES, evening primrose D6DES, perilla FAD2 are very similar to among them (Additional file [2](#MOESM2){ref-type="media"}: Figure S2).Fig. 1Nucleotide and deduced amino acid sequences of the PcD6DES gene. Lowercase italics and capital letters indicate 5′/3′-untranslated region and coding sequence, respectively. Bold capital letters represent amino acid residues. The cytochrome b5 domain (the main characteristic of a front-end desaturase) is underlined. Thick underline indicates the heme-binding motif, HPGG. Gray and white boxes indicate the transmembrane domain and histidine box, respectively. Asterisk indicates the translation termination sequence Phylogenetic analysis {#Sec15} --------------------- We performed phylogenetic analysis of D6DES peptide sequences from 25 species belonging to the Protista, Fungi, Plantae and Animalia kingdoms (Fig. [2](#Fig2){ref-type="fig"}). The D6DES sequences formed groups within each kingdom. The identity between PcD6DES (DQ3605) and PinD6DES (JF910287), which were the first and second reported D6DES in the Phytophthora genus, respectively, was 90.8%. However, the identity between PcD6DES and other fungal D6DES proteins was at most 64.1%. Furthermore, for the Fungi and Protista, the identities among deduced amino acids of D6DES genes were low (38.2 and 55.2%, respectively).Fig. 2Phylogenetic analysis of the deduced amino acid sequences of D6DES genes from various organisms. D6DES from microalgae (Protista), fungi (Fungi), plants (Plantae) and vertebrates (Animalia) are separately grouped by kingdom. Letters and numbers represent GenBank accession numbers. The origin of each D6DES is as follows: AF126798, Mus musculus; AF419296, Pythium irregulare; AY08239, Phaeodactylum tricornutum; AY234125, Primula farinosa; AY63057, Glossomastix chrysoplasta; AY952780, Echium plantagineum; BC123735, Bos taurus; DQ177498, Cunninghamella echinulata; DQ83605, Phytophthora citrophthora; EF413025, Mortierella alpina; EF636888, Gallus gallus; EU416278, Oenothera biennis; GQ162822, Sparus aurata; GU198926, Ribes nigrum; GU237486, Echium amoenum; GU390532, Parietochloris incisa; JF910287, Phytophthora infestans; KC817461, Pythium aphanidermatum; KP874952, Umbelopsis isabellina; KX584737, Mortierella alpina; KY214451, Nannochloropsis oceanica; NM_001093384, Xenopus laevis; NM_004265, Homo sapiens; U79010, Borago officinalis; XM_008589390, Galeopterus variegatus. Open box indicates PcD6DES. Sequences were aligned using DNASTAR MegAlign (Ver. 8.1.4) with the ClustalW method. The phylogenetic tree was generated using TreeView (Ver. 1.6.6) with the aligned data. Scale bar indicates 0.1 amino acid substitution per site Functional analysis in Saccharomyces cerevisiae {#Sec16} ------------------------------------------------- We compared the fatty acid composition between the control yeast strain and pYES2-PcD6DES yeast to investigate the production of SDA and GLA and confirm PcD6DES function. Above all, the expression of PcD6DES in transformed yeast cells was confirmed using RT-PCR (Additional file [2](#MOESM2){ref-type="media"}: Figure S3). Yeast harboring the pYES2 empty vector, which served as a control, only produced hexadecanoic acid (palmitic acid; C16:0), cis-9-hexadecanoic acid (palmitoleic acid; C16:1Δ^9^), octadecanoic acid (stearic acid; C18:0) and cis-9-octadecenoic acid (oleic acid; C18:1Δ^9^). Furthermore, when provided with LA, this control yeast strain did not produce any other fatty acids. However, pYES2-PcD6DES yeast supplemented with LA produced GLA. In addition, pYES2-PcD6DES yeast supplied with LA and ALA synthesized SDA as well as GLA (Table [1](#Tab1){ref-type="table"}). These results demonstrate that the PcD6DES gene encodes a protein that can convert LA and ALA to GLA and SDA, respectively, in yeast.Table 1Fatty acid composition of pYES2-PcD6DES yeast cultured in medium containing fatty acid substrates. Trace indicates below 0.1 mole%. Data represent mole% of fatty acid methyl esters. Experiments were carried out in triplicate, and the mean values are displayedFatty acidpYES2pYES2-PcD6DES-+LA+LA+LA and ALAC16:017.418.120.715.9C16:1Δ^9^41.215.215.86.8C16:2Δ^6,9^\--3.10.6C18:07.27.17.97.7C18:1Δ^9^34.213.815.88.3C18:2Δ^6,9^\--tracetraceLA-45.825.121.5GLA\--11.65.3ALA\-\--25.1SDA\-\--8.8Conversion rate (%)\--26.421.6Saturated FA: unsaturated FA1:3.071:2.971:2.501:3.24 We also analyzed the conversion rate of products by PcD6DES. In the case of pYES2-PcD6DES supplied with LA, the conversion rate of GLA was 11.6/(25.1 + 11.6) = 31.6%, putative C16:2Δ^6,9^ was 3.1/(15.8 + 3.1) = 16.4% and the total conversion rate was 26.4% (Table [1](#Tab1){ref-type="table"}). In the case of pYES2-PcD6DES supplied with both LA and ALA, the conversion rate of GLA was 5.3/(21.5 + 5.3) = 19.8%, SDA was 8.8/(25.1 + 8.8) = 26.0%, putative C16:2Δ^6,9^ was 0.6/(6.8 + 0.6) = 8.1% and the total conversion rate was 21.6% (Table [1](#Tab1){ref-type="table"}). The ratios of saturated fatty acids to unsaturated fatty acids were not significantly different in yeast cultures supplemented with LA and/or ALA and without LA and/or ALA (Table [1](#Tab1){ref-type="table"}). A putative cis-6,9-octadecadienoic acid (C16:2Δ^6,9^) peak was detected in the samples and putative C18:2Δ^6,9^ was also detected, but at a much lower proportion than C16:2Δ^6,9^ (Table [1](#Tab1){ref-type="table"}). Fatty acid analysis and segregation ratio of transgenic perilla {#Sec17} --------------------------------------------------------------- Five T~0~ PcD6DES transgenic perilla plants (PD6Ds) were obtained by Agrobacterium-mediated transformation. The transformants were confirmed by PCR of the PcD6DES gene and phosphinothricin acetyltransferase gene, which confers resistance to the herbicide Basta (Bayer Crop Science, Republic of Korea). We analyzed the fatty acid compositions of the T~2~ PD6D seeds from two T~1~ PD6Ds of each line (Table [2](#Tab2){ref-type="table"}). Three new peaks, which were absent in Yeobsil, appeared in the chromatogram from PD6D seeds (Fig. [3](#Fig3){ref-type="fig"}). The retention times of two peaks of them, located earlier and later than that of ALA, are the same as that of GLA and SDA in the external standard, respectively (Fig. [3](#Fig3){ref-type="fig"}). The remaining new peak that appeared in front of the LA peak was putative C18:2Δ^6,9^, as expected (Fig. [3](#Fig3){ref-type="fig"}), as this compound is found in some fungi (Table [2](#Tab2){ref-type="table"}) \[[@CR12], [@CR13]\]. In transgenic PD6D plants, the proportions of GLA, SDA and putative C18:2Δ^6,9^ increased while the proportions of oleic acid, LA and ALA decreased. In particular, the ALA content was significantly reduced in PD6D, likely due to GLA and SDA synthesis expending their respective substrates LA and ALA. Oleic acid content decreased in PD6D compared with Yeobsil (Table [2](#Tab2){ref-type="table"}), likely as a consequence of increasing PUFA content. There were two types of T~1~ PD6Ds whose T~2~ seeds contained over 46% or 28--35% GLA and SDA content in seed oil, respectively. We hypothesized that the variance resulted from the difference in PcD6DES gene expression levels between the homozygote and hemizygote. To measure the segregation ratio, we treated 40--50 T~1~ seedlings with 0.3% Basta and investigated the segregation ratios of the progenies of four T~0~ PD6D lines. All four T~1~ perilla lines segregated at a ratio of 3:1 (Additional file [1](#MOESM1){ref-type="media"}: Table S2).Table 2Fatty acid composition of mature D6DES T~2~ perilla (PD6D) seeds. Data represent mole% of fatty acid methyl esters. Experiments were performed in triplicate, and the mean values are givenFatty acidYeobsilPD6D 1-1PD6D 1-3PD6D 2-1PD6D 2-3PD6D 3-1PD6D 3-3PD6D 4-1PD6D 4-3C16:07.77.37.17.27.27.37.67.57.3C18:02.42.62.62.32.42.72.72.42.2C18:1Δ^9^18.515.714.412.914.714.213.313.712.6C18:2Δ^6,9^-1.62.00.71.81.11.71.80.6LA11.59.38.19.88.610.47.77.211.6GLA-16.724.915.924.616.824.824.414.2ALA60.129.920.832.821.030.221.021.537.6SDA-16.920.218.519.717.421.121.513.8D6DES products-35.147.035.146.135.347.647.728.7Fig. 3Chromatogram of PcD6DES perilla analyzed by GC. External standard for the mixture of LA, GLA, ALA and SDA was transmethylated. Yeobsil perilla seeds contain common fatty acids C16:0, C18:0, C18:1Δ^9^, LA and ALA. PcD6D transgenic perilla seeds contain C18:2Δ^6,9^, GLA and SDA, which are absent in Yeobsil Confirmation of the putative C18:2Δ^6,9^ peak {#Sec18} --------------------------------------------- To confirm the identity of the putative C18:2Δ^6,9^, we analyzed this compound from PcD6DES perilla seed oil using Pegasus HT GC-TOF MS (LECO, USA). LA and C18:2Δ^6,9^ are isomers whose double bond positions differ from each other. In the GC-TOF MS results, two slightly different peaks and mass spectra were observed (Fig. [4](#Fig4){ref-type="fig"}). In addition, these peaks were identified by matching their mass spectra from the NIST11 and Wiley9 mass libraries. Finally, the peak between the oleic acid and LA peaks was possibly C18:2Δ^6,9^ .Fig. 4Selected-ion chromatogram and mass spectra for LA methyl ester and putative C18:2Δ^6,9^ methyl ester (molecular mass: 294) from PcD6DES perilla seed. a Selected-ion chromatogram for m/z 294 and (b) mass spectra of LA methyl ester and putative C18:2Δ^6,9^ methyl ester as methyl ester derivatives separated on a 30 m\0.25 mm i.d. fused-silica capillary column coated with 0.25 μm CP-SIL 8 CB Low Bleed PcD6DES* expression in leaves and developing seeds of transgenic PcD6DES perilla {#Sec19} ----------------------------------------------------------------------------------- We performed quantitative RT-PCR (qRT-PCR) to measure the expression levels of PcD6DES and other fatty acid desaturase genes in leaves and developing seeds from Yeobsil and PD6D (Fig. [5](#Fig5){ref-type="fig"}). In DS3 of Yeobsil or PD6D 4--1-1, the expression of fatty acid desaturase 2 gene from P. frutescens (PfFAD2) and PfFAD3 was relatively high compared to that of PfFAD7--1 and PfFAD7--2. PcD6DES was highly expressed during DS3 of PD6D 4--1-1; however, it was not expressed in Yeobsil at DS3 (Fig. [5a](#Fig5){ref-type="fig"}). In leaves of Yeobsil or PD6D 4--1-1, PfFAD7--1 and PfFAD7--2 were expressed at higher levels than PfFAD2 and PfFAD3. PcD6DES was expressed at low levels similar to those of PfFAD2 and PfFAD3 (Fig. [5b](#Fig5){ref-type="fig"}). Bar (Basta resistance) was expressed during DS3 and in leaves of PD6D 4--1-1, but not in either DS3 or leaves of Yeobsil (Fig. [5](#Fig5){ref-type="fig"}a, b). In particular, the expression level of bar was much higher (54.7-fold) than that of other genes in PD6D 4--1-1 leaves (Fig. [5](#Fig5){ref-type="fig"}b). We also determined the expression level of PcD6DES gene in DS1 to DS4 and leaf. The expression of PcD6DES gene in PD6D 4--1-1 was low in DS1 to DS2 and very high in DS3 to DS4 (Fig. [5c](#Fig5){ref-type="fig"}). PcD6DES gene was also highly expressed in leaf tissue more than expected. No expression was detected in all Yeobsil samples.Fig. 5Relative expression levels of PfFAD2, PfFAD3, PfFAD7--1, PfFAD7--2, PcD6DES, and bar in (a) DS3, (b) leaves and (c) that of PcD6DES in DS1 to DS4 and leaf using quantitative RT-PCR. All experiments were carried out three times, and error bars indicate standard deviation Fatty acid composition in PcD6DES transgenic perilla leaves {#Sec20} ------------------------------------------------------------- To investigate the changes in fatty acid composition in PD6D leaves, we analyzed the fatty acid composition of 4-week-old leaves from T~2~ homozygous transgenic plants. Unlike the fatty acid composition of perilla seeds, leaves contained much higher levels of C16 fatty acids and LA but lower levels of oleic acid and ALA (Table [3](#Tab3){ref-type="table"}). Although the expression of PcD6DES was driven by the seed-specific vicilin promoter from Pisum sativum \[[@CR34]\], GLA and SDA were still synthesized and accumulated in PD6D leaves, albeit at a lower proportion than in seeds (Table [3](#Tab3){ref-type="table"}). PD6D seeds showed similar proportions of fatty acids among PD6D homozygous lines (PD6D \#1--3, \#2--3, \#3--3, \#4--1) (Table [2](#Tab2){ref-type="table"}). However, PD6D leaves exhibited different proportions of the fatty acids LA, GLA and ALA among PD6D homozygous lines, and C18:2Δ^6,9^ was not detected in leaves (Table [3](#Tab3){ref-type="table"}).Table 3Fatty acid composition of leaves from D6DES T~2~ perilla (PD6D) and Yeobsil plants. Data represent mole% of fatty acid methyl esters. Experiments were performed in triplicate, and the mean values are shownFatty acidsYeobsilPD6D 1-3-1PD6D 2-3-2PD6D 3-3-2PD6D 4-1-1C16:025.521.522.224.720.4C16:1Δ^3t^3.33.23.23.12.8C16:20.90.50.60.60.4C16:32.53.13.43.73.3C18:03.34.54.34.04.4C18:1Δ^9^4.13.53.64.13.3LA23.014.513.911.39.5GLA-6.08.810.16.7ALA35.737.333.131.942.9SDA-4.25.15.14.9C20:01.81.91.81.61.5D6DES products0.010.113.915.211.6Total PUFA62.165.564.862.567.7 Fatty acid composition in developing seeds from PcD6DES transgenic perilla {#Sec21} ---------------------------------------------------------------------------- GLA and SDA accumulated to high levels in PD6D mature seeds. We measured GLA and SDA, as well as fatty acids, at different stages of seed development to determine how the compositions of these molecules changed throughout seed development (Table [4](#Tab4){ref-type="table"}). During early seed development in Yeobsil, saturated fatty acid content was relatively high compared to the late stage. In addition, the proportions of LA and GLA were similar. However, as the seeds approached the late stage of development, saturated fatty acid contents became lower and a large proportion of LA was converted to ALA. The fatty acid composition in developing seed stage 1 (DS1) and the mature stage DS4 resembled that of mature perilla leaves. The saturated fatty acid content in PD6D DS1 was almost the same as that in Yeobsil DS1. During late seed development, saturated fatty acid contents were lower and PUFAs contents were higher than at the early stage in both Yeobsil and PD6D.Table 4Fatty acid composition of developing seeds from PcD6DES T~2~ perilla (PD6D) and Yeobsil plants. Data represent mole% of fatty acid methyl esters. Experiments were repeated in triplicate, and the mean values are givenFatty acidYeobsilPD6D 4-1-1DS1DS2DS3DS4DS1DS2DS3DS4C16:021.920.412.18.221.819.311.98.0C18:06.26.52.52.16.36.92.62.0C18:1Δ^9^6.05.910.110.75.05.48.811.9C18:2Δ^6.9^\-\-\-\-\--0.30.9LA32.330.419.518.632.728.914.47.8GLA\-\-\--2.23.118.025.4ALA33.736.955.860.430.332.025.322.0SDA\-\-\--1.74.418.722.0 The change in the proportions of PUFA during seed development in Yeobsil and PD6D are shown in Table [4](#Tab4){ref-type="table"} and Fig. [6](#Fig6){ref-type="fig"}. In Yeobsil, the proportions of LA and ALA were similar in DS1, and after DS1, LA levels gradually decreased, whereas ALA levels gradually increased (Table [4](#Tab4){ref-type="table"}, Fig. [6a](#Fig6){ref-type="fig"}). In PD6D seeds, the proportions of fatty acids did not differ from those of Yeobsil in DS1. However, after DS1, the proportion of ALA decreased and SDA increased at the expense of ALA. In addition, the proportion of LA was lower than that of Yeobsil, and GLA appeared to be produced from LA (Table [4](#Tab4){ref-type="table"}, Fig. [6b](#Fig6){ref-type="fig"}). PUFAs were diversified, and the degree of unsaturation became higher in PD6D seeds, which is similar to Yeobsil at all stages of seed development (Fig. [6c](#Fig6){ref-type="fig"}).Fig. 6Changes in the proportion of each PUFA in (a) Yeobsil, (b) PD6D, and (c) changes in the proportion of total PUFAs during seed development Fatty acid analysis of neutral lipids and polar lipids in mature perilla seeds {#Sec22} ------------------------------------------------------------------------------ To investigate the differences in fatty acid compositions of polar lipids and neutral lipids from mature Yeobsil and PD6D (DS4) seeds, we extracted total lipids from the seeds, separated them using TLC (Additional file [2](#MOESM2){ref-type="media"}: Figure S4) and analyzed the fatty acid composition of each lipid using GC. The fatty acid compositions of neutral lipids, TAG, diacylglycerol and polar lipids were analyzed separately. The fatty acid composition of polar lipids in mature Yeobsil DS4 seeds was similar to that at DS1 (Tables [4](#Tab4){ref-type="table"} and [5](#Tab5){ref-type="table"}). The polar lipids from mature PD6D seeds contained more GLA and SDA than those of PD6D DS1 (Table [5](#Tab5){ref-type="table"}). GLA and SDA associated more with neutral lipids than with polar lipids in PD6D but were not detected in Yeobsil seeds.Table 5Fatty acid composition of neutral lipids and polar lipids from mature perilla seeds. Data represent mole% of fatty acid methyl esters. Experiments were repeated in triplicate, and the mean values are presentedPolar lipidsNeutral lipidsYeobsilPD6D 4-1-1YeobsilPD6D 4-1-1C16:020.222.27.87.4C18:07.27.92.32.3C18:1Δ^9^6.89.111.613.3C18:2Δ^6.9^\-\--1.3LA30.119.117.67.2GLA-15.7-25.9ALA35.719.860.821.8SDA-6.2-20.8 Seed weight and seed oil content of transgenic PcD6DES perilla {#Sec23} ---------------------------------------------------------------- To investigate the characteristics of transgenic PcD6DES perilla seeds compared with Yeobsil seeds, we measured seed weight and oil content. We weighed 100 seeds three times and calculated the average seed weights. The seed weight of Yeobsil was the highest (4.70 mg/seed), and average seed weight of T~2~ perilla seeds was slightly less (4.36 mg/seed; 4.09--4.52 mg/seed) than Yeobsil seeds (Fig. [7a](#Fig7){ref-type="fig"}). The seed weights measured in this study are similar to those reported by Asif \[[@CR22]\]. Meanwhile, the seed oil content showed different trends compared to seed weight. The fatty acid contents in PD6D seeds were 397.6 μg/mg seeds and was similar or 3.3--3.6% higher than that of Yeobsil seeds. The fatty acid contents in PD6D 1--3-1, 3--3-2 and 4--1-1 were 398.9, 410.6 and 411.8 μg/mg seeds, respectively (Fig. [7b](#Fig7){ref-type="fig"}), and the average seed oil content was 407.1 μg/mg seeds. Based on these data, the FAME levels per seed were as follows: Yeobsil, 1.87 mg FAME/seed; PD6D 1--3-1, 1.80 mg FAME/seed; PD6D 3--3-2, 1.84 mg FAME/seed; PD6D 4--4-1, 1.68 mg FAME/seed. The FAME levels per seed in the PD6D lines were almost the same or 89.8% those of Yeobsil seeds. The total seed oil content was approximately 40% in perilla, which is in agreement with the data from Asif \[[@CR22]\] and Shin and Kim \[[@CR24]\]. Compared to Yeobsil, the seed weight of PD6D was slightly lower, but these seeds possessed slightly higher oil contents.Fig. 7Analysis of (a) weight and (b) oil content of 100 WT perilla and PcD6DES perilla seeds. All experiments were performed in triplicate, and error bars indicate standard deviation Discussion {#Sec24} ========== In this study, we characterized PcD6DES, the first D6DES identified in Phytophthora spp., and found it to resemble other known fatty acid desaturases. PcD6DES contains cytochrome b5 domain, three histidine boxes and six TM domains (Fig. [1](#Fig1){ref-type="fig"}). Thus, we conclude that PcD6DES encodes a protein with characteristics of a 'front-end' fatty acid desaturase. Saccharomyces cerevisiae has only one fatty acid desaturase, Ole1p which catalyzes the conversion C16:0 and C18:0 into C16:1Δ^9^ and C18:1Δ^9^, respectively \[[@CR35]\]. Therefore, S. cerevisiae contains mainly four kinds of fatty acids, C16:0, C16:1Δ^9^, C18:0 and C18:1Δ^9^. Functional characterization of PcD6DES in budding yeast showed PcD6DES produce C16:2Δ^6,9^ and C18:2Δ^6,9^, although the proportion of C18:2Δ^6,9^ was barely detectable (Table [1](#Tab1){ref-type="table"}). This result suggests that PcD6DES might have a weak affinity for monounsaturated fatty acids, including C16:1Δ^9^ and C18:1Δ^9^ (Table [1](#Tab1){ref-type="table"}). The ratios of saturated fatty acids to unsaturated fatty acids did not differ much from those of yeast cultured with LA and/or ALA and without LA and/or ALA. These results likely indicate that fatty acid metabolism is regulated in yeast cells to maintain the appropriate levels of unsaturated fatty acids while they take up unsaturated fatty acids. However, unlike the fatty acid composition of budding yeast expressing PcD6DES, we detected C18:2Δ^6,9^ in PcD6DES perilla seeds (Fig. [3](#Fig3){ref-type="fig"}). This is likely because perilla seed oil contains little C16:1Δ^9^ and relatively high levels of C18:1Δ^9^, which is consistent with reports describing the detection of C18:2Δ^6,9^ in transgenic oilseed crops expressing a fungal D6DES \[[@CR12], [@CR13]\]. The sum of GLA and SDA levels from each progeny of the same T~0~ plant was highly variable (Table [2](#Tab2){ref-type="table"}, Additional file [1](#MOESM1){ref-type="media"}: Table S3). We divided the progenies into those with high and low contents of D6DES product, which we attributed to the presence of the transgene in a homozygous vs. hemizygous state. The results of genotyping by Basta treatment supported this hypothesis (Additional file [1](#MOESM1){ref-type="media"}: Table S3). Under Basta treatment, seedlings of the high GLA and SDA lines (putative homozygous lines) all survived, whereas those of low GLA and SDA lines (putative hemizygous lines) showed a 3:1 segregation ratio (Additional file [1](#MOESM1){ref-type="media"}: Table S3). Therefore, it appears GLA and SDA contents depend on zygosity, with higher levels seen in homozygous plants and lower levels detected in hemizygous plants. PcD6DES was expressed and PcD6DES products accumulated not only in seeds but also in leaves of transgenic perilla (Table [3](#Tab3){ref-type="table"}; Fig. [5](#Fig5){ref-type="fig"}), despite PcD6DES being expressed from a seed-specific vicilin promoter. It is hard to conclude vicilin promoter shows leaky expression pattern because the expression pattern of vicilin promoter from Pisum sativum has not been reported. We supposed a few possibilities which results in this phenomenon. First, vicilin promoter from Pisum sativum might be originally leaky promoter which is not regulated tightly. Second, when vicilin promoter moved to perilla from pea, it may not be spatially regulated in the same manner as it is in native species. There was a report when the seed-specific promoters from wheat and barley directed the expression of green fluorescence protein, the expression was leaky \[[@CR36]\]. Third, when T-DNA harboring the expression cassette of PcD6DES under the control of vicilin promoter was integrated into perilla genome, the spatial regulation of PcD6DES expression might be changed by positional effect. Although the expression of the vicilin promoter does not appear to be entirely exclusive to seed tissue, the expression of PcD6DES was 47.6-fold higher in seeds than in leaves. Seeds contained much higher levels of substrates for PcD6DES (71.6%) than leaves (58.7%) (Tables [2](#Tab2){ref-type="table"} and [3](#Tab3){ref-type="table"}). This difference is likely due to the varied PcD6DES expression levels and the differential availability of precursor contents between seeds and leaves. When the borage D6DES gene was expressed under the control of the cauliflower mosaic virus 35S promoter in tobacco (Nicotiana tabacum), the levels of substrates and products of D6DES were 74.2 and 22.8%, respectively, and the conversion rate was 31.5% \[[@CR20]\]. Meanwhile, in the current study, the levels of substrates and products of D6DES in transgenic perilla leaves were 58.7 and 15.2%, respectively, and the conversion rate was 26.0% (Table [3](#Tab3){ref-type="table"}). This difference is likely because the constitutive 35S promoter drove D6DES expression more strongly in leaves than the seed-specific promoter used in the current study, as well as the higher substrate content in tobacco leaves than in perilla leaves. Overall, these results support our findings described above. In the fatty acids of perilla leaves, C16:1Δ^3t^ is produced by FAD4 in chloroplasts \[[@CR37]\]. D6DES can convert C16:1Δ^9^ and C18:1Δ^9^ into C16:2Δ^6,9^ and C18:2Δ^6,9^, respectively, in budding yeast (Fig. [2](#Fig2){ref-type="fig"}). Therefore, C16:1Δ^3t^, not a substrate for D6DES, is not converted into C16:2Δ^6,9^. The fatty acid compositions of DS1 and polar lipids in mature seeds in Yeobsil were similar (Tables [4](#Tab4){ref-type="table"} and [5](#Tab5){ref-type="table"}). Seeds at the early stage of development contain little TAG \[[@CR23]\], instead mainly containing polar lipids. On the contrary, PD6D did not reflect this trend. PcD6DES products are thought to accumulate in polar lipids of mature PD6D seeds during seed development. The fatty acid compositions from DS4 and neutral lipids of mature seeds in both PD6D and Yeobsil were similar (Tables [4](#Tab4){ref-type="table"} and [5](#Tab5){ref-type="table"}), likely because almost all seed oil comprises neutral lipids. Given that polar lipids incorporate more 16:0 at sn-1 position than TAG \[[@CR38]\], polar lipids and DS1 contains more 16:0 than DS4 and neutral lipids (Tables [4](#Tab4){ref-type="table"} and [5](#Tab5){ref-type="table"}). Severe alteration of 16:0 from DS1 to DS4 was not by D6DES but by the relative proportion change of polar lipids and TAG. SDA of DS4 was gradually increased in PD6D because TAG content of DS4 is higher than earlier stage. TAG contains higher PUFAs than polar lipids in perilla (Table [5](#Tab5){ref-type="table"}). In Table [4](#Tab4){ref-type="table"}, Yeobsil DS4 contains more PUFAs than Yeobsil DS1. Thus, PD6D DS4 contains more GLA and SDA than PD6D earlier stage. The fatty acid composition of polar lipids from mature seeds indicated that GLA and SDA associate with membrane lipids and could not be completely transferred to TAG (Table [5](#Tab5){ref-type="table"}). The levels and patterns of PfFAD2, PfFAD3, PfFAD7--1 and PfFAD7--2 expression coincided with the previous report \[[@CR33]\]. The expression levels of endogenous genes, including PfFAD2 and PfFAD3 in DS3 and PfFAD7--1 and PfFAD7--2 in leaves, were lower in PD6D than in Yeobsil (Fig. [5](#Fig5){ref-type="fig"}a, b). Perhaps the high expression levels of PcD6DES and bar genes in DS3 and leaves, respectively, influence the endogenous genes responsible for the synthesis of PUFAs and lowered their expression. The expression level of PcD6DES gene in PD6D 4--1-1 is much higher in late stage than early stage (Fig. [5c](#Fig5){ref-type="fig"}). This result is in accordance with the expression of seed storage protein. The PcD6DES products of developing seeds in PD6D 4--1-1 were low in DS1 (3.9%) and DS2 (7.5%) but dramatically increased in DS3 (37.0%) and DS4 (48.3%) (Table [4](#Tab4){ref-type="table"}). The fatty acid analysis of developing seeds in PD6D 4--1-1 is consistent with the expression level of developing seeds in PD6D 4--1-1. The most common omega-3 and omega-6 fatty acids in vegetable oil are ALA and LA, respectively. Notably, these fatty acids are essential for human health. Vegetable oils from oilseed crops such as corn, sunflower, safflower, sesame, cottonseed and soybeans contain high levels of omega-6 fatty acid but little omega-3 fatty acid. If the ratio of omega-3 to omega-6 fatty acids decreases below the recommended 1:4 ratio due to the overconsumption of omega-6 fatty acid oil or cooking food in omega-6 fatty acid, there could be detrimental consequences to health \[[@CR39]\]. Studies have shown that a high intake of omega-6 fatty acids increases blood viscosity, vasospasm and vasoconstriction and decreases bleeding time \[[@CR39]\]. The ratio between omega-3 and omega-6 in PD6D seed oil is 1.35:1, which certainly exceeds the healthy recommended ratio. Moreover, PD6D is more beneficial to health because it can bypass the rate-limiting step from ALA to SDA, allowing SDA to be more efficiently converted to DHA \[[@CR3]\]. In PD6D seed oil, GLA and SDA accumulated to levels of up to 24 and 21%, respectively (Table [2](#Tab2){ref-type="table"}). By contrast, borage seeds contain 20--25% GLA, and evening primrose seeds contain 10% GLA, but they do not contain SDA \[[@CR20]\]. Blackcurrant seeds contain 15.8% GLA and approximately 2% SDA \[[@CR40], [@CR41]\], and hemp seeds contain 3.6% GLA and 2--3% SDA \[[@CR10], [@CR42]\]. Echium seeds contain 11.8% GLA and 13% SDA, which is the highest SDA content in natural land plants \[[@CR43]\]. While the sum of GLA and SDA from the plant seeds described above is up to 25%, PD6D seeds contain a similar amount of GLA to borage and a higher content of SDA than echium (Table [2](#Tab2){ref-type="table"}). The seed weight in perilla measured in the current study (\~ 4 mg) was similar to that measured by Asif \[[@CR22]\]. We detected a seed oil content of approximately 40% in perilla, which is also in agreement with previous results \[[@CR22], [@CR24]\]. Indeed, the introduction of fatty acid desaturase genes such as D6DES has not previously been shown to increase seed weight or seed oil content. Furthermore, transgenic plants generally demonstrate poor agronomic performance in traits other than their modified target traits. In PcD6DES perilla with the beneficial transgene activity the overall plant phenotype was similar to that of Yeobsil. There have been several reports of transgenic plants accumulating GLA and/or SDA in their seeds via the use of a D6DES transgene alone or in tandem with other fatty acid desaturase genes. In an early study, the expression of D6DES from cyanobacteria in transgenic tobacco resulted in GLA and SDA accumulation in seed oil \[[@CR44]\]. This was the first report of the biotechnological production of GLA and SDA in transgenic plants. Later, transgenic tobacco constitutively expressing D6DES from borage (Borago officinalis) was found to accumulate 13% GLA and 10% SDA in its seeds \[[@CR20]\]. In addition, canola plants coexpressing D6DES from the oleaginous fungus Mortierella alpina and Δ12 desaturase gene (Brassica napus) specifically in their seeds produced 40% GLA \[[@CR12]\]. Similarly, when D6DES from the oleaginous fungus Pythium irregulare was expressed under the control of the seed-specific napin promoter in Brassica juncea, GLA comprised 40% of seed oil \[[@CR13]\]. When the borage D6DES gene and Arabidopsis Δ15 desaturase gene were coexpressed in soybean driven by the soybean seed-specific β-conglycinin promoter, SDA accumulated to 29% of seed oil content \[[@CR45]\]. Linseed expressing the SDA-specific D6DES gene from Primula vialii under the control of the Vicia faba seed-specific USP promoter had a 13% SDA content in its seed oil \[[@CR15]\]. More recently, when the D6DES gene from the protozoan Saprolegnia diclina was expressed under the control of the Arabidopsis OLEOSIN promoter in safflower, GLA accumulated to 77% of the seed oil content, i.e., the highest reported GLA content for transgenic safflower \[[@CR46]\]. It is important to note that the GLA levels in transgenic seed oil reported by Liu et al. \[[@CR12]\], Hong et al. \[[@CR13]\] and Nykiforuk et al. \[[@CR46]\] were higher than those found in the current study. Furthermore, the SDA content in transgenic seed oil reported by Eckert et al. \[[@CR45]\] was also higher than we achieved. However, the results of Liu et al. \[[@CR12]\] and Eckert et al. \[[@CR45]\] were achieved via coexpression of D6DES and another desaturase gene, and there has been no report of higher GLA and SDA production in transgenic seed oil due to the introduction of a single gene. In addition, the production of perilla seeds containing 47.7% D6DES products (GLA, SDA and C18:2Δ^6,9^) due to the incorporation of only D6DES gene represents a dramatic improvement (Table [2](#Tab2){ref-type="table"}). Looking forward, SDA could be produced at very high levels if the ALA-preferred D6DES were introduced into perilla. For example, D6DES enzymes from Primula vialii and Primula luteola showed high ALA substrate specificity and produced SDA exclusively \[[@CR14], [@CR47]\]. Furthermore, perilla that produces very high levels of SDA could be used to produce EPA and DHA by introducing fatty acid elongase, Δ5 desaturase and Δ4 desaturase. Conclusions {#Sec25} =========== Two decades have been spent creating transgenic plants that produce higher levels of expensive functional fatty acids such as GLA and SDA in their seeds beyond what wild plants are capable of producing. In this study, we developed transgenic perilla with the very high content over 45% of both GLA and SDA. These plants might serve as an important resource for producing omega-3 oil capsules as health food and promoting human health. In addition, other genes could be added to these plants to create transgenic perilla that produce fish-oil-like oil in their seeds and provide further health benefits. Additional files ================ {#Sec26} Additional file 1:Table S1. Primers used in this study. Nucleotide symbols are as follows: Y, C/T; R, G/A; W, A/T; D, G/A/T; N, A/T/G/C. Table S2. Segregation ratio of D6DES T~1~ perilla plants treated with Basta. Table S3. Genotyping of D6DES T~2~ perilla plants treatment with Basta. (ZIP 3970 kb) Additional file 2:Figure S1. Vector constructs containing the PcD6DES gene. (A) Vector for yeast transformation. PGAL1 and CYS TT represent galactose-inducible GAL1 promoter and CYC1 transcriptional terminator, respectively. URA encodes a biosynthetic [enzyme](https://en.wikipedia.org/wiki/Enzyme) of uracil, as a marker gene for yeast selection. Amp^R^ encodes β-lactamase that inactivates antibiotics ampicillin, as a marker gene for E. coli selection. (B) Vector for plant transformation. pCAMBIA3300 was used as a backbone vector. Pvic and Tocs indicate vicilin promoter and octopine synthase III terminator, respectively. LB and RB represent left border and right border, respectively. Each box represents a gene expression cassette. B, BamHI; C, ClaI; H3, HindIII; K, KpnI; N, NotI; P, PstI; R1, EcoRI; Sc, SacI; X, XbaI, Xh, XhoI. Figure S2. The predicted transmembrane domains of fatty acid desaturases including (A) Phytophthora citrophthora D6DES, (B) evening primrose (Oenothera biennis) D6DES (GenBank accession No. EU416278) and (C) Perilla frutescens var. frutescens FAD2 (GenBank accession No. KP070823) by TOPCONS. Figure S3. The expression from PcD6DES gene in RNA level from S. cerevisiae. RT-PCR from total RNAs of PcD6DES yeast. pYES2 is yeast cells harboring a blank vector as an negative control. PcD6DES is yeast cells carrying pYES2-PcD6DES. ScAct1 is a reference gene from S. cerevisiae actin gene (GenBank accession No. L00026). -- and + indicate non-induction and induction, respectively. The induction method of yeast was described in Methods section. M, 1 kb DNA ladder. Figure S4. TLC analysis of lipids extracted from perilla mature seeds. The lipids were developed and visualized under the ultra violet after the primuline spraying. The spots corresponding neutral lipids (TAG and DAG) and polar lipids were scraped off and the fatty acid composition was analyzed with GC. The method using this experiment is described in the 'Thin layer chromatography (TLC)' subsection of Methods section (ZIP 537 kb) ALA : α-linolenic acid D6DES : Δ6 desaturase DHA : cis-4,7,10,13,16,19-docosahexaenoic acid DS : developing seed stage EPA : cis-5,8,11,14,17-eicosapentaenoic acid FID : flame ionization detector GLA : γ-linolenic acid LA : linoleic acid SDA : stearidonic acid TM : transmembrane domain VLCPUFA : very long chain polyunsaturated fatty acid Not applicable. Funding {#FPar1} ======= The overall process of this research was supported by a research grant of Rural Development Administration's project (Project No. PJ01257102, K-RL), Republic of Korea, and the TLC data analysis was separately supported by the Mid-Career Researcher Program of the National Research Foundation of Korea (NRF-2017R1A2B4007096, HUK), Republic of Korea. Availability of data and materials {#FPar2} ================================== The sequence of PcD6DES gene from this study has been deposited to the NCBI GenBank (<https://www.ncbi.nlm.nih.gov/genbank/>) as an accession No. DQ836059. K-HK performed gene cloning, functional analysis in yeast and Perilla transformation; K-RL, JBK, JKK carried out the fatty acid analysis; S-BH screened the Phytophthora strain; K-RL, IJ conducted qRT-PCR and TLC experiments; MHL raised perilla plants to supply seeds for transformation; K-RL, K-HK, HUK analyzed the data; K-RL, K-HK wrote the paper. All authors read and approved the final manuscript. Ethics approval and consent to participate {#FPar3} ========================================== Not applicable. Consent for publication {#FPar4} ======================= Not applicable. Competing interests {#FPar5} =================== The authors declare that they have no competing interests. Publisher's Note {#FPar6} ================ Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The outdoor opera, Dante's "La Vita Nuova", which Dr. Lecter and Mr. Pazzi see in Florence, was especially composed for the movie. Composer Patrick Cassidy did not stop at the three minute part as performed in the movie, but composed an entire aria, "Vide Cor Meum". Hannibal asks Pazzi about being demoted from the Il Mostro case. Il Mostro was a serial killer about whom Hannibal gives clues to Pazzi. This was a subplot that was filmed but never used as it was thought to be too complicated. The right side of the van following Clarice from her house is damaged with a headlight that does not match the undamaged, left side. Later, as the van is seen before crashing into items, the damage is missing and the headlight matches the other side. Hannibal Lecter: Dear Clarice, I have followed with enthusiasm the course of your disgrace and public shaming. My own never bothered me, except for the inconvenience of being incarcerated. But you may lack perspective. It's never made certain. Hannibal, when he says "above or below the wrist?" suggests that he did but he could have been threatening to cut off Clarice's hand in order to scare her into giving him the key. It's also possible Hannibal chopped off only his thumb to wriggle out of the cuff. What is certain is that he definitely did not try to cut through the chain on the cuffs; it would have been too unbelievable and he clearly doesn't have the use of that hand in the final scene. Q Why did Mason Verger cut off his own face? A Mason was a sexual deviant who was also infatuated with Lecter. Lecter had given him a 'popper' [in the book, a mixture of hallucinogenic and hypnotic drugs] before suggesting that he cut off his face and feed it to the dogs. Verger was based on the real case of a man named Michael who, while under the influence of PCP, did the same thing -- cut off parts of his face and fed them to some dogs. For more information on Michael, see here. Q Why didn't Jodie Foster return to play Clarice Starling? A In an interview for Total Film magazine, Foster said:The official reason I didn't do Hannibal is I was doing another movie, Flora Plum. So I get to say, in a nice dignified way, that I wasn't available when that movie was being shot... Clarice meant so much to Jonathan and I, she really did, and I know it sounds kind of strange to say but there was no way that either of us could really trample on her.
Jehovah's Witnesses with OBVIOUS drinking problems? My in-laws hide liquor in their room. They said it's to keep it from their son and it helps my MIL sleep. My kids found it and brought it up in front of them. Two different stories at once, ahahhahaa. I think they were embarrased. The trouble with "modest" consumption of alcohol is that every JW has their own idea of what constitutes "modest consumption." Early on, I was warned off the JWs a non-JW relative, following her attendance at a Jehovahs Witness wedding reception. She was quite appalled by the heavy drinking that she saw going on at that event. Later, I knew an elder who was rather concerned when named to attend the next session of the Kingdom Ministry School. He told us that he was going to "have to dry himself out beforehand" - referring to his fondness for apple wine, which he consumed for by the flagon full. For nine months after the 1975 debacle, that same elder never ventured out once in field service, and would regularly demolish a 2 litre flagon of sherry over the course of one night. Throughout all this, he kept his position, and was always quite highly regarded in the JW community. (a lot to do with his being a "closet" drinker, I think - you would never ever see him in any public bar around the place). I myself was not exactly squeaky clean when it came to the subject of the brown bottle. Raised by parents who were modest drinkers, I was first introduced to drinking when I began associating with the local congregation. There was considerable social pressure to indulge in the stuff, and as others have noted, it was an easy habit to adopt - being one of the few escapes / indulgences / releases (call it what you will!) that a Witness is permitted to have. The "guidance" that I received from the brother whom I studied with was that it was all-right to have the "occassional" heavy session on the grog, but one should still at all times "have all their faculties" about them. (This is indeed what he - an elder and regular pioneer - did). The immediate problem here is in precisely defining what constitutes "occassional", and where the boundary line between "still having all ones faculties" and having lost them is located! In my 28 years "in the Truth", I both witnessed - and participated in - much abuse of alcohol. Reminds me of something that happened shortly after I'd disassociated... I had remarried a nice non-JW, and we were visiting my dad's sister and her hubby up in Klamath Falls, Oregon. My aunt and uncle-by-marriage were also non-JWs... I told them a story about how my brother and I [both bullied into the JW religion, me from the age of 5, him from birth] used to sneak into the kitchen and get my dad's bottle of booze out of the refrigerator, pour some of the stuff into the sink, and set it on fire. We'd crouch in the dark around the kitchen sink, watching that pretty blue and multi-colored flame as the booze burned. My uncle looked at me, startled, and said, "That must have been some pretty hard liquor!" At that instant, I realized that my dad must have been a closet alcoholic, all those years that he was beating the "truth™ " into me and my brother.... Because he ALWAYS had some kind of hard liquor around.... A lot of things about my parents' Jehovah's Witness-run family system snapped into focus, then. Dear old self-righteous Daddy was a blazing alcoholic, and all those temper tantrums that he threw were probably fueled by alcohol. the head with A beer bottle and broke it ( thank goodness I was sporting AFRO,A hairstyle in the60,s) My ex had A bad temper especially when she drink. After we became JW, that anger turn to the kids. The funny thing about the beer bottle over the head, she called the police in order for me to leave. When the police got there, they ask me did I want to press charges against her. The good old days.
Partitioning of uncharged local anesthetic benzocaine into model biomembranes. The partitioning of uncharged local anesthetic benzocaine (BzC) into molecular aggregates formed by cationic surfactant decylammonium chloride (DeAC) and phospholipid dipalmitoylphosphatidylcholine (DPPC) was studied from the surface tension and light transmittance measurements. The quantities concerning the partitioning of BzC, the compositions of BzC in the surface-adsorbed film and micelle and three kinds of differential partition coefficients corresponding to phase transitions of the DPPC bilayer membrane were evaluated from thermodynamic analysis of the experimental data. The surface-adsorbed film and micelle were more abundant in BzC than the aqueous solution and significantly large differential partition coefficients for the DPPC membranes were observed. The results clearly showed that the BzC molecules greatly partitioned into hydrophobic environments produced by surfactant-monolayer and phospholipid-bilayer membranes. The partitioning behavior of BzC was also compared with that of charged local anesthetic procaine hydrochloride (PC.HCl). It was shown that the PC.HCl molecule did not or hardly partition into such hydrophobic environments. The contrasting results of the partitioning between BzC and PC.HCl are attributable to the drastic decrease of hydrophilicity of BzC due to the lacking of ionic polar head group in comparison with PC.HCl.
Vivian Green Vivian Sakiyyah Green (born May 22, 1979) is an American R&B singer-songwriter and pianist. Early life Green was born May 22, 1979 in the East Oak Lane neighborhood of Philadelphia, and took an interest in singing, playing the piano, and songwriting at a very young age. At the age of thirteen, she became a member of a female quintet called Younique. She is a graduate of what is now Parkway Northwest High School for Peace and Social Justice. Green has credit for writing "Dear God" by Boyz II Men, from their 1997 album Evolution. Green received her big break at the age of nineteen when she became a backup singer for Jill Scott, who took her on an international tour. She signed to Columbia Records in November 2002. Career 2001–2003: A Love Story In 2002, Green released her debut album, A Love Story, which featured the number-one single "Emotional Rollercoaster". In the meantime, Green made a cameo appearance in the Cole Porter biopic De-Lovely singing a cover version of Porter's 1930 song "Love for Sale", which made the film's soundtrack album. She also played Brenda Holloway in an episode of the first season of NBC's drama series American Dreams, entitled "The Carpetbaggers" (originally aired on April 6, 2003), performing a rendition of Holloway's 1964 hit "Every Little Bit Hurts". 2004–2006: Vivian In 2005, she appeared on Cyndi Lauper's The Body Acoustic album on the tracks "I'll Be Your River" and "Sisters of Avalon". During the spring of 2005, three years after the release of her debut album, Green released her second studio album Vivian. It featured the lead single "Gotta Go Gotta Leave (Tired)", which peaked at No. 24 on the R&B chart and No. 1 on the dance charts The song also charted No. 1 on the Hot Adult Airplay. The track known as "I Like It (But I Don't Need It)" followed up as the album's second single. The song followed up the previous single's success by also reaching #1 on the dance charts. 2007–2011: Beautiful In 2007, Green appeared on Guru's album Jazzmatazz, Vol. 4: The Hip-Hop Jazz Messenger: Back to the Future on the track "Fine and Free". While performing at a gig in support of her second album, Green announced that she is currently recording her third full-length album on Koch Records. In April 2009, she signed a 3-album deal with E1 Music with the first album under the deal set to be released in Summer 2009. Her third album titled Beautiful was released April 6, 2010. The songs explore the ins and outs of love from a variety of perspectives, from the youthful romanticism of "Somewhere" to the playful insight of "So Good" and "Better Man" to the hard-won intensity of "Masterpiece" and "Beautiful." In contrast to her first two albums, which were recorded in a variety of studios with multiple producers, Vivian approached the recording of Beautiful in a more intimate, organic manner. With the exception of "Save Me," which she cut with Jason Farmer (Keyshia Cole, Wyclef Jean, Rihanna) in the producer's seat, Vivian recorded the entire album with Grammy-nominated producer Anthony Bell, a longtime friend and collaborator who made key production contributions to her first two albums, and whose extensive resume also includes work with Jazmine Sullivan, Jewel, Musiq, Raheem DeVaughn and Jill Scott. In 2011, she collaborated with Phoe Notes for a winter single titled "Missing You". It was released digitally on December 9. Phoe Notes and Green shot a video for the track on December 16. Additionally, she recorded the track "Keep On Going" for the Good Times – London and "Let It Burn" for the Birds Eye Riddim compilations. 2012–2013: The Green Room In 2012, her single, "Oh Freedom" for the Soundtrack for a Revolution was released on January 3, 2012. Later in the year, she did a couple of collaborations which included "Love" (w/Zion) for the album Legacy, "La La Means I Love You" (w/Bob Baldwin) for the album Betcha By Golly Wow: The Songs Of Thom Bell, and "Still Here" (w/Brian Culbertson) for the album Dreams. On August 7, 2012, Green released "Anything Out There" the lead single from her fourth album The Green Room. The album was released on October 9, 2012. In 2013, she undertook a few festivals and concerts in addition to TV appearances on BET and Centric's music series. 2014–2016: Vivid In 2014, she became the first artist signed to rapper/producer Kwamé's record label, Make Noise Recordings. Vivid, her fifth studio album was distributed via Caroline Records. On April 7, 2015, the first single released from the album was "Get Right Back to My Baby". In 2015 "Get Right BackTo My Baby" went to No. 2 on Billboard's UAC chart. Vivian was also nominated for a Soul Train Award . In 2016 Vivian released "Grown Folks Music(Work" which went to the top 15 on Billboard's UAC chart. 2017–present: VGVI On July 7, 2017, Vivian Released the first single off her sixth album VGVI, "I Don't Know." The song became a top-10 hit on Billboard's Adult R&B chart. VGVI was released on September 15, 2017. Personal life Between her first and second albums, she took a three-year hiatus. In 2004, she gave birth to her son Jordan. Vivian is now a full-time advocate for special needs children, publicly speaking about her experiences. Discography Studio albums A Love Story (2002) Vivian (2005) Beautiful (2010) The Green Room (2012) Vivid (2015) VGVI (2017) Award history BET Awards 2003: Best R&B Female Artist (nominated) Lady of the Soul Train Awards 2003: Best Solo R&B/Soul Single "Emotional Rollercoaster" (nominated) 2003: Best Solo R&B/Soul Album of the Year A Love Story (nominated) 2003: Best Solo R&B/Soul or Rap New Artist: Vivian Green (nominated) Soul Train Awards 2015: Centric Certified Award (nominated) References External links Official website Category:African-American female singer-songwriters Category:African-American singer-songwriters Category:American female singer-songwriters Category:African-American pianists Category:American women pianists Category:American rhythm and blues singer-songwriters Category:American soul singers Category:Columbia Records artists Category:Living people Category:Neo soul singers Category:Musicians from Philadelphia Category:Rhythm and blues pianists Category:1979 births Category:Singers from Pennsylvania Category:Songwriters from Pennsylvania Category:American contemporary R&B singers Category:21st-century American women singers Category:Ballad musicians Category:21st-century American singers Category:21st-century American pianists
Oxidative susceptibility of low-density lipoproteins--influence of regular alcohol use. In population studies, a low-to-moderate intake of alcohol has been consistently linked to a lower risk of coronary artery disease. The recent suggestion that alcoholic beverages may be conferring this decrease in risk because they contain antioxidant phenolic compounds that reduce the oxidizability of low-density lipoprotein (LDL) has to be reconciled with the possible counteracting influence of a pro-oxidant effect of alcohol. In a controlled crossover study, we have now measured the oxidizability of LDL in 27 regular beer drinkers during consecutive 4-week periods, wherein they consumed a high versus low alcohol beer (4.9 vs. 0.9% alcohol v/v, respectively), with the two beers being similar in phenolic content. This resulted in a decrease in alcohol consumption by approximately 80% (408 +/- 25 ml/week vs. 75 +/- 11 ml/week). During the low alcohol period, there was no change in LDL vitamin E or its cholesterol or protein content. Analysis of LDL oxidation kinetics revealed an increase in oxidizability during the high alcohol phase. This was despite a decrease in arachidonic acid content of LDL and a corresponding increase in palmitic acid during high alcohol intake--a change in fatty acid composition that has the potential to favor a decrease in oxidizability. Our results suggest that alcohol ingestion increases LDL oxidation, despite reducing the polyunsaturated fatty acid composition. The overall effect of alcoholic beverages on LDL oxidation may be a balance between the pro-oxidant and antioxidant activity of its various constituents. The predominant pro-oxidant effect demonstrated in these beer drinkers, although not relevant to any potential decrease in coronary artery disease, may be important in the pathogenesis of alcohol-related disease in other organ systems.
Libya: France urges special UN support Published duration 28 August 2014 image copyright EPA image caption Tripoli's international airport has been closed since mid-July because of heavy fighting France is calling for "exceptional support" for Libya, warning the country could fall into chaos without United Nations intervention. If no action is taken, French President Francois Hollande warned, "terrorism will spread across the region." His comments come a day after the UN Security Council called for an immediate ceasefire in Libya. It is also seeking sanctions against those involved in the surge in violence between rival militias. The names of those to face sanctions have not yet been decided. However, the Security Council has been alarmed by the increase in fighting between militia groups and Libya's army factions in recent weeks. On 23 August a coalition of militias, including some Islamist groups, operating under the banner Libya Dawn, seized control of the international airport in the capital, Tripoli from a Zintan-based militia. The victory, which secures the alliance's control over the capital, ends a five-week siege.
A group of north Dartmouth teens will become beekeepers this summer through a program called the Healthy Honeybees Project. There will be six active "queen bee" teens, who will help raise the bees, extract the honey, sell and market it, and another 10 or 15 "worker bees," who will help out where they can. They'll have two experienced beekeepers involved to oversee the progress and look out for any safety issues. This social enterprise is the brainchild of Stewart Zaun, program coordinator with Family S.O.S., a non-profit organization that helps out both parents and youth with in-class and after-school programs. Up and buzzing by June "We were trying to come up with some kind of enterprise project, and the usual ideas, like bracelets and bake-sales, were going around," he said. "My cousin's a beekeeper. I was sitting on her porch watching the bees flying around, and it came to me." The teens, who meet at the Dartmouth North Community Centre, will be spearheading the project with community partners, such as the Centre for Entrepreneurship, Education, and Development and Scotian Bees and Honey, who are donating one of the hives. Two hives will be located at The Guy Jacobs Community Garden in Dartmouth. Zaun says the city has all but signed off on the project. He's expecting the hives to be up and buzzing by June.
Scott Ocamb I have been delivering software solutions since the 1980's. I began my career as a developer and architect using Microsoft technologies. I always had a passion when it comes to software. Since my early days, I worked evenings and weekends learning the next new thing. I have consulted at dozens of firms, large and small in the Delaware Valley. This has exposed me to both the good and the bad in the software world. Seeing things done right and perhaps more importantly wrong gives me a unique perspective on delivering software. In 2006, I began to focus on delivering software following Agile principles. I discovered that practicing Agile is hard. As I moved between various consulting assignments, I noticed many firms missed some fundamental points of agile. It is easy to follow the steps but miss the point of Agile and thus dilute much of its value. I discovered that I have a knack for noticing these deficiencies and recommending alternatives that make a difference. Risk Free Pricing for New Customers Agile philosophy embraces small batch sizes and short Build - Measure - Learn feedback cycles. I incorporate this idea for customers who have never worked with me before. Every situation is different but in general an engagement with me begins with a short discovery phase of a week or two. If you are following Scrum, the timing of the phase coincides with the Scrum cycle. I attend the Scrum meetings so I can observe the team. If your team is new to agile I interview stake holders and together we come to and understand about how agile would work in your firm. The deliverable of the Discovery Phase is a detailed set of recommendations. If you are happy my work, we work together to develop a statement of work to implement any necessary improvements. This will be billed at the normal rate for as long as you need me. If you are not happy with my work, you are not obligated to pay for the discovery phase. My hope is, new customers will feel comfortable working with me for the first time. Selected Recommendations Darren Talham - Chief Software Architect at FidleiTrade Scott and I worked together for over a year at FideliTrade where he played a critical role in transforming the development group into an Agile Scrum team. Scott was extremely effective at introducing Scrum to the business owners and stakeholders, and he quickly gained their confidence and buy-in for the Scrum methodology. During his tenure, he built two Scrum teams from the ground up and acted as Scum Master and Agile Coach for the organization. Scott has thorough knowledge of the Agile Scrum methodology, and his knowledge goes far beyond theory. He is very hands on and is able to take complicated and difficult concepts and turn them into working processes. Not only did Scott implement our Agile process, he also configured and managed our toolsets to fit our specific needs. When Scott left us we had a fully functioning Agile process in place as well as all the tools we need to keep the process running smoothly. In addition to his Agile expertise, Scott has expert knowledge of the DevOps approach to software delivery. He was instrumental in setting up our DevOps procedures on Azure, and helped us automate our build and release pipelines integrating Team Services and Azure. I highly recommend Scott for any organization looking to implement an Agile process, or improve on their existing processes. Scott's knowledge and experience, along with his passion, guarantees that he will add value everywhere he goes.
Q: Can't build working Java app with gRPC, Protobuf and BoringSSL to JAR using Maven I have problem with building my Java app to jar file using Maven. Application is using gRPC and Protobuf. When I start my app in IntelliJ everything work just fine, problem is when I want to build jar with Maven... I don't have much experience with creating pom files. I tried to find some solution but nothing works and I ended up with pom.xml as below: [...] <properties> <grpc.version>1.17.1</grpc.version> <protoc.version>3.5.1-1</protoc.version> <netty.tcnative.version>2.0.13.Final</netty.tcnative.version> [...] </properties> <dependencies> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-protobuf</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-stub</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-netty</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.netty</groupId> <artifactId>netty-tcnative-boringssl-static</artifactId> <version>${netty.tcnative.version}</version> <scope>runtime</scope> </dependency> [...] </dependencies> <build> <extensions> <extension> <groupId>kr.motd.maven</groupId> <artifactId>os-maven-plugin</artifactId> <version>1.5.0.Final</version> </extension> </extensions> <plugins> <plugin> <groupId>org.xolstice.maven.plugins</groupId> <artifactId>protobuf-maven-plugin</artifactId> <version>0.5.1</version> <configuration> <protocArtifact>com.google.protobuf:protoc:${protoc.version}:exe:${os.detected.classifier} </protocArtifact> <pluginId>grpc-java</pluginId> <pluginArtifact>io.grpc:protoc-gen-grpc-java:${grpc.version}:exe:${os.detected.classifier} </pluginArtifact> </configuration> <executions> <execution> <goals> <goal>compile</goal> <goal>compile-custom</goal> </goals> </execution> </executions> </plugin> <plugin> <groupId>org.apache.maven.plugins</groupId> <artifactId>maven-enforcer-plugin</artifactId> <version>1.4.1</version> <configuration> <source>1.8</source> <target>1.8</target> </configuration> <executions> <execution> <id>enforce</id> <goals> <goal>enforce</goal> </goals> <configuration> <rules> <requireUpperBoundDeps/> </rules> </configuration> </execution> </executions> </plugin> <plugin> <artifactId>maven-assembly-plugin</artifactId> <configuration> <archive> <manifest> <mainClass>pl.test.Main</mainClass> </manifest> </archive> <descriptorRefs> <descriptorRef>jar-with-dependencies</descriptorRef> </descriptorRefs> </configuration> </plugin> </plugins> </build> And this is the exception when I try to start gRPC server with SSL context: Exception in thread "Thread-2" java.lang.UnsatisfiedLinkError: failed to load the required native library at io.netty.handler.ssl.OpenSsl.ensureAvailability(OpenSsl.java:346) at io.netty.handler.ssl.ReferenceCountedOpenSslContext.<init>(ReferenceCountedOpenSslContext.java:202) at io.netty.handler.ssl.OpenSslContext.<init>(OpenSslContext.java:43) at io.netty.handler.ssl.OpenSslServerContext.<init>(OpenSslServerContext.java:347) at io.netty.handler.ssl.OpenSslServerContext.<init>(OpenSslServerContext.java:335) at io.netty.handler.ssl.SslContext.newServerContextInternal(SslContext.java:422) at io.netty.handler.ssl.SslContextBuilder.build(SslContextBuilder.java:447) at pl.test.grpc.GrpcServer.start(GrpcServer.java:80) at pl.test.app.Main.lambda$new$0(Main.java:80) at java.lang.Thread.run(Thread.java:748) Caused by: java.lang.ClassNotFoundException: io.netty.internal.tcnative.SSL at java.net.URLClassLoader.findClass(URLClassLoader.java:381) at java.lang.ClassLoader.loadClass(ClassLoader.java:424) at sun.misc.Launcher$AppClassLoader.loadClass(Launcher.java:349) at java.lang.ClassLoader.loadClass(ClassLoader.java:357) at java.lang.Class.forName0(Native Method) at java.lang.Class.forName(Class.java:348) at io.netty.handler.ssl.OpenSsl.<clinit>(OpenSsl.java:85) at io.grpc.netty.GrpcSslContexts.configure(GrpcSslContexts.java:194) at pl.test.grpc.GrpcServer.getSslContextBuilder(GrpcServer.java:72) ... 3 more I'm building it using command: mvn clean compile assembly:single Can someone help with creating working pom file? The result doesn't have to be single jar file, it might be multiple jars. A: I found solution, maybe it will help someone deal with the same problem. We have to add dependency io.netty.netty-handler and set compatible versions of io.grpc.grpc-netty, io.netty.netty-tcnative-boringssl-static and io.netty.netty-handler as it is described in table over here https://github.com/grpc/grpc-java/blob/master/SECURITY.md#netty. Here's my current pom.xml [...] <properties> <grpc.version>1.17.1</grpc.version> <protoc.version>3.5.1-1</protoc.version> <netty.tcnative.version>2.0.17.Final</netty.tcnative.version> <netty.handler.version>4.1.30.Final</netty.handler.version> [...] </properties> <dependencies> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-protobuf</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-stub</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.grpc</groupId> <artifactId>grpc-netty</artifactId> <version>${grpc.version}</version> </dependency> <dependency> <groupId>io.netty</groupId> <artifactId>netty-handler</artifactId> <version>${netty.handler.version}</version> </dependency> <dependency> <groupId>io.netty</groupId> <artifactId>netty-tcnative-boringssl-static</artifactId> <version>${netty.tcnative.version}</version> <scope>runtime</scope> </dependency> [...] </dependencies> <build> <extensions> <extension> <groupId>kr.motd.maven</groupId> <artifactId>os-maven-plugin</artifactId> <version>1.5.0.Final</version> </extension> </extensions> <plugins> <plugin> <groupId>org.xolstice.maven.plugins</groupId> <artifactId>protobuf-maven-plugin</artifactId> <version>0.5.1</version> <configuration> <protocArtifact>com.google.protobuf:protoc:${protoc.version}:exe:${os.detected.classifier} </protocArtifact> <pluginId>grpc-java</pluginId> <pluginArtifact>io.grpc:protoc-gen-grpc-java:${grpc.version}:exe:${os.detected.classifier} </pluginArtifact> </configuration> <executions> <execution> <goals> <goal>compile</goal> <goal>compile-custom</goal> </goals> </execution> </executions> </plugin> <plugin> <groupId>org.apache.maven.plugins</groupId> <artifactId>maven-enforcer-plugin</artifactId> <version>1.4.1</version> <configuration> <source>1.8</source> <target>1.8</target> </configuration> <executions> <execution> <id>enforce</id> <goals> <goal>enforce</goal> </goals> <configuration> <rules> <requireUpperBoundDeps/> </rules> </configuration> </execution> </executions> </plugin> <plugin> <artifactId>maven-assembly-plugin</artifactId> <configuration> <archive> <manifest> <mainClass>pl.test.Main</mainClass> </manifest> </archive> <descriptorRefs> <descriptorRef>jar-with-dependencies</descriptorRef> </descriptorRefs> </configuration> </plugin> </plugins> </build> And now I can build jar using command: mvn clean compile assembly:assembly
LOS ANGELES – The sheriff's deputy who arrested Mel Gibson for drunken driving six months ago says his superiors have harassed him ever since a report detailing the star's anti-Semitic tirade was leaked to a celebrity news Web site. Deputy James Mee was transferred to another assignment and interrogated for several hours, and investigators seized a computer and phone records during a search of his home, his attorney told The Los Angeles Times for its Thursday editions. "His life and career would be a lot different had he not made that arrest," attorney Richard Shinee said. Neal Tyler, a division chief who oversees the sheriff's office where Gibson was booked, denied that Mee was singled out and said he didn't know of any problems with Mee's treatment. He declined to discuss Mee's specific complaints because of confidentiality rules, but he said, "I disagree with the assessment that personnel in the department or at the station have been relating to him or supervising him in an unfair manner." Mee arrested Gibson July 29 in Malibu on suspicion of driving under the influence of alcohol. An arrest report signed by Mee and posted on the celebrity news Web site TMZ.com said Gibson was belligerent and quoted him as saying: "The Jews are responsible for all the wars in the world." The actor-director later apologized to the Jewish community and pleaded no contest to a misdemeanor charge of drunken driving. After Gibson's much-publicized arrest, investigations were opened into whether Gibson received preferential treatment, and into who leaked Mee's report to TMZ.
Q: How to create a week, month, year summary of a database I want to create an application which one is summary the values of each column. I have a table like this: Each rows contains one goods Date \| Company_Name \| Order_cost \| Weight \| 2013-05-15\| Dunaferr \| 310 \| 1200 \| 2013-05-18\| Pentele \| 220 \| 1600 \| 2013-05-25\| Dunaferr \| 310 \| 1340 \| and what I exactly need is a table or view which contains the totals for the weights column for each week which is supposed to be extracted from the date column! Something like that company_name \| week1 \| week2 \| week3 \| week4 ... dunaferr \| 35000 \| 36000 \| 28000 \| 3411 pentele \| 34000 \| 255000 \| 3341 \| 3433 Is there any way to do this? A: I would do this in two steps: First step complete an sql query getting a summary with a sum for weight with a group by for yearweek SELECT Company_Name, YEARWEEK(Date), sum(weight) FROM table GROUP BY Company_Name, YEARWEEK(Date) http://dev.mysql.com/doc/refman/5.5/en/date-and-time-functions.html#function_yearweek. Second step would be to process this into the required format in the application year. If you absolutely have to do this in the database, then you are looking at implementing a pivot table, which has previously been covered here: MySQL pivot table
Q: Php api via array Am trying to read a script api which returns an array: $api_key = "Uez4TWYH6OAQQHoUcICWJ8UUFYmwQ"; $file_id = "LNzcOp2b1352047884"; $ch=curl_init(); curl_setopt($ch,CURLOPT_URL,'http://ads.ngsms.tk/api/info.php?api_key='.$api_key.'&file_id='.$file_id); curl_setopt($ch, CURLOPT_RETURNTRANSFER, true); $api = curl_exec($ch); $api = print_r($api); Echo $api['file_id']; The above displays: Array ( [file_id] => LNzcOp2b1352047884 [file_name] => sic_ftp_3rda.sisx [file_type] => application/octet-stream [file_size] => 65144 ) How can I get the file_name and other values? A: To get any value within the array reference it in the same way you have done for file_id but instead replace the key with the value you are after e.g: $api['file_id']; $api['file_name']; $api['file_type']; $api['file_size']; Then to simply show this on the page, you can use echo: echo $api['file_id']; echo $api['file_name']; echo $api['file_type']; echo $api['file_size']; So your full code would be: <?php $api_key = "Uez4TWYH6OAQQHoUcICWJ8UUFYmwQ"; $file_id = "LNzcOp2b1352047884"; $ch=curl_init(); curl_setopt($ch,CURLOPT_URL,'http://ads.ngsms.tk/api/info.php?api_key='.$api_key.'&file_id='.$file_id); curl_setopt($ch, CURLOPT_RETURNTRANSFER, true); $api = curl_exec($ch); //print_r($api); $fileid = get_string_between($api, "[file_id] => ", "[file_name] "); $filename = get_string_between($api, " [file_name] => ", " [file_type] => "); $filetype = get_string_between($api, " [file_type] => ", " [file_size] =>"); $filesize = get_string_between($api, " [file_size] => ", ")"); echo "ID: $fileid <br /> name: $filename <br />type: $filetype <br /> size: " .$filesize; function get_string_between($string, $start, $end){ $string = " ".$string; $ini = strpos($string,$start); if ($ini == 0) return ""; $ini += strlen($start); $len = strpos($string,$end,$ini) - $ini; return substr($string,$ini,$len); }
Characterization of the caspase cascade in a cell culture model of SOD1-related familial amyotrophic lateral sclerosis: expression, activation and therapeutic effects of inhibition. There is increasing evidence that apoptosis or a similar programmed cell death pathway is the mechanism of cell death responsible for motor neurone degeneration in amyotrophic lateral sclerosis. Knowledge of the relative importance of different caspases in the cell death process is at present incomplete. In addition, there is little information on the critical point of the death pathway when the process of dying becomes irreversible. In this study, using the well-established NSC34 motor neurone-like cell line stably transfected with empty vector, normal or mutant human Cu-Zn superoxide dismutase (SOD1), we have characterized the activation of the caspase cascade in detail, revealing that the activation of caspases-9, -3 and -8 are important in motor neurone death and that the presence of mutant SOD1 causes increased activation of components of the apoptotic cascade under both basal culture conditions and following oxidative stress induced by serum withdrawal. Activation of the caspases identified in the cellular model has been confirmed in the G93A SOD1 transgenic mice. Furthermore, investigation of the effects of anti-apoptotic neuroprotective agents including specific caspase inhibitors, minocycline and nifedipine, have supported the importance of the mitochondrion-dependent apoptotic pathway in the death process and revealed that the upstream caspase cascade needs to be inhibited if useful neuro-protection is to be achieved.
AudioXpress One year (12 issues) for €122.50 (USD 124.94) AudioXpress Magazine is devoted to do-it-yourself audio. From speakers to amplifiers and preamps, vacuum tube technology to the newest in digital, audioXpress features construction projects to build, along with tips and tweaks to upgrade equipment, as well as articles and reviews to inform. Each issue of AudioXpress is filled with design ideas, projects to build, and articles on cutting-edge audio topics.
Open reduction, ulnar osteotomy and external fixation for chronic anterior dislocation of the head of the radius. We reviewed 15 patients, nine girls and six boys, with chronic anterior dislocation of the radial head which was treated by ulnar osteotomy, external fixation and open reconstruction of the elbow joint but without repair of the annular ligament. Their mean age was 9.5 years (5 to 15) and the mean interval between the injury and reconstruction was 22 months (2 months to 7 years). All radial heads remained reduced at a mean follow-up of 20 months (6 months to 5 years). Normal ranges of movement for flexion, extension, pronation and supination were unchanged in 96.1% (49/51) and worse in 3.9% (2/51). Limited ranges of movement were improved in 77.8% (7/9), unchanged in 11% (1/9) and further decreased in 11% (1/9).There were two superficial pin-track infections and two cases of delayed union but with no serious complications. Reconstruction of the radiocapitellar joint is easier using external fixation since accurate correction of the ulna can be determined empirically and active functional exercises started immediately. Only patients with a radial head of normal shape were selected for treatment by this method.
Due to color differences in monitors, the colors on this site are for reference only. Please contact Epic Sports if you have any color questions. Frequently Bought With Customer Reviews W. KELLY (South Dakota) on May 6, 2013 4 Stars High quality jerseys that show really well. Purchased for a 12U fastpitch team and the girls love them. Only reason it gets 4 stars is the buttons are a translucent white while the jersey is deep purple. Really don't understand that, but the moms are fixing it! Otherwise everything was great.
There is a method for increasing a data area into which user data is to be written in a magnetic disc apparatus by which a servo pattern is divided into a plurality of zones from the inner periphery to outer periphery of a magnetic disc and the write frequency (reference frequency) of the servo pattern in the outer periphery zone is made higher than that in the inner periphery zone (zone servo method).
The present invention relates to a fluid control system, and in particular to a modular, valve-operated fluid control system. In many industrial applications, it is necessary to provide a large number of individually-controllable pneumatic or hydraulic fluid lines. In practice, this requires at least one electronically-operated solenoid valve to be provided for each fluid line. Rather than provide each valve with its own power and control leads, which would be impractical, it is known to connect all of the solenoid valves to a single power supply, provide a common data bus on which control signals are transmitted, and provide each valve with a controller for interpreting the control signals and operating the valve as required. EP-A-0299655 discloses one example of such a fluid control system. Such fluid control systems are generally complex, requiring elaborate control protocols and data decoders within the valve controllers to derive the specific instructions for each valve. In addition, it is usually necessary to provide each valve with a unique pre-set address or means for setting a unique address, such as a position encoder, to enable instructions to be transmitted to particular valves. This requirement introduces further complexity and leads to problems if addresses become non-unique. Furthermore, although some of the fluid control systems of the above-described kind may be described as xe2x80x9cmodularxe2x80x9d, for example, the system disclosed in U.S. Pat. No. 5,522,431 in which a common fluid manifold is provided by combining a plurality of separate manifold modules, those systems do not allow simple system construction or system expansion. Those systems, which are sold through a distributor, are pre-configured by the manufacturer according to a particular specification. As such, those systems do not allow for alteration by adding or removing valves without the need for substantial re-adjustment or system re-wiring/re-programming. It is thus an aim of the present invention to provide a modular fluid control system which can be easily configured, typically by distributors, by simply fitting together the required components in the desired configuration from a small range of different standard modules, and which, when powered up, is fully configured and ready for operation without the need for additional complicated wiring. Accordingly, the present invention provides a modular fluid control system, comprising: a control module for receiving parallel electronic control signals as a plurality of data streams, the control module including a control unit configured to convert the data streams of the parallel electronic control signals to serial electronic control signals, each including a plurality of data pulses as control instruction signals, and an electrical connector; a plurality of valve modules, each valve module including at least one valve operable to control the flow of pressurized fluid; and a plurality of manifold modules connectable in series to the control module and connected to respective ones of the valve modules, each manifold module including a fluid supply conduit to provide a common manifold for receiving pressurized fluid, first and second electrical connectors for connection with ones of the connectors of adjacent manifold modules and the connector of the control module to provide an electrical bus for transmission of the serial control signals and power supply, and a control unit configured to decode one or more of the first-received data pulses of the serial control signals, control the respective valve module accordingly, and pass any remaining data pulses as a modified serial control signal from which the decoded data pulses have been one of removed or blocked to the control unit of any downstream manifold module. Preferably, the manifold modules are non-addressed. In one embodiment the control system comprises a single group of series-connected manifold modules. In another embodiment the control system comprises a plurality of interconnected groups of series-connected manifold modules, and further comprises intermediate connection modules connected to the intermediate ends of the groups of manifold modules. Preferably, the control system further comprises an end connection module connected to the end of the series-connected manifold modules. Preferably, one of the control module or the end connection module includes a port for connection to a supply of pressurised fluid. Preferably, the serial control signals are pulse width modulated signals. More preferably, data pulses having different pulse widths designate different control states. Yet more preferably, the pulse widths are the active pulse widths. Preferably, the control unit of each manifold module is further configured to operate the respective valve module only on consecutively receiving the one or more data pulses having the same pulse widths a predetermined number of times. More preferably, the control unit of each manifold module is configured to operate the respective valve module only on consecutively receiving the one or more data pulses having the same pulse widths at least three times. Preferably, the valve modules include one of mono-stable or bi-stable valves. More preferably, the control unit of any manifold module connected to a valve module including a mono-stable valve is configured to decode the first-received data pulse of each of the received serial control signals. More preferably, the control unit of any manifold module connected to a valve module including a bi-stable valve is configured to decode the first- and second-received data pulses of each of the received serial control signals. Preferably, the control unit of the control module is further configured to terminate each of the serial control signals generated thereby with a termination signal to denote the end of each of the serial control signals. Preferably, the control unit of each manifold module is further configured to transmit return data signals to the control module. More preferably, the control unit of each manifold module is configured to transmit return data signals to the control module on receipt of the termination signal. More preferably, the control unit of the control module is further configured to convert the return data signals to parallel return data signals. Preferably, the manifold modules each comprise a body which includes a passage, and a printed circuit board housed in the passage which includes the connectors and the control unit, with the passages together defining a common passage in which the printed circuit boards are connected. Preferably, the main body of each manifold module is formed as an integral component. The fluid control system of the present invention, in being simple and requiring no re-wiring of the component parts, allows for configuration by non-skilled technicians, thus allowing for configuration by parties other than the manufacturer, such as a distributor. In its preferred embodiments the fluid control system of the present invention automatically provides a xe2x80x9cvirtual connectionxe2x80x9d between valve modules at any given location with reference to the respective pin or pins of the external connector. In the event that alteration of the configuration of the system is required, the system may be quickly disassembled, manifold modules and associated valve modules added, removed or re-arranged and then re-assembled. The new positions of the re-arranged valve modules will automatically correspond to the correct pin or pins of the external connector without the need to re-wire the system.
