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We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the r th $r^{\mathrm{th}}$ central derivative of non-singular Fourier coefficients of a normalized Siegel–Eisenstein series, and (2) the degree of special cycles of “virtual dimension 0” on the moduli stack of hermitian shtukas with r $r$ legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series.

Fix a positive integer n and a finite field F_q. We study the joint distribution of the rank rk (E), the n-Selmer group Sel_n (E), and the n-torsion in the Tate–Shafarevich group III(E)[n] as E varies over elliptic curves of fixed height d ≥ 2 over F_q (T). We compute this joint distribution in the large q limit. We also show that the "large q, then large height" limit of this distribution agrees with the one predicted by Bhargava–Kane–Lenstra–Poonen–Rains.

Pathogenic variants in the voltage-gated sodium channel gene family lead to early onset epilepsies, neurodevelopmental disorders, skeletal muscle channelopathies, peripheral neuropathies and cardiac arrhythmias. Disease-associated variants have diverse functional effects ranging from complete loss-of-function to marked gain-of-function. Therapeutic strategy is likely to depend on functional effect. Experimental studies offer important insights into channel function but are resource intensive and only performed in a minority of cases. Given the evolutionarily conserved nature of the sodium channel genes, we investigated whether similarities in biophysical properties between different voltage-gated sodium channels can predict function and inform precision treatment across sodium channelopathies. We performed a systematic literature search identifying functionally assessed variants in any of the nine voltage-gated sodium channel genes until 28 April 2021. We included missense variants that had been electrophysiologically characterized in mammalian cells in whole-cell patch-clamp recordings. We performed an alignment of linear protein sequences of all sodium channel genes and correlated variants by their overall functional effect on biophysical properties. Of 951 identified records, 437 sodium channel-variants met our inclusion criteria and were reviewed for functional properties. Of these, 141 variants were epilepsy-associated (SCN1/2/3/8A), 79 had a neuromuscular phenotype (SCN4/9/10/11A), 149 were associated with a cardiac phenotype (SCN5/10A) and 68 (16%) were considered benign. We detected 38 missense variant pairs with an identical disease-associated variant in a different sodium channel gene. Thirty-five out of 38 of those pairs resulted in similar functional consequences, indicating up to 92% biophysical agreement between corresponding sodium channel variants (odds ratio = 11.3; 95% confidence interval = 2.8 to 66.9; P < 0.001). Pathogenic missense variants were

Brain voltage-gated sodium channel Na(V)1.1 (SCN1A) loss-of-function variants cause the severe epilepsy Dravet syndrome, as well as milder phenotypes associated with genetic epilepsy with febrile seizures plus. Gain of function SCN1A variants are associated with familial hemiplegic migraine type 3. Novel SCN1A-related phenotypes have been described including early infantile developmental and epileptic encephalopathy with movement disorder, and more recently neonatal presentations with arthrogryposis. Here we describe the clinical, genetic and functional evaluation of affected individuals. Thirty-five patients were ascertained via an international collaborative network using a structured clinical questionnaire and from the literature. We performed whole-cell voltage-clamp electrophysiological recordings comparing sodium channels containing wild-type versus variant Na(V)1.1 subunits. Findings were related to Dravet syndrome and familial hemiplegic migraine type 3 variants. We identified three distinct clinical presentations differing by age at onset and presence of arthrogryposis and/or movement disorder. The most severely affected infants (n = 13) presented with congenital arthrogryposis, neonatal onset epilepsy in the first 3 days of life, tonic seizures and apnoeas, accompanied by a significant movement disorder and profound intellectual disability. Twenty-one patients presented later, between 2 weeks and 3 months of age, with a severe early infantile developmental and epileptic encephalopathy and a movement disorder. One patient presented after 3 months with developmental and epileptic encephalopathy only. Associated SCN1A variants cluster in regions of channel inactivation associated with gain of function, different to Dravet syndrome variants (odds ratio = 17.8; confidence interval = 5.4-69.3; P = 1.3 x 10(-7)). Functional studies of both epilepsy and familial hemiplegic migraine type 3 variants reveal alterations of gating properties in keeping with neuronal hy

We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Zp(2 k- 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.

