Pub Date : 2024-02-01Epub Date: 2023-08-31DOI: 10.1007/s12070-023-04115-3
Ahmed Yahia Yahia Fouda, Hussein Magdy Abdelkader, Esmail Hassan Ramadan Ahmed, Marwan Ahmed Ibrahim
Tracheal resection and anastomosis is characterized in the last years by significant innovations which are well codified and standardized. Although the mortality rate is markedly reduced, the operation is still not free from risk of complications such as recurrent laryngeal nerve injury, anastomosis dehiscence, granulation tissue formation and restenosis. Pearson FG, Cooper ID, Nelems JL (1975) Primary tracheal anastomosis after resection of the cricoide cartilage with preservation of the recurrent laryngeal nerves. J Thorac Cardiovasc Surg 70:806-16.
Supplementary information: The online version contains supplementary material available at 10.1007/s12070-023-04115-3.
{"title":"Role of Loupes Magnification in Tracheal Resection and Anastomosis.","authors":"Ahmed Yahia Yahia Fouda, Hussein Magdy Abdelkader, Esmail Hassan Ramadan Ahmed, Marwan Ahmed Ibrahim","doi":"10.1007/s12070-023-04115-3","DOIUrl":"10.1007/s12070-023-04115-3","url":null,"abstract":"<p><p>Tracheal resection and anastomosis is characterized in the last years by significant innovations which are well codified and standardized. Although the mortality rate is markedly reduced, the operation is still not free from risk of complications such as recurrent laryngeal nerve injury, anastomosis dehiscence, granulation tissue formation and restenosis. Pearson FG, Cooper ID, Nelems JL (1975) Primary tracheal anastomosis after resection of the cricoide cartilage with preservation of the recurrent laryngeal nerves. J Thorac Cardiovasc Surg 70:806-16.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s12070-023-04115-3.</p>","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"84 1","pages":"153-157"},"PeriodicalIF":0.6,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10908748/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88103075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1215/00127094-2022-0090
Jonas Luhrmann, Wilhelm Schlag
We establish the asymptotic stability of the sine-Gordon kink under odd perturbations that are sufficiently small in a weighted Sobolev norm. Our approach is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key elements of our proof are a specific factorization property of the linearized operator around the sine-Gordon kink, a remarkable nonresonance property exhibited by the quadratic nonlinearity in the Klein–Gordon equation for the perturbation, and a variable coefficient quadratic normal form. We emphasize that the restriction to odd perturbations does not bypass the effects of the odd threshold resonance of the linearized operator. Our techniques have applications to soliton stability questions for several well-known nonintegrable models, for instance, to the asymptotic stability problem for the kink of the ϕ4 model as well as to the conditional asymptotic stability problem for the solitons of the focusing quadratic and cubic Klein–Gordon equations in one space dimension.
{"title":"Asymptotic stability of the sine-Gordon kink under odd perturbations","authors":"Jonas Luhrmann, Wilhelm Schlag","doi":"10.1215/00127094-2022-0090","DOIUrl":"https://doi.org/10.1215/00127094-2022-0090","url":null,"abstract":"We establish the asymptotic stability of the sine-Gordon kink under odd perturbations that are sufficiently small in a weighted Sobolev norm. Our approach is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key elements of our proof are a specific factorization property of the linearized operator around the sine-Gordon kink, a remarkable nonresonance property exhibited by the quadratic nonlinearity in the Klein–Gordon equation for the perturbation, and a variable coefficient quadratic normal form. We emphasize that the restriction to odd perturbations does not bypass the effects of the odd threshold resonance of the linearized operator. Our techniques have applications to soliton stability questions for several well-known nonintegrable models, for instance, to the asymptotic stability problem for the kink of the ϕ4 model as well as to the conditional asymptotic stability problem for the solitons of the focusing quadratic and cubic Klein–Gordon equations in one space dimension.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1215/00127094-2022-0080
Jessica Fintzen, Tasho Kaletha, Loren Spice
We give a modification of Yu’s construction of supercuspidal representations of a connected reductive group G over a non-Archimedean local field F. This modification restores the validity of certain key intertwining property claims made by Yu, which were recently proved to be false for the original construction. This modification is also an essential ingredient in the construction of supercuspidal L-packets in a preprint by the second author. As further applications, we prove the stability and many instances of endoscopic character identities of these supercuspidal L-packets, subject to some conditions on the base field F. In particular, for regular supercuspidal parameters, we prove all instances of standard endoscopy. In addition, we prove that these supercuspidal L-packets satisfy a recent conjecture by the second author, which, together with standard endoscopy, uniquely characterizes the local Langlands correspondence for supercuspidal L-packets (again subject to the conditions on F). These results are based on a statement of the Harish-Chandra character formula for the supercuspidal representations arising from the twisted Yu construction.