圖、文／卡卡洛普相信各位對於「一人約會系列」都印象深刻吧。之前有過「跟假女友搭車出遊拍照」之類的辦法，「教你拍出一個人甜蜜約會照」這系列照片更加生動，作者地主惠亮又想出新辦法，讓一人約會照片更加逼真了！！那就是讓女朋友的手也入鏡拉！！「一人約會」超閃餵食閃光照～更逼真的方法來了 ▼總羨慕人家總有甜蜜女友的餵食照嗎？ ▼但是實際上都一個人孤苦伶仃出去吃飯…… 不過沒關係，只要搬出一個人的閃光餵食照拍攝法 ▼相信你的FB打卡也可以變成這樣~ ▼嗚噢~超級甜蜜的來吧跟著地主惠亮一起做，你也可以辦得到唷!不過先必須找一個角落來處理一下~ ▼拿出女生用的粉底液，塗抹在手上然後再戴上之前一人約會照買的髮圈，還有塗上一人約會照進階版買的指甲油。這些買一次通通都還用的到喔！ ▼就可以變成女孩子的手了 ▼接下來在餐廳裡只要把手放在自己的臉周圍做做樣子~像是塗番茄醬 ▼拍起來就會變這樣 ▼女朋友餵食 ▼是不是超逼真的 ▼當然也可以拍出這種出去野餐在玩的照片 ▼也可以自己在家裡房間玩，感覺好像在同居只是這些照片只能近拍不要遠拍喔!不然就露餡了~~ 照片來源：portal.nifty.com 你累了嗎？快點進來看看「鍵盤大檸檬」平淡生活加點酸～點此到看更多介紹
By applying advances in molecular biology and molecular genetics to population based studies of HIV-1 infection, Viral Epidemiology Branch investigators help elucidate the distribution, determinants, and natural history of this cancer-associated virus.Chemokine Receptor Gene Polymorphisms Both the natural history of HIV infection and the response to antiretroviral therapy are heterogeneous, and it is known that polymorphisms in chemokine receptor genes modulate the natural history. We recently demonstrated that polymorphisms in chemokine receptor genes may also explain some of the heterogeneity in sustaining viral suppression observed among patients receiving potent antiretroviral therapy. We continued to lead the international meta-analysis of the effect of host genetics on the outcome of HIV infection. The meta-analysis seeks to increase statistical precision over that available from any single study. HIV RNA Levels The HIV RNA level is the strongest known predictor of prognosis among HIV-infected patients. We collaborated to demonstrate that a simple mathematical relationship exists between the HIV RNA level and survival time, such that a patient's cumulative exposure to viral replication predicts their survival. In developed areas, HIV-infected infants have high virus levels. We assessed HIV levels in untreated infants in Malawi by analysis of dried blood spots. We found that the median initial HIV level was higher among perinatally infected infants than among infants infected by breast-feeding, but that neither age at infection nor route of infection significantly influenced HIV levels measured 1 year after infection. We also participated in a collaboration that demonstrated that the HIV RNA level and the CD4 cell count are the main predictors of mortality among HIV-infected African children, as is true in developed countries. Effect of Recent Thymic Emigrants on HIV-1 disease The concentration of T-cell receptor-rearrangement excision DNA circles (TREC) in peripheral-blood T cells is a marker of recent thymic emigrant T cells. We collaborated in a study of the predictive ability of measurements of TREC for clinical outcome in HIV-1-infected individuals. We found that the concentration of TREC in the peripheral T-cell pool complements HIV-1 RNA load and CD4 T-cell count in predicting the rate of HIV-1 disease progression. These data suggest that recent thymic emigrants have a role in the pathogenesis of HIV-1 disease.
AEEE Important Dates 2019 AEEE Important Dates 2019 - The admission authorities of Amrita Vishwa Vidyapeetham has released the important dates for AEEE 2019. Candidates can check AEEE 2019 important dates to know about the commencement of admissions. AEEE will be conducted as a CBT (computer-based test) as well as a pen and paper test (offline). The CBT will be conducted from April 22-26, while a pen-and-paper test will be held on April 27, 2019. The application form of AEEE 2019 is released on October 19, 2018, both in online and offline mode. Candidates are advised to check the AEEE important dates 2019 to ensure that no important event related to the exam is missed. The result of AEEE 2019 will be declared on May 5, 2019. Read the full article to know further details about AEEE important dates 2019. AEEE 2019 Important Dates Candidates can check the important dates of AEEE 2019 given in the table below. The dates given are tentative and will be updated when declared by the official authorities. S.No. Events Important Dates 1 Release of Application form October 19, 2018 2 Commencement of Slot Booking for CBT April 5, 2019 3 Last Date for submission of Application Form and Slot Booking for CBT April 10, 2019 4 Last date of application submission for PPT April 25, 2019 5 AEEE 2019 Hall Ticket First Week of April 2019 6 AEEE 2019 Exam (Computer Based Test) April 22-26, 2019 (3 slots per day) 7 AEEE 2019 Offline Exam (Pen and Paper Based Exam) April 27, 2019 8 Declaration of Result May 5, 2019 9 Option open to change the academic preference & profile data. Entry of JEE Main scores May 5 to May 8 10 Trial Allotment and clarification of doubts (for both the modes- AEEE and JEE) May 10, 2019 11 Last date for fee payment of first allotment May 20, 2019 12 Second Allotment May 25, 2019 13 Last date for fee payment of second allotment May 30, 2019 14 Third Allotment June 5, 2019 15 Last date for fee payment of third allotment June 10, 2019 16 Verification of documents & filling the vacant seats. June 15 to 25, 2019 Highlights of AEEE Important Dates 2019 AEEE 2019 Application Form - The application form of AEEE 2019 is available from October 19, 2018. The application form is available both in online and offline mode. Candidates applying through JEE Main 2019 rank will also be required to fill the application form. To fill the application form of AEEE 2019 - Click here Or Apply from the window given below: AEEE 2019 Slot Booking & Hall Ticket - The slot booking process for AEEE 2019 CBT will start from April 5 and will close on April 10. The hall ticket will be available only after the slots are successfully booked by the candidates. AEEE 2019 Examination- The AEEE 2019 computer-based examination will be conducted from April 22-26. Pen and Paper test of AEEE 2019 will be held on May 27. The candidates will have to qualify the examination to be eligible for admissions. AEEE 2019 Counselling – The selected candidates will be called in for counselling which will commence from May 10. Allotment will be done as per the ranking of the candidates and his/her preference of courses.
[Streptomycin--an activator of persisting tick-borne encephalitis virus]. The effect of streptomycin (C) on persistence of tick-borne encephalitis (TBE) virus in Syrian hamsters infected with 3 strains of the virus (41/65, Aina/1448, Vasilchenko ) intracerebrally or subcutaneously was studied. In the animals not given C the infectious virus could be detected in the brain for 8-14 days but not later although their organs (mostly brains and spleens) contained the hemagglutinating antigen and viral antigen detectable by immunofluorescence. Intramuscularly C was given twice daily for 13-35 days in a daily dose of 200 mg/kg. The C-treated hamsters yielded 7 virulent TBE virus strains: 3 from the brain, 3 from the spleen, and one from the blood. No virus could be isolated from the liver, kidneys, or lungs despite the use of various methods for isolation including tissue explantation. The activating effect of C was observed against the background of 4-fold decrease in the titre of complement-fixing and antihemagglutinating antibodies. C exerted its activating effect both at early (70 days) and late (9 months) stages of TBE virus persistence. The activating effect of C appears to be due to its immunosuppressive properties and neurotoxic action on the CNS.
One of the treatment strategies being explored for the management of lipodystrophy has been to replace a protease inhibitor with a non-nucleoside reverse transcriptase inhibitor (NNRTI). This poster was a meta-analysis of eighteen trials evaluating the impact of switching from a protease inhibitor to either nevirapine or efavirenz on the progression of body shape changes and hyperlipidemia. All studies published in peer-reviewed journals or presented at international conferences between 1999 and February 2001 were evaluated. Switching of NRTIs was permitted. The switch from the protease inhibitor must have been due to clinical or metabolic manifestations of lipodystrophy. There was no restriction on ARV therapy history including time on protease inhibitors. Blood cholesterol and triglycerides data, before and after the switch to the NNRTI, were pooled in a composite analysis. Some values were derived from graphs. Changes in body shape following the switch were collected, but could have been determined by patient self-report, physician assessment, anthropometric measurement or DEXA. In all eighteen studies, virologic suppression was maintained in the vast majority of patients (although the numbers are not given in this poster). There was a decrease in CHO and TG in all studies examining the switch from protease inhibitor to nevirapine. One study reported an increase in HDL, while another trial reported a reduction in LDL following the switch to nevirapine, but not following the switch to efavirenz. Insulin resistance normalized in two studies following the switch to nevirapine. Elevations in CHO and TGI were observed in a number of studies following the switch to efavirenz. Five studies demonstrated elevations in total CHO. Only one study showed improvement. Four studies showed increased TG levels, while four others showed improvements. Four studies showed an increase in HDL, whereas one study showed elevations in HDL and also in LDL and glucose. "Significant" changes in body shape were reported in three trials looking at a switch to nevirapine (although again, what "significant" means and how it was determined is not noted on the poster). "Limited, nonsignificant" improvement in body shape was reported in two studies of efavirenz switch. Subjective improvement (patient self-report) in body shape or quality of life was reported in four studies examining the switch to nevirapine, whereas "partial" improvement was reported in two studies of the switch to efavirenz. Figure 1. Changes in Total Cholesterol Following Switch from PI to NVP or EFV, or with Ongoing PI Figure 2. Changes in Triglyceride Following Switch from PI to NVP or EFV, or with Ongoing PI The authors of this poster conclude that the replacement of the protease inhibitor with nevirapine was associated with a reduction in mean blood cholesterol and triglycerides levels, leading to normalization in many patients. The switch to efavirenz was not associated with such improvement. They felt that the investigation of physical changes yielded less conclusive findings. The authors' conclusions about lipid changes fit with the generally accepted interpretation of the studies in the past few years. The changes in triglycerides with a switch to nevirapine have been quite marked, as have the changes in cholesterol. However, this poster suffers from several flaws. First, one must take note that this is a poster done by two people working for Boehringer Ingelheim. While there is no disputing the findings, the spin on this poster favoring nevirapine against efavirenz is unmistakable. Second, many of the switch studies have been seriously flawed in their collection of lipid data. A number of them have collected non-fasting samples and it is not clear how the authors reconcile this kind of data with properly collected fasting levels, since they make no distinction. Third, it is impossible to draw any real conclusions about body-shape changes given the variety of ways that data was collected, from DEXA scans to patient self-report. Certainly, no quantitative conclusions can be reached when so much subjective data is used. Most authors have concluded that there may be some resolution of fat accumulation, manifested as abdominal distention or buffalo hump, but no resolution of fat wasting, one of the most deforming aspects of lipodystrophy. Fourth, it is well known that efavirenz can increase total cholesterol, but most studies have found that the increase is in HDL, with unknown consequences. Despite these flaws, the authors' conclusions, listed below, were all very reasonable: a switch from protease inhibitor to NNRTI improves at least some of the lipid abnormalities; This article was provided by TheBodyPRO.com. It is a part of the publication The 1st International AIDS Society Conference on HIV Pathogenesis and Treatment. Please note: Knowledge about HIV changes rapidly. Note the date of this summary's publication, and before treating patients or employing any therapies described in these materials, verify all information independently. If you are a patient, please consult a doctor or other medical professional before acting on any of the information presented in this summary. For a complete listing of our most recent conference coverage, click here. TheBodyPRO.com is a service of Remedy Health Media, LLC, 750 3rd Avenue, 6th Floor, New York, NY 10017. 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Q: How to extract text from a several "div class" (html) using R? My goal is to extract info from this html page to create a database: https://drive.google.com/folderview?id=0B0aGd85uKFDyOS1XTTc2QnNjRmc&usp=sharing One of the variables is the price of the apartments. I've identified that some have the div class="row_price" code which includes the price (example A) but others don't have this code and therefore the price (example B). Hence I would like that R could read the observations without the price as NA, otherwise it will mixed the database by giving the price from the observation that follows. Example A <div class="listing_column listing_row_price"> <div class="row_price"> $ 14,800 </div> <div class="row_info">Ayer 19:53</div> Example B <div class="listing_column listing_row_price"> <div class="row_info">Ayer 19:50</div> I think that if I extract the text from "listing_row_price" to the beginning of the "row_info" in a character vector I will be able to get my desired output, which is: ... 10 4000 11 14800 12 NA 13 14000 14 8000 ... But so far I've get this one and another full with NA. ... 10 4000 11 14800 12 14000 13 8000 14 8500 ... Commands used but didn't get what I want: html1<-read_html("file.html") title<-html_nodes(html1,"div") html1<-toString(title) pattern1<-'div class="row_price">([^<])<' title3<-unlist(str_extract_all(title,pattern1)) title3<-title3[c(1:35)] pattern2<-'>\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t([^<])' title3<-unlist(str_extract(title3,pattern2)) title3<-gsub(">\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t $ ","",title3,fixed=TRUE) title3<-as.data.frame(as.numeric(gsub(",","", title3,fixed=TRUE))) I also try with pattern1<-'listing_row_price">([<div class="row_price">]?)([^<])< that I think it says to extract the "listing_row_price" part, then if exist extract the "row_price" part, later get the digits and finally extract the < thats follows. A: There are lots of ways to do this, and depending on how consistent the HTML is, one may be better than another. A reasonably simple strategy that works in this case, though: library(rvest) page <- read_html('page.html') # find all nodes with a class of "listing_row_price" listings <- html_nodes(page, css = '.listing_row_price') # for each listing, if it has two children get the text of the first, else return NA prices <- sapply(listings, function(x){ifelse(length(html_children(x)) == 2, html_text(html_children(x)[1]), NA)}) # replace everything that's not a number with nothing, and turn it into an integer prices <- as.integer(gsub('[^0-9]', '', prices))
Giannis Kyriakopoulos Giannis Kyriakopoulos (alternate spellings: Yiannis, Yannis, Ioannis, Kiriakopoulos) (; born June 6, 1983) is a Greek professional basketball player. He is 1.88 m (6'2") in height, and he plays at the point guard position. Professional career In his pro career, Kyriakopoulos has played with the Greek Basket League clubs Panionios, AEL 1964, AEK Athens, and Panelefsiniakos. He was named the Greek 2nd Division Guard of the Year for the 2005–06 season, by the website Eurobasket.com. In the 2013–14 season, he played with Doxa Lefkadas in the Greek National B League (the 3rd level of Greece), and won the B League's north division championship with them. References External links FIBA Game Center Profile Eurobasket.com Profile Draftexpress.com Profile Greek Basket League Profile AEK Athens Profile Category:1983 births Category:Living people Category:AEK B.C. players Category:AEL 1964 BC players Category:Doxa Lefkadas B.C. players Category:Egaleo B.C. players Category:Greek men's basketball players Category:Greek Basket League players Category:KAOD B.C. players Category:Kastorias B.C. players Category:Olympias Patras B.C. players Category:Panelefsiniakos B.C. players Category:Panionios B.C. players Category:Point guards Category:Rethymno B.C. players
Absolutism Absolutism may refer to: Government Absolute monarchy, in which a monarch rules free of laws or legally organized opposition; especially in the period c. 1610 – c. 1789 in Europe Enlightened absolutism, influenced by the Enlightenment (18th- and early 19th-century Europe) Autocracy, a political theory which argues that one person should hold all power Philosophy Morality Moral absolutism, the belief in absolute standards against which moral questions can be judged, regardless of context Graded absolutism, the view that a moral absolute, such as "Do not kill", can be greater or lesser than another moral absolute, such as "Do not lie" Other topics in philosophy Absolute (philosophy), an objective and unconditioned reality said to underlie perceived objects Absolute idealism, an ontologically monistic philosophy attributed to G. W. F. Hegel Physics Absolute theory, in physics Absolute space, a theory that space exists absolutely; contrast with relationalism
Use of hearing aids by patients with closed mastoid cavity. Twenty-five patients who had undergone a closed-cavity tympanomastoidectomy in our Unit and wore a hearing aid in the operated ear were reviewed, and information was recorded on the use of the aid, and the patients' impression about it. The information obtained was analysed and compared with similar data from 39 hearing aid users of similar age with no history of ear surgery. Eighty per cent of the patients with a closed mastoid cavity were satisfied with the aid, and no significant difference was found between the two groups regarding the impression about the aid (chi square 3.06, p = 0.08), or the problems with it, which, in most of the cases, were related to several changes of mould (chi square 2.19, p = 0.13). The various recorded parameters are discussed, and it is concluded that the patients with a closed mastoid cavity can tolerate a hearing aid in the operated ear at least as well as the control subjects with no ear surgery.
//------------------------------------------------------------------------------------------------------- // Copyright (C) Microsoft. All rights reserved. // Licensed under the MIT license. See LICENSE.txt file in the project root for full license information. //------------------------------------------------------------------------------------------------------- export function throwError() { throw new Error("This is an error"); }
Alfaro District San Juan is a district in San Ramón Canton, Costa Rica. References Category:Districts of Alajuela Province
To use the new Pods, you'll need to be running one of the newer Xfinity home "Gateway" routers, something that Comcast says the majority of its customers (15 million of the total 26 million internet subscribers) have in their homes. Assuming that's the case, setup should be a breeze: Plug the pods in where you need better coverage, open the xFi WiFi app on your iPhone or Android device and then follow the on-screen directions. Comcast's Eric Schaefer (Senior VP of Broadband, Automation and Communications) said that his company bought the rights to Plume's WiFi management systems to integrate into Xfinity's WiFi products, but the Pods themselves look essentially identical to what Plume sells. They're small hexagons that plug into an outlet and include an ethernet port if you want to run a wired setup. Overall, the whole setup sounds near-identical to what Plume has sold for a few years (not that that's a bad thing). Schaefer also admits that mesh WiFi networks is a bit of a niche product for its customer base. "Blending the average across the country, about 70 percent of our homes had great coverage, and about 80 percent had acceptable coverage," he said, referencing surveyed homes that had been optimized for WiFi. That means the potential number of customers who'd benefit from isn't exactly massive, but it does help Comcast position Xfinity as a one-stop solution for all WiFi customers, regardless of how big their house might be. Of course, a lot of people who know enough to know they need a mesh network might also already be looking at third-party products like the aforementioned Plume, Eero or Google WiFi. But Comcast will also make it easy for new customers to determine if they'd benefit from Pods during the setup process; the xFi app can also help users figure out extending their network would be useful. Given Comcast's overall strategy of hooking customers up to additional services like home security and home automation, being able to make sure home WiFI stands up to the ever-growing number of devices on our networks is a smart priority.
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Locked nucleic acid oligonucleotides: the next generation of antisense agents? Locked nucleic acid (LNA) is the term for oligonucleotides that contain one or more nucleotide building blocks in which an extra methylene bridge fixes the ribose moiety either in the C3'-endo (beta-D-LNA) or C2'-endo (alpha-L-LNA) conformation. The beta-D-LNA modification results in significant increases in melting temperature of up to several degrees per LNA residue. The alpha-L-LNA stereoisomer, which also stabilizes duplexes, lends itself to use in triplex-forming oligonucleotides and transcription factor decoys, which have to maintain a B-type (C2'-endo) DNA conformation. LNA oligonucleotides are synthesized in different formats, such as all-LNA, LNA/DNA mixmers, or LNA/DNA gapmers. Essentially, all aspects of antisense technology have profited from LNA due to its unprecedented affinity, good or even improved mismatch discrimination, low toxicity, and increased metabolic stability. LNA is particularly attractive for in vivo applications that are inaccessible to RNA interference technology, such as suppression of aberrant splice sites or inhibition of oncogenic microRNAs. Furthermore, the extreme antisense-target duplex stability (formation of persistent steric blocks) conferred by beta-D-LNA also contributes to the capacity to invade stable secondary structures of RNA targets. The in vivo studies reported so far indeed point to LNA as a promising antisense player at the horizon of clinical applications.
Trump derangement syndrome Trump derangement syndrome (TDS) is a term for criticism or negative reactions to United States President Donald Trump that are alleged to be irrational and have little regard towards Trump's actual positions or actions taken. The term has been used by Trump supporters to discredit criticism of his actions, as a way of reframing the discussion by suggesting that his opponents are incapable of accurately perceiving the world. Origin of term The origin of the term is traced to political columnist and commentator Charles Krauthammer, a psychiatrist, who originally coined the phrase Bush derangement syndrome in 2003 during the presidency of George W. Bush. That "syndrome" was defined by Krauthammer as "the acute onset of paranoia in otherwise normal people in reaction to the policies, the presidency—nay—the very existence of George W. Bush". The first use of the term "Trump Derangement Syndrome" may have been by Esther Goldberg in an August 2015 op-ed in The American Spectator; she applied the term to "Ruling Class Republicans" who are dismissive or contemptuous of Trump. Krauthammer, in an op-ed harshly criticizing Trump, commented that—in addition to general hysteria about Trump—the "Trump Derangement Syndrome" was the "inability to distinguish between legitimate policy differences and... signs of psychic pathology" in his behavior. Definition Fareed Zakaria defined the syndrome as "hatred of President Trump so intense that it impairs people's judgment". CNN's editor-at-large Chris Cillizza called TDS "the preferred nomenclature of Trump defenders who view those who oppose him and his policies as nothing more than the blind hatred of those who preach tolerance and free speech". Pointing to previous allegations of Bush Derangement Syndrome and Obama Derangement Syndrome, Cillizza suggested, "Viewed more broadly, the rise of presidential derangement syndromes is a function of increased polarization—not to mention our national self-sorting—at work in the country today." Bret Stephens has described the term as something used by conservative groups whenever someone speaks out critically against Trump, regardless of political affiliation. Usage The term has been widely applied by pro-Trump writers to critics of Trump, accusing them of responding negatively to a wide range of Trump's statements and actions. The use of the term has been called part of a broader GOP strategy to discredit criticisms of Trump's actions, as a way of "reframing" the discussion by suggesting his political opponents are incapable of accurately perceiving the world. However, according to Kathleen Hall Jamieson of Annenberg Public Policy Center, the term could backfire on Trump supporters because people might interpret it to mean that Trump is the one who is "deranged", rather than those who criticize him. Some Trump supporters have asserted that he plays a form of "multi-dimensional chess" on a mental level his critics cannot comprehend, which they say explains why critics are frustrated and confused by Trump's words and actions. Fox News anchor Bret Baier and former House speaker Paul Ryan have characterized Trump as a "troll" who makes controversial statements to see his adversaries' "heads explode". The term has been used by journalists critical of Trump to call for restraint. Fareed Zakaria, who urged Americans to vote against Trump calling him a "cancer on American democracy", argues that every Trump policy "cannot axiomatically be wrong, evil and dangerous". Adam Gopnik, who takes a strong anti-Trump position, responded to these assertions that it is a "huge and even fatal mistake for liberals (and constitutional conservatives) to respond negatively to every Trump initiative, every Trump policy, and every Trump idea". Arguing that Trump's opponents must instead recognize that the real problem is "Deranged Trump Self-Delusion", which Gopnik defined the "Syndrome" as President Trump's "daily spasm of narcissistic gratification and episodic vanity". Examples of use Senator Rand Paul has cited the so-called syndrome several times. In a July 16, 2018, interview he said investigators should simply focus on election security and stop "accusing Trump of collusion with the Russians and all this craziness that's not true"—accusations which he said were entirely motivated by "Trump derangement syndrome". Trump used the term in a tweet following the 2018 Russia–United States summit in Helsinki: He also used it in a tweet about Alan Dershowitz's book The Case Against Impeaching Trump: In July 2018, Jeanine Pirro accused Whoopi Goldberg of suffering from Trump Derangement Syndrome during a guest appearance on The View to promote her newly published book. This occurred while Pirro was responding to a question about how the "deep state" really works. In July 2018, Eric Zorn wrote in the Chicago Tribune that the syndrome afflicts Trump's supporters more than his critics, as "what Team Trump is calling derangement is, in most cases, rational concern about his behavior and the direction he's taking the country.... The true Trump Derangement Syndrome loose on the land is the delusion suffered by those who still think he's going to make this country a better place for average people." White House Press Secretary Sarah Huckabee Sanders also used the term in this tweet: In September 2018, Fox News personality and Trump supporter, Sean Hannity criticized The Washington Post as having Trump Derangement Syndrome for stating in an editorial that Trump, because of his attitude toward climate change, is "complicit" in hurricanes battering the United States; Hannity said "it is now a full-blown psychosis, it is a psychological level of unhingement I have never seen." In November 2018, Michael Goodwin, writing in the New York Post, discussed a variant of Trump Derangement syndrome he called "Trump Imitation Syndrome". In August 2019, Anthony Scaramucci, Trump's former White House Communications Director, said in interviews with Vanity Fair and CNN that he had "Trump fatigue syndrome" instead of Trump derangement syndrome. In September 2019, Sean Hannity characterized as "Trump derangement syndrome" the continuing press coverage of Trump's days-long insistence that he was correct to state on September1 that Hurricane Dorian posed a danger to Alabama, asserting "pretty much every newsroom in America screwed this up and lied to you," adding there were "a lot of psychotic jackasses in the media mob". See also Public image of George W. Bush § Bush Derangement Syndrome neologism Clinton crazies References Category:Donald Trump Category:American political neologisms Category:Reactions to the election of Donald Trump Category:Words coined in the 2010s Category:Words and phrases introduced in 2015
High mobility group nucleosome-binding family proteins promote astrocyte differentiation of neural precursor cells. Astrocytes are the most abundant cell type in the mammalian brain and are important for the functions of the central nervous system. Although previous studies have shown that the STAT signaling pathway or its regulators promote the generation of astrocytes from multipotent neural precursor cells (NPCs) in the developing mammalian brain, the molecular mechanisms that regulate the astrocytic fate decision have still remained largely unclear. Here, we show that the high mobility group nucleosome-binding (HMGN) family proteins, HMGN1, 2, and 3, promote astrocyte differentiation of NPCs during brain development. HMGN proteins were expressed in NPCs, Sox9(+) glial progenitors, and GFAP(+) astrocytes in perinatal and adult brains. Forced expression of either HMGN1, 2, or 3 in NPCs in cultures or in the late embryonic neocortex increased the generation of astrocytes at the expense of neurons. Conversely, knockdown of either HMGN1, 2, or 3 in NPCs suppressed astrocyte differentiation and promoted neuronal differentiation. Importantly, overexpression of HMGN proteins did not induce the phosphorylation of STAT3 or activate STAT reporter genes. In addition, HMGN family proteins did not enhance DNA demethylation and acetylation of histone H3 around the STAT-binding site of the gfap promoter. Moreover, knockdown of HMGN family proteins significantly reduced astrocyte differentiation induced by gliogenic signal ciliary neurotrophic factor, which activates the JAK-STAT pathway. Therefore, we propose that HMGN family proteins are novel chromatin regulatory factors that control astrocyte fate decision/differentiation in parallel with or downstream of the JAK-STAT pathway through modulation of the responsiveness to gliogenic signals.
Our Opinion: Kosel has right idea about sunshine in Illinois Comment The State Journal-Register Writer Posted Apr. 14, 2014 at 1:10 AM Posted Apr. 14, 2014 at 1:10 AM Illinois lawmakers are not shy about trying to change the state’s Freedom of Information Act — the law that enables citizens and taxpayers to gain access to documents and information about how government operates and spends money. Unfortunately, not all of the changes lawmakers seek are good for the public. In early 2010, after an overhaul of the state’s FOIA law, it was a matter of weeks before lawmakers began looking for ways to water it down. They sought to bar the release of performance reviews of teachers, school administrators, police officers and other public employees. They wanted to allow governmental bodies to charge the citizens more to gain access to public documents. They sought to eliminate a provision that allows citizens who successfully sue public bodies for violating FOIA to collect attorney fees. Sadly, attempts to weaken Illinois’ sunshine laws continue. For example, Sen. Bill Cunningham, D-Chicago, recently proposed legislation that would exempt 911 recordings from FOIA, saying they have no news value and amount to an invasion of privacy. Cunningham, a former police spokesman, said he decided to introduce Senate Bill 3072 after hearing broadcasts of panicked 911 calls from the December 2012 Sandy Hook School shootings in Newtown, Conn. “The thousands of media outlets that aired those recordings weren’t acting as government watchdogs trying to shed light on the conduct of law enforcement,” he was quoted as saying. “They were simply looking to create shocking program content in order to boost ratings and drive visits to their websites.” It’s unclear how Cunningham knows so confidently what motivation the media had in airing those 911 recordings. But there are valid reasons why 911 calls should be a matter of public record. They provide a level of accountability for emergency response workers who are supposed to serve the public but who also face a multitude of challenges in doing so. Allowing the public to hear 911 calls helps them gain a better understanding of emergency events, how they were handled and what, if any, policy changes need to occur as a result. In addition, taxpayers provide the money that supports 911 operations and most first responder agencies. On the flip side, a different law pending at the Statehouse would strengthen the public’s right to know in Illinois. House Bill 3664, sponsored by Rep. Renee Kosel, R-New Lenox, would ban confidentiality clauses on settlement and severance agreements involving governmental bodies. This is sunshine we can get behind. The bill was prompted by outrage over a confidential $871,000 severance agreement negotiated between Chicago’s troubled Metra board and its former CEO Alex Clifford, who resigned last summer amid a patronage scandal that involved allegations that House Speaker Michael Madigan wielded influence over hiring at the commuter rail agency. Just last week, Madigan spokesman Steve Brown released a letter indicating the legislative inspector general cleared Madigan of any wrongdoing and that the investigation is now closed. Page 2 of 2 - But taxpayers were on the hook for Clifford’s severance package. And although they had to foot the bill, they were not privy to the details because the board agreed to a confidentiality clause that prohibited members or Clifford from discussing his separation or the details of the agreement. “These clauses seem little more than ‘hush money’ to keep an outgoing employee quiet,” Kosel said in a post on her website. Confidentiality clauses aren’t just a Chicago thing. They’re standard operating procedure for many public bodies. The District 186 school board’s nearly $178,000 separation agreement with former superintendent Walter Milton last year included a confidentiality clause. The agreement eventually became public after The State Journal-Register obtained a copy through FOIA, but board members had to abide by the confidentiality agreement, former board president Susan White said at the time. And in 2009 the University of Illinois Springfield paid $200,000 to a student to settle allegations of sexual impropriety involving a coach. The university resisted releasing the settlement agreement for two years, citing privacy concerns and other arguments, until the Illinois attorney general stepped in. Kosel’s bill, which cleared the House unanimously last week, makes sense for Illinois taxpayers and government accountability. Cunningham’s, not so much.
Improved outcomes from tertiary center pediatric intensive care: a statewide comparison of tertiary and nontertiary care facilities. To compare outcomes from pediatric intensive care in hospitals with different levels of resources. Prospective, blinded comparison of outcome and care. Tertiary (n = 3) and nontertiary (n = 71) hospitals in Oregon and southwestern Washington. All critically ill children admitted with respiratory failure and head trauma for 6 months. Severity of illness adjusted mortality rates were determined using admission day, physiologic profiles (Pediatric Risk of Mortality score) and care modalities were assessed daily. The crude mortality rate of the tertiary patients was four times higher than for the nontertiary patients (23.4% vs. 6.0%, p less than .0001). In the tertiary patients, the numbers of outcomes were accurately predicted by physiologic profiles (observed: 30 deaths and 98 survivors; predicted: 29.3 deaths and 98.7 survivors, z = -.25, p greater than .4). However, for the nontertiary patients, the number of the deaths were significantly different than predicted (observed: 20 deaths and 315 survivors; predicted: 14.4 deaths and 320.6 survivors, z = -2.08, p less than .05). The odds ratios of dying in a nontertiary vs. a tertiary facility were about 1.1, 2.3, and 8 (p less than .05) for mortality risk groups of less than 5%, 5% to 30%, and greater than 30%. Patients in tertiary facilities received more (p less than .05) invasive (e.g., arterial catheters) and complex (e.g., mechanical ventilation) care, whereas patients in nontertiary facilities received more (p less than .05) labor-intensive care (e.g., hourly vital signs). Care of the most seriously ill children in tertiary pediatric ICUs could improve their chances of survival.
Reforming the Medicare payment structure to reward market-driven entrepreneurial innovations would cut healthcare costs by nearly $2.5 trillion by mid-century, according to a new study from the National Center for Policy Analysis (NCPA).
The Red Sox have “keen interest” in Phillies righty Pat Neshek, reports WEEI.com’s Rob Bradford. The 36-year-old Neshek (who has already tossed a scoreless inning in tonight’s All-Star Game) is widely expected to be traded, given his status as an impending free agent on baseball’s worst team. The sidearmer has worked to a pristine 1.27 ERA with 9.2 K/9, 1.3 BB/9 and a 36.5 percent ground-ball rate thus far in 2017. And, unlike in many previous seasons, Neshek has held left-handed opponents in check quite well. Right-handed opponents are hitting .234/.253/.286 against Neshek this season, while lefties are hitting .180/.231/.313. The Boston Globe’s Nick Cafardo reported that the Sox had scouted Neshek over the weekend as well, and he’s also been linked to the Nationals this summer. More on the Red Sox…
SIM card maker Gemalto has dismissed recent reports that U.K. and U.S. spies obtained encryption keys protecting millions of mobile phones by hacking its network. Secret documents revealed last week suggested that spies from the U.S. National Security Agency and the U.K. Government Communications Headquarters had stolen SIM card encryption keys from Gemalto, allowing them to intercept the conversations of millions of mobile phone users. The GCHQ documents, dating from 2010, were among those leaked by former NSA contractor Edward Snowden. On Wednesday, though, Gemalto said that while it had detected sophisticated attacks on its office networks in 2010 and 2011 that it now believed were probably conducted by the NSA and GCHQ, these could not have led to the massive theft of SIM encryption keys. While the leaked documents showed the spies boasting “(We) believe we have their entire network,” Gemalto said that its internal investigation showed that the intrusions only breached its office network, and not the entirely separate infrastructure used for generating and transmitting the SIM card encryption keys. By 2010 those keys were being exchanged with its network operator customers by secure means in all but a few cases, making the wholesale theft of the keys unlikely and meaning that Gemalto could not have been the source of the massive leaks reported, it said. Furthermore, Gemalto had never sold SIM cards to four of the 12 networks named in the leaked documents, so it could not have been the source of, for example, 300,000 SIM encryption keys stolen from a Somali carrier, it said. That doesn’t exclude the possibility that the keys were stolen from other SIM manufacturers, though: Gemalto is the largest, but not the only, supplier of the devices. Even if the spy agencies had somehow stolen SIM encryption keys from Gemalto, only communications on second-generation mobile networks such as GSM would be vulnerable, not the newer 3G and 4G networks introduced by many operators after 2010, the company said. Gemalto assumed for the purposes of its investigation that the leaked documents were genuine and accurate, but did not seek to confirm or refute the documents’ claims, it said. Outsiders regularly—and unsuccessfully—try to hack its networks, it said, and only a few attempts breach even the outer levels of its network. In June 2010, it detected and immediately countered an attack seeking to spy on the office network at one of its French sites. The following month, some of its network operator customers received emails from spoofed Gemalto addresses, with attachments containing malware. Around that time, attacks were also made on the PCs of Gemalto staff in contact with customers. Following its investigation, Gemalto said it planned to improve its security processes and continue monitoring its networks. Barring further developments in this case, though, however, it plans to make no further comment on the matter.
Recent advances in bulk metallic glasses for biomedical applications. With a continuously increasing aging population and the improvement of living standards, large demands of biomaterials are expected for a long time to come. Further development of novel biomaterials, that are much safer and of much higher quality, in terms of both biomedical and mechanical properties, are therefore of great interest for both the research scientists and clinical surgeons. Compared with the conventional crystalline metallic counterparts, bulk metallic glasses have unique amorphous structures, and thus exhibit higher strength, lower Young's modulus, improved wear resistance, good fatigue endurance, and excellent corrosion resistance. For this purpose, bulk metallic glasses (BMGs) have recently attracted much attention for biomedical applications. This review discusses and summarizes the recent developments and advances of bulk metallic glasses, including Ti-based, Zr-based, Fe-based, Mg-based, Zn-based, Ca-based and Sr-based alloying systems for biomedical applications. Future research directions will move towards overcoming the brittleness, increasing the glass forming ability (GFA) thus obtaining corresponding bulk metallic glasses with larger sizes, removing/reducing toxic elements, and surface modifications. Bulk metallic glasses (BMGs), also known as amorphous alloys or liquid metals, are relative newcomers in the field of biomaterials. They have gained increasing attention during the past decades, as they exhibit an excellent combination of properties and processing capabilities desired for versatile biomedical implant applications. The present work reviewed the recent developments and advances of biomedical BMGs, including Ti-based, Zr-based, Fe-based, Mg-based, Zn-based, Ca-based and Sr-based BMG alloying systems. Besides, the critical analysis and in-depth discussion on the current status, challenge and future development of biomedical BMGs are included. The possible solution to the BMG size limitation, the brittleness of BMGs has been proposed.
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Aggregation Profiling of C9orf72 Dipeptide Repeat Proteins Transgenically Expressed in Drosophila melanogaster Using an Analytical Ultracentrifuge Equipped with Fluorescence Detection. The recent development of a fluorescence detection system for the analytical ultracentrifuge has allowed for the characterization of protein size and aggregation in complex mixtures. Protocols are described here to analyze protein aggregation seen in various human neurodegenerative diseases as they are presented in transgenic animal model systems. Proper preparation of crude extracts in appropriate sample buffers is critical for success in analyzing protein aggregation using sedimentation velocity methods. Furthermore, recent advances in sedimentation velocity analysis have led to data collection using single multispeed experiments, which may be analyzed using a wide distribution analysis approach. In this chapter, we describe the use of these new sedimentation velocity methods for faster determination of a wider range of sizes. In Chapter 7 of this book, we describe how agarose gel electrophoresis can be used to complement the analytical ultracentrifugation work, often as a prelude to careful biophysical analysis to help screen conditions in order to improve the success of sedimentation velocity experiments.
Everything Old Is New Again, and a Compiler Bug - AndreyKarpov https://randomascii.wordpress.com/2016/09/16/everything-old-is-new-again-and-a-compiler-bug/ ====== Annatar The author of the article is obviously very experienced and extremely talented. Personally, I find it a tragedy that he is wasting his time on Windows, on a platform, which in his own words, _in the crazy world of Windows there are a lot of programs that think that injecting their DLLs into all processes is a good idea. Whether malware or anti-malware or something else these injected DLLs end up causing a good portion of all of Chrome’s crashes. And in this case one of these injected DLLs decided that changing the FPU exception flags in somebody else’s process was a good idea._ _The fld instruction is part of the x87 FPU and it loads a floating-point value onto the x87’s peculiar eight-register stack, so it seems initially plausible that it could have caused a FLT_STACK check._ _Who designs a stack with just eight entries? Intel. It must have seemed like a good idea at the time._ Not to mention something those of us who grew up on Motorola MOS 6502, MC68000, SPARC, UltraSPARC and MIPS families always knew: intel might be really fast now, but under the hood, the architecture was and still is really, really shoddy. It's covered up by raw speed, but woe to one if they have to work with things "under the hood". I chuckled, half in amusement and half in grotesque disgust, when I read the bit about the stack with only eight entries, because the first thing I thought of when I read that was of UltraSPARC and register windows, effectively giving one 256 stacks by means of i0-i7 and o0-o7 registers (which in reality are part of the r0-r31 physical registers). I'm kind of comparing apples to oranges, but the difference in design approaches is striking. What a contrast! intel designers were always bad, even from the very first 4004, through 8008 to 8086. Their two shots at making things right, the i960 and Itanium RISC processors were both epic failures. They are so bad at designing _clean, elegant architectures_ , that a competitor, Advanced Micro Devices, had to implement 64-bit extensions on _their_ processors, and then intel had to license that from them. How much longer is intel going to be _the_ mainstream, I wonder? Is there any will for change of the status quo?
Q: Multiple SQL or Case statements in Scalar function I am struggling with a SQL function for a report I am writing. The function polls an audit table for the original value of a particular field (SecondarySchoolCode). If it finds a value in the audit table for the current row it should return the value, if there is no value for the current row then the original parameter I supplied to the function should be returned instead. I have tried using a Case statement but it is not returning the parameter back if there is no match in the audit table. Any suggestions on how to accomplish this? ALTER FUNCTION [dbo].[fn_AuditOriginalHSAttendingCode] ( @StudentID VARCHAR(255), @SecondarySchoolCode VARCHAR(255), @ColumnName VARCHAR(255) ) RETURNS VARCHAR(255) AS BEGIN DECLARE @Result AS VARCHAR(255); RETURN (SELECT TOP (1) CASE WHEN @ColumnName <> 'SecondarySchoolCode' THEN @SecondarySchoolCode ELSE dbo.GDSAuditDetail.ValueBeforeChange END FROM dbo.GDSAuditDetail INNER JOIN dbo.StudentSchool INNER JOIN dbo.Student ON dbo.StudentSchool.StudentId = dbo.Student.ID INNER JOIN dbo.SecondarySchool ON dbo.StudentSchool.SecondarySchoolId = dbo.SecondarySchool.ID INNER JOIN dbo.GDSAudit ON dbo.Student.ID = dbo.GDSAudit.EntityId ON dbo.GDSAuditDetail.GDSAuditId = dbo.GDSAudit.ID WHERE (dbo.Student.ID = @studentID) and dbo.GDSAuditDetail.GDSColumn='SecondarySchoolCode' ORDER BY dbo.GDSAudit.InsertedDate ASC) The call to the function looks like this: dbo.fn_AuditOriginalHSAttendingCode(dbo.Student.ID , dbo.SecondarySchool.SecondarySchoolCode , dbo.GDSAuditDetail.GDSColumn) A: I'm not sure what all of your relationships are, but based on your stated requirements and your current query, you are joining to some tables you don't need. The reason you don't get anything back when the audit doesn't exist is because there are no rows from which to select a TOP 1. This should always return at least one row for an existing Student. SELECT TOP (1) ISNULL(dbo.GDSAuditDetail.ValueBeforeChange, @SecondarySchoolCode) FROM dbo.Student LEFT JOIN dbo.GDSAudit ON dbo.Student.ID = dbo.GDSAudit.EntityId LEFT JOIN dbo.GDSAuditDetail ON dbo.GDSAuditDetail.GDSAuditId = dbo.GDSAudit.ID AND dbo.GDSAuditDetail.GDSColumn='SecondarySchoolCode' WHERE (dbo.Student.ID = @studentID) ORDER BY dbo.GDSAudit.InsertedDate ASC
Please help with verifying or updating older sections of this article. At least some were last verified for version 1.24. The religion that a nation follows and how tolerant it is of other faiths is an important aspect of gameplay in EUIV. The religion of a nation will confer specific benefits, enable different mechanics, and affect diplomatic actions as nations of mutually accepted religions have a better chance of reaching agreements with one another. Religion is also connected to unrest and provinces of non-tolerated religions are more rebellious. The player has some control over religion by having the option to change the state religion, send missionaries to convert heathen or heretic provinces to the state religion, and carry out religious decisions. Religions and denominations [ edit ] Religion by province in 1444. For more details use the navigation box (legend) above. Since EU4 first came out many of its featured religions have been further developed and fleshed out with unique mechanics. The following table details which religions are expanded by which DLC (in order of appearance). DLC Expanded mechanics Wealth of Nations Reformed Reformed Hindu Hindu Norse El Dorado Inti Inti Mayan Mayan Nahuatl Common Sense Protestant Protestant Mahayana Mahayana Theravada Theravada Vajrayana The Cossacks Tengri Rights of Man Coptic Coptic Fetishist Mandate of Heaven Confucian Confucian Shinto Third Rome Orthodox Cradle of Civilization Sunni Sunni Shia Shia Ibadi Rule Britannia Anglican Emperor Hussite Hussite Catholic Religious unity [ edit ] Religious unity is the percentage of a country's development provided by provinces that follow the state religion or a positively tolerated heretic or heathen religion, excluding any assigned to trade companies. Provinces of the state religion always contribute 100% unity regardless of tolerance. Provinces of a heretic or heathen religion contribute a percentage determined by how tolerated they are. The effects of tolerance on religious unity per province are as follows: Tolerance Contribution < 0 +0% 0 +25% 1 +50% 2 +75% 3 +100% For example, suppose a Catholic country has a 10 development Catholic province, a 4 development Protestant province, and a 16 development Sunni province. If heretic tolerance is +1 and heathen tolerance is -2, the country's religious unity will be (100% * 10 + 50% * 4 + 0% * 16) / (10 + 4 + 16) = 40% Ideas and policies which increase religious unity: Traditions Ideas Bonuses Policies +50% — Bengali idea 1: Bengali Hindu-Sufi Syncretism Gujarat Sultanate idea 1: Garba! Indian Sultanate idea 1: Tolerate the Idol Worshipers Jaunpuri idea 3: Sants and Sufis — — +33% South Indian traditions — — — +30% Sami traditions — — — +25% Bosnian traditions Granadan traditions Papal traditions Punjabi traditions Humanist idea 1: Tolerance Bahmani idea 2: Legacy of Gisu Daraz Ferraran idea 1: Papal Recognition Hessian idea 3: Welcome the Reformers Kazani idea 1: Steppe Tolerance Malvi idea 2: Malvi Art & Architecture Permian idea 6: Komi Tolerance Urbinate idea 4: A Humanist Court Zaporozhian idea 6: Steppe Tolerance — — +20% Ayutthayan traditions Bamberger idea 1: Bishop of Bamberg East Frisian idea 3: Center of Religious Thought Javan idea 1: Candi Shrines Karamanid idea 6: Home of the Whirling Dervishes Burmese idea 3: Nat Worship West African idea 4: Ancestors and Crescent — Humanist-Aristocratic: Enlightened Aristocracy Religious-Diplomatic: Policy of Calculated Delay Religious-Offensive: The Anti-Heresy Act +15% — Luccan idea 1: Mending the Papal Schisms Smolenskian idea 1: Smolenskian Resolve — — +10% — Ansbach idea 3: Franconian Reformers Bayreuther idea 4: Franconian Reformers Gond idea 2: Tribal Religion Highlander idea 4: Episcopalianism Pueblo idea 6: Clown Societies — — Religious unity directly affects the following: for each percentage point of religious unity:[1] +0.01 Monthly fervor +0.05 Maximum absolutism +5% Clergy loyalty equilibrium +5% Brahmins loyalty equilibrium for each percentage point of religious unity below 100%:[2] +1.0% Stability cost modifier +0.03 National unrest −1.0% Church power −0.01 Yearly devotion +0.001 Yearly corruption Tolerance [ edit ] Countries have three tolerance values. These tolerance values are national, but have provincial effects depending on the province's religion, relative to the state religion. Each point of positive tolerance gives:[3] −1 Local unrest Each point of negative tolerance gives:[4] +1.25 Local unrest −10% Local tax modifier −10% Local goods produced modifier Additionally, positive tolerance of heretics and heathens allows those provinces to contribute to religious unity (see above). Note that there are some national ideas which remove all penalties for having negative tolerance. Traditions Ideas Bonuses Policies yes Colonial traditions Texan traditions Vermont traditions Hungarian idea 7: Create the Estates General Kiwi idea 1: Maori Seats Piratical idea 1: Religious Apathy Rothenburg idea 1: Zarfat Registry — — Tolerance of the true faith [ edit ] This refers to the state religion. For example, if the state religion is Catholic, Catholic provinces will use this tolerance value. The base value of tolerance of the true faith is +3, and there is no maximum value. Ideas and policies that affect tolerance of the true faith: Traditions Ideas Bonuses Policies +3 Byzantine traditions — — — +2 Ladakh traditions Lan Xang traditions Laotian traditions Leonese traditions Lusatian traditions Québécois traditions Romanian traditions Sukhothai traditions Tapuian traditions Tirhuti traditions Trierian traditions Religious idea 4: Devoutness *Ainu idea 6: Yukar Al-Haasa idea 2: Lord of the Bedouin of the East Anhalt idea 3: Incorporation of the Bishopric Amago idea 6: Kizuki Antemoro idea 5: Religious Control Ardabili idea 3: Leader of all Shiites Asakura idea 6: Control of Buddhist Sects Asturian idea 2: Camino de Santiago Bamberger idea 6: Vierzehnheiligen Berg idea 7: Respecting the Autonomy of the Clergy Bharathi idea 5: Ganga Bremish idea 2: Memories of Verden Cham idea 1: Memory of the My Son Temples Chernihiv idea 6: Renovate the Transfiguration Cathedral Chosokabe idea 7: Support of the Temples Cornish idea 3: Prayer Book Traditionalism Dithmarscher idea 2: Kirchspiele Farsi idea 1: Land of the Persians French ducal idea 4: Religious Conviction Fulani Jihad idea 5: Islamic Scholarship Garhwali idea 6: Protecting the Land of the Gods Garjati idea 6: Jagannath Cult Georgian idea 3: Legacy of Saint Nino Greek idea 1: Greek Orthodox Faith Hejazi idea 1: Custodian of the Two Holy Cities Herzegovinian idea 1: Eparchy Interlacustrine idea 4: Holy Lineages Khorasani idea 6: Great Sheiks of Khorasan Kitabatake idea 2: Blessing of Amaterasu Lan Na idea 4: The White Elephant Lorraine idea 6: Trois-Évêchés Manipur idea 4: Mayek Medri Bahri idea 2: Christian Legacy Miao idea 1: Sacrificing to the Spirits Moravian idea 2: Religious Sanctuary Mossi idea 6: Honoring the Masks Münster idea 1: Great Procession Najdi idea 7: Enforce Tawhid Northumbrian idea 3: Cradle of British Christianity Offaly idea 4: The Fear of God Ogasawara idea 7: Zenko-ji Orleanaise idea 3: Faith and Devotion Papal idea 1: Ecclesiastical Primacy Pegu idea 3: Dhammazedi Perugian idea 3: Meeting of the Five Conclaves Pueblo idea 6: Clown Societies Rajputana idea 5: Protectors of the Dharma Rostov idea 3: Ecclesiastical Center Sami idea 5: Defend the Noaidi Traditions Samtskhe idea 7: A Sacred Land Songhai idea 6: Sharia Tokugawa idea 6: Toshogu Transylvanian idea 6: Unitarian Zeal Trent idea 1: Prince-Bishop Tumbuka idea 4: Office of the Mulwa Tyrconnell idea 3: Religious Patrons Ulmer idea 7: Finish the Ulm Minster Württemberger idea 5: Grosse Kirchenordnung Yarkandi idea 4: Empower the Khojas Yi idea 5: Promote the Bimoism Mushasha ambition — +1 Clanricarde traditions Thomondian traditions Croatian idea 4: Antemurale Christianitatis Dhundhari idea 3: Restore Hindu Ceremonies Genevan idea 4: Spiritual Leader of Geneva Gujarati Princedom idea 5: Protect the Dwarkadhish Temple Hatakeyama idea 3: Mount Koya Kanem Bornuan idea 4: House of Kanem Khmer idea 2: Theravada Buddhism Kievan idea 5: Center Of Orthodox Church Montenegrin idea 2: Metropolitanate of Montenegro Muscovite idea 3: Seat of Metropolitan Bishop Nepalese Princedom idea 3: Institute New Festivals Prussian idea 1: Legacy of the Teutonic Knight Ruthenian idea 7: Birth of Russian Orthodoxy Saluzzo idea 6: Chiesa San Giovanni Sardinian idea 2: Papal Restoration Sindhi idea 4: Expand the Makli Necropolis Swahili idea 3: Great Mosque of Kilwa Teutonic idea 7: One State, One Religion Theodorian idea 7: Cave Monasteries Three Leagues idea 2: The League of God's House Tunisian idea 7: Tunisian Caliphate Utrecht idea 1: Devotio Moderna Vindhyan idea 3: A Sacred Land Welsh idea 7: Welsh Church — — Additional modifiers: +0.5 for ‘Trading in’ incense for ‘Trading in’ incense –2 for ruler with ‘Sinner’ personality Tolerance of heretics [ edit ] This refers to different religions within the same religious group. For example, if the state religion is Catholic, the religion group is Christian, and provinces that are Protestant, Reformed, Coptic, Orthodox, or Anglican will use this tolerance value. The base value of tolerance of heretics is −2. The possible maximum value is +3. Ideas and policies that affect tolerance of heretics: Traditions Ideas Bonuses Policies +5 — American idea 1: Freedom of Religion — — +4 Athenian traditions Bosnian traditions Cypriot traditions Epirote traditions Naxian traditions — — — +3 Dali traditions Lithuanian traditions Ajami idea 2: In Honor of Ali Bohemian idea 1: Compacta of Prague Dutch idea 5: Embrace Humanism Lusatian idea 6: Rights for all Religions Qara Qoyunlu 3: In Honor of Ali Saxon idea 4: Wittenberg University Transylvanian idea 5: Patent of Toleration Polish ambition — +2 Al-Haasa traditions Humanist idea 3: Ecumenism Alaskan idea 5: Alaskan Religious Diversity Baden idea 4: Cuius Regio, Eius Religio Burgundian idea 6: Allow Freedom of Worship Canadian idea 5: The Quebec Act Dortmund idea 7: Reinoldikirche East Frisian idea 5: Refuge of the Mennonites French idea 7: Liberté, Égalité, Fraternité Ilkhanid idea 2: Favor Sufism Kurdish idea 2: Li Gora Gawirî Kurd Misilman e Luccan idea 1: Mending the Papal Schisms Lur idea 4: Popular Religion Pomeranian idea 4: Religious Freedom Ruthenian idea 2: Foreign Influences Swiss idea 2: Swiss Tolerance Thüringian idea 3: Protector of Reformers Utsunomiya idea 7: Mount Nikko Gelre ambition Religious-Plutocratic: The Tolerance Act +1 — Albanian idea 6: Albanian Tolerance Arawak idea 4: Tribal Tolerance Circassian idea 7: Religious Flexibility Frisian idea 6: Difference of Opinion Garhwali idea 7: Crossroads of Faith Kikuchi idea 5: Religious Coexistence Ouchi idea 6: Welcome the Westerners Prussian idea 7: Religious Toleration Sligonian idea 7: Pragmatism Over All Tibetan idea 4: The Way of Virtue Urbinate idea 4: A Humanist Court Vijayanagar idea 4: Tolerance Westphalian idea 6: Religious Toleration — — Additional modifiers: +1 for ruler with ‘Tolerant’ personality Heretic conversion events [ edit ] Tolerance of heretics of ≥ 2 will allow provinces to randomly convert to those heretic religions. The mean time to happen is 5000 months, lowered by Innovative Ideas and having a neighboring province with the new religion while increased by having the theocracy government type. Provinces with the "Religious Zeal" modifier will not receive these events at all. A province is more likely to convert via event to a particular religion if a neighboring province has that religion. Adjacency is not required for most conversions. However, the following conversions only occur if a neighboring province has the new religion: Orthodox ↔ other Christian Buddhist, Shinto → Confucian In addition, only Japanese-culture provinces can convert to Shinto as the result of an event. Tolerance of heathens [ edit ] This refers to religions of other religious groups. For example, if the state religion group is Christian, provinces that are of Muslim, Eastern, or Pagan religious groups will use this tolerance value. The base value of tolerance of heathens is −3. The possible maximum value is +3. Ideas and policies that affect Tolerance of heathens: Traditions Ideas Bonuses Policies +3 Ottoman traditions Semien traditions Andalusian idea 3: Alh Ulh Dhimma Granada idea 1: People of the Book Rûmi idea 4: Sultan of Rûm Siddi idea 1: Goma — — +2 Javan traditions Kaffan traditions Kazani traditions Malian traditions Pagarruyung traditions Permian traditions Humanist idea 7: Humanist Tolerance Arakanese idea 2: Rohingya Immigrants Carib idea 6: Religious Syncretism French idea 7: Liberté, Égalité, Fraternité Golden Horde idea 7: Religious Pragmatism Guarani idea 4: Jesuit Conversions Ito idea 6: Sympathy for New Faiths Kutai idea 2: Muslim Trading Communities Laotian idea 3: Satsana Phi Luzon idea 4: Tagalog Syncretism Malayan sultanate idea 2: Sufi Legacy Mindanao idea 1: An Islamicized Barangay Mysorean idea 3: Religious Tolerance Omani idea 3: Association With Unbelievers Sadiyan idea 2: Crossroad of Religions Tripuran idea 3: Religious Syncretism Samtskhe ambition — +1 — Albanian idea 6: Albanian Tolerance Circassian idea 7: Religious Flexibility Frisian idea 6: Difference of Opinion Garhwali idea 7: Crossroads of Faith Kikuchi idea 5: Religious Coexistence Ouchi idea 6: Welcome the Westerners Sligonian idea 7: Pragmatism Over All Tibetan idea 4: The Way of Virtue Vijayanagar idea 4: Tolerance Westphalian idea 6: Religious Toleration — — Additional modifiers: +1 for ruler with ‘Tolerant’ personality Defender of the Faith [ edit ] Each Christian or Muslim denomination can have one Defender of the Faith. It costs 500 ducats for a country to claim the title. Countries with female rulers, regencies or which are subject nations cannot claim the title. Being Defender of the Faith gives the following modifiers (without ): +1 Missionary +5% Morale of armies +5% Morale of navies −0.03 Monthly war exhaustion +1 Yearly prestige +5% Technology cost +1 Yearly papal influence +0.5 Yearly devotion Additionally, all other countries of the same religion get a +10 “Defender of Faith” relations boost with the title holder. Countries automatically call the Defender of the Faith of their religion to arms if attacked by a nation of another religion. Since patch 1.8, it seems the Defender of the Faith gets a call to arms only for countries on the same continent or sharing their border. The Defender of the Faith doesn't get a call to arms if the country attacked is a co-belligerent (e.g., if France is the Catholic Defender of the Faith and Venice (Catholic) is allied with Serbia (Orthodox), then if Ottomans (Sunni) attack Serbia and make Venice co-belligerent, France doesn't get a call to arms). Catholic countries that hold the Defender of the Faith title cannot be excommunicated by the Papacy, regardless of relations. The Defender of the Faith loses the title, but no prestige, if they refuse or lose the war. If Defender of the Faith refuses a call to war, it gets a 5-years truce with the country that was calling. Therefore, if your ally is Defender of the Faith and you have a common enemy of the "defended" religion, this ally will not be able to join you in an offensive war against this enemy, as AI wouldn't break a truce. Note: If the title holder ends any war with a result other than a white peace or victory, the title will be lost. Depending on the strength of the Faith (based on number of countries), multiple tiers of Defender of the Faith are available:[5] Amount of countries Effects – Defender of the Faith Effects – All countries with the true faith 1–5 +1 Missionary Missionary −10% Missionary maintenance cost 5–10 +1 Missionary Missionary −10% Missionary maintenance cost Missionary maintenance cost +0.5 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion 10–20 +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige 20–50 +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion Monthly war exhaustion +20% Manpower in true faith provinces 50+ +1 Missionary Missionary −20% Missionary maintenance cost Missionary maintenance cost +5% Morale of armies Morale of armies +5% Morale of navies Morale of navies +1.0 Yearly prestige Yearly prestige −0.03 Monthly war exhaustion Monthly war exhaustion +20% Manpower in true faith provinces −20% Missionary maintenance cost[6] Achievements [ edit ] God Tier Become a Tier 5 Defender of the Faith as a nation that is neither Catholic nor Sunni. Conversion [ edit ] Province conversion [ edit ] The most common way to convert provinces is the use of missionaries, but there are also several other methods. If you have the Cradle of Civilization DLC , you have the ability to directly convert your subjects' provinces to your subjects' State religion.[7] Missionaries are envoys that can convert a province to a nation's official religion. Missionaries slowly convert provinces over time: each month, the effective missionary strength in that province is added as ongoing progress, and when it reaches 100% the province is converted. If strength is insufficient (less than 0%), the province will never convert (although the missionary will not lose progress). An active missionary in a province will increase the unrest there by +6%. [8] Each country has 1 missionary by default. More can be obtained through the following: Ideas and policies: Traditions Ideas Bonuses Policies +1 Asturian traditions Bamberger traditions Colognian traditions Divine traditions Sindhi traditions Religious idea 1: Missionary Schools Ajuuraan idea 3: Gareen Imams Castilian idea 2: Spanish Inquisition Circassian idea 4: Franciscan Missionaries Ethiopian idea 5: The Ark of the Covenant Fulani Jihad idea 1: Wandering Scholars Herzegovinian idea 2: Saint Sava Jerusalem idea 4: Land of the Heathen Lotharingian idea 6: Land of Bishops Münster idea 3: Founding of Monasteries Mushasha idea 2: Messianic Legacy of Muhammad bin Falah Najdi idea 2: Hanbali School Otomo idea 5: Christian Converts Perugian idea 5: Heartbeat of Christianity Teutonic idea 6: Promote Prussian Bishops Tyrconnell idea 4: St Patrick's Purgatory Utrecht idea 5: City of Churches Bremish ambition Leinster ambition Munster ambition Najdi ambition Northumbrian ambition — Decisions and events: Event modifier Trigger Duration +2 Counter-Reformation Decision: “Embrace the Counter-Reformation” until one of the four “The Counter-Reformation Ends” events. +1 Melchior Klesl Austrian event: “Melchior Klesl” Option: ‘Such devotion! We have need of this man on the privy council.’ until ruler changes. Missionary maintenance [ edit ] The player can adjust the missionary maintenance cost by a slider on the economy interface between zero and full funding. Reducing the funding reduces missionary strength linearly, up to −5% missionary strength without funding. At full funding the costs of an active missionary per month is calculated based on the development and local autonomy of the province as follows[9]: The following ideas reduce missionary maintenance cost: Traditions Ideas Bonuses Policies −50% — Religious idea 6: Inquisition — — −25% Jerusalem traditions — — — Base missionary strength is 2%. Modifiers that increase strength include: Advisors: +2% from an Inquisitor advisor from an Inquisitor advisor Stability: +0.5% for each point of positive stability for each point of positive stability Piety: Up to +3% for Muslim states that are inclined towards Mysticism Up to for Muslim states that are inclined towards Mysticism Patriarch Authority: Up to +2% for Orthodox states that have Patriarch Authority. Up to for Orthodox states that have Patriarch Authority. Coptic Blessing: +1.5% for Coptic states that have the Send Monks to Establish Monasteries blessing. ( Rights of Man only) for Coptic states that have the Send Monks to Establish Monasteries blessing. ( Rights of Man only) Building: +3% for a Cathedral for a Cathedral Decisions: A number of national decisions increase (or decrease) missionary strength. A number of national decisions increase (or decrease) missionary strength. Events: Many events give a temporary bonus (or penalty) to missionary strength. Many events give a temporary bonus (or penalty) to missionary strength. Province's current religion: +2% in pagan provinces. in pagan provinces. Holy Roman Empire: +1% for being the dominant religion in the Holy Roman Empire for being the dominant religion in the Holy Roman Empire State Edict: +1% enacting Enforce Religious Unity (provinces within the stated area) enacting Enforce Religious Unity (provinces within the stated area) Converting religions through the Religion tab gives a +10% "Religious Zeal" bonus for ten years, but only to converting heretics, not heathens. "Religious Zeal" bonus for ten years, but only to converting heretics, not heathens. Several ideas also affect missionary strength: Traditions Ideas Bonuses Policies +3.0% — Religious idea 3: Divine Supremacy Byzantine idea 7: Restore the Ecumenical Patriarch — — +2.0% Bremish traditions Jerusalem traditions Najdi traditions Armenian idea 1: Apostolic Church Austrian idea 5: Edict of Restitution Asturian idea 5: Millenarian Revival Castilian idea 2: Spanish Inquisition Divine idea 4: Let No Man Tolerate the Witch Hindustani idea 6: Patronize Sufi Missionaries Javan idea 3: Dharmasastra Kanem Bornuan idea 4: House of Kanem Moldavian idea 5: Metropolis of Moldavia Nubian idea 5: Nubian Religious Unity Nuremberger idea 5: Franconian Centre of Reformation Pagarruyung idea 1: Tantric Legacy Palatinate idea 5: Heidelberg Catechism Rigan idea 4: Denounce Witchcraft Savoyard idea 4: Crush the Vaudois Sindhi idea 2: Bab ul Islam Sumatran idea 2: Porch of Mecca Teutonic idea 4: Assume Religious Authority Trent idea 7: Trent Religious Unity Utrecht idea 5: City of Churches Tsutsui ambition — +1.0% Ajuuraan traditions Lan Xang traditions Tibetan traditions Air idea 7: Ineslemen Teachings Arabian idea 4: Spreading the Prophet's Word Athenian idea 6: Preserve Archbishop of Athens Breton idea 4: Breton Catholicism Fulani Jihad idea 3: Fulani Jihads Genevan idea 5: Calvin's Laws German idea 5: Cuius Regio, Eius Religio Hejazi idea 6: Hajj Icelandic idea 3: Christian Identity Khivan idea 4: Djuma Mosque Kievan idea 5: Center Of Orthodox Church Leinster idea 1: Legacy of Palladius Muscovite idea 3: Seat of Metropolitan Bishop Novgorod idea 2: City of Churches Québécois idea 7: Jesuit Missions Saluzzo idea 6: Chiesa San Giovanni Sukhothai idea 4: Wat Si Sawai Sami ambition Religious-Aristocratic: The Witchcraft Act Religious-Diplomatic: Policy of Calculated Delay Religious-Espionage: Enforce Religious Law Religious-Trade: Religiously Sponsored Guilds In addition, a few ideas specifically affect missionary strength when converting heretics, but have no effect when converting heathens. Traditions Ideas Bonuses Policies +3% — Bavarian idea 4: Establish the Geistlicher Rat Colognian idea 5: Pivotal Ecclesiastic Territory Rûmi idea 7: Protector of Dar al-Islam — Religious-Offensive: The Anti-Heresy Act +2% — Aachen idea 5: Expel Heretical Officials Anhalt idea 7: The Confessor Ardabili idea 4: Conversion of the Masses Bamberger idea 5: Witch Burner Bulgarian idea 2: Root Out the Heresies Flemish idea 3: Beeldenstorm Irish idea 4: Loyal Catholics Manx idea 6: Burn the Heretic Mushasha idea 7: Sufis and Shias of the Middle East Ulster idea 5: Catholic Ascendency Finnish ambition Münster ambition — +1% Kievan traditions Clevian idea 3: Avid Reformers Herzegovinian idea 2: Saint Sava Welsh idea 7: Welsh Church — — Things that decrease this speed include: Province's current religion: −2% in Coptic, Muslim and Shinto provinces. in Coptic, Muslim and Shinto provinces. Province's current religion: −1% in Orthodox and Sikh provinces. in Orthodox and Sikh provinces. Culture: −2% for non-accepted cultures. for non-accepted cultures. Territories : provinces in territories get −2% . The penalty is only removed when the province is fully cored. : provinces in territories get . The penalty is removed when the province is fully cored. Trade company provinces get −100% provinces get Provincial development: −0.1% for each point of a province development level. for each point of a province development level. Religious Centers: Rome, Mecca, the initial Sikh province and all Protestant and Reformed Centers of Reformation get −5% . Rome, Mecca, the initial Sikh province and all Protestant and Reformed Centers of Reformation get . Recently converted provinces get −100% , called Religious Zeal for 30 years. Centers of reformation [ edit ] The first three European nations to convert to Protestant, the first three to convert to Reformed, and a British nation if it takes one of the appropriate choices to convert to Anglicanism, have a random European province designated as a Center of Reformation. These centers of reformation will automatically convert nearby provinces to their religion. Provinces converted by a center of reformation get the −100% religious zeal modifier to missionary strength in that province for 30 years. Missionaries can't work in the same province that is being converted by a center of reformation. Each center of reformation can only convert one province at a time. Players will receive a notification if all provinces within the center's range have been converted to its religion. A center of reformation is destroyed if its province is converted to another religion. The primary method for a Catholic nation to slow or stop the spread of the reformation is to conquer and convert a province with a center of reformation, thereby eliminating its missionary effect on neighboring provinces. A center of reformation will cease to convert provinces after start of the Age of Absolutism. Conversion using trade policy [ edit ] Muslim nations can enable "Propagate religion" policy in trade nodes inside a trade company region, provided that they control at least 50% of trade power in this node. While this policy is active, it will work the same way as a center of reformation. National conversion [ edit ] There are several different ways a country may change religion. By direct action [ edit ] Some religions may convert among certain heresies/sects via the Religion panel, at a cost of 100 prestige. This is true for Catholic, Protestant and Reformed Christians, Hindus and Sikhs once Sikhism is unlocked, as well as all Buddhists. Conversion by this method will give a whopping 10% missionary strength against Heretics for ten years, making conversion of provinces of the old faith quite rapid, unless it is entirely blocked due to local Religious Zeal modifiers. Sikhs can also convert to Sunni or Shia Islam this way. Conversion is also possible through decisions in some cases, which causes a -4 stability hit (except for Sikh or Sunni/Shia conversion, which only reduces it by 2). With the Sword and Crescent DLC, Sunni and Shiite (but not Ibadi) Muslims may convert to the other denomination if both their capital and the majority of their province development follows the other denomination. Without Mandate of Heaven, Japanese daimyos, but not the Shogun or Japan itself, may convert to Catholicism by decision if the majority of their territories are Catholic, which can happen following certain events in the 16th century. With Mandate of Heaven, the Open outcome for the Ikko - Ikki, Neo-Confucianism, and Spread of Christianity Incidents will unlock a decision to convert to Mahayana, Confucianism, and Catholic respectively. Pagan nations that are not Tengri may convert to any non-Pagan faith if they control a province of that faith; Tengri nations are limited to Vajrayana Buddhism. Muslims owning a Sikh province may decide to convert to Sikhism - this decision probably mostly exists to allow Punjab to easily follow its historical religion. By event [ edit ] Totemist and Animist pagans get events to convert to Catholic, Protestant, or Reformed Christianity if they have neighbors of the appropriate denomination and a sufficient positive opinion with that neighbor. Tengri pagans with a dominant secondary faith may be prompted to change to it or face a -3 stability hit; they also have event chains that end in conversion to their secondary religion. Kongo and Ming have special event chains to convert to Catholicism. A nation in the British region, typically England, can get an event, based on the wives of Henry VIII, to convert to Anglicanism with the Rule Britannia DLC. Some nations, for example Sweden, have unique events enabling them to change religion. Countries that have the Indian Sultanate government by default, but are neither Muslim nor were forcefully converted to another religion, will quickly be forced to choose by event between conversion to the appropriate branch of Islam, or facing a large amount of rebels and a stability hit. This generally only is the case if they have been released as a vassal or in a peace deal, which will likely make them Hindu initially, because Indian sultanates rarely convert the local religion, and indeed have no need to due to their large bonus to heathen tolerance. AI will always choose to convert. Forced conversion by other nations [ edit ] A nation can force a heretic country to change their state religion as part of a peace deal. The revolutionary target may also do this to heathens. Without an appropriate casus belli such as "Cleansing of Heresy" or "Religious Conformance" (unique to the Holy Roman Emperor against HRE members), this will have the same war score cost as annexing the nation. When a country is converted this way, only the state religion and the capital province's religion change. Note that at 100 war score, you can make the defeated opponent force convert you this way even if he wouldn't want that as part of a peace deal. Once the religion of the Holy Roman Empire has been locked, the emperor can also request a prince to change their state religion depending on their opinion of the Emperor. Similarly to when forcing a religion of an enemy country, the prince has its capital converted while the rest of the provinces remained unaffected. With the Common Sense DLC, suzerains may force their subject nations to change religions if they follow a different faith. If heretic, this gives +50 liberty desire, and if heathen +100 liberty desire, both gradually ticking down. Forced conversion by rebels [ edit ] Nations can support religious zealots in other countries. These rebels convert a province's religion to the one they represent when occupation is achieved. Supporting religious zealots is only possible if the desired religion is present in the target nation and is the likely rebel type in a province with unrest above 0. If there are no such provinces in the target nation, one way to achieve it is to sell the target a province of the correct religion. Generally the nation will be able to overpower the rebels if left to its own devices, so it is critical to support them militarily. This can be done by declaring war against the target nation using the "Support Rebels" casus belli. A nation that is broken by religious rebels, or that accepts their demands, will convert to the rebels' religion provided that the rebels' religion is the plurality religion in terms of development. For most countries, giving in to religious rebels is the only way to change between religious groups. However, only Animist rebels, not other types, can convert a non-Pagan nation to a Pagan faith. Thus Animism must serve as a springboard to conversion to other pagan faiths. Strategy [ edit ]
IN THE SUPREME COURT OF PENNSYLVANIA EASTERN DISTRICT COMMONWEALTH OF PENNSYLVANIA, : No. 495 EAL 2018 : Respondent : : Petition for Allowance of Appeal from : the Order of the Superior Court v. : : : QUINCEY ROSSER, : : Petitioner : ORDER PER CURIAM AND NOW, this 12th day of March, 2019, the Petition for Allowance of Appeal is DENIED.