We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Zp(2 k- 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.

Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for GL[subscript n] over local function fields. This generalizes a theorem of Ngô, who proved the base change fundamental lemma for spherical Hecke algebras for GL[subscript n] over local function fields, and extends to positive characteristic (for GL[subscript n]) a fundamental lemma originally introduced and proved by Haines for p-adic local fields.

Thesis (S.M. in Real Estate Development)--Massachusetts Institute of Technology, Program in Real Estate Development in Conjunction with the Center for Real Estate , 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 141-142)., Real estate investment firms have the ever increasing need for understanding their firm's strengths and weaknesses, their performance relative to their peers and competitors, and for developing assessment tools for facilitating more informed investment and management decisions. One potentially very useful tool to further these objectives, a tool that is so far underutilized and underappreciated, is investment performance attribution analysis. Such performance attribution may be broadly characterized as the partitioning of the total investment return of a particular manager or portfolio in order to quantify and help to understand and assess the components and determinants of the overall investment performance. Traditional investment attribution analysis, adopted from the securities investment industry, has focused primarily on the portfolio level, where property selection and allocation factors are the two primary attributes of total return that can be parsed and benchmarked. In the case of real estate investments, property-level investment functions such as operational management and asset transaction execution, which are not captured by a traditional attribution analysis, also play a major role in the overall investment returns. During the past two decades a system to drill the investment performance attribution down to a deeper level, separating the asset "selection" component into further breakouts, including income return and components of the capital return (cash flow change and yield change), have been propounded by influential firms such as the Investment Property Databank (IPD) based in the UK. In a 2003 article David Geltner proposed a system for property-level performance attribution (PPA) based on the since-inception IRR of each individual property investment. This thesis furthered Geltner's work on PPA by an in depth exploration of the application of the IRR-Based Property-Level Performance Attribution analysis based on a large-scale, real-world-based ca, by Tony Feng., S.M.in Real Estate Development

Thesis (S.M. in Real Estate Development)--Massachusetts Institute of Technology, Program in Real Estate Development in Conjunction with the Center for Real Estate , 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 141-142)., Real estate investment firms have the ever increasing need for understanding their firm's strengths and weaknesses, their performance relative to their peers and competitors, and for developing assessment tools for facilitating more informed investment and management decisions. One potentially very useful tool to further these objectives, a tool that is so far underutilized and underappreciated, is investment performance attribution analysis. Such performance attribution may be broadly characterized as the partitioning of the total investment return of a particular manager or portfolio in order to quantify and help to understand and assess the components and determinants of the overall investment performance. Traditional investment attribution analysis, adopted from the securities investment industry, has focused primarily on the portfolio level, where property selection and allocation factors are the two primary attributes of total return that can be parsed and benchmarked. In the case of real estate investments, property-level investment functions such as operational management and asset transaction execution, which are not captured by a traditional attribution analysis, also play a major role in the overall investment returns. During the past two decades a system to drill the investment performance attribution down to a deeper level, separating the asset "selection" component into further breakouts, including income return and components of the capital return (cash flow change and yield change), have been propounded by influential firms such as the Investment Property Databank (IPD) based in the UK. In a 2003 article David Geltner proposed a system for property-level performance attribution (PPA) based on the since-inception IRR of each individual property investment. This thesis furthered Geltner's work on PPA by an in depth exploration of the application of the IRR-Based Property-Level Performance Attribution analysis based on a large-scale, real-world-based ca, by Tony Feng., S.M.in Real Estate Development

Thesis (S.M. in Real Estate Development)--Massachusetts Institute of Technology, Program in Real Estate Development in Conjunction with the Center for Real Estate , 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 141-142)., Real estate investment firms have the ever increasing need for understanding their firm's strengths and weaknesses, their performance relative to their peers and competitors, and for developing assessment tools for facilitating more informed investment and management decisions. One potentially very useful tool to further these objectives, a tool that is so far underutilized and underappreciated, is investment performance attribution analysis. Such performance attribution may be broadly characterized as the partitioning of the total investment return of a particular manager or portfolio in order to quantify and help to understand and assess the components and determinants of the overall investment performance. Traditional investment attribution analysis, adopted from