{"title":"A twisted Yu construction, Harish-Chandra characters, and endoscopy","authors":"Jessica Fintzen, Tasho Kaletha, Loren Spice","doi":"10.1215/00127094-2022-0080","DOIUrl":"https://doi.org/10.1215/00127094-2022-0080","url":null,"abstract":"We give a modification of Yu’s construction of supercuspidal representations of a connected reductive group G over a non-Archimedean local field F. This modification restores the validity of certain key intertwining property claims made by Yu, which were recently proved to be false for the original construction. This modification is also an essential ingredient in the construction of supercuspidal L-packets in a preprint by the second author. As further applications, we prove the stability and many instances of endoscopic character identities of these supercuspidal L-packets, subject to some conditions on the base field F. In particular, for regular supercuspidal parameters, we prove all instances of standard endoscopy. In addition, we prove that these supercuspidal L-packets satisfy a recent conjecture by the second author, which, together with standard endoscopy, uniquely characterizes the local Langlands correspondence for supercuspidal L-packets (again subject to the conditions on F). These results are based on a statement of the Harish-Chandra character formula for the supercuspidal representations arising from the twisted Yu construction.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135637920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1215/00127094-2022-0082
Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong
We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a Z∞-subgroup and a Z-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks, Manolescu, and Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.
{"title":"An infinite-rank summand of the homology cobordism group","authors":"Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong","doi":"10.1215/00127094-2022-0082","DOIUrl":"https://doi.org/10.1215/00127094-2022-0082","url":null,"abstract":"We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a Z∞-subgroup and a Z-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks, Manolescu, and Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135387806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1215/00127094-2022-0081
Jens Marklof, Matthew Welsh
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence μ2≡Dmodm, with D>0 square-free and D≢1mod4. This is achieved by translating the problem to convergence of certain geodesic random line processes in the hyperbolic plane. This geometric interpretation allows us in particular to derive an explicit expression for the pair correlation density of the roots.
{"title":"Fine-scale distribution of roots of quadratic congruences","authors":"Jens Marklof, Matthew Welsh","doi":"10.1215/00127094-2022-0081","DOIUrl":"https://doi.org/10.1215/00127094-2022-0081","url":null,"abstract":"We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence μ2≡Dmodm, with D>0 square-free and D≢1mod4. This is achieved by translating the problem to convergence of certain geodesic random line processes in the hyperbolic plane. This geometric interpretation allows us in particular to derive an explicit expression for the pair correlation density of the roots.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bessel models for real unitary groups: The tempered case","authors":"Hang Xue","doi":"10.1215/00127094-2022-0018","DOIUrl":"https://doi.org/10.1215/00127094-2022-0018","url":null,"abstract":". We prove the local Gan–Gross–Prasad conjecture for tempered L -packets of real unitary groups. The proof is based on theta lifts and is very simple.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42615128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1215/00127094-2022-0088
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. Combined with the range of repulsive kernels, already treated in the s{'e}minaire Laurent Schwartz proceeding [https://slsedp.centre-mersenne.org/journals/SLSEDP/ ], we provide the full proof of results announced by the authors in [C. R. Acad. Sciences Section Maths (2019)].