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A local Teamsters union and two of its members sought to intervene in a class action lawsuit brought by United Parcel Service employees against the trustees of the New England Teamsters and Trucking Industry Pension Fund ("the Fund"). The district court left open the possibility of intervention at the remedial stage of the case--if one is required--but denied intervention for the liability proceedings on two grounds: appellants' motion was untimely and their interests were adequately represented by the existing parties. We find no abuse of discretion in the decision to deny intervention, and therefore affirm. I. 2 Five UPS employees filed this lawsuit in December 1986, claiming that the Fund's trustees had breached their fiduciary duty by assigning the UPS workers an unreasonably low benefit level and by prohibiting transfer of assets contributed on the workers' behalf to a separate pension plan. Plaintiffs claim entitlement to a higher benefit than other employees whose employers contribute to the Fund at the same rate as UPS because of their uniquely favorable actuarial characteristics. See Affidavit of Steven H. Klubock at p 7, Appendix at 138. Plaintiffs argue that these actuarial attributes mean that contributions made on their behalf end up heavily subsidizing the pensions of non-UPS workers; plaintiffs argue that UPS dollars instead should be used to support an increased benefit for UPS pensioners.1 3 The prospective intervenors--two non-UPS employees and the local union that represents them, Teamsters Local 122--claim entitlement to the same benefit as the UPS class members because their employer pays into the Fund at the same rate as UPS. In light of their assertedly equal standing, the intervenors contend that any resolution of the present parties' claims without their participation presents a strong possibility of unfairness to them. 4 Appellants first sought to intervene as defendants in March 1990, more than three years after the action began. Discovery had closed in mid-1989, and in October of that year the court had scheduled trial for June 25, 1990. In addition, substantial other pretrial activity had occurred. In July 1987, the district court denied the defendants' motion to dismiss. In October 1988, the district court denied cross-motions for summary judgment. On March 29, 1989, the court granted plaintiffs' motion to certify the plaintiff class. 5 The district court denied the motion to intervene on May 8, 1990, with a brief notation written at the bottom of the first page of applicants' motion. The court's ruling was as follows: 6 Motion to Intervene is denied. The Court will entertain a renewed Motion to Intervene at the remedy stage of the case, if such a stage is required. 7 The proposed intervenors then appealed to this court. After oral argument, we remanded the case because, without a statement of reasons from the district court, we were unable to perform a meaningful review of that court's action. See Fed.R.Civ.P. 24(a) and (b) (enumerating requirements for intervention). We therefore directed the court to submit an explanation "specify[ing] which intervention requirement, or combination of requirements, it found that appellants have failed to meet" and "its reasons for so finding," Order of the Court, Sept. 24, 1990. 8 The district court responded by listing two requirements. First, it held that "[a]ppellants failed to establish that their interests would not be adequately represented at the liability stage by the [D]efendants." Memorandum, Sept. 27, 1990 (emphasis in original). Second, the court held that the intervention motion was not timely filed: "To have granted said Motion at that late date would have caused a delay in the trial of a 1986 case which had been scheduled since October 6, 1989 for trial on June 25, 1990. Fed.R.Civ.P. 24(b)(2)." Id. 9 We now resume consideration of the appeal. II. 10 Appellants moved to intervene as defendants in this action either as of right under Rule 24(a) or permissively under Rule 24(b). We concentrate our discussion on Rule 24(a) because our conclusion that the court acted within its discretion in denying intervention as of right effectively disposes of the permissive intervention question as well. See International Paper Co. v. Town of Jay, 887 F.2d 338, 344 (1st Cir.1989) (A " 'district court has less discretion to limit the participation of an intervenor of right than that of a permissive intervenor.' ") (quoting Stringfellow v. Concerned Neighbors in Action, 480 U.S. 370, 382, 107 S.Ct. 1177, 1185, 94 L.Ed.2d 389 (1987) (Brennan, J., concurring)) (emphasis in International Paper). 11 Rule 24(a) provides that an applicant seeking intervention as of right must meet four requirements. First, the application must be timely. Second, the applicant must have a direct and substantial interest in the subject matter of the litigation. Third, the applicant must be so situated that the disposition of the action may as a practical matter impair or impede its ability to protect that interest. Finally, the applicant's interest must be inadequately represented by existing parties. Travelers Indemnity Co. v. Dingwell, 884 F.2d 629, 637 (1st Cir.1989); International Paper, 887 F.2d at 342. 12 An applicant's failure to meet any one of these requirements is a sufficient basis for denying intervention as of right, Travelers, 884 F.2d at 637, and our review is strictly limited to deciding whether the district court abused its discretion. International Paper, 887 F.2d at 344. In this case, although the district court gave two bases for its decision--adequacy of representation and untimeliness--we need go no further than the court's conclusion that intervention in the liability phase of the case should be denied as untimely sought. 13 The timeliness requirement "is of first importance," United Nuclear Corp. v. Cannon, 696 F.2d 141, 143 (1st Cir.1982), and the trial court's determination on that factor is entitled to substantial deference. See NAACP v. New York, 413 U.S. 345, 366, 93 S.Ct. 2591, 2603, 37 L.Ed.2d 648 (1973) (establishing abuse of discretion standard for timeliness factor); United States v. Metropolitan Dist. Comm'n, 865 F.2d 2, 5 (1st Cir.1989). Despite limited analysis by the district court, we are unable to say that its decision to reject the application as untimely fell outside the wide boundaries of its discretion. 14 In Culbreath v. Dukakis, 630 F.2d 15, 17, 20-24 (1st Cir.1980), we specified four factors to be considered in evaluating the timeliness of an intervention motion. These factors, as recently reiterated in Metropolitan Dist. Comm'n, 865 F.2d at 5, are: 15 (i) the length of time the prospective intervenors knew or reasonably should have known of their interest before they petitioned to intervene; (ii) the prejudice to existing parties due to the intervenor's failure to petition for intervention promptly; (iii) the prejudice the prospective intervenors would suffer if not allowed to intervene; and (iv) the existence of unusual circumstances militating for or against intervention. 16 We regret that the district court, in its response after remand, failed to address each of these factors. The court instead referred only to an anticipated delay in the trial if intervention were granted, a circumstance relevant to the prejudice factor. We nevertheless have chosen not to remand the case again and instead have examined whether the decision to deny intervention is supportable upon full application of the four-part Culbreath test to the facts contained in the record. See Fiandaca v. Cunningham, 827 F.2d 825, 833-35 (1st Cir.1987) (applying Culbreath test, "a step not taken by the district court," to determine whether that court could have found application to be untimely). We thus turn to the four Culbreath factors. 17 (i) The promptness of applicants' motion. The individual applicants claim not to have known anything about this case until the first week of March 1990. The union's chief executive officer, however, acknowledged in an affidavit dated March 15, 1990, that he had read about the litigation in a Boston newspaper "[s]ome time ago." The officer, John F. Murphy, recalled that the news story "indicated that several UPS employees were suing the Pension Fund to get a better pension." Murphy stated that he learned in November 1989 for the first time "that this lawsuit involved more than a few employees and could have an impact on the Union and its participants." 18 The applicants argue that their motion was prompt for purposes of the Culbreath test, despite the passage of more than three years since filing of the case, because they acted quickly after learning of the lawsuit's potential impact on themselves. At least with respect to the union, this argument is without merit. 19 Murphy admitted that he saw a newspaper report on the case long before March 1990. Even if the report Murphy saw referred only to the original five UPS plaintiffs, subsequent publicity and minimal investigation should have alerted him to the fact that this could become a substantial class action lawsuit. The plaintiffs' 1986 complaint requested class certification. Two articles in Boston newspapers in 1988 also reported the large numbers of UPS employees potentially involved. See The Boston Globe, Oct. 7, 1988, at 90 ("Teamsters pension fund attacked; Move is made to split 12,000 UPS workers from the program"); The Boston Herald, Aug. 12, 1988, at 58 ("UPS drivers consider breakaway from Teamsters"). Moreover, it seems that a lawsuit in which only a few UPS employees challenged the benefit procedure would have had the same impact on the union at the liability stage as a lawsuit involving thousands of UPS employees; in either case, the issue would be the propriety of the benefit levels set for UPS employees. 20 In addition, Murphy does not, and cannot, argue that the union's interest only recently developed because of a change in the nature of plaintiffs' claims. From the outset, the UPS employees asserted entitlement to higher pension benefits, the same claim that the applicants now say implicates their rights. Cf. Fiandaca, 827 F.2d at 834 (applicants had no inherent interest in the merits of the litigation until after defendant proposed to settle dispute by implicating plaintiffs' residence). 21 It was incumbent upon Murphy, as the union's top executive, to probe behind the headlines that he admitted seeing about this case. Cf. Culbreath, 630 F.2d at 21 ("We see no excuse for the failure of large, sophisticated labor unions to learn of a suit and reported decisions so related to the promotion prospects of their members."). See also Narragansett Indian Tribe v. Ribo, Inc., 868 F.2d 5, 7 (1st Cir.1989) ("Parties having knowledge of the pendency of litigation which may affect their interest sit idle at their peril.") (emphasis added). Local 122's delay in seeking intervention is therefore not excusable. 22 The circumstances differ somewhat with respect to the individual applicants, who did not become aware of the lawsuit at all until March 1990. They, too, however, had access to information about the litigation through the news coverage. In addition, the individuals' lack of knowledge is directly attributable to the union's failing to pursue the information it possessed. We think it is within the trial court's discretion to refuse to allow the individual applicants to evade, through personal ignorance, the repercussions of dilatory action on the part of their group representative--at least when the individuals, as in this case, had the opportunity to learn of the lawsuit through the press or other public means. 23 The district court, therefore, properly could have found that the applicants unduly delayed in filing their intervention motion. 24 (ii) Prejudice to existing parties. This factor apparently weighed heavily in the district court's mind. Avoiding such prejudice has, in fact, been "described as 'the purpose of the basic requirement that the application to intervene be timely,' " United Nuclear Corp., 696 F.2d at 143 (quoting Culbreath, 630 F.2d at 22). The court believed that allowing intervention just over three months before the scheduled trial date, and months after the close of discovery, inevitably would delay the start of the trial--unquestionably a detriment to the plaintiffs.2 Appellants sought to defuse the potency of this factor by stating in their motion that, if permitted to intervene, they would not seek to reopen discovery. The fact remains, however, that plaintiffs almost certainly would need to conduct discovery of appellants to adequately prepare for a trial that included the appellants as defendants. We previously have noted that intervention is less likely to cause prejudice when it relates to an ancillary issue than when it relates to the merits, see Public Citizen v. Liggett Group, Inc., 858 F.2d 775, 786 (1st Cir.1988). In this case, the applicants seek to oppose plaintiffs' primary argument that UPS employees are entitled to higher benefits than other employees, such as themselves. The district court evidently recognized that plaintiffs would want to understand the nature of the applicants' argument in order to meet it, and would need time to prepare. As a result, a delay in the trial reasonably could be expected. 25 Thus, the second factor supports the district court's conclusion of untimeliness. 26 (iii) Prejudice to the prospective intervenors. Appellants argue that this factor weighs in their favor because they will be required to abide by the results of a litigation that directly impacts them without having had a voice in the decision. In our view, however, the potential harm to appellants from exclusion on liability issues is minimal. Indeed, appellants' brief fails to explain how their absence from the liability phase would be likely to affect the outcome on liability, and it instead concentrates on the ways in which exclusion from the remedial phase of the case would be prejudicial. The nature of the case reveals that this was not an accidental imbalance of attention. 27 The question on liability is whether the defendant trustees breached their fiduciary duty to the UPS employees by setting pension benefits without regard to those employees' uniquely favorable actuarial characteristics. We think it unlikely that the applicants' position on this particular question would differ from that of the Fund. Both presumably would seek to show that the UPS plaintiffs are not entitled to singularly high benefits, and that the Fund properly may refuse to allow the UPS plaintiffs to set up a separate pension plan. It is not until there is a finding of liability against the trustees that the interests of the applicants would be likely to diverge markedly from that of the trustees. Once the focus turns toward developing a remedy, the trustees' responsibility would be to balance the interests of the UPS employees against the other employees served by the Fund, including the applicants. At that point, it would be important for the applicants to have a voice in the process equivalent to that of the plaintiffs.3 28 This, at least, must have been the view of the district court judge, who explicitly acknowledged that the intervention factors might play out differently when, and if, remedial issues are reached. We find no abuse of discretion in this view, and thus conclude that the third timeliness factor also supports the court's decision.4 29 (iv) Unusual circumstances. Although no special circumstance appears to militate for intervention, it is significant that the district court's decision against intervention did not deny all participation by the applicants in this litigation. The district court obviously anticipates two discrete parts of the case, and has indicated its willingness to consider intervention again if it is necessary to conduct proceedings on a remedy. We are confident that the court would give serious consideration to a renewed motion to intervene and, indeed, think it unlikely based on our review of the case that the court would deny such a motion. Thus, it appears that the applicants will have the opportunity to participate in the case at the stage they acknowledge is the most critical for them. In our view, this later opportunity to participate supports the district court's decision not to delay the start of the liability phase of the case. Any possible prejudice resulting from plaintiffs' exclusion from the first part of the case would likely be offset by their later participation. 30 In summary, then, our review of the Culbreath factors fails to turn up any indication that the district court acted outside its discretion in denying the motion to intervene at this juncture of the case. Because our task is to determine only whether the court properly balanced the timeliness factors, it is clear that in this case, where the factors uniformly support the court's decision, there was no abuse of discretion. Our scrutiny suggests that the court articulated only the delay factor because that loomed large in its mind and none of the other factors counseled in favor of intervention at the liability stage. 31 Accordingly, the judgment of the district court is affirmed. This court having issued a decision on the merits, plaintiffs' motion regarding jurisdiction is dismissed as moot. Costs to plaintiffs. This description of plaintiffs' argument is based primarily on oral argument, the affidavit of actuary Steven Klubock and the Joint Stipulation dated June 4, 1990 that was signed by counsel for both plaintiffs and defendants. Plaintiffs' argument apparently has been refined during the pendency of the litigation. In their complaint, plaintiffs seem to have raised a more general claim, that the benefit for employees whose employers historically contributed to the Fund at the maximum rate was lower relative to the contributions made on their behalf than the benefits of employees whose employers contributed to the Fund at a lower rate. See Complaint at pp 36-38. See also District Court Memorandum of Decision, July 31, 1987 (denying defendants' motion to dismiss). This more general argument would seem applicable to all employees, whether or not working for UPS, whose employers made contributions on their behalf at the maximum rate for an extended period of time. The present argument, however, distinguishes UPS employees from all other Fund participants We recognize that plaintiffs' argument originally was formulated more broadly in that it challenged generally the benefit level set for employees whose employers had contributed to the Fund at the maximum rate for a substantial period of time. See supra at note 1. Under that formulation, the applicants, who claim to fall in that category and thus be similarly situated to the plaintiffs, would have more of a direct interest in the liability issue. We question whether the prejudice from a denial of intervention would be any greater, however, even if we analyzed the issue in the context of the broader argument. It seems that the applicants' interest then would be aligned with one or the other of the parties, depending upon applicants' outlook. They could join the plaintiffs in claiming entitlement to a higher benefit for their class of employees or join the trustees in claiming that the health of the Fund requires the benefit system to continue in its present form This factor--the prejudice suffered by the prospective intervenors from a denial of intervention--sometimes turns solely on whether the applicant demonstrates inadequate representation by an existing party, which is also a general intervention requirement. See, e.g., Narragansett Indian Tribe, 868 F.2d at 8; United Nuclear Corp., 696 F.2d at 143. We do not believe, however, that a finding of no prejudice as part of the timeliness inquiry, based on adequate representation, necessarily leads to a finding of adequate representation on the general requirement, and, as earlier stated, we explicitly refrain from deciding the issue of adequate representation in this case. But it is worth noting that "the adequacy of existing representation is sometimes regarded as only a minimal barrier to intervention," Moosehead San. Dist. v. S.G. Phillips Corp., 610 F.2d 49, 54 (1st Cir.1979), and that "[i]f the applicant shows that the representation may be inadequate ..., then the court is precluded from finding that the interest is adequately represented," Flynn v. Hubbard, 782 F.2d 1084, 1090 (1st Cir.1986) (Coffin, J., concurring) (emphasis in original). See also Trbovich v. United Mine Workers, 404 U.S. 528, 538 n. 10, 92 S.Ct. 630, n. 10, 30 L.Ed.2d 686 (1972). Moreover, the burden of persuasion that representation is adequate appears to rest on the party opposing intervention. See Flynn, 782 F.2d at 1090 n. 4; C. Wright, A. Miller & M. Kane, 7C Federal Practice and Procedure Sec. 1909 at 314 (1986). Thus, it may be that the inadequate representation requirement would be met in circumstances that do not establish prejudice under the Culbreath test. We raise this point only to clarify that our opinion does not address the question of adequate representation; we express no view at this time on whether the two factors should lead to similar results
A 5-kilobase pair promoter fragment of the murine epididymal retinoic acid-binding protein gene drives the tissue-specific, cell-specific, and androgen-regulated expression of a foreign gene in the epididymis of transgenic mice. The murine epididymis synthesizes and secretes a retinoic acid-binding protein (mE-RABP) that belongs to the lipocalin superfamily. The gene encoding mE-RABP is specifically expressed in the mouse mid/distal caput epididymidis under androgen control. In transgenic mice, a 5-kilobase pair (kb) promoter fragment, but not a 0.6-kb fragment, of the mE-RABP gene driving the chloramphenicol acetyltransferase (CAT) reporter gene restricted high level of transgene expression to the caput epididymidis. No transgene expression was detected in any other male or female tissues. Immunolocalization of the CAT protein and in situ hybridization of the corresponding CAT mRNA indicated that transgene expression occurred in the principal cells of the mid/distal caput epididymidis, thereby mimicking the spatial endogenous mE-RABP gene expression. Transgene and mE-RABP gene expression was detected from 30 days and progressively increased until 60 days of age. Castration, efferent duct ligation, and hormone replacement studies demonstrated that transgene expression was specifically regulated by androgen but not by any other testicular factors. Altogether, our results demonstrate that the 5-kb promoter fragment of the mE-RABP gene contains all of the information required for the hormonal regulation and the spatial and temporal expression of the mE-RABP gene in the epididymis.
«Nous refusons la passivité face à l’abstention, au vote Front national et à la droitisation de la société. Nous refusons les renoncements face aux inégalités sociales, à la dégradation environnementale, aux discriminations et à l’affaissement démocratique. Nous refusons la paralysie de nos institutions. «Nous n’acceptons pas que la menace du FN, le risque terroriste et l’état d’urgence permanent servent de prétexte pour refuser de débattre des défis extraordinaires auxquels notre société est confrontée. Il n’y a pas de fatalité à l’impuissance politique. La France est riche de son énergie vitale et de ses talents qui aspirent à forger un avenir bienveillant. Nous voulons faire de la prochaine élection présidentielle la conclusion d’un débat approfondi qui est passionnément désiré et attendu dans le pays. «Nous voulons du contenu, des idées, des échanges exigeants. Nous appelons à une grande primaire des gauches et des écologistes. Notre primaire est la condition sine qua non pour qu’un candidat représente ces forces à l’élection présidentielle en incarnant le projet positif dont la France a besoin pour sortir de l’impasse. Elle est l’opportunité de refonder notre démocratie. En signant cet appel, je m’engage à voter lors de la primaire des gauches et des écologistes. Je participerai dans la mesure du possible aux débats qui seront organisés pour la nourrir. Signez et faites signer, pour réanimer le débat politique, pour se réapproprier l’élection présidentielle, pour choisir notre candidat-e !» Pour signer et faire signer l'appel, rendez-vous sur le site notreprimaire.fr Les premiers signataires A lire la version longue de l'appel
Red cell associated IgG in patients suffering from Plasmodium falciparum malaria. Quantitation of red cell associated IgG in 62 Gambian patients with P. falciparum malaria and 23 normal adult controls was carried out, using a purified 125I-labelled anti IgG. The number of IgG molecules per red cell was found to be between 90-897 molecules for patients with malaria and 100-233 for controls. 12 patients with malaria had raised levels of RBC associated IgG. There was no correlation between severity of anaemia and RBC associated IgG levels in patients with malaria nor was there a correlation between reticulocytosis and RBC associated IgG levels. It is concluded that although immune haemolysis may occur in some patients with malaria who have high levels of IgG or activated complement components on their red cells, other factors such as marrow suppression or ineffective erythropoiesis play an important role in the pathogenesis of the post-malaria anaemia.
1. Field of the Invention The present invention relates to the treatment of allergic or inflammatory diseases or other Syk-mediated diseases or conditions. More particularly, the present invention relates to the topical or systemic administration of certain 3,6-substituted imidazol[1,2-b]pyridazine analogs for the treatment of such diseases or conditions. 2. Description of the Related Art Syk is a tyrosine kinase that plays a critical role in mast cell degranulation, eosiniphil activation, lipid mediator synthesis and cytokine production. Accordingly, Syk kinase is implicated in various inflammatory and allergic disorders in particular asthma. It has been shown that Syk binds to the phosphorylated gamma chain of the high affinity IgE receptor (Fcε RI) signaling via N-terminal SH2 domains and is essential for downstream signaling [Taylor et al, Molecular and Cellular Biology 1995; 15:4149-4157]. Syk kinase is important in the intracellular propagation of signaling following the crosslinking of the high affinity IgG receptor (FcγRI) by IgG. Since the mediators released as the results of Fcε RI and FcγRI are responsible at least in part for adverse effects associated with allergic responses or inflammation, compounds that inhibit Syk kinase may be effective in inhibiting those adverse effects [Sirganian et. al. Molecular Immunology 2002, 38:1229-1233]. The term “Syk-mediated disease” or “Syk-mediated condition”, as used herein, means any disease or other deleterious condition in which Syk protein kinase is known to play a role. Such conditions include, without limitation, inflammation and allergic disorders, especially asthma. As taught in WO 2004/014382 (Rigel Pharmaceuticals) certain 2,4-pyridinediamine compounds have Syk kinase inhibitory activity. Lai et. al. describe a series of oxindoles having Syk kinase activity [Biorganic and Medicinal Chemistry Letters 2003, 13:3111-3114. Cywin et. al. describe the activity of a series of [1,6]naphthyridine compounds that inhibit Syk kinase [Biorganic and Medicinal Chemistry Letters 2003, 13:1415-1418]. Yamamoto et. al. describe an orally available imidazo[1,2,c]pyrimidine Syk kinase inhibitor [Journal of Pharmacology and Experimental Theapeutics 2003, 306:1174-1181]. WO2004/085409 discloses 5-substituted 2,3-diaminopyrazines.
import unittest class TestKnittingJob(unittest.TestCase): def test___init__(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) assert True # TODO: implement your test here def test_configure_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.configure_job()) assert True # TODO: implement your test here def test_get_plugin_name(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.get_plugin_name()) assert True # TODO: implement your test here def test_knit_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.knit_job()) assert True # TODO: implement your test here def test_start_job(self): # knitting_job = KnittingJob(plugin_class, port, knitpat_file) # self.assertEqual(expected, knitting_job.start_job()) assert True # TODO: implement your test here if __name__ == '__main__': unittest.main()
Respecification of ectoderm and altered Nodal expression in sea urchin embryos after cobalt and nickel treatment. In the sea urchin embryo, Nodal is the earliest known signal to play a role in the specification of the oral ectodermal territory. Nodal, a TGF-beta ligand, is first expressed in the presumptive oral ectoderm at approximately 7 H of development. Nodal overexpression produces a distinctive bell-shaped phenotype with expanded oral ectoderm, which resembles the oralized phenotype obtained as a result of nickel (Ni) treatment. To date, a detailed analysis of gene expression in Ni-treated embryos has not been undertaken. Because treatment with cobalt (Co) produces similar results to those seen with Ni treatment in other systems, we were interested in determining how Co influences sea urchin embryonic development. Here we report that Co also induces oralization of the ectoderm, and the effects of Ni and Co depend on functional Nodal signaling. Although both metals upregulate nodal gene expression, they do not initiate nodal transcription precociously. Analysis of the perturbation of Nodal receptor function suggests that Ni and Co contribute to nodal upregulation in the absence of nodal autoregulation, but cannot fully oralize the ectoderm in the absence of Nodal signaling.
--- abstract: 'The detection of a gravitational capture of a stellar-mass compact object by a massive black hole (MBH) will allow us to test gravity in the strong regime. The repeated, accumulated bursts of gravitational radiation from these sources can be envisaged as a geodesic mapping of space-time around the MBH. These sources form via two-body relaxation, by exchanging energy and angular momentum, and inspiral in a slow, progressive way down to the final merger. The range of frequencies is localised in the range of millihertz in the case of MBH of masses $\sim 10^6\,M_{\odot}$, i.e. that of space-borne gravitational-wave observatories such as LISA. In this article I show that, depending on their orbital parameters, intermediate-mass ratios (IMRIs) of MBH of masses between a hundred and a few thousand have frequencies that make them detectable (i) with ground-based observatories, or (ii) with both LISA and ground-based ones such as advanced LIGO/Virgo and third generation ones, with ET as an example. The binaries have a signal-to-noise ratio large enough to ensure detection. More extreme values in their orbital parameters correspond to systems detectable only with ground-based detectors and enter the LIGO/Virgo band in particular in many different harmonics for masses up to some $2000,\,M_{\odot}$. I show that environmental effects are negligible, so that the source should not have this kind of complication. The accumulated phase-shift is measurable with LISA and ET, and for some cases also with LIGO, so that it is possible to recover information about the eccentricity and formation scenario. For IMRIs with a total mass $\lessapprox 2000\,M_{\odot}$ and initial eccentricities up to $0.999$, LISA can give a warning to ground-based detectors with enough time in advance and seconds of precision. The possibility of detecting IMRIs from the ground alone or combined with space-borne observatories opens new possibilities for gravitational wave astronomy.' author: - 'Pau Amaro-Seoane' title: 'Detecting Intermediate-Mass Ratio Inspirals From The Ground And Space' --- Introduction {#sec:intro} ============ The typical size of a massive black hole (MBH), i.e. its Schwarzschild radius, is from the point of view of the host galaxy extremely tiny. For a $10^6\,M_{\odot}$ MBH, this difference spans over ten orders of magnitude. However, we have discovered a deep link between the properties of the galaxy and those of the MBH, in particular between the mass of the MBH and the velocity dispersion $\sigma$ of the spheroidal component of the galaxy [@KormendyHo2013]. Because the region of interest is difficult to resolve, the lower end of this correlation is uncertain. However, if we extend these correlations to smaller systems, globular clusters, or ultra-compact dwarf galaxies should harbour black holes with masses ranging between $10^2$ and $10^4,\,M_{\odot}$, i.e. intermediate-mass black holes, IMBHs [for a review, see the work of @Mezcua2017; @LuetzgendorfEtAl2013], although such black holes have never been robustly detected. The best way to probe the nature of the MBH is with gravitational waves, which allow us to extract information that is unavailable electromagnetically. The gravitational capture and plunge of a compact object through the event horizon is one of the main goals of the Laser Interferometer Space Antenna (LISA) mission [@Amaro-SeoaneEtAl2017]. A compact object of stellar mass, so dense that it defeats the tidal forces of the MBH, is able to approach very closely the central MBH, emitting a large amount of gravitational radiation as orbital energy is radiated away. This causes the semi-major axis to shrink. This “doomed” object spends many orbits around the MBH before it is swallowed. The radiated energy which can be thought of as a snapshot containing detailed information about the system will allow us to probe strong-field gravitational physics. Depending on the mass ratio $q$, we talk about either extreme-mass ratio inspirals, $q \gtrsim 10^4:1$ (EMRI, see [@Amaro-SeoaneLRR2012; @Amaro-SeoaneGairPoundHughesSopuerta2015]) or intermediate-mass ratio inspirals, $q \sim 10^2-10^4:1$ (IMRI, see e.g. [@Amaro-SeoaneEtAl07; @BrownEtAl2007; @RodriguezEtAl2012]). In galactic nuclei the predominant way of producing EMRIs is via two-body relaxation [@Amaro-SeoaneLRR2012]. At formation, these sources have extremely large eccentricities, particularly if the MBH is Kerr [@Amaro-SeoaneSopuertaFreitag2013], which is what we should expect from nature. However, in globular clusters, which harbour MBH in the range of IMBHs, the loss-cone theory, which is our tool to understand how EMRIs form, [see e.g. @BinneyTremaine08; @HeggieHut03; @Spitzer87] becomes very complex, mostly due to the fact that the IMBH is not fixed at the centre of the system. It becomes even more difficult when we add the emission of GWs—another layer of complication to the Newtonian problem. As of now, we must rely on computer simulations to address this problem. The joint detection of a GW source with different observatories has been already discussed in the literature but not in the mass ratio range that is addressed in this work. The series of works [@ASF06; @Amaro-SeoaneEtAl09a; @AS10a; @Amaro-SeoaneSantamaria10] investigated the formation, evolution, inspiraling and merger of IMBH binaries with a mass ratio not larger than 10 and the prospects of multiband detection with LISA and LIGO/Virgo. The work of [@KocsisLevin2012] explored a joint detection by different GW detectors in more detail than the previous references in the context of bursting sources emitted by binaries in galactic nuclei, also with a mass ratio not larger than 10. After the first detections of LIGO, the prospect for the detection of similar-mass ratio stellar-mass black holes with masses of about $30\,M_{\odot}$ with LIGO/Virgo and LISA was discussed in [@Sesana2016], and [@ChenAmaro-Seoane2017] clarified that this is only possible for eccentric binaries in that mass rage. In this paper I show that IMRIs, typically forming in globular clusters, but without excluding larger systems such as galactic nuclei and dense nuclear clusters, can be jointly detected with ground-based observatories and space-borne ones. In particular, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo, and the proposed third generation Einstein Telescope [@SathyaprakashEtAl2012; @HildEtAl2011], will be able to detect IMRIs from very eccentric and hard binaries, which form via two-body relaxation or the parabolic capture of a compact object and abrupt loss of energy. This idea was first presented in the work of [@QuinlanShapiro1989], while the energy and angular momentum changes in the case of a hyperbolic orbit were presented previously in [@Hansen1972], and see [@KocsisEtAl2006; @MandelEtAl2008; @OlearyEtAl09; @LeeEtAl2010; @HongLee2015] for more recent works. LISA however is deaf to these kind of sources. For milder eccentricities and semi-major axis, however, the combined detection with LISA and LIGO/Virgo or the ET of IMRIs is a real possibility. Due to the range of frequencies that these sources have, a decihertz observatory such as the DECi-hertz Interferometer Gravitational Wave Observatory [@KawamuraEtAl2011], the Superconducting Omni-directional Gravitational Radiation Observatory [SOGRO, see @PaikEtAl2016; @HarmsPaik2015] or the proposed geocentric Tian Qin [@LuoEtAl2016] would enhance the prospects of detection. For some systems, LISA can give advance warning to ground-based detectors weeks before the source appears in their bandwidth and with an accuracy of seconds (and possibly below) before the merger. Formation of Intermediate-mass ratio inspirals in globular clusters =================================================================== In this work the sources of interest are inspirals of compact objects on to an IMBH with a mass ratio of about $\sim 10^2-10^4:1$. The most accurate simulations of a globular cluster are the so-called direct-summation $N-$body algorithms. In this scheme, one directly integrates Newton’s equations of motion between all stars in a cluster at every timestep, with a regularisation algorithm for binaries, so that any phenomenon associated with gravity naturally arises [see e.g. @Aarseth99; @Aarseth03; @AarsethZare74 and the latter for the concept of regularisation]. Following the first implementation of [@KupiEtAl06], many modern direct-summation codes can mimic the effects of general relativity via a post-Newtonian expansion of the forces to be integrated [see section 9 of @Amaro-SeoaneLRR for a review of stellar-dynamical relativistic integrators]. The first dynamical simulation that presented the formation and evolution of an IMRI down to a few Schwarzschild radii from coalescence using this scheme is the work of [@KonstantinidisEtAl2013]. In one of the simulations we presented, we observed and tracked the spontaneous production of an IMRI between an IMBH of mass $M_{\rm BH}=500\,M_{\odot}$ and a stellar-mass black hole of mass $m_{\rm CO}=26\,M_{\odot}$. After a few Myrs, the IMRI merges and the IMBH receives a relativistic recoil [@CampanelliEtAl2006; @BakerEtAl2006; @GonzalezEtAl2007] and escapes the whole cluster. It must be noted that the IMBH was in a binary for almost all of the simulation time with another compact object, a stellar-mass black hole. The IMBH exchanged companions a few times and was ionised for a last time very abruptly to form the last binary. This binary started at a very small semi-major axis, of about $a \sim 10^{-5}$ pc, and a very large eccentricity, of $e=0.999$, which fits in the parabolic capture mechanism of [@QuinlanShapiro1989]. A few years later, [@LeighEtAl2014] find similar results for a close range of masses but with a different approach. The work of [@HasterEtAl2016] follows very closely the initial setup of [@KonstantinidisEtAl2013] and reproduces our results with a different integrator, which corroborates our findings. Last, the numerical experiments of [@MacLeodEtAl2016] explore IMBHs in a lighter range, of masses around $M_{\rm BH}=150\,M_{\odot}$. They however also report that the IMBH forms a binary for about 90% of the time. The probability distribution of semi-major axis peaks at about $\lesssim 10^{-5}$ pc. Light and Medium-size IMRIs {#sec.light} =========================== The characteristic amplitude and the GW harmonics in the quadrupolar radiation approximation can be calculated following the scheme of [@PM63], in which the orbital parameters change slowly due to the emission of radiation. This is emitted at every integer multiple of the orbital frequency, $\omega_n=n\,\sqrt{G\,M_{\rm BH}/a^3}$, with $a$ the semi-major axis. The strain amplitude in the n-th harmonic at a given distance $D$, normalized to the typical values of this work is $$\begin{aligned} h_n &= g(n,e) \frac{G^2\,M_{\rm BH} m_{\rm CO}}{D\,a\,c^4} \\ \nonumber &\simeq 8\times 10^{-23} g(n,e) \left(\frac{D}{500\,\mathrm{Mpc}}\right)^{-1} \left(\frac{a}{10^{-5}\,\mathrm{pc}}\right)^{-1} \nonumber \\ & \left(\frac{M_{\rm BH}}{10^3\,M_{\odot}}\right) \left(\frac{m_{\rm CO}}{10\,M_{\odot}}\right).\end{aligned}$$ In this expression $M_{\rm BH}$ is the mass of the IMBH, $m_{\rm CO}$ is the mass of the compact object (CO), and $g(n,\,e)$ is a function of the harmonic number $n$ and the eccentricity $e$ [see @PM63]. We consider the RMS amplitude averaged over the two GW polarizations and all directions. Other alternatives to this approach, such as the works of [@PPSLR01; @GlampedakisEtAl2002; @BarackCutler2004; @GG06] give a more accurate description of the very few last orbits, but remain substantially equivalent to [@PM63] at previous stages of the evolution. This approach gives a correct estimation of the frequency cutoff at the innermost stable circular orbit (ISCO) frequency and is enough for the main goal of this work [and see the work of @VeitchEtAl2015 for a discussion about the detection of binaries with mass ratios of 0.1 with advanced ground-based detectors using aligned-spin effective-one-body waveforms]. With this approximation, I show in Fig. (\[fig.100\]) $h_{\rm c}$ as function of the frequency of two different IMRIs, and a few moments in the evolution before the final merger, which happens at a time $T_{\rm mrg}$. For the kind of eccentricities that I am considering in this work, this time can be estimated following [@Peters64] for typical values as $$\begin{aligned} T_\mathrm{mrg} &\cong \frac{24\sqrt{2}}{85} \frac{(1-e_0)^{7/2} c^5} {G^3 M_\mathrm{BH}^2 m_{\rm CO}} a_0^4 \cong 6.4\times 10^{5} \mathrm{yrs} \\ & \nonumber \times \left(\frac{M_{\rm BH}}{10^3\,M_{\odot}}\right)^{2} \left(\frac{m_{\rm CO}}{10\,M_{\odot}}\right)^{-1} \left(\frac{R_\mathrm{P}^0}{200\,R_{\rm S}}\right)^{4}\nonumber \\ & \left(\frac{1-e_0}{10^{-5}}\right)^{-1/2}, \label{eq.Tmrg}\end{aligned}$$ where $R_\mathrm{P}^0$ and $e_0$ are the initial pericenter distance and eccentricity, respectively. In this Fig. (\[fig.100\]) the IMBH has a mass of $M_{\rm BH}=100\,M_{\odot}$ and the mass of the compact object (CO) is set to $10\,M_{\odot}$. I depict the LISA sensitivity curve and those of Advanced LIGO (LIGO, henceforth) and the ET in its D configuration [@HildEtAl2011], although I have shortened the characteristic amplitude to start at lower values for clarity, since none of the sources I have considered achieves higher values. For reference, I include as well the full waveform in the LIGO sensitivity curve as estimated by the IMRPhenomD approach of [@HusaEtAl2016; @KhanEtAl2016], which has been developed to study sytems with mass ratios of up to $q=18$. This curve is close to the peak of harmonics in amplitude for this specific case but in general this is not true, and depends on the specifics of the binary such as periastron argument, inclination angle, precession of the orbital plane, to mention a few. We can see that eccentricities corresponding to those that we can expect for a dynamical capture as described in the introduction produce IMRIs which are observable with LISA and both the ET and LIGO. In particular, the left panel corresponds to an IMRI which spends half a minute in LIGO. For lighter masses of the CO, this time becomes larger. For higher eccentricities, which can be achieved via two-body relaxation or in the parabolic braking scenario, at these masses the IMRIs can be seen only by ground-based detectors, with a significant amount of time and the vast majority of the harmonics in band. It is interesting to note that the ET has been estimated to be able to detect up to several hundred events per year, see [@Miller02; @GairEtAl09]. In Fig. (\[fig.300\]) I show a more massive system, with a total mass of $310\,M_{\odot}$. The source recedes in frequency due to the larger mass. For the systems considered in the upper panels, this allows IMRIs to spend more time in LISA and accumulate more SNR, with the resulting shortened time in the ground-based detectors which, however, is still significant. For the lower panels, however, LISA is again deaf to these sources. Finally, in Fig. (\[fig.500\]) I show a system similar to what is found in the numerical simulations of [@KonstantinidisEtAl2013]. The mass of the IMBH is set to $500\,M_{\odot}$ Higher frequencies lead the source to be observable by only ground-based detectors. Large-mass IMRIs ================ In Figs. (\[fig.1000\]), (\[fig.2000\]) and (\[fig.3000\]) we can see IMBHs with masses $M_{\rm BH}=1000\,M_{\odot}$, $2000\,M_{\odot}$ and $3000\,M_{\odot}$, respectively. For more moderate eccentricities, the IMRIs in the examples can be detected with LISA and the ET, but they do not enter the LIGO detection band. More extreme eccentricities lead to a large amount of harmonics entering the ET band for significant amounts of time. In the case of a $2000\,M_{\odot}$ IMBH, it can spend as much as 10 minutes in band in different harmonics. Larger masses, i.e. $3000\,M_{\odot}$ produce short-lived sources that however spend up to one minute in band of the ET. Environmental effects ===================== In the previous sections I have shown the evolution of an IMRI under the assumption that the binary is perfectly isolated from the rest of the stellar system. I.e. the binary evolves only due to the emission of GWs. The reason for this is that the problem is cleaner and easier to understand. However, the binary is located in a dense stellar system, typically a globular cluster. While the role of gas is negligible, since the gas density in these systems is very low. Hence, so as to assess whether surrounding stars could vary or modify the evolution after the IMRI has formed, in this section I investigate the impact of the stellar system in a semi-analytical approach. The basic idea is to split the evolution of both the semi-major axis and the eccentricity in two contributions, one driven by the dynamical interactions with stars (subscript [D]{}) and one due to emission of GWs (subscript [GW]{}), $\dot{a} = \dot{a}_{\rm GR} + \dot{a}_{\rm D}$, and $\dot{e} = \dot{e}_{\rm GR} + \dot{e}_{\rm D}$ with dots representing the time derivative. From [@Peters64], $$\begin{aligned} \dot{a}_{\rm GW} = &-\frac{64}{5}\frac{G^3{M}_{\rm BH}\,{m}_{\rm CO}({M}_{\rm BH}+{m}_{\rm CO})}{c^5a^3(1-e^2)^{7/2}} \\ \nonumber & \Big(1+\frac{73}{24}e^2+\frac{37}{96}e^4 \Big)\nonumber\\ \dot{e}_{\rm GW} = &-\frac{304}{15}\frac{G^3{M}_{\rm BH}\,{m}_{\rm CO}({M}_{\rm BH}+{m}_{\rm CO})}{c^5a^4(1-e^2)^{5/2}} \\ \nonumber & e\Big(1+\frac{121}{304}e^2\Big)\end{aligned}$$ The [GW]{} terms are as given in [@Peters64]. Using the relationships of [@Quinlan96], we have that $$\dot{a}_{\rm D}=-H\,\frac{G\rho}{\sigma}a^2.$$ Following the usual notation, $G$ is the gravitational constant, $\rho$ is the stellar density around the binary, $\sigma$ the corresponding velocity dispersion of the cluster and $H$ the so-called hardening constant, as introduced in the work of [@Quinlan96]. For the kind of binaries I am considering in this work, i.e. hard ones, we have that $\left({de}/{d\ln(1/a)}\right)_{\rm D}=K(e)$. Since the density drops significantly during the evolution, we can regard $\sigma$ as approximately constant and hence $de=K(e)\,d\ln(1/a)=-{K(e)}/{a}\,da$, so that $H\simeq 16$, as in the original work of [@Quinlan96] and see also [@SesanaEtAl04]. Therefore, $$\dot{e}_{\rm D}=\frac{H}{\sigma}\,{G\rho\,a}\,K(e),$$ with $K(e)\sim K_0\,e(1-e^2)$, as in the work of [@MM05]. As an example, in Fig. (\[fig.100-30-Vacuum-Dynamics\]) I show an IMRI formed by an IMBH of mass $M_{\rm BH}=100\,M_{\odot}$ and a CO of mass $m_{\rm CO}=30\,M_{\odot}$. The left panel corresponds to the case in vacuum, i.e. the binary evolves only due to the emission of GWs and the right panel takes into account stellar dynamics. The reason for this choice of parameters is twofold: On the one hand, the impact of stellar dynamics on a lighter IMRI is more pronounced and, on the other hand, $K_0$ has been estimated for more equal-mass binaries than the other cases. As expected, the role of stellar dynamics on to the binary at such a hardening stage is negligible, so that the previous results hold even if we do not take into account the surrounding stellar system around the IMRI from the moment of formation. The previous dynamical story is however crucial for the initial orbital parameters of the binary. Loudness of the sources {#sec.SNR} ======================= Low-eccentricity sources: LIGO {#sec.low-ecc} ------------------------------ As it progresses in the inspiral, a compact binary becomes observable and more circular. The characteristic amplitude $h_{\rm c}$ of an IMRI emitting at a given frequency $f$ is given by $$h_{\rm c} = \sqrt{(2\dot E/\dot f)}/(\pi D),$$ with $\dot E$ the power emitted, $\dot f$ the time derivative of the frequency and $D$ the distance to the source [@FinnThorne2000]. The sky and orientation-averaged SNR of a monochromatic source with the ansatz of ideal signal processing is given by the equation $$\left(\frac{S}{N}\right)^2 = \frac{4}{\pi D^2} \int \frac{\dot{E}}{\dot{f} \, S_h^{SA}(f)} \frac{{\rm d}f}{f^2}$$ as derived in [@FinnThorne2000], where $D$ is the distance to the source, $\dot{E}$ is the rate of energy lost by the source, $\dot{f}$ is the rate of change of frequency and $S_h^{SA}(f) \approx 5 S_h(f)$ is the sky and orientation average noise spectral density of the detector. For a source with multiple frequency components, the total SNR$^2$ is obtained by summing the above expression over each mode. In Fig. (\[fig.Enigma\]) I show the Fourier-transformed waveform of both panels of Fig (\[fig.100\]), as approximated by the algorithm of [@HuertaEtAl2018]. Theirs is a time-domain waveform that describes binaries of black holes evolving on mildly eccentric orbits, not exceeding $e\lesssim 0.2$. When the binaries enter the LIGO/Virgo band, even if they start with initially high eccentricities, they reach values below the threshold of the algorithm, which therefore is a good approximant to estimate the waveform and compute the SNR. For the IMRI examples given in Figs. (\[fig.100\]), assuming a distance of $D=500\,\textrm{Mpc}$, I find a SNR in the LIGO bandwidth of 42.87 and 42.55, for the left and right panels, respectively. In Figs. (\[fig.300\]), at the same distance, I find 17.12, 17.13 for the top-left, and top-right panels, respectively and 17.15, 16.40 for the lower-left and lower-right ones. High-eccentricity sources ------------------------- When moving to lower frequencies, the eccentricity exceeds by far the limit of the approximation of [@HuertaEtAl2018] that I have used to derive the SNR. To calculate it when the IMRIs sweep the LISA bandwidth, I use the expression (derived from Eq. 20 of [@PM63], Eq. 2.1 of [@FinnThorne2000] and Eq. 56 of [@BarackCutler2004]) $$\left(\frac{S}{N} \right)^2_n = \int^{f_n(\rm t_{fin})}_{f_n(\rm t_{ini})} \left(\frac{h_{\rm c,\,n}(f_n)}{h_{\rm det}(f_n)} \right)^2 \underbrace{\frac{1}{f_n}\,d\left(\ln(f_n) \right)}_{\textrm{simply}~ df_n}.$$ In this Eq. $f_n(t)$ is the (redshifted) frequency of the n harmonic at time $t$ ($f_n=n \times f_{\rm orbital}$), $h_{\rm c,\,n}(f_n)$ is the characteristic amplitude of the $n$ harmonic when the frequency associated to that component is $f_n$, and $h_{\rm det}$ is the square root of the sensitivity curve of the detectors. A few examples of the SNRs for the IMRI systems in the LISA band of the previous sections (and ET in parentheses for the same source) , assuming a distance of 500 Mpc and taking the contribution of the first 100 harmonics are: Fig. (\[fig.100\]) 15 (1036), left panel, and virtually 0, 0.01 (1087) for the right one. For Fig. (\[fig.300\]), the upper, left panel 50 (1994) and the upper, right panel 24 (1995), while the lower, left panel has 2 (1991), and the lower, right one approximately 0, 0.01 (2231). In Fig. (\[fig.500\]), the left panel yields an SNR of 36 (1449), and the right one of about zero, 0.05 (1461). In Fig. (\[fig.1000\]), the left panel has 79 (328), and the right one approximately zero, 0.4 (305). Fig. (\[fig.2000\]) has 7 (15) in the left panel and approximately 0 in the right one, 0.1 (37). Finally, Fig. (\[fig.3000\]) has 5 (1). In Figs. (\[fig.SNR\_Fig2bottomright\_and\_Fig3right\_ET\]) and (\[fig.SNR\_Fig3Left\_LISA\]) I give three examples of the accumulated SNR as calculated in this section. In the first figure I display in the left panel the SNR in ET of the system of Fig. (\[fig.300\]), bottom, right panel and, on the right panel, of Fig. (\[fig.500\]), right panel, also for ET. In the second one I show the accumulated SNR of the system depicted in Fig. (\[fig.500\]), left panel, for LISA. However, and for the case of LISA, this is the total accumulated SNR for the total time that the source spends on band. The observational time, the time during which we retrieve data from the source, is in all cases shorter and, hence, the accumulated, observed SNR is lower. As an example, for Fig. (\[fig.500\]), left panel, if we integrate all of the time the source spends on band, we obtain the aforementioned SNR of 36. However, if we integrate the last 10 yrs before merger, the SNR goes down to 23, and to 19 for the last 5 yrs. If we observed the source earlier in the evolution, say, e.g. 10 yrs before merger to 5 yrs before it, the SNR would be 14 and 100 yrs before merger to 95 yrs, 3. I show an example for the accumulated SNR for this system in Fig. (\[fig.SNR\_500\_10-5-yrs-before-plunge\]), 10 and 5 yrs before the final plunge. This only applies to LISA, because the time spent on the ground-based detector ET is much shorter. So as to assess whether this approach is robust, I give now the SNR for the systems of Sec. (\[sec.low-ecc\]) in the LIGO band, which have been calculated with the waveform model introduced in that section. In Fig. (\[fig.100\]), as estimated with this approach, the SNR is 41 and 40, for the left and right panels, respectively. In Fig. (\[fig.300\]) I find, from left to right, top to bottom, 12, 12, 11 and 14. These results are very close to those of Sec. (\[sec.low-ecc\]). The small differences arise from the fact that eccentricity tends to enhance the amount of energy emitted during the inspiral as the system radiates in band for longer. It is reasonable to take these estimates for circular orbits as a guideline for eccentric systems of similar mass to these. If the source is eccentric, since $a=R_{\rm per}/(1-e)$, $a$ is larger at the time the source reaches a frequency of 10 Hz. The inspiral time depends on the value of $a$, and is larger for larger $a$. Another way to see this is that $dE/dt$ is smaller when $e$ is larger at fixed periapsis (or frequency in our approximation). This is because at fixed periapsis, increasing the eccentricity puts more of the orbit further from the MBH and hence the energy flux is on average reduced. As $dE/dt$ is smaller, it takes longer to inspiral. This also explains why the SNR is slightly lower – $dE/dt$ is lower at fixed periapsis and thus at fixed frequency in this approximate model (physically, energy is being radiated out of band so we do not detect it all). Accumulated phase shift ======================= Understanding how IMRIs form and what are their orbital parameters can help us to reverse-engineer the environmental properties of the host cluster. Although the IMRIs considered in this work have very large initial eccentricities, when they reach the LIGO/Virgo band the eccentricity is virtually zero. It is however important to measure a non-zero eccentricity, because it can be a constraint on the formation mechanism as well as the stellar enviroment of the IMRI. If a residual eccentricity is present, it will induce a difference in the phase evolution of the signal as compared to a circular inspiral. Thanks to the derivation of [@KrolakEtAl1995] of the phase correction due to non-zero eccentricities, we can estimate the accumulated phase shift to lowest post-Newtonian order and to first order in $e^2$ with $$\begin{aligned} \Delta \Psi_{e}(f) & = \Psi_{\rm last} - \Psi_{\rm i} \cong - \Psi_{\rm i} =\nonumber \\ & \frac{7065}{187136}\,e_i^2\left(\pi\,f\,M_{\rm z} \right)^{-5/3}. \label{eq.Psi}\end{aligned}$$ In the last equation $e_i$ is the eccentricity at the frequency of the dominant harmonic at which it enters the detector bandwidth, $f$ is the frequency for the $n=2$ harmonic, and I have introduced the quantity $M_{\rm z}:= (1+z) G\left( M_{\rm BH} \times m_{\rm CO}\right)^{3/5} (M_{\rm BH}+m_{\rm CO})^{-1/5}/c^3$. Also, I make the approximation that $\Delta \Psi_{e}(f) = \Psi_{\rm last} - \Psi_{\rm i} \simeq -\Psi_{\rm i}$, with $\Psi_{\rm last}$ and $\Psi_{\rm i}$ the final and initial phase. This is so because of the pronounced fall-off of $\Psi_{e}(f)$ with increasing frequency, see discussion in section B.2 of [@CutlerHarms2006]. So as to derive the accumulated phase shift in terms of $f$ and the remaining time to merger, we now recall from [@Kepler1619] that the semi-major axis of the binary is $$a^3 = \frac{G\left(M_{\rm BH}+m_{\rm CO} \right)}{\left(\pi\,f\right)^2}. \label{eq.K}$$ The time for merger for $e \ll 1$ can be derived from [@Peters64] as follows, $$\begin{aligned} T_{\rm mrg} & \cong \frac{5}{256} \frac{c^5}{G^3M_{\rm BH} \times m_{\rm CO} \left(M_{\rm BH}+m_{\rm CO} \right)} \nonumber \\ & \left[\frac{G(M_{\rm BH}+m_{\rm CO})}{(\pi\,f)^2} \right]^{4/3}. \label{eq.TmrgLowEcc}\end{aligned}$$ Last, let us recall that $$e^2\,f^{19/9} \cong \textrm{constant}, \label{eq.efconst}$$ which can be derived from relation 5.12 of [@Peters64] with $1/(1-e^2) \simeq 1$ combined with Eq. (\[eq.K\])[^1] , i.e. $a \propto f^{-2/3}$. Therefore, if we use Eq. (\[eq.K\]) in Eq. (\[eq.TmrgLowEcc\]), we obtain $$\pi f \cong \left( \frac{5}{256} \right)^{3/8} M_{\rm z}^{-5/8} T_{\rm mrg}^{-3/8}. \label{eq.pif}$$ Hence, using Eqs. (\[eq.Psi\], \[eq.efconst\], \[eq.pif\]), we have that the accumulated phase shift in terms of $f$, $e_i(f)$, $M_{\rm z}$ and $T_{\rm mrg}$ is $$\begin{aligned} \Delta \Psi_{e}(f) & = \left(\frac{5}{256}\right)^{-17/12}\frac{7065}{187136} \nonumber \\ & \left(\pi f_i \right)^{19/9}e_i^2 M_{\rm z}^{25/36} T_{\rm mrg}^{17/12} \nonumber \\ & \cong 10 \left(\pi f_i \right)^{19/9}e_i^2 M_{\rm z}^{25/36} T_{\rm mrg}^{17/12}\end{aligned}$$ The accumulated phase shift is detectable if $\gtrsim \pi$. With this approximation, I find the following phase shifts in radians, for the IMRI systems presented in the previous sections, imposing a minimum threshold SNR of 5 (the numbers correspond to the panels of the figures from the top to the bottom, left to right): \(i) For LISA, and taking into account only the last five years before merger, Fig. (\[fig.100\]) has a negligible phase shift. Fig. (\[fig.300\]) 180, $3.4\times 10^6$, while the other two panels have a a negligible phase shift. Fig. (\[fig.500\]) $1.5\times 10^6$ and the right panel is negligible. Fig. (\[fig.1000\]) 8200 and the right panel is negligible. Fig. (\[fig.2000\]) $9.7\times 10^5$ and the right panel is negligible. Least, Fig. (\[fig.3000\]) has also a negligible phase shift. \(ii) For the ET, Fig. (\[fig.100\]) $\sim 5.1\times 10^{-3}$, 19000 for the left and right panels. Fig. (\[fig.300\]) $\sim 2.6\times 10^{-7}$, $\sim 3.4\times 10^{-3}$, 0.66 and 4600. Fig. (\[fig.500\]) $1.3\times 10^-3$ and 3900. Fig. (\[fig.1000\]) $3.5\times 10^{-6}$ and 450. Fig. (\[fig.2000\]) $1.3\times 10^{-2}$ and 2600. Fig. (\[fig.3000\]) has a negligible phase shift. \(iii) For LIGO, Fig. (\[fig.100\]) $4\times 10^{-6}$ and 1.2. Fig. (\[fig.300\]) $1.1 \times 10^{-10}$, $1.4 \times 10^{-6}$, $2.3 \times 10^{-4}$ and 10. The rest of the cases have negligible phase shifts. Conclusions =========== Intermediate-mass ratio inspirals are typically formed in dense stellar systems such as galactic nuclei and globular clusters, with typically very large eccentricities (from $e=0.999$) and small semi-major axis (below $a \sim 10^{-5}$pc), as found in a number of stellar-dynamics simulations of globular clusters [@KonstantinidisEtAl2013; @LeighEtAl2014; @HongLee2015; @MacLeodEtAl2016; @HasterEtAl2016]. Besides classical two-body relaxation, an interesting way of explaining the formation of these sources is the parabolic capture mechanism described by [@QuinlanShapiro1989; @KocsisEtAl2006]. In this work I show that IMRIs in clusters are detectable not only by space-borne observatories such as LISA. Depending on the properties of the IMRI, it can be detected in conjunction with LIGO/Virgo or the ET, so that ground-based and space-borne observatories should be envisaged as one instrument if they are simulataneously operative. I have considered IMBHs with masses ranging between $M_{\rm BH}=100\,M_{\odot}$ up to $3000\,M_{\odot}$ and COs with different masses. I have separated them in light and medium-size IMRIs, for IMBHs with masses up to $500\,M_{\odot}$ (which is a particular case based on the findings of [@KonstantinidisEtAl2013]) and large-mass IMRIs, for masses between $1000\,M_{\odot}$ and $3000\,M_{\odot}$. I find that light and medium-size IMRIs can be observed by LISA and ground-based detectors for eccentricities starting at $0.99$ and up to $0.9995$. In the range of frequencies of LIGO/Virgo they spend a maximum of about one minute on band. Higher eccentricity sources, however, can only be detected by ground-based detectors (see [@ChenAmaro-Seoane2017] for a discussion on the role of eccentricity for low mass ratio binaries). This is due to the fact that, as the eccentricity increases, the pericenter distance decreases, so that the characteristic frequency of the GWs emitted at the pericenter increases (see [@Wen2003], Eq. 37 for a derivation of the peak frequency in the same approximation used in this work). In some cases, the full cascade of harmonics falls entirely in the bandwidth of the ground-based detectors. The peak of large-mass IMRIs recedes in frequency as compared to light and medium-size ones, so that the cascade of harmonics is shifted towards the LISA domain. However, for eccentricities below $0.9995$, IMRIs with IMBHs covering the full range of masses considered in this work ($100\,M_{\odot}$ up to $3000\,M_{\odot}$) should be detectable with LISA with modest to large SNRs, from a few to tens, depending on the eccentricity and duration of the observation. For ground-based detectors, I compute the SNR for LIGO using the waveforms from a Fourier-transformation of the time domain Taylor T4 algorithm of [@HuertaEtAl2018] (limited to eccentricities $\lesssim 0.2$) and derive large enough SNRs, always of a few tens. Lower-frequency sources require larger eccentricities, and we cannot use these waveforms. For these detectors I use an approximate scheme to calculate the SNR, and I have compared it with the previous results for LIGO and I find that the approach is robust. The values for ET can reach as much as $\sim 2000$, and are of typically a few hundred and of tens for masses up to $2000\,M_{\odot}$. LISA has SNRs of a few tens to then significantly drop when the IMRI system has the peak of harmonics closer to the ground-based regime. By combining ground-based and space-borne observations we can impose better constraints on the system’s parameters. On the one hand, LISA can observe the inspiral and hence provide us with measurements of parameters such as the chirp mass. On the other hand, ground-base detectors detect the merger and ringdown, and therefore measure other parameters such as the final mass and spin. Thanks to this joint detection, one can split various degeneracies and get better measurements of the parameters, as compared to individual detections[^2]. I have estimated with a semi-analytical approach the possible influence of the environment [after]{} their formation and I find no impact, which will make it easier to detect and interpret these sources. By looking at the accumulated phase shift, one could investigate the origin of light IMRIs thanks to a residual eccentricity. I find that LISA binaries accumulate typically hundred of thousands and up to millions of radians, while ET binaries can accumulate up to 19000 radians, and typically of a few thousands. While IMRI binaries in LIGO live much shorter time, there is a case which does accumulate enough radians. LISA can warn ground-based detectors with at least one year in advance and seconds of precision, so that this observatory and LIGO/Virgo and the ET should be thought of as a single detector, if they are operating at the same time. Until LISA is launched, the perspective of detecting IMRIs from the ground opens new possibilities. Acknowledgments {#acknowledgments .unnumbered} =============== I acknowledge support from the Ram[ó]{}n y Cajal Programme of the Ministry of Economy, Industry and Competitiveness of Spain, as well as the COST Action GWverse CA16104. I thank Marc Freitag for his help in the implementation of the SNR equations in the plotting subroutines, and for extended discussions about the phase shift. I am indebted with Leor Barack, Chen Xian, Bernard Schutz, Thomas Dent, and Matthew Benacquista for general comments, with Frank Ohme for his help with the waveforms, and with Jon Gair for discussions about SNR. This work started during a visit to La Sapienza university in May 2018. I thank Roberto Capuzzo Dolcetta, Raffaella Schneider, Piero Rapagnani, Luigi Stella, Valeria Ferrari, Paolo Pani and Leonardo Gualtieri for their extraordinary hospitality. In particular I thank the students who took part in my course, because the many discussions and homework preparation led me to think about this problem. [65]{}ifxundefined \[1\][ ifx[\#1]{} ]{}ifnum \[1\][ \#1firstoftwo secondoftwo ]{}ifx \[1\][ \#1firstoftwo secondoftwo ]{}““\#1””@noop \[0\][secondoftwo]{}sanitize@url \[0\][‘\ 12‘\$12 ‘&12‘\#12‘12‘\_12‘%12]{}@startlink\[1\]@endlink\[0\]@bib@innerbibempty [**, ()](\doibase 10.1146/annurev-astro-082708-101811), [, ()](\doibase 10.1142/S021827181730021X), [, ()](\doibase 10.1051/0004-6361/201321183), @noop [ ()]{}, @noop [ ()]{}, [, ()](\doibase 10.1088/1742-6596/610/1/012002), [, ()](\doibase 10.1088/0264-9381/24/17/R01), [, ()](\doibase 10.1103/PhysRevLett.99.201102), [, ()](\doibase 10.1103/PhysRevD.85.062002), [, ()](\doibase 10.1093/mnras/sts572), @noop []{}, edited by and (, ) @noop []{}, edited by () @noop []{} (, ) [**, ()](\doibase 10.1086/510405), [, ()](\doibase 10.1088/0004-637X/692/1/L50), [, ()](\doibase 10.1111/j.1365-2966.2009.15842.x), [, ()](\doibase 10.1088/0004-637X/722/2/1197), [, ()](\doibase 10.1103/PhysRevD.85.123005), [, ()](\doibase 10.1103/PhysRevLett.116.231102) [, ()](\doibase 10.3847/2041-8213/aa74ce), @noop [ ]{} @noop [ ]{} [, ()](\doibase 10.1086/167745) [, ()](\doibase 10.1103/PhysRevD.5.1021) [, ()](\doibase 10.1086/505641), [, ()](\doibase 10.1086/588246), [, ()](\doibase 10.1111/j.1365-2966.2009.14653.x) [, ()](\doibase 10.1088/0004-637X/720/1/953), [, ()](\doibase 10.1093/mnras/stv035), [, ()](\doibase 10.1088/0264-9381/28/9/094011) [, ()](\doibase 10.1088/0264-9381/33/7/075003) [, ()](\doibase 10.1103/PhysRevD.92.022001), [, ()](\doibase 10.1088/0264-9381/33/3/035010), @noop [, ()]{} @noop []{} (, ) [**, ()](\doibase 10.1007/BF01227619) [ ()](\doibase 10.1111/j.1745-3933.2006.00205.x), [, ()](\doibase 10.1007/s41114-018-0013-8) [, ()](\doibase 10.1051/0004-6361/201219620), [, ()](\doibase 10.1103/PhysRevLett.96.111101), [, ()](\doibase 10.1086/510448), [, ()](\doibase 10.1103/PhysRevLett.98.091101), [, ()](\doibase 10.1093/mnras/stu1437), [, ()](\doibase 10.3847/0004-637X/832/2/192), [, ()](\doibase 10.3847/0004-637X/819/1/70), @noop [, ()]{} @noop [, ()]{} [, ()](\doibase 10.1103/PhysRevD.66.064005), [, ()](\doibase 10.1103/PhysRevD.69.082005), [, ()](\doibase 10.1103/PhysRevD.73.064037), [, ()](\doibase 10.1103/PhysRevLett.115.141101), [, ()](\doibase 10.1103/PhysRevD.93.044006), [, ()](\doibase 10.1103/PhysRevD.93.044007), @noop [, ()]{} [, ()](\doibase 10.1086/344156), @noop [ ()]{}, @noop [, ()]{} [, ()](\doibase 10.1086/422185), @noop [, ()]{}, [, ()](\doibase 10.1103/PhysRevD.62.124021), [, ()](\doibase 10.1103/PhysRevD.97.024031) [, ()](\doibase 10.1103/PhysRevD.52.2089) [, ()](\doibase 10.1103/PhysRevD.73.042001), @noop [ ()]{} [**, ()](\doibase 10.1086/378794), [^1]: “Sed res est certissima exactissimaque quod proporti[$\rm \bar{o}$]{} qua est inter bin[$\rm \bar{o}$]{}rum qu[$\rm \bar{o}$]{}rumcunque Planet[$\rm \bar{a}$]{}rum tempora periodica, sit praecise sesquialtera proportionis medi[$\rm \bar{a}$]{}rum distanti[$\rm \bar{a}$]{}rum (...)” [^2]: Christopher Berry, personal communication.
Glycogen determination using periodic acid-schiff: artifact of muscle preparation. It is common practice for the staining of muscle glycogen with periodic acid-Schiff (PAS) to thaw and dry muscle sections before staining. The goal is to investigate whether this thawing step results in a systematic error that is independent of muscle fiber type and muscle physiological state. Muscle samples from six fasted male subjects were obtained before or after 3 min of high-intensity cycling. Each sample was sectioned; some sections were assessed for muscle fiber composition, and others were either thawed for 20 min or kept frozen before being PAS-stained for glycogen. The response to a 20-min freeze-thaw cycle was also assessed using rested and exercised rats as our experimental model, and the changes in glycogen were measured enzymatically. The inclusion of a 20-min thawing step resulted in a significant reduction (P < 0.05) in the weighted average of the optical density of PAS (ODPAS) staining in both the nonexercised (15 +/- 1.4%) and exercised human muscles (15 +/- 1.3%), with the absolute extent being greater in the nonexercised muscle samples (P < 0.05). Moreover, the observed decrease in ODPAS was greatest in Type IIa fibers for both the nonexercised (P < 0.05) and exercised (P < 0.05) muscle samples. The findings in rats suggest that the muscle damage associated with freeze-thawing is responsible for this stimulation of glycogenolysis. For the quantitative histochemical measurement of glycogen content in skeletal muscle, the common practice of thawing unfixed muscle sections before PAS staining should be abandoned because this causes glycogen breakdown, the extent of which varies across muscle fiber types and prior exercise history.
Former Philadelphia Phillies closer Ryan Madson has agreed to a minor league contract with the Kansas City Royals that includes an invitation to major league spring training camp, the team announced Sunday. Madson, 34, is 47-30 with a 3.59 ERA and 52 saves in eight career seasons with Philadelphia. He hasn't pitched in the major leagues since 2011 because of elbow problems. Ryan Madson went 47-30 with a 3.59 ERA and 52 saves in eight career seasons with Philadelphia. Howard Smith/USA TODAY Sports Madson assumed the closer's job in Philadelphia from Brad Lidge in 2011 and saved 32 games, but a reported four-year, $44 million deal fell through and sparked a disagreement between Phillies general manager Ruben Amaro Jr. and Madson's former agent, Scott Boras. The Phillies quickly changed course in November 2011 and signed Jonathan Papelbon to a four-year, $50 million deal. Madson signed a one-year, $8.5 million contract with the Cincinnati Reds, but he underwent Tommy John surgery in spring training and missed the 2012 season. He made a failed comeback attempt with the Los Angeles Angels in 2013 and sat out the entire 2014 season. Madson has two connections in the Kansas City front office. Jim Fregosi Jr., now a special assistant to Royals general manager Dayton Moore, was the scout who signed Madson out of the 1998 first-year player draft with the Phillies. Mike Arbuckle, currently a senior advisor in Kansas City, was Philadelphia's scouting director in 1998 when the Phillies selected Madson in the ninth round of the draft.
Expert Commercial Roofing Solutions for Businesses in the Dallas/Fort Worth, TX, Area The harsh sun experienced during summers in the Dallas/Fort Worth area is hard on roofs. The UV rays break down the chemicals in the roofing system, causing them to deteriorate more rapidly than they would in more temperate climates. Luckily, the professionals at Beldon® are experts when it comes to commercial roofing systems that are specifically designed to withstand the Texas climate. We use high-performance materials and know how to apply them correctly so that you will have protection for your business well into the future. Beldon® is the Commercial Roofing Company to Trust for All Types of Systems The experts at Beldon® will analyze your commercial structure to determine the best type of roofing system based on local building codes, the shape of your roof, how much foot traffic and equipment your roof holds, and numerous other factors. 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To learn more about the commercial roofing services we can provide for your business in Dallas/Fort Worth, contact Beldon® today. commercialroofing offered across the United States. Call us today to see how we can help you! New orders only. Discount applied by sales representative at time of contract execution. The installation cost equals to approximately 12% of the total project cost. Void where prohibited by law or regulation. Offer may be cancelled without prior notice. Loans provided by EnerBank USA, Member FDIC, (1245 Brickyard Rd., Suite 600, Salt Lake City, UT 84106) on approved credit, for a limited time. Repayment term is 60 months. 4.99% fixed APR, effective as of January 1, 2019. Minimum loan amounts apply. The first monthly payment will be due 30 days after the loan closes. Offer Expires 01/31/19. Windows Restrictions New orders only. The Visa Gift Card will only be provided after installation and the job being paid in full. Minimum purchase of $5,000 required for Visa Gift Card promotion. Loans provided by EnerBank USA, Member FDIC, (1245 Brickyard Rd., Suite 600, Salt Lake City, UT 84106) on approved credit, for a limited time. Repayment term is 60 months. 4.99% fixed APR, effective as of January 1, 2019. Minimum loan amounts apply. The first monthly payment will be due 30 days after the loan closes. Offer Expires 01/31/19. Siding New orders only. The Visa Gift Card will only be provided after installation and the job being paid in full. Minimum purchase of $5,000 required for Visa Gift Card promotion. Loans provided by EnerBank USA, Member FDIC, (1245 Brickyard Rd., Suite 600, Salt Lake City, UT 84106) on approved credit, for a limited time. Repayment term is 60 months. 4.99% fixed APR, effective as of January 1, 2019. Minimum loan amounts apply. The first monthly payment will be due 30 days after the loan closes. Offer Expires 01/31/19. San Antonio Residential Roofing Restrictions $250 Bonus VISA gift card with purchase will be mailed after installation and payment in full. Loans by Synchrony Bank. Offer applies only to single-receipt qualifying purchases. A promo fee will be charged and included in the promo purchase balance equal to $50. No monthly interest will be charged on the promotional balance if you pay the following (the “promotional balance”) in full within 18 Months: 1) the promotional purchase amount, and 2) any related promo fee. If you do not, monthly interest will be charged on the promotional balance from the purchase date. Depending on purchase amount, promotion length and payment allocation, the required minimum monthly payments may or may not pay off purchase by end of promotional period. Regular account terms apply to non-promotional purchases and, after promotion ends, to promotional balance. For new accounts: Purchase APR is 26.99%; Minimum Interest Charge is $2. 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[The effects of heat shock protein 90 and glucocorticoid receptor on apoptosis in T lymphocytes from asthmatic patients]. Using GA (geldanamycine), which specifically binding to HSP90, to induce the imbalance of HSP90/GR in function (low ratio) and analyzing the effect of low HSP90/GR ratio on T lymphocytes apoptosis induced by Dex from asthmatic patients. The expression of HSP90 and GR mRNA of T lymphocytes influenced by Dex and GA was also studied. Peripheral blood T lymphocytes were enriched from 10 asthmatic subjects and 7 healthy volunteers by nylon column. T lymphocytes were cultured in vitro with Dex and / or GA for 72 hours. Apoptosis of T lymphocytes were measured by propidium iodide staining and flowcytometry. With reverse transcription-polymerase chain reaction (RT-PCR), the expression of HSP90 and GR mRNA was detected. Dex could obviously induce the apoptosis of T lymphocytes from asthmatic patients (33.8% +/- 3.2% vs 23.2% +/- 1.5% , P < 0.01). GA had no effect on the apoptosis of T lymphocytes but could inhibit the effect of Dex (24.5% +/- 6.0% vs 33.8% +/- 3.2% , P < 0.01). Dex also had the effect of inducing apoptosis of T lymphocytes from health volunteers but the effect was less potent than that from asthmatic patients (25.9% +/- 3.5% vs 23.1% +/- 1.5 %, P < 0.05). Dex inhibited the expression of HSP90 and GR mRNA of T lymphocytes from asthmatic patients (1.23 +/- 0.16 vs 1.68 +/- 0.38 and 0.42 +/- 0.06 vs 0.54 +/- 0.07, respectively, P all < 0.05). GA could interrupt the inhibiting effect of Dex on the expression of HSP90 and GR mRNA but had no effect on it. The low ratio of HSP90/GR could reduce the inducing apoptosis effect of Dex. Dex could down-regulate the mRNA expression of HSP90 and GR and GA could interrupt the inhibiting effect of Dex.
Selective increases in regional brain glucocorticoid: a novel effect of chronic alcohol. The hypothalamo-pituitary-adrenal axis shows functional changes in alcoholics, with raised glucocorticoid release during alcohol intake and during the initial phase of alcohol withdrawal. Raised glucocorticoid concentrations are known to cause neuronal damage after withdrawal from chronic alcohol consumption and in other conditions. The hypothesis for these studies was that chronic alcohol treatment would have differential effects on corticosterone concentrations in plasma and in brain regions. Effects of chronic alcohol and withdrawal on regional brain corticosterone concentrations were examined using a range of standard chronic alcohol treatments in two strains of mice and in rats. Corticosterone was measured by radioimmunoassay and the identity of the corticosterone extracted from brain was verified by high performance liquid chromatography and mass spectrometry. Withdrawal from long term (3 weeks to 8 months) alcohol consumption induced prolonged increases in glucocorticoid concentrations in specific regions of rodent brain, while plasma concentrations remained unchanged. This effect was seen after alcohol administration via drinking fluid or by liquid diet, in both mice and rats and in both genders. Shorter alcohol treatments did not show the selective effect on brain glucocorticoid levels. During the alcohol consumption the regional brain corticosterone concentrations paralleled the plasma concentrations. Type II glucocorticoid receptor availability in prefrontal cortex was decreased after withdrawal from chronic alcohol consumption and nuclear localization of glucocorticoid receptors was increased, a pattern that would be predicted from enhanced glucocorticoid type II receptor activation. This novel observation of prolonged selective increases in brain glucocorticoid activity could explain important consequences of long term alcohol consumption, including memory loss, dependence and lack of hypothalamo-pituitary responsiveness. Local changes in brain glucocorticoid levels may also need to be considered in the genesis of other mental disorders and could form a potential new therapeutic target.
Sunday 30th April 1993, Edwards shot dead Mrs. Turvey as she walked along Milton Road in the Farley hill area of Luton. He then snatched their daughter Charlene, who he had been denied access to. He drove to a nearby wooded area, sat cuddled with the seven month old who would not stop crying. He lay her on the ground and shot her. Wednesday 15th December 1993, At St. Albans crown court he pleased guilty to manslaughter on the grounds of diminished responsibility. But denied murder. Thursday 16trh December 1993, Edwards changed his plea to guilty to murdering Marina Turvey having previously admitted manslaughter. His not guilty plea to murdering baby Charlene was accepted by the prosecution. He had already pleaded guilty to her manslaughter on the grounds of diminished responsibility, for which he was jailed for eight years. Friday 17th December 1993, Edwards found guilty, and sentenced to life.
Despite the warmth of the green color itself, I get a very cooling feeling from this work. It is lush, well-detailed, and interesting to look at; it is obviously deserving of the Daily Deviation. Congratulations! Is it me, or does the rock to the very left of the dark, auburn berry-bearing bush look a little like a human?
Q: Best/Fastest Way To Change/Access Elements of a Matrix I'm quite new to C# and I'm having difficult with our arrays, arrays of arrays, jagged arrays, matrixes and stuff. It's quite different from the C++ , since I can't get a reference (unless I use unsafe code) to a row of a matrix, using pointers and stuff. Anyway, here's the problem: I have a struct/class called "Image" that cointains 1024 columns and 768 lines. For each line/column theres a 'pixel' struct/class that contains 3 bytes. I'd like to get/set pixels in random places of the matrix as fast as possible. Let's pretend I have a matrix with 25 pixels. That is 5 rows and 5 columns, something like this: A B C D E F G H I J K L M N O P Q R S T U V X W Y And I need to compare M to H and R. Then M to L and N. Then I need to 'sum' G+H+I+L+M+N+Q+R+S. How can I do that? Possibilities: 1) Create something like pixel[5][5] (that's a jagged array, right?), which will be slow whenever I try to compare elements on different columns, right? 2) Create something like pixel[25] , which won't be as easy to code/ready because I'll need to do some (simple) math each and everything I want to access a element 3) Create something like pixe[5,5] (that's a multi-dimensional array, right?)... But I don't know how that will be translated to actual memory... If it's going to be a single block of memory, like the pixe[25], or what... Since I intend to do this operations ('random' sums/comparison of elements that are in different rows/columns) tens of thousands of times per image. And I have 1000+ imagens. Code optimization is a must... Sadly I'm not sure which structure / classe I should use. TL;DR: Whats the FASTEST and whats the EASIEST (coding wise) way of getting/setting elements in random positions of a (fixed size) matrix? edit: I do not want to compare C++ to C#. I'm just saying I AM NEW TO C# and I'd like to find the best way to accomplish this, using C#. Please don't tell me to go back to C++. A: I just finished testing, heres the result: SD Array Test1: 00:00:00.9388379 SD Array Test2: 00:00:00.4117926 MD Array Test1: 00:00:01.4977765 MD Array Test2: 00:00:00.8950093 Jagged Array Test1: 00:00:03.6850013 Jagged Array Test2: 00:00:00.5036041 Conclusion: Single dimensional array is the way to go... Sadly we lose in readability. And heres the code: int[] myArray = new int[10000 * 10000]; for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { myArray[(i10000)+j] = i+j; } } Stopwatch sw = new Stopwatch(); int sum = 0; sw.Start(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += myArray[(j 10000) + i]; } } sw.Stop(); Console.WriteLine("SD Array Test1: " + sw.Elapsed.ToString()); sum=0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += myArray[(i * 10000) + j]; } } sw.Stop(); Console.WriteLine("SD Array Test2: " + sw.Elapsed.ToString()); myArray = null; int[,] MDA = new int[10000, 10000]; for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { MDA[i, j] = i + j; } } sum = 0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += MDA[j, i]; } } sw.Stop(); Console.WriteLine("MD Array Test1: " + sw.Elapsed.ToString()); sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += MDA[i, j]; } } sw.Stop(); Console.WriteLine("MD Array Test2: " + sw.Elapsed.ToString()); MDA = null; int[][] JA = new int[10000][]; for (int i = 0; i < 10000; i++) { JA[i] = new int[10000]; } for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { JA[i][j] = i + j; } } sum = 0; sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += JA[j][i]; } } sw.Stop(); Console.WriteLine("Jagged Array Test1: " + sw.Elapsed.ToString()); sw.Restart(); for (int i = 0; i < 10000; i++) { for (int j = 0; j < 10000; j++) { sum += JA[i][j]; } } sw.Stop(); Console.WriteLine("Jagged Array Test2: " + sw.Elapsed.ToString()); MDA = null; Console.ReadKey();
Schamberg disease Schamberg's disease, (also known as "progressive pigmentary dermatosis of Schamberg", "purpura pigmentosa progressiva" (PPP), and "Schamberg's purpura") is a chronic discoloration of the skin found in people of all ages, usually only affecting the feet, legs or thighs or a combination. It may occur as a single event or subsequent bouts may cause further spread. It is most common in males. It is named after Jay Frank Schamberg, who described it in 1901. There is no known cure for this disease but it is not a life-threatening condition and is mainly of cosmetic concern, although, because it can appear so suddenly, so extensively and because it usually leaves permanent discoloration of the skin, it can cause understandable psychological concern. The skin lesions sometimes cause itching, which can be treated by applying cortisone cream. The cortisone cream will only help with the itching and does not improve the discoloration of the skin. Schamberg's disease causes no other symptoms beside skin discoloration and itching. The condition is caused by inflammation of capillaries near the surface of skin and subsequent leaking of red blood cells into surrounding tissues. As the red blood cells break down and get mostly resorbed, some of the iron released by the red blood cells remains in the skin and causes the characteristic rust-colored appearance. The cause of the capillary inflammation is usually unknown. Symptoms The lesions are most frequent on the lower limbs, but may occur anywhere on the body, including the hands, arms, torso and even the neck. They may vary in number and erupt in mass numbers. They consist of irregular patches of orange or brown pigmentation with characteristic "cayenne pepper" spots appearing within and at the edge of old lesions. There are usually no symptoms, although there may be some slight itching, but there is no pain. The eruption may persist for many years. The pattern of the eruption changes, with slow extension and often some clearing of the original lesions. Schamberg's disease, or progressive pigmented purpuric dermatosis, is a chronic discoloration of the skin which usually affects the legs and often spreads slowly. This disease is more common in males and may occur at any age from childhood onward. This condition is observed worldwide and has nothing to do with race or ethnic background. Causes Schamberg's disease is caused by leaky blood vessels near the surface of the skin, capillaries, which allow red blood cells to slip through into the skin. The red blood cells in the skin then fall apart and release their iron, which is released from hemoglobin. The iron causes a rust color and this accounts for the orange tint of the rash. Although the underlying cause for the leaky blood vessels is almost always unknown, researchers suggest some potential triggers. These include the body's inflammatory reaction to some agent, such as a viral infection or a prescription or over the counter medication or supplement, such as thiamine and aspirin. Even though there is no correlation with genetics, there have been a few cases where few people in a family had this condition. Although a definite cause for capillary inflammation is almost always unknown, certain preventive measures can be taken. Doctors may prescribe medications that enhance the circulation of blood, which can keep blood vessels strong and healthy. Mechanism Schamberg's disease is a skin disorder that causes a discoloration of the lower extremities. It usually occurs in the lower extremities and rarely elsewhere. This condition is caused by leaky blood vessels near the surface of the skin. The cause of the leaky capillaries is usually not known. When the red blood cells escape the blood vessels, they end up close under the skin surface, where they break apart, releasing hemoglobin, which in turn breaks apart, releasing Iron. (Iron is the part of hemoglobin that enables it to transfer oxygen from the lungs to the cells and carbon dioxide from the cells to the lungs.) The iron released into the skin gets bound up into a complex called hemosiderin, which causes the discoloration of the skin. Diagnosis With a complete history, the results from visual examination, and the aid of appropriate laboratory testing, a dermatologist can usually determine whether the skin lesions are in fact due Schamberg's disease. Schamberg's disease can only be properly diagnosed by a healthcare provider. For a trained skin specialist such as a dermatologist, the condition is often readily diagnosed, because the visual appearance of the lesions on the skin itself usually suggests the possibility that the cause may be Schamberg's disease. While reviewing medical history is important to diagnose this condition, it is essential that the skin be physically examined. To ensure that the skin lesions are not caused by other skin conditions or infections, a doctor will often order a complete blood count (CBC) and other blood tests. Blood test results are usually normal. They are performed primarily to rule out other bleeding disorders that cause purpura. Since Schamberg's disease is usually asymptomatic beyond the visible lesions themselves, few other tests are usually indicated. Additional testing may aid diagnosis. A skin biopsy may be taken to determine capillaritis of dermal vessels. Capillaritis or pigmented purpura is skin condition that has brown-reddish patches on the skin, which is caused by leaky capillaries. Such skin biopsies are sent to a laboratory for a pathological examination, where each biopsy is observed under a microscope. A dermatologists may also perform a dermatoscopy. Treatment There is no cure for Schamberg's disease, however, this condition is not life-threatening or a major health concern. The most usual problems that patients will encounter is discoloration of the skin and, occasionally, itching. Itching may be improved by applying a cortisone cream. Rarely, in very severe or concerning cases, Colchicine treatment has been used to prevent recurrence. Some recommend that patients take a vitamin C supplement to promote collagen production, but this is not proven to be helpful. In cases where there is a known trigger, people should avoid re-exposure to that trigger, e.g., people suspected to be sensitive to food with artificial colors or preservatives should avoid foods containing those items. This is because some people have been observed to be sensitive to these agents, and the body initiates an inflammatory reaction if exposed to them again, which causes further capillary inflammation and red blood cell leakage. Several research studies have indicated that Schamberg's disease can be controlled and the number of lesions can be reduced with use a drug called aminaphtone. This drug helps reduce capillary fragility and red blood cell leakage. A study published in 2014 on the Journal of the German Society of Dermatology (Deutsche Dermatologische Gesellschaft) concludes that oral rutoside and ascorbic acid may be an efficient and well tolerated treatment for PPPD, with a recommendation for early treatment for best clinical outcome. Prognosis A patient with Schamberg's disease can live a normal and healthy life. Since there is no proven cure for this condition, the patient will have to endure the lesions on his or her skin. With appropriate treatments, the condition may get better. Although the skin lesions are not life-threatening, it may cause a cosmetic concern for some individuals. Skin lesions may cause psychological discomfort, where patients may require reassurance to help with stress and anxiety. There are a few rare cases of T-cell lymphoma that have developed from Schamberg's disease. This is not a cause for concern, since the risk factors associated with Schamberg's disease are relatively low. Recent research A few very small non-blinded studies of treatment with narrow-band ultraviolet light have been reported as promising. References External links Category:Disturbances of human pigmentation Category:Vascular-related cutaneous conditions
Taking a scenic stroll to the Pope’s Summer residence, viewing Rome from the Colosseum’s upper rings, visiting Vatican Museum’s many secret rooms, preparing seasonal dishes from a Roman farm house…Even in Rome, one of the world’s oldest touristic cities, there are still genuine experiences known to only a few. Many foreign tourists ask me the question, “are there any Italian living in Rome?” My answer is, “Of course there are, but unfortunately they never go to the places normal tourists go.” After giving travelers advices on where to go in Rome for a few years, I think it’s time to reveal the secrets. You probably already get the idea – Locals in Rome hide their secrets well. Rome is multi-layered, on the outside it seems unbearably touristic, yet on the inside there is still a strong culture core. If you are a culture-savvy traveler that looks beyond the mass-produced touristic things, keep reading. You’re about to uncover a Rome that is still quaint, old-fashioned, and unmistakably Italian. 1. Visit Castel Gandolfo – the Pope’s Summer residence Just 12 miles out of the Eternal City, the Pope’s country retreat recalls the grandeur of times gone by. Popes have come to this picturesque, lake-side town for generations, and so did his pilgrims. Perfectly curated gardens, ancient stoned roads, and carefully paired flower pots everywhere make Castel Gandolfo the best place for a scenic stroll. Not to mention the turquoise lake surrounded the town – a real gem to treasure in Rome’s hot summer days. 2. See the Grottos (Pope’s Tombs) under the ground Lots of Rome’s best secrets are under the ground. The Grottos, Rome’s vast underground graveyards house tombs of Popes. This underground world is extremely sophisticated, consisting of tombs, rooms, chapels, and encompassing structures that make meaningful connections in the past. You’ll want to go with an experienced guide that read Latin to help you decode the inscriptions on the tombs. It is truly a hidden Rome experience, and emotional. 3. View Rome from Colosseum’s upper level Nobody would miss Colosseum, but only a few know that the best views stay on top. Going to the Colosseum’s upper ring not only excludes you from the hectic tourist crowd, but also offers you a bird’s-eye view of the ancient Forum. You’ll admire the arch of Constantine and surrounding monuments from above and get a panoramic city view. I call this a true “Instagram-worthy” moment. 4. Private visit to Vatican and Sistine Chapel’s secret rooms Not many rooms of the Vatican museums and Sistine Chapel are open to the public, and the best rooms are always the hidden ones. I always strongly recommend travelers with higher budget to take the private tour, mainly because the private visit best keeps the sensory experience. Based on private connections, guards will open certain rooms just for private viewings, and you’ll admire Michelangelo and Raffaele in absolute silence. You’ll even smell the aromas from the ancient paints, and have the private space to meditate under Rome’s best masterpieces. It’s hard to imagine getting that sensory experience in a room packed with massive tour groups. 5. Meet an Italian tailor for your wardrobe classic Why do you need a tailor-made clothing when you can simply buy a designer dress in stores? Well, not only does a tailored clothing fits better, accentuates your figure, it also makes the occasion all the more special. What gets better than having a suit or dress artfully made for you in Rome? And I have to be honest, Italians simply dress better. The secret? They still do it the old-fashioned way – custom-made tailoring. Some of the best tailors in Rome have their own artisan workshops, and you’ll need to come over to have every details measured. In fact, simply visiting the pattern-filled studio is quite an experience in itself. It starts from getting to know you personally, the tailor then creates the patterns, selects the fabric, cuts and fits the finished piece on you. The ultimate Italian experience from the bygone era. Comments (0) Leave a Reply Your actual name, not your online persona, website name, company name or keywords, otherwise your comment won't be published Email (required) (will not be published) Website Comment (required) Please do not advertise and make sure your comment adds value, otherwise we regret that it won't be published. Links are not allowed here - if you would like to advertise, please contact us for details.
/* * Copyright 2003-2013 JetBrains s.r.o. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. / package jetbrains.mps.workbench.dialogs.project.newproject; import com.intellij.openapi.extensions.ExtensionPointName; import org.jetbrains.annotations.NotNull; import java.util.Collection; /* * Implementation of this interface extends list of groups in 'New project dialog' */ public interface ProjectTemplatesGroup { ExtensionPointName<ProjectTemplatesGroup> EP_NAME = ExtensionPointName.create("com.intellij.mps.projectGroupTemplateEP"); @NotNull String getName(); @NotNull Collection<MPSProjectTemplate> getTemplates(); }
Go Haim or Go Home Tee + Album Go Haim or Go Home + Album
Pump devices are commonly used to deliver one or more fluids to a targeted individual. For example, a medical infusion pump device may be used to deliver a medicine to a patient as part of a medical treatment. The medicine that is delivered by the infusion pump device can depend on the condition of the patient and the desired treatment plan. For example, infusion pump devices have been used to deliver insulin to the vasculature of diabetes patients so as to regulate blood-glucose levels. In some circumstances, the dosage of medicine delivered by the infusion pump acts within the patient's body over a long period of time. Such conditions, for example, may cause a patient to have an amount of non-activated insulin in his or her system even thought the infusion pump is programmed to deliver the next dosage in a series of insulin dosages.
Inga bijuga Inga bijuga is a species of legume in the family Fabaceae. It is found only in Venezuela. References bijuga Category:Endemic flora of Venezuela Category:Vulnerable flora of South America Category:Taxonomy articles created by Polbot
Q: Code separation in symfony 2 - Controller vs Service vs entity I am using symfony 2 and I have question about code separation. I would like to make sure that I correctly understand what elements should be in a controller, what in a service and what in a entity. Let's imagine that I have list of documents that I need to display. On each document before displaying I have to also perform some logic operation (e.g. add two variables). As in understand entity class takes care only on data retrieval and operation on single entity. I should not input there any custom code. As I understand this should be done by a service. But should I: use a service to pass to controller list of documents based on some criteria after performing the required logic, or use a controller to download list of documents, and than pass document to service to perform some logic? I would rather think that the first approach is appropriate to keep controller thin (thin controllers, big models) but is this approach right? What code should be in entity, what in controller and what in a service? In particular where should I relate to entity manager - in a controller or rather in service? Let's also pretend that in many place in my app I need to check if document is finalized before allowing user to perform any action (e.g. edit it). This definitely should be either in a service, as another service would be required to check this. Should I however load the document entity object in controller, send it to service to verify whether it may be finalized or rather load document in service and there perform a check? A: My Symfony 2 architecture is (with Doctrine ORM): Thin controllers with just the routing logic A service (a.k.a. "Manager") for each entity (all the business logic is here) Custom services for my other needs (ie, for using external tools like Amazon S3 or Mandrill mailing system) A repository for each entity (just methods to read entities from the DB) Each action inside a controller calls one or more methods from the entity's manager; I always try to avoid using directly the respository's "magic methods" in favor of custom made methods: inside the action, instead of calling $this->getDoctrine()->getRepository(<entity>)->findBy(array('parent' => null)); I create this method inside the repository: public function findParents() { return $this->findBy(array('parent' => null)); } And inside the action I use: $this->getDoctrine()->getRepository(<entity>)->findParents(); Of course this is a simple example, but it works quite well with more complex findBy or findOneBy queries. A: In Symfony2 is super easy decouple logic using repositories and services. For example: A entity repository with aditional custom finder use Doctrine\ORM\EntityRepository; class MyEntityRepository extends EntityRepository { public function findAllWithX($parameter) { // your DQL. manipule own data. filters. } } A fat service to handle the main business logic // could be a listener class MyFatService { public function __construct(MyEntityRepository $mer, AnotherRepository $aor, MisteriousService $mis) { $this->mer = $mer; $this->aor = $aor; $this->mis = $mis; } public function someBigAction($paramX, $paramY) { $foo = $this->mer->findAllWithX($paramX); $bar = $this->aor->findBy(....); // manipule data. complex operations. // call related services. // manipule data related to many repositories } } To define services: services: my_entity_repository: class: AppBundle\Repository\MyEntityRepository factory: [@doctrine, getRepository] arguments: - %entity.my_entity% my_another_repository: class: AppBundle\Repository\AnotherRepository factory: [@doctrine, getRepository] arguments: - %entity.my_another_entity% my_fat_service: class: AppBundle\MyFatService arguments: - @my_entity_repository - @my_another_repository - @misterious_service In your controller: public function blaAction($x, $y) { // leave the heavy work to services. // just handle request and send the response $data = $this->get('my_fat_service') ->someBigAction($x, $y); return $this->render('template.twig', ['data' => $data]); } ps: sorry for my english
The effect of the pressure-volume curve for positive end-expiratory pressure titration on clinical outcomes in acute respiratory distress syndrome: a systematic review. Methods to optimize positive end-expiratory pressure (PEEP) in acute respiratory distress syndrome (ARDS) remain controversial despite decades of research. The pressure-volume curve (PVC), a graphical ventilator relationship, has been proposed for prescription of PEEP in ARDS. Whether the use of PVC's improves survival remains unclear. In this systematic review, we assessed randomized controlled trials (RCTs) comparing PVC-guided treatment with conventional PEEP management on survival in ARDS based on the search of the National Library of Medicine from January 1, 1960, to January 1, 2010, and the Cochrane Central Register of Controlled Trials. Three RCTs were identified with a total of 185 patients, 97 with PVC-guided treatment and 88 with conventional PEEP management. The PVC-guided PEEP was associated with an increased probability of 28-day or hospital survival (odds ratio [OR] 2.7, 95% confidence interval [CI] 1.5, 4.9) using a random-effects model without significant heterogeneity (I (2) test: P = .75). The PVC-guided ventilator support was associated with reduced cumulative risk of mortality (-0.24 (95% CI -0.38, -0.11). The PVC-managed patients received greater PEEP (standardized mean difference [SMD] 5.7 cm H2O, 95% CI 2.4, 9.0) and lower plateau pressures (SMD -1.2 cm H2O, 95% CI -2.2, -0.2), albeit with greater hypercapnia with increased arterial pCO2 (SMD 8 mm Hg, 95% CI 2, 14). Weight-adjusted tidal volumes were significantly lower in PVC-guided than conventional ventilator management (SMD 2.6 mL/kg, 95% CI -3.3, -2.0). This analysis supports an association that ventilator management guided by the PVC for PEEP management may augment survival in ARDS. Nonetheless, only 3 randomized trials have addressed the question, and the total number of patients remains low. Further outcomes studies appear required for the validation of this methodology.
Effects of hip and head position on ankle range of motion, ankle passive torque, and passive gastrocnemius tension. Ankle joint range of motion (ROM) is notably influenced by the position of the hip joint. However, this result remains unexplained. Thus, the aim of this study was to test if the ankle passive torque and gastrocnemius muscle tension are affected by the hip and the head positions. The torque and the muscle shear elastic modulus (measured by elastography to estimate muscle tension) were collected in nine participants during passive ankle dorsiflexions performed in four conditions (by combining hip flexion at 90 or 150°, and head flexed or neutral). Ankle maximum dorsiflexion angle significantly decreased by flexing the hip from 150 to 90° (P < 0.001; mean difference 17.7 ± 2.5°), but no effect of the head position was observed (P > 0.05). Maximal passive torque and shear elastic modulus were higher with the hip flexed at 90° (P < 0.001). During submaximal ROM, no effects of the head and hip positioning (P > 0.05) were found for both torque and shear elastic modulus at a given common ankle angle among conditions. Shifts in maximal ankle angle due to hip angle manipulation are not related neither to changes in passive torque nor tension of the gastrocnemius. Further studies should be addressed to better understand the functional role of peripheral nerves and fasciae in the ankle ROM limits.
UNITED STATES of America, Plaintiff-Appellee, v. Angelo Eugene WILLIAMS, Defendant-Appellant. No. 98-8986. United States Court of Appeals, Eleventh Circuit. Dec. 8, 1999. Appeal from the United States District Court for the Southern District of Georgia.(No. CR498-43), B. Avant Edenfield, Judge. Before EDMONDSON and BIRCH, Circuit Judges, and OWENS, Senior District Judge. EDMONDSON, Circuit Judge: Defendant Angelo Eugene Williams, under 18 U.S.C. § 2244(a)(1), was convicted of abusive sexual contact in the territorial jurisdiction of the United States. We vacate the conviction and sentence and remand. BACKGROUND This case arises from an incident at the Hunter Army Airfield Youth Center ("Youth Center") in October 1997. At that time, Defendant was employed as a computer specialist at the Youth Center, a recreational facility for children living on the base. Defendant's duties included maintaining the Youth Center computer room and supervising children's use of the computers. According to the Government's evidence at trial, Defendant engaged in abusive sexual contact with K.T., a ten year-old female, in the Youth Center computer room on October 14, 1997. The Government's evidence established that K.T. arrived at the Youth Center and that she went to the computer room. In the computer room, K.T., with Defendant's permission, seated herself at Defendant's computer terminal. K.T. testified that, while sitting at Defendant's terminal, Defendant touched her leg and chest and asked her for a kiss. An Army investigator testified that K.T. told him that Defendant touched her chest, Honorable Wilbur D. Owens, Jr., Senior U.S. District Judge for the Middle District of Georgia, sitting by designation. buttocks, and vaginal area. The Government also introduced a statement in which Defendant admitted that he rubbed the inside of K.T.'s leg, that he hugged her, that he touched her chest and buttocks, and that he asked her to kiss him. At trial, Defendant testified that K.T. had indeed come to the computer room and that he had permitted her to use his computer. He testified, however, that after K.T. had used his computer for some time, he asked her to get up because he needed to use the computer. He stated that, as he instructed K.T. to leave his terminal, he rolled toward her in a roll-away chair, hitting her leg with his hand. K.T., according to Defendant, then moved away from the terminal, but later returned and attempted to use Defendant's computer again. Defendant said that he, at that point, grabbed K.T.'s shoulder and instructed her to leave his computer alone. Defendant testified that K.T. used another computer for some time and then left the computer room. Defendant admitted giving an incriminating statement to investigators, but he denied the statement was true, explaining that he caved in to the investigator's promise that he could "put this thing behind [him]" if he made a statement. Defendant requested at trial that the district court give a lesser included offense jury instruction on simple assault (18 U.S.C. § 113(a)(5)). The court refused to give the instruction, explaining that "[t]he evidence does not fit." Defendant was then convicted of violating § 2244. DISCUSSION Defendant asserts five grounds for his appeal.1 We find it necessary to address two of Defendant's contentions here. First, we address Defendant's claim that the Speedy Trial Act was violated in his case and, concluding that this claim has merit, vacate the conviction. Second, because the Government may seek to 1 Defendant claims that the district court erred by refusing to: (1) dismiss the indictment under the Speedy Trial Act; (2) charge the jury on assault as a lesser included offense; (3) appoint an expert to testify on whether Defendant fit the profile of a child molester; (4) admit favorable evidence of a Georgia Department of Family and Children's Services (DFACS) report regarding Defendant; and (5) allow Defendant to ask K.T.'s sister whether she would believe K.T. under oath with regard to the crime charged. 2 retry Defendant for this offense, we also address Defendant's claim that the district court erred in refusing to give an instruction on assault as a lesser included offense of abusive sexual contact. 1. THE SPEEDY TRIAL ACT Defendant contends that the district court erred by denying his motion to dismiss the indictment under the Speedy Trial Act, 18 U.S.C. § 3161 et seq.2 In particular, Defendant argues that the district court, in finding that the seventy-day limitation had not been violated in Defendant's case, improperly excluded from its Speedy Trial Act calculation twenty days allowed for the filing of pretrial motions. We agree that these days were improperly excluded.3 The Speedy Trial Act provides that a defendant must be brought to trial within seventy days of the filing of his indictment, or his first appearance before a judicial officer, whichever is later. United States v. Davenport, 935 F.2d 1223, 1227 (11th Cir.1991). Certain periods, however, are excluded from the seventy-day limit. United States v. Schlei, 122 F.3d 944, 985 (11th Cir.1997). "Any period of delay resulting from other proceedings concerning the defendant" must be excluded from the seventy-day calculation. 18 U.S.C. § 3161(h)(1). In this case, the Magistrate Judge voluntarily ordered that all pretrial motions be filed no later than twenty days after the Defendant's arraignment.4 The district court excluded this twenty-day period from its Speedy Trial Act calculations. The Government urges that this exclusion was proper under § 3161(h)(1) and our decision in United States v. Mejia, 82 F.3d 1032 (11th Cir.1996). We disagree. 2 The remedy for violation of the Speedy Trial Act's seventy-day limitation period is dismissal of the indictment. 18 U.S.C. § 3162(a)(2). 3 We review the district court's construction and interpretation of the Speedy Trial Act de novo. We review the district court's factual determinations on excludable time for clear error. United States v. Schlei, 122 F.3d 944, 984 (11th Cir.1997). 4 Defendant took full advantage of the twenty-day deadline, filing several discovery motions on the twentieth day. This fact, however, has no bearing upon our analysis. See United States v. Mejia, 82 F.3d 1032, 1036 (11th Cir.1996) ("Whether motions are actually filed during the extension is unimportant."). 3 In Mejia, we decided that, where a defendant moved for, and the court granted, an extension of time for filing additional pretrial motions, the district court properly excluded the extension period from Speedy Trial Act calculations. Id. at 1035-36. We reasoned that such an extension falls within § 3161(h)(1)'s language about "[a]ny period of delay resulting from other proceedings concerning the defendant." Id. It does not follow from Mejia, however, that the twenty-day period in the instant case is excludable.5 Instead, we think that Mejia presented a case different from the present case. In Mejia, the defendant sought and obtained an extension of time in which to file his motions. Id. at 1035. Implicit in the term "extension" is the notion that the defendant sought additional time not normally permitted for the filing of motions. In other words, he sought to delay the forward progression of the proceedings. That an extension of time in which to file motions will work a delay in bringing the defendant to trial seems likely. Here, on the other hand, there was no extension of time; twenty days after arraignment was the original deadline set by the court for filing pretrial motions. Moreover, twenty days after arraignment is, by local rule, the ordinary time allowed for the filing of motions in the Southern District of Georgia. See S.D. Ga. Local Criminal Rule 12.1. Therefore, even if the Magistrate by order had entered no deadline in this case, the parties would have had twenty days after the arraignment to prepare and to file their pretrial motions. In our view, such a routine time prescription is no "delay" in bringing the defendant to trial. To qualify as an excluded period under § 3161(h)(1), the period must constitute a "delay." 18 U.S.C. § 3161(h)(1). Moreover, the twenty-day period in this case was hardly extraordinary or specifically-tailored to the needs of this case. It was not the result of a motion to enlarge the time to file motions. Instead, it was "based merely upon the entry of a standard scheduling order." See United States v. Hoslett, 998 F.2d 648, 656 (9th Cir.1993). An exclusion based on a case-specific determination that additional time is needed for the 5 The court in Mejia expressly declined to comment on a case more like the instant one, where the district court sua sponte sets a deadline for the filing of pretrial motions. See Mejia, 82 F.3d at 1036 n. 3 ("[W]e decide nothing today about whether extensions for the preparation and filing of pretrial motions granted by the court upon motion of the government or by the court sua sponte result in excludable days under § 3161(h)(1)"). 4 disposition of pretrial motions is one matter; an across-the board exclusion of twenty days in every case arising in a judicial district is quite another. See id. Therefore, Mejia does not control the outcome of this case. Because our duty is to carry out the intent of Congress, we must look to the language of the statute itself. As noted previously, § 3161(h)(1) requires a "delay" as a prerequisite to exclusion. On this record, we see no indication that the judge's setting of a deadline for the filing of motions worked a "delay" within the meaning of the statute. We also look to the structure of the statute as a whole. The Speedy Trial Act makes allowance for the delay occasioned by the exigencies of particular cases. The automatic exclusions of § 3161(h)(1)(A)-(J) take account of the delay that may result from an array of particular pretrial circumstances. In addition, § 3161(h)(8)(A) excludes delay resulting from a continuance where the court specifically finds that the interests of justice furthered by the continuance outweigh the interests of the public and the defendant in a speedy trial. But, none of the exclusion provisions of the Act specifically address the situation in this case; and, they do not indicate, in our view, an intention on the part of Congress to allow for broad, across-the-board exclusions created by a district court's standard scheduling practices or local rule.6 See generally 18 U.S.C. § 3161(h)(8)(C) (providing that no continuance "because of general congestion of the court's calendar" is excludable). 6 If the customary time allowances for the filing of motions resulted in excludable time, each judicial district, in effect, would be free to amend the Speedy Trial Act by local rule. For example, considering its local rule, it appears that in the Southern District of Georgia the seventy-day limit always (or almost always) would be transformed into a ninety-day limit. We are unable to believe that Congress intended that result. 5 The twenty days allowed for the filing of pretrial motions were not properly excludable in this case.7 Therefore, more than seventy—at least eighty-one—non-excludable days elapsed between the Defendant's first appearance and the commencement of his trial. The trial court thus erred in denying Defendant's motion to dismiss the indictment under the Speedy Trial Act. 2. LESSER INCLUDED OFFENSE Defendant also asserts, on appeal, that the district court erred in declining to instruct the jury on assault as a lesser included offense of abusive sexual contact. We agree. And, because the Government may re-indict and retry Defendant for abusive sexual contact, and because the pertinent evidence in a new trial may be like the evidence in this trial, we address the issue. To establish that the district court erred in refusing to give the lesser included offense instruction, Defendant must satisfy a two-part test. First, he must show that the charged offense encompasses all of the elements of the lesser offense ( the "elements" test). Schmuck v. United States, 489 U.S. 705, 716, 109 S.Ct. 1443, 1450, 103 L.Ed.2d 734 (1989). Second, he must establish that the district court abused its discretion in failing to give the instruction. An abuse of discretion may occur where the evidence would permit the jury rationally to acquit the defendant of the greater, charged offense and convict him of the lesser. United States v. Cornillie, 92 F.3d 1108, 1109 (11th Cir.1996). Applying this two-part test, we believe that the district court erred in this case when it refused to instruct the jury on assault as a lesser included offense. 7 We follow the Sixth and Ninth Circuits. See United States v. Moran, 998 F.2d 1368, 1370-71 (6th Cir.1993); United States v. Hoslett, 998 F.2d 648, 656 (9th Cir.1993). We recognize that the Seventh Circuit has said that a sua sponte scheduling order, however routine, setting a deadline for filing motions results in excludable time. United States v. Montoya, 827 F.2d 143, 153 (7th Cir.1987). The Seventh Circuit's decision in Montoya is grounded in the premise that "[i]f the defendant believes no time or less time is needed he can so advise the court and the case may proceed without regard to possible pretrial motions." Id. We disagree, for we believe that "the burden should not be on the defendant to take affirmative steps to keep the speedy-trial clock running." Moran, 998 F.2d at 1371. The duty to comply with the Speedy Trial Act lies with the courts, not with defense counsel. By the way, the Government does not contend, nor does the record suggest, that defense counsel in this case should have known, when the twenty-day deadline was announced, that a violation of the seventy-day limit would necessarily occur. 6 First, abusive sexual contact with a child, under 18 U.S.C. § 2244(a)(1), encompasses all of the elements of simple assault under 18 U.S.C. § 113(a)(5). The elements of abusive sexual contact with a child under § 2244(a)(1) are: (1) in the special maritime and territorial jurisdiction of the United States, (2) the defendant intentionally (3) touched the genitalia, anus, groin, breast, inner thigh, or buttocks (4) of a child less than twelve years of age (5) "with an intent to abuse, humiliate, harass, degrade, or arouse or gratify the sexual desire of any person." 18 U.S.C. § 2244(a)(1); 18 U.S.C. § 2246(3). A person commits assault under § 113 when, (1) in the special maritime and territorial jurisdiction of the United States, (2) he "assaults" another person. 18 U.S.C. § 113(a). Section 113 does not define "assault", so we give that term its meaning at common law. United States v. Guilbert, 692 F.2d 1340, 1343 (11th Cir.1982). At common law, an assault was either a battery, an attempted battery, or an act that puts another in reasonable apprehension of receiving immediate bodily harm. See id. Given the arguments of the parties in this case, we focus on assault committed by a battery. The Government contends that abusive sexual contact with a child does not encompass all of the elements of common law battery; the Government says that battery requires an intent to do bodily harm. We disagree. In his Commentaries, Blackstone observed: The least touching of another's person wilfully, or in anger, is a battery; for the law cannot draw the line between different degrees of violence, and therefore totally prohibits the first and lowest stage of it: every man's person being sacred, and no other having a right to meddle with it, in any the slightest manner. United States v. Stewart, 568 F.2d 501, 505 (6th Cir.1978) (quoting 3 Blackstone, Commentaries on the Law of England 120 (E. Christian ed., 1822)). Case law is in accord with Blackstone: the intention to do bodily harm is not a necessary element of battery. State v. Duckett, 306 Md. 503, 510 A.2d 253, 257 (1986). The slightest willful offensive touching of another constitutes a battery at common law, regardless of whether the defendant harbors an intent to do physical harm. See Gates v. State, 110 Ga.App. 303, 138 S.E.2d 473, 473- 74 (1964) (affirming battery conviction on evidence that defendant intentionally "tapped" woman on buttocks 7 in public store); Wood v. Commonwealth, 149 Va. 401, 140 S.E. 114, 116 (1927) (affirming conviction for assault and battery where defendant fondled fourteen year-old girl). Furthermore, the view that common law battery (and, thus, § 113(a)(5) assault) does not contain an intent to harm element is borne out by § 113 itself. Section 113 identifies seven kinds of assault. See 18 U.S.C. § 113(a). For some of these offenses, the statute specifically sets forth a specific intent requirement. See 18 U.S.C. § 113(a)(1) (assault with intent to commit murder); 18 U.S.C. § 113(a)(3) (assault with a dangerous weapon and intent to do bodily harm). The subsections identifying assault by striking, beating or wounding, assault resulting in serious bodily injury, and simple assault (the subsection at issue in this case), however, contain no language setting out a specific intent requirement. The courts have recognized this omission, concluding that no specific intent element exists for assault by striking, beating, or wounding, United States v. Martin, 536 F.2d 535, 535-36 (2d Cir.1976), and assault resulting in serious bodily injury. United States v. Juvenile Male, 930 F.2d 727, 728-29 (9th Cir.1991). Our view of assault is also consistent with authorities recognizing that sex offenses frequently encompass simple assault as a lesser included offense. See United States v. Eades, 633 F.2d 1075, 1077 (4th Cir.1980) ("[T]he great majority of the offenses proscribed by Maryland's sexual offense statutes may be said to encompass simple assault as a lesser included offense."); see also Sills v. State, 36 Ga.App. 103, 135 S.E. 758, 758 (1926) ("An assault or assault and battery is necessarily involved in every case of rape."). Thus, we conclude that simple assault under § 113(a)(5) is a lesser included offense of abusive sexual contact under § 2244(a)(1). Next, we must decide whether an evidentiary basis exists for a rational jury to have found Defendant guilty of simple assault but not guilty of abusive sexual contact.8 We believe such a basis does exist. Defendant testified that he hit the victim, K.T., on the leg with his hand. Defendant further testified that he grabbed K.T.'s shoulders. Defendant testified that K.T. responded to being struck on the leg by stating: "Oh, 8 Excerpts from Defendant's testimony at trial are reprinted in the Appendix to this opinion to show more fully the evidentiary basis for a jury instruction on assault. 8 Mr. Williams, you didn't have to push me. Mr. Angelo, you didn't have to push me." We conclude that such testimony, if accepted by a jury, could give a rational factfinder a sufficient basis upon which to find that Defendant did touch K.T., and that the touching was offensive and not consented to by her, but that the touching was not of a sexual nature. Thus, the jury could decide that Defendant committed simple assault, rather than abusive sexual contact. 18 U.S.C. § 113(a)(5); 18 U.S.C. § 2244(a)(1). CONCLUSION Because we conclude that the district court erred in denying Defendant's motion to dismiss the indictment for violation of the Speedy Trial Act, we VACATE the conviction and sentence and REMAND to the district court with directions to dismiss the indictment without prejudice.9 VACATED AND REMANDED. APPENDIX SELECTED TESTIMONY OF DEFENDANT Q: What happened, if anything ... as far as [K.T.]? Do you remember anything about the 14th? A: Yes, she was on, she was on my system playing the games. And Ms. McMillan, the director, had come and told me about a roster, because we were planning some trips. She had sent it to Fort Stewart, but she didn't type it. I had to type it for her. So, I asked [K.T.] to get up. Now, I don't allow anybody to sit in my chair. It is like one of those big roll away chairs. And as I sit in my chair, I rolled towards [K.T.]. And with the back of my hand, I hit the chair and part of her leg. And the chair flew away, just, you know, because it had, it had rollers on it. Okay. So, I mean, my chair had rollers on it. So, when I rolled over there, I hit her chair. And that chair moved some distance, because they are regularly like homeroom chairs, you know, that they use. Right? So, the chair slid and her reaction, you know how kids are, "Oh, Mr. Williams, you didn't have to push me. Mr. Angelo, you didn't have to push me." I said, "No, I didn't push you. You just need to put meat on your bones." That's all, which I tease all the kids all the time, you know, in various ways, the different ways. 9 The preexisting case law of this Circuit was not certain on whether or not the twenty days in this case would be excludable. The charged offense is a serious one. The delay in going to trial was not great. Therefore, the indictment should be dismissed without prejudice. See 18 U.S.C. § 3162(a)(2). 9 So, I got down at the system and started typing. And I had a phone call. Q: Who? A: Yes, as a matter of fact, I had a phone call from the director asking me about the roster. So, as I was walking away, I saw [K.T.] getting ready to sit back down to finish her game. And that's when I turned and said, "No, honey, you can't mess with it now, because I have opened up some of my admin stuff, and I don't want you to mess with any of it." (R2:144-46). Q: Okay. When you said you touched her, when you grabbed her, where did you grab her? A: On her shoulders. (R2:146). Q: Did you in fact touch [K.T.] in a sexual manner? A: No, sir, I didn't. Q: Did you touch her on her breast? A: No, sir, I didn't. Q: Did you touch her on the vaginal area, on the crotch? A: No, sir, I didn't. Q: Did you touch her on her inner thigh? A: No, sir, I didn't. Q: Okay. Did you touch her on the buttocks? A: No, sir, I didn't. Q: Did you have any bent to touch her in a sexual manner? A: No, I didn't. No, I didn't. (R2:153-54). 10
A spectacular and likely unforgettable show will take place in the sky Aug. 21. “Have you ever seen a total solar eclipse?” asks Cynthia Peterson, professor emerita of physics. “It’s a really, really exciting event!” The reason she and so many others are excited for this event has a lot to do with its rarity. The last time a total solar eclipse was visible from the mainland United States was 38 years ago, in February 1979. Very specific conditions have to be met to create an eclipse that can be viewed from Earth. The Earth and the moon must align perfectly with the sun as they speed through space, an amazing coincidence. To fully understand how this happens, Peterson says, it’s helpful to know some basic astronomy. Conditions for a Total Solar Eclipse The Earth moves in space around the sun, completing a full orbit once every 365.25 days, she explains. As the Earth and other members of our solar system travel around the sun, they continue in essentially the same plane, on a path called the ecliptic. Some celestial bodies, such as our moon, deviate from the ecliptic slightly. The orbit of the moon is inclined on the ecliptic plane at an inclination of 5 degrees. As the moon deviates 5 degrees above or below the ecliptic plane, it will cross the plane at points called nodes. “That is the first essential piece of the eclipse puzzle,” says Peterson. “The moon must be at a node for an eclipse to occur. Otherwise, the moon will not align and no eclipse will be seen from Earth.” The moon’s position in the lunar cycle is another vital eclipse component. As the Earth travels in its orbit, the moon tags along, keeping its gaze locked on Earth, always facing from the same side as it completes its own orbit around Earth once every 29.5 days. Over the course of a month, the moon’s appearance changes, from crescent to full to crescent again and finally to what appears to be its absence, when it’s called a new moon. A new moon is the other requirement for a solar eclipse. “The basic rule for a solar eclipse is to have a new moon at a node,” Peterson points out. But during an eclipse, how can our moon, which is relatively small, appear almost as big as the sun, which is pretty gigantic? Peterson explains, “The sun is 400 times bigger than the moon and the sun is also 400 times farther away from the moon, so the moon appears to fit exactly during an eclipse, when they are both the same angular size.” Holding up her fist, she demonstrates: “Find a large object ahead of you and pretend it is the sun and your fist is the moon. If you hold up your fist and look with one eye, you can’t see the object/sun.” These are the conditions for a total solar eclipse like the one coming up. “Solar eclipses happen when the new moon obstructs the sun and the moon’s shadow falls on the earth, creating a total solar eclipse.” Peterson moves her fist slightly away from herself until the edges of the object can be seen around it. “Or, when the moon covers the Sun’s center and creates a ‘ring of fire’ around the moon, it’s what’s called an annular eclipse.” It’s those bits of the sun peeking out from behind the moon – in both partial and total eclipses – that everyone needs to be careful of. It’s extremely important to view the eclipse safely, Peterson stresses. “The problem with the eclipse is that every time it happens, some people are blinded [from looking at it unprotected]. The shadow goes whipping by at 1,000 miles per hour, and you never want to stare at the sun, even a sliver of it.” So be prepared, and ensure you wear proper solar eclipse eye protection. Regular sunglasses will not help. Solar eclipse glasses can be used, welder’s goggles, or telescopes with proper lenses. Be sure the eye protection you choose is certified by the International Organization for Standardization (ISO). Other popular viewing methods are DIY viewing boxes like these. Peterson, like many others who wish to get the full eclipse experience, will be traveling to an area directly in the path of the eclipse’s shadow. These areas are called totality. The Aug. 21 eclipse will cover an expansive area of totality that will include 14 states and 14 major U.S. cities, stretching from Lincoln Beach, Oregon to Charleston, South Carolina. For a map of the path of totality, go to the NASA website. Connecticut is unfortunately hours of travel from the nearest totality. Peterson will go as far as Nebraska for the experience. “You’ll only see a partial eclipse here in Connecticut,” she says. “It will get a little darker, like a cloud covering part of the sun, and then brighten up again.” She encourages those who can to try to travel to a viewing point for the total eclipse, where they may see “amazing phenomena” like the diamond ring, shadowbands, crescent-shaped solar images under trees (instead of the usual ‘coins’ which are pinhole images of the sun), and extremely sharp shadows in the final minute before totality, due to the very narrow sun at that time. “These phenomena can only be seen in totality,” she says. The next chance to see a total solar eclipse will be in 2024, when its shadow will be cast closer to Connecticut. It will start in the U.S. in Texas, then make its way north, through northern Vermont and New Hampshire. “That’s less than seven years from now,” Peterson points out, “but that’s the end of eclipses crossing the U.S. until the 2050s.” For those on campus next week, you aren’t out of luck. For this eclipse there will be a viewing party on Horsebarn Hill behind the Dairy Bar, from 1 to 4 p.m., hosted by the Department of Physics. “We’ll have solar telescopes, a pinhole camera activity, and will do some short mini-lectures on astronomy at UConn and about how eclipses work,” says assistant professor of physics Jonathan Trump, one of the faculty members who will lead the viewing party. Peterson, longtime astronomer and scientist, says witnessing an eclipse – especially a total eclipse – can be extremely emotional. She suggests reading Annie Dillard’s essay about solar eclipses, where the author compares the contrast between viewing a partial eclipse and viewing a total eclipse to the difference between flying in an airplane versus falling out of the airplane. “Those are very different experiences.” But wherever you are on the afternoon of Aug. 21, Peterson says, stop and enjoy the show: “Good luck and clear skies!” The eclipse will be live-streamed by NASA, and can also be viewed on PBS’ NOVA at 9 p.m. on Aug. 21.
INTRODUCTION ============ B cells are important for antibody (Ab) production and for antigen presentation and cytokine production ([@R1]). In particular, cytokine-producing B cells play critical roles in multiple aspects of immunity. There are two opposing B cell subsets: regulatory B cells (Bregs) and effector B cells (Beffs) ([@R2]). Interleukin-10 (IL-10)--producing Bregs are now recognized as negative regulators of the immune system, inflammation, and autoimmunity based on studies with human subjects and mouse models of autoimmune diseases such as rheumatoid arthritis, systemic lupus erythematosus (SLE), and multiple sclerosis (MS) ([@R3]--[@R6]). The phenotype of mouse splenic Bregs is derived from two different B cell subsets: marginal zone (MZ) and B1 B cells ([@R7]). Furthermore, it was reported that the CD9^+^ B cell subset is enriched in IL-10--producing Bregs ([@R7], [@R8]), since this subset includes both the MZ and B1 B cell subsets ([@R9]). By contrast, cytokine-producing Beffs can positively modulate the immune response through the production of various cytokines ([@R2]). For example, lymphotoxin-producing Beffs are essential for the ontogenesis, homeostasis, and activation of secondary lymphoid organs, as well as for the development of tertiary lymphoid tissues at ectopic sites ([@R10]). Other Beffs have been shown to modulate the development of effector and memory CD4^+^ T cell responses via the production of cytokines such as IL-6, interferon-γ, and tumor necrosis factor ([@R11]). Therefore, a protocol that selectively depletes Beffs while sparing Bregs would represent a potent therapy for autoimmune diseases. Systemic sclerosis (SSc; also known as scleroderma) is a connective tissue disorder characterized by excessive fibrosis in the skin and various internal organs with an autoimmune etiology. More than 90% of SSc patients are positive for autoantibodies such as anti--DNA topoisomerase I, anticentromere, and anti--RNA polymerase Abs. One study demonstrated that SSc patients displayed distinct abnormalities of blood B cell compartments characterized by expanded naïve B cells and activated memory B cells ([@R12]). B cell activating factor (BAFF) has been shown to be present at elevated levels in patients with SSc and is correlated with disease severity ([@R13]). B cells of patients with SSc that were stimulated by BAFF exhibited an enhanced ability to produce IL-6 ([@R13]). In addition, B cells and BAFF were shown to promote collagen production by dermal fibroblasts in SSc ([@R14]). IL-6 plays an important role in tissue fibrosis and autoimmunity in the SSc pathogenesis ([@R15], [@R16]) and is thus considered a candidate therapeutic target. The skin fibrosis of two patients with diffuse SSc was markedly improved after treatment with the anti--IL-6 receptor Ab tocilizumab ([@R17]). A phase 2 trial of tocilizumab demonstrated clinically significant improvement of skin fibrosis in patients with SSc ([@R18]). Thus, IL-6--producing Beffs may play a critical role in the development of scleroderma; however, there is no reliable detection method for IL-6--producing Beffs, and the resulting phenotype remains unclear. By contrast, IL-10--producing Bregs were shown to suppress the skin fibrosis of the Scl-cGVHD model, an animal model for human SSc ([@R19]). IL-10--producing Bregs have been reported to be decreased in patients with SSc and were associated with disease activity ([@R20]). Here, we investigated the intracellular staining and phenotype of IL-6--producing Beffs. Furthermore, we evaluated the role of IL-6--producing Beffs and IL-10--producing Bregs in the pathogenesis of scleroderma using B cell--specific cytokine-deficient mice. On the basis of these results, we propose a new potential therapeutic strategy for SSc via alteration of the Beff and Breg balance. RESULTS ======= CD40 and lipopolysaccharide synergistically induce IL-6 production from B cells ------------------------------------------------------------------------------- To identify the stimulation condition of IL-6 production from B cells, we cultured B cells with various Toll-like receptor (TLR) agonists with or without agonistic CD40 monoclonal Ab (mAb). The TLR4 agonist \[lipopolysaccharide (LPS)\] and TLR9 agonist induced IL-6 production from B cells. Addition of the agonistic CD40 mAb in combination with LPS or TLR9 agonist signals significantly enhanced IL-6 production from B cells ([Fig. 1A](#F1){ref-type="fig"}). Similar to the results for IL-6, IL-10 production was induced by LPS and the TLR9 agonist. By contrast, addition of agonistic CD40 mAb in combination with LPS signals significantly reduced IL-10 production from B cells ([Fig. 1A](#F1){ref-type="fig"}). Thus, agonistic CD40 mAb accelerates IL-6 production from B cells stimulated with LPS, while agonistic CD40 mAb attenuates IL-10 production from B cells stimulated with LPS. ![CD40 and LPS synergistically induce IL-6 production from B cells.\ (A) B cells were isolated from spleens of naïve mice by magnetic sorting based on CD19 expression. Sorted B cells were cultured for 72 hours with media alone or media containing anti-CD40 mAb, along with the indicated TLR agonists. After in vitro stimulation for 72 hours, IL-6 (left) and IL-10 (right) levels in supernatants were quantified by enzyme-linked immunosorbent assay (ELISA). Bars represent the means ± SD from three independent experiments (n = 3 mice). Significant differences between means of media alone and individual stimuli are indicated: \*P \< 0.001, \\P \< 0.0001, analysis of variance (ANOVA) followed by Tukey's multiple comparison test. Significant differences between cultures with or without anti-CD40 mAb are indicated: ^\#^P \< 0.05, ^\#\#^P \< 0.01, ^\#\#\#^P \< 0.001, ^\#\#\#\#^P \< 0.0001, Student's t test. (B) IL-6--producing B cells were determined after in vitro stimulation by LPS, anti-CD40 mAb, and LPS + anti-CD40 mAb, with PIB \[phorbol 12-myristate 13-acetate (PMA), ionomycin, and brefeldin A\] added during the final 5 hours of cultures (5 to 48 hours). Isotype control Ab was used as negative controls for IL-6 staining. Percentages indicate the frequencies of cytoplasmic IL-6^+^ B cells within the indicated gates among total CD19^+^ B cells. Bars represent the means ± SD from three independent experiments (n = 3 mice). \*P \< 0.0001, ANOVA followed by Tukey's multiple comparison test. (C) Representative cell surface phenotype of spleen IL-6--producing B cells after stimulation with LPS + anti-CD40 mAb for 24 hours with PIB added during the final 5 hours of culture. Cultured cells were stained for viability and cell surface molecule expression (using LEGENDScreen Mouse PE Kit from BioLegend), permeabilized, stained with anti--IL-6 mAb, and analyzed by flow cytometry. Representative cell surface molecule expression by IL-6^+^ (red line) and IL-6^−^ (black line) CD19^+^ B cells from three individuals is shown. Shaded histograms represent isotype-matched control mAb staining.](aas9944-F1){#F1} To visualize IL-6--producing B cells, we established a detection method of intracellular IL-6 staining by fluorescence-activated cell sorting (FACS). We cultured splenocytes with LPS, agonistic CD40 mAb, or LPS + agonistic CD40 mAb for various time courses (5, 12, 24, or 48 hours). We added PIB during the final 5 hours of cultures. In line with the results described above, LPS and agonistic CD40 mAb signals cooperatively induced the IL-6 production of B cells ([Fig. 1B](#F1){ref-type="fig"}). In addition, the 24-hour culture was found to be the best condition for the detection of IL-6--producing B cells, and approximately 40% of the B cells produced IL-6 ([Fig. 1B](#F1){ref-type="fig"}). Therefore, the culture with LPS and agonistic CD40 mAb for 24 hours appears to be the best condition for visualizing IL-6--producing B cells. MZ B cell-related cell surface markers are highly expressed in IL-6--producing B cells -------------------------------------------------------------------------------------- To identify whether IL-6--producing B cells represent a unique or known B cell subset, we analyzed the cell surface phenotype. We assessed the phenotype of IL-6--producing B cells following 24 hours of culture with LPS and agonistic CD40 mAb, along with 5 hours of PIB stimulation. On average, IL-6^+^ B cells expressed higher densities of CD1d, CD9, CD21, CD23, CD25, CD80, CD86, CD150 \[SLAM (Signaling lymphocyte activation molecule)\], CD155 \[PVR (Poliovirus receptor)\], CD200 (OX2), and CD267 \[TACI (transmembrane activator and calcium-modulator and cyclophilin ligand interactor)\], which is one of the BAFF receptors, when compared with IL-6^−^ B cells ([Fig. 1C](#F1){ref-type="fig"} and fig. S1). Although naïve B cells do not express CD25, we induced most of the B cells to express CD25 after 24 hours of culture with LPS and agonistic CD40 mAb, followed by 5 hours of PIB stimulation (fig. S2). By contrast, on average, IL-6^+^ B cells expressed lower densities of CD43, immunoglobulin M (IgM), and Ly-6D when compared with IL-6^−^ B cells (fig. S1). The higher expression of CD1d, CD9, and CD21 on IL-6^+^ B cells suggests that IL-6^+^ B cells might be predominantly found within the MZ B cell subset. Furthermore, IL-6^+^ B cells show higher expression of TACI, a receptor of BAFF. The MZ B cell subset is a major source of IL-6--producing B cells ----------------------------------------------------------------- We previously reported that IL-10--producing Bregs were predominantly found within the splenic CD1d^hi^ MZ and CD5^+^ B1 B cell subsets ([@R7]). To determine which B cell subsets secreted IL-6, we stained and sorted splenic B cells into three fractions \[follicular B cells (CD1d^int^CD5^−^), MZ B cells (CD1d^hi^CD5^−^), and B1 B cells (CD1d^int^CD5^+^)\] before in vitro 24-hour stimulation with LPS and agonistic CD40 mAb, followed by 5 hours of PIB stimulation ([Fig. 2A](#F2){ref-type="fig"}). The frequency of IL-6--producing B cells among sorted follicular B cells was comparable with that detected in pan-B cells. The frequency of IL-6--producing B cells among sorted B1 B cells was decreased compared with that of pan-B cells. By contrast, the frequency of IL-6--producing B cells in sorted MZ B cells was significantly increased compared with that in other B cell subsets ([Fig. 2](#F2){ref-type="fig"}, B and C). As previously reported, MZ and B1 B cell subsets produced IL-10, while the follicular B cell subset did not produce IL-10 ([Fig. 2](#F2){ref-type="fig"}, B and C). In addition, the frequency of IL-10--producing B cells in B1 B cells was significantly increased compared with that in MZ B cell subsets ([Fig. 2](#F2){ref-type="fig"}, B and C). Next, to examine whether B cells simultaneously produce IL-6 and IL-10, we stained B cells with both IL-6 and IL-10 and analyzed them by FACS. We found that IL-6-- and IL-10--producing B cells exist mutually exclusively (fig. S3). Thus, MZ B cells represent a major subset of IL-6--producing B cells in the spleen. ![The MZ B cell subset is a major source of IL-6--producing B cells.\ (A) Splenic B cells from wild-type mice were isolated by Miltenyi MACS enrichment; stained for CD1d, CD5, and CD19 expression; and sorted into follicular B cell (CD1d^int^CD5^−^), MZ B cell (CD1d^hi^CD5^−^), and B1 B cell (CD1d^int^CD5^+^) populations before stimulation. (B) Sorted B cells were cultured with LPS + anti-CD40 mAb for 24 hours with PIB added during the final 5 hours of culture (for IL-6) or LPS + PIB for 5 hours (for IL-10). IL-6^+^ or IL-10^+^ B cells derived from each purified population were then analyzed by flow cytometry. All data are representative of two independent experiments. (C) Bars represent the means ± SD from four mice in each group. Significant differences between pan-B cell versus other B cell subsets are indicated: \*P \< 0.05, \\P \< 0.01, \\\*P \< 0.001, ^\#^P \< 0.05, ^\#\#^P \< 0.01, ^\#\#\#^P \< 0.001, ANOVA followed by Tukey's multiple comparison test.](aas9944-F2){#F2} IL-6 is increased in bleomycin-induced scleroderma -------------------------------------------------- To determine whether and when the levels of IL-6 and IL-10 are increased in the bleomycin-induced scleroderma model, we measured the serum cytokine levels and the frequency of splenic cytokine-producing B cells. Serum IL-6 levels were gradually increased along with bleomycin treatment, while there was no change in serum IL-10 levels with bleomycin treatment ([Fig. 3A](#F3){ref-type="fig"}). In addition, the frequency of splenic IL-6--producing B cells at 3 weeks after bleomycin treatment was significantly increased compared with that detected at 3 weeks after phosphate-buffered saline (PBS) treatment ([Fig. 3B](#F3){ref-type="fig"}). ![IL-6 is increased in bleomycin-induced scleroderma.\ (A) Serum samples were collected from bleomycin-induced scleroderma mice. Serum IL-6 or IL-10 levels were determined by ELISA. Bars represent the means ± SD from four mice in each group. Significant differences between means of naïve mice and bleomycin (Bleo)--treated mice are indicated: \*P \< 0.05, \\P \< 0.001, ANOVA followed by Tukey's multiple comparison test. (B) Splenocytes were isolated from bleomycin-induced scleroderma mice on day 21 after treatment. Splenocytes were cultured with LPS + anti-CD40 mAb for 24 hours with PIB added during the final 5 hours of culture (for IL-6) or LPS + PIB for 5 hours (for IL-10). Left: Percentages indicate the frequencies of cytoplasmic IL-6^+^ or IL-10^+^ B cells within the indicated gates among total CD19^+^ B cells. Right: Bars represent the means ± SD from four mice in each group. \*P \< 0.001, Student's t test. (C) Skin-infiltrating cells were isolated from bleomycin-induced scleroderma mice on day 21 after treatment. Lymphocytes were cultured with LPS + anti-CD40 mAb for 24 hours with PIB added during the final 5 hours of culture (for IL-6) or LPS + PIB for 5 hours (for IL-10). Left: Percentages indicate the frequencies of cytoplasmic IL-6^+^ or IL-10^+^ B cells within the indicated gates among total CD19^+^ B cells. Right: Bars represent the means ± SD from four mice in each group. \*P \< 0.001, Student's t test. (D and E) Inflamed skin sample was collected from mice treated with bleomycin. Immunofluorescence histology of frozen skin sections detecting IL-6 production by B220^+^ skin B cells. DAPI (4′,6-diamidino-2-phenylindole) was used to visualize nuclei. Scale bars, 25 μm (D) and 5 μm (E). All data are representative of two independent experiments.](aas9944-F3){#F3} Next, to determine whether IL-6--producing Beffs infiltrate the inflamed skin, we analyzed the cytokine-producing B cells by FACS and immunohistochemistry. For FACS analysis, we collected B cells infiltrating the inflamed skin and stimulated them in vitro. The number of IL-6--producing Beffs in inflamed skin with bleomycin treatment was significantly increased compared with that in the skin of mice that received PBS treatment ([Fig. 3C](#F3){ref-type="fig"}). The numbers of IL-10--producing Bregs in inflamed skin with bleomycin treatment were also significantly increased compared with those in the skin of PBS-treated mice ([Fig. 3C](#F3){ref-type="fig"}). In addition, immunohistochemical analysis revealed the presence of IL-6--producing Beffs (IL-6^+^B220^+^) in the inflamed skin in the bleomycin-induced scleroderma model ([Fig. 3](#F3){ref-type="fig"}, D and E). Unlike in the spleen, most IL-6--producing Beffs were found in the CD1d^int^CD5^−^, not in the CD1d^hi^ B cell subset (fig. S4). Thus, IL-6--producing Beffs are increased and infiltrated the inflamed skin in the bleomycin-induced scleroderma model. Skin and lung fibrosis are attenuated in mice with B cell--specific IL-6 deficiency ----------------------------------------------------------------------------------- We next evaluated whether cytokine-producing B cells regulate the skin fibrosis of the bleomycin-induced scleroderma model. To this end, we generated mixed bone marrow chimeric mice with a B cell--specific deficiency in IL-6 production (B-IL-6^−/−^) or IL-10 production (B-IL-10^−/−^), together with control chimeras (control). The schema and validation of these mixed bone marrow chimeric mice are outlined in fig. S5. Although B cells showed complete lack of IL-6 or IL-10 production in B-IL-6^−/−^ or B-IL-10^−/−^ mice, B-IL-6^−/−^ or B-IL-10^−/−^ mice demonstrated 20% IL-6 or IL-10 deficiency in all hematopoietic cells. To compensate for the effect of this deficiency outside the B cell compartment, we generated control mice against B-IL-6^−/−^ or B-IL-10^−/−^ mice as IL-6^20%^ or IL-10^20%^ chimeras, respectively, which showed 20% IL-6 or IL-10 deficiency in all hematopoietic compartments. We left the hematopoietic compartment for 8 to 10 weeks to repopulate, and then, we injected the chimeric mice with bleomycin to induce scleroderma. IL-6 deficiency of B cells caused significant reduction in dermal thickness, type 1 collagen mRNA expression, and lung fibrosis ([Fig. 4](#F4){ref-type="fig"}, A and B, and fig. S6, A to C). In contrast, B cell IL-10 deficiency significantly augmented the dermal thickness, type 1 collagen mRNA expression, and lung fibrosis ([Fig. 4](#F4){ref-type="fig"}, C and D, and fig. S6, D to F). ![Skin fibrosis is attenuated in mice with B cell--specific IL-6 deficiency.\ (A to D) Bleomycin-induced scleroderma was induced in mice with B cell--specific IL-6 deficiency (B-IL-6^−/−^; wild-type mice lethally irradiated and reconstituted with 80% μMT plus 20% Il6^−/−^ bone marrow) or B cell--specific IL-10 deficiency (B-IL-10^−/−^; wild-type mice lethally irradiated and reconstituted with 80% μMT plus 20% Il10^−/−^ bone marrow) and control chimera groups \[wild-type mice lethally irradiated and reconstituted with 80% wild-type plus 20% Il6^−/−^ or Il10^−/−^bone marrow (IL-6^20%^ or IL-10^20%^, respectively)\]. (A and C) Skin samples were harvested 4 weeks after PBS or bleomycin treatment. Masson's trichrome stain. Representative images. Arrows indicate dermis. Scale bars, 100 μm. Right: Dermal thickness (distance from the dermal-epidermal junction to the adipose layer), shown as the means ± SD of triplicate determinations per hpf from 10 mice per group. (B and D) Expression of col1a2 mRNA in the skin was measured by real-time polymerase chain reaction (PCR), shown as the means ± SD of triplicate determinations per hpf (high power field) from 10 mice per group. Open circles, PBS; closed circles, bleomycin. \*P \< 0.05, \\\*P \< 0.001, \\\\P \< 0.0001, one-way ANOVA followed by Tukey's multiple comparison test. (E and F) B cells and fibroblasts were cocultured. Collagen release by fibroblasts was determined by the Sirius red assay in 72-hour culture supernatants of fibroblast cultured alone, cocultured with B cells, or recombinant TGF-β1 (5 ng/ml). IL-6 was determined by ELISA in 72-hour culture supernatants. B cells from wild-type, Il6^−/−^, or Il10^−/−^ mice were isolated by Miltenyi MACS enrichment. B cells were either in cell-cell contact with fibroblast (contact) or seeded in the upper chamber of a Transwell culture insert (Transwell). Bars represent the means ± SD from two independent experiments (n = 4 mice). Significant differences between fibroblast only versus other groups are indicated: \*P \< 0.05, \\P \< 0.01, \\\*P \< 0.001, \\\\P \< 0.0001, ^\#^P \< 0.05, ^\#\#^P \< 0.01, ^\#\#\#^P \< 0.001, ^\#\#\#\#^P \< 0.0001, ANOVA followed by Tukey's multiple comparison test.](aas9944-F4){#F4} IL-6--producing Beffs promote collagen secretion by fibroblasts --------------------------------------------------------------- To further determine the role of cytokine-producing B cells in the regulation and development of skin fibrosis, we cocultured and analyzed B cells and fibroblasts ([Fig. 4E](#F4){ref-type="fig"}). B cells from wild-type mice strongly induced collagen secretion by fibroblasts (white bars in "Fibro-contact B cell" versus "Fibro only"), with a magnitude comparable to that observed under stimulation with recombinant transforming growth factor--β (TGF-β; black bar in "Fibro + TGF-β"). In addition, B cells from IL-6^−/−^ mice showed significantly decreased levels of collagen secretion by fibroblasts compared with B cells from wild-type mice (P \< 0.001; white versus blue bars in "Fibro-contact B cell"; [Fig. 4E](#F4){ref-type="fig"}). By contrast, B cells from IL-10^−/−^ mice showed significantly increased collagen secretion by fibroblasts compared with those from wild-type mice (P \< 0.05; white versus red bars in "Fibro-contact B cell"). Similarly, IL-6 secretion into the supernatant was significantly induced in coculture of fibroblasts and B cells from wild-type mice (P \< 0.0001; white bars in "Fibro-contact B cell" versus "Fibro only"; [Fig. 4F](#F4){ref-type="fig"}). IL-6 production was significantly lower in the coculture with B cells from IL-6^−/−^ mice than with those of wild-type mice (P \< 0.05; white versus blue bars in "Fibro-contact B cell"; [Fig. 4F](#F4){ref-type="fig"}), while IL-6 production was stronger with B cells from IL-10^−/−^ mice than with those from wild-type mice (P \< 0.01; white versus red bars in "Fibro-contact B cell"; [Fig. 4F](#F4){ref-type="fig"}). However, we could not detect IL-10 production in the supernatant of these coculture systems. We then evaluated whether the increased collagen secretion induced by B cells is dependent on cell-cell contact through interactions between B cells and fibroblasts. B cell--induced collagen production by fibroblasts was significantly inhibited when we used Transwells (P \< 0.0001, B cells from wild-type mice; P \< 0.0001, B cells from IL-10^−/−^ mice; [Fig. 4E](#F4){ref-type="fig"}). Similarly, IL-6 production was significantly inhibited when we used Transwells (P \< 0.0001, B cells from wild-type mice; P \< 0.0001, B cells from IL-10^−/−^ mice; [Fig. 4F](#F4){ref-type="fig"}). Thus, IL-6--producing Beffs promote collagen secretion by fibroblasts through the interaction with B cells and fibroblasts. BAFF increases IL-6--producing Beffs but attenuates IL-10--producing Bregs -------------------------------------------------------------------------- BAFF exhibits a strong costimulatory function for B cell activation in vitro ([@R21]). We found that the IL-6^+^ B cells showed high expression levels of the BAFF receptor ([Fig. 1C](#F1){ref-type="fig"}). To determine whether BAFF modulates the cytokine production of B cells, we cultured splenic B cells with BAFF along with LPS and/or CD40. BAFF significantly enhanced IL-6 production from B cells stimulated with LPS alone and LPS + CD40 (P \< 0.01; [Fig. 5A](#F5){ref-type="fig"}), although only BAFF stimulation failed to induce IL-6 from B cells. By contrast, BAFF significantly inhibited IL-10 production from B cells stimulated with LPS (P \< 0.0001; [Fig. 5A](#F5){ref-type="fig"}). ![BAFF enhances IL-6 production from B cells, while BAFF attenuates IL-10 production from B cells.\ (A) B cells were isolated from spleens of naïve mice by magnetic sorting based on CD19 expression. Sorted B cells were cultured for 72 hours with or without BAFF, along with LPS, anti-CD40 mAb, or LPS + anti-CD40 mAb. After in vitro stimulation for 72 hours, IL-6 (left) and IL-10 (right) levels in supernatants were quantified by ELISA. Bars represent the means ± SD from three independent experiments (n = 3 mice). Significant differences between means of media alone and individual stimuli are indicated: \*P \< 0.001, \\P \< 0.0001, ANOVA followed by Tukey's multiple comparison test. Significant differences between cultures with or without BAFF are indicated: ^\#^P \< 0.01, ^\#\#^P \< 0.0001, Student's t test. (B) Wild-type mice were treated with BAFFR-Fc or Fc control protein (control). Spleens were collected 1 week after treatment. IL-6-- or IL-10--producing B cells were determined after in vitro stimulation. CD1d^hi^MZ B cells and CD5^+^ B1 B cells from spleens of mice treated with BAFFR-Fc or Fc control protein were examined by flow cytometry. Percentages indicate the frequencies of various B cell subsets within the indicated gates among total CD19^+^ B cells. Bars represent the means ± SD from four mice. NS, not significant. \*P \< 0.001, \\P \< 0.0001, Student's t test. All data are representative of two independent experiments.](aas9944-F5){#F5} We next evaluated whether BAFF inhibition would modulate cytokine production from B cells in vivo. To this end, we administered BAFFR (BAFF-receptor)--Fc, which neutralizes BAFF, or Fc control protein (control) to naïve mice. The frequency and number of IL-6--producing Beffs in the BAFFR-Fc--treated mice were significantly decreased compared with those of control mice ([Fig. 5B](#F5){ref-type="fig"}). By contrast, the frequency of IL-10--producing Bregs in the BAFFR-Fc--treated mice was significantly increased compared with that in control mice, although the number of IL-10--producing Bregs did not differ between the BAFFR-Fc--treated mice and control mice ([Fig. 5B](#F5){ref-type="fig"}). In addition, BAFFR-Fc significantly decreased the number of MZ B cells, the major subset of IL-6--producing Beffs ([Fig. 5B](#F5){ref-type="fig"}), but did not influence the number of B1 B cells, the major subset of IL-10--producing Bregs ([Fig. 5B](#F5){ref-type="fig"}). These results suggest that BAFF increases IL-6--producing Beffs but attenuates IL-10--producing Bregs. BAFF inhibition attenuates the skin and lung fibrosis of bleomycin-induced scleroderma -------------------------------------------------------------------------------------- Dysregulation of serum BAFF levels in Tsk/+ mice, a genetic mouse model for scleroderma, has been demonstrated ([@R15]). Thus, we explored the timing of changes in serum BAFF in bleomycin-induced scleroderma using ELISA. Serum BAFF levels in the bleomycin-induced scleroderma model gradually increased after bleomycin treatment ([Fig. 6A](#F6){ref-type="fig"}). To determine whether BAFF inhibition affects the skin fibrosis in the bleomycin-induced scleroderma model, we treated the mice with BAFFR-Fc, which neutralizes BAFF, or Fc control protein (control) three times a week for 4 weeks. The skin and lung fibrosis in the mice that received BAFFR-Fc treatment was significantly attenuated compared to that of the control group ([Fig. 6](#F6){ref-type="fig"}, B to E). In addition, BAFFR-Fc significantly decreased the number of IL-6--producing Beffs but did not influence the number of IL-10--producing Bregs ([Fig. 6F](#F6){ref-type="fig"}). These results suggest that BAFF inhibition is a potential therapeutic strategy for SSc via alteration of the Beff and Breg balance ([Fig. 6G](#F6){ref-type="fig"}). ![BAFF inhibition attenuates skin fibrosis in bleomycin-induced scleroderma.\ (A) Serum samples were collected from bleomycin-induced scleroderma mice. Serum BAFF levels were determined by ELISA. Bars represent the means ± SD from five mice in each group. Significant differences between means of naïve mice and bleomycin (Bleo)--treated mice are indicated: \*P \< 0.001, ANOVA followed by Tukey's multiple comparison test. (B) Bleomycin-induced scleroderma was induced in mice treated with BAFFR-Fc or Fc control protein (control). Skin samples were harvested 4 weeks after bleomycin treatment. Left: Masson's trichrome stain. Representative images. Arrows indicate dermis (distance from the dermal-epidermal junction to the adipose layer). Scale bar, 100 μm. (B and C) Analysis of dermal thickness (B, right) and expression of col1a2 mRNA in the skin (C). (D) Lung samples were harvested 4 weeks after bleomycin treatment. Left: Hematoxylin and eosin (H&E). Representative images. Scale bar, 100 μm. (D and E) Analysis of the lungs for determination of lung fibrosis scores (D, right) and collagen content (E). (B to D) Values are means ± SD of five mice per group. Open circles, PBS; closed circles, bleomycin. \*P \< 0.05, \\P \< 0.01, \\\*P \< 0.001, \\\\P \< 0.0001, one-way ANOVA followed by Tukey's multiple comparison test. (F) Spleens from bleomycin-induced scleroderma mice were collected 4 weeks after treatment. IL-6-- or IL-10--producing B cells were determined after in vitro stimulation. Percentages indicate the frequencies of IL-6-- or IL-10--producing B cells within the indicated gates among total CD19^+^ B cells. Bars represent the means ± SD from five mice. \*P \< 0.0001, Student's t test. All data are representative of two independent experiments. (G) BAFF increased the IL-6--producing Beffs but suppressed the IL-10--producing Bregs. Furthermore, Beffs play a pathogenic role in scleroderma, while Bregs play a protective role.](aas9944-F6){#F6} DISCUSSION ========== Despite their recognized importance, the phenotype and function of IL-6--producing Beffs have thus far remained poorly understood, although B cells are known to produce large amounts of IL-6. Here, we demonstrated that CD40 and LPS synergistically induce IL-6 production from B cells and that the MZ B cell subset is a major source of IL-6--producing B cells. Furthermore, IL-6--producing Beffs play a pathogenic role in the bleomycin-induced scleroderma model, whereas IL-10--producing Bregs play a protective role. Moreover, we found that BAFF inhibition attenuates skin and lung fibrosis in the bleomycin-induced scleroderma model with reduction of IL-6--producing Beffs. Collectively, these findings suggest that B cells have reciprocal roles in the pathogenesis of SSc, exhibiting both pathogenic and protective functions ([Fig. 6G](#F6){ref-type="fig"}). CD40 is expressed on the surface of B cells, as well as dendritic cells and monocytes/macrophages, while the CD40 ligand (CD40L) is expressed on activated T cells. The CD40-CD40L interaction induces B cell survival, Ig class switching, and cytokine production and has been shown to play an important role in the pathogenesis of SSc ([@R22]). The CD40-CD40L interaction and antigen-specific signals were reported to be essential for IL-10 production from B cells ([@R3]), while TLR signals strongly augment the production of IL-10 in mice ([@R23]) and humans ([@R24]). The current study and previous ones have shown that CD40 and a TLR signal (LPS) synergistically promote IL-6 production from B cells, whereas the CD40 signal inhibited IL-10 production ([@R11], [@R23]). Although the fact that we found the MZ B cell subset to be a major source of IL-6--producing B cells is consistent with the literature ([@R11], [@R25]), this subset is also known to be a major component of IL-10--producing Bregs ([@R5], [@R7], [@R26]). Thus, the CD1d^high^ MZ B cell subset has the ability to become either IL-10--producing Bregs or IL-6--producing Beffs, and its fate depends on the stimulation by CD40 and TLR signals. Thus, it is difficult to evaluate the adaptive transfer of the CD1d^high^ MZ B cell effect in the bleomycin-induced scleroderma model. Together, these results suggest that TLR stimulation induces B cells into Bregs, while the T cell--B cell interaction upon TLR stimulation induces B cells into IL-6--producing Beffs. IL-6 is a multifunctional cytokine produced by various cell types such as B cells, T cells, monocytes, natural killer cells, and fibroblasts, although B cells are the major source of IL-6 ([@R11], [@R25]). Serum IL-6 levels are elevated in patients with diffuse SSc and are associated with the extent of skin thickness ([@R27]), and IL-6 plays a critical role in tissue fibrosis and autoimmunity in mouse models of SSc ([@R15], [@R16]). Inhibition of IL-6 suppresses skin fibrosis in a mouse model of SSc ([@R28]), and a phase 2 trial of tocilizumab showed clinically significant improvement of skin fibrosis in patients with SSc ([@R18]). Notably, the current study revealed that IL-6 deficiency in B cells alone attenuates the skin fibrosis in the bleomycin-induced scleroderma model, while IL-10 deficiency in B cells augments the skin fibrosis. B cells were shown to promote collagen production by dermal fibroblasts of SSc patients ([@R14]). IL-6--producing Beffs could infiltrate the inflamed skin tissue and promote collagen secretion by fibroblasts, although the phenotype of IL-6--producing Beffs in the skin was not consistent with that in the spleen. In contrast, the current study showed that IL-10--producing Bregs were increased in inflamed skin. Therefore, Bregs may infiltrate into the inflamed skin to attenuate the inflammation. The current study also revealed that IL-6--producing Beffs promote collagen secretion by fibroblasts through interaction with B cells and fibroblasts. B cells without stimulation did not produce IL-6; however, B cells cocultured with fibroblasts did produce IL-6. Thus, cell-cell contact with fibroblasts induces IL-6 production from B cells and augments collagen secretion by fibroblasts. Since these effects were inhibited when we used Transwells, additional factors, such as adhesion molecules, may play a role in these effects. In addition, IL-6 production was increased in coculture with B cells from IL-10^−/−^ mice, resulting in increased collagen secretion by fibroblasts. Collectively, these results suggest that IL-6 and IL-10 secretion from B cells promotes and inhibits the fibrosis in SSc, respectively. BAFF plays a critical role in the survival, maturation, and activation of B cells ([@R21]), and the serum BAFF levels are elevated in patients with various diseases, including SSc ([@R13]). B cells from SSc patients stimulated by BAFF exhibited enhanced ability to produce IL-6 ([@R13]). Consistent with these previous findings, in the present study, BAFF increased the numbers of IL-6--producing Beffs but attenuated IL-10--producing Bregs. However, Yang et al. ([@R29]) reported that BAFF enhanced IL-10 production of B cells from DBA/1J mice. This discrepancy may be due to the different mouse genetic backgrounds. By contrast, BAFF inhibition decreased IL-6--producing Beffs, but not IL-10--producing Bregs. Similarly, BAFF receptor--deficient mice showed depletion of B2 but not B1a B cells, a major subset of IL-10--producing Bregs ([@R30]). BAFF inhibition attenuated the skin fibrosis of the present SSc mouse model, which confirms the results of a previous study ([@R15]). There has been some success with respect to targeting B cells for SSc therapy. B cell depletion therapy with rituximab, a CD20 mAb that depletes human pan-B cells, has shown beneficial effects on skin and lung fibrosis in patients with SSc ([@R31], [@R32]); however, a phase 3 randomized controlled study is required to confirm the efficacy and safety of rituximab for the treatment of SSc. Two large randomized controlled trials of rituximab have been conducted in patients with SLE, with the expectation that it would be effective; however, these trials failed to achieve the primary end points ([@R33], [@R34]). Our present findings suggest that this ineffectiveness may have been due to depletion of not only Beffs but also Bregs. Thus, the outcome of pan-B cell depletion depends on the balance between Beffs and Bregs in a given patient. Moreover, the effect of B cell depletion was shown to be dependent on the timing and balance of the two opposing B cell functions in mouse models of SLE and MS ([@R6], [@R35]). By contrast, phase 3 clinical trials demonstrated the efficacy of belimumab, an anti-BAFF Ab, in patients with SLE ([@R36], [@R37]); belimumab has been approved by the U.S. Food and Drug Administration. Our results further shed light on the most likely reason for the superior effects of partial B cell depletion with BAFF inhibition compared to pan-B cell depletion with a CD20 mAb, given that BAFF inhibition therapy selectively depletes Beffs while sparing Bregs. However, a phase 2 study of atacicept, an inhibitor of BAFF and a proliferation-inducing ligand, did not reveal efficacy in the patients with MS ([@R38]). The effect of selective B cell depletion is not always beneficial, and it may depend on the contribution of B cells to the particular disease. BAFF inhibition therapy, rather than pan-B cell depletion, could be a potent therapeutic strategy for SSc ([Fig. 6G](#F6){ref-type="fig"}). Here, we have investigated the intracellular staining and phenotype of IL-6--producing Beffs. IL-6--producing Beffs play a pathogenic role in scleroderma, whereas IL-10--producing Bregs play a protective role. Furthermore, BAFF contributes to SSc pathogenesis by modulating cytokine-producing B cells. Thus, our study reveals that BAFF inhibition is a potential therapeutic strategy for SSc via alteration of the Beff and Breg balance. MATERIALS AND METHODS ===================== Study design ------------ We performed this study to determine whether cytokine-producing B cells control the development of scleroderma in a mouse model. To establish the model, we treated B cell--specific cytokine-deficient mice with bleomycin. The skin and lung fibrosis of the bleomycin-induced scleroderma model was attenuated in B cell--specific IL-6--deficient mice, while B cell--specific IL-10--deficient mice showed more severe skin and lung fibrosis. Subsequent histological analysis confirmed these findings. Sample sizes and end points were selected on the basis of our extensive experience with these systems. In selected experiments, the mice were randomly assigned to treatment groups, and the researchers were blinded to the treatment group during experimental procedures and raw data analysis. All animal experiments were performed according to institutionally approved protocols and in compliance with the guidelines of the Committee on Animal Experimentation of the Kanazawa University Graduate School of Medical Sciences. No animals or potential outliers were excluded from the data sets analyzed and presented herein. All in vitro studies were performed in replicates (n = 3, unless otherwise specified). Mice ---- Wild-type C57BL/6 mice, Il10^−/−^ mice, and μMT mice were obtained from the Jackson Laboratory. Il6^−/−^ mice were generated as previously reported ([@R39]). All mice were on the C57BL/6 background. For experiments, all mice used were 8 to 10 weeks of age and housed in a specific pathogen--free barrier facility. Generation of mixed bone marrow chimeras ---------------------------------------- Mice with B cell--specific IL-6 deficiency or B cell--specific IL-10 deficiency were generated using the mixed bone marrow chimera system, as described previously ([@R3], [@R10]). Briefly, recipient wild-type mice received 1000 cGy of x-ray irradiation. One day later, the recipients were reconstituted with a mixed inoculum of 80% μMT bone marrow cells supplemented with 20% bone marrow cells from Il6^−/−^ or Il10^−/−^ mice (a total of 2 × 10^6^ cells). Control groups received 80% wild-type and 20% bone marrow cells from Il6^−/−^ or Il10^−/−^ mice (a total of 2 × 10^6^ cells). Chimeric mice were left to fully reconstitute their lymphoid system for at least 8 to 10 weeks before bleomycin treatment. Chimerism was confirmed by B cell cytokine production using ELISA. Characterization of chimeras is outlined in fig. S5. Bleomycin-induced scleroderma model ----------------------------------- Bleomycin (Nippon Kayaku) was dissolved in sterile saline at a concentration of 1 mg/ml. The mice were treated with intradermal injections of either bleomycin or saline (300 μl; administered using a 27-gauge needle) into their shaved backs (the para-midline, lower back region) every other day for 4 weeks. BAFFR-Fc treatment ------------------ In vivo treatment murine BAFFR-Fc Chimera (BioLegend), which were made by fusing their extracellular domains to the Fc portion of human IgG1 and neutralize murine BAFF, and Fc control protein (BioLegend) were used in this study. To neutralize BAFF in vivo, mice received either murine BAFFR-Fc (2.5 mg/g, intraperitoneally, three times per week) or the same dose of Fc control protein. Determination of collagen content --------------------------------- The collagen content of the culture supernatant was determined using QuickZyme Soluble Collagen Assay (QuickZyme Biosciences), according to the manufacturer's instructions. The collagen content of the mouse and lung tissues was determined using QuickZyme Total Collagen Assay (QuickZyme Biosciences), according to the manufacturer's instructions. Total right lungs were used. Histological examination of skin and lung fibrosis -------------------------------------------------- All skin sections were obtained from the bleomycin-injected region of the lower back, as full-thickness sections extending down to the body wall musculature. Lung sections were obtained from the bleomycin-induced scleroderma model. The skin and lung samples were fixed in formalin, dehydrated, embedded in paraffin, and used for immunostaining. Sections (6 μm thick) were stained with H&E and Masson's trichrome to identify collagen deposition in the skin and lung. Dermal thickness, which was defined as the thickness of skin from the top of the granular layer to the junction between the dermis and intradermal fat, was evaluated. The severity of lung inflammation was determined by a semiquantitative scoring system, as previously described ([@R40]). Briefly, lung fibrosis in randomly chosen fields of sections from the left middle lobe examined at 100× magnification was graded on a scale of 0 (normal lung) to 8 (total fibrous obliteration of fields). All sections were evaluated independently by two investigators (Kie Mizumaki and Miyu Kano), in a blinded manner. Flow cytometry and intracellular cytokine staining analysis ----------------------------------------------------------- Single-cell leukocyte suspensions from spleens were generated by gentle dissection. The following mAbs were used: fluorescein isothiocyanate--, PE (phycoerythrin)--, PE-Cy5--, PE-Cy7--, PerCP-Cy5.5--, APC (allophycocyanin)--, APC-PECy7--, and BV421-conjugated mAbs to mouse CD4 (RM4-5), CD8 (53-6.7), CD11b (M1-70), CD19 (1D3), CD25 (MF-14), CD44 (IM7), IL-10 (MP5-20F3), and IL-10 (JES5-16E3), using LEGENDScreen Mouse PE Kit from BioLegend; CD1d (1B1), CD5 (53-7.3), CD21/CD35 (7G6), CD23 (B3B4), CD24 (M1/69), and CD45R/B220 (RA3-6B2) from BD Biosciences; and BAFF (121808) from R&D Systems. For two- to six-color immunofluorescence analysis, single-cell suspensions (10^6^ cells) were stained at 4°C using predetermined optimal concentrations of mAb for 20 min. Blood erythrocytes were lysed after staining using FACS Lysing Solution (Becton Dickinson). For intracellular staining, cells were fixed and permeabilized with a Cytofix/Cytoperm kit (BD Biosciences). Dead cells were detected by using LIVE/DEAD Fixable Aqua Dead Cell Stain Kit (Invitrogen Molecular Probes) before cell surface staining. Cells with the forward and side light scatter properties of lymphocytes were analyzed using a BD FACSCanto II (BD Biosciences). Data were analyzed with FlowJo software (version 10.2; Tree Star). B cell stimulation ------------------ Splenic B cells were purified with anti-CD19 mAb--coated microbeads or the Pan B cell isolation kit (Miltenyi Biotec) or by means of cell sorting with the FACSAria Fusion (BD Bioscience). B cells (2 × 10^6^ cells/ml) were resuspended in complete medium \[RPMI 1640 media containing 10% fetal bovine serum, penicillin (200 μg/ml), streptomycin (200 U/ml), 4 mM [l]{.smallcaps}-glutamine, and 5 × 10^−5^ M 2-mercaptoethanol (all from Gibco)\]. B cells were stimulated with an agonistic anti-CD40 mAb (10 μg/ml; FGK45, Enzo Life Sciences), BAFF (100 ng/ml; R&D Systems), LPS (10 μg/ml; Escherichia coli serotype 0111: B4, Sigma-Aldrich), or other TLR agonists (TLR1, Pam3CSK4, 300 ng/ml; TLR2, heat-killed Listeria monocytogenes, 10^8^ cells/ml; TLR3, polyriboinosinic acid/polyribocytidylic acid, 10 μg/ml; TLR5, Salmonella Typhimurium flagellin, 1 μg/ml; TLR6, Pam2CGDPKHPKSF, 100 ng/ml; TLR7, ssRNA40/LyoVec, 5 μg/ml; and TLR9, ODN1826, 5 μM; Invivogen). Enzyme-linked immunosorbent assay --------------------------------- IL-6, IL-10, or BAFF levels were determined by specific ELISA kits (R&D Systems) Intracellular cytokine staining ------------------------------- Intracellular cytokine expression was visualized by immunofluorescence staining and analyzed by flow cytometry as previously described. For IL-6 detection, cells (2 × 10^6^ cells/ml) were cultured with LPS (10 μg/ml) and anti-CD40 mAb (10 μg/ml; FGK45) for 24 hours with PIB \[PMA (50 ng/ml; Sigma-Aldrich), ionomycin (1 μg/ml; Sigma-Aldrich), and brefeldin A (supplied as 1000× solution; c)\] added during the final 5 hours of culture. PIB \[PMA (50 ng/ml; Sigma-Aldrich), ionomycin (1 μg/ml; Sigma-Aldrich), and brefeldin A (supplied as 1000× solution; BioLegend)\] was added for 5 hours. For IL-10 detection, cells (2 × 10^6^ cells/ml) were cultured with LPS (10 μg/ml) and PIB for 5 hours. Fc receptors were blocked with mouse Fc receptor mAb (2.4G2, BD Pharmingen) with dead cells detected using a LIVE/DEAD Fixable Aqua Dead Cell Stain Kit (Invitrogen) before cell surface staining. Stained cells were fixed and permeabilized using a Cytofix/Cytoperm kit (BD Pharmingen) according to the manufacturer's instructions and stained with APC-conjugated mouse anti--IL-6 or anti--IL-10 mAb. Preparation of skin cell suspensions for flow cytometry ------------------------------------------------------- A 1 cm × 1 cm piece of the bleomycin-injected skin region was minced and then digested in 7 ml of RPMI 1640 and 10% fetal bovine serum containing collagenase (2 mg/ml; Sigma-Aldrich), hyaluronidase (1.5 mg/ml; Sigma-Aldrich), and deoxyribonuclease (DNase) I (0.03 mg/ml; Sigma-Aldrich) at 37°C for 90 min. Digested cells were then passed through a 70-μm cell Falcon Cell Strainer (BD Biosciences) to generate single-cell suspensions. The cell suspension was centrifuged at 300g for 10 min. The pellet was resuspended in 70% Percoll solution (GE Healthcare) and then overlaid by 37% Percoll solution followed by centrifugation at 500g for 20 min at room temperature. Cells were aspirated from the Percoll interface and passed through a 70-μm cell strainer. Subsequently, the cells were harvested by centrifugation and washed. Immunohistochemical staining of mouse skin ------------------------------------------ Mice were treated with bleomycin for 2 weeks, and brefeldin A (250 μg per mouse; Sigma-Aldrich) was intravenouslly injected 6 hours before sample prepararion. The skin samples from bleomycin-injected mice were removed and frozen in liquid nitrogen using embedding medium for frozen tissue specimens \[Tissue-Tek OCT (optimum cutting temperature) Compound, Sakura Finetek\] and stored at −70°C until use. Frozen sections (5 μm thick) were immediately fixed in cold acetone and were incubated with rat anti-mouse B220 mAb (RA3-6B2 clone, BD Biosciences) and polyclonal goat anti-mouse IL-6 Ab (R&D Systems). Donkey anti-rat IgG with Alexa Fluor 488 or donkey anti-goat IgG with Alexa Fluor 594 (Thermo Fisher Scientific) were used as secondary Abs of rat anti-mouse B220 mAb or goat anti-mouse IL-6 mAb, respectively. Coverslips were mounted by using ProLong Diamond Antifade Mountant with DAPI (Thermo Fisher Scientific). Fluorescence microscopy was performed using a KEYENCE BZ-X710 fluorescence microscope (KEYENCE). Fibroblast culture ------------------ Skin samples were taken from E14.5 embryos of naïve wild-type mice. To obtain fibroblasts, the skin tissue was cut into 1-mm^3^ pieces, placed in sterile plastic dishes, and cultured in Dulbecco's modified Eagle's medium (Invitrogen) containing 10% heat-inactivated fetal bovine serum, penicillin (100 U/ml), and streptomycin (100 μg/ml; Invitrogen) at 37°C in a humidified 5% CO~2~ atmosphere. After 2 to 3 weeks of incubation, outgrowing fibroblasts were detached by brief trypsin treatment and recultured in the medium. Fibroblasts (10^5^ cells) were cultured without or with B cells (5 × 10^5^ cells) in 24-well plates for 3 days. For Transwell experiments, B cells (5 × 10^5^ cells) and fibroblasts (10^5^ cells) were seeded in the upper and lower chambers, respectively, of a 0.4-μm polycarbonate membrane Transwell (Nunc Dominique Dutscher). For fibroblast stimulation, cells were cultured with recombinant TGF-β1 (5 ng/ml; R&D Systems). The supernatant was harvested after culture. All experiments used fibroblasts between passages 2 and 5, depending on the number of cells obtained initially from the tissue samples. Cultured fibroblasts were adherent to the dish and maintained the typical spindle-shaped aspect. The purity of fibroblasts, as confirmed by flow cytometry, was \>99%, with no leukocytes found in the harvested cells. In each experiment, all the cell lines were examined at the same time and under the same conditions of culture (for example, cell density, passage, and days after plating). Reverse transcription polymerase chain reaction ----------------------------------------------- Total RNA was isolated from inflamed skin using RNeasy spin columns (Qiagen) and digested with DNase I (Qiagen) to remove chromosomal DNA. Total RNA was reverse-transcribed to a cDNA using a reverse transcription system with random hexamers (Promega). Cytokine mRNA was analyzed using real-time reverse transcription PCR (RT-PCR) quantification (Applied Biosystems). Real-time RT-PCR was performed on an ABI Prism 7000 sequence detector (Applied Biosystems). TaqMan probes and primers for collagen alpha-2(I) (col1a2) and glyceraldehyde-3-phosphate dehydrogenase (gapdh) were purchased from Applied Biosystems. GAPDH was used to normalize the mRNA. The relative expression of real-time RT-PCR products was determined according to the ΔΔC~t~ method to compare target gene and GAPDH mRNA expression. Statistical analysis -------------------- Data are presented as means ± SD. Two-tailed Student's t test was used for comparisons between two groups, and P \< 0.05 was considered significant. Comparisons among three or more groups were performed with ANOVA followed by Tukey's multiple comparison test. Data were analyzed with GraphPad Prism (version 7; GraphPad Software). Study approval -------------- Animal studies were approved by the Committee on Animal Experimentation of the Kanazawa University Graduate School of Medical Sciences. Supplementary Material ====================== ###### http://advances.sciencemag.org/cgi/content/full/4/7/eaas9944/DC1 We thank M. Matsubara, Y. Yamada, and Y. Iwauchi for technical assistance. Funding: This work was supported by Japan Society for the Promotion of Science KAKENHI (grant no. JP16K10147). Author contributions: T.M., T.K., K.M., M.K., T.S., M.T., and A.O. contributed to data collection, analysis, and interpretation. Y.I. generated IL-6--deficient mice. T.M., Y.H., M.H., M.F., and K.T. designed the study and wrote the manuscript. All authors discussed the results and commented on the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Supplementary material for this article is available at <http://advances.sciencemag.org/cgi/content/full/4/7/eaas9944/DC1> Fig. S1. Phenotypes of IL-6--producing B cells after in vitro culture. Fig. S2. CD25 expression on B cell is enhanced after stimulation. Fig. S3. IL-6-- and/or IL-10--producing B cells. Fig. S4. Phenotype of IL-6--producing B cells in the skin. Fig. S5. Scheme for the generation of B-IL-6^−/−^ or B-IL-10^−/−^ and corresponding control mice. Fig. S6. Lung fibrosis is attenuated in mice with B cell--specific IL-6 deficiency.
1. Field of the Invention The present invention relates to a production method of silver halide photographic emulsion in which reaction, mixing or the like in a production process of silver halide photographic emulsion is carried out by a chemical unit operation, and a production apparatus thereof. 2. Description of the Related Art In general, a silver halide photographic emulsion used for a photosensitive material is produced through a pre-ripening process in which a nucleus forming process (formation of a microcrystal dispersion of silver halide in protective colloid), a physical ripening process (crystal growth for obtaining a desired grain shape and size), and a crystal growth process are performed to form silver halide photographic emulsion grains having an objective size, shape and structure, a desalting process (removal of soluble salts from the dispersion), a sensitizing process (heat treatment performed in the presence of a sensitizing agent, for increasing sensitivity to light) for increasing the sensitivity of the emulsion after desalting, and a after-ripening process for adding various agents (sensitizing dye, stabilizing agent, and etc.) for giving various properties to the emulsion required as the need arises. Incidentally, in the foregoing production process of the silver halide photographic emulsion, two or more processes among these processes, may be combined and carried out in one operation. Further, in the foregoing production process, one or more production stages may be omitted from the production process. Furthermore, there is also a case where plural operations are repeated in each stage in order to obtain a desired emulsion. In addition, in a production system for industrially mass-producing silver halide emulsion, a so-called batch type production system using a large capacity reaction container is usually used. As a conventional batch-type production system for producing silver halide emulsion, there is proposed one using a tank 10 as a reaction container as exemplified in FIG. 37 (for example, see JP-A No. 5-173267). This tank 10 is constituted as a batch type reaction container apparatus having an agitator capable of producing of silver halide photographic emulsion at a time in a predetermined large amount, for example, 1000 l (1 t) In this tank 10, in order to agitate a solution with which the tank is filled, a magnetic agitation means 16 is provided such that an agitation vane 12 is rotatively driven through a transmission means 14 for transmitting a rotation driving force of a motor 15 in a non-contact manner by using a magnetic force. In addition, in order to perform a temperature control of the solution with which the tank is filled, a temperature control means 18 for heating or cooling the reaction solution is disposed at the outer peripheral part of the tank 10. The temperature control means 18 is constituted by use of means for heating or cooling by allowing a heat exchange medium (water, water vapor, liquid organic material, flame gas, etc.) to flow to a temperature control part, or a means for performing a temperature control by installing an element for electrically heating or cooling at the temperature control part. The tank 10 is constituted to be capable of being hermetically closed by mounting a sealing lid 20 to the tank 10. Further, an emulsion introduction pipe 22 with an opening and closing cock is disposed in the sealing lid 20 of the tank 10. Furthermore, a liquid transfer pipe 24 with an opening and closing cock is disposed at the bottom of the tank 10. In the butch type production system using this tank 10, at the nucleus forming process in the pre-ripening process at the time of producing a silver halide emulsion, a predetermined quantity of an aqueous dispersion medium solution containing at least a dispersion medium and water is injected through the emulsion introduction pipe 22 into the tank 10, and further, a silver salt solution or a silver salt solution and a halide solution are added under the conditions of pBr 2.5 or less and are agitated by the magnetic agitation means 16 for a predetermined time (several minutes), and temperature is controlled by means of a temperature control means 18 so as to keep the reaction solution in the tank 10 within a predetermined temperature range (for example, 5° C. to 45° C.), so that nuclei of minute tabular grains including, for example, a parallel twinning plane are formed. In this nucleus forming process, since solute ions are randomly walking in the solution when the nuclei are formed, minute tabular grain nuclei and a large number of other minute grains (especially, non-twin, single twin, or non-parallel double twin grains) are simultaneously formed in the tank 10. Next, in the butch-type production system using this tank 10, at the ripening process in the pre-ripening process at the time when the silver halide photographic emulsion is produced, grains other than the tabular grain nucleus are made to disappeared by the Ostwald ripening process, and the tabular grain nucleus is made to grow. In this ripening process, three ripening methods that have conventionally been used described below can be used. The first type of the ripening method is a method in which after nucleus formation, a pBr value of the reaction solution in the tank 10 is adjusted to 2.5 to 1.0, preferably 2.3 to 1.4, a solvent for AgX is added through the emulsion introduction pipe 22 (AgNO3 may be added during the ripening), agitation is performed by the magnetic agitation means 16, and the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, sob that ripening is performed for predetermined several minutes or more. The second type of the ripening method is a method in which after nucleus formation, a pBr value of the solution is adjusted to 2.5 or less, preferably 1.0 to 2.0, a first ripening is performed for predetermined several minutes or more in a state where there is no solvent for AgX, and next, AgNO3 is added through the emulsion introduction pipe 22 to increase the pBr value by 0.1 or more, preferably 0.3 or more, the solvent for AgX is added through the emulsion introduction pipe 22, agitation is performed by the magnetic agitation means 16, and the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, so that second type of ripening is performed for predetermined several minutes or more. The third type of ripening method is a method in which after nucleus formation, a pBr value of the solution is adjusted to 2.5 or less, preferably 1.0 to 2.0, agitation is performed by the magnetic agitation means 16 in a state where there is no solvent for AgX, the temperature of the reaction solution in the tank 10 is raised by the temperature control means 18 by preferably 10° C. or higher, more preferably 20° C. or higher with respect to the nucleus formation temperature, so that the third type of ripening is performed for predetermined several minutes or more. Incidentally, there is also a method in which AgNO3 is added during the ripening. Further, in the foregoing first to third type of ripening methods, there is also a method using a pressure ripening method in which the tank 10 is made a hermetically sealed system only at the time of ripening, and ripening is performed in a state where the pressure in the tank 10 at the time of nucleus ripening is more than several times as high as the atmospheric pressure. Further, there is also a method in which the ripening is performed by the foregoing first to third ripening methods in the presence of an anti-fogging agent. Next, in the batch type production system using this tank 10, after the ripening process in the pre-ripening process at the time of production of the silver halide emulsion has been ended, tabular grain nuclei are made to grow in the crystal growth process. In the crystal growth process, it is possible to use a method of adding a silver salt solution and a halide solution as a solute for growing a crystal of tabular grain nuclei, a flow acceleration addition method, a concentration acceleration addition method, and a combined addition method of two or more of these methods. In the batch type production system using this tank 10, also at the crystal growth stage in the pre-ripening process at the time of production of the silver halide emulsion, a predetermined quantity of silver salt solution and halide solution as solutes for growing the crystals of the tabular grain nuclei is injected from the emulsion introduction pipe 22 into the reaction solution stored in the tank 10, agitation is performed by the magnetic agitation means 16 for a predetermined time (several minutes), a temperature control is performed by the temperature control means 18 to bring the reaction solution in the tank 10 to a predetermined temperature, and a chemical reaction for suitably allowing to grow crystals is accelerated (see, for example, Japanese Patent Application Nos. 2-142635 and 2-43791). In the batch type production system using this tank 10, after the crystal growth process in the pre-ripening process at the time of production of the silver halide emulsion has been ended, the desalting process is carried out. The desalting process is a process of removing unnecessary materials (for example, K, Na) formed during the emulsion grain formation of the pre-ripening process, excessively existing ions (for example, Ag, Br, Cl) and the like. In the desalting process, various desalting methods, such as a flocculation method or a noodle washing method in which water washing is performed to effect desalting, or an ultrafiltration or an electro dialysis method in which desalting is carried out by separation (film), can be used. In the desalting process, for example, in the case where the flocculation method is used, the reaction solution which has been subjected to the pre-ripening process in the tank 10 as shown in FIG. 37 is taken out from the liquid transfer pipe 24, and is transferred to a desalting tank (not-show), and a flocculant is added to the reaction solution in the desalting tank, and a pH value of the solution is adjusted, so that emulsion grains together with gelatin, are flocculating-sedimented (natural sedimentation), a supernatant liquid containing unnecessary materials is removed, and next, after washing water is newly added into the desalting tank, the flocculation of gelatin is deflocculated by adjusting pH value of the solution. These processes are repeated two or three times. Further, in this batch type production system, after the desalting process at the time of production of the silver halide emulsion has been ended, an after-ripening process is carried out. This after-ripening process is a process in which the emulsion having a low sensitivity in the reaction solution after desalting process is sensitized to impart sensitivity suitable for practical use. In the sensitizing method at the after-ripening process in the batch type production system, there are a chemical sensitizing method and a spectral sensitizing method. The chemical sensitizing method is a method for increasing the intrinsic sensitivity of the emulsion. A typical chemical sensitizing method includes three kinds of methods, that is, a sulfur sensitizing method, a gold sensitizing method and a reduction sensitizing method. In the case where this chemical sensitizing method is performed, the reaction solution which has been subjected to the desalting process is transferred to a tank as a reaction container (not-shown) constituted similarly to the foregoing tank 10, a chemical sensitizing agent is metered and a predetermined quantity of the agent is added through an agent introduction pipe to the reaction solution stored in the tank. An agitation vane stirs the solution, and the temperature of the solution is controlled by a temperature control means so that the chemical sensitizing agent is uniformly distributed to emulsion grains to complete a desired chemical reaction equally. In addition, the spectral sensitizing method as the sensitizing method in the after-ripening process is a method in which in the case where the emulsions are used in a color photosensitive material or the like, sensitizing wavelength ranges are respectively widened into the wavelength ranges of the three primary colors of light, that is, blue (400 to 500 nm), green (500 to 600 nm), and red (600 to 700 nm) from the intrinsic sensitivities of the emulsions in the reaction solutions. The spectral sensitizing method is generally performed by adsorbing a sensitizing dye onto an emulsion. As the sensitizing dye used here, there is an orthochromatic sensitizing dye (for green) or a panchromatic dye (for red). The sensitizing dyes are dissolved in methanol to form a solution, or are made a dye solid dispersed solution in gelatin, and are added to the emulsion as the reaction solution. Incidentally, the dye solid dispersed solution in gelatin is prepared at a preparation process, and is temporarily refrigerated, and at the time of use, it is melted to add to the emulsion. When the spectral sensitizing method is used, the reaction solution which has been subjected to the desalting process is transferred to a tank as a reaction container (not-shown) constituted similarly to the foregoing tank 10, a solution in which a sensitizing dye is dissolved in methanol or a solution in which a sensitizing dye is made to a solid dispersed solution in gelatin (this solid dispersed solution in gelatin is prepared at a preparation process, is temporarily refrigerated, is melted at the time of use to be added to the emulsion) is metered and a predetermined quantity of solution is added through an agent introduction pipe to the reaction solution stored in the tank. The solution is stirred well by an agitation vane, the temperature of the solution is controlled by a temperature control means so that the chemical sensitizing agent is uniformly distributed to the emulsion grains and is uniformly adsorbed by the grains. In this batch type production system, after the after-ripening process in the production processes of the silver halide emulsion has been completed, a storage process is performed. The storage process is a process of temporarily storing the emulsion prepared in the batch operation for the purpose of supplying the emulsion to an emulsion coating process in continuous operation. Further, in addition to the function of temporal storage, this storage process also provides a function to stop the progress of ripening by cooling the emulsion to eliminate differences in characteristics among emulsion preparation batches by batch-blending a plurality of the same kind emulsions, as well as a function for quality assurance by measuring physical properties of the prepared emulsions to assure the characteristics of the emulsions. Thus, in the batch type production system, the equipment for the storage process is constituted by a cooling apparatus, a blend tank, a storage apparatus and the like. The cooling apparatus for stopping the progress of ripening may be constituted by a heat exchange system using a plate type heat exchanger or the like, or by a vacuum cooling system for effecting cooling by utilizing latent heat of vaporization. In this batch type production system, in order to perform the production process of the silver halide emulsion in one or plural stages, the tank 10 as the batch type reaction container device equipped with the agitator is used, and a plurality of chemicals in large amounts introduced into the tank 10 for producing an emulsion are forcibly mixed by a magnetic agitation means 16. The tank 10 as the batch type reaction container device equipped with the agitator is suitable for production of a large quantity of emulsion. However, when another new liquid chemical is injected through the emulsion introduction pipe 22 to the chemicals for producing the emulsion stored in the tank 10, and a plurality of chemicals in a large amount introduced into the tank 10 are agitated by the agitation vane 12 and are mixed, the liquid chemicals newly injected through the emulsion introduction pipe 22 are stagnant in the vicinity of the injection port of the emulsion introduction pipe 22 or circulates in the tank 10. Accordingly, in the initial state where a plurality of liquid chemicals in a large quantity for producing the emulsion are agitated by the agitation vane 12 to start mixing thereof, it is inevitable such a state that the liquid chemical newly injected through the injection port of the emulsion introduction pipe 22 is locally mixed at a high concentration into a part of the liquid chemicals for producing the emulsion stored in the tank 10 existing at a place where the chemicals are circulated in the tank 10, and a mixing concentration of the liquid chemicals becomes low at a portion which is remote from the injection port of the emulsion introduction pipe 22 and which the newly injected liquid chemical does not reach through the circulation by the agitation vane 12. Accordingly, when a plurality of liquid chemicals in a large amount for producing an emulsion are stirred by the agitation vane 12, a difference in history of a chemical change arises between one where mixing of the newly injected liquid chemical is started at a high concentration thereof and one where mixing of the newly injected liquid agent is started at a low concentration thereof, so that the compounds formed become non-uniform in the entire tank 10. Further, a non-uniform chemical reaction may occur due to a dead space existing in a small part in the tank 10, or due to variation in the liquid flow when the liquid chemicals for producing the emulsion is stirred by the agitation vane 12. In addition, when the liquid chemicals in a large quantity for producing an emulsion in the tank 10 are heated by the temperature control means 18, since the temperature control means 18 heats the chemicals through the wall of the tank 10, there is a case where when a heating process is started, the liquid chemicals for producing the emulsion in the tank 10 are rapidly heated only at the place close to the wall of the tank 10, and the temperature is not raised at the center in the tank 10, so that the temperature distribution of the liquid chemicals for producing the emulsion in the tank 10 becomes uneven, a history difference in the chemical change, and compounds formed becomes non-uniform in the entire tank 10. Furthermore, in the method of forming silver halide grains constituting the silver halide emulsion, which is industrially carried out today, there is a process in which a silver nitrate solution and a halide solution are added to a dispersion medium solution (protective colloid solution) typified by gelatin under vigorous agitation, and are mixed as quickly as possible to form silver halide grains. In this silver halide grain forming process, since an ionic reaction in which a silver ion and a halogen ion react with each other to form silver halide is very rapid, it is essential to quickly agitate and mix these two ionic solutions in a short time in order to perform a uniform reaction. Here, for example, in the case where nucleus formation is performed by a method in which a silver salt solution and a halide solution are added to a dispersion medium in the tank 10 from the emulsion introduction pipe 22 and are agitated by the agitation vane 12, a vortex is generated by the agitation vane 12 rotating at a high speed in the liquid chemicals for producing the emulsion in which the silver salt solution and the halide solution are added in the dispersion medium in the tank 10, and mixing by turbulent flow is carried out in the process in which the vortex is subdivided. Even in this case, once the nuclei thus formed circulate in the tank 10 to cause a so-called local recycling, and at the same time as the formation of the nuclei, crystal growth from the nuclei occurs in parallel, so that it is difficult to form mono dispersed nuclei. Further, in the field of silver halide photography, a tabular silver halide grain having a large light receiving area is widely used as a photosensitive element. In order to increase a light receiving efficiency, a thin tabular silver halide grain is preferable. However, in the batch type production system using the tank 10 and the agitation vane 12 mentioned above, when the agitation is performed by the agitation vane 12 to produce the silver halide emulsion, the tabular silver halide grains during the process of crystal growth pass through a high supersaturation region in the vicinity of the injection port of the emulsion introduction pipe 22 for adding silver ion or halide ion, and an adverse effect such that the thickness of the tabular grains increases is apt to occur. Furthermore, in the batch type production system using the tank 10 and the agitation vane 12, on the assumption that the quantity of silver halide emulsion produced at one time in the tank 10 is a predetermined constant quantity, the shape of the agitation vane 12 is determined to obtain an appropriate agitating state in the tank 10. Accordingly, when a production scale is changed to produce a desired quantity of emulsion, there is a fear that the characteristics of the emulsion are changed, and the preparation scale cannot be changed. Therefore, a predetermined quantity of silver halide emulsion larger than a desired quantity of emulsion must be produced, and as a result, there is a drawback that the silver halide emulsion produced in an excess amount is wastefully discarded. On the other hand, with respect to a newly prescribed silver halide emulsion developed by using an experimental apparatus, in the case where a small production system using the experimental apparatus is scaled up to a mass production system using a mass production apparatus, it is necessary to repeat trial production and product test many times in order to verify conditions under which the same characteristics as the emulsion characteristics obtained by the experimental apparatus for small production can be achieved in the newly prescribed silver halide emulsion produced by the production apparatus for mass production. Accordingly, there are problems that it takes a long time to develop the production system for mass production, and the loss of raw material consumed for the product test is large. Furthermore, it has been proposed that a microreactor is used for a part of a production process of silver halide photographic emulsion used for photosensitive material (see, for example, Japanese Patent Application No. 2001-76564). The microreactor used in this method is one of micro devices, in which a plurality of solutions introduce into each mixing space through microchannels having an equivalent diameter of several μm to several hundred μm having a cross-section when converted into a circle, to cause a chemical reaction. In such a microreactor, two kinds of solutions are made to flow through fine liquid supply passages called microchannels and are supplied as very thin lamella-like laminar flows into the mixing space, so that the two kinds of solutions are mixed and are allowed to react with each other in the mixing space (see, for example, JP-W No. 9-512742, WIPO International Publication WO 00/62913). In a fluid circuit used in such a microreactor, there is a case where it is required that three or more kinds of fluids are allowed to rapidly react with one another by the microreactor. However, the conventional microreactor is constituted such that two kinds of fluids are allowed to react with each other. Thus, in the case where three or more kinds of fluids are made to react with each other by the conventional microreactor, it is necessary that a fluid circuit is constituted such that two or more microreactors are connected in series by piping or the like, and three or more kinds of fluids are made to react with each other step wisely by using this fluid circuit. In such a fluid circuit, there is a limit in shortening a distance between a microreactor disposed at the upstream side and a microreactor disposed at the downstream side, a certain period of time is necessary to mix another fluid with two kinds of fluids in a reaction container to make to react with the fluids each other. Therefore, it is impossible to make to react with three kinds of fluids one another at the same time. Moreover, in the fluid circuit, as the kinds of fluids to be supplied are increased, the number of elements (microreactors) constituting the circuit is increased, so that the circuit structure becomes complicated. Incidentally, this applies in the case where three or more kinds of fluids are mixed at the same time. In addition, in the conventional microreactor, plural liquid supply passages respectively-have liquid supply ports facing a mixing space so as to open respective liquid supply openings, and solutions are introduced into the mixing space through these plural liquid supply ports. However, there exists a portion where the cross-section of the mixing space is abruptly enlarged with respect to the sum of the opening areas of these liquid supply ports, and there exists a portion in the mixing space where the direction of flow of solutions to be mixed is abruptly changed. The solutions are apt to stagnate in the vicinity of the portion where the cross-section is abruptly enlarged in this mixing space or in the vicinity of the portion where the direction of the flow of the solutions to be mixed is abruptly changed, and especially in the case where a reaction between solutions is a precipitation generation reaction accompanied by coalescence or growth, aggregation or deposition occurs in the stagnant part, and there is a fear that there occurs clogging due to this, or reduction of uniformity of a reaction product due to the mixture of aggregates or deposits. Further, in the conventional microreactor, according to the kinds of solutions supplied to plural liquid supply passages, a time when these solutions are mixed or a time when the mixing of the solutions accompanying a chemical reaction is performed, (hereinafter referred to as “mixing time”) is changed. That is, as the viscosity of the solution becomes high, the mixing time becomes longer in general, and in the case where the aggregation or deposition occurs accompanying the chemical reaction between the solutions, the aggregates or deposits become an inhibiting factor of mixing, that is, causes the lowering of diffusing power to the solution, and the mixing time is changed. In such a microreactor, since the passage length in the flow direction of the solutions in the mixing space is constant, in the case where the flow rate of the solutions is constant, a time (passing time) when the solutions pass through the mixing space becomes constant. Accordingly, in the case where the mixing time of the solutions in the mixing space is longer than the passing time, it is necessary to reduce the flow rate of the solutions in the mixing space, so that the processing rate of the solutions in the microreactor is lowered. At this time, in order to prevent the decrease in the process rate of the solution, it is conceivable to extend the passage length of the mixing space. However, in the case where such measures are taken, the microreactor is enlarged or the production cost is increased. Further, in the case where the passage length of the mixing space is extended more than needs, the aggregation, deposition or the like of the solution is promoted by contraries, the clogging occurs in the mixing space, and the maintenance of the microreactor becomes troublesome. Accordingly, in the foregoing conventional microreactor, an actuator is coupled to a block-shaped mixer element in which liquid supply passages branching from a supply part of a solution in the shape of the teeth of a comb are formed, a mechanical vibration is given to the mixer element by this actuator, and the mixing of plural solutions is accelerated by this mechanical vibration. However, in this conventional microreactor, the vibration is given to only the mixer element in which plural liquid supply passages are formed, and this vibration is transmitted to the solutions in the mixing space through the solutions in the liquid supply passages, so that the mixing of the solutions in the mixing space is accelerated. Thus, in such a microreactor, it is difficult to control the progress of the mixing of the solutions in the mixing space and the progress of the chemical reaction accompanying the mixing with high accuracy. For example, in the case where the chemical reaction between the solutions in the mixing space is desired to be performed stepwise, or in the case where the solution and reaction product are desired to be diffused and mixed over the whole length of the mixing space, it is difficult to realize such progress of the mixing or the chemical reaction.
1. Field of the Invention The present invention relates to a technology of setting a link to medical image data contained in enhanced image data composed of a plurality of medical image data recorded in one file, and extracting the medical image data contained in the enhanced image data, based on the link. 2. Description of the Related Art A medical image diagnosis apparatus captures an image of a subject and creates medical image data. A medical image diagnosis apparatus is, for example, an X-ray CT apparatus, an MRI apparatus, an ultrasound diagnosis apparatus, and a nuclear medical diagnosis apparatus. Medical image data generated by a medical image diagnosis apparatus is managed by a server for managing an image, and is readable at a terminal within a network. A report creation terminal for assisting creation of an interpretation report receives medical image data from the server, and displays on a monitor. This report creation terminal is used for interpretation of a medical image. An interpretation report is a document describing a problem presumed form interpretation of a displayed medical image by an interpreting doctor. For example, as disclosed in Japanese Unexamined Patent Application Publication JP-A 2005-301453, there is a case in which the report creation terminal links medical image data to an interpretation report. The report creation terminal generates link data indicating the storage destination of medical image data, and embeds the link data into an interpretation report. To embed into an interpretation report means a process of including the link data into data of the interpretation report. In a conventional technology, each medical image data composes one file, so that it is possible to include the name of a file into link data and thereby specify medical image data to link. In recent years, in the DICOM standard, a concept of enhanced image data (also referred to as bundle image data or multi-frame image data) composed of a plurality of medical image data recorded in one file, has appeared. In this DICOM standard, a plurality of medical image data generated by a medical image diagnosis apparatus are compiled in one file. In a case in which each medical image data composes one file, there is a need for establishment of communication every time the medical image data is sent and/or received. Therefore, numerous interactions between an apparatus sending the medical image data and an apparatus receiving the data are required, whereby an enormous load on the communication traffic is generated. On the contrary, in the case of the enhanced image data, all medical images can be sent and/or received in one communication, and therefore, numerous interactions are not required. Consequently, the load on the communication traffic is reduced. However, for reading an interpretation report, it is enough to acquire only a medical image that should be referred to. Medical image data actually cited in an interpretation report is only part of the enhanced image data. However, a conventional linking method is a method in which a file name is included in the link data, and the file name does not exist in the medical image data recorded in the enhanced image data. Therefore, in the case of employing the conventional linking method, it is necessary to receive the entire enhanced image data. As a result, a significant amount of time is required to display desired medical image data, and the efficiency of medical practices using an interpretation report as a reference is extremely decreased. In some terminals reading an interpretation report, resources cannot tolerate such large volume of enhanced image data, and the decrease of the medical efficiency in this case is significant. Moreover, in a case in which the entire enhanced image data is received, an enormous load is generated in the communication traffic within the network.
His remarks came after American and European bombs battered the coastal city of Surt — the rebels’ next objective — in Colonel Qaddafi’s tribal homeland on Sunday night, permitting the insurgents to advance to within 45 miles of the city. The rebels had pushed west on Sunday from Ajdabiya past the oil towns of Brega and Ras Lanuf, recapturing the two important refineries, and then set their sights on Surt. But on Monday there was no sign of a rebel takeover of Surt and the city seemed quiet, although a stream of civilian cars and some military vehicles was seen heading west from Surt toward Tripoli, 225 miles away. By late afternoon, however, hundreds of rebel cars and trucks came speeding down the road to a checkpoint near Bin Jawwad, a town directly east of Surt that has switched hands three times in the last month and seems to have split loyalties, rebel fighters said. The rebel advance had been too easy, and there had been no resistance, said Sherif Layas, a marketing manager from Tripoli who fought with the rebels. “This made us go forward,” he said. “And then we met the tanks.” With that, he said, they panicked and retreated en masse.
Q: Netbeans and C++ installation i have a litle problem using Netbeans 7.4 and Cygwin 4.x for compiling my C++ programms. I've done everything as in netbeans tutorial. I've installed gcc, gdb, g++ and make compilers. Everything is setup properly in Netbeans properties, every path. But i still get the same problem, i don't know what is this problem. I'm trying to compile Hello sample from Netbeans. Please help me. Here is the error log: "/usr/bin/make" -f nbproject/Makefile-Debug.mk QMAKE= SUBPROJECTS= .build-conf make[1]: Entering directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' "/usr/bin/make" -f nbproject/Makefile-Debug.mk dist/Debug/Cygwin_4.x-Windows/welcome_2.exe make[2]: Entering directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' mkdir -p build/Debug/Cygwin_4.x-Windows g++ -c -g -o build/Debug/Cygwin_4.x-Windows/welcome.o welcome.cc In file included from /usr/include/sys/reent.h:14:0, from /usr/include/wchar.h:6, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/cwchar:44, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/bits/postypes.h:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iosfwd:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ios:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ostream:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iostream:39, from welcome.cc:31: /usr/include/sys/_types.h:72:20: fatal error: stddef.h: No such file or directory #include <stddef.h> ^ compilation terminated. nbproject/Makefile-Debug.mk:66: recipe for target 'build/Debug/Cygwin_4.x-Windows/welcome.o' failed make[2]: * [build/Debug/Cygwin_4.x-Windows/welcome.o] Error 1 make[2]: Leaving directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' nbproject/Makefile-Debug.mk:59: recipe for target '.build-conf' failed make[1]: * [.build-conf] Error 2 make[1]: Leaving directory '/cygdrive/c/Users/Dragosh/Documents/NetBeansProjects/Welcome_2' nbproject/Makefile-impl.mk:39: recipe for target '.build-impl' failed make: *** [.build-impl] Error 2 BUILD FAILED (exit value 2, total time: 467ms) A: Got this issue with cygwin too, after last update to 2.830 (see setup.exe version). I am using 64 bit version. To verify that we have the same issue, try manualy compiling something supersimple with g++ usgin cygwin terminal. I checked with: $ echo -e "#include <iostream>\n int main() { return 0; }" \| g++ -xc++ - And got: In file included from /usr/include/sys/reent.h:14:0, from /usr/include/wchar.h:6, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/cwchar:44, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/bits/postypes.h:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iosfwd:40, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ios:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/ostream:38, from /usr/lib/gcc/x86_64-pc-cygwin/4.8.1/include/c++/iostream:39, from <stdin>:1: /usr/include/sys/_types.h:72:20: fatal error: stddef.h: No such file or directory #include <stddef.h> ^ compilation terminated. I noticed that there are two folders of gcc here C:\cygwin\lib\gcc\x86_64-pc-cygwin\4.8.1 C:\cygwin\lib\gcc\x86_64-pc-cygwin\4.8.2 and g++ --version gives 4.8.2 Running Cygwin's latest Setup.exe and looking for installed packets showed that versions mismatch for gcc-core and gcc-g++ : gcc-core = 4.8.2-1 gcc-c++ = 4.8.1-3 I downgraded gcc-core to 4.8.1-3 and fixed the issue.
The past reporting week (October 12-18) saw very little solar activity, with a sunspot number of 12 on October 15, meaning the average daily sunspot number was only 1.7, down from the already low average of 8.4 over the previous seven days.
Cytomorphology Versus Conventional Microbiological Tests in the Diagnosis of Tuberculous Lymphadenitis. To determine the accuracy of Fine Needle Aspiration Cytology (FNAC) in the diagnosis of tuberculous lymphadenitis. Comparative cross-sectional study. Department of Pathology, Khalifa Gul Nawaz Teaching Hospital (KGNTH), Bannu, from September 2012 to March 2013. FNAC of enlarged lymph nodes was performed in the Department of Pathology, KGNTH, Bannu. Smears of the aspirates were examined under light microscope after staining with Haematoxylin and Eosin (H & E) stains. In cases of chronic lymphadenitis, the smears were stained with Ziehl-Neelsen (ZN) stain for Acid Fast Bacilli (AFB). If no AFB was visualized, the aspirate was subjected to culture on Lowenstein Jensen (LJ) medium for yield of AFB. The results were analyzed by Microsoft Excel software. Chronic granulomatous lymphadenitis was found in 110 (46.81%) out of 235 cases. AFB were seen in aspirates of 43/110 (39.09%) cases by direct microscopy. Among the remaining 67 aspirates subjected to LJ medium, only 07 (10.45%) yielded growth of AFB. Smears of 4/15 (3.6%), 13/47 (11.7%) and 33/48 (29.7%) cases with haemorrhagic, inflammatory and caseous background respectively, were confirmed by conventional microbiologic tests. Out of 125 nongranulomatous lymphadenitis cases only 05 were confirmed to be due to tuberculosis by direct microscopy while culture was not positive in any case. Thus accuracy of FNAC was 72.34%. FNAC has a good accuracy in diagnosing tuberculous lymphadenopathy.
Asymmetric halogeno-bridged complexes: new reagents in organometallic synthesis and catalysis. Several methods to synthesize bimetallic complexes in which two different metal fragments are connected by halide bridges are described. Using simple starting materials a large pool of structurally defined bimetallic complexes with unique chemical reactivities can be prepared in short time. Applications in organometallic synthesis and homogeneous catalysis are discussed.
My love of JRPGs began in childhood and remains to this day. There is something about the genre’s anime-style graphics, simplistic tunes, turn-based battles, and quests to save the world that are qualities that I cannot resist. In many ways, Fernz Gate captures the essence of the genre. However, the game is imperfect and it often feels like a shell of what a JRPG could be. Telling stories of grand adventures should be at the center of any quality JRPG. Fernz Gate makes a solid attempt at crafting an engaging tale. Players follow the main character, a typical high school boy named Alex. One day, Alex awakens to find himself in Fernland, an alternate dimension full of swords and sorcery. Disoriented by his new surroundings, Alex is fortunate enough to be found by a kind girl named Toril. She provides Alex with all the important knowledge regarding Fernland, a place to which individuals from other worlds are randomly transported. In the past, these lost souls would be guided home by a powerful Goddess. However, at the time of Alex’s arrival in Fernland, this isn’t possible. The Goddess’ magic is being subdued by the evil Overlord Clangorrah, who is attempting to gain power for himself. Consequently, the number of people from other dimensions in Fernland has been steadily increasing. As Alex’s time in Fernland progresses, he meets other displaced people. Alex joins these other lost souls in a resistance group to fight the power-hungry Clangorrah. This is Toril, a party member and the first friendly face Alex meets in Fernland. It is very likely that the plot sounds vaguely familiar here, and that’s because this game is chock-full of cliches. A perfect example of this is the Overlord, whose flimsy motivations for committing acts of evil accompany his unsettling green skin, muscular body, and not-quite-human features. To their credit, the writers did attempt to stray away from pure cliche, as the plot throws some curveballs near the end of the story. That said, even these surprises lean on tried-and-true tropes. However, Cliched or not, there is something to be said for a timeless tale of saving the world. You can tell this is an evil character just by looking at him. When I’m in the mood for a self-indulgent game, I want the mechanics to be well crafted. Fernz Gate does a decent job of implementing solid gameplay that’s admittedly uninspired. The battles are simple and turn-based, which means they sometimes get repetitive. There is also an upgrade menu to improve your weapons. It is not the most intuitive upgrade system and often felt as if I was randomly fusing weapons together, but it is acceptable. Interestingly enough, the game also includes a mini farm simulator. Players can grow fruit that increases character stats, such as speed or strength. All of these mechanics are decently executed, but they are by no means groundbreaking. In other areas, Fernz Gate utilizes fresher mechanics. The simple battle system is reinvigorated with the use of “buddies”. Players assign these buddies to members of your party and join you in battle. Specific combinations of party members and buddies unlock unique bonuses, such as increased magic damage. This kept battles entertaining because I was constantly trying out new combinations of characters. Implemented correctly, the buddy system can make battles a breeze. Fernz Gate‘s dungeon exploration is well-executed. As someone who has played a lot of JRPGs, random battles can get irritating while exploring dungeons. Fernz Gate addresses this common problem by placing Curios, in the form of purple monuments, in every dungeon. These monuments allow players to choose the rate of random encounters. I loved this feature because it let me explore dungeons quickly without running into an excessive number of enemies. As evident from the Curios mechanic, this is a game that strives to meet players’ individual needs. Upon starting a new game, players choose a difficulty setting; these range from easy to expert and can be adjusted at any time. As the difficulty increases, so do the in-game rewards. Furthermore, there is a lot of content packed into the game. This includes side quests, battle arenas, and high-level areas full of monsters. There is even an unlockable “true ending” to reward dedicated players. I may have been able to beat the main quest in 13 hours, but Fernz Gate easily contains several more hours of content. The design of the start menu makes it quite clear that this was originally a mobile game. Fernz Gate does some things right, but it also disappoints. The games most glaring issues all stem from the fact that this is clearly a mobile port. Some design and technical decisions that work on a phone do not always work on a console, including the option to buy gems to purchase in-game items. This is a mobile game standard, and it doesn’t feel right on the Switch. Likewise, the game’s mobile roots are apparent in its design. The start menu buttons look like they were intended for a touchscreen. On the Switch, they can only be selected with a controller, which is a shame because the system has touchscreen capabilities. These details hurt the overall gameplay experience. These “Get Item!” buttons would be so satisfying to physically tap using the touch screen. Beyond the port-related issues, the game also suffers from some clunky controls. Although they are solid in battle, the controls are a real issue when wandering the map. Characters move very quickly and without precision, which ends up looking very silly. This was distracting at times. One of my biggest grievances with Fernz Gate is with its stylistic choices and character design. I have always enjoyed exploring towns in JRPGs, but this was not the case in Fernz Gate. The level designs felt awkward; houses and items had strange shading and proportions. I might have been able to overlook this if the game had offered unique town designs. However, the towns all look rather similar and this eventually gets boring. The same can be said of the music. Although it never actively hindered my gameplay experience, the music was wholly forgettable. Sadly, the poor world building here makes it nearly impossible to become immersed. The disappointing level design is in stark contrast to the adorable, anime-style characters. The art is well done and charming. However, many of the characters fall back on cliches while others bear uncanny resemblances to other famous characters. This left me feeling disappointed. Some may consider this a homage to other JRPGs, but it felt like lazy and uninspired character design to me. This character with an adorable animal that lives in his ‘fro reminds me of a certain AAA JRPG. In many ways, Fernz Gate feels like the skeleton of a good JRPG. There are elements that I found quite fun. The story has a few surprising moments, the characters are lovable, and the buddy system keeps battles interesting. However, this game fails to do anything truly innovative and some features feel out of place on the Switch. If you’re gaming on a budget and absolutely need to get that JRPG fix, Fernz Gate is a decent game for $12.99. However, personally, I was rather indifferent to the whole experience it offered. Craving an RPG, but not digging this one? Personally, I enjoyed Earthlock. If sci-fi is more your thing, check out Zeno’s review of Cosmic Star Heroine. I’m always looking for JRPG recommendations, so come join our Discord and ping me @pechorin19 with some suggestions! With that, I’d like to remind our lovely readers that this site is run by passionate, Nindie-loving volunteers. Reaching out to developers, keeping a site running, writing, and editing are all time consuming. If you’d like to keep us ad-free, consider becoming a Patron or buying us a Ko-Fi.
Zviad Zviad (Georgian: ზვიად) is a Georgian masculine given name. Notable people with the name include: Zviad Endeladze (born 1966), Georgian footballer Zviad Gamsakhurdia (1939–1993), dissident, scientist, writer; the first elected post-Soviet President of the Republic of Georgia Zviad Izoria (born 1984), chess grandmaster Zviad Jeladze (born 1973), Georgian footballer Zviad Kvachantiradze (born 1965), Georgian diplomat Zviad Sturua (born 1978), Georgian association footballer Category:Georgian masculine given names es:Zviad
--- abstract: 'This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on $\Zd$. We now present an analysis of the relevant interaction functional of the supersymmetric field theory, which permits a nonperturbative analysis to be carried out in the critical dimension $d = 4$. The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. These results are essential for the analysis of the general renormalisation group step in the fifth paper in the series.' author: - 'David C. Brydges[^1] and Gordon Slade$^$' bibliography: - '../../bibdef/bib.bib' title: ' A renormalisation group method. IV. Stability analysis ' --- Introduction {#sec:ie} ============ This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method. The method has been applied to analyse the critical behaviour of the continuous-time weakly self-avoiding walk [@BBS-saw4-log; @BBS-saw4], and the $n$-component $\|\varphi\|^4$ spin model [@BBS-phi4-log], in the critical dimension $d = 4$. In both cases, logarithmic corrections to mean-field scaling are established using our method. In part I [@BS-rg-norm] of the series, we presented elements of the theory of Gaussian integration and developed norms and norm estimates for performing analysis with Gaussian integrals involving both boson and fermion fields. In part II [@BS-rg-loc], we defined and analysed a localisation operator whose purpose is to extract relevant and marginal directions in the dynamical system defined by the renormalisation group. In part III [@BBS-rg-pt], we began to apply the formalism of parts I and II to a specific supersymmetric field theory that arises as a representation of the continuous-time weakly self-avoiding walk [@BIS09; @BBS-saw4-log], by studying the flow of coupling constants in a perturbative analysis. We now prove several nonperturbative estimates for the supersymmetric field theory studied in part III. These estimates are essential inputs for our analysis of a general renormalisation group step in part V [@BS-rg-step], and therefore for the analysis of the critical behaviour of the continuous-time weakly self-avoiding walk in dimension $d = 4$ in [@BBS-saw4-log; @BBS-saw4]. The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis of part III and thereby confirm that the perturbative analysis does indeed isolate leading contributions, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. All these results are needed in our analysis of a general renormalisation group step in part V. The methods and results developed in this paper are of wider applicability, but for the sake of concreteness, and for the purposes of our specific application in [@BBS-saw4-log; @BBS-saw4], we formulate the discussion in the context of the supersymmetric field theory studied in part III. Supersymmetry is helpful: it ensures that the partition function is equal to $1$, so it need never be estimated. Several mathematically rigorous approaches to renormalisation in statistical mechanics and quantum field theory have been proposed in recent decades, e.g., the books [@BG95; @Riva91; @Salm99]. Characteristic features of the approach we develop are: (i) there is no partition of unity in field space to separate large and small fields, and (ii) fluctuation fields have finite range of dependence. The avoidance of partitions of unity is important for us because it is easier to maintain supersymmetry without them. The use of finite-range fluctuation fields bears some similarity to the wavelet program reviewed in [@Fede87], but has better translation invariance properties. An attractive feature of (ii) is that independence of Gaussian fields replaces cluster expansions. The price to be paid for avoiding partitions of unity is that norms must control the size of the basic objects in all of field space, including large fields. The goal of the present paper is to acquire this control. Our analysis has antecedents in [@Abde07; @BDH95; @MS08], though our setting includes fermions as well as bosons. A systematic development of appropriate norms is given in [@BS-rg-norm]. Part of the need for these norms is to define complete spaces in order to apply the dynamical system analysis of [@BBS-rg-flow] (discussion of past errors related to completeness can be found in [@Abde07]). The norms include a notion that we call “regulators” because they control (regulate) growth when fields are large. These are always a delicate part in this approach and important ideas that guide their choice appear in [@DH00; @Falc12]. For our field theory, the choice of regulators is less delicate because the $\phi^4$ term suppresses large fields. Another feature of our analysis is the inclusion of observable fields to permit control of correlation functions; somewhat related ideas were introduced in [@DH92]. Different methods to construct the correlations in the infinite volume have been developed in [@Falc13]. The renormalisation group can be defined directly in infinite volume, but until [@Dimo09] and [@Falc13] it was not demonstrated that the infinite volume theory defined in this way coincides with the infinite volume defined by taking limits of correlation functions and pressures defined in finite volume. Our analysis also prepares the way for results about this question for the weakly self-avoiding walk. In the remainder of Section \[sec:ie\], we give the fundamental definitions and provide an informal overview of the results of this paper. The main results are then stated precisely in Section \[sec:IE\]. Proofs are given in Sections \[app:sp\]–\[sec:ipcl\]. In Appendix \[sec:Lp\], we prove a lattice Sobolev inequality that lies at the heart of our stability estimates. Finally, Appendix \[sec:further-ie\] concerns estimates of a more specialised nature that are required for the analysis of a single renormalisation group step in part V [@BS-rg-step]. Our focus throughout the paper is on the case $d=4$. Object of study {#sec:study} --------------- We begin with several definitions needed to formulate our results. Many of these definitions are recalled from parts III and I. We begin by introducing the covariance decomposition which provides the basis for a multi-scale analysis. We then introduce the space of boson and fermion fields, and define the interaction functional $I$. We also recall the definition of the renormalised polynomial $\Vpt$ from part III, and the definitions of the norms and regulators from part I. ### Covariance decomposition {#sec:cd} Let $d \ge 4$ and let $\Lambda = \Zd/L^N\Z$ denote the discrete $d$-dimensional torus of side $L^N$, with $L>1$ fixed (large). We are interested in results which remain useful in the infinite volume limit $N \to \infty$. There are several places in this paper where $L$ must be taken large, depending on unimportant parameters such as the dimension $d$, or combinatorial constants. We do not comment explicitly on each occasion where $L$ must be taken to be large, but instead we assume throughout the paper that $L$ is large enough to satisfy each such requirement that is encountered. For $e$ in the set $\units$ of $2d$ nearest neighbours of the origin in $\Zd$, we define the finite difference operator $\nabla^e \phi_x = \phi_{x+e}-\phi_x$, and the Laplacian $\Delta_\Zd = -\frac{1}{2}\sum_{e \in \units}\nabla^{-e} \nabla^{e}$. Let $C= (-\Delta_\Lambda + m^2)^{-1}$, where $m^2>0$ is a positive parameter and $\Delta_\Lambda$ denotes the discrete Laplacian on $\Lambda$. We fix $N$ large and $m^2$ small, and wish to perform an analysis which applies uniformly in $N,m^2$. We require decompositions of the covariances $(\Delta_\Zd + m^2)^{-1}$ and $C=(-\Delta_\Lambda +m^2)^{-1}$. For the former, the massless Green function is well-defined for $d>2$ and we may consider $m^2 \ge 0$, but for the latter we must take $m^2>0$. In [@BBS-rg-pt Section \[pt-sec:Cdecomp\]], there is a detailed discussion of decompositions we use for each of these covariances, based on [@Baue13a] (see also Section \[sec:frp\] below). In particular, in [@BBS-rg-pt Section \[pt-sec:Cdecomp\]] a sequence $(C_j)_{1 \le j < \infty}$ (depending on $m^2 \ge 0$) of positive definite covariances on $\Zd$ is defined, such that $$\lbeq{ZdCj} (\Delta_\Zd + m^2)^{-1} = \sum_{j=1}^\infty C_j \quad \quad (m^2 \ge 0).$$ The covariances $C_j$ are translation invariant and have the finite-range* property $$\label{e:fin-range} C_{j;x,y} = 0 \quad \text{if \; $\|x-y\| \geq \frac{1}{2} L^j$}.$$ For $j<N$, the covariances $C_j$ can therefore be identified with covariances on $\Lambda$, and we use both interpretations. We define $$\begin{aligned} \lbeq{wjdef} w_j &= \sum_{i=1}^j C_i \quad\quad (1 \le j < \infty),\end{aligned}$$ and note that $w_j$ also obeys . There is also a covariance $C_{N,N}$ on $\Lambda$ such that $$\lbeq{NCj} C=(-\Delta_\Lambda + m^2)^{-1} = \sum_{j=1}^{N-1} C_j + C_{N,N} \quad \quad (m^2 > 0).$$ Thus the finite volume decomposition agrees with the infinite volume decomposition except for the last term in the finite volume decomposition, which is the single term that accounts for the torus. The expectation $\Ex_C$ denotes the combined bosonic-fermionic Gaussian integration on $\Ncal$, with covariance $C$, defined in [@BS-rg-norm Section \[norm-sec:Grass\]]. The integral is performed successively, using $$\lbeq{progexp} \Ex_C = \Ex_{C_N} \circ \Ex_{C_{N-1}} \theta \circ \cdots \circ \Ex_{C_1}\theta,$$ where $\theta$ defines a type of convolution and is discussed further below. ### Fields and field polynomials We study a field theory which consists of a complex boson field $\phi : \Lambda \to \C$ with its complex conjugate $\bar\phi$, a pair of conjugate fermion fields $\psi,\bar\psi$, and a constant complex observable boson field $\sigma \in \C$ with its complex conjugate $\bar\sigma$. The fermion field is given in terms of the 1-forms $d\phi_x$ by $\psi_x = \frac{1}{\sqrt{2\pi i}} d\phi_x$ and $\bar\psi_x = \frac{1}{\sqrt{2\pi i}} d\bar\phi_x$, where we fix some square root of $2\pi i$. This is the supersymmetric choice discussed in more detail in [@BS-rg-norm Sections \[norm-sec:df\]–\[norm-sec:supersymmetry\]] and used in [@BBS-rg-pt]. Let two points $\pp,\qq \in \Lambda$ be fixed. We work with an algebra $\Ncal$ which is defined in terms of a direct sum decomposition $$\label{e:Ncaldecomp} \Ncal = \Ncal^\varnothing \oplus \Ncal^a \oplus \Ncal^b \oplus \Ncal^{ab}.$$ Elements of $\Ncal^\varnothing$ are given by finite linear combinations of products of an even number of fermion fields with coefficients that are functions of the boson fields. This restriction to forms of even degree results in a commutative algebra. Elements of $\Ncal^a, \Ncal^b , \Ncal^{ab}$ are respectively given by elements of $\Ncal^\varnothing$ multiplied by $\sigma$, by $\bar\sigma$, and by $\sigma\bar\sigma$. For example, $\phi_x \bar\phi_y \psi_x \bar\psi_x \in \Ncal^\varnothing$, and $\sigma \bar\phi_x \in \Ncal^a$. There are canonical projections $\pi_\alpha: \Ncal \to \Ncal^\alpha$ for $\alpha \in \{\varnothing, a, b, ab\}$. We use the abbreviation $\pi_=1-\pi_\varnothing = \pi_a+\pi_b+\pi_{ab}$. The algebra $\Ncal$ is discussed further around [@BS-rg-loc] (there $\Ncal$ is written $\Ncal/\Ical$ but to simplify the notation we write $\Ncal$ here instead). The parameter $p_\Ncal$ which appears in its definition is a measure of the smoothness of elements of $\Ncal$ (see [@BS-rg-norm Section \[norm-sec:Ncal\]]); its precise value is unimportant and can be fixed to be larger than the degree of polynomials encountered in practice in the application of the stability bounds. Constants in estimates may depend on its value, in an unimportant way. We define the forms $$\label{e:addDelta} \tau_x = \phi_x \bar\phi_x + \psi_x \bar\psi_x, \quad\quad \tau_{\nabla \nabla,x} = \frac 12 \sum_{e \in \units} \left( (\nabla^e \phi)_x (\nabla^e \bar\phi)_x + (\nabla^e \psi)_x (\nabla^e \bar\psi)_x \right) ,$$ $$\begin{aligned} \tau_{\Delta,x} &= \frac 12 \left( (-\Delta \phi)_{x} \bar{\phi}_{y} + \phi_{x} (-\Delta \bar{\phi})_{y} + (-\Delta \psi)_{x} \bar{\psi}_{y} + \psi_{x} (-\Delta \bar{\psi})_{y} \right) .\end{aligned}$$ Let $\Qcalnabla$ denote the vector space of polynomials of the form $$\begin{gathered} V = V_{\varnothing} + V_{\pp} + V_{\qq} + V_{\pp\qq},\end{gathered}$$ where $$\begin{gathered} V_{\varnothing} = g \tau^{2} + \nu \tau + z \tau_{\Delta} + y \tau_{\nabla \nabla}, \quad V_{\pp} = \lambda_{\pp} \sigma \bar{\phi}, \quad V_{\qq} = \lambda_{\qq}\bar{\sigma} \phi, \quad V_{\pp \qq} = q_{\pp\qq} \bar{\sigma}\sigma \label{e:Vx} ,\end{gathered}$$ $$\begin{aligned} \label{e:lambda-defs} & \lambda_{\pp} = -\lambdaa \,\1_{\pp}, \quad\quad \lambda_{\qq} = -\lambdab \,\1_{\qq}, \quad\quad q_{\pp\qq} = -\frac{1}{2} (\qa\1_{\pp} + \qb\1_{\qq}) ,\end{aligned}$$ $g,\nu,y,z,\lambdaa,\lambdab,\qa,\qb \in \C$, and the indicator functions are defined by the Kronecker delta $\1_{a,x}=\delta_{a,x}$. For $X \subset \Lambda$, we write $$\label{e:VXdef} V(X)=\sum_{x\in X}V_x.$$ There is an important scale, called the coalescence scale, defined by $$\label{e:Phi-def-jc} j_{\pp \qq} = \big\lfloor \log_{L} (2 \|\pp - \qq\|) \big\rfloor .$$ We assume that $\pi_{ab}V=0$ for $j<j_{ab}$; note that if the coefficient $q$ is initially equal to zero, then under the flow [@BBS-rg-pt] it remains zero below the coalescence scale due to the assumption . The goal of our analysis is to understand the Gaussian integral $\Ex_C e^{-V(\Lambda)}$. Given a positive-definite matrix $C$ whose rows and columns are indexed by $\Lambda$, we define the Laplacian* $$\label{e:LapC} \Lcal_C = \frac 12 \Delta_{C} = \sum_{u,v \in \Lambda} C_{u,v} \left( \frac{\partial}{\partial \phi_{u}} \frac{\partial}{\partial \bar\phi_{v}} + \frac{\partial}{\partial \psi_{u}} \frac{\partial}{\partial \bar\psi_{v}} \right)$$ (see [@BS-rg-norm]). The Laplacian is intimately related to Gaussian integration. To explain this, suppose we are given an additional boson field $\xi,\bar\xi$ and an additional fermion field $\eta, \bar\eta$, with $\eta = \frac{1}{\sqrt{2\pi i}}d\xi$, $\bar\eta = \frac{1}{\sqrt{2\pi i}}d\bar\xi$, and consider the “doubled” algebra $\Ncal(\Lambdabold\sqcup \Lambdabold')$ containing the original fields and also these additional fields. We define a map $\theta : \Ncal(\Lambdabold) \to \Ncal(\Lambdabold\sqcup \Lambdabold')$ by making the replacement in an element of $\Ncal$ of $\phi$ by $\phi+\xi$, $\bar\phi$ by $\bar\phi+\bar\xi$, $\psi$ by $\psi+\eta$, and $\bar\psi$ by $\bar\psi+\bar\xi$. According to [@BS-rg-norm Proposition \[norm-prop:conv\]], for a polynomial $A$ in the fields, the Gaussian expectation with covariance $C$ can be evaluated using the Laplacian operator via $$\label{e:EWick} \Ex_C \theta A = e^{\Lcal_C} A,$$ where the fields $\xi,\bar\xi,\eta,\bar\eta$ are integrated out by $\Ex_C$, with $\phi, \bar\phi, \psi, \bar\psi$ kept fixed, and where $e^{\Lcal_C}$ is defined by its power series. ### Form of interaction {#sec:formint} In [@BBS-rg-pt Section \[pt-sec:WPjobs\]], we discussed reasons to define an interaction $$I_{j}(V,\Lambda)= e^{-V(\Lambda)} (1+ W_{j}(V,\Lambda)),$$ where $W_{j}$ is a certain non-local polynomial in the fields whose definition is recalled below. Our main object of study in this paper is a modified version of $I_{j}$ which is defined on subsets of $\Lambda$. We recall the relevant definitions from [@BBS-rg-pt]. For polynomials $V',V''$ in the fields, we define bilinear functions of $V'$ and $V''$ by $$\begin{aligned} \label{e:FCAB} F_{C}(V',V'') & = e^{\Lcal_C} \big(e^{-\Lcal_C}V'\big) \big(e^{-\Lcal_C}V'' \big) - V'V'', \\ \label{e:Fpi} F_{\pi ,C}(V',V'') &= F_{C}(V',\pi_\varnothing V'') + F_{C}(\pi_* V',V'').\end{aligned}$$ By definition, when $V'$ is expanded in $F_{C} (V',V'')$ as $V'=\pi_{\varnothing} V' + \pi_{} V'$, there are cross-terms $F_C(\pi_\varnothing V', \pi_ V'') + F(\pi_* V',\pi_\varnothing V'')$, and is obtained from by replacing these cross-terms by $2 F_{C}(\pi_{}V' , \pi_{\varnothing}V'')$. This unusual bookkeeping is appropriate (indeed necessary) in the proof of Proposition \[prop:Wbounds\]. For nonempty $X \subset \Lambda$, the space $\Ncal (X)$ is defined in [@BS-rg-norm] as consisting of elements of $\Ncal$ which depend on $\phi_x,\bar\phi_x,\psi_x,\bar\psi_x$ only with $x \in X$. Recall from [@BS-rg-loc] that we defined $F \in \Ncal_{X}$ to mean that there exists a coordinate patch $\Lambda '$ such that $F \in \Ncal (\Lambda')$ and $X \subset \Lambda'$, and we defined the condition $F \in \Ncal_X$ to guarantee that neither $X$ nor $F$ “wrap around" the torus. The operator $\LT_X : \Ncal_X \to \Vcal(X)$ is defined in [@BS-rg-loc Definition \[loc-def:LTsym\]], and the particular specification we use is that described in [@BBS-rg-pt Section \[pt-sec:loc-specs\]]. In particular, the field dimensions* are $[\phi]=[\bar\phi]=[\psi]=[\bar\psi] =\frac{d-2}{2}$, and we set $d_+ = d$ on $\Ncal^\varnothing$. On $\Ncal^{ab}$, we take $d_+=0$. When $\LT$ acts at scale $k$ (in the sense discussed in [@BBS-rg-pt Section \[pt-sec:loc-specs\]]), on $\Ncal^a$ and $\Ncal^b$ we take $d_+=[\phi]=\frac{d-2}{2}=1$ if $k<j_{\pp\qq}$, and $d_+=0$ for $k \ge j_{\pp\qq}$. For $x\in \Lambda$, with $w_j$ given by we define $$\begin{aligned} \label{e:Wwdef} W_j(V,x) &= \frac 12 (1-\LT_{x}) F_{\pi,w_j}(V_x,V(\Lambda)) \quad\quad (j<N).\end{aligned}$$ For $j<N$, the above application of $\LT_x$ is well-defined since $F_{\pi,w_j}(V_x,V(\Lambda)) \in \Ncal_x$ due to the finite-range property of $w_j$. For $X \subset \Lambda$, we then define $$\label{e:WLTF} W_j(V,X)= \sum_{x \in X} W_j(V,x).$$ By definition, $w_0=0$ and $W_0=0$. We consider the natural paving of $\Lambda$ by disjoint blocks of side length $L^j$, for $j=0,\ldots, N$. The set of all scale-$j$ blocks is denoted $\Bcal_j$, and $\Pcal_j$ denotes the set whose elements are finite unions of blocks in $\Bcal_j$. We refer to elements of $\Pcal_j$ as scale-$j$ polymers. Given a polynomial $V\in \Vcal$, and $X \subset \Lambda$, let $$\label{e:Icaldef} \Ical(V,X) = e^{-V(X)}.$$ The interaction is defined, for $B \in \Bcal_j$ and $X \in \Pcal_j$, by $$\label{e:Fsoptb} I_j(V,B) = \Ical(V,B) \left( 1+W_j(V,B) \right) , \quad \quad I_j(V,X) = \prod_{B \in \Bcal_{j}(X)} I_j(V,B).$$ Due to the finite-range property , $I_j(V,B)\in \Ncal(B^+)$, where $B^+$ denotes the union of $B$ with every block $B'$ such that $B \cup B'$ is connected. We often write $I_j(V,X) = I_j^X(V)$. We also consider the interaction defined, for $b \in \Bcal_{j-1}$ and $X \in \Pcal_{j-1}$, by $$\label{e:Itildef} \tilde I_{j}(V,b) = \Ical(V,b)(1+W_j(V,b)), \quad \quad \Itilde_j(V,X) = \prod_{b \in \Bcal_{j-1} (X)} \Itilde_j(V,b).$$ Thus $\tilde I_j$ is defined on blocks and polymers of scale $j-1$, whereas $I_j$ is defined on blocks and polymers of scale $j$. An element $F \in \Ncal$ is said to be gauge invariant if it is invariant under the gauge flow $q \mapsto e^{-2\pi i t}q$, $\bar q \mapsto e^{+2\pi i t}\bar q$; for all $q = \phi_{x} ,\psi_{x}, \sigma$; $\bar q = \bar\phi_{x} , \psib_{x}, \bar\sigma$; and $x \in \Lambda$. The basic objects we study, including $V,F,W,I,\tilde{I}$, are all gauge invariant. Also, since we assume $V_{ab}=0$ for $j<j_{ab}$, it follows that none of these basic objects has a nonzero component in $\Ncal_{ab}$ unless $j \ge j_{ab}$. ### The renormalised field polynomial {#sec:Vpt} To simplify the notation, we write $\Lcal_{j} = \Lcal_{C_{j}}$. Given $V\in \Qcalnabla$, as in [@BBS-rg-pt] we define $$\begin{aligned} \label{e:PWdef} P_{j}(V,x) &= \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V,x) + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}}V_x,e^{\Lcal_{j+1}} V(\Lambda)) \right) \quad (j+1<N),\end{aligned}$$ and we write $P_j(V,X)=\sum_{x\in X}P_j(V,x)$ for $X \subset \Lambda$. The local polynomial $\Vpt$ is defined, as in [@BBS-rg-pt], by $$\label{e:Vptdef} V_{\pt,j+1}(V,x) = e^{\Lcal_{j+1}} V_x - P_j(V,x) \quad (j+1<N) .$$ By definition, $V_{\pt,j+1}(B)$ depends on fields and their derivatives at sites in $B$, in contrast to $I_j(V,B)$ which depends on fields in the larger region $B^{+}$ because of $W_j(V,B)$. By [@BBS-rg-pt Lemma \[pt-lem:EV\]] we have $e^{\Lcal_{j+1}}V =V+ 2gC_{j+1;0,0}\tau$, so $$\lbeq{VptE} V_{\pt,j+1} = V+ 2gC_{j+1;0,0}\tau -P_j(V) \quad (j+1<N) .$$ For $j<N$, an explicit formula $V_{\pt,j} = \varphi_{\pt,j-1}$ is given in [@BBS-rg-pt Proposition \[pt-prop:Vptg\]]. In particular, $P \in \Qcal$. The definition of $\Vpt$ is motivated by the fact (shown in [@BBS-rg-pt Section \[pt-sec:WPjobs\]]) that the definitions of $W$ and $\Vpt$ cooperate to arrange that, as formal power series, $$\lbeq{fps} \Ex \theta I_j(V,\Lambda) \approx I_{j+1}(\Vpt,\Lambda) +O(V^3).$$ For $B \in\Bcal_j$, we make the abbreviation $$\label{e:Ipttildef} \Ipttil(B) = \tilde{I}_{j+1}(\Vpt,B ),$$ ### The final scale {#sec:finalscale} The above definitions have been given for scales below but not including the final scale $N$. At scale $N$, the torus consists of a single block $\Lambda \in \Bcal_N$, the periodicity of the torus becomes preponderant, the definition of $\LT_x F_{\pi,w_{N,N}}(V_x,V(\Lambda))$ breaks down due to lack of a coordinate patch, and the definitions of $W$ and $P$ in and can no longer be used. Initially this may appear problematic, since we are ultimately interested in performing the last expectation and computing $I_N$. However, any apparent difficulty is only superficial. There is only one problematic scale out of an unbounded number of scales. Moveover, the covariance $C_{N,N}$ is extremely small for large $m^2L^{2N}$ (see below), and we do take the limit $N \to \infty$ before $m^2 \downarrow 0$, so the last expectation is insignificant. Nevertheless it is necessary to make appropriate definitions of $\Vpt$ and $W$ at scale $N$. We do this in such a way that the analysis at scale $N$ differs minimally from that at previous scales. For $\Vpt$, the natural choice $V_{\pt,N}=\varphi_{\pt,N-1}$ is made in [@BBS-rg-pt Definition \[pt-def:VptZd\]]; this choice defines $V_{\pt,N}$ to be equal to what it would be if the torus side length were at a higher scale than scale $N$. In terms of this choice, we define $P_{N-1}$ so that remains valid for scale $N$, namely $$\begin{aligned} \label{e:PNdef} P_{N-1}(V) & = -V_{\pt,N}(V) + \Ex_{C_{N}}\theta V .\end{aligned}$$ There is no $P_N$, the last $P_j$ is $P_{N-1}$ since the last $\Vpt$ is $V_{\pt,N}$. Thus we have arranged the definitions at the last scale in such a way that $V_{\pt,N}$ agrees with what it would be on a torus of scale greater than $N$ (the use of $\Ex_{C_N}$ rather than $\Ex_{C_{N,N}}$ is intentional and for this reason). For $W_N$, our choice is inspired by a key identity obeyed by $W_j$ for $j<N$, proved in Lemma \[lem:EW\]. The identity implies in particular that $$\begin{aligned} W_{j} (V,x) &= e^{\Lcal_j} W_{j-1} (e^{-\Lcal_j}V,x) - P_{j-1}(e^{-\Lcal_j}V,x) + \frac{1}{2} F_{\pi,C_j }( V_x,V(\Lambda)) \quad (j<N) .\end{aligned}$$ The above identity is instrumental in the proof that the perturbative analysis of [@BBS-rg-pt] is accurate beyond formal power series, and thus plays a fundamental role. We define $W_N$ to maintain this identity. Thus, with $P_{N-1}$ given by , we define $$\begin{aligned} \label{e:WNdef} W_{N}(V,x) & = e^{\Lcal_{N,N}} W_{N-1}(e^{-\Lcal_{N,N}}V,x) -P_{N-1}(e^{-\Lcal_{N,N}}V,x) + \frac 12 F_{\pi,C_{N,N}}(V_x,V(\Lambda)) .\end{aligned}$$ ### Norms and field regulators {#sec:reg} Our estimates are typically expressed in terms of the $T_\phi$ semi-norm and two important functions of $\phi$ that we refer to as field regulators. We now recall the relevant definitions. ### The $T_\phi$ semi-norm {#the-t_phi-semi-norm .unnumbered} We make heavy use of the $\Phi_j(\h_j)$ norm on test functions and the $T_{\phi,j}(\h_j)$ semi-norm on $\Ncal$. The definition of the $\Phi_j(\h_j)$ norm on test functions is given in [@BS-rg-norm Example \[norm-ex:h\]] in terms of a parameter $p_\Phi \ge d+1-\frac{d-2}{2}=\frac{d+4}{2}$ (consistent with the requirement above the statement of [@BS-rg-loc Proposition \[loc-prop:LTKbound\]]), and here we take $R=L^j$ in [@BS-rg-norm Example \[norm-ex:h\]] where $j$ is the scale. The value of $p_\Phi$ is fixed but unimportant, and constants in estimates may depend on it. The space $\Phi(\h)$ consists of test functions $g : \vec\Lambdabold^* \to \C$. The definition of the norm requires the specification of its “sheets” and the values of the components of $\h_j$ for each sheet (particular choices are made in Section \[sec:hex\] below). We assume that in the definition of the norm there are sheets for each of the fields $\phi,\bar\phi,\psi,\bar\psi,\sigma,\bar\sigma$. The boson and fermion fields have a common component of $\h_j$, and we sometimes abuse notation by writing $\h_j$ for this particular component value. Also, the fields $\sigma,\bar\sigma$ have a common value $\h_{\sigma,j}$. The $T_\phi(\h)$ semi-norm is defined in [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], and provides a family of semi-norms indexed by the vector $\h$. We often keep $\h$ as a parameter in our results, as our applications ultimately use more than one choice. Properties of the $T_\phi$ semi-norm are derived in [@BS-rg-norm]; prominent among them is the product property of [@BS-rg-norm Proposition \[norm-prop:prod\]] which asserts that $\\|FG\\|_{T_\phi} \le \\|F\\|_{T_\phi}\\|G\\|_{T_\phi}$ for all $F,G \in \Ncal$. ### Fluctuation-field regulator {#sec:ffreg .unnumbered} A special case of the $\Phi(\h)$ norm is obtained by regarding the boson field as a test function: given $\h_j>0$ its $\Phi_j=\Phi_j(\h_j)$ norm is \_[\_j(\_j)]{} = \_j\^[-1]{} \_[x]{} \_[\|\|\_1 p\_]{} L\^[j\|\|\_1]{} \|\^ \_x\|. The estimates given in [@BBS-rg-pt Proposition \[pt-prop:Cdecomp\]] (see [@BBS-rg-pt]) for the covariance decomposition show, in particular, that $$\label{e:scaling-estimate} \|\nabla_x^\alpha \nabla_y^\beta C_{j;x,y}\| \leq cL^{-(j-1)(2[\phi]+(\|\alpha\|_1+\|\beta\|_1))}.$$ with $[\phi]$ the field dimension $$[\phi]=\frac{d-2}{2}$$ and where $c$ is independent of $j,L$ and $m^2\in[0,\delta]$ for $j<N$, while in the special case $C_j=C_{N,N}$, $c$ is independent of $N,L,m^2$ as long as $m^2 \in [\varepsilon L^{-2(N-1)},\delta]$ with the constant $c$ now depending on $\varepsilon>0$. This suggests that under the expectation $\Ex_{C_j}$, $\|\nabla^{\alpha} \phi_x\|$ is typically $O(L^{-(j-1)([\phi]+(\|\alpha\|_1))})$. We choose a value $\ell_j$ for $\h_j$ which makes the norm $\\|\phi\\|_{\Phi_j(\ell_j)}$ be small for typical $\phi$, i.e., we choose for $\h_j$ the value $$\lbeq{elldef} \ell_j = \ell_0 L^{-j[\phi]},$$ with an $L$-dependent (large) constant $\ell_0$ whose value gets fixed at below. As in [@BS-rg-norm (\[norm-e:PhiXdef\])], for $X \subset \Lambda$ we define a local norm of the boson field $\phi$ by $$\begin{aligned} \label{e:PhiXdef} \\|\phi\\|_{\Phi_j(X)} &= \inf \{ \\|\phi -f\\|_{\Phi_j} : \text{$f \in \C^\Lambda$ such that $f_{x} = 0$ $\forall x\in X$}\}.\end{aligned}$$ This definition localises the norm to $X$ by minimising over all extensions to the complement of $X$. A small set is defined to be a connected polymer $X \in \Pcal_j$ consisting of at most $2^d$ blocks (the specific number $2^d$ plays a role only in the combinatorial geometry of [@BS-rg-step Section \[step-sec:gl\]] and it is only important in this paper that it be a finite constant independent of $L$). The set of small sets is denoted $\Scal_j \subset \Pcal_j$. The small set neighbourhood of $X \subset \Lambda $ is the enlargement of $X$ defined by $$\label{e:ssn} X^{\Box} = \bigcup_{Y\in \Scal_{j}:X\cap Y \not =\varnothing } Y.$$ Given $X \subset \Lambda$ and $\phi \in \C^{\Lambda}$, we recall from [@BS-rg-norm Definition \[norm-def:ffregulator\]] that the fluctuation-field regulator $G_j$ is defined by $$\begin{aligned} \label{e:GPhidef} G_j(X,\phi) = \prod_{x \in X} \exp \left(\|B_{x}\|^{-1}\\|\phi\\|_{\Phi_j (B_{x}^\Box,\ell_j )}^2 \right) ,\end{aligned}$$ where $B_{x}\in \Bcal_j$ is the unique block that contains $x$, and hence $\|B_x\| = L^{dj}$. ### Large-field regulator {#sec:lfr .unnumbered} For $j<N$ (and $L$ large), and for $B \in \Bcal_j$, the diameter of $B^\Box$ is less than the period of the torus. We can therefore identify $B^\Box$ with a subset of $\Zd$ and use this identification to define polynomial functions from $B^\Box$ to $\C$. More generally, for $X$ with diameter less than the period of the torus, we define $$\label{e:Phipoltildef} \Phipoltil (X) = \left\{ f \in \C^{\Lambda} \mid \text{$f$ restricted to $X$ is a linear polynomial }\right\}.$$ Then, for $\phi \in \C^{\Lambda}$, we define the semi-norm $$\label{e:Phitilnorm} \\| \phi \\|_{\tilde{\Phi} (X)} = \inf \{ \\| \phi -f\\|_{\Phi} : f \in \Phipoltil (X) \}.$$ We recall from [@BS-rg-norm Definition \[norm-def:regulator\]] that the large-field regulator $\tilde G_j$ is defined by $$\begin{aligned} \label{e:9Gdef} \tilde G_j (X,\phi) = \prod_{x \in X} \exp \left( \frac 12 \|B_{x}\|^{-1}\\|\phi\\|_{\tilde\Phi_j (B_{x}^\Box,\ell_j)}^2 \right) .\end{aligned}$$ The definition is only used for $j<N$, since the norm on its right-hand side is not defined at the final scale $j=N$. Since $\\| \phi \\|_{\tilde{\Phi} (B^\Box)} \le \\| \phi \\|_{\Phi (B^\Box)}$ by definition, $\tilde G_j(X,\phi) \le G_j(X,\phi)^{1/2}$. The $\frac 12$ in the exponent of is a convenience that was used in [@BS-rg-norm Proposition \[norm-prop:KKK\]]. The role of $\tilde G_j$ is discussed in Section \[sec:lfp\] below. ### Regulator norms {#regulator-norms .unnumbered} The two regulators lead us to the following definition. \[def:Gnorms\] Norms on $\Ncal (X^{\Box})$ are defined, for $F \in \Ncal (X^{\Box})$ and $\Gtilp \in (0,1]$, by $$\begin{aligned} \label{e:Gnormdef1} \\| F\\|_{G_j} &= \sup_{\phi \in \C^\Lambda} \frac{\\|F\\|_{T_{\phi,j}}}{G_{j}(X,\phi)} \quad j \le N, \\ \label{e:Gnormdef2} \\|F\\|_{\tilde G_j^{\Gtilp}} &= \sup_{\phi \in \C^\Lambda} \frac{\\|F \\|_{T_{\phi,j}}}{\tilde{G}^{\Gtilp}_{j}(X,\phi)} \quad j<N.\end{aligned}$$ The norms depend on the choice of $\h_j$ used in the $T_{\phi,j}(\h_j)$ semi-norm on the right-hand sides. We write $\\|F\\|_j$ for the left-hand sides of – in statements that apply to both the $G$ and $\tilde G$ norms. Note that the norm $\\| F\\|_{G_j}$ is defined for all scales $j\le N$ whereas we $\\| F\\|_{\tilde G_j}$ is undefined at the last scale. At scale $N$, statements about the norm $\\|F\\|_j$ are to be understood as applying only to the $G$ norm. A fundamental property of the norms – is that each obeys the product property $$\label{e:norm-fac} \\|F G \\|_j \le \\|F \\|_j \\|G \\|_j \qquad \text{when $F\in \Ncal(X), G \in \Ncal(Y)$ for \emph{disjoint} $X,Y\in \Pcal_{j}$}.$$ This is an immediate consequence of the above mentioned product property which states that $\\|FG\\|_{T_\phi} \leq \\|F\\|_{T_\phi}\\|G\\|_{T_\phi}$ for any $F,G \in \Ncal$, together with the fact that by definition $G_j(X\cup Y,\phi)=G_j(X,\phi)G_j(Y,\phi)$ for disjoint $X,Y$, and similarly for $\tilde G_j$. Overview of results ------------------- Our goal in this paper is to obtain a thorough understanding of the interaction functional $I =I_{j}$. The main results are stated in Section \[sec:IE\], with proofs deferred to Sections \[app:sp\]–\[sec:ipcl\]. The results include proof of stability bounds for $I$, estimates on Gaussian expectations involving both boson and fermion fields, estimates verifying the accuracy of the perturbative calculations in [@BBS-rg-pt], and proof of the crucial contraction property needed to control irrelevant directions in the flow of the renormalisation group. These all play a role in the analysis of a single renormalisation group step in [@BS-rg-step]. Before making precise statements in Section \[sec:IE\], in this section we provide an informal overview of and motivation for the results. ### Stability, expectation and the large-field problem {#sec:lfp} In Section \[sec:stab\], we state a series of stability estimates. In particular, Proposition \[prop:Iupper\] provides the bound $$\lbeq{intro-Ibd} \\|I_j(V,B)F(B)\\|_{T_\phi(\ell_j)} \le 2 \\|F(B)\\|_{T_0(\ell_j)}G_j(B,\phi)$$ for $B \in \Bcal_j$, and for a polynomial $F(B)$ in the fields in $B$ of degree at most the parameter $p_\Ncal$ in the definition of the space $\Ncal$, under suitable hypotheses expressing a smallness condition on the coupling constants in $V$. Since $G_j(B,\phi)= \exp[\\|\phi\\|_{\Phi(B^\Box, \ell_j)}^2]$, provides information on the growth of the left-hand side for large fields $\phi$. This estimate does not take advantage of the quartic decay provided by $e^{-g\tau^2}$ to compensate for the quadratic part $e^{-\nu\tau}$ in $e^{-V}$ (with $\nu$ possibly negative). This is reflected by the quadratic growth in the exponent on the right-hand side of . The renormalisation group method is based on iterated expectation to progressively take into account fluctuations on increasingly larger scales. One difficulty with is that it degenerates under expectation and change of scale, as we discuss next. These ideas play a role in the proof of Proposition \[prop:ip\], which is our main estimate on Gaussian expectation. We make the abbreviation $\Ex_j = \Ex_{C_j}$ for the Gaussian expectation with covariance $C_j$. Since the expectation involves both boson and fermion fields (see [@BIS09; @BS-rg-norm]), it would more accurately be termed “super-expectation” but we use the term “expectation” for brevity. It is shown in [@BS-rg-norm Proposition \[norm-prop:EK\]], that for any $K \in \Ncal$, $$\lbeq{intro-EI00} \\|\Ex_{j+1}\theta K\\|_{T_\phi(\h_j)} \le \Ex_{j+1}\\|K\\|_{T_{\phi\sqcup \xi}(\h_j \sqcup \ell_j)}.$$ In more detail, in [@BS-rg-norm Proposition \[norm-prop:EK\]] we choose $w=\h_j$ and $w'=\ell_j$, and the hypothesis $\\|C_{j+1}\\|_{\Phi_{j+1}(\ell_{j+1})} \le 1$ is verified at below. The integrand on the right-hand side of is a function only of the boson field, so the super-expectation reduces to a standard Gaussian expectation with covariance $C_{j+1}$ (see [@BS-rg-norm Section \[norm-sec:cbf\]]). The fermion field ceases to play a significant role in the analysis once this inequality has been applied, and this is a beneficial aspect of our method. By – and , and by the inequality $\\|\phi+\xi\\|^2 \le 2(\\|\phi\\|^2+\\|\xi\\|^2)$, $$\lbeq{intro-EI0} \\|\Ex_{j+1}\theta I_j(V,B)\\|_{T_\phi(\ell_j)} \le \Ex_{j+1}\\|I_j(V,B)\\|_{T_{\phi\sqcup \xi}(\ell_j\sqcup \ell_j)} \le 2 G_j(B,\phi)^2 \Ex_{j+1} G_j(B,\xi)^2.$$ According to [@BS-rg-norm Proposition \[norm-prop:EG2\]], $ \Ex_{j+1} G_j(B,\xi)^2 \le 2$. Therefore, $$\lbeq{intro-EI1} \\|\Ex_{j+1}\theta I_j(V,B)\\|_{T_\phi(\ell_j)} \le 4 G_j(B,\phi)^2.$$ The left-hand side can only become smaller when the semi-norm is changed from scale $j$ to scale $j+1$ (this useful monotonicity property is proved in Lemma \[lem:Imono\] below). To see the effect of a change of scale on the right-hand side, consider the particular case $\phi_x = a$ for all $x$, where $a$ is a constant. In this case, by definition, $$\begin{aligned} L^{-dj}\\|\phi\\|^2_{\Phi_j(B_{x,j}^\Box, \ell_j)} &= L^{-dj} \ell_j^{-2} a^2 = L^{2} L^{-d (j+1)} \ell_{j+1}^{-2} \, a^2 = L^{2} L^{-d (j+1)} \\|\phi\\|^2_{\Phi_{j+1}(B_{x,j}^\Box, \ell_{j+1})} \nnb & = L^{2} L^{-d(j+1)} \\|\phi\\|^2_{\Phi_{j+1}(B_{x,j+1}^\Box, \ell_{j+1})} , \lbeq{martGfail}\end{aligned}$$ so for this case $G_{j}(B,a)=G_{j+1}^{L^2}(B,a)$. Thus the estimate after expectation and change of scale is substantially worse than (it is the growth in $\phi$ that is problematic, the constant $4$ in is not). It is in this way that the so-called large-field problem enters our analysis. We postpone the problem by setting $\phi=0$, so that the regulator plays no role in . With $\phi=0$, becomes $$\lbeq{intro-EI0a} \\|\Ex_{j+1}\theta I_j(V,B)\\|_{T_0(\ell_j)} \le \Ex_{j+1}\\|I_j(V,B)\\|_{T_{0\sqcup \xi}(\ell_j\sqcup \ell_j)} \le 4 .$$ From this, we see that control of $I_j$ is needed for all field values in order to estimate the expectation of the fluctuation field $\xi$, even when $\phi=0$. Thus we are able to obtain a useful estimate in the $T_0$ semi-norm at scale $j+1$, but this is not sufficient to be able to iterate these estimates as the scale advances. To deal with the large-field problem, we do not perform a separate analysis on regions of space where the field is large and where it is small, as has been done in other renormalisation group methods, e.g., [@Bala82; @Dimo13; @GK85; @GK86]. Instead, we take advantage of the factor $e^{-g\sum_{x\in B}\|\phi_x\|^4}$ in $I(B)$ and exploit it to capture the notion that a typical field should roughly have size $g^{-1/4}L^{-jd/4}$. For this, we need information about the size of $g$. Our ansatz is that at scale $j$, $g$ is close in size to $\gbar_j$, which is defined by the recursion $$\label{e:gbardef} \gbar_{j+1} = \gbar_j - \beta_j \gbar_j^2$$ of [@BBS-rg-pt], with a fixed initial condition $\gbar_0$, and with $\beta_j$ given in terms of the covariance $w_j$ of by $$\beta_j = 8\sum_{x \in \Lambda}(w_{j+1;0,x}^{2}-w_{j;0,x}^{2}).$$ The sequence $\beta_j$ is closely related to the bubble diagram $\sum_{x \in \Zd} [(-\Delta_{\Zd}^{-1})_{0x}]^2$, which diverges for $d=4$ but converges for $d>4$ since the inverse Laplacian is asymptotically a multiple of $\|x\|^{-(d-2)}$. By [@BBS-rg-pt Lemma \[pt-lem:betalim\]], $\beta_j \to 0$ for $d>4$ whereas $\beta_j \to \pi^{-2}\log L$ for $d=4$. Also, by choosing $\gbar_0$ to be sufficiently small, it follows that $\gbar_j$ is uniformly small. In the present paper, our focus is on the advancement of one scale to the next, rather than on all scales simultaneously. Because of this, and to provide flexibility, rather than using $\gbar_j$, we introduce a small positive $\ggen_j$ and consider $g$ at scale $j$ to be close to $\ggen_j$. We do not assume that $\ggen_j$ is given by (a different but closely related choice of $\ggen$ is used in [@BBS-saw4-log]), but we do assume that $\ggen_j$ is uniformly small for all $j$, and that we are free to choose how small it is depending on $L$. Thus we introduce $h_j \propto \ggen_j^{-1/4}L^{-jd/4}$ and seek estimates in terms of the $T_\phi(h_j)$ semi-norm. Note that for $d=4$, $h_j$ is larger than $\ell_j$ by a factor $\ggen_j^{-1/4}$. We employ the $T_\phi(h_j)$ semi-norm in conjunction with the large-field regulator $\tilde G_j$. An essential property of $\tilde G_j $ (used in the proofs of Propositions \[prop:Istab\]–\[prop:Ianalytic1:5\] and \[prop:ip\]–\[prop:cl\] below) is given in the following lemma. We apply Lemma \[lem:mart\] with specific choices of $p$, and do not thereby lose control of the size of $L$. \[lem:mart\] Let $X \subset \Lambda$. For any fixed $p >0$ (no matter how large), if $L$ is large enough depending on $p$, then for all $j+1<N$, $$\label{e:mart} \tilde{G}_{j}(X, \phi)^{p} \le \tilde{G}_{j+1}(X, \phi).$$ By definition of the regulator in , it suffices to prove that $$\lbeq{martwant} pL^{-dj}\\|\phi\\|^2_{\tilde\Phi_j(B_{j,x}^\Box,\ell_j)} \le L^{-(j+1)d} \\|\phi\\|^2_{\tilde\Phi_{j+1}(B_{j+1,x}^\Box,\ell_{j+1})}.$$ Let $d_{+} = [\phi]+1 = \frac{d-2}{2} + 1 = \frac d2$. By the definition of dimension of a polynomial given in [@BS-rg-loc Section \[loc-sec:oploc\]], a linear polynomial has dimension $ [\phi]+1 = d_+$. It is a consequence of [@BS-rg-loc Lemma \[loc-lem:phij\]], with $d_+'= d_{+}+1 = \frac{d}{2} + 1$, that $$\begin{aligned} \label{e:phij-pre} \\|\phi\\|_{\tilde{\Phi}_{j} (B_{j,x}^\Box,\ell_j)} & \le c L^{-d/2 - 1} \\|\phi\\|_{\tilde{\Phi}_{j+1} (B_{j,x}^\Box,\ell_{j+1})}.\end{aligned}$$ Therefore, since the semi-norm is non-decreasing in $X$ by definition, $$\begin{aligned} \\|\phi\\|^2_{\tilde\Phi_j(B_{j,x}^\Box,\ell_j)} &\le c^2 L^{-d-2} \\|\phi\\|^2_{\tilde\Phi_{j+1}(B_{j+1,x}^\Box,\ell_{j+1})} , \label{e:tilnormrescale}\end{aligned}$$ from which follows when $L$ is large enough that $pc^{2} L^{-2} \le 1$. The inequality does not hold for the regulator $G$: we have concluded from that for a constant field we have $G_j=G_{j+1}^{L^2}$. In contrast, the norm in $\tilde G$ scales down, because it does not examine the constant and linear parts of $\phi$. By the use of a lattice Sobolev inequality (proved in Appendix \[sec:Lp\]), we take advantage of the decay in $e^{-g\tau^2}$ to cancel the exponential quadratic $\\|\phi\\|_\Phi^2$ at the cost of an exponential of $\\|\phi\\|_{\tilde \Phi}^2$. By pursuing this strategy, we prove in Proposition \[prop:Iupper\] below that for $F(B)$ as in , $$\lbeq{intro-Ibdh} \\|I_j(V,B)F(B)\\|_{T_\phi(h_j)} \le 2 \\|F(B)\\|_{T_0(h_j)}\tilde G_j(B,\phi) ,$$ and now with this leads as above to $$\lbeq{intro-EIh} \\|\Ex_{j+1}\theta I_j(V,B)F(B)\\|_{T_\phi(h_j)} \le 4 \\|F(B)\\|_{T_0(h_j)} \tilde G_j(B,\phi)^2 \le 4 \\|F(B)\\|_{T_0(h_j)} \tilde G_{j+1}^{\Gtilp}(B,\phi),$$ for any fixed choice of $\Gtilp\in (0,1]$, e.g., $\Gtilp = 1/2$, with $L$ large depending on $\Gtilp$. Thus the $h$ bound reproduces itself after expectation and change of scale. In fact, our ability to choose $\Gtilp <1$ shows that the $h$ bound improves. On the other hand, the $\ell$ bound degrades after expectation and change of scale. However, together the scale-$(j+1)$ $\ell$ and $h$ bounds can be combined using [@BS-rg-norm Proposition \[norm-prop:KKK\]] to infer a $G_{j+1}$ bound for all $\phi$ from the $T_{0}(\ell_{j+1})$ and $\tilde G_{j+1}$ bounds. In this way it is possible to obtain bounds at scale $j+1$ of the same form as the bounds at scale $j$. We postpone the application of [@BS-rg-norm Proposition \[norm-prop:KKK\]] to the proof of [@BS-rg-step Theorem \[step-thm:mr\]]. With this motivation, throughout this paper we prove estimates in terms of the two norm pairs $$\label{e:np1} \\|F\\|_j = \\|F\\|_{G_j(\ell_j)} \quad \text{and} \quad \\|F\\|_{j+1} = \\|F\\|_{T_{0,j+1}(\ell_{j+1})},$$ and $$\label{e:np2} \\|F\\|_j = \\|F\\|_{\tilde{G}_j(h_j)} \quad \text{and} \quad \\|F\\|_{j+1} = \\|F\\|_{\tilde{G}_{j+1}^{\Gtilp}(h_{j+1})},$$ i.e., estimates on $\\|F\\|_{j+1}$ are expressed in terms of $\\|F\\|_j$ for each of the pairs and . We distinguish the cases and by writing $\h_j=\ell_j$ to indicate , and $\h_j=h_j$ to indicate . The values of $\h_\sigma$ in the $T_\phi$ norms, for sheets corresponding to the observable fields $\sigma,\bar\sigma$, are specified in below (see [@BS-rg-loc] for the $T_\phi$ norm with observables). Iteration of estimates using is possible without the accompaniment of . However, estimates in terms of the $\tilde G(h)$ norm are insufficient on their own to make estimates on remainder terms in the flow of coupling constants, and without such estimates we are unable to study critical behaviour. In the flow of coupling constants determined in [@BS-rg-step], the interaction polynomial $V_{j+1}$ at scale $j+1$ is expressed in terms of $V_{\pt,j+1}(V_j)$ plus a non-perturbative remainder $\rho_{j+1}\in \Qcal$ whose coupling constants must be shown to be third order in $\ggen_j$. Our control over these coupling constants is obtained via the $T_0$ semi-norm. To illustrate this, consider the case of $d=4$, and suppose that the $\tau^2$ term in $\rho_{j+1}$ were simply $\ggen_j^3 \tau^2$. The calculation of the $T_\phi$ semi-norm of $\tau^2$ is straightforward, and a small extension of [@BS-rg-norm Proposition \[norm-prop:taunorm\]] gives $\\|\ggen_j^3\tau^2_x\\|_{T_0(\h_j)} \asymp \ggen_j^3 \h_j^4$ (the symbol $\asymp$ means upper and lower bounds with different constants). Focussing only on the power of $\ggen_j$, the choice $\h_j =h_j$ gives an overall power $\ggen_j^3 ( \ggen_j^{-1/4})^4= \ggen_j^2$, which is second order rather than the desired third order. For this reason, estimates in terms of norms with $\h=h$ are insufficient. On the other hand, with the $T_0(\ell)$ semi-norm there is no loss of powers of $\ggen_j$ arising from $\\|\tau^2_x\\|_{T_0(\ell_j)} \asymp \ell_j^4$, and the $T_0(\ell)$ semi-norm indeed identifies $\ggen_j^3\tau^2$ as a third-order term. \[rk:h++\] In the $j+1$ members of the norm pairs –, the parameter $\h_{j+1}$ may be replaced by $\h_{++}=c\h_{j+1} >\h_{j+1}$ for any fixed $c>1$. More precisely, in Definition \[def:Gnorms\], with $j$ replaced by $j+1$, $\h_{j+1}$ becomes replaced by $\h_{++}$ in the $T_{\phi,j+1}(\h_{j+1})$ norm. Our convention is to leave $\ell_{j+1}$ in the regulator unchanged; it does not become $\ell_{++}$ in the replacement of $\h_{j+1}$ by $\h_j$. All our results remain valid with $\h_{++}$ replacing $\h_{j+1}$, with changes in constants whose precise values are without significance and indeed are not specified in our results. To avoid further elaboration of our notation, we do not make the role of $\h_{++}$ explicit in the rest of the paper, apart from one additional comment below . \[rk:scaleNnorm\] The advancement of estimates to the final scale $N$ is special, since the $\tilde G$ norm is undefined at that scale. However, the work of the $\tilde G$ norm is complete by scale $N$, as there is no further difficulty concerning degradation of estimates since the scale no longer advances. Thus, at scale $N$, we can consider the norm to be the $G$ norm with regulator $G$ replaced by a suitable large power of $G_{N-1}$, such as $G_{N-1}^{10}$ (using $G_{N-1}^2$ would be sufficient for but higher powers are required later). Then a scale-$N$ estimate $\\|F\\|_N \le C$ is interpreted as stating that $\\|F\\|_{T_\phi,N} \le C G_{N-1}(\Lambda,\phi)^{10}$. In some applications, the $T_0$ estimate obtained by setting $\phi=0$ is sufficient. More generally, the estimate states that $\\|F\\|_{T_\phi,N} \le C\exp[O(\\|\phi\\|^2)]$ (with $L$-dependent constant in the exponent), and this provides additional information concerning the growth in $\phi$. We are not always careful to distinguish the special nature of $\\|\cdot\\|_N$, but inspection reveals that our conclusions indeed hold with this choice. ### Accuracy of perturbative analysis One of our main results is a proof of a version of that goes beyond formal power series. The version we prove is a local one, which permits accurate estimates with errors bounded uniformly in the volume. However, the local analysis comes with a cost, which is that an explicit second-order leading term arises along with the third-order error. For simplicity, for the present discussion we set $\lambdaa=\lambdab=\qa=\qb=0$ so that observables play no role. In this setting, a particular case of what we prove is that for $b \in \Bcal_j$ and $B \in \Bcal_{j+1}$, $$\lbeq{pt-eg} \Itilde_\pt^{B\setminus b} \Ex_{j+1} \theta I(V,b) \approx \Ipttil^B \Big( 1 - \frac 12 \Ex_{j+1} \theta (V_j(b);V_j(\Lambda \setminus b) \Big) ,$$ where the truncated expectation (or covariance) is defined by $$\label{e:trun-exp-eg} \Ex_C (A; B) = \Ex_C(AB) - (\Ex_CA)(\Ex_CB).$$ We prove precise versions of with third-order error estimates, for both norm pairs –. For example, in the proof of Proposition \[prop:h\], for the norm pair we show that $$\label{e:want2-eg} \\| \Itilde_\pt^{B\setminus b}\Ex_{j+1} (\theta I(V,b) - \Ipttil(b)) + \Itilde_\pt^{B} \frac 12 \Ex_{j+1} \theta (V_j(b);V_j(\Lambda \setminus b) \\|_{T_{0,j+1}(\ell_{j+1})} \le O(\ggen_j^3).$$ The bound on the right-hand side is third-order as desired, but there is a second-order leading term on the left-hand side. Its origin can be seen from a small extension of the argument in [@BBS-rg-pt Section \[pt-sec:WPjobs\]], as follows. Proceeding as in [@BBS-rg-pt Section \[pt-sec:WPjobs\]], formally, to a third-order error, we obtain $$\begin{aligned} \Ex \theta I(b) & \approx e^{-\Ex \theta V(b)} \left[ 1 + \Ex \theta W(b) + \frac 12 \Ex \theta (V(b);V(b)) \right].\end{aligned}$$ The bilinear term $W(b)$ involves $V(b)$ in one argument and $V(\Lambda)$ in the other, and its partner to make the argument of [@BBS-rg-pt Section \[pt-sec:WPjobs\]] apply here has to be $\frac 12 \Ex \theta (V(b);V(\Lambda))$ rather than $ \frac 12 \Ex \theta (V(b);V(b))$. Thus we rewrite the right-hand side as $$\begin{aligned} \Ex \theta I(b) & \approx e^{-\Ex \theta V(b)} \left[ 1 + \Ex \theta W(b) + \frac 12 \Ex \theta (V(b);V(\Lambda)) - \frac 12 \Ex \theta (V(b;V(\Lambda\setminus b)) \right].\end{aligned}$$ After multiplication by $\Itilde_\pt^{B\setminus b}$, the extra term produces $-\Itilde_\pt^{B}\frac 12 \Ex \theta (V(b;V(\Lambda\setminus b))$, which is what appears in . In Proposition \[prop:hldg\], we prove that the leading term in the perturbative estimates we require is indeed second order. This is a straightforward consequence of the stability bounds. The fact that the remainder beyond the leading term is third order is proved in Proposition \[prop:h\], which is more substantial, and is our full implementation of the formal arguments of [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. For the reasons discussed in Section \[sec:lfp\], we need versions of these two propositions for both norm pairs. ### Loc and the crucial contraction {#sec:cc} The renormalisation group creates an infinite-dimensional dynamical system, which has a finite number of relevant or marginal directions and infinitely many irrelevant directions. A crucial aspect of our analysis is to employ the operator $\LT$ defined and developed in [@BS-rg-loc] to extract the relevant and marginal parts of a functional of the fields, with $(1-\LT)$ projecting onto the irrelevant parts. The specific result we prove in this respect is Proposition \[prop:cl\]. A special case of Proposition \[prop:cl\] is as follows. Let $X$ be a small set as defined above . Let $U$ be the smallest collection of blocks in $\Bcal_{j+1}$ which contains $X$ ($U$ is the closure $U = \overline X$). Let $F(X) \in \Ncal(X^\Box)$ be such that $\LT_X F =0$; this should be interpreted as a statement that $F(X)$ is irrelevant for the renormalisation group. We prove in Proposition \[prop:cl\] that, under appropriate assumption on $V$, $$\begin{aligned} \label{e:cl-eg} \\|\tilde I^{U\setminus X} \Ex \theta \left( \Itilde^{X}F (X) \right) \\|_{j+1} & \le {\rm const}\, L^{-d-1} \\|F(X)\\|_{j} ,\end{aligned}$$ where the pair of norms is given by either choice of or . The number of distinct $X$ with closure $U$ produces an entropic factor of order $L^d$, and hence $$\begin{aligned} \label{e:cl-sum-eg} \sum_{X \in \Scal_j: \overline X =U}\\|\tilde I^{U\setminus X} \Ex \theta \left( \Itilde^{X}F (X) \right) \\|_{j+1} & \le {\rm const} \, L^{-1} \\|F(X)\\|_{j} .\end{aligned}$$ Thus a contractive factor $L^{-1}$ remains also after summation. This plays a crucial role in [@BS-rg-step] in showing that the coordinate of the dynamical system that is meant to represent the irrelevant directions is in actual fact contractive. Parameters and domains ---------------------- In this section, we reformulate estimates on the covariance decomposition that are stated in [@BBS-rg-pt], we specify the parameters that define the $T_\phi$ norms we use, we define the small parameters $\epV,\epdV$ that permeate our analysis, and we discuss the domains for $V$ which ensure stability of $I$. ### Estimate on covariance decomposition {#sec:frp} We now discuss the size of the covariances arising in the covariance decomposition, in more detail. Recall from the definition $\ell_j = \ell_0 L^{-j[\phi]}$. We may regard a covariance $C$ as a test function depending on two arguments $x,y$, and with this identification its $\Phi_j(\ell_j)$ norm is $$\begin{aligned} & \label{e:Phinorm} \\|C\\|_{\Phi_{j}(\ell_j)} = \ell_j^{-2} \sup_{x,y\in \Lambda} \; \sup_{\|\alpha_{1}\|_1 + \|\alpha_{2}\|_1 \le p_\Phi} L^{(\|\alpha_{1}\|_1+ \|\alpha_{2}\|_1)j} \|\nabla_x^{\alpha_1} \nabla_y^{\alpha_2} C_{x,y}\| ,\end{aligned}$$ where $\alpha_i$ is a multi-index. The norm of the covariance $C_j$ in the covariance decomposition can be estimated using an improved version of from [@Baue13a; @BBS-rg-pt]. For this, given $\Omega >1$ we define the $\Omega$-scale $\jm$ by $$\lbeq{mass-scale} \jm = \inf \{ k \geq 0: \|\beta_j\| \leq \Omega^{-(j-k)} \\|\beta\\|_\infty \text{ for all $j$} \} ,$$ and we set $$\lbeq{chidef} \chi_j = \Omega^{-(j-\jm)_+}.$$ The $\Omega$-scale indicates a scale at which the mass term in the covariance starts to play a dominant role in dramatically reducing the size of the covariance; further discussion of this point can be found in [@BBS-rg-pt Section \[pt-sec:Greekpfs\]]. It is within a constant of the value $j_m$ defined by $j_m=\lfloor \log_{L^2}m^{-2}\rfloor$, as shown in [@BBS-rg-pt Proposition \[pt-prop:rg-pt-flow\]], and $\chi_j$ could alternately be defined in terms of $j_m$. We always take the infinite volume limit before letting $m^2 \downarrow 0$, so we may assume that $m^2 \in [\varepsilon L^{-2(N-1)},\delta^2]$ for small fixed $\delta, \varepsilon$. It is shown in [@BBS-rg-pt] that there is an $L$-independent constant $c$ such that for $m^2 \in [0, \delta]$ and $j=1,\ldots,N-1$, or for $m^2 \in [\varepsilon L^{-2(N-1)},\delta]$ for $N$ large in the special case $C_j=C_{N,N}$, $$\label{e:scaling-estimate-Omega} \|\nabla_x^\alpha \nabla_y^\beta C_{j;x,y}\| \leq c \chi_j L^{-(j-1)(2[\phi]+(\|\alpha\|_1+\|\beta\|_1))}.$$ Let $$\lbeq{Ckstardef} C_{j}= \begin{cases} C_j & j<N \\ C_{N,N} & j=N. \end{cases}$$ By , given $\ellconst \in (0,1]$ we can choose $\ell_0$ large depending on $L$ to obtain, for $j=1,\ldots,N$, $$\lbeq{CLbd} \\|C_{j}\\|_{\Phi_j^+(\ell_j)} \le \ellconst \chicCov_j \le \min\{\ellconst, \chicCov_j\},$$ where $\Phi^+$ refers to the norm with $p_\Phi$ replaced by $p_\Phi+d$. Let $c_G=c(\alpha_G)$ be the (small) constant of [@BS-rg-norm Proposition \[norm-prop:EG2\]]. We fix the value $\ellconst = \frac{1}{10}c_G$. Then [@BS-rg-norm Proposition \[norm-prop:EG2\]] ensures that $$\begin{aligned} \max_{k=j,j+1}\Ex_{k} ( G_{j} (X) )^{10} & \le 2^{\|X\|_j} \quad\quad X \in \Pcal_{j}, \label{e:EG}\end{aligned}$$ where $\|X\|_j$ denotes the number of scale-$j$ blocks comprising $X$ (the constants $10$ and $2$ in are convenient but somewhat arbitrary choices). The use of $\Phi^+$ in is to satisfy the hypotheses of [@BS-rg-norm Proposition \[norm-prop:EG2\]]. ### Choice of norm parameters {#sec:hex} We restrict attention here to $d=4$. For the $G$ norm, for the boson and fermion fields we choose $\ell_0$ according to and set $$\label{e:hl} \h_j = \ell_j = \ell_0 L^{-j[\phi]} .$$ For the $\tilde G$ norm, we fix a parameter $k_0$ (small, chosen as discussed under Proposition \[prop:Iupper\]), we set $$\label{e:h-def} \h_j = h_{j} = k_0 \ggen_j^{-1/4}L^{-jd/4}.$$ We assume that $\ggen_j$ can be taken to be as small as desired (uniformly in $j$, and depending on $L$), and that $$\label{e:gbarmono} \frac 12 \ggen_{j+1} \le \ggen_j \le 2 \ggen_{j+1}$$ (the above two inequalities hold for the sequence $\gbar_j$ by [@BBS-rg-pt]). For the observables, we set $$\lbeq{newhsig} \h_{\sigma,j}= \begin{cases} \ggen_j L^{(j\wedge j_{ab})[\phi]} 2^{(j-j_{ab})_+} & \h=\ell \\ \ggen_j^{1/4} L^{(j\wedge j_{ab})[\phi]} 2^{(j-j_{ab})_+} & \h=h; \end{cases}$$ see Remark \[rk:hsigmot\] for motivation of this definition. By , the above choices obey: $$\begin{aligned} \label{e:h-assumptions} \h_j \ge \ell_{j}, \quad\quad \frac{\h_{j+1}}{\h_j} L^{[\phi]} &\le 2, \quad\quad \frac{\h_{\sigma,j+1}}{\h_{\sigma,j}} \le {\rm const}\, \begin{cases} L^{[\phi]} & j < j_{ab} \\ 1 & j \ge j_{ab}. \end{cases}\end{aligned}$$ Our results for the norm pairs – require only the bounds on $\h_{j+1}$ in . However, the choice of $2$ that appears there and in is arbitrary, and, e.g., $3$ would do as well. For this reason, we can replace $\h_{j+1}$ by a larger $\h_{++}=c\h_{j+1}$, as claimed in Remark \[rk:h++\]. ### Definition of small parameter epsilonV {#sec:spdefs} The stability estimates are expressed in terms of domains defined via parameters $\epV$ and $\epVbar$, which we discuss now. Given $V \in \Qcalnabla$, we write $V_\varnothing = \sum_{M}M$ for the decomposition of its bulk part as a sum of individual field monomials such as $\nu \phi\bar\phi$, $\nu \psi\bar\psi$, $z(\Delta \phi)\bar\phi$, and so on. Then, for $0 \le j \le N$, we define $$\label{e:monobd} \epV =\epsilon_{V,j} = L^{dj} \sum_{M : \pi_M=0} \\|M_0\\|_{T_{0,j}(\h_j)} + (\|\lambdaa\|+\|\lambdab\|)\h_j\h_{\sigma,j} + (\|\qa\|+\|\qb\|)\h_{\sigma,j}^2 ,$$ where $M_0$ denotes the monomial $M_x$ evaluated at $x=0$. Thus $\epV$ is a function (in fact, a norm) of the coupling constants in $V$ and of the parameters $\h_j$ and $\h_{\sigma,j}$ which define the $T_0$ semi-norm. The value of $\epV$ depends on the scale $j$, but we often leave this implicit in the notation. It measures the size of $V$ on a block $B \in \Bcal_j$ consisting of $L^{dj}$ points, and is worst case in the sense that it includes a contribution from observables whether or not the points $a$ or $b$ lie in $B$. The term $g\tau^2$ plays a special role in providing the important factor $e^{-g\|\phi\|^4}$ in $e^{-V}$, and we define $$\label{e:epVbar-def-old} \epVbar = \epsilon_{g\tau^2,j} = L^{dj} \\|g\tau^2_0 \\|_{T_{0,j}(\h_j)}.$$ By definition, $\epVbar \le \epV$. Also, there is a universal constant $C_0>0$ such that $$\label{e:epVbarasymp} C_0^{-1} \|g\|\h_j^4 L^{dj} \le \epVbar \le C_0 \|g\|\h_j^4 L^{dj} .$$ In fact, the upper bound is proved in [@BS-rg-norm Proposition \[norm-prop:taunorm\]], while the lower bound follows directly from the definition of the $T_{\phi}$ norm (see [@BS-rg-norm Definition \[norm-def:Tphi-norm\]]) since the supremum of the pairing over all unit norm test functions is larger than the pairing with a constant unit norm test function. ### Stability domains To enable the use of analyticity methods in [@BS-rg-step], we employ complex coupling constants. Given a (large) constant $C_{\DV}$, we define a domain $$\begin{aligned} \lbeq{DV1-bis} \DV_j = \{(g,\nu,z,y,\lambdaa,\lambdab,\qa,\qb)\in \C^{8} : C_\DV^{-1} \ggen_j < {\rm Re} g < C_\DV \ggen_j, & \; \|{\rm Im} g\| < \textstyle{\frac {1}{10}} {\rm Re} g, \nnb & \|x\| \le r_x \; \text{for $x\neq g$}\},\end{aligned}$$ where $r_x$ is defined (with $\lambda$ equal to $\lambdaa$ or $\lambdab$ and similarly for $q$) by $$\begin{gathered} L^{2j}r_{\nu,j} = r_{z,j}= r_{y,j}= C_{\DV} \ggen_j, \quad\quad r_{\lambda,j} = C_{\DV}, \nnb L^{2j_{ab}[\phi]}2^{2(j-j_{ab})}r_{q,j} = \begin{cases} 0 & j < j_{ab} \\ C_{\DV} & j \ge j_{ab}. \end{cases} \label{e:h-coupling-def-1-bis}\end{gathered}$$ We also use two additional domains in $\C^{8}$, which depend on the value of $\h$ (namely $\h=\ell$ or $\h=h$), as well as on parameters $\alpha,\alpha',\alpha''>0$. Given these parameters, we define $$\begin{aligned} \label{e:DVell} \bar\DV_j(\ell) &= \{V \in \Qcal : \; \|{\rm Im} g\| < \textstyle{\frac {1}{5}} {\rm Re} g, \; \epsilon_{V,j}(\ell_j) \le \alpha''\ggen_j \}, \\ \lbeq{DVh} \bar\DV_j(h) &= \{V \in \Qcal : \; \|{\rm Im} g\| < \textstyle{\frac {1}{5}} {\rm Re} g, \; \alpha \le \epsilon_{g\tau^2,j}(h_j), \; \epsilon_{V,j}(h_j) \le \alpha' \}.\end{aligned}$$ We permit the parameters $\alpha,\alpha' >0$ to depend on $C_\DV$, and $\alpha''=\alpha''_L >0$ to depend on $C_\DV, L$. Their specific values are of no importance. We sometimes need versions with larger $\alpha',\alpha''$ and smaller $\alpha$, and we denote these by $\bar\DV_j'$. This is the case in the following proposition, which is proved in Section \[app:sp\]. \[prop:monobd\] Let $d=4$. If $V \in \DV_j$ then there is a choice of parameters defining the domains – such that $$\begin{aligned} \lbeq{VDbar} V &\in \bar\DV_j(\ell) \cap \bar\DV_j(h) \quad\quad (j \le N),\end{aligned}$$ and if $V \in \bar\DV_j(\h)$ (for $\h=h$ or $\ell$) then with a new choice of parameters for $\bar\DV'$, $$\begin{aligned} \lbeq{Vptbar} V_{\pt,j+1}(V) &\in \bar\DV_{j}'(\h) \cap \bar\DV_{j+1}'(\h) \quad\quad (j < N) .\end{aligned}$$ The domain $\bar\DV_j$ is the principal domain for $V$ throughout the paper. By Proposition \[prop:monobd\], we know that $\DV_j \subset \bar\DV_j(\h_j)$ for both $\h=\ell$ and $\h=h$, so all assertions valid for $V \in \bar\DV_j$ are valid for $V\in \DV_j$. In particular, asserts that if $V \in \DV_j$, then $$\begin{aligned} \label{e:epVbarepV} \alpha &\le \epsilon_{g\tau^2,j}(h), \quad\quad \epsilon_{V,j} \le \begin{cases} \alpha''_L \ggen_j & \h = \ell \\ \alpha' & \h = h. \end{cases}\end{aligned}$$ From and , we see that $$\lbeq{epVbark0} \epVbar(h) \asymp k_0^4,$$ where $k_0$ is the small constant in the definition of $h_j$. From we see that the $g\tau^2$ term dominates $V$ in the $h$-norm, in the sense that (h) ’\^[-1]{} (h) . Together with the lower bound on $\epVbar(h)$, this is important in using the $e^{-g\tau^2}$ factor in $e^{-V}$ to obtain effective stability bounds. A bound like also holds for the case $\h=\ell$, but with an $L$-dependent constant; this follows since $\epV(\ell)$ and $\epVbar(\ell)$ are both of order $\ggen_j$ by and . However in this case, since we are interested in situations where $\ggen_j \to 0$ as $j \to \infty$, we do not have a uniform lower bound on $\epVbar(\ell)$. Our analysis throughout the paper rests on the estimates of Proposition \[prop:monobd\] but does not depend on the particular form of the observable terms in and their counterparts on the right-hand side of . If different observable terms were used instead then there is no significant change in the analysis as long as the statements of Proposition \[prop:monobd\] remain valid; this observation is useful in [@ST-phi4]. ### Definition of small parameter epsilonbar {#sec:epdVdef} An additional small parameter which is important for our analysis is $\epdV = \epdV(\h)$, which takes on different values for the two cases $\h=\ell$ and $\h=h$. Recall that the sequence $\chi_j = \Omega^{-(j-\jm)_+}$ was defined in . We define \[e:epdVdef\] = \_[j]{} = \_[j]{}\^[1/2]{} \_[j]{} & \_[j]{}=\_[j]{}\ \_[j]{}\^[1/2]{} \_[j]{}\^[1/4]{} & \_[j]{}= h\_[j]{}. In view of our assumption throughout the paper that $\ggen_j$ is small (uniformly in $j$, and small depending on $L$), we can assume that $\epdV$ is as small as desired (depending on $L$). The sequence $\chi_j$ occurring in $\epdV^2$ provides useful exponential decay beyond the $\Omega$-scale . The small parameter $\epdV$ plays a role in many aspects of the paper. For example, it arises as an upper bound for $W$ of – and for $P$ of , in the sense that there is an $L$-dependent constant $c_L$ such that for $1 \le j \le N$ and $V \in \bar\DV_j$, $$\begin{aligned} \lbeq{WBbd} \max_{B \in \Bcal_j} \\|W_j(V,B)\\|_{T_{0,j}(\h_j)} &\le c_L \epdV^2, \\ \lbeq{PBbd} \max_{B \in \Bcal_j} \\|P_j(V,B)\\|_{T_{0,j}(\h_j)} &\le c_L \epdV^2.\end{aligned}$$ The inequalities – are proved in Proposition \[prop:Wnorms\] below. Main results {#sec:IE} ============ We now state our main results. We begin in Section \[sec:stab\] with stability estimates on the interaction $I$ and a statement of the analyticity of $I$ in the polynomial $V$. In Section \[sec:pt\] we state our results concerning the accuracy of the perturbative calculations of [@BBS-rg-pt]. Finally, in Section \[sec:scale\], we state estimates on Gaussian expectation, and on the operator $(1-\LT)$ which extracts the irrelevant part of an element of $\Ncal$; both of these estimates involve advancement of the scale. Proofs are deferred to Sections \[sec:I-estimates\]–\[sec:ipcl\]. Stability estimates {#sec:stab} ------------------- In this section, we state stability estimates on $I$, and formulate the analyticity of $I$ in $V$. Proofs are given in Section \[sec:I-estimates\]. Fundamental stability bounds are given in the following proposition, which is valid for arbitrary choice of $\h$ in the definition of the norms, with corresponding $\epV, \epVbar$ as defined in Section \[sec:spdefs\]. According to , if $V \in \bar\DV$ then $\\|W(V,B)\\|_{T_0}$ (which occurs in the hypothesis) is of order $\epdV^2$ so can be made small by the requirement that $\ggen_j$ be uniformly sufficiently small. Recall that the norm $\\|\phi\\|_{\tilde\Phi(X)}$ was defined in ; it appears in the last exponent in . All norms in Proposition \[prop:Iupper\] are at scale $j$. The proof of makes use of the Sobolev inequality proved in Appendix \[sec:Lp\] to take advantage of the quartic decay in $e^{-g\tau^2}$. The restriction to $j<N$ in is connected with the fact that we do not define the $\tilde G$ norm at scale $N$. \[prop:Iupper\] Let $V \in \Qcal$ with $0\le \|{\rm Im} g\| \le \frac 12 {\rm Re}g$. Let $j \le N$ and $B \in \Bcal_j$. Let $\omega = \max_{B \in \Bcal_j}\\|W(V,B)\\|_{T_0}$ and fix any $u \ge 6(L^{2d}\omega)^{1/3}$. Let $F\in \Ncal(B^\Box)$ be a polynomial of degree $r \le p_\Ncal$. Let $I^$ denote any one of the following choices:\ (a) $I_j(B)$, (b) $\tilde I_j(B)$, (c) $\Itilde_j(B \setminus X)$ with $X \in \Scal_{j-1}(B)$, (d) any of (a-c) with any number of their $1+W$ factors omitted (thus, in particular, including the case $\Ical(B)$ of ).\ (i) Then $$\begin{aligned} \label{e:Iupper-a} & \\|I^ F\\|_{T_{\phi}} \le \left(\frac{2r}{u} \right)^{r} \\| F\\|_{T_{0}} e^{O (\epV +u)(1+ \\|\phi\\|_{\Phi(B^{\Box})}^2)} .\end{aligned}$$ (ii) Suppose in addition that there is a constant $C$ such that $\epV \le C\epVbar$. Fix any $q \ge 0$, and let $q_1= q +2u\epVbar^{-1}$. Then for $j <N$, $$\begin{aligned} \label{e:Iupper-b} & \\|I^* F\\|_{T_{\phi}} \le \left(\frac{2r}{u} \right)^{r} \\| F\\|_{T_{0}} e^{O [(1+q_1^{2})\epVbar+u]} e^{-q \epVbar \\|\phi\\|_{\Phi(B^{\Box})}^2} e^{O (1+q_1) \epVbar \\|\phi\\|_{\tilde\Phi(B^{\Box})}^2}.\end{aligned}$$ When $r=0$, – both hold with the prefactor $\left(\frac{2r}{u} \right)^{r}$ replaced by $1$. Notation. We write $a \prec b$ when there is a constant $c>0$, independent of $L$ and $j$, such that $a \le c b$. If there is an $L$-dependent such constant, we write $a \prec_L b$. We write $a \asymp b$ when $a \prec b$ and $b \prec a$. We now discuss applications of Proposition \[prop:Iupper\] under the assumption that $V \in \bar\DV_j$ of –. Application of . Let $\h_j=\ell_j$ (defined in ) and let $V \in \bar\DV_j (\ell)$. By and , we obtain the hypotheses for when $\ggen_j$ is small uniformly in $j$. Furthermore, $u>0$ can also be chosen small enough, independently of $j$, so that $\exp [O(\epV +u)] \le 2$. With these choices, and with the fluctuation-field regulator defined by , we can restate as $$\begin{aligned} \label{e:Iupper-a-c} & \\|I^* F\\|_{T_{\phi}(\ell)} \le \left(\frac{2r}{u} \right)^{r} \\| F\\|_{T_{0}(\ell)}\, 2e^{\\|\phi\\|_{\Phi}^2} = \left(\frac{2r}{u} \right)^{r} \\| F\\|_{T_{0}(\ell)}\, 2 G(B,\phi) ,\end{aligned}$$ again with the convention that $(\frac{2r}{u} )^{r} =1$ when $r=0$. Application of . We apply with the choice $\h_j=h_j$ of . By and , for $V \in \bar\DV_j(h_j)$, with this choice $$\epVbar \asymp k_0^4, \quad\quad \\|W(B)\\|_{T_0} \prec_L\; \ggen_j^{1/2}.$$ We choose $k_{0}>0$ and take $u=\epVbar$. Then $$(1+q_1^2)\epVbar + u = \left(2+(q+2)^2 \right)\epVbar, \quad\quad (1+q_1)\epVbar = (3+q) \epVbar.$$ We conclude from that there is a constant $a$ such that, for $V \in \bar\DV(h_j)$, $$\begin{aligned} \label{e:Iupper-b-c} & \\|I^* F\\|_{T_{\phi}(h)} \le \left(\frac{2r}{ak_0^4} \right)^{r} \\| F\\|_{T_{0}(h)}\, 2 e^{-q\epVbar \\|\phi\\|_{\Phi(B^{\Box},h)}^2} e^{(3+q) \epVbar \\|\phi\\|_{\tilde\Phi(B^{\Box},h)}^2} ,\end{aligned}$$ with the usual convention when $r=0$. Since $h \ge \ell$, we have $\\|\phi\\|_{\Phi(\h)} \le \\|\phi\\|_{\Phi(\ell)}$ and hence also $\\|\phi\\|_{\tilde\Phi(\h)} \le \\|\phi\\|_{\tilde\Phi(\ell)}$. This allows us to conclude from that, for $V \in \bar\DV(h_j)$, if $q \le \bar q$ for some fixed $\bar q >0$ then we can choose $k_0$ small depending on $\bar q$ and $\Gtilp$ such that $$\begin{aligned} \label{e:Iupper-b-d} & \\|I^* F\\|_{T_{\phi}(h)} \le \left(\frac{2r}{ak_0^4} \right)^{r} \\| F\\|_{T_{0}(h)}\, 2 e^{-q ak_0^4 \\|\phi\\|_{\Phi(B^{\Box},h)}^2} \tilde{G}^{\Gtilp}(B,\phi).\end{aligned}$$ Vanishing at weighted infinity. In , a stronger bound in which $G(B,\phi)$ is replaced by a smaller power $G^{\gamma}(B,\phi)$ also holds, by the same proof. In combination with , and with $\Gcal$ denoting $G$ when $\h=\ell$ and $\tilde G$ when $\h=h$, in either case this shows that if $V \in \bar\DV$ then $$\lbeq{vai} \lim_{\\|\phi\\|_{\Phi(B^\Box)} \to \infty} \\|I^* F\\|_{T_\phi}\Gcal(X,\phi)^{-\Gtilp} =0.$$ This fact is useful in [@BS-rg-step] to establish the property used there called “vanishing at weighted infinity.” The following proposition extends and reformulates the above estimates in terms of the four norms $\\|\cdot\\|_j, \\|\cdot\\|_{j+1}$ appearing in either of –. However, here and throughout the paper, as discussed in Remark \[rk:scaleNnorm\], statements about the scale-$N$ norm are to be interpreted as applying only to the $G_{N-1}^{10}$ norm, and not also to the $\tilde G$ norm: scale-$N$ is always considered to correspond to $j+1$ and never to $j$ in –. \[prop:Istab\] Let $I_$ denote either of $I_j,\Ipttil$, with $j_=j$ for $I_j$, and either $j_=j$ or $j_=j+1$ for $\Ipttil$. We assume $j_* \le N$. Alternately, let $I_$ denote any of the above with any number of their $1+W$ factors omitted. Let $B\in \Bcal_j$. Let $V \in \bar\DV_j$ and let $F\in \Ncal(B^{\Box})$ be a gauge-invariant polynomial in the fields of degree at most $p_\Ncal$ with $\pi_{ab}F=0$ if $j < j_{\pp \qq}$. Then $$\begin{aligned} \label{e:IF} \\|I_(B) F\\|_{j_} & \prec \\|F\\|_{T_{0,j}} , \\ \label{e:Iass} \\|I_(B)\\|_{j_} & \le 2 , \\ \label{e:I-b:5} \\|I_^{-B}\\|_{T_{0,j_} } & \le 2 .\end{aligned}$$ In addition, for $j+1 \le N$ and for a scale-$(j+1)$ block $\hat B \in \Bcal_{j+1}$, and for $X$ either a small set $X \in \Scal_j$ or the empty set $X=\varnothing$, $$\label{e:Iptass} \\|\Ipttil^{\hat B\setminus X}\\|_{j+1} \le 2 .$$ The following proposition states our analyticity result for the interaction, again in terms of the four norms $\\|\cdot\\|_j, \\|\cdot\\|_{j+1}$ appearing in –. We show that $I$ is analytic in $V$ by proving that there is a norm-convergent expansion of $I$ in powers of $V$. \[prop:Ianalytic1:5\] Let $I_$ denote either of $I,\Ipttil$, with $j_=j$ for $I$, and either* $j_=j$ or $j_=j+1$ for $\Ipttil$. We assume $j_* \le N$. Alternately, let $I_$ denote any of the above with any number of their $1+W$ factors omitted. Let $B\in \Bcal_j$. Then $I(B)$ and $\Ipttil(B)$ are analytic functions of $V \in \bar\DV_j$, taking values in $\Ncal(B^\Box), \\|\cdot\\|_{j_}$. In addition, $I(B)^{-1}$ is an analytic function of $V \in \bar\DV_j$ taking values in $\Ncal(B^\Box), \\|\cdot\\|_{T_{0,j}}$. Recall that $\epdV$ was defined in , and that we use $\h=\ell$ for quantities related to the norm pair , and $\h=h$ for the norm pair . The following proposition measures the effect of a change in $I$ due to a change in $V$ that is appropriately bounded by $\epdV$. \[prop:JCK-app-1\] Let $j<N$, $B \in \Bcal$, $V \in \bar\DV$, $Q \in \Qcal$ with $\\|Q(B)\\|_{T_0} \prec \epdV$, and set $\Ihat = I(V-Q)$ and $I=I(V)$. Then $V-Q \in \bar\DV'$, $\Ihat(B)$ obeys the $I_$ estimates of Proposition \[prop:Istab\], is an analytic function of $V\in \bar\DV$ taking values in $\Ncal(B^\Box), \\|\cdot\\|_j$, and obeys the estimates $$\begin{aligned} \label{e:JCK1-app} \\|\Ihat(B)- I(B)\\|_j &\prec \epdV , \\ \label{e:JCK2-app} \\| \Ihat(B)- I(B)(1+ Q(B) ) \\|_{T_{0} } &\prec_{L} \epdV^{2} .\end{aligned}$$ All quantities and norms are at scale $j$, norms are computed with either $\h=\ell$ or $\h=h$, and holds for either choice of $\\|\cdot \\|_j$ in –. Perturbative interaction estimates {#sec:pt} ---------------------------------- In this section, we formulate two propositions which enable a rigorous implementation of the formal perturbative calculations of [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. The two propositions are applied in [@BS-rg-step Section \[step-sec:Map3estimates\]]. Their statements are in terms of the small parameter $\epdV$ defined in . Recall the map $\theta$ defined below , the polynomial $\Vpt$ defined in (and above for scale-$N$), and $\Ipttil$ defined in . For $B \in \Bcal_j$ and $X \in \Pcal_j$, we define $\delta I^X \in \Ncal (\Lambdabold \sqcup \Lambdabold')$ by $$\label{e:dIdef} \delta I (B) = \theta I_j(B) - \Ipttil(B) = \theta I_j(V,B)-\Itilde_{j+1}(\Vpt,B) , \quad\quad \delta I^X = \prod_{B \in \Bcal_j(X)}\delta I(B).$$ For small sets $U\in \Scal_{j+1}$ we define $$\hred (U) = \sum_{X \in\overline{\Pcal}_{j}(U): \|X\|_j \le 2} \Ipttil^{-X}\Ex_{j+1} \delta I^X, \label{e:hred-def}$$ where $\|X\|_j$ denotes the number of scale-$j$ blocks in $X$, and $X \in \overline\Pcal_j(U)$ indicates the restriction that $U$ is the smallest polymer in $\Pcal_{j+1}$ that contains $X$. The subscript “red” indicates that $h$ is “reduced” by the restriction $\|X\|_j\le 2$. (In [@BS-rg-step] we define a version without this restriction.) For [@BS-rg-step], we need to compute $\hred$ accurately to second order in $\epdV$. For this, we first recall from the definition of the truncated expectation $$\label{e:trun-exp} \Ex_C (A; B) = \Ex_C(AB) - (\Ex_CA)(\Ex_CB).$$ We also define (cf. ) $$\begin{aligned} \label{e:Epi} \Ex_{\pi ,C} (A;B) &= \Ex_C ( A;\pi_{\varnothing}B) + \Ex_C ( \pi_ A; B) .\end{aligned}$$ Then for $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$ we define $\hldg (U,B)$ by $$\label{e:hptdefqq} \hldg (U,B) = \begin{cases} -\frac{1}{2}\Ex_{\pi ,j+1} \theta ( V_j(B); V_j(\Lambda \setminus B)) & U=B \\ \;\;\; \frac{1}{2} \Ex_{\pi ,j+1}\theta ( V_j(B); V_j(U\setminus B)) & U \supset B, \|U\|_{j+1}=2 \\ \;\;\; 0 &\text{otherwise} , \end{cases}$$ where we have abbreviated the subscript $C_{j+1}$ to $j+1$ on $\Ex$. For $U \in \Pcal_{j+1}$ we define $$\label{e:hldgUdef} \hldg(U) = \sum_{B \in \Bcal_{j+1} (U)} \hldg (U,B) .$$ Due to the finite-range property , $$\sum_{U \supset B : U \neq B} \hldg(U,B) = \frac{1}{2} \Ex_{\pi ,j+1}\theta (V_{j}(B) ; V_{j}(\Lambda \setminus B)) ,$$ and therefore $\hldg$ obeys the identity $$\label{e:hpt0bis} \sum_{U \supset B} \hldg (U,B) = 0.$$ The following two propositions, which are proved in Section \[sec:interaction-estimates444\], show that $\hldg$ is second order in $\epdV$, and that $\hldg(U)$ is the leading part of $\hred(U)$. The latter is a much more substantial result than the former, and is our implementation of the formal power series statement of [@BBS-rg-pt Proposition \[pt-prop:I-action\]]. \[prop:hldg\] There is a positive constant $\cldg = \cldg(L)$ such that for $j<N$, $V \in \bar\DV_j$ and $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$, $$\begin{aligned} \label{e:want1} \\|\Ipttil (U) \hldg (U,B)\\|_{j+1} & \le \cldg \epdV^2 ,\end{aligned}$$ where $\\|\cdot \\|_{j+1}$ represents either of the two options –, with corresponding $\epdV$ of . \[prop:h\] There is a positive constant $c_{\pt}=c_{\pt}(L)$ such that for $j<N$, $V \in \bar\DV_j$ and $U \in\Scal_{j+1}$ with $\|U\|_{j+1}\in \{1,2\}$, $$\begin{aligned} \label{e:want2} \\|\Ipttil (U) [\hred(U)-\hldg (U)]\\|_{j+1} & \le c_{\pt} \epdV^{3} ,\end{aligned}$$ where $\\|\cdot \\|_{j+1}$ represents either of the two options –, with corresponding $\epdV$ of . Bound on expectation and crucial contraction {#sec:scale} -------------------------------------------- The next two propositions play a key role in our analysis of a single renormalisation group step in [@BS-rg-step Section \[step-sec:Map3estimates\]]. \[prop:ip\] There is an $\Econst >0$ (independent of $L$) and a $C_{\delta V}>0$ (depending on $L$) such that for $j<N$, $V \in \bar\DV_j$, disjoint $X,Y \in \Pcal_j$, and for $F(Y) \in \Ncal(Y^\Box)$, $$\label{e:integration-property} \\|\Ex_{j+1} \delta I^X \theta F(Y) \\|_{j+1} \le \Econst^{\|X\|_j+\|Y\|_j} (C_{\delta V}\epdV)^{\|X\|_j}\\|F(Y)\\|_j,$$ where the pair of norms is given by either of or with corresponding $\epdV$ of . The proof of Proposition \[prop:ip\] is given in Section \[sec:ippf\]. We refer to the important inequality as the integration property. It shows that when estimating the scale-$(j+1)$ norm of an expectation of a product involving factors of $\delta I(B)$ for scale-$j$ blocks, each factor gives rise to a small factor $\epdV$. In the next proposition, the notation $U = \overline X$ again indicates the restriction that $U$ is the smallest polymer in $\Pcal_{j+1}$ that contains $X$. As in [@BS-rg-loc Definition \[loc-def:LTXYsym\]], we use the notation $X(\varnothing)=X$, $X(a) = X \cap \{a\}$, $X(b)=X \cap \{b\}$, and $X(ab) = X \cap\{a,b\}$. Given $X \subset \Lambda$, we define $$\label{e:gamLdef} \gamma(X) = L^{-d -1} + L^{-1}\1_{X \cap \{a,b\} \not = \varnothing}.$$ \[prop:cl\] Let $j<N$ and $V\in \DV_j$. Let $X \in \Scal_j$ and $U = \overline X$. Let $F(X) \in \Ncal(X^\Box)$ be such that $\pi_\alpha F(X) =0$ when $X(\alpha)=\varnothing$, and such that $\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ (recall ). Then $$\begin{aligned} \label{e:contraction3z-new} \\|\Ipttil^{U\setminus X} \Ex_{C_{j+1}} \theta F (X) \\|_{j+1} & \prec \cgam(X) \kappa_F + \kappa_{\LT F} ,\end{aligned}$$ with $\kappa_F=\\|F (X)\\|_{j}$ and $\kappa_{\LT F} =\\|\Ipttil^X \LT_X \Ipttil^{-X} F(X) \\|_j$, and where the pair of norms is given by either of or . The proof of the Proposition \[prop:cl\] is given in Section \[sec:contraction3-proof\]. We refer to the inequality as the crucial contraction; its importance is discussed in Section \[sec:cc\] above. Estimates on small parameters {#app:sp} ============================= In this section, we provide estimates on the small parameters $\epV,\epdV$ which drive our analysis. In particular, we prove Proposition \[prop:monobd\]. Preliminaries ------------- We begin with two general lemmas. The first relates $\epsilon_{V,j}$ to $\\|V(B)\\|_{T_{0,j}}$ for a scale-$j$ block $B \in \Bcal_j$, and the second expresses an important monotonicity property of the $T_\phi$ semi-norm under change of scale. Recall from [@BS-rg-loc] that it follows from the definition of the $T_\phi$ semi-norm that under the direct sum decomposition of $F \in \Ncal$ due to , F\_[T\_]{} &= \_[,a,b,ab]{}\_F \_[T\_]{} = F\_\_[T\_]{} + \_F\_a\_[T\_]{} + \_F\_b\_[T\_]{} + \_\^2 F\_[ab]{}\_[T\_]{} . ### The T0 semi-norm and epsilonV \[lem:T0ep\] For $V \in \Qcal$ and $j<N$, $\epsilon_{V,j} \asymp \max_{B \in \Bcal_j} \\|V(B)\\|_{T_{0,j}}$. Given $V \in \Qcalnabla$, as in we write $V_\varnothing = \sum_{M} M$ for the decomposition of its bulk part as a sum of individual field monomials such as $\nu \phi\bar\phi$, $\nu \psi\bar\psi$, $z(\Delta \phi)\bar\phi$, and so on. For $0 \le j \le N$, in we defined $$\label{e:monobd-bis} \epV = L^{dj} \sum_{M : \pi_M=0} \\|M_0\\|_{T_{0,j}(\h_j)} + (\|\lambdaa\|+\|\lambdab\|)\h_j\h_{\sigma,j} + (\|\qa\|+\|\qb\|)\h_{\sigma,j}^2 .$$ By direct calculation, $\\|\lambda_\pp \bar\phi_{x}\\|_{T_0}=\1_{x=\pp}\|\lambda^a\|\h$, $\\|\lambda_\qq \phi_{x}\\|_{T_0} = \1_{x=\qq}\|\lambdab\|\h$, and $\|q_{\pp\qq}\| = \frac{1}{2}(\|\qa\|\1_{x=\pp}+\|\qb\|\1_{x=\qq})$. Thus the last two terms on the right-hand side of are bounded above and below by multiples of $\max_{B \in \Bcal_j}\\|\pi_V(B)\\|_{T_0}$, and it suffices to consider the case $V=\pi_\varnothing V$, which we assume henceforth. It follows from the triangle inequality that $\\|V(B)\\|_{T_0} \prec \epV$, and it suffices to prove the reverse inequality. Let $M$ be a scalar multiple of one of $g\phi\bar\phi\phi\bar\phi, g\phi\bar\phi\psi\bar\psi, \nu\phi\bar\phi, \ldots$. It suffices to prove that $$\lbeq{M0V} \\|M_0\\|_{T_0}\|B\| \prec \\|V(B)\\|_{T_0}.$$ For this, we employ the pairing of [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], and seek dual test functions for the monomials. In more detail, given a monomial $M$ we seek a unit $\Phi$-norm test function $f_M$ such that, for all $x\in B$, $\pair{M_x,f_M}=\\|M_x\\|_{T_0}$ but $\pair{M'_x,f_M} = 0$ if $M' \neq M$. It then follows that $$\begin{aligned} \lbeq{T0epid} \\|M_{0}\\|_{T_{0}} & = \|\pair{ M_{x},f_M}_{0}\| = \frac{1}{\|B\|} \|\pair{M (B),f_M}_{0}\| = \frac{1}{\|B\|} \|\pair{V (B),f_M}_{0}\| \le \frac{1}{\|B\|} \\|V (B)\\|_{T_{0}},\end{aligned}$$ which is equivalent to the desired estimate for this monomial. For the existence of $f_M$, we proceed as follows (cf. [@BS-rg-loc Lemma \[loc-lem:dualbasis\]] for related ideas). Consider first the case $M=g\phi\bar\phi\phi\bar\phi$. We choose $f_M$ to be zero on all sequences except those of length four whose components are in the $\phi, \phib, \phi, \phib$ sheets, and choose it to be constant on the set of these sequences, with the constant such that $f_M$ has unit norm. This choice can be seen to have the desired properties, and it generalises in a straightforward way to all the monomials arising from $g\tau^2$ and $\nu\tau$. Next, we consider $M = \frac 12 \sum_{e \in \units}(\nabla^e\phi)(\nabla^e\bar\phi)$ (the coupling constant plays an insignificant role so we omit it for simplicity). By translation invariance, we may assume that $B$ is centred at $0\in \Lambda$, and since $j<N$ we can identify $B$ with a subset of $\Zd$. Let $v_{x_{1},x_{2}}= x_{1}\cdot x_{2} + c$ for $x_{1}$ in the $\phi$ sheet and $x_{2}$ in the $\phib$ sheet. Let $M'=\phi\bar\phi$. Then the pairing of $v$ with any monomial other than $M,M'$ vanishes. In particular, $\pair{M_x,v}_0= \frac 12 \sum_{e \in \units} \nabla_{x_1}^e \nabla_{x_2}^e v_{x,x} = d$. Also, $\pair{M_{x}',v}_{0} \asymp x\cdot x + c$, and by choosing $c\asymp L^{2j}$ such that $\sum_{x \in B}(x\cdot x + c)=0$, we can arrange that $\pair{M'(B),v}_0=0$. Let $f = v/\\|v\\|_{\Phi}$. Then we have $\pair{V(B),f}_0=\pair{M(B),f}_0 = \|B\|\pair{M_0,f}_0$ and we obtain in this case, as in . The case $M = \bar\phi \Delta\phi$ is similar, with the test function constructed from $v_{x_{1},x_{2}} = x_{1}\cdot x_{1} + c$. This completes the proof. ### Scale monotonicity We now prove a monotonicity property of the $T_\phi$ semi-norm under change of scale, which is used repeatedly throughout the paper. The property is more general than our specific application, and we formulate it under assumptions on $\h=(\h_\phi,\h_\sigma)$ obeyed by our particular choices. In our application, with $\h'=\h$ follows from the last two bounds of . \[lem:Imono\] Suppose that $F \in \Ncal$ is gauge invariant and such that $\pi_{ab}F=0$ when $j<j_{ab}$, that $\h_{\phi,j}'' \le \h_{\phi,j}' \prec L^{-[\phi]}\h_{\phi,j-1}$, that $\h_{\sigma,j}'' \prec \h_{\sigma,j}'$, and that for all $j$, $$\label{e:hprod-bis} \h_{\sigma,j}' \prec \begin{cases} L^{[\phi]}\h_{\sigma,j-1} & j < j_{ab} \\ \h_{\sigma,j-1} & j \ge j_{ab}, \end{cases} \quad\quad \h_{\sigma,j+1}'\h_{\phi,j+1}' \prec \h_{\sigma,j}\h_{\phi,j}.$$ Then, for $L$ large depending on the constant in $\prec$ in the hypothesis, $$\label{e:scale-change} \\|F\\|_{T_{\phi,j}(\h_{j}'')} \prec \\|F\\|_{T_{\phi,j}(\h_j') } \prec \\|F\\|_{T_{\phi,j-1}(\h_{j-1}) } .$$ By it suffices to prove that for each $\alpha$, $\\|\pi_\alpha F\\|_{T_\phi}$ individually obeys . Case $\alpha = \varnothing$. By definition of the norm on test functions (recall [@BS-rg-norm Example \[norm-ex:h\]]), for a test function $g$ with none of its variables corresponding to observable sheets, $$\label{e:g-norms} \\|g\\|_{\Phi_{j-1}(\h_{j-1})} \le \\|g\\|_{\Phi_{j}(\h_j')} \le \\|g\\|_{\Phi_{j}(\h_j'')} ,$$ provided $L$ is chosen large so that the hypothesis $\h_{\phi,j}' \prec L^{-[\phi]}\h_{\phi,j-1}$ implies that $\h_{\phi,j}' \le \h_{\phi,j-1}$. As a direct consequence of the definition $\\|F\\|_{T_\phi} = \sup_{\\|g\\|_\Phi \le 1}\|\pair{F,g}_\phi\|$ of the $T_\phi$ semi-norm in [@BS-rg-norm Definition \[norm-def:Tphi-norm\]], we obtain with $F$ replaced by $\pi_{\varnothing}F$ as was to be proved. In fact for this case we obtain the stronger inequality with $\prec$ replaced by $\le$. Case $\alpha = \pp\qq$. By $\\|\pi_{ab} F\\|_{T_\phi} = \h_\sigma^2 \\|F_{ab}\\|_{T_\phi}$, so the first inequality of follows immediately from the hypothesis $\h_{\sigma,j}'' \prec \h_{\sigma,j}'$ and case $\alpha =\varnothing$. Likewise the second inequality for $j \ge j_{ab}$ follows from the hypothesis $\h_{\sigma,j}' \prec \h_{\sigma,j-1}$. The second inequality for $j<j_{ab}$ is vacuous because, by hypothesis, $\pi_{ab}F=0$ for $j<j_{ab}$. Cases $\alpha=\pp$ or $\alpha=\qq$. These are similar, and we consider only $\alpha =\pp$. The fact that $\pi_\pp F = \sigma F_{\pp}$ is gauge invariant implies that its pairing with a test function $g$ is zero unless exactly one argument of $g$ has species $\sigma$ and at least one other argument has species $\phi$ or $\psi$. Therefore, for gauge invariant $F$, we can refine [@BS-rg-norm Definition \[norm-def:Tphi-norm\]] by restricting the supremum to unit norm test functions with this support property. By the second inequality of test functions with this support property satisfy with $\prec$ in place of $\le$. The constants in $\prec$ must be independent of $j$, and they are because there is only one $\sigma$ and $L$ is large. This implies for case $\alpha =\pp$ and completes the proof. The small parameter epsilonV: Proof of Proposition \[prop:monobd\] {#sec:epVW} ------------------------------------------------------------------ It suffices to prove that:\ (i) For $j \le N$ and $V \in \DV_j$, there exist $a,A >0$ (depending on $C_\DV$) and $A_L >0$ (depending on $C_\DV, L$) such that $$\begin{aligned} \label{e:epVbardefz-app} \|{\rm Im} g\| < \textstyle{\frac {1}{5}} {\rm Re} g, \quad\quad a k_0^4 &\le \epsilon_{g\tau^2,j}(h_j), \quad\quad \epsilon_{V,j} \le \begin{cases} A_L \ggen_j & \h = \ell \\ A k_0 & \h = h. \end{cases}\end{aligned}$$ (ii) For $j < N$ and $V \in \bar\DV_j$, the bounds hold (with different constants) when $V$ is replaced by $V_{\pt,j+1}$ (and $g$ by $\gpt$), and also when $j$ is replaced by $j+1$. We prove the above two statements in sequence.\ (i) For $j \le N$ and $V \in \DV_j$, the coupling constants obey $$C_{\DV}^{-1} \ggen_j < {\rm Re} g < C_{\DV} \ggen_j, \quad \|{\rm Im} g\| < \textstyle{\frac {1}{10}}{\rm Re} g < \textstyle{\frac {1}{5}} \ggen_j, \quad$$ $$\begin{gathered} \label{e:ccbds} L^{2j}\|\nu\|,\|z\| , \|y\| \le C_{\DV} \ggen_j, \quad \|\lambda\| \le C_{\DV} , \quad L^{2j_{ab}[\phi]}2^{2(j-j_{ab})}\|q\|\le \begin{cases} 0 & j < j_{ab} \\ C_{\DV} & j \ge j_{ab}, \end{cases}\end{gathered}$$ for $\lambda$ equal to $\lambdaa$ or $\lambdab$ and similarly for $q$. The first inequality of holds by definition. As noted in , $$\label{e:epVbardef-h-i} \epsilon_{g\tau^2,j}(\h_j) \asymp L^{dj} \|g\| \h_j^4 .$$ In particular, since $\|g\|\asymp \ggen_j $ by hypothesis, $$\label{e:epVbardef-h} \epsilon_{g\tau^2,j}(h_j) \asymp L^{dj} \|g\| h_j^4 \asymp k_0^4 ,$$ which proves the second bound of . The last bound of for the bulk part $V_\varnothing$ of $V$ similarly follows from direct calculation as in [@BS-rg-norm Proposition \[norm-prop:taunorm\]]; e.g., $\\|\phi_x\bar\phi_x\\|_{T_{0,i}} = \h_i^2$, $\\|\phi_x\bar\phi_x\phi_x\bar\phi_x\\|_{T_{0,i}} = \h_i^4$, $\\|\phi_x\Delta \bar\phi_x\\|_{T_{0,i}} = L^{-2i} \h_i^2$, while the observables contribute $$\begin{aligned} \lbeq{hsigh} \|\lambda\| \h_i \h_{\sigma,i} &= \|\lambda\| \times \begin{cases} \ggen_i \ell_0 (2/L)^{(i-j_{ab})_+ } & \h =\ell \\ k_0 (2/L)^{(i-j_{ab})_+ } & \h = h , \end{cases} \\ \lbeq{qhsig} \|q\|\h_{\sigma,i}^2 & \prec \begin{cases} \ggen_i^2 & \h=\ell \\ \ggen_i^{1/2} & \h=h \end{cases}\end{aligned}$$ (for we can restrict to $i \ge j_{ab}$ since otherwise $q=0$). The combination of these bounds completes the proof of , after taking into account that $\ell_0$ depends on $L$ and $k_0^4 \le k_0$. \(ii) Let $V \in \bar\DV_j$. We first consider the case $j+1<N$, $n=j$ of . By , $\Vpt =V + 2gC_{0,0}\tau - P$, with $C=C_{j+1}$ and $P=P_j$. By , $$\\|2gC_{0,0}\tau_x\\|_{T_{0,j}} \prec \|g\|L^{-2j}\h_j^2 .$$ By , Lemma \[lem:T0ep\], and , $$\begin{aligned} \lbeq{epVptbd} \epsilon_{\Vpt} & \prec \epV + \|g\|L^{2j} \h_j^2 + \epsilon_P \prec \epV + \|g\|L^{2j}\h_j^2 + \max_{B \in \Bcal_j}\\|P(B)\\|_{T_{0,j}} \nnb & \prec \epV + \|g\|L^{2j}\h_j^2 + O_L(\epdV^2).\end{aligned}$$ With the definition of $\h_j$ in –, this shows that $\epsilon_{\Vpt}$ obeys the last bound of . For the second bound of , we restrict to $\h=h$, and note that the lower bound follows from the lower bound on the $\tau^2$ term of $V$, together with the fact that the contribution to $\tau^2$ from $P$ is bounded above by $\epsilon_P \prec_L \ggen_j^{1/2}$. Finally, for the bound on the imaginary part of $\gpt$ we use the fact that it changes insignificantly from the imaginary part of $g$, since the coupling constant $g_P$ of $P$ obeys $\|g_P\| \prec \epsilon_{g_p\tau^2,j}(\ell_j) \le \epsilon_P(\ell_j) \prec_L \ggen_j^2$ (the first of these inequalities follows from ). For the case $j+1=N$, $n=j$ of , we simply observe that our definition of $V_{\pt,N}$ is identical to what it would be on a torus of scale larger than $N$, so the bound in this case follows from the above argument applied to the torus of scale $N+1$. For the $n=j+1$ case of , note that the computations in the proof of (i) lead to the same conclusion when $\h_j$ is replaced by $\h_{j+1}$ and $\|B\|=L^{dj}$ is replaced by $L^{d(j+1)}$, and since $\ggen_{j+1}\asymp \ggen_j$ by , we conclude that $V \in \bar\DV_{j+1}(\ell_{j+1}) \cap \bar\DV_{j+1}(h_j)$ (with adjusted constants). The desired result then follows exactly as in the proof of (ii), now with applied at scale-$(j+1)$. This completes the proof. \[rk:hsigmot\] The choice of $\h_\sigma$ in can be motivated as follows; we discuss this for the case $\h=\ell$. Since the norm gives a better bound on the observables when $\h_\sigma$ is chosen large, as a first attempt it would be natural to choose $\ell_\sigma$ as large as possible to make the norm of $\lambdaa\sigma\bar\phi$ agree with (or be bounded by) that of $g\tau^{2}$ on a block, namely $\ggen_j\ell_j^4 L^{dj}=\ggen_j\ell_0^4$. The coupling constant $\lambdaa$ is $O(1)$. The $T_0$ norm of $\sigma\bar\phi$ is $\ell_\sigma \ell$, and to make this no larger than the norm of $g\tau^{2}$ a block, we could choose $\ell_{\sigma,j} = \ggen_j L^{[\phi]j}$. In addition, our choice of $\ell_\sigma$ must also be appropriate for the $\sigma\bar\sigma$ term which arises in $\Vpt$. Our procedure is to take $\qa=\qb=0$ in $V$. Thus, according to the flow of $q$ given in [@BBS-rg-pt], the $\sigma\bar\sigma$ term in $\Vpt$ is given by the increment $\lambdaa\lambdab C_{j+1;a,b}\sigma\bar\sigma$ (which is only nonzero above the coalescence scale $j_{ab}$). According to , with the above choice of $\ell_\sigma$ the norm of this term is of order $L^{-2[\phi]j} \ell_\sigma^2 = \ggen_j^2$, and this is significantly smaller than the norm of the $\lambdaa \sigma \bar\phi$ term (which is good). However, a disadvantage of the choice $\ell_{\sigma,j} = \ggen_j L^{[\phi]j}$ is that it would make the monomial $\sigma\bar\sigma\phi\bar\phi$ be marginal (scale invariant), hence in the range of $\LT$ and thus in $\Vpt$. This monomial only appears after the coalescence scale, and we would prefer it to be irrelevant. To achieve this, we decrease the size of $\ell_\sigma$ to the choice $\ell_\sigma = \ggen_j 2^{(j-j_{ab})_+}L^{[\phi](j \wedge j_{ab})}$ made in . Then $\ell_\sigma$ grows as a power of $L$ below the coalescence scale, but only by a power of $2$ above the coalescence scale. This power of 2 plays a role in the proof of [@BBS-saw4 Theorem \[saw4-thm:wsaw4\]]. The small parameter epsilonbar {#sec:epdV-app} ------------------------------ For $j <N$, we define $$\lbeq{ellhatdef} \hat \ell_j^2 = \hat\ell_0^2 \ell_j^2 \\|C_{(j+1)}\\|_{\Phi_{j}^+(\ell_{j})},$$ with $C_{k}$ defined by . We choose $\hat\ell_0^2 = 100/ c_G$, where $c_G=c(\alpha_G)$ is the constant of [@BS-rg-norm Proposition \[norm-prop:EG2\]] (this choice is useful in the proof of Lemma \[lem:dIipV\] below), so that $$\lbeq{ellhatdef-1} \\|C_{(j+1)}\\|_{\Phi_{j}^+(\hat\ell_{j})} = \\|C_{(j+1)}\\|_{\Phi_{j}^+(\ell_{j})} \frac{\ell_j^2}{\hat\ell_j^2} = \hat\ell_0^{-2} = \frac{1}{100} c_G.$$ Below the $\Omega$-scale defined by , $\hat\ell_j$ and $\ell_j$ are of the same order of magnitude, but well above the $\Omega$-scale $\hat\ell_j \ll \ell_j$. We use $\hat\ell_j$ in estimates involving integration, as a parameter which captures the size of the covariance effectively. Let $$\label{e:dVdef} \delta V = \theta V - \Vpt = \theta V - V_{\pt,j+1}(V).$$ Recall the definition of $\epdV$ from . The following lemma justifies the notation used for $\epdV$, by showing that it provides an upper bound for $\delta V$. Its restriction to $j<N$ is to keep $\delta V$ defined in . \[lem:epdV\] Let $j<N$. There is an $L$-dependent constant $C_{\delta V}$ such that for all $V \in \bar\DV_j$, and for $j_=j$ or $j_=j+1$, $$\label{e:dVbd} \max_{b \in \Bcal_j} \\|\delta V(b)\\|_{T_{0,j_}(\h_{j_} \sqcup \hat\ell_{j_})} \le C_{\delta V} \epdV.$$ We fix $j<N$, concentrate first on the case $j_=j$, and drop subscripts $j$. We show that for $V \in \Qcalnabla$ and $b \in \Bcal_j$, $$\label{e:dVbdz-old} \\|\delta V(b)\\|_{T_{0}(\h \sqcup \hat\ell)} \prec_L \frac{\hat\ell}{\h} \epsilon_{V} + \epdV^2 .$$ This suffices, since (using ) the first term on the right-hand side of obeys $$\frac{\hat\ell}{\h} \epsilon_{V} = \\|C\\|_{\Phi^+(\ell)}^{1/2} \frac{\ell}{\h} \epsilon_{V} \prec \chicCov_{j}^{1/2} \frac{\ell}{\h} \epsilon_{V} \prec_L \begin{cases} \chicCov_{j}^{1/2}\ggen = \epdV(\ell) & \h=\ell \\ \chicCov_{j}^{1/2}\ggen^{1/4} = \epdV(h) & \h=h. \end{cases}$$ This gives and reduces the proof to showing . We now prove . By and , with $C=C_{j+1}$, $$\Vpt -V= 2gC_{0,0}\tau - P.$$ Therefore, by definition of $\delta V$ in and by the triangle inequality, $$\begin{aligned} \\|\delta V(b)\\|_{T_{0}(\h \sqcup \hat\ell)} & \le \\|\theta V(b) - V(b)\\|_{T_{0}(\h\sqcup \hat\ell)} + \\|V(b)-\Vpt (b)\\|_{T_{0}(\h)} \nnb & \le \\|\theta V(b) - V(b)\\|_{T_{0}(\h \sqcup \hat\ell)} + \\|C\\|_{\Phi(\h)} \h^2 \\|2g \tau(b)\\|_{T_0(\h)} + \\|P(b)\\|_{T_{0}(\h)} . \label{e:dVbd1}\end{aligned}$$ For the first term on the right-hand side of , we use the triangle inequality to work term by term in the monomials in $V$. For example, the $\tau$ term makes a contribution $$\\|\nu(\theta \tau(b) - \tau(b))\\|_{T_{0}(\h \sqcup \hat\ell)}.$$ After expansion in the fluctuation fields $\xi,\bar\xi,\eta,\bar\eta$, the difference $\theta \tau(b) - \tau(b)$ is given by a sum of products of fluctuation fields and $\phi,\bar\phi,\psi,\bar\psi$ fields, with each term containing two fields of which at least one is a fluctuation field. Thus it is bounded by $O(\hat\ell \h)$. The end result is a bound on $\\|\theta V(b) - V(b)\\|_{T_{0}(\h \sqcup \hat\ell)}$ equal to $\hat\ell/\h$ times the $T_0(\h)$ semi-norm of the worst monomial in $V$ (but without the $\sigma\bar\sigma$ term which cancels). This gives $$\label{e:epsthetaV} \\|\theta V(b) - V(b)\\|_{T_{0}(\h \sqcup \hat\ell)} \prec \frac{\hat\ell}{\h} \gh.$$ For the second term on the right-hand side of , $$\\|C\\|_\Phi \h^2 \\|2g \tau(b)\\|_{T_0} \prec \\|C\\|_{\Phi(\h)} \epV = \frac{\hat\ell^2}{\h^2} \\|C\\|_{\Phi(\hat\ell)} \gh .$$ For the last term, we use to obtain $$\\|P(b)\\|_{T_0} \prec_L \epdV^2 .$$ The combination of the last three inequalities gives and the proof for the case $j_=j$ is complete. Finally, for the case $j_=j+1$, we start with the first line of with norms at scale $j+1$. The norm of $V-\Vpt$ is bounded by its scale-$j$ counterpart, by Lemma \[lem:Imono\]. In addition, applies also at scale $j+1$, and this give the desired conclusion and completes the proof. Estimates on field polynomials {#sec:W} ============================== In this section, we prove the following proposition, which gives our main estimates on the field polynomials $F,W,P$. As usual, $\epdV$ depends on whether $\h=\ell$ or $\h=h$, as indicated in . Recall that $P_j$ is defined for $0 \le j <N$, so there is no bound missing in . \[prop:Wnorms\] For $L$ sufficiently large and $V \in \bar\DV_j$, $$\begin{aligned} \label{e:Fepbd} \max_{B \in \Bcal_{j}} \sum_{x \in B} \sum_{B' \in \Bcal_j(\Lambda)} \\|F_{\pi,C_{j}}(V_x,V(B'))\\|_{T_{0,j}(\h_{j})} &\prec_L \epdV_{j}^2 \quad (j \le N) , \\ \label{e:Wbomega} \max_{B \in \Bcal_{j}} \sum_{x\in B} \\|W_j(V,x)\\|_{T_{0,j}(\h_j)} &\prec_L \epdV_{j}^2 \quad (j \le N) , \\ \label{e:epP} \max_{B \in \Bcal_{j}} \sum_{x\in B} \\|P_j(V,x)\\|_{T_{0,j}(\h_{j})} &\prec_L \epdV_{j}^2 \quad (j < N) .\end{aligned}$$ \[rk:sm\] Scale mismatch.* The bounds of Proposition \[prop:Wnorms\] continue to hold if $T_{0,j\pm 1}(\h_{j\pm 1})$ would be used on the left-hand sides instead of $T_{0,j}(\h_{j})$ (for indices that do not exceed the final scale). In fact, $F$ and $W$ are (non-local) polynomials of degree at most six, and $P$ is a (local) polynomial of degree at most four. A change of $\pm 1$ in $j$ in the evaluation of on of these $T_0$ semi-norms can therefore only give rise to a bounded power of $L$, and constants in – are permitted to depend on $L$. We prepare for the proof in Section \[sec:Pformula\] with useful identities for $P$ and $W$, and the proof is concluded in Section \[sec:examples4\]. The proof is based on a crucial contraction estimate from [@BS-rg-loc] for the operator $\LT$, which we recall below as Proposition \[prop:1-LTdefXY-loc\]. Preliminary identities {#sec:Pformula} ---------------------- The first lemma provides a formula for the expectation of $F$. \[lem:EthF\] For polynomials $A,B$ in the fields, and for covariances $C,w$, $$\label{e:EthF} e^{\Lcal_C} F_{\pi,w} (A,B) = F_{\pi,w+C}(e^{\Lcal_C} A, e^{\Lcal_C} B) - F_{\pi,C}(e^{\Lcal_C} A, e^{\Lcal_C} B).$$ By the definition of $F$ in , $$\begin{aligned} F_{w+C}(e^{\Lcal_C}A,e^{\Lcal_C}B) &= e^{\Lcal_C} e^{\Lcal_w} \big(e^{-\Lcal_{w}}A\big) \big(e^{-\Lcal_{w}} B\big) -(e^{\Lcal_C}A)(e^{\Lcal_C}B) \nnb &= e^{\Lcal_C} F_{w}( A, B) + e^{\Lcal_C} \left(AB \right) - (e^{\Lcal_C}A)(e^{\Lcal_C}B) \nnb &= e^{\Lcal_C} F_{w}( A, B) + F_{C}(e^{\Lcal_C}A,e^{\Lcal_C}B) . \label{e:EFAB}\end{aligned}$$ Rearrangement gives $$\label{e:EthFnopi} e^{\Lcal_C} F_{w} (A,B) = F_{w+C}(e^{\Lcal_C} A, e^{\Lcal_C} B) - F_{C}(e^{\Lcal_C} A, e^{\Lcal_C} B),$$ and, by and the fact that the projection operators commute with $e^{\Lcal_C}$, extends to the same equation with $F$ replaced by $F_\pi$. For the next lemma, we define $$\begin{aligned} \label{e:Pxydef} P_j(V'_x,V''_y) &= \frac{1}{2} \LT_{x} F_{\pi,w_{j+1}} (e^{\Lcal_{j+1}} V'_x,e^{\Lcal_{j+1}} V''_y) - \frac{1}{2} e^{\Lcal_{j+1}}\LT_{x} F_{\pi,w_{j}} ( V'_x, V''_y) \nnb & \hspace{60mm} (0 \le j < N-1) , \\ \label{e:Wpoint} W_j(V'_x,V''_y) &= \frac 12 (1-\LT_x) F_{\pi,w_j}(V'_x,V''_y) \quad (1 \le j < N) .\end{aligned}$$ Both definitions will be extended to the final scale in Section \[sec:Pbd\], but this extension is not yet needed here. By definition, for $j<N$, $$\lbeq{WVVsum} W_j(V,x) = \sum_{y \in \Lambda}W_j(V_x,V_y).$$ With the definition of $P_j(V)$ in , the next lemma shows that, for $j<N-1$, $$\lbeq{PVVsum} P_j(V,x) = \sum_{y \in \Lambda}P_j(V_x,V_y).$$ For its proof, we observe that since $e^{\Lcal_C}$ reduces the dimension of a monomial in the fields, $e^{\Lcal_C} : \Vcal \to \Vcal$, and since $\LT_X$ acts as the identity on $\Vcal$, it follows that $$\label{e:LTELT} \LT_X e^{\Lcal_C} \LT_X = e^{\Lcal_C} \LT_X.$$ \[lem:Palt\] For $x,y\in \Lambda$, $0\le j < N-1$, and for $V',V'' \in \Vcal$, $$\begin{aligned} \label{e:Palt0} P_j(V'_x,V''_y) &= \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V_x',V_y'') + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}}V_x',e^{\Lcal_{j+1}} V_y'') \right) .\end{aligned}$$ Consider first the case $j<N-1$. By definition of $W_j$ in , the right-hand side of can be rewritten as $$\label{e:Pxformula} \frac 12 \LT_x \big( e^{\Lcal_{j+1}} (1-\LT_x)F_{\pi,w_{j}}( V_x', V_y'') + F_{\pi,C_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \big).$$ Application of shows that is equal to $$\begin{aligned} & \frac 12 \LT_x \big( e^{\Lcal_{j+1}} F_{\pi,w_{j}}( V_x', V_y'') + F_{\pi,C_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \big) - \frac{1}{2} e^{\Lcal_{j+1}} \LT_x F_{\pi,w_{j}}( V_x', V_y'') . \label{e:Pxformula1}\end{aligned}$$ By , is equal to $$\begin{aligned} \frac 12 \LT_{x} F_{\pi,w_{j+1}} (e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') - \frac 12 e^{\Lcal_{j+1}}\LT_{x} F_{\pi,w_{j}} ( V_x', V_y'') ,\end{aligned}$$ which is . The following lemma computes the expectation of $W$. \[lem:EW\] For $x,y \in \Lambda$, $j < N$, and for $V',V'' \in \Vcal$, $$\begin{aligned} \label{e:Palt1b} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) &= W_{j} (e^{\Lcal_j} V'_x, e^{\Lcal_j} V''_y) + P_{j-1}(V'_x,V''_y) - \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) .\end{aligned}$$ By and the formula for $P$, $$\begin{aligned} \label{e:Palt5} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) &= \frac{1}{2} e^{\Lcal_j} F_{\pi,w_{j-1}}( V'_x,V''_y) - \frac{1}{2} e^{\Lcal_j} \LT_x F_{\pi,w_{j-1} }(V'_x,V''_y) \nnb & = \frac{1}{2} e^{\Lcal_j} F_{\pi,w_{j-1}}( V'_x,V''_y) + P_{j-1}(V'_x,V''_y) \nnb & \qquad - \frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) .\end{aligned}$$ Substitution of into gives $$\begin{aligned} e^{\Lcal_j} W_{j-1} (V'_x,V''_y) & = F_{\pi,w_j}(e^{\Lcal_j}V_x',e^{\Lcal_j}V_y'') -F_{\pi,C_j}(e^{\Lcal_j}V_x',e^{\Lcal_j}V_y'') \nnb & \quad + P_{j-1}(V'_x,V''_y) - \frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) ,\end{aligned}$$ which is the same as . The next lemma applies Lemma \[lem:EW\] to obtain a formula that enables us to bound $W$ recursively, in Proposition \[prop:Wbounds\] below. \[lem:W-explicit\] For $x,y \in \Lambda$, $j<N$, and $V',V'' \in \Vcal$, $$\label{e:WWF} W_{j} (V'_x,V''_y) = (1-\LT_{x}) \Big( e^{\Lcal_j} W_{j-1} (e^{-\Lcal_j} V'_x , e^{-\Lcal_j} V''_y) + \frac{1}{2} F_{\pi ,C_j} ( V'_x,V''_y ) \Big) .$$ The equalities $$\begin{aligned} &W_{j}(e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) - P_{j-1}(V'_x,V''_y) + \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) \nnb &\quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) -\frac{1}{2} \LT_{x} F_{\pi,w_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) + \frac{1}{2} e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) \nnb & \quad + \frac{1}{2} F_{\pi,C_j }(e^{\Lcal_j} V_x,e^{\Lcal_j} V''_y) \nnb & \quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) + \frac{1}{2} e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) +\frac{1}{2} F_{\pi,C_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) \nnb & \quad - \frac{1}{2}\LT_x F_{\pi,C_j} (e^{\Lcal_j}V'_x,V''_y) - \frac{1}{2}\LT_x e^{\Lcal_j} F_{\pi,w_{j-1}}(V'_x,V''_y) \nnb & \quad = e^{\Lcal_j} W_{j-1} (V'_x,V''_y) +\frac{1}{2}(1-\LT_x) F_{\pi,C_j} (e^{\Lcal_j} V'_x,e^{\Lcal_j} V''_y) \nnb & \quad + \frac{1}{2} \LT_x e^{\Lcal_j}\LT_{x} F_{\pi,w_{j-1}} ( V'_x, V''_y) - \frac{1}{2}\LT_x e^{\Lcal_j} F_{\pi,w_{j-1}}(V'_x,V''_y) \end{aligned}$$ give the desired result. The first equality is , the second follows from the formula for $P$ in , the third uses , and for the last we used to insert an operator $\LT_x$ acting on the second term of the third right-hand side. Proof of Proposition \[prop:Wnorms\] {#sec:examples4} ------------------------------------ We now prove the estimates on $F,W,P$ stated in Proposition \[prop:Wnorms\]. We first consider $F$, then recall the crucial contraction estimate from [@BS-rg-loc] concerning the operator $\LT$, then apply the contraction estimate to obtain bounds on $W$ and $P$. ### Bound on F {#sec:Fbds} We now prove the bound on $F$. Operator bounds on the Laplacian as a map on $T_\phi$ are given in [@BS-rg-norm Proposition \[norm-prop:Etau-bound\]], which asserts that the operators $\Lcal_C$ and $e^{\pm \Lcal_C}$, restricted to the subspace of $\Ncal$ consisting of polynomials of degree $A$ with semi-norm $\\|\cdot \\|_{T_{\phi}}$, are bounded operators whose norms obey $$\label{e:eDC} \\|\Lcal_C\\| \leq A^2 \\|C\\|_\Phi, \quad \quad \\|e^{\pm \Lcal_C }\\| \le e^{A^2 \\|C\\|_{\Phi}}.$$ The above operator norms are for operators acting on $T_{\phi}$, with the scale fixed. Let $Y(C,x)= \{y : C_{x,y} \neq 0\}$. Recall , which implies that the diameter and volume of $Y(C_k,x)$ obey $$\label{e:YCbd} {\rm diam}\left(Y(C_k,x)\right) \le L^k, \quad\quad \|Y (C_{k},x)\| \le L^{dk}.$$ We recall the definition of $\Lcallr_w$ from [@BBS-rg-pt], and also recall [@BBS-rg-pt Lemma \[pt-lem:Fexpand\]], which asserts that for $V',V''$ of degree at most $A$, $$\label{e:FCsum} F_{w} (V'_{x} , V''_{y} ) = \sum_{n=1}^A \frac{1}{n!} V_x' (\Lcallr_w)^n V_y''.$$ \[lem:Fpibd-bis\] Suppose that $\\|C\\|_\Phi \le 1$. Then for $x,y \in \Lambda$ and $V' ,V'' \in \Vcal$, $$\label{e:FCABX} \\| F_{\pi ,C} (V'_{x} , V''_{y} ) \\|_{T_{0}} \prec \\|C\\|_{\Phi} \\|V'_{x}\\|_{T_{0}} \\|V''_y\\|_{T_{0}}\1_{y \in Y(C,x)} .$$ Also, $ F_{\pi ,C} (V'_{x} , V''_{y} ) \in \Ncal(Y(C,x))$ and $ \sum_{y \in \Lambda}W_{w} (V_x' , V_y'' ) \in \Ncal(Y(w,x))$. By , it follows from that $ F_{\pi ,C} (V'_{x} , V''_{y} ) \in \Ncal(Y(C,x))$. It then follows from that $ W_{w} (V' , V'',\{x\} ) \in \Ncal(Y(w,x))$. Now we prove . We have already shown that the left-hand side is zero for $y \not \in Y(C,x)$, so it suffices to prove without the factor $\1_{y \in Y(C,x)}$. Furthermore, by , it is enough to prove with $F_{\pi ,C}$ replaced by $F_{C}$. For $t\ge 0$, let $$\label{e:F1} F (t) = e^{\Lcal_{tC}} \left( (e^{-\Lcal_{tC}}V_x') (e^{-\Lcal_{tC}}V_y'') \right) .$$ Since $V',V''$ are polynomials in fields, by expanding each of the exponentials we find that $F (t)$ is a polynomial $\sum_{n= 0}^m F_{n}t^{n}$, for some finite $m$. According to the second inequality of , there is a $k>0$ determined by $\\|tC \\|_{\Phi}$ such that $$\sum_{n= 0}^m \\|F_{n}\\|_{T_{0}}\|t\|^{n} \le k \\|V'_{x}\\|_{T_{0}} \\|V''_y\\|_{T_{0}} .$$ Although $k$ depends on $\\|tC \\|_{\Phi}$, it is uniform for $\\|tC \\|_{\Phi} \le 1$. By , $$F_{C} (V'_{x} , V''_{y} ) = F (1) - F (0) = \sum_{n= 1}^m F_{n} .$$ Therefore, taking $t = \\|C\\|_{\Phi}^{-1} \ge 1$, we obtain $$\\|F_{C} (V'_{x} , V''_{y} )\\|_{T_{0}} \le \sum_{n= 1}^m \\|F_{n}\\|_{T_{0}} \le \frac{1}{t} \sum_{n= 1}^m \\|F_{n}\\|_{T_{0}}t^{n} \le k \\|C\\|_{\Phi} \\|V'_{x}\\|_{T_{0}} \\|V''_y\\|_{T_{0}} ,$$ which completes the proof. To estimate the covariance of $C_j$, we use to conclude that for $j \le N$, $$\begin{aligned} \lbeq{Chbd} \\|C_{j}\\|_{\Phi_j(\h_k)} &\prec_L \begin{cases} \chi_j & \h_j=\ell_j \\ \chi_j \ggen_j^{1/2} & \h_j=h_j . \end{cases}\end{aligned}$$ The case $\h_j=\ell_j$ follows immediately from , and the case $\h_j=h_j$ follows from $$\label{e:ellh} \\|C_{j}\\|_{\Phi_j(h_j)} = \left( \frac{\ell_{j}}{h_j}\right)^2 \\|C_{j}\\|_{\Phi_j(\ell_j)} = \left( \frac{\ell_0}{k_0} \right)^2 \ggen_j^{1/2} \\|C_{j}\\|_{\Phi_j(\ell_j)} \prec_L \; \ggen_j^{1/2} \chi_j.$$ Let $1 \le j \le N$. Summation of gives, for any $B \in \Bcal_{j}$, the upper bound $$\label{e:FepWbd} \sum_{x \in B} \sum_{y \in \Lambda } \\|F_{\pi,C_{j}}(V'_x,V'_y)\\|_{T_{0,j}(\h_j)} \prec \\|C_j \\|_{\Phi_j(\h_j)} \epsilon_{V',j} \epsilon_{V'',j}.$$ We set $V'=V''=V$ in . Since $V \in \bar\DV_j$, $\epsilon_{V,j}$ is bounded by a multiple of $\ggen_j$ for $\h=\ell$, and of $1$ for $\h=h$. With , this gives $$\label{e:Fepbd-bis} \max_{B \in \Bcal_{j}} \sum_{x \in B} \sum_{y \in \Lambda } \\|F_{\pi,C_{j}}(V_x,V_y)\\|_{T_{0,j}} \prec_L \epdV^2 ,$$ which is the desired estimate . ### Loc and the crucial contraction {#sec:cl} It is shown in [@BS-rg-loc Proposition \[loc-prop:opLTdefXY\]] (with $R=L^{-j}$) that $\LT_X$ is a bounded operator on $T_0$ in the sense that if $F \in \Ncal(X)$ then $$\label{e:LTXY5} \\|\LT_{X}F\\|_{T_0} \le \bar{C}' \\|F\\|_{T_0},$$ where $\bar{C}'$ depends on $L^{-j}{\rm diam}( X)$. We also recall [@BS-rg-loc Proposition \[loc-prop:1-LTdefXY\]], which is the crucial contraction estimate which we state here as follows. As in [@BS-rg-loc Definition \[loc-def:LTXYsym\]], we use the notation $X(\varnothing)=X$, $X(a) = X \cap \{a\}$, $X(b)=X \cap \{b\}$, and $X(ab) = X \cap\{a,b\}$. As discussed in Section \[sec:formint\], $d_+ = d$ on $\Ncal^\varnothing$, $d_+=0$ on $\Ncal^{ab}$, whereas when $\LT$ acts at scale $k$ on $\Ncal^a$ and $\Ncal^b$, $d_+=[\phi]=\frac{d-2}{2}=1$ if $k<j_{\pp\qq}$ and $d_+=0$ for $k \ge j_{\pp\qq}$. For $\alpha,\beta \in \{ \varnothing, a,b,ab\}$, we define $d_{\alpha}'=d_\alpha +1$, and $$\label{e:cgamobs-loc} \cgam_{\alpha,\beta} = (L^{-d_{\alpha}'} + L^{-(A+1)[\phi]}) \left( \frac{\h'_\sigma}{\h_\sigma} \right)^{\|\alpha \cup \beta\|} .$$ \[prop:1-LTdefXY-loc\] Let $A < p_\Ncal$ be a positive integer, and let $\varnothing \not = Y \subset X \in \Pcal_j$. Let $F_{1} \in \Ncal (X)$, and let $F_2 \in \Ncal(Y)$ with $\pi_{\alpha}F_{2}=0$ when $Y(\alpha)=\varnothing$. Let $F = F_1(1-\LT_{Y})F_2$. Let $T_\phi'$ denote the $T_{\phi,j+1}(c\h_{j+1})$ semi-norm for any fixed $c \ge 1$, and let $T_\phi$ denote the $T_{\phi,j}(\h_{j})$ semi-norm. Then $$\begin{aligned} \label{e:LTXY5a-loc} \\|F\\|_{T_{\phi}'} &\le \bar{C} \sum_{\alpha,\beta=\varnothing ,\pp ,\qq,\pp\qq} \cgam_{\alpha,\beta} \left(1 + \\|\phi\\|_{\Phi'}\right)^{A'} \nnb & \quad \quad \times \sup_{0\le t \le 1} \big( \\|\pi_\beta F_{1} \pi_\alpha F_{2}\\|_{T_{t\phi}} + \\|\pi_\beta F_{1}\\|_{T_{t\phi}}\\|\pi_\alpha F_{2}\\|_{T_{0}}\big) \\|\sigma^{\alpha\cup\beta}\\|_{T_0},\end{aligned}$$ where $A'=A+d_{\alpha}/[\phi] +1$, and $\bar C$ depends on $c$ and $L^{-j}{\rm diam}( X)$. As a corollary, we specialise to our particular setting to obtain the following proposition. We state Proposition \[prop:1-LTdefXY\] in a more general form than is needed to bound $W$, but the additional generality is used in the proof of Proposition \[prop:cl\]. \[prop:1-LTdefXY\] Let $d\ge 4$, $A=\lceil 2(d+1)/(d-2)\rceil$, and assume that $p_\Ncal >A$. Let $\varnothing \not = Y \subset X \in \Pcal_j$. Let $F_{1} \in \Ncal (X)$, let $F_2 \in \Ncal(Y)$ with $\pi_{\alpha}F_{2} =0$ when $Y(\alpha)=\varnothing$, and let $F = F_1(1-\LT_{Y})F_2$. Suppose that each of $F_1,F_2, F_1F_2$ has no component in $\Ncal_{ab}$ unless $j \ge j_{ab}$ (recall ). Let $T_\phi'$ denote the $T_{\phi,j+1}(c\h_{j+1})$ semi-norm for some fixed $c \ge 1$, and let $T_\phi$ denote the $T_{\phi,j}(\h_{j})$ semi-norm. There is a constant $\bar C$ depending on $c$ and $L^{-j}{\rm diam}( X)$ such that $$\begin{aligned} \label{e:LTXY5a} \\|F\\|_{T_{\phi}'} &\le \bar{C} \cgam \left(1 + \\|\phi\\|_{\Phi'}\right)^{A+d+1} \sup_{0\le t \le 1} \big( \\|F_{1}F_{2}\\|_{T_{t\phi}} + \\|F_{1}\\|_{T_{t\phi}}\\|F_{2}\\|_{T_{0}}\big) ,\end{aligned}$$ with $$\label{e:cgamobs} \gamma = \gamma(Y) = L^{-d -1} + L^{-1}\1_{Y \cap \{a,b\} \not = \varnothing}.$$ Moreover, if $\pi_F_2=0$ then we can replace by $\gamma = L^{-d-1}$. In our setting, $d_\varnothing =d$, $d_{ab}=0$, and $d_a=d_b=1$ if $j<j_{ab}$ whereas $d_a=d_b=0$ if $j\ge j_{ab}$. Also, $[\phi]=\frac{d-2}{2}\ge 1$ for all $\alpha$. In particular, $A+d_{\alpha}/[\phi] +1 \le A+d+1$. Our choice of $A$ ensures that $(A+1) [\phi] \ge d+1 \ge d_\alpha + 1$ for all $\alpha$. By , $$\frac{\h_{\sigma,j+1}}{\h_{\sigma,j}} \le {\rm const}\, \begin{cases} L^{[\phi]} & j < j_{ab} \\ 1 & j \ge j_{ab}. \end{cases}$$ By assumption, when $\|\alpha \cup \beta\|=2$ we can use the $j \ge j_{ab}$ version of the above bound. Also by assumption, for $\alpha =a,b,ab$ we have $\pi_\alpha F_{2} =0$ when $Y \cap \{a,b\} = \varnothing$. Taking these points into account, from we obtain $$\gamma_{\alpha,\beta} \le 2\, \begin{cases} L^{-d-1} & \|\alpha \cup \beta\| =0 \\ L^{-1}\1_{Y \cap \{a,b\} \not = \varnothing} & \|\alpha \cup \beta\| =1,2. \end{cases}$$ This shows that $\gamma_{\alpha,\beta} \le 2 \gamma$ uniformly in $\alpha,\beta$. It follows from that $$\big( \\|\pi_\beta F_{1} \pi_\alpha F_{2}\\|_{T_{t\phi}} + \\|\pi_\beta F_{1}\\|_{T_{t\phi}}\\|\pi_\alpha F_{2}\\|_{T_{0}}\big) \\|\sigma^{\alpha\cup\beta}\\|_{T_0} \le \\|F_{1}F_{2}\\|_{T_{t\phi}} + \\|F_{1}\\|_{T_{t\phi}}\\|F_{2}\\|_{T_{0}}.$$ Together with Proposition \[prop:1-LTdefXY-loc\], these facts give the desired estimate and the proof is complete. ### Bound on W {#sec:Wbds} We now prove for $j<N$, beginning with the following proposition, whose proof requires our assumption that $L$ is large. We defer the case $j=N$ of (and also of ) to Sections \[sec:Pbd\]–\[sec:Waux\]. \[prop:Wbounds\] Let $j<N$. In general, $\pi_{ab}W_j =0$. Let $V',V'' \in \Vcal$. Suppose there is a sequence $v_k'$ with $v_{k-1}' \prec v_k'$ for all $k \le j$, such that $\max_{B \in \Bcal_k} \sum_{x \in B}\\|V'_x\\|_{T_{0,k}} \le v_k'$, and similarly for $V''$. Then there is a constant $c$ such that $$\label{e:Wbound2az} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \\|W_{j}(V'_x,V''_y)\\|_{T_{0,j}(\h_j)} \le c \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' .$$ In $W$, we can exclude the $\sigma\bar\sigma$ terms in each of $V',V''$ since these contribute zero to $F$. Thus the only possible $\sigma\bar\sigma$ contribution to $W$ can be due to the contribution to $F$ due to a contraction of $\sigma\bar\phi_a$ with $\bar\sigma \phi_b$. Such a contraction contains no boson or fermion fields, so is annihilated by $1-\LT_{\{x\}}$. This proves that $\pi_{ab}W=0$, and it remains to prove . We prove , by induction on $j$. Our induction hypothesis is that holds for $j-1$, and we use this to prove that it also holds for $j$. Initially $W_0=0$, so it is trivial to begin the induction. The starting point is Lemma \[lem:W-explicit\], which implies that $$\label{e:WWFj} W_{j} (V'_x,V''_y) = (1-\LT_{x}) \Big( e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y) + \frac{1}{2} F_{\pi ,C_{j}} ( V'_x,V''_y ) \Big) .$$ We estimate using the triangle inequality on the right-hand side, retaining the cancellation in $1-\LT_{\{x\}}$ for the first term but not for the second. With , this gives $$\begin{aligned} \label{e:WWFj2} \\|W_{j} (V'_x,V''_y)\\|_{T_{0,j}} & \le \\|(1-\LT_{x}) e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y)\\|_{T_{0,j}} \nnb & \quad + \frac{1}{2}(1+\bar C) \\| F_{\pi ,C_{j}} ( V'_x,V''_y )\\|_{T_{0,j}}.\end{aligned}$$ The constant $\bar C$ is independent of $j$, as a consequence of together with the fact that $ F_{\pi ,C_j} (V'_{x} , V''_{y} ) \in \Ncal(Y(C_j,x))$ by Lemma \[lem:Fpibd-bis\]. We begin with the second term on the right-hand side of . After application of Lemma \[lem:Fpibd-bis\] and , and summation over $x,y$, we find that there is a constant $\Fconst$ such that $$\label{e:ind2nd} \frac{1}{2}(1+\bar C) \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \\| F_{\pi ,C_{j}} ( V'_x,V''_y )\\|_{T_{0,j}} \le \bar\Fconst \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j''.$$ For the first term on the right-hand side, we apply Proposition \[prop:1-LTdefXY\] with $F_1=1$ and $F_2 = e^{\Lcal_{j}} W_{j-1} (e^{-\Lcal_{j}} V'_x , e^{-\Lcal_{j}} V''_y)$. Note that, as required by the hypotheses of Proposition \[prop:1-LTdefXY\], $\pi_F_2 =0$ unless $x \in \{a,b\}$; this is a consequence of the careful definition of $F_{\pi,C}$ in , which ensures that if one of $\pi_V'$ or $\pi_V''$ is nonzero then $\pi_V'$ must be nonzero. The application of Proposition \[prop:1-LTdefXY\] gives the estimate $$\lbeq{ind-1Loc} \\|(1-\LT_{x})F_2\\|_{T_{0,j}} \le \bar{C} \gamma_x \\|F_2\\|_{T_{0,j-1}} ,$$ with $$\gamma_x = L^{-d-1}+L^{-1}\1_{x \in \{a,b\}},$$ and with a scale-independent constant $\bar C$ since $F_2 \in \Ncal(Y (C_{j-1},x))$ by Lemma \[lem:Fpibd-bis\]. The operators $e^{\pm \Lcal_j}$ are bounded on $T_{0,j-1}$, by and the fact that $$\lbeq{Cnormcomp} \\|C_{j}\\|_{\Phi_{j-1}(\h_{j-1})} \le \\|C_{j}\\|_{\Phi_{j}(\h_{j-1})} = (\ell_{j}/\h_{j-1})^2 \\|C_{j}\\|_{\Phi_{j}(\ell_{j})} \le (\ell_{j}/\h_{j-1})^2 \ellconst \le 1$$ using and . Thus, by the induction hypothesis, there is a constant $\bar A$ such that $$\label{e:W22} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \gamma_x \\|F_2\\|_{T_{0,j}} \le \bar{A} c L^{-1} \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' ,$$ where we have used the fact that $B$ contains $L^d$ blocks of scale $j-1$, our assumption on the sequences $v_k'$ and $v_k''$, and that the factors involving $\chi$ and $\ell/\h$ change only by a constant factor under a single advance of scale. The combination of , and gives $$\label{e:Wind} \max_{B \in \Bcal_j} \sum_{x \in B} \sum_{y \in \Lambda} \\|W_{j}(V'_x,V''_y)\\|_{T_{0,j}(\h_j)} \le (\bar C \bar A c L^{-1} + \Fconst) \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j' v_j'' \1_{y \in Y(C_k,x)} .$$ We require that $L > \bar C \bar A$ (which we can do in view of our general hypothesis that $L$ is large enough). Then advances the induction with the choice $c= \Fconst/(1 - \bar C \bar A L^{-1})$, since this choice gives $\bar C \bar A c L^{-1} + \Fconst =c$. This completes the proof. Let $j<N$. For $V \in \bar\DV_j$, by direct computation as in the proof of Proposition \[prop:monobd\], we find that, for any $k \le j$ and $b \in \Bcal_k$, $\sum_{x \in B}\\|V_x\\|_{T_{0,k}}$ is bounded above by a multiple of $\ggen_j$ for $\h=\ell$, and of $\ggen_j/\ggen_k$ for $\h=h$. We apply Proposition \[prop:Wbounds\] with these two choices for $v_k$, which do obey its hypothesis by . This gives $$\begin{aligned} \sum_{x \in B} \\|W_{j}(V,x)\\|_{T_{0,j}} & \prec_L\; \begin{cases} \chi_j \ggen_j^2 & \h=\ell \\ \chi_j \ggen_j^{1/2} & \h=h. \end{cases} \label{e:Wepbd-bis}\end{aligned}$$ The right-hand side is $\epdV_j^2$ and this completes the proof. ### Bound on P {#sec:Pbd} We now prove , and also prove the case $j=N$ of . We first consider $j<N-1$, and recall from Lemma \[lem:Palt\] that $$\begin{aligned} \lbeq{PVV} P_j(V_x',V_y'') & = \LT_{x}\left( e^{\Lcal_{j+1}} W_{j}(V_x',V_y'') + \frac{1}{2} F_{\pi,C_{j+1}}(e^{\Lcal_{j+1}} V_x',e^{\Lcal_{j+1}} V_y'') \right) .\end{aligned}$$ We bound the operator norms of $\LT_x$ and $e^{\Lcal_{j+1}}$ as discussed previously (using ), and apply and , to conclude that under the same hypothesis on $V',V''$ as in Proposition \[prop:Wbounds\], $$\begin{aligned} \lbeq{PVVsumbd} \max_{B \in \Bcal_j} \sum_{x\in B} \sum_{y \in \Lambda} \\|P_j(V_x',V_y'')\\|_{T_{0,j}(\h_{j})} & \prec \chi_j \left( \frac{\ell_j}{\h_j} \right)^2 v_j'v_j'' .\end{aligned}$$ Then we set $V'=V''=V \in \bar\DV_j$ and as in the proof of we obtain $$\max_{B \in \Bcal_{j}} \sum_{x\in B} \\|P_j(V,x)\\|_{T_{0,j}(\h_{j})} \prec_L\; \epdV_{j}^2$$ as desired. This completes the proof of for $j<N-1$. As discussed in Section \[sec:finalscale\], our definition of $P_{N-1}$ is designed so that $P_{N-1}$ for the torus of scale $N$ is the same local polynomial as $P_{N-1,N+1}$ on the torus of scale $N+1$. Consequently we can apply on the torus of scale $N+1$ to obtain the desired estimate on $P_{N-1}$. According to , $$\begin{aligned} \label{e:WNdef-bis} W_{N}(V,x) & = e^{\Lcal_{N,N}} W_{N-1}(e^{-\Lcal_{N,N}}V,x) -P_{N-1}(e^{-\Lcal_{N,N}}V,x) + \frac 12 F_{\pi,C_{N,N}}(V_x,V(\Lambda)) .\end{aligned}$$ This obeys by using and together with the estimates on $W_{N-1}$, $P_{N-1}$, $F_{\pi,C_{N,N}}$ obtained above. ### Auxiliary estimates on W {#sec:Waux} In , we defined $P_{N-1}(V)$ to be equal to the common value that would give on any torus of scale larger than $N$. Similarly, we extend the definition of $P_j(V'_x,V''_y)$ to $j=N-1$ by defining it to be the common value of the right-hand side of , with $j=N-1$, on any torus of scale larger than $N$. In addition, we adapt the identity to define $W_N(V_x',V''_y)$ (which has not yet been defined for distinct $V',V''$) as $$\begin{aligned} \label{e:WNVV} W_{N} ( V'_x, V''_y) &= e^{\Lcal_{N,N}} W_{N-1} (e^{-\Lcal_{N,N}}V'_x,e^{-\Lcal_{N,N}}V''_y) - P_{N-1}(e^{-\Lcal_{N,N}}V'_x,e^{-\Lcal_{N,N}}V''_y) \nnb & \quad + \frac{1}{2} F_{\pi,C_{N,N} }(V_x,V''_y) .\end{aligned}$$ Then from we see that the identity extends to scale $j=N$: $$W_N(V,x) = \sum_{y \in \Lambda} W_N(V_x,V_y).$$ Also, the estimate of Proposition \[prop:Wbounds\] now extends to scale $N$. To see this, we use the definition , the fact that $e^{\pm\Lcal_{N,N}}$ is a bounded operator, the bounds on $W_{N-1}$ and $F$ obtained previously, and finally the fact that extends to its final scale $N-1$ by application of on a larger torus. The next lemma provides a concrete upper bound on $W_j(V',V'')$ when observables are absent. \[lem:W-logwish\] Suppose that $V',V'' \in \pi_\varnothing \Vcal$, and let $\|V\|_j = \max \{ \|g\|,L^{2j}\|\nu\|, \|z\|, \|y\|\}$. For $j \le N$, $$\begin{aligned} \max_{B \in \Bcal_j} \sum_{x \in B}\sum_{y \in \Lambda} \\|W_{j}(V'_x,V_y'')\\|_{T_{0,j}(\ell_j)} & \prec_L\; \chi_j \|V'\|_j \|V''\|_j. \label{e:W-logwish}\end{aligned}$$ Let $v_k=L^{dk}\\|V_x\\|_{T_{0,k}(\ell_k)}$. Direct computation of the $T_{0,k}(\ell_k)$ norm shows that $v_k \prec \|V\|_k \le \|V\|_j$ for $k \le j$. Then Proposition \[prop:Wbounds\] (extended as noted above to include $j=N$) gives a bound on the left-hand side of of order $v_{j}^2$, as desired. Finally, the next lemma provides estimates for later use. \[lem:Wbil\] For $j+1\le N$, $B \in \Bcal_j$, and $V\in \bar\DV_j$, $$\begin{aligned} \label{e:Wbil} \\|W_{j+1}(e^{\Lcal_{j+1}} V,B) -W_{j+1}(\Vpt,B)\\|_{T_{0,j+1}} &\prec_L \epdV_j^3.\end{aligned}$$ For $j \le N$, $B \in \Bcal_j$, $V\in \bar\DV_j$, and for $Q \in \Qcal$ with $\\|Q(B)\\|_{T_{0,j}} \prec \epdV_{j}$, $$\begin{aligned} \lbeq{Wprimebd-app} \\|W_j(Q(B),V(\Lambda))\\|_{T_0,j} &\prec_L \begin{cases} \epdV_j^2 & \h=\ell \\ \epdV_j^2 \ggen_j^{1/4} & \h=h, \end{cases} \\ \lbeq{Wprimebd-app2} \\|W_j(Q(B),Q(\Lambda))\\|_{T_0,j} &\prec_L \begin{cases} \epdV_j^2 & \h=\ell \\ \epdV_j^2 \ggen_j^{1/2} & \h=h. \end{cases}\end{aligned}$$ By linearity and the triangle inequality, W\_[j+1]{}(e\^[\_[j+1]{}]{} V) -W\_[j+1]{}()\_[T\_[0,j+1]{}]{} & W\_[j+1]{}(P,e\^[\_[j+1]{}]{} V)\_[T\_[0,j+1]{}]{} + W\_[j+1]{}(,P)\_[T\_[0,j+1]{}]{}. We apply Proposition \[prop:monobd\], use Proposition \[prop:Wnorms\] to see that for $B_k \in \Bcal_k$ it is the case that $\sum_{x \in B_k}\\|P_x\\|_{T_{0,k}} \prec_L \epdV_k^2$, and then apply Proposition \[prop:Wbounds\] (including its extension to scale $N$), to see that W\_[j+1]{}(e\^[\_[j+1]{}]{} V) -W\_[j+1]{}()\_[T\_[0,j+1]{}]{} & \_L \_j ( \_j/\_j)\^2 \_j\^2 \_j & =\ 1& =h \_j\^3 , \[e:Wbilbdell-app\] as required. For –, a similar calculation, using $\epsilon_Q \prec \epdV$ (by Lemma \[lem:T0ep\] and assumption) gives the desired result. This completes the proof. Proof of Propositions \[prop:Iupper\]–\[prop:JCK-app-1\] {#sec:I-estimates} ======================================================== In this section, we prove Propositions \[prop:Iupper\]–\[prop:JCK-app-1\]. Attention is restricted here to $d=4$. We begin by proving estimates on $\Ical=e^{-V}$ of . Since norms in the global space $\Phi=\Phi(\Lambda)$ can be replaced in upper bounds by the local space $\Phi (X)$ whenever an element of $\Ncal (X)$ is being estimated (as discussed around [@BS-rg-norm]), we sometimes write simply $\Phi$ rather than $\Phi(X)$. However, decay estimates (such as below) must always be stated in localised form. Temporarily, we write $a_0,b_0$ (rather than the usual $a,b$) for the points where observables are located in $V$, and instead we use $b$ for a block in $\Bcal_{j-1}$. Also, we write $$\epV(b) = \begin{cases} L^{-d} \epsilon_{V_\varnothing} & \{a_0,b_0\} \cap b = \varnothing \\ L^{-d} \epsilon_{V_\varnothing} + (\|\lambda^{a_0}\|+\|\lambda^{b_0}\|)\h\h_\sigma + \textstyle{\frac 12}(\|\q^{a_0}\|+\|\q^{b_0}\|)\h_\sigma^2 & \{a_0,b_0\} \cap b \neq \varnothing, \end{cases}$$ as opposed to $\epV$ which always includes the contribution from the observables. \[prop:Iupperzz\] Let $j \le N$. Let $V \in \Qcal$ with $0 \le \|{\rm Im}g \| \le \frac 12 {\rm Re}g$.\ (i) For $b \in \Bcal_{j-1}$, $$\label{e:Iupper0zz} \\|\Ical(b)\\|_{T_{\phi}} \le e^{O (\epV(b)) (1+ \\|\phi\\|_\Phi^2)} .$$ (ii) Fix any $q \ge 0$. Suppose that $\epV \le C \epVbar$ for some $C>0$. For $B \in \Bcal_j$, and $X \in \Scal_{j-1}(B)$ or $X=\varnothing$, $$\begin{aligned} & \\|\Ical(B\setminus X) \\|_{T_{\phi}} \le e^{O (1+q^{2})\epV} e^{-q \epVbar \\|\phi\\|_{\Phi(B^{\Box})}^2} e^{O (1+q) \epV \\|\phi\\|_{\tilde\Phi(B^{\Box})}^2} . \label{e:IcalB}\end{aligned}$$ \(i) We write $V=g\tau^2 +Q$. By [@BS-rg-norm Proposition \[norm-prop:taunorm\]] (with $q_2 =0$) and , $$\\|e^{-g\tau_x^2}\\|_{T_{\phi}} \le e^{O (\|g\|\h^4)} = e^{O (L^{-dj}\epVbar)} .$$ By the product property, $$\begin{gathered} \label{e:egtbd} \\|e^{-g\tau^2(b)}\\|_{T_{\phi}} \le \prod_{x\in b} \\|e^{-g\tau_{x}^2}\\|_{T_{\phi}} \le e^{O (L^{-d}\epVbar)} .\end{gathered}$$ Also, since $Q$ is quadratic, from [@BS-rg-norm Proposition \[norm-prop:T0K\]] and we obtain $$\\|Q (b)\\|_{T_{\phi}} \le \\|Q (b)\\|_{T_{0}} (1+\\|\phi\\|_\Phi)^2 \le 2 \epV(b) (1+\\|\phi\\|_\Phi^2) .$$ Therefore, by the power series expansion of the exponential and the product property, $$\label{e:apos-e} \\|e^{-Q (b)}\\|_{T_{\phi}} \le e^{\\|Q (b)\\|_{T_{\phi}}} \le e^{2\epV(b) (1+\\|\phi\\|_\Phi^2)} .$$ With the product property, then follows from , , and the fact that $\epVbar \le \epsilon_{V_\varnothing}$. \(ii) Fix any $q'\ge 0$. Since ${\rm Re} g \le \|g\| \le \frac 32 {\rm Re}g$ by hypothesis, we can conclude from [@BS-rg-norm Proposition \[norm-prop:taunorm\]] that $$\\|e^{-g\tau_x^2}\\|_{T_{\phi}} \le e^{O (1+q'^{2})\| g\|\h^4} e^{-q' \|g\|\h^4 \|\phi_x/\h\|^2} .$$ By the product property and , this gives $$\begin{gathered} \label{e:egtau2} \\|e^{-g\tau^2(B \setminus X)}\\|_{T_{\phi}} \le e^{O (1+q'^{2}) \epVbar} e^{-q' \|g\|\h^4 \sum_{x\in B \setminus X}\|\phi_x/\h\|^2} .\end{gathered}$$ For $Y \subset \Lambda$, we define the $L^2(Y)$ norm by $$\\|\phi \\|^{2}_{L^2(Y)} = \frac{1}{\|Y\|} \sum_{x\in Y}\frac{\|\phi_{x} \|^{2}}{\h^{2}} .$$ Then, again writing $V=g\tau^2 +Q$, we combine with , using the product property, , and $\|B\setminus X\| \ge \frac 12 \|B\|$, to obtain $$\begin{aligned} \label{e:Ical-1} \\|\Ical(B\setminus X) \\|_{T_{\phi}} &\le e^{O (1+q'^{2}) \epVbar} e^{- q' \|g\|\h^4 \|B \setminus X\| \, \\|\phi\\|_{L^{2} (B\setminus X)}^2} e^{2\epV(1+\\|\phi\\|_\Phi^2)} \nnb &\le e^{O (1+q'^{2}) \epVbar} e^{- \frac 12 q' C_0^{-1}\epVbar \, \\|\phi\\|_{L^{2} (B\setminus X)}^2} e^{2\epV(1+\\|\phi\\|_\Phi^2)}\end{aligned}$$ (no $L^d$ factor is produced for the observables). By our hypothesis on $X$ and Proposition \[prop:equivalent-norms\], $$\label{e:Sob2} \\|\phi\\|_{L^2(B\setminus X)}^2 \geq \frac{1}{2c_2^2} \\|\phi\\|_{\Phi(B^{\Box})}^2 - \\|\phi\\|_{\tilde \Phi(B^{\Box}) }^2 .$$ We insert this into and localise the $\Phi $ norm to $\Phi (B^{\Box})$ to obtain $$\begin{aligned} \\|\Ical(B\setminus X) \\|_{T_{\phi}} &\le e^{O (1+q'^{2}) \epV} e^{- (\frac {1}{4}C_0^{-1} c_2^{-2} q'\epVbar -2\epV) \, \\|\phi\\|_{\Phi(B^\Box)}^2} e^{\frac 12 q' \epV \\|\phi\\|_{\tilde\Phi(B^\Box)}^2} .\end{aligned}$$ Then follows by choosing $q'=4 C_0 c_2^{2} (q+2C)$, which is $O(q)$. We prove Proposition \[prop:Iupper\] by combining Proposition \[prop:Iupperzz\] with the following elementary lemma. \[lem:exp-bounds\] For $x, u>0$ and any integer $r \ge \max\{1,u\}$, $$\begin{aligned} \label{e:exp1} (1 + x)^{2r} & \le (2r/ u)^{r} e^{u x^{2}} \\ \label{e:exp2} 1 + u^{r} (1+x)^{2r} & \le e^{2ru (1+ x^{2})} .\end{aligned}$$ For the first bound, we combine $(1+x)^{2r} \le 2^r (1+x^2)^r$ with the inequality $1+x^2 \le (r/u) e^{u x^2/r}$ (since $r \ge u$). The second bound follows from $$\begin{aligned} 1 + u^{r} (1+x)^{2r} &\le 1 + ( 2u)^{r} (1+x^{2})^{r} \le (1+2u + 2u x^{2})^{r} \le (e^{2u + 2 u x^{2}})^{r},\end{aligned}$$ where we used $r \ge 1$ in the second inequality. We first consider the choice $I^=I(B)$. By the product property and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $$\begin{aligned} \\|I (B) F\\|_{T_{\phi}} &\le \\|\Ical (B)\\|_{T_{\phi}} \\|1+W(B)\\|_{T_{\phi}} \\| F\\|_{T_{\phi}} \nnb & \le \\|\Ical (B)\\|_{T_{\phi}} \\|1+W(B)\\|_{T_{\phi}} \\| F\\|_{T_{0}} \left( 1 + \\|\phi\\|_{\Phi}\right)^r,\end{aligned}$$ where $r$ denotes the degree of $F$. By , $W$ is a degree-six polynomial in the boson and fermion fields. By and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $$\begin{aligned} \label{e:1Wbd} \\|1+W(B)\\|_{T_{\phi}} &\le 1+\\|W(B)\\|_{T_{\phi}} \le 1+\\|W(B)\\|_{T_{0}}\left( 1 + \\|\phi\\|_{\Phi}\right)^6 \le e^{6\omega^{1/3} (1+\\|\phi\\|_{\Phi}^2)}.\end{aligned}$$ where $\omega = \max_{B \in \Bcal_j}\\|W(B)\\|_{T_0}$. Then, since $6(L^{2d}\omega)^{1/3} \le u$ by hypothesis, gives $$\\|I(B) F\\|_{T_{\phi}} \le \\|\Ical (B)\\|_{T_{\phi}} \\| F\\|_{T_{0}} \left(\frac{2r}{u} \right)^{r} e^{u + 2u \\|\phi\\|_{\Phi}^{2}} .$$ Then with $I^=I(B)$ follows from . For , fix $q \ge 0$ to be the desired parameter in , and choose the variable called $q$ in to be $q_1$ defined by $q_1= q+2u\epVbar^{-1}$. This gives for the choice $I^=I(B)$. For the case $\tilde{I}(B \setminus X)$ with $X=\varnothing$ or $X\in \Scal_{j-1}$, we replace by $$\\|\prod_{b \in \Bcal_{j-1}(B\setminus X)}(1+W(b))\\|_{T_{\phi}} \le e^{6L^d (L^{-d } \omega)^{1/3} (1+\\|\phi\\|_{\Phi}^2)} \le e^{u (1+\\|\phi\\|_{\Phi}^2)},$$ and proceed similarly. Omitting factors $1+W$ in the above bounds only makes it easier, so we also have the bounds if we choose $I^$ with factors of $1+W$ missing, and the proof is complete. Let $V \in \bar\DV$. We first consider the case $I_=I$ (possibly with some $1+W$ factors omitted) and $j_=j$. The bound follows from and (with $q=0$), and follows similarly from the case $r=0$. Also, for $B \in \Bcal_j$, it follows from the definition of $I$, the product property, and , that $$\label{e:I-b} \\|I(B)^{-1}\\|_{T_0} \le e^{\\|V(B)\\|_{T_0}} \frac{1}{1-\\|W(V,B)\\|_{T_0}} \le (1 +O (\epV+\epW)) \le 2 ,$$ which gives . This completes the proof for the case $I_=I$. Next, we consider the case $I_=\Ipttil$. It follows from Proposition \[prop:monobd\] that $\Vpt \in \bar\DV'$, and the above result for $I_=I$ then gives – also for $\Ipttil$ when $j_=j$. This leaves – for the case $I_=\Ipttil$ with $j_=j+1$, as well as . For , we apply Lemma \[lem:Imono\] and the scale-$j$ case of (now $W_{j+1}$ occurs rather than $W_j$ but it is bounded by Remark \[rk:sm\]) to obtain $$\begin{aligned} \\|\Ipttil (B)F\\|_{T_{\phi,j+1} (\h_{j+1})} &\le \\|\Ipttil (B)F\\|_{T_{\phi,j} (\h_{j})} \prec \\|F\\|_{T_{0,j}} \Gcal_{j} (B,\phi) ,\end{aligned}$$ where $\Gcal_j = G_j$ for $\h_j=\ell_j$, and $\Gcal_j=\tilde G_j$ for $\h_j=h_j$. For $\h=\ell$ we set $\phi=0$ and immediately follows for $j+1$. For $\h=h$ we use the fact that $\tilde G_{j}(X,\phi) \le \tilde G_{j+1}^{\Gtilp}(X,\phi)$ by Lemma \[lem:mart\], and also follows in this case. Note that $\\|F\\|_{T_0,j}$ occurs in both for $j_=j$ and $j_=j+1$. The estimate follows similarly, and for $j+1$ follows from for $j$ by Lemma \[lem:Imono\], which implies that the $T_{\phi,j+1}$ norm is bounded above by the $T_{\phi,j}$ norm. Finally, to prove , we recall from Proposition \[prop:monobd\] that $\Vpt\in \bar\DV_{j+1}'$, and then follows exactly as the scale-$j$ case of for $\Ipttil$. This completes the proof. We first prove the analyticity of $V \mapsto \Ical = e^{-V}$ for $V$ in $\bar\DV_j$; in this case $j_=j$. We fix $B$ and drop it from the notation. Fix $V \in \bar\DV_j$ and let $\dot{V} \in \Qcal$. We prove analyticity by showing that $I(V+\dot V)$ has a norm convergent power series expansion in $\dot V$, if $\|\dot g\| \le \frac{1}{8} {\rm Re}g$ and $\epsilon_{\dot{V}}$ is sufficiently small. By the integral form of the remainder in Taylor’s theorem, together with the product property of the $T_\phi$ semi-norm, $$\begin{aligned} \big\\|e^{-(V+\dot V)} - \sum_{n=0}^N e^{-V} \frac{(-\dot V)^n}{n!}\big\\|_{j} &= \big\\| \int_0^1 \frac{1}{N!} e^{-(V+s\dot V)}\dot V^{N+1}(1-s)^{N} ds\big\\|_{j} \nnb & \le \sup_\phi \Gcal(\phi)^{-1} \frac{1}{(N+1)!}\\|e^{-V}\dot V^{N+1}\\|_{T_\phi} e^{\\|\dot V\\|_{T_\phi}},\end{aligned}$$ where $\Gcal$ denotes the regulator, either $G_j$ or $\tilde G_j$. It suffices to show that the above right-hand side goes to zero as $N \to \infty$, and for this it suffices to show that insertion of summation over $N$ under the supremum leads to a convergent result. Since \_[N=0]{}\^ e\^[-V]{}V\^[N+1]{}\_[T\_]{} e\^[V\_[T\_]{}]{} e\^[-V]{} \_[T\_]{} e\^[2V\_[T\_]{}]{}, it suffices to show that $$\lbeq{eVanal} \sup_\phi \Gcal(\phi)^{-1} \\|e^{-V} \\|_{T_\phi} e^{2\\|\dot V\\|_{T_\phi}} < \infty.$$ We isolate the $\tau^2$ terms by writing $V=g\tau^2 + Q$ and $\dot V =\dot g \tau^2 + \dot Q$. By [@BS-rg-norm Proposition \[norm-prop:taunorm\]], $\\|\tau_x\\|_{T_\phi}=\h^2P(t)$, where $P(t)=t^2+2t+2$ and $t=\|\phi_x\|/\h$. Let $\epsilon = \epV + 2\epsilon_{\dot{V}}$. We use the product property of the $T_\phi$ norm, as well as [@BS-rg-norm Proposition \[norm-prop:T0K\]], to obtain $$\begin{aligned} \\|e^{-V_x} \\|_{T_\phi} e^{2\\|\dot V_x\\|_{T_\phi}} &\le \\|e^{-g\tau_x^2 }\\|_{T_\phi} e^{2\|\dot g\| \,\\|\tau_x^2\\|_{T_\phi}+ \\|Q_x\\|_{T_\phi} + 2\\|\dot Q_x\\|_{T_\phi}} \nnb & \le \\|e^{-g\tau_x^2 }\\|_{T_\phi} e^{2\|\dot g \|\h^4 P(t)^2 + \epsilon L^{-dj}(1+\\|\phi\\|_\Phi^2)}.\end{aligned}$$ By [@BS-rg-norm Proposition \[norm-prop:taunorm\]], together with the assumption in the definition of $\bar\DV$ that $\|{\rm Im}g\| < \frac 15 {\rm Re}g$, e\^[-g\_x\^2]{}\_[T\_]{} e\^[([Re]{}g)\^4\[-2t\^2 + 32 P(t)\^2\]]{}. Since $\|\dot g\| \le \frac18 {\rm Re}g$, this gives e\^[-g\_x\^2 ]{}\_[T\_]{} e\^[2\|g \|\^4 P(t)\^2 ]{} e\^[([Re]{}g)\^4\[-2t\^4 + 74 P(t)\^2\]]{} e\^[([Re]{}g)\^4\[q\_1-q\_2t\^2\]]{}, where $q_2 \ge 0$ can be chosen arbitrarily with a corresponding choice of $q_1$. Therefore, $$\\|e^{-V_x} \\|_{T_\phi} e^{2\\|\dot V_x\\|_{T_\phi}} \le e^{({\rm Re}g)\h^4[q_1-q_2t^2] + \epsilon L^{-dj}(1+\\|\phi\\|_\Phi^2)} .$$ To conclude for the $G$ norm, we take $q_2=0$ and $\epsilon_{\dot V} =\epV$, and the desired estimate follows for uniformly small $\ggen_j$. The proof of for the $\tilde G$ norm can be completed by applying the Sobolev inequality exactly as in the proof of Proposition \[prop:Iupperzz\], using the fact that we do have $\epV \le C\epVbar$ in this case by . It remains to consider the effect of $1+W$ on the above argument. Since $1+W$ is a degree-6 polynomial in the fields, it is analytic for the case of the $G$ norm, and its effect is therefore unimportant. For the case of the $\tilde G$ norm, $1+W$ is not analytic because polynomial growth in the absolute value of $\phi$ is not cancelled by the regulator in this case (since the regulator has linear functions factored out). However, it is an exercise to include the factor $1+W$ alongside the $e^{-V}$ factor in the above argument and thereby conclude analyticity also in this case. To prove the analyticity of $\Ipttil$ in $V \in \bar\DV_j$, it again suffices to consider $e^{-\Vpt}$. Let $V \in \bar\DV_j$ and consider first the case $j_=j$. We can regard $e^{-\Vpt}$ as the composition of $V \mapsto \Vpt$ and $\Vpt \mapsto e^{-\Vpt}$. The first of these maps is polynomial in $V$. Thus, for the case of the $G$ norm, $V \mapsto \Vpt$ is analytic, while the second map is analytic by the previous argument together with the fact that $\Vpt \in \bar\DV'$ when $V \in \bar\DV$ by Proposition \[prop:monobd\]. This proves the desired analyticity when $j_=j$ for the $G$ norm. The analyticity for the case of the $\tilde G$ norm can be established with small additional effort. Next, we consider the case $j_=j+1$. As above, the main work lies in showing that $e^{-\Vpt}$ is an analytic function of $\Vpt \in \bar\DV$ when measured in the $\\|\cdot\\|_{j+1}$ norm. But it follows from Lemmas \[lem:Imono\] and \[lem:mart\] that for either of the choices – for the norm pairs, $\\|F\\|_{j+1} \le C\\|F\\|_j$ for some $C>0$ and for all $F$. Thus convergence of a power series in a neighbourhood in the $j$-norm implies convergence in a neighbourhood in the $j+1$-norm, and the analyticity for $j_=j+1$ follows from the analyticity for $j_=j$. Finally, it follows similarly that $I(B)^{-1}$ is analytic in $V$, as a map into the space with norm $\\|\cdot\\|_{T_{0,j}}$. For example, the factor $e^{g\tau^{2} (Y)}$ in $I(B)^{-1}$ is analytic in $g$ because it has an absolutely convergent power series, $$\begin{gathered} \\|e^{g \tau^{2} (B)}\\|_{T_{0} (\ell)} \le \sum_{n\ge 0} \frac{1}{n!} \\|g\tau^{2} (B)\\|_{T_{0} (\ell)}^{n} \le \sum_{n\ge 0} \frac{1}{n!} \epsilon_{g\tau^{2}}^{n} .\end{gathered}$$ A similar argument applies to the inverse of $1-W$. This completes the proof. Let $j<N$, $V \in \bar\DV$, and $Q\in\Qcal$ with $\\|Q(B)\\|_{T_0} \prec \epdV$. We first show that $V-Q \in \bar\DV'$. This implies that the estimates of Proposition \[prop:Istab\] apply to $\Ihat$, and that the desired analyticity follows from Proposition \[prop:Ianalytic1:5\], so then it will remain only to prove the estimates –. By Lemma \[lem:T0ep\], $\epsilon_{V-Q} \le \epV + \epsilon_{Q} \prec \epV + \max_B \\|Q(B)\\|_{T_0}$. The last bound of (with worse constants) then follows from the assumption on $Q$. For the middle bound of , let $g_Q$ denote the coefficient of $\tau^2$ in $Q$. By hypothesis, $L^{dj} \|g_Q\| \\|\tau^2_0\\|_{T_0(h)} \prec \ggen_j^{1/4}$, and hence $$L^{dj} \|g- g_Q\| \\|\tau^2_0\\|_{T_0(h)} \ge L^{dj} \|g\| \\|\tau^2_0\\|_{T_0(h)}-c_L\ggen_j^\eta \ge ak_0^4 - c \ggen_j^{1/4} \ge \frac 12 ak_0^4,$$ by taking $\ggen_j$ sufficiently small. Finally, for the first inequality of , we apply to see that $$\|{\rm Im}g_Q\| \le \|g_Q\| \prec \frac{\epsilon_{Q,j}(\h_j)}{L^{dj}\h_j^4} .$$ By the hypothesis on $Q$, for $\h=\ell$ the right-hand side is at most $c\ell_0^{-4} \ggen_j$, which is at most $\frac{1}{10}C_{\DV}^{-1}\ggen_j < \frac{1}{10}{\rm Re}g$ for $L$ sufficiently large (hence $\ell_0$ large). Similarly, for $\h=h$ the right-hand side is $\prec \ggen_j^{5/4}$, and hence the effect of $Q$ on the imaginary part of $g$ is negligible. This completes the proof that $V-Q\in \bar\DV'$. It remains to prove –. For $s \in [0,1]$, we write $V_s=V-sQ$, $I_s=I(V_s)$, $\Ical_s = e^{-V_{s}}$, and $W_s=W(V_{s})$, and omit the $B$ arguments. Direct calculation gives $$\begin{aligned} \label{e:Isprime} I_s' & = I_s Q + \Ical_s W_s', \\ \label{e:Isprime2} I_s'' &= I_s Q^2 + 2\Ical_s Q W_s' + \Ical_s W_s'', \\ \lbeq{Wprime} W_s' &= -W(Q,V_s) - W(V_s,Q), \\ \lbeq{Wprime2} W_s'' & = -2W(Q,Q).\end{aligned}$$ By Lemma \[lem:Wbil\], W\_s’\_[T\_0]{} \_L \_j \_j\^2 & =\ \_j \_j\^[3/4]{} & =h W\_s”\_[T\_0]{} \_L \_j \_j\^2 & =\ \_j \_j & =h. Let $\Ihat(B) = I(V-Q,B)$. By the Fundamental Theorem of Calculus, $\Ihat-I=\int_0^1 I_s' ds$, and hence by $$\lbeq{IIhatdif} \\|\hat I - I\\|_{j} \le \sup_{s\in [0,1]} \left( \\|I_s Q\\|_{j} + \\|\Ical_s W_s'\\|_j \right).$$ We have shown above that $V-sQ \in \bar\DV'$ (in fact this holds uniformly in $s$), and consequently holds with $V$ replaced by $V-sQ$. By , the first term on the right-hand side of is of order $\\|Q\\|_{T_0} \prec \epdV$. By and , the second term of is negligible compared to the first. This proves . For , we first note that $I_1 -I_0-I_0' = \hat I - I - IQ - \Ical_0 W_0'$. Using this, with a second-order Taylor remainder estimate followed by , gives $$\begin{aligned} \\|\hat I - I - IQ\\|_{T_0} &\le \\|\Ical_0 W_0'\\|_{T_0} + \sup_{s\in [0,1]} \\| I_s''\\|_{T_0} \nnb & \prec \\|W_0'\\|_{T_0} + \\|Q\\|_{T_0}^2 + \sup_{s\in [0,1]} \left( \\| Q \\|_{T_0} \\| W_s'\\|_{T_0} + \\| W_s''\\|_{T_0} \right) \prec_{L} \epdV^2 ,\end{aligned}$$ where for the last step we used together with the fact that its right-hand sides are at most $\epdV^2$. This proves . Proof of Propositions \[prop:hldg\]–\[prop:h\] {#sec:interaction-estimates444} ============================================== In this section, we prove Propositions \[prop:hldg\]–\[prop:h\]. The proof of Proposition \[prop:hldg\] is short, whereas the proof of Proposition \[prop:h\] is substantial. In the proof of Proposition \[prop:h\] it is important that $W$ and $\Vpt$ be defined as they are, and it is here that we implement the ideas in [@BBS-rg-pt Section \[pt-sec:WPjobs\]]. Proof of Proposition \[prop:hldg\] ---------------------------------- Let $j<N$ and $V \in \bar\DV_j$. Recall from that $\hldg (U,B)$ is defined for $(U,B) \in \Scal_{j+1}\times \Bcal_{j+1}$ by $$\label{e:hptdefqqz} \hldg (U,B) = \begin{cases} -\frac{1}{2} \Ex_{\pi ,j+1} \theta ( V_j(B); V_j(\Lambda \setminus B)) & U=B \\ \;\;\; \frac{1}{2} \Ex_{\pi ,j+1}\theta ( V_j(B); V_j(U\setminus B)) & U \supset B, \|U\|_{j+1}=2 \\ \;\;\; 0 &\text{otherwise} . \end{cases}$$ By , and , $$\label{e:EABbis} \Ex_{\pi,C} (\theta A; \theta B) = F_{\pi,C}( e^{ \Lcal_{C}} A , e^{ \Lcal_{C}} B).$$ By Proposition \[prop:Wnorms\], $$\begin{aligned} \label{e:Fepbd-xxx} \max_{B \in \Bcal_{j+1}} \sum_{x \in B} \sum_{B' \in \Bcal_{j+1}(\Lambda)} \\|F_{\pi,C_{j+1}}(V_x,V(B'))\\|_{T_{0,j+1}} & \prec_L\; \epdV^2 .\end{aligned}$$ As an operator on the subspace of $\Ncal$ consisting of bounded-degree polynomials in the fields, $e^{\pm \Lcal_{C_k}}$ is bounded (uniformly in $k$), due to and . With and , this gives $$\label{e:EtruncT0} \max_{B \in \Bcal_{j+1}} \sum_{x \in B} \sum_{B' \in \Bcal_{j+1}(\Lambda)} \\|\Ex_{\pi,C_{j+1}}(\theta V_x;\theta V(B'))\\|_{T_{0,j+1}} \prec_{L} \epdV^2,$$ from which we conclude that $$\begin{aligned} \label{e:Etruncbd} \\|\hldg(U,B)\\|_{T_0,j+1} &\prec_{L} \epdV^2 .\end{aligned}$$ By Proposition \[prop:Istab\], this implies that $$\begin{aligned} \label{e:2Lprimeh1} \\|\Ipttil(U)\hldg(U,B) \\|_{j+1} & \prec_L \epdV^2 .\end{aligned}$$ This gives and completes the proof of Proposition \[prop:hldg\]. Proof of Proposition \[prop:h\] ------------------------------- We require some preparation for the proof of Proposition \[prop:h\]. By –, $$\begin{aligned} \hldg (B) &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(\Lambda \setminus B)) \nnb &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} ( \theta V(b);\theta V(\Lambda \setminus b)) + \sum_{b\not =b' \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(b')) .\end{aligned}$$ It follows from that $$\label{e:EpiE} \frac 12 \Ex_{\pi} (V';V'') + \frac 12 \Ex_{\pi}(V'';V') = \Ex (V';V''),$$ from which we conclude that $$\begin{aligned} \hldg (B) &= -\sum_{b \in \Bcal_j(B)} \frac{1}{2} \Ex_{\pi} (\theta V(b);\theta V(\Lambda \setminus b)) + \sum_{b\not =b' \in \Bcal_j(B)} \frac{1}{2} \Ex (\theta V(b);\theta V(b')). \label{e:hleadnew}\end{aligned}$$ For distinct $b,b' \in \Bcal_j$, $B \in \Bcal_{j+1}$, and for $U \in \Scal_{j+1}$ with $\|U\|_{j+1}\in \{1,2\}$, we define $$\begin{aligned} \label{e:R1def} R_1(b;B) & = \Ipttil^{B\setminus b} \Ex \delta I^b + \Ipttil^{B} \frac{1}{2} \Ex_{\pi} (\theta V_j(b);\theta V_j(\Lambda \setminus b)) , \\ \label{e:R2def} R_2(b,b';U) & = \frac{1}{2} \left[ \Ipttil^{U\setminus (b\cup b')}\Ex \delta I^{b\cup b'} - \Ipttil^{U} \Ex (\theta V_j(b);\theta V_j(b')) \right] ;\end{aligned}$$ note that $\Ex_{\pi}$ appears in $R_1$ but not in $R_2$. Then, by , –, and , $$\begin{aligned} \label{e:hhptB} \Ipttil^B [\hred (B) - \hldg (B)] & = \sum_{b \in \Bcal_j(B)} R_1(b;B) + \sum_{b\neq b' \in \Bcal_j} R_2(b,b';B) , \\ \label{e:hhptU} \Ipttil^U [\hred (U) - \hldg (U)] & = \sum_{b\neq b' : \overline{b\cup b'}=U} R_2(b,b';U) \quad \quad \quad\quad \|U\|_{j+1}= 2.\end{aligned}$$ By the triangle inequality and –, to prove Proposition \[prop:h\] it suffices to show that $$\begin{aligned} \label{e:R12suff} \\| R_1(b;B) \\|_{j+1} & \prec_L \, \epdV^3 , \quad\quad \\| R_2(b,b';U) \\|_{j+1} \prec_L \, \epdV^3 ,\end{aligned}$$ where the constants in the upper bounds depend on $L$, and $\epdV$ is given by . The appearance of $\delta I$ leads naturally to the study of $\delta V$, which was defined in as $\delta V = \theta V - \Vpt$. As a first step in the proof of , we prove the following lemma which relies heavily on results from [@BS-rg-norm]. The “5” appearing in its statement has been chosen as a convenient positive constant and is not significant. The parameter $\hat\ell_j >0$ is defined in . The constant $C_{\delta V}$ is the $L$-dependent constant of Lemma \[lem:epdV\]. \[lem:dIipV\] Let $j<N$, $b,b' \in \Bcal_j$, and $n,n' \ge 0$. Suppose that $F \in \Ncal((b\cup b')^\Box)$ obeys $\\|F\\|_{T_\phi(\h+\hat\ell)} \le c_F e^{\alpha \\|\phi\\|_{\Phi(\h)}^{2}}$ for some $c_F,\alpha >0$. If $u \in (0,2]$ obeys $\alpha + \frac{1}{20}(n+n')u \le 5$, then $$\begin{aligned} \label{e:ip-V1} \\| \Ex_{j+1} \left[(\delta V(b))^n (\delta V(b'))^{n'} \theta F \right] \\|_{T_{\phi}(\h)} &\prec_L c_F (C_{\delta V}\epdV)^{n+n'} e^{(2\alpha + (n+n')u) \\|\phi\\|_{\Phi(\h)}^2}, \end{aligned}$$ where the constant in the upper bound depends on $u,n,n'$, and where $\h$, $\hat\ell$ and all norms are at scale $j+1$. By [@BS-rg-norm Proposition \[norm-prop:EK\]] (with to provide its hypothesis on the covariance), and by the product property of the $\Ttimes_{\phi\sqcup\xi}$ semi-norm, $$\begin{aligned} &\\|\Ex \left[ (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F \right] \\|_{T_{\phi}} \leq \Ex \\| (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F \\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \nnb & \hspace{30mm} \leq \Ex \left[\\| \delta V(b)\\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)}^{n} \\| \delta V(b')\\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)}^{n'} \\|\theta F \\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \right].\end{aligned}$$ We apply [@BS-rg-norm Proposition \[norm-prop:T0K\]] to the $\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)$ semi-norm of $\delta V$, with a multi-component field with $\h=\hat\ell$ for $\xi$. With , this gives $$\\| \delta V(b)\\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \le \epdV (1+\\|\phi\\|_{\Phi(\h)})^4 (1 + \\|\xi\\|_{\Phi(\hat\ell)})^4.$$ For any $u \in (0,2]$, then gives (with a $u$-dependent constant and with $\hat{u}=u(\ell/\hat\ell)^2$) $$\label{e:dVbdpf} \\| \delta V(b)\\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} \prec C_{\delta V} \epdV e^{u(\\|\phi\\|_{\Phi(\h)}^2 + \\|\xi\\|_{\Phi(\hat\ell)}^2)} = C_{\delta V} \epdV e^{u\\|\phi\\|_{\Phi(\h )}^2 } G(b,\xi)^{\hat{u}} .$$ Similarly, by [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], by hypothesis, by $\\|\phi+\xi\\|^2 \le 2(\\|\phi\\|^2+\\|\xi\\|^2)$, and by $\h \ge \ell$, $$\begin{aligned} \\|\theta F \\|_{\Ttimes_{\phi\sqcup\xi}(\h\sqcup\hat\ell)} & \le \\| F \\|_{T_{\phi+\xi}(\h+\hat\ell)} \le c_F e^{2\alpha(\\|\phi\\|_{\Phi(\h)}^2 + \\|\xi\\|_{\Phi(\h)}^2)} \nnb & \le c_F e^{2\alpha\\|\phi\\|_{\Phi(\h)}^2 }G(b\cup b', \xi)^{2\alpha}.\end{aligned}$$ Therefore, with $s=n+n'$, since $G(b\cup b')=G(b)G( b')$ by [@BS-rg-norm], $$\begin{aligned} \label{e:EGpapp} \\|\Ex [ (\delta V(b))^{n} (\delta V(b'))^{n'} \theta F ] \\|_{T_{\phi}} & \prec (C_{\delta V}\epdV)^{s} c_F e^{(2\alpha +su)\\|\phi\\|_{\Phi(\h )}^2 } \Ex \left[ G(b \cup b',\xi)^{2\alpha +s\hat{u}} \right] .\end{aligned}$$ It suffices now to bound the expectation on the right-hand side by a constant. By , by our choice $\ellconst = \frac{1}{10}c_G$ above , and by and , $$\begin{aligned} (2\alpha +s\hat{u}) \\|C\\|_{\Phi^+(\ell)} & = 2\alpha \\|C\\|_{\Phi^+(\ell)} +su \\|C\\|_{\Phi^+(\hat\ell)} \nnb & \le 2\alpha \ellconst + su \frac{c_G}{100} \le \left( \frac{\alpha}{5} + \frac{su}{100} \right) c_G \le c_G ,\end{aligned}$$ with the last inequality true by hypothesis. Then [@BS-rg-norm Proposition \[norm-prop:EG2\]] yields the desired bound on the expectation, and the proof is complete. For $j \ge 1$, we define $A_j$ by $$\label{e:Ajdef} A_j = e^{-\delta V} - \sum_{i=0}^{j-1} \frac{(-\delta V)^i}{i!}.$$ By Taylor’s theorem with integral form of the remainder, $$\label{e:AjTaylor} A_j = \frac{1}{(j-1)!} \int_0^1 (1-t)^{j-1} (\delta V)^j e^{-t\delta V} dt.$$ It follows from the definitions that $e^{-\theta V}=e^{-\Vpt}e^{-\delta V}$, and that for $b \in \Bcal_j$, $$\begin{aligned} \delta I(b) & = e^{-\Vpt(b)}\left( A_1(b) + Z(b) \right), \label{e:dIexpansion}\end{aligned}$$ with $$\label{e:ZdefW} Z = e^{-\delta V}\theta W - W_{j+1}.$$ It is in the following proof that it is important that $W$ and $\Vpt$ be defined as they are, and our implementation of the ideas laid out in [@BBS-rg-pt Section \[pt-sec:WPjobs\]] occurs here. In particular, the identity $$\label{e:EW} \Ex_{j+1} \theta W_{j} (V, X) = W_{j+1} (\Ex_{j+1}\theta V ,X) + P (X) - \frac{1}{2} \Ex_{\pi ,j+1}\big(\theta V(X);\theta V(\Lambda)\big)$$ of Lemma \[lem:EW\] enters the proof of in a crucial manner, as does the definition $\Vpt = \Ex \theta V - P$ of (recall ). All norms in this proof are at scale $j+1$. Fix $B\in \Bcal_{j+1}$ and $b \in \Bcal_j(B)$ for $R_1$, and fix $U \in \Scal_{j+1}$ with $\|U\|\in \{1,2\}$ and $b\neq b' \in \Bcal_j$ with $\overline{b \cup b'}=U$ for $R_2$. To prove , it suffices to prove that $$\begin{aligned} \label{e:ExIb} \\| R_1(b;B) \\|_{T_\phi} &\prec_L \epdV^3 \Gcal(B,\phi) , \\ \label{e:ExIbb} \\| R_2(b,b';U) \\|_{T_\phi} &\prec_L \epdV^3 \Gcal(U,\phi) ,\end{aligned}$$ where $\Gcal$ represents $G$ or $\tilde G^{\Gtilp}$ according to the choice $\h=\ell$ or $\h=h$. We first prove the bound for $R_1$, and then the bound for $R_2$. Identity for $R_1$.* We apply , , and the definition $\Vpt=\Ex\theta V -P$, to obtain $$\begin{aligned} \delta I & = e^{-\Vpt}\left( -\delta V + A_2 + Z \right) \nnb & = e^{-\Vpt}\left( -\delta V + \frac 12 (\delta V)^2 + A_3 + (1+A_1)\theta W -W_{j+1} \right) \nnb & = e^{-\Vpt}\left( \Ex\theta V -\theta V - P + \frac 12 (\theta V - \Ex\theta V)^2 + \theta W -W_{j+1}(\Ex\theta V) + \Ecal_1 \right), \label{e:dIexpansion2}\end{aligned}$$ where $$\Ecal_1 = (\theta V - \Ex\theta V)P + \frac 12 P^2 + A_3 + A_1 \theta W + W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt) .$$ Then, taking the expectation, we obtain $$\begin{aligned} \Ex \delta I(b) & = e^{-\Vpt}\left( - P + \frac 12 \Ex(\theta V(b) ; \theta V(b)) + \Ex\theta W -W_{j+1}(\Ex\theta V) + \Ex\Ecal_1 \right) ,\end{aligned}$$ with $$\label{e:ExEcal1} \Ex \Ecal_1 = \frac 12 P^2 + \Ex A_3 + \Ex (A_1 \theta W) + \big[ W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt) \big] .$$ It follows from that $\Ex(\theta V(b) ; \theta V(b)) = \Ex_\pi(\theta V(b) ; \theta V(b))$. Thus, after application of , together with use of the identity $$\Ex_\pi(\theta V(b); \theta V(b)) - \Ex_\pi(\theta V(b); \theta V(\Lambda)) = - \Ex_\pi(\theta V(b); \theta V(\Lambda \setminus b)),$$ we obtain $$\begin{aligned} \Ipttil^{B\setminus b}\Ex \delta I(b) & = \Ipttil^{B \setminus b} e^{-\Vpt(b)}\left( - \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ex\Ecal_1 (b) \right) \nnb & = -\Ipttil^B \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) \nnb & \quad + \Ipttil^{B \setminus b} e^{-\Vpt(b)}W_{j+1} \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ipttil^{B \setminus b} e^{-\Vpt(b)} \Ex\Ecal_1 (b) . \label{e:EdIid}\end{aligned}$$ By definition of $R_1$, this gives $$\lbeq{R1identity} R_1(b;B) = \Ipttil^{B \setminus b} e^{-\Vpt(b)}W_{j+1} \frac{1}{2} \Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b)) + \Ipttil^{B \setminus b} e^{-\Vpt(b)} \Ex\Ecal_1 (b) .$$ The use of has led to an important cancellation which the definitions of $W$ and $\Vpt$ were engineered to create. Bound on $R_1$. It suffices to obtain a bound of the form $\epdV^3 \Gcal(B,\phi)$ for the $T_\phi$ semi-norms of each of the two terms on the right-hand side of , with the last of these terms given by . The resulting five terms are of two types: one type involves $\Ipttil^{B \setminus b} e^{-\Vpt}$ multiplied by the polynomials $W_{j+1}\Ex_{\pi}(\theta V (b); \theta V(\Lambda \setminus b))$, $P^2$, $[ W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt)]$, and the second type involves two terms with expectations of the non-polynomial quantities $A_1$ and $A_3$. For the first type of term, we apply (the version with factor $(1+W(b))$ omitted) to conclude that, for a polynomial $Q$, $$\\|\Ipttil^{B \setminus b} e^{-\Vpt(b)} Q(b)\\|_{j+1} \prec \\|Q(b)\\|_{T_{0,j}}.$$ Bounds on the $T_0$ semi-norm of $W_{j+1}$, $\Ex_{\pi}(\theta V (b);\theta V(\Lambda \setminus b))$ and $P$ follow from , , and . Also, the norm of $W_{j+1}(\Ex\theta V) -W_{j+1}(\Vpt)$ is bounded in . With these bounds, we obtain an upper bound of order $\epdV^3$ for the $(j+1)$-norm of the three terms with polynomials. For the second type of term, we apply Lemma \[lem:dIipV\]. For the $A_3$ term, it follows from and the product property that $$\begin{aligned} \label{e:A3term} \\|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\\|_{T_{\phi}} & \le \sup_{t\in [0,1]} \\|\Ipttil^{B \setminus b} e^{-(1-t)\Vpt(b)}\\|_{T_{\phi}} \\| \Ex \delta V(b)^3 e^{-t\theta V(b)}\\|_{T_{\phi}} .\end{aligned}$$ By and (for its hypothesis on $\omega$ we see from that $\omega \prec_L \epdV^2$), given any small $u_1>0$, $$\\|e^{-t V(b)}\\|_{T_{\phi}(\h+\hat\ell)} \le \\|e^{-t V(b)}\\|_{T_{\phi}(2\h)} \le e^{O(\epV(2\h) +u_1) \\|\phi\\|_{\Phi(2\h)}^2} \le e^{O(\epV(\h) +u_1) \\|\phi\\|_{\Phi(\h)}^2} .$$ It therefore follows from Lemma \[lem:dIipV\] that given any small $u>0$, with a constant depending on $u$ we have $$\label{e:A3term-a} \\| \Ex \delta V(b)^3 e^{-t\theta V(b)}\\|_{T_{\phi}} \prec_L \epdV^3 e^{O(\epV + u) \\|\phi\\|_\Phi^2}.$$ For the case of the regulator $G$, we bound the first factor on the right-hand side of as follows. By , the product property, and , $$\\|\Ipttil^{B \setminus b} e^{-(1-t)\Vpt(b)}\\|_{T_{\phi,j+1}} \le \\|\Ipttil^{B \setminus b}\\|_{T_{\phi,j+1}} \\| e^{-(1-t)\Vpt(b)}\\|_{T_{\phi,j}} \le e^{O(\epV + u) \\|\phi\\|_\Phi^2}.$$ Thus we obtain $$\begin{aligned} \\|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\\|_{T_{\phi}} & \prec_L \epdV^3 G(B,\phi) ,\end{aligned}$$ as required. For the case of the regulator $\tilde G$, we take $u=u_1=\epVbar$ and recall from and that $\epV \prec \epVbar \asymp k_0^4$, with $k_0$ chosen small (recall the discussion above ). Then gives, for some $c_0>0$, $$\label{e:A3term-b} \\| \Ex \delta V(b)^3 e^{-t\theta V(b)}\\|_{T_{\phi}} \prec_L \epdV^3 e^{c_0\epVbar \\|\phi\\|_\Phi^2}.$$ We apply , with $q = c_0$, to see that $$\begin{aligned} \\|\Ipttil^{B \setminus b} e^{-\Vpt(b)}\Ex A_3(b)\\|_{T_{\phi}} & \prec_L \epdV^3 \tilde G^{\Gtilp} (B,\phi) ,\end{aligned}$$ as required. The $A_1\theta W_j$ term can be treated similarly, using Lemma \[lem:dIipV\] with $F=e^{-tV}W_j$. This completes the discussion of the bound on $R_1$. Bound on $R_2$. Starting from the first line of , and recalling that $Z$ is defined in , a little algebra leads to $$\Ex \delta I^{b \cup b'} = e^{-\Vpt(b\cup b')} \big( \Ex (\theta V(b) ; \theta V(b')) + \Ecal_2(b,b') \big), \label{e:EdIbb}$$ where $$\begin{aligned} \Ecal_2(b,b') & = P(b)P(b') - \Ex \big(\delta V(b) A_2(b')\big) - \Ex \big(A_2(b) \delta V(b')\big) + \Ex \big(A_2(b)A_2(b')\big) \nnb & \quad\quad + \Ex \big(A_1(b) Z(b')\big) + \Ex \big(Z(b)A_1(b')\big) + \Ex \big(Z(b)Z(b')\big).\end{aligned}$$ Therefore, $$\begin{aligned} & 2R_2(b,b';U) = \Ipttil^{U\setminus (b\cup b')}e^{-\Vpt(b \cup b')} \Ecal_2(b,b') \\ \nonumber & \quad + \Ipttil^{U\setminus (b\cup b')}e^{-\Vpt(b\cup b')}[(1+W_{j+1}(b))(1+W_{j+1}(b'))-1] \Ex (\theta V(b) ; \theta V(b')) .\end{aligned}$$ By (with two missing $1+W$ factors), the $(j+1)$-norm of the second term on the right-hand side is bounded by a multiple of the $T_0$ semi-norm of the polynomial factor, which by and is of order $\epdV^4$. The contribution due to the $PP$ term in $\Ecal_2$ can be bounded in the same way, using . The six remaining terms in $\Ecal_2$ can be handled in the same way as the $A_3$ and $A_1$ terms in $\Ecal_1$, and we omit the details. Using Lemma \[lem:dIipV\], the $\delta V A_2$ and $A_1Z$ terms are seen to be order $\epdV^3$, while the $A_2A_2$ and $ZZ$ terms are order $\epdV^4$. In particular, it is not necessary to make use of any cancellation within $Z$. Together, these estimates produce an overall bound of order $\epdV^3$, and the proof is complete. Proof of Propositions \[prop:ip\]–\[prop:cl\] {#sec:ipcl} ============================================= In this section, we prove Propositions \[prop:ip\]–\[prop:cl\]. Proof of Proposition \[prop:ip\] {#sec:ippf} -------------------------------- The main step in the proof of Proposition \[prop:ip\] is provided by the following lemma. The constant $C_{\delta L}$ is the $L$-dependent constant of Lemma \[lem:epdV\]. \[lem:dIip\] Let $X,Y \in \Pcal_j$ be disjoint. Let $F(Y) \in \Ncal (Y^{\Box})$. There is an $\Econst>0$ (independent of $L$) and a $C_{\delta V}>0$ (depending on $L$) such that $$\begin{aligned} \label{e:integration-property-a} \\|\Ex \delta I^X \theta F(Y) \\|_{T_{\phi}(\h/2)} &\leq \Econst^{\|X\|_j+\|Y\|_j} (C_{\delta V} \epdV)^{\|X\|_j} \\| F(Y) \\|_{\Gcal(\h)} \Gcal(X\cup Y,\phi)^5, \end{aligned}$$ where $\Gcal$ denotes $G$ or $\tilde G$ when $\h=\ell$ or $\h=h$, respectively. Norms and regulators are at scale $j$, the expectation represents $\Ex_{C_{j+1}}$, and $\delta I$ is given by . We write $\h'=\h/2$ and $\hat\ell' = \hat\ell/2$. By [@BS-rg-norm Proposition \[norm-prop:EK\]] (with to provide its hypothesis), and by the product property of the $\Ttimes_{\phi\sqcup\xi}$ semi-norm, $$\begin{aligned} \\|\Ex \delta I^X \theta F(Y) \\|_{T_{\phi}(\h')} & \leq \Ex \left[\\| \delta I^X \\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup \hat\ell')} \\|\theta F(Y) \\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup \hat\ell')} \right]. \label{e:ip1}\end{aligned}$$ By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]] and (with the fact that $\h \ge \hat\ell$ for uniformly small $\ggen_j$), $$\begin{aligned} \lbeq{ip1.1} \\|\theta F(Y) \\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \\| F(Y) \\|_{T_{\phi+\xi}(\h'+\hat\ell')} \leq \\| F(Y) \\|_{T_{\phi+\xi}(\h)} \leq \\| F(Y) \\|_{\Gcal(\h)} \Gcal(Y,\phi+\xi).\end{aligned}$$ Since $\\|\phi+\xi\\|^2 \le 2\\|\phi \\|^2 + 2\\|\xi\\|^2$, and since $\Gcal \le G$ because $\tilde G \le G$, this gives $$\begin{aligned} \\|\theta F(Y) \\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \\| F(Y) \\|_{\Gcal(\h)} \Gcal(Y,\phi)^2 \Gcal(Y,\xi)^2 \le \\| F(Y) \\|_{\Gcal(\h)} \Gcal(Y,\phi)^2 G(Y,\xi)^2. \label{e:ip1.5}\end{aligned}$$ By –, for $b \in \Bcal_j$, $$\begin{aligned} \\|\delta I(b)\\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} & \!\! \le \!\! \\|\delta V(b)\\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \!\! \sup_{t\in [0,1]} \\|e^{-(1-t)\Vpt(b)}\\|_{T_{\phi}(\h')} \\|\theta e^{-t V(b)}\\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \nnb & \quad \quad + \\|\theta(e^{-V(b)}W(b)) \\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} + \\|e^{-\Vpt}W_{j+1}(b)\\|_{T_{\phi}(\h')}. \label{e:delItimes}\end{aligned}$$ By (now interpreted at scale $j$ rather than $j+1$; recall that the bound of Lemma \[lem:epdV\] applies to either scale), for any choice of small positive $u$, and with $\hat{u}=u(\ell/\hat\ell)^2$, $$\\| \delta V(b)\\|_{\Ttimes_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} \prec C_{\delta V} \epdV e^{u\\|\phi\\|_{\Phi(\h' )}^2 } G(b,\xi)^{\hat{u}} .$$ We now consider the supremum on the right-hand side of . Either $t \ge \frac 12$ or $1-t \ge \frac 12$. Suppose that $t \ge \frac 12$; the other case is simpler and we omit its details. By and , $\\|e^{-(1-t)\Vpt(b)}\\|_{T_{\phi}(\h')} \le 2\Gcal(b,\phi)$. By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], , the inequality $\\|\phi\\|^2 \le 2\\|\phi+\xi\\|^2 + 2\\|\xi\\|^2$, and the identity $\\|\phi\\|_{\Phi(\h')}=2\\|\phi\\|_{\Phi(\h)}$, $$\begin{aligned} \\|\theta e^{-t V(b)}\\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} e^{u\\|\phi\\|_{\Phi(\h' )}^2 } &\le \\|e^{-t V(b)}\\|_{T_{\phi+\xi}(\h'+\hat\ell')}e^{u\\|\phi\\|_{\Phi(\h' )}^2 } \nnb & \le \\|e^{-t V(b)}\\|_{T_{\phi+\xi}(\h)} e^{8u\\|\phi+\xi\\|_{\Phi(\h )}^2 } e^{8u\\|\xi\\|_{\Phi(\h )}^2 } \nnb & \le \\|e^{-t V(b)}\\|_{T_{\phi+\xi}(\h)} e^{8u\\|\phi+\xi\\|_{\Phi(\h )}^2 } G(b,\xi)^{1/2}, \label{e:thetaeV}\end{aligned}$$ where we used $8u\\|\xi\\|_{\Phi(\h)}^2 \le \frac 12 \\|\xi\\|_{\Phi(\ell)}^2$ in the last step (we can take $u \le \frac {1}{16}$). Next, we apply when $\Gcal =G$, and with $u=\epVbar$ and $q= 8$ when $\Gcal =\tilde G$ , to obtain $$\\|e^{-t V(b)}\\|_{T_{\phi+\xi}(\h)} e^{8u\\|\phi+\xi\\|_{\Phi(\h )}^2 } \prec \Gcal(b,\phi+\xi),$$ and hence $$\begin{aligned} \\|\theta e^{-t V(b)}\\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} e^{u\\|\phi\\|_{\Phi(\h' )}^2 } & \prec \Gcal(b,\phi+\xi)G(b,\xi)^{1/2} \nnb & \le \Gcal(b,\phi)^2 \Gcal(b, \xi)^2 G(b,\xi)^{1/2}. \label{e:thetaeV-bis}\end{aligned}$$ Since $\Gcal \le G$, we conclude from the above estimates that $$\begin{aligned} \label{e:supdV} &\\|\delta V(b)\\|_{T_{\phi\sqcup\xi}} \sup_{t\in [0,1]} \\|e^{-(1-t)\Vpt(b)}\\|_{T_{\phi}} \\|\theta e^{-t V(b)}\\|_{T_{\phi\sqcup\xi}} \nnb & \quad\quad \prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{\hat u + 5/2} \prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{3(\ell/\hat\ell)^2} ,\end{aligned}$$ using the fact that $u$ is small and that $\hat\ell \le \ell$ by definition. To complete the estimate on $\delta I(b)$, we now consider the two $W$ terms in . By [@BS-rg-norm Proposition \[norm-prop:derivs-of-tau-bis\]], and the fact that $\h \ge \ell$, , and , $$\begin{aligned} \\|\theta(e^{-V(b)}W(b)) \\|_{T_{\phi\sqcup\xi}(\h'\sqcup\hat\ell')} &\le \\|e^{-V(b)}W(b) \\|_{T_{\phi+\xi}(\h'+\hat\ell')} \prec \\|e^{-V(b)}W(b) \\|_{T_{\phi+\xi}(\h)} \nnb & \prec \\|W(b)\\|_{T_0} \Gcal(b,\phi+\xi) \prec_L \epdV^2 \Gcal(b,\phi)^2 \Gcal(b,\xi)^2. \label{e:eVW}\end{aligned}$$ Similarly (recall Remark \[rk:sm\]), $$\begin{aligned} \\|e^{-\Vpt}W_{j+1}(b)\\|_{T_{\phi}(\h')} & \!\! \prec \\|e^{-\Vpt}W_{j+1}(b)\\|_{T_{\phi}(\h)} \!\! \prec \\|W_{j+1}(b)\\|_{T_{0}(\h)}\Gcal(b,\phi) \prec_L \epdV^2 \Gcal(b,\phi). \label{e:eVW+}\end{aligned}$$ We are free to take $\epdV$ small depending on $L$, so that in the above two bounds $\prec_L \epdV^2$ can be replaced by a bound $\prec \epdV$. The combination of with – gives $$\begin{aligned} \label{e:dIass} \\|\delta I (b) \\|_{\Ttimes_{\phi\sqcup\xi} (\h\sqcup\ell)} &\prec C_{\delta V}\epdV \Gcal (b,\phi)^3 G(b,\xi)^{3(\ell/\hat\ell)^2}.\end{aligned}$$ As noted below Definition \[def:Gnorms\], $\Gcal(X)\Gcal(Y)=\Gcal(X\cup Y)$. Thus there is a constant $c$ (independent of $L$) such that $$\label{e:ip2} \\| \delta I^X \\|_{\Ttimes_{\phi\sqcup\xi}} \leq \prod_{b \in \Bcal_j(X)} \\| \delta I(b) \\|_{\Ttimes_{\phi\sqcup\xi}} \leq (cC_{\delta V}\epdV)^{\|X\|_j} \Gcal(X,\phi)^3 G(X,\xi)^{3(\ell/\hat\ell)^2}.$$ The proof is completed by inserting and into , also noting that $$\Ex G(X \cup Y,\xi)^{3(\ell/\hat\ell)^2} \le 2^{\|X\|_j+\|Y\|_j}.$$ This last inequality is a consequence of [@BS-rg-norm Proposition \[norm-prop:EG2\]], whose hypothesis is supplied by the fact that $3(\ell/\hat\ell)^2 \\|C\\|_{\Phi^+(\hat\ell)} = 3\\|C\\|_{\Phi^+(\ell)} \le 3 \ellconst \le c_G$ by our choice of $\ellconst$. We apply Lemma \[lem:dIip\] with scale-$j$ norms and $\h=\h_{j}$. Since $\h_{j+1} \le \h' = \h_j/2$, we can apply to the left-hand side of to conclude that $$\begin{aligned} \label{e:integration-property-pf} \\|\Ex \delta I^X \theta F(Y) \\|_{T_{\phi,j+1}(\h_{j+1})} &\leq \Econst^{\|X\|_j+\|Y\|_j} (C_{\delta V} \epdV)^{\|X\|_j} \\| F(Y) \\|_{\Gcal_j(\h_{j})} \Gcal_j(X\cup Y,\phi)^5.\end{aligned}$$ For the norm pair , it suffices to consider the case $\phi =0$, for which the regulator on the right-hand side of reduces to unity and the integration property immediately follows in this case. For the norm pair , Lemma \[lem:mart\] gives $$\label{e:Gtilmart} \tilde{G}_j(X,\cup Y,\phi)^5 \le \tilde{G}_{j+1}^{\Gtilp}(X\cup Y,\phi),$$ and with this gives in this case. This completes the proof. Proof of Proposition \[prop:cl\] {#sec:contraction3-proof} -------------------------------- For convenience, we restate Proposition \[prop:cl\] as Proposition \[prop:cl-bis\]. Its proof uses Proposition \[prop:1-LTdefXY\] in a crucial way. \[prop:cl-bis\] Let $j<N$ and $V\in \bar\DV_j$. Let $X \in \Scal_j$ and $U = \overline X$. Let $F(X) \in \Ncal(X^\Box)$ be such that $\pi_\alpha F(X) =0$ when $X(\alpha)=\varnothing$. We assume that $\pi_{ab}V=\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ (recall ). Then $$\begin{aligned} \label{e:contraction3z} \\|\Ipttil^{U\setminus X} \Ex_{C_{j+1}} \theta F (X) \\|_{j+1} & \prec \cgam(X) \kappa_F + \kappa_{\LT F} ,\end{aligned}$$ where $\kappa_F=\\|F (X)\\|_{j}$, $\kappa_{\LT F} =\\|\Ipttil^X \LT_X \Ipttil^{-X} F(X) \\|_j$, and where the pair of norms is given by either of or . We make the decomposition $$\label{e:KLTdeca} F(X) = D(X)+E(X),$$ with $$\begin{aligned} \label{e:EXdef} D(X) & = \Ipttil^X \LT_X \Ipttil^{-X} F(X), \quad\quad\quad E(X) = \Ipttil^X (1-\LT_X) \Ipttil^{-X} F(X).\end{aligned}$$ By the triangle inequality and the product property, $$\\|\Ipttil^{U\setminus X} \Ex \theta F (X) \\|_{j+1} \le \\|\Ipttil^{U\setminus X} \\|_{j+1} \\|\Ex \theta D (X) \\|_{j+1} + \\|\Ipttil^{U\setminus X} \Ex \theta E (X) \\|_{j+1}.$$ Since $X\in\Scal_{j}$, its closure $U$ lies in $\Scal_{j+1}$ and hence consists of at most $2^d$ blocks. Therefore, by the product property and , $\\|\Ipttil^{U\setminus X} \\|_{j+1}\le 2^{2^d}$. By the integration property of Proposition \[prop:ip\], $$\begin{aligned} \\|\Ex \theta D (X) \\|_{j+1} &\prec \\|D(X)\\|_j = \kappa_{\LT F}. \label{e:Lkpfii-1zbis}\end{aligned}$$ Thus the $D$ term in leads to the final term of . For the term involving $E$, we first apply the product property and [@BS-rg-norm Proposition \[norm-prop:EK\]] (with its assumption given by $h \ge \ell$ and ) to obtain $$\lbeq{cl-0} \\|\Ipttil^{U\setminus X} \Ex \theta E (X) \\|_{T_{\phi,j+1}(\h_{j+1})} \le \\|\Ipttil^{U\setminus X} \\|_{T_{\phi,j+1}(\h_{j+1})} \Ex \\| E (X) \\|_{T_{\phi+\xi,j+1}(2\h_{j+1})}.$$ We recall the inequality $$\begin{aligned} \label{e:FXbdKz} \\|F_1(1-\LT_X) F_2\\|_{T_{\phi}'} &\le \bar{C} \cgam(Y) \left(1 + \\|\phi\\|_{\Phi'}\right)^{A+d+1} \sup_{0\le t \le 1} \big( \\|F_{1}F_{2}\\|_{T_{t\phi}} + \\|F_{1}\\|_{T_{t\phi}}\\|F_{2}\\|_{T_{0}}\big)\end{aligned}$$ from Proposition \[prop:1-LTdefXY\] (where its notation is defined). To bound the semi-norm of $E(X)$, we apply (writing $a=A+d+1$ and $\cgam=\cgam(X)$), to obtain $$\begin{aligned} \lbeq{cl-1} & \\| E(X) \\|_{T_{\phi+\xi,j+1}(2\h_{j+1})} \prec \gamma \left(1+\\|\phi+\xi\\|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \\ \nonumber & \quad \times \sup_{0 \le t\le 1} \left( \\|F(X)\\|_{T_{t(\phi+\xi),j}(\h_{j})} + \\|\Ipttil^X\\|_{T_{t(\phi+\xi),j}(\h_{j})} \\|\Ipttil^{-X}\\|_{T_{0,j}(\h_{j})} \\|F(X)\\|_{T_{0,j}(\h_{j})} \right) .\end{aligned}$$ Our assumption that $\pi_{ab}V=\pi_{ab}F(X)=0$ unless $j \ge j_{ab}$ provides a corresponding assumption for Proposition \[prop:1-LTdefXY\]. By the triangle inequality, the polynomial factor can be bounded as $$\begin{aligned} \left(1+\\|\phi+ \xi\\|_{\Phi_{j+1}(X^\Box)} \right)^{a} &\le \left(1+\\|\phi\\|_{\Phi_{j+1}(X^\Box )} \right)^{a} \left(1+\\|\xi\\|_{\Phi_{j+1}(X^\Box )} \right)^{a} \nnb & \prec \left(1+\\|\phi\\|_{\Phi_{j+1}(X^\Box )} \right)^{a} G_{j+1}(X,\xi),\end{aligned}$$ where in the last step we used $\h_{j+1}\ge\ell_{j+1}$ to conclude the inequality $\\|\xi\\|_{\Phi_{j+1}(2\h_{j+1})}\le \\|\xi\\|_{\Phi_{j+1}(\ell_{j+1})}$, together with the fact that the regulator dominates polynomials by . Next, we apply – (the latter in conjunction with the product property), together with the definition of $\kappa_F$, to see that the quantity under the supremum in is bounded above by a constant multiple of $\kappa_F \Gcal_j(X,\phi+\xi)$. Using $\\|\phi+\xi\\|^2 \le 2\\|\phi\\|^2 + 2\\|\xi\\|^2$ to estimate this last regulator, we obtain $$\begin{aligned} \\| E(X) \\|_{T_{\phi+\xi,j+1}(2\h_{j+1})} & \prec \gamma \kappa_F \left(1+\\|\phi \\|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \nnb & \quad \times \Gcal_j(X,\phi)^2 \Gcal_j(X,\xi)^2 G_{j+1}(X,\xi) . \lbeq{cl-2}\end{aligned}$$ Since $\Gcal \le G$, we can then take the expectation using (with Cauchy–Schwarz to separate the regulators at the two different scales), to obtain $$\begin{aligned} \Ex \\| E(X) \\|_{T_{\phi+\xi,j+1}(2\h_{j+1})} & \prec \gamma \kappa_F \left(1+\\|\phi \\|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \Gcal_j(X,\phi)^2 . \lbeq{cl-3}\end{aligned}$$ With , this gives $$\begin{aligned} \lbeq{cl-4} \\|\Ipttil^{U\setminus X} \Ex \theta E (X) \\|_{T_{\phi,j+1}(\h_{j+1})} & \prec \gamma \kappa_F \\|\Ipttil^{U\setminus X} \\|_{T_{\phi,j+1}(\h_{j+1})} \nnb & \quad \times \left(1+\\|\phi \\|_{\Phi_{j+1}(X^\Box,2\h_{j+1})} \right)^{a} \Gcal_j(X,\phi)^2 .\end{aligned}$$ With an application of Proposition \[prop:Iupper\], this gives $$\lbeq{cl-5} \\|\Ipttil^{U\setminus X} \Ex \theta E (X) \\|_{T_{\phi,j+1}(\h_{j+1})} \prec \gamma \kappa_F \Gcal_{j+1}(U,\phi)^{\Gtilp/2} \Gcal_j(X,\phi)^2 ,$$ where the exponent $\Gtilp/2$ on $\Gcal_{j+1}$ is a convenient choice. For the norm pair we set $\phi=0$, the regulators become equal to $1$, and the desired result follows from . For the norm pair , we apply Lemma \[lem:mart\] and $X \subset U$ to obtain $$\begin{aligned} \tilde G_{j+1}(U,\phi)^{\Gtilp/2} \tilde G_j(X,\phi)^2 & \prec \tilde G_{j+1}(U,\phi)^{\Gtilp/2} \tilde{G}_{j+1}(X,\phi)^{\Gtilp/2} \le \tilde G_{j+1}^{\Gtilp}(U,\phi) , \label{e:FXbdKzzz}\end{aligned}$$ and the desired result follows from . This completes the proof. Lp norm estimates {#sec:Lp} ================= Let $\phi : \Lambda \to \C$, and let $X \subset \Lambda$ be a subset of cardinality $\|X\|$. For $p\in [1,\infty )$, we define the $L^{p}$ norm $$\label{e:Lp-def} \\|\phi\\|_{L^{p} (X)} = \frac{1}{\h}\left(\frac{1}{\|X\|}\sum_{x\in X} \|\phi (x)\|^{p}\right)^{1/p}.$$ The weight $\h$ is included in the norm so that, according to and , $$\label{e:equivalent-norms4} \\|\phi\\|_{L^{p}(X)}^{p} \le \\| \phi\\|_{\Phi (X)}^{p}.$$ Proposition \[prop:equivalent-norms\] below provides a lattice Sobolev inequality which shows that can be reversed at the cost of an additional term. Our application of Proposition \[prop:equivalent-norms\] occurs in , with $p=2$. To prepare for the proposition, we first prove a lemma which shows that the reversal is possible for polynomials, even with an increase in the size of the domain of the $\Phi$ norm (recall that the small set neighbourhood $X^\Box$ of $X$ was defined in ). Throughout this appendix, we write $R=L^j$. The hypothesis below, that $R \ge R_0$, can then be achieved uniformly in $j$ by taking $L$ sufficiently large. Outside this appendix, we take the parameter $p_\Phi$ in the definition of the $\Phi$ norm to obey $p_\Phi \ge \frac{d+4}{2}$ (as mentioned in Section \[sec:reg\]), but this restriction is unnecessary in the following lemma. \[lem:PhiLp\] Let $p_\Phi, q\ge 0$ be integers. Let $Q$ denote the vector space of complex-valued polynomials defined on $\Rd$ and of degree at most $q$. Let $f$ be the restriction of any polynomial in $Q$ to $\Zd$. Let $B$ be a block of side $R$ in $\Zd$. There exists $c_0 = c_0(q,p)>0$ such that for $R\geq R_0(q,p)$ sufficiently large, $$\label{e:fequiv} \\| f\\|_{\Phi (B^\Box)} \le c_0 \\|f\\|_{L^{p} (B)} .$$ The inequality is homogeneous in $\h$ so without loss of generality we take $\h =1$. It suffices to consider the case where $p_\Phi=q$. In fact, derivatives of $f \in Q$ having order higher than $q$ vanish so the left-hand side of is constant in $q \ge p_\Phi$, and the left-hand side is an increasing function of $p_\Phi$ so the statement is strongest when $p_\Phi=q$. Thus we take $p_\Phi=q$ throughout the proof. Moreover, is trivial if $f$ is a constant, so we consider the case $q \ge 1$. Let $\Ccal^{q}$ denote the space of $q$-times differentiable functions on $\R^{d}$ with norm given by $$\\|G\\|_{\Ccal^{q}} = \sup_{x\in\Rd}\sup_{\|\alpha\| \leq q} \|D^\alpha G (x)\|,$$ where $\alpha$ is a multi-index and $D^\alpha$ is the derivative on $\R^d$. Without loss of generality, we assume that $B$ is centred at the origin of $\Zd$. We obtain a continuum version $\hat B^\Box\subset \Rd$ of $B^\Box$ by placing a unit $\Rd$-cube centred at each point in $B^\Box$. Let $I^\Box = R^{-1}\hat B^\Box \subset \Rd$ be its rescaled version. For $P \in Q$, let $$\\|P\\|_{\Ccal^{q}(I^\Box)} = \inf \{ \\|P-G\\|_{\Ccal^{q}} : G \in \Ccal^{q}, G\|_{I^\Box}=0\} .$$ This defines a norm on $Q$. Given $F \in Q$, let $f$ be the restriction of $F$ to $\Zd$, and let $\hat F \in Q$ be defined by $\hat F(x)=F(Rx)$ for $x \in \R^d$. We prove that $$\label{e:sob1} \\|f\\|_{\Phi (B^\Box)} \le \\|\hat F\\|_{\Ccal^{q}(I^\Box)},$$ and that there is a $c_0(q,p)>0$ and an $R_0(q,p)$ such that for $R \geq R_0$, $$\label{e:sob2} \\|\hat F\\|_{\Ccal^{q}(I^\Box)} \le c_0 \\|f\\|_{L^{p} (B)}.$$ Together, these two inequalities give . We first prove . By Taylor’s theorem, $R \|\nabla^{e} f (x) \| \le \\|D^{e} \hat F \\|_{\Ccal^{0}}$. By induction on $\|\alpha \|$, this gives $$\label{e:finite-diff} \sup_{x \in \R^d} \|\nabla_R^\alpha f(x)\| \le \\|\hat F\\|_{\Ccal^{q}}, \quad\quad \|\alpha\| \le q ,$$ where $\nabla_R^\alpha = R^{\|\alpha\|}\nabla^\alpha$. Given $\hat G \in \Ccal^{q}$, let $g(x)= \hat G(R^{-1}x)$. By definition, $f(x)-g(x) = \hat{F}(R^{-1}x)- \hat{G}(R^{-1}x)$, so by with $\hat F$ replaced by $\hat{F}- \hat{G}$, $$\lbeq{fghats} \sup_{x \in \Z^d} \|\nabla_R^\alpha[f(x)-g(x)]\| \le \\|\hat F - \hat G\\|_{\Ccal^{q}}, \quad\quad \|\alpha\| \le q.$$ Therefore, $$\lbeq{fginf} \inf \left\{ \\|f -g \\|_\Phi : \hat G \in \Ccal^{q}, \hat G\|_{I^\Box}=0 \right\} \le \\|\hat F \\|_{\Ccal^{q}(I^\Box)}.$$ The set of all lattice functions $g$ with $g\|_{I^\Box}=0$ includes all functions $g$ arising on the left-hand side, and the infimum over this larger class is smaller that the infimum in . Thus the left-hand side of is greater than or equal to $\\|f\\|_{\Phi (B^\Box)}$. This proves . To prove , we define a second norm on $Q$, as follows. For $P \in Q$, let $$\\|P\\|_{L^p(I)} = \left( \int_I \|P(x)\|^p dx \right)^{1/p}.$$ Since all norms on the finite-dimensional vector space $Q$ are equivalent, there exists a constant $c_1 = c_1(q,p)$ such that, for all $P \in Q$, $$\label{e:equivalent-norm1} \\|P\\|_{\Ccal^{q}(I^\Box)}^p \leq c_1 \\|P\\|_{L^p(I)}^p.$$ The difference $$\begin{aligned} \\|P\\|_{L^p(I)}^p - \frac{1}{\|B\|} \sum_{x\in B} \|P(R^{-1}x)\|^p &= \int_I\|P(x)\|^p dx - \frac{1}{\|B\|} \sum_{x\in B} \|P(R^{-1}x)\|^p\end{aligned}$$ is a Riemann sum approximation error. It is therefore bounded in absolute value by $R^{-1}$ times the maximum over $I$ of $\|DP^{p}\|$, which is less than $pR^{-1} \\|P\\|_{\Ccal^{q}(I^\Box)}^p$ (here we use $q \ge 1$). Therefore, $$\label{e:equivalent-norm2} \left(1 - \frac{p}{R}c_{1} \right) \\|P\\|_{\Ccal^{q}(I^\Box)}^{p} \leq c_1\frac{1}{\|B\|} \sum_{x\in B} \|P(R^{-1}x)\|^p .$$ We take $R$ large enough that $1 - \frac{p}{R}c_{1} \ge 1/2$, and set $P= \hat F$ in , to conclude with $c_0 = (2c_1)^{1/p}$. This completes the proof of , and hence of . \[prop:equivalent-norms\] Let $B$ be a block of side $R=L^j$ in the torus $\Lambda$ of side length $L^N$, with $j \le N-1$. There are constants $c_{1}$, $c_2$ and $R_{0}$ (depending on $p_{\Phi},p$) such that for $X \subset B$ with $\|X\|\le c_{1} \|B\|$, and for $R \ge R_0$, $$\label{e:fequiv0} \\|\phi\\|_{\Phi (B^\Box)} \le c_2 \left( \\|\phi\\|_{L^{p} (B\setminus X)} + \\|\phi\\|_{\tilde{\Phi} (B^\Box)} \right).$$ The inequality is homogeneous in $\h$ so we may assume that $\h=1$. For any $f \in \C^\Lambda$, $$\begin{aligned} \\|f\\|_{L^p(B\setminus X)}^p & \geq \frac{\|B\setminus X\|}{\|B\|}\\|f\\|_{L^{p} (B\setminus X)}^{p} = \\|f \\|_{L^{p} (B)}^{p} - \frac{\|X\|}{\|B\|}\, \\|f\\|_{L^p(X)}^{p} .\end{aligned}$$ The restriction $j \le N-1$ is imposed to ensure that the periodicity of $\Lambda$ plays no role, and we may assume that we are working on $\Zd$ rather than on $\Lambda$. We apply Lemma \[lem:PhiLp\] with $q=1$. With $c_{0}$ the constant of Lemma \[lem:PhiLp\], let $c_{1}=(2c_0^p)^{-1}$. By hypothesis, $\| X\| \le (2c_0^p)^{-1}\|B\|$. Let $f \in Q$, with $Q$ as in Lemma \[lem:PhiLp\]. By and the fact that $X\subset B^\Box$, $\\|f\\|_{L^p(X)} \le \\|f\\|_{\Phi (X)} \le \\|f\\|_{\Phi (B^\Box)}$. With Lemma \[lem:PhiLp\], this gives $$\begin{aligned} \\|f\\|_{L^p(B\setminus X)}^p & \ge \\|f \\|_{L^{p} (B)}^{p} - \frac{\|X\|}{\|B\|}\, \\|f\\|_{\Phi (B^\Box)}^{p} \ge \left[\frac {1}{c_0^p} - \frac{1}{2 c_0^p}\right]\\|f \\|_{\Phi (B^\Box)}^{p}.\end{aligned}$$ Therefore, $$\label{e:fequiv2} \\|f\\|_{\Phi (B^\Box)} \le 2^{1/p}c_0\\|f\\|_{L^{p} (B\setminus X)}.$$ Given $\phi :\Zd \to \C$ and $f \in Q$, we apply the triangle inequality (twice), and to see that $$\begin{aligned} \\|\phi\\|_{\Phi (B^\Box)} &\le \\|f\\|_{\Phi (B^\Box)} + \\|\phi -f\\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\\|f\\|_{L^{p} (B\setminus X)} + \\|\phi -f\\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\\|\phi\\|_{L^{p} (B\setminus X)} + 2^{1/p}c_0\\|\phi-f\\|_{L^{p} (B\setminus X)} + \\|\phi -f\\|_{\Phi (B^\Box)}\nnb &\le 2^{1/p}c_0\\|\phi\\|_{L^{p} (B\setminus X)} + \big(2^{1/p}c_0+1\big)\\|\phi -f\\|_{\Phi (B^\Box)}.\end{aligned}$$ The desired inequality , with $c_2=2^{1/p}c_0+1$, then follows by minimising over $f \in Q$ once we note that {-f\_[(B\^)]{}: f V } = \_[(B\^)]{} by definition of the norms in and . Further interaction estimates {#sec:further-ie} ============================= This section comprises estimates of a more specialised nature, which are required in [@BS-rg-step]. The estimates are stated as three lemmas. For the first lemma, for $B \in \Bcal_{j}$ we define $$\begin{aligned} \label{e:DeltaIdef} \Delta I(B) & = \tilde{I}(V,B) - I_{}(V,B) = e^{-V(B)} \left[ \prod_{b \in \Bcal_{j-1}(B)} (1+W_{j}(V,b)) - (1+W_{j}(V,B)) \right] .\end{aligned}$$ \[lem:DelIbd\] For $j \le N$, for both choices of $\\|\cdot \\|_j$ in –, for $B \in \Bcal_{j}$ and $V \in \bar\DV_j$, $$\begin{aligned} \label{e:DelIbd} \\|\Delta I(B)\\|_{j} &\prec_{L} \epdV^{4} .\end{aligned}$$ By , together with the fact that $W_j(V,B)=\sum_{b \in \Bcal_{j-1}(B)} W_{j}(V,b)$ by , $$\begin{aligned} \Delta I(B) & = e^{-V(B)} \!\!\!\!\!\!\!\! \sumtwo{X \in \Pcal_{j-1}(B) :}{\|X\|_{j-1} \ge 2} \prod_{b \in \Bcal_{j-1}(X)} W_{j}(V_{j},b) .\end{aligned}$$ Then gives a bound of order $(\epdV^2)^2$ for the $T_{0}$ semi-norm of the above sum, and the desired estimate follows from this together with . \[lem:JCK-app-2\] For $V \in \bar\DV$, $X \in \Scal$ and $F \in\Ncal(X^\Box)$, $$\label{e:JCK3-app} \left\\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\\|_{T_{0} } \prec \; C_{\delta V}\epdV \\|F\\|_{T_0 } .$$ All quantities and norms are at scale $j<N$, and norms are computed with either $\h=\ell$ or $\h=h$. It follows from [@BS-rg-loc Proposition \[loc-prop:opLTdefXY\]] that $$\left\\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\\|_{T_{0} } \prec \left\\| \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\\|_{T_{0} }$$ To estimate the right-hand side, we use the identity $$\prod_{i}a_{i}^{-1} - \prod_{i}b_{i}^{-1} = \sum_{k}\Big(\prod_{i\le k}a_{i}^{-1}\Big) (a_{k}-b_{k}) \Big(\prod_{i\ge k}b_{i}^{-1}\Big) ,$$ the triangle inequality, the product property of the norm, and , to obtain $$\label{e:JCK3-1} \left\\| \LT_X \left( (I^{-X}- \Itilde_{\pt}^{-X} )F\right) \right\\|_{T_{0}} \prec \sup_{B \in \Bcal (X)} \\| I (B) - \Itilde_{\pt} (B) \\|_{T_{0}} \\|F\\|_{T_{0}} .$$ We are thus reduced to estimates on a single block, and we henceforth omit $B$ arguments. To account for the fact that $I$ involves $W_j$ whereas $\Itilde_{\pt}$ involves $W_{j+1}$, we define $\Ipt = I(\Vpt) = I_j(\Vpt)$. Then I - \_ \_[T\_[0]{}]{} I - \_[T\_[0]{}]{} + - \_ \_[T\_[0]{}]{}. By and , the second term on the right-hand side obeys $$\begin{aligned} \label{e:JCK3-2} \\|\Ipt - \Itilde_{\pt}\\|_{T_{0}} &= \\|e^{-\Vpt} (W_{j}-W_{j+1})\\|_{T_{0}} \prec_{L} \epdV^2 .\end{aligned}$$ To estimate the first term on the right-hand side of , we proceed as in the proof of and now define $V_s= V + s(\Vpt -V)$, $I_s=I(V_s)$, $\Ical_s = e^{-V_{s}}$, and $W_s=W(V_{s})$. The steps leading to give $$\\|I - \Ipttil\\|_{T_0} \le \sup_{s\in [0,1]} \left( \\|I_s\\|_{T_0} \\| (\Vpt -V)\\|_{T_0} + \\|\Ical_s\\|_{T_0} \\| W_s'\\|_{T_0} \right).$$ The norms of $I_s$ and $\Ical_s$ are bounded by $2$, by . Also, $ \\| \Vpt -V\\|_{T_0}$ was encountered in and proved to be at most $C_{\delta V}\epdV$. With , we then obtain $\\| W_s'\\|_{T_0} \prec_l \epdV^2$. This completes the proof. The next lemma is applied in [@BS-rg-step Lemmas \[step-lem:K4\]–\[step-lem:K7a\]]. To prepare for its statement, given $V' \in \Qcal$ we define a new element $V'' \in \Qcal$ by $$\label{e:VptVplus} V'' = V' + y (\tau_{\Delta} - \tau_{\nabla\nabla}),$$ where $y$ is the coefficient of $\tau_{\nabla\nabla}$ in $V'$. Thus the term $y\tau_{\nabla\nabla}$ in $V'$ is replaced by $y\tau_\Delta$ to produce $V''$. We also define $$\begin{aligned} \delta I^{+}(B) &= e^{-V'(B)}\big(W_{j+1}(V',B) - W_{j+1}(V'',B)\big) .\end{aligned}$$ The definition of $V''$ is motivated by the fact that, for a polymer $X$, $V''(X)$ and $V' (X)$ are equal up to a polynomial in the fields that is supported on the boundary of $X$. To see this let $\chi$, $f$ and $g$ be functions on $\Lambda$. Then $$\begin{aligned} - \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} \big(\nabla^{e} (fg)\big)_{x} = \sum_{x \in \Lambda}\chi_{x} \Big((\Delta f)_{x}g_{x} + f_{x} (\Delta g)_{x}\Big) \nonumber \\+ \sum_{x \in \Lambda,e \in \Ucal} \chi_{x} (\nabla^{e}f)_{x}(\nabla^{e}g)_{x} .\end{aligned}$$ This is proved by using summation by parts ($\nabla^{e}$ and $\nabla^{-e}$ are adjoints) to rewrite the summand on the left as $\chi_{x} (\Delta fg)_{x}$, followed by writing $\Delta (fg)_{x}$ as the sum over $e\in\Ucal$ of $f_{x+e} g_{x+e} - f_{x}g_{x}$ and using simple algebra. Choosing $f = \phi,\psi$ and $g= \bar{\phi},\bar{\psi}$ and referring to we obtain $$- \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} (\nabla^{e}\tau)_{x} = 2\sum_{x \in \Lambda}\chi_{x} \Big(- \tau_{\Delta ,x} + \tau_{\nabla\nabla,x}\Big) .$$ For a polymer $X$ in $\Pcal_{j+1}$ let $\chi$ be the indicator function of $X$. Then from , $$V''(X) - V'(X) = \frac{1}{2}y \sum_{x \in \Lambda,e \in \Ucal} (\nabla^{e} \chi)_{x} (\nabla^{e}\tau)_{x} .$$ Let $\partial X$ denote the points in $X$ with a neighbour in $\Lambda \setminus X$. The right hand side is a sum of $\tau_{z'}-\tau_{z}$ over nearest neighbours $z',z$ where $z$ is in $X$ and $z'$ is not in $X$. By rewriting the fields in $\tau_{z'}$ using $f_{z'} = f_{z}+ (\nabla^{e}f)_{z}$ we find that there exists a polynomial $V_\partial$ which is quadratic in the fields and their derivatives such that $$V''(X) - V'(X) = \sum_{z \in \partial X} V_{\partial,z}$$ and every term in $V_{\partial,z}$ has at least one derivative. For $X \in \Pcal_{j+1}$ and $B \in \Bcal_{j+1} (\Lambda \setminus X)$, we set $R_{X} (B)=\delta I_{X}^{(6)} (B)=0$ if $B$ does not have a neighbour in $\partial X$, and otherwise define $$\begin{aligned} R_{X} (B) & = e^{- V_{\partial} (\partial X \cap B^1)}-1 , \quad\quad \delta I_{X} (B) = R_{X} (B) I(V'',B) ,\end{aligned}$$ where $B^1 = B \cup \partial(\Lambda \setminus B)$. \[lem:sbp-bds\] Let $j<N$, and $B \in \Bcal_{j+1}$. Suppose that $V' \in \bar\DV_{j+1}$ has $y \tau_{\nabla\nabla}$ term which obeys $\\|y \tau_{\nabla\nabla}(b)\\|_{T_{0,j}} \prec \epdV$ when $b \in \Bcal_j$. Let $X \in \Pcal_{j+1}$. Then for both choices of $\\|\cdot \\|_{j+1}$ in –, $$\begin{aligned} \label{e:map6-bd0} \\|\delta I^+(B)\\|_{j+1} & \prec_{L} \epdV^2 , \\ \lbeq{delI6bd} \\|\delta I_X (B)\\|_{j+1} & \prec \; \epdV .\end{aligned}$$ By direct calculation, $\\|\tau_{\nabla\nabla}(b)\\|_{T_{0,j}} \asymp L^{(d-2)(j)}\h_{j}^2$, and the right-hand side is $\ell_0^2$ for $\h=\ell$ and $k_0^2 \ggen_{j}^{-1/2}$ for $\h=h$. Therefore, by hypothesis and by definition of $\epdV$, we have $$\|y\| \prec \begin{cases} \ell_0^{-2} \epdV & \h=\ell \\ k_0^{-2} \ggen_j^{1/2} \epdV & \h=h. \end{cases}$$ Since $V_{\partial}$ is given by a sum over $O(L^{(d-1)(j+1)})$ boundary points of terms containing at least one gradient and two fields, this gives $$\begin{aligned} \lbeq{Vpartialbd} \\| V_\partial (\partial X \cap B)\\|_{T_0} &\prec \begin{cases} \ell_0^{-2}\epdV L^{(d-1)(j+1)} L^{- (j+1)} \ell^{2}_{j+1} & \h=\ell \\ k_0^{-2}\ggen^{1/2} \epdV L^{(d-1)(j+1)} L^{- (j+1)} h^{2}_{j+1} & \h=h \end{cases} \nnb & = \epdV.\end{aligned}$$ To prove , we apply to obtain $$\\|\delta I^+(B)\\|_{j+1} \prec \\|W_{j+1}(V',B) - W_{j+1}(V'',B)\\|_{T_0 (\h)} ,$$ and then use – to see that the right-hand side is $\prec_l \, \epdV^2$ as required. (In fact we use a small variation of – in which we regard $V'-V''$ as supported on $\partial X \cap B$, with .) To prove , we set $I_\partial(t) = I(V'',B) e^{- tV_{\partial}}$, with $V_{\partial}=V_{\partial}(\partial X \cap B)$. By the Fundamental Theorem of Calculus, $$\delta I_{X} (B) = V_{\partial} \int_0^1 I_\partial(t) dt ,$$ and hence $$\\| \delta I_{X} (B) \\|_{j+1} \le \sup_{t \in [0,1]} \\|I_\partial(t) V_{\partial} \\|_{j+1} .$$ The polynomial $V''$ obeys our stability estimates since compared to $V'$ its $z\tau_\Delta$ term is modified by $z \mapsto z+y$ and this change is such that $\epsilon_{V''} \le \epsilon_{V'}$, and hence $V''\in\bar\DV$. By [@BS-rg-norm] and [@BS-rg-norm Proposition \[norm-prop:T0K\]], $\\|e^{-tV_\partial}\\|_{T_\phi} \le e^{\\|V_\partial\\|_{T_\phi}} \le e^{\\|V_\partial\\|_{T_0}(1+\\|\phi\\|_{\Phi}^2)}$. The bound on $\\|e^{-tV_\partial}\\|_{T_\phi}$ is no larger than the effect of $Q$ handled in , and thus $ e^{- tV_{\partial}}$ is a negligible perturbation of $I(V'',B)$, and $I_\partial(t)$ also obeys the stability bounds. Thus we obtain from and that $$\\| \delta I_{X} (B) \\|_{j+1} \prec \\| V_{\partial} \\|_{T_0} \prec \epdV ,$$ and the proof is complete. Acknowledgements {#acknowledgements .unnumbered} ================ The work of both authors was supported in part by NSERC of Canada. DB gratefully acknowledges the support and hospitality of the Institute for Advanced Study at Princeton and of Eurandom during part of this work. GS gratefully acknowledges the support and hospitality of the Institut Henri Poincaré, and of the Mathematical Institute of Leiden University, where part of this work was done. We thank Roland Bauerschmidt for numerous helpful discussions. [^1]: Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2. E-mail: [[email protected]]{}, [[email protected]]{}.
Q: Java Geocoding - convert latitude and longitude into an address I need for my Android App the name of the city where my car is located in the moment. I have the latitude and longitude and want to convert this with the geocoder in the address and want to get the city. I read some blocks but because I'm new to this I dont get the clue. Please can anyone help me how to do this? EDIT: I dont use this geocoding in my app. I want to use it in my Java web service and I think I have to this with HTTPRequest, is it? and with the google api url. A: What you are looking for is Reverse Geocoding. The Geocoder class should help you do what you need (taken from here): public static void getAddressFromLocation( final Location location, final Context context, final Handler handler) { Thread thread = new Thread() { @Override public void run() { Geocoder geocoder = new Geocoder(context, Locale.getDefault()); String result = null; try { List<Address> list = geocoder.getFromLocation( location.getLatitude(), location.getLongitude(), 1); if (list != null && list.size() > 0) { Address address = list.get(0); // sending back first address line and locality result = address.getAddressLine(0) + ", " + address.getLocality(); } } catch (IOException e) { Log.e(TAG, "Impossible to connect to Geocoder", e); } finally { Message msg = Message.obtain(); msg.setTarget(handler); if (result != null) { msg.what = 1; Bundle bundle = new Bundle(); bundle.putString("address", result); msg.setData(bundle); } else msg.what = 0; msg.sendToTarget(); } } }; thread.start(); } EDIT: As per your comment, then no, you can't use the Geocoder class on a normal Java web service. That being said, there are alternatives. The Google Geocoding API is usually a good place to start, that being said, they do seem to have limits. Alternatively, you could take a look at Nominatim which is an open source Reverse Geocoding service albeit it seems to be slightly limited when compared to Google's services.
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1. The Field of the Invention This invention relates to a liquid crystal display, and more particularly to a back light unit in the liquid crystal display that minimizes a reflection of the pattern on a wall surface of a light-guide plate and bright lines from a light input. 2. Description of the Related Arts Generally, a liquid crystal display (LCD) controls an amount of light transmitted from a back light unit. The transmission is controlled by means of a liquid crystal panel including a number of liquid crystal cells arranged in a matrix and a number of control switches for switching video signals to be applied to the liquid crystal cells, thereby displaying a desired picture on a screen. Conventional back light units will be described with reference to FIG. 1 and FIG. 2. Referring to FIG. 1, the first conventional back light unit includes a light-guide plate 4 for guiding light passing through a light input 20; a reflective plate 2 disposed under the light-guide plate 4 for reflecting light escaping from a lower and side surfaces of the light-guide 4 in an upper direction toward an upper surface of the light guide 4; a first diffusion sheet 6 for diffusing light passing through the light-guide plate 4; first and second prism sheets 8 and 10 for controlling the direction of light passing through the first diffusion sheet 6; and a second diffusion sheet 12 for diffusing light passing through the prism sheets 8 and 10. The light input 20 includes a lamp 22 for generating light, and a lamp housing 24 for housing the lamp 22. The lamp housing also reflects the tight into the light-guide plate 4. A printed pattern is provided on the lower surface of the light-guide plate 4. This printed pattern does not allow the light-guide plate 4 to exhibit total internal reflection, which would allow light to be uniformly distributed out of the upper surface of the light-guide plate 4. As mentioned above, the light escaping from the lower surface and the side surface of the light-guide plate 4 are redirected by the reflective plate 2. The light passing through the light-guide plate 4 are diffused into an entire surface area of a liquid crystal panel (not shown) by the first diffusion sheet 6. The light entering the liquid crystal panel at right angles has a large light efficiency. Thus, it is preferred that the light enter the liquid crystal panel perpendicular to the surface of the liquid crystal panel. Towards this end, two forward prism sheets are disposed to make the angle of the light exiting from the light-guide plate 4 perpendicular to the liquid crystal panel. Referring to FIG. 1, the light passing through the first and second prism sheets 8 and 10 is incident to the liquid crystal panel via the second diffusion sheet 12. The first conventional back light unit cannot obtain a desired visual angle profile until the two prism sheets are included. The extra prism and the diffusion sheets absorb more light and thus cause an increased loss of light being transmitted to the liquid crystal panel. Also, the manufacturing cost rises. A suggested structure to solve the above-mentioned problems is shown in FIG. 2. The second conventional back light unit includes a light-guide plate 4′ for guiding light passing through a light input 20; a reflective plate 2 disposed under the light-guide plate 4′ for reflecting light escaping from a lower and side surfaces of the light-guide 4′ in an upper direction toward an upper surface of the light guide 4′; a backward prism sheet 14 for controlling the direction of light passing through the light-guide plate 4′; and a diffusion sheet 12 for diffusing light passing through the prism sheet 14. The light input 20 and the reflective plate 2 have the same function and operation as those in FIG. 1. A prism-shaped pattern is provided on the lower surface of the light-guide plate 4′. This prism-shaped pattern does not allow the light-guide plate 4′ to exhibit total internal reflection, which would allow the light to be uniformly distributed out of the upper surface of the light-guide plate 4′. In this case, it is desirable that, since the angle of the light outputted from the light-guide plate 4′ is more than about 65°, vertical angles of the prism sheet 14 should be between 63° to 70°. Thus, the light passing through the prism sheet 14 make right angles with respect to the surface of the liquid crystal panel. The light passing through the prism sheets 14 are diffused into the entire surface area of the liquid crystal panel by the diffusion sheet 12. In the second conventional back light unit, the wall surface of the light-guide plate 4′ are reflected and the bright lines of the light input 20 are seen due to the backward prism sheet 14. To solve the problems of the conventional art, a new scheme is needed to reduce the manufacturing cost as well as minimize the wall surface reflection and the bright lines of the light input.
Q: How to extract text FAST 'N FREE with BeautifulSoup I'd to extract the text between the strong tags below: <div class="u-flL sh-col"> <span id="shSummary"> <div class=" vi-fnf-ship fnfvar0"> <img alt="Estimated by eBay FAST 'N FREE " src="https://ir.ebaystatic.com/rs/v/xmyxg1ubry1npie2zlpan5za3yu.png" class="vi-fnf-ship-img"> <span class="vi-fnf-ship-txt "><strong class="sh_gr_bld">FAST 'N FREE</strong></span> I took a hit-or-miss approach on the following but no luck: # shippingCost = soup.find('strong', {'class':"sh_gr_bld"}).text.strip() #shippingCost = soup.find('div', {'class': ' vi-fnf-ship fnfvar0'}).find('span', {'class': 'vi-fnf-ship-txt'})\ # .find('strong', {'class': 'sh_gr_bld'}).text # shippingCost = soup.find_all('strong[class="sh_gr_bld"]').text # shippingCost = soup.find('span', {'class': 'vi-fnf-ship-txt'}).text#.find('b', {'class': 'sh_gr_bld'}).text # shippingCost = soup.find('div') # shippingCost = soup.find_all('span', {'class': 'vi-fnf-ship-txt'}).text#.find('span').next_sibling # shippingCost = soup.select('.vi-fnf-ship-txt'):nth-of-type(1).text shippingCost = soup.select('img.vi-fnf-ship-img span.vi-fnf-ship-txt strong.sh_gr_bld').text Thanks. ==== UPDATE What I did was to prettify the soup but to no avail: soup = BeautifulSoup(response.text, 'html.parser') print(soup.prettify()) ==== NEW UPDATE I redirected the prettify output to a file.txt and saw the code. So it is in there for sure with the same tags as above. The URL of the item is: https://www.ebay.com/itm/Mens-Legacy-Air-Bubble-90-Running-Trainers-Shoes/323806767262?_trkparms=ispr%3D1&hash=item4b6463289e:m:m_fYF4CZiE5Q9q08V38EY5w&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829 The FREE 'N FAST text in the shipping section. A: The "trick" is to set shipping preferences to United Kingdom before getting the main page: import requests from bs4 import BeautifulSoup url = 'https://www.ebay.com/itm/Mens-Legacy-Air-Bubble-90-Running-Trainers-Shoes/323806767262?_trkparms=ispr%3D1&hash=item4b6463289e:m:m_fYF4CZiE5Q9q08V38EY5w&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829&enc=AQAEAAACQBPxNw%2BVj6nta7CKEs3N0qWNuu8y9VA2HEw0wmPsL5MTRFTJmnuraG452Pk3WQNpsgmrIf6ePIv561MkEiJV0pbFv9zmD1JW8JOdsIntwNXTFqw1McvYYqbaOR4YjsvuadL81czU45zEDv4c6pnAr%2FxMKDDYWViq81G9CPiJps3CAXKI8YcKTdUooXwBzpWHe0mCqp9WtgKcdyEUl85CxBxnYT7lC9lE%2BuZeNSfmbUfYMdiOxpjW8bZGX39SM8wagpyNHh79ILbJzX49%2BBpK0I11nzUm8xxnTPF53XqIKksC20%2BA0LHzrHYhV%2FwiuVk0Pb6t%2BUbTHPnUPbe%2B2OX4Pq8o8WvpergM0K2HXjzK2YOkP0M69O%2FjtCEpv22Gd0tP5MMLmsk4fuNxzQIADa2P199CYxynr76eLUr2u63alCb3heTTvPncuJzk02EGEdi38Nm%2BPcq2PTwjY1S%2F4mZ1ZolPl4lPxmfVr4gXrCaXfMExPYokV4FOmo46FJovcncwt4oHFjpSDCufOrbH4xcqrjfTRQ%2BigsxPaH5hWpzILfWTPNXbcIcaJRceFBFZrg8Ysa3oFuHEBgaBZKHRnZmWuFqPB%2B68WmqbZ1tunmg%2BXBKzGqLLfqnBWWw3qDXYr0V2AbALr73VLCeWzQIJzm0E0D%2FdB0KTn2YTHZzfD%2FrXYEUz2i19CwLG7SA8S9no0IFA16%2BpqE4G3s%2FE%2BAKFz3aQJZVpxSTc7Imy0CTF%2FjsA92yilzyIlsIeTc2AjaKy%2BTM%2Fjg%3D%3D&checksum=323806767262b0325dcc5d12405d9773312793615829' set_ship_to_url = 'https://www.ebay.com/gh/setuserpreference' with requests.session() as s: r = s.post(set_ship_to_url, json={"userPreferedCountry":"GBR"}) # <-- set Ship To preference to United Kingdom soup = BeautifulSoup(s.get(url).content, 'html.parser') print(soup.select_one('strong.sh_gr_bld').text) Prints: FAST 'N FREE
Court of Appeals of the State of Georgia ATLANTA,____________________ December 22, 2014 The Court of Appeals hereby passes the following order: A15D0183. JOHNNY BRETT GREGORY v. J. STEPHEN SCHUSTER, JUDGE. Johnny Brett Gregory, a prison inmate, seeks to vacate an order entered in a civil action for damages. The order, which was entered on July 28, 2011, granted the defendant’s motion to have UCC documents filed by Gregory removed from the transaction registry. We lack jurisdiction.1 An application for discretionary appeal must be filed within 30 days of the entry of the order to be appealed. OCGA § 5-6-35 (d); Hill v. State, 204 Ga. App. 582 (420 SE2d 393) (1992). Gregory, however, filed his case more than three years after the entry of the trial court’s order. For this reason, this application for discretionary appeal is DISMISSED for lack of jurisdiction. Court of Appeals of the State of Georgia 12/22/2014 Clerk’s Office, Atlanta,____________________ I certify that the above is a true extract from the minutes of the Court of Appeals of Georgia. Witness my signature and the seal of said court hereto affixed the day and year last above written. , Clerk. 1 Gregory originally filed his case in the Supreme Court, which ordered that the case be re-docketed as a discretionary application and transferred to this Court. Even utilizing the date provided on the proof of service supplied by Gregory, October 2, 2014, his appeal is nonetheless untimely.
The top of the beach house will be called "The Dock at Bradford Beach." Beach house at Bradford Beach to be used as new restaurant Members of the Milwaukee County Board got a better idea of what will happen this summer at Bradford Beach. In previous years, SURG Restaurant Group ran the tiki bars on the beach. On Monday a group from Chicago who is known for running restaurants on their lakefront, CCH Management, brought the board members up to speed on their plans."Principally we envision taking our concept which is at Montrose Beach and having a version of that at Bradford. So, we'd like to brand it The Dock at Bradford Beach. The beach house, right now you have the tiki huts that are on the beach, we envision actually using the beach house, at the top of it and making that a restaurant space where we're going to have umbrellas and tables and servers," said one of the members of CCH Management.As for a menu, the group said you can expect menu items such as "fish tacos, grass fed beef burgers, lots of salads, and some seared tuna."Also the tiki bars will still be used as remote sites, essentially to deliver drinks and food from the restaurant.To get an idea of what to expect at Bradford, click here for a look at The Dock at Montrose Beach. Members of the Milwaukee County Board got a better idea of what will happen this summer at Bradford Beach. In previous years, SURG Restaurant Group ran the tiki bars on the beach. On Monday a group from Chicago who is known for running restaurants on their lakefront, CCH Management, brought the board members up to speed on their plans. "Principally we envision taking our concept which is at Montrose Beach and having a version of that at Bradford. So, we'd like to brand it The Dock at Bradford Beach. The beach house, right now you have the tiki huts that are on the beach, we envision actually using the beach house, at the top of it and making that a restaurant space where we're going to have umbrellas and tables and servers," said one of the members of CCH Management. As for a menu, the group said you can expect menu items such as "fish tacos, grass fed beef burgers, lots of salads, and some seared tuna." Also the tiki bars will still be used as remote sites, essentially to deliver drinks and food from the restaurant. To get an idea of what to expect at Bradford, click here for a look at The Dock at Montrose Beach.