{"title":"Mean field limit and quantitative estimates with singular attractive kernels","authors":"Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang","doi":"10.1215/00127094-2022-0088","DOIUrl":"https://doi.org/10.1215/00127094-2022-0088","url":null,"abstract":"This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. Combined with the range of repulsive kernels, already treated in the s{'e}minaire Laurent Schwartz proceeding [https://slsedp.centre-mersenne.org/journals/SLSEDP/ ], we provide the full proof of results announced by the authors in [C. R. Acad. Sciences Section Maths (2019)].","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"115 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136008444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01Epub Date: 2023-05-18DOI: 10.3389/fopht.2023.1175568
Takae Kiyama, Halit Y Altay, Tudor C Badea, Chai-An Mao
More than 40 retinal ganglion cell (RGC) subtypes have been categorized in mouse based on their morphologies, functions, and molecular features. Among these diverse subtypes, orientation-selective Jam2-expressing RGCs (J-RGCs) has two unique morphologic characteristics: the ventral-facing dendritic arbor and the OFF-sublaminae stratified terminal dendrites in the inner plexiform layer. Previously, we have discovered that T-box transcription factor T-brain 1 (Tbr1) is expressed in J-RGCs. We further found that Tbr1 is essential for the expression of Jam2, and Tbr1 regulates the formation and the dendritic morphogenesis of J-RGCs. However, Tbr1 begins to express in terminally differentiated RGCs around perinatal stage, suggesting that it is unlikely involved in the initial fate determination for J-RGC and other upstream transcription factors must control Tbr1 expression and J-RGC formation. Using the Cleavage Under Targets and Tagmentation technique, we discovered that Pou4f1 binds to Tbr1 on the evolutionary conserved exon 6 and an intergenic region downstream of the 3'UTR, and on a region flanking the promoter and the first exon of Jam2. We showed that Pou4f1 is required for the expression of Tbr1 and Jam2, indicating Pou4f1 as a direct upstream regulator of Tbr1 and Jam2. Most interestingly, the Pou4f1-bound element in exon 6 of Tbr1 possesses high-level enhancer activity, capable of directing reporter gene expression in J-RGCs. Together, these data revealed a Pou4f1-Tbr1-Jam2 genetic hierarchy as a critical pathway in the formation of J-RGC subtype.
{"title":"Pou4f1-Tbr1 transcriptional cascade controls the formation of Jam2-expressing retinal ganglion cells.","authors":"Takae Kiyama, Halit Y Altay, Tudor C Badea, Chai-An Mao","doi":"10.3389/fopht.2023.1175568","DOIUrl":"10.3389/fopht.2023.1175568","url":null,"abstract":"<p><p>More than 40 retinal ganglion cell (RGC) subtypes have been categorized in mouse based on their morphologies, functions, and molecular features. Among these diverse subtypes, orientation-selective Jam2-expressing RGCs (J-RGCs) has two unique morphologic characteristics: the ventral-facing dendritic arbor and the OFF-sublaminae stratified terminal dendrites in the inner plexiform layer. Previously, we have discovered that T-box transcription factor <i>T-brain 1</i> (<i>Tbr1</i>) is expressed in J-RGCs. We further found that <i>Tbr1</i> is essential for the expression of <i>Jam2</i>, and Tbr1 regulates the formation and the dendritic morphogenesis of J-RGCs. However, Tbr1 begins to express in terminally differentiated RGCs around perinatal stage, suggesting that it is unlikely involved in the initial fate determination for J-RGC and other upstream transcription factors must control <i>Tbr1</i> expression and J-RGC formation. Using the Cleavage Under Targets and Tagmentation technique, we discovered that Pou4f1 binds to <i>Tbr1</i> on the evolutionary conserved exon 6 and an intergenic region downstream of the 3'UTR, and on a region flanking the promoter and the first exon of <i>Jam2</i>. We showed that Pou4f1 is required for the expression of <i>Tbr1</i> and <i>Jam2</i>, indicating Pou4f1 as a direct upstream regulator of <i>Tbr1</i> and <i>Jam2</i>. Most interestingly, the Pou4f1-bound element in exon 6 of <i>Tbr1</i> possesses high-level enhancer activity, capable of directing reporter gene expression in J-RGCs. Together, these data revealed a <i>Pou4f1-Tbr1-Jam2</i> genetic hierarchy as a critical pathway in the formation of J-RGC subtype.</p>","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":"163 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10926710/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88882283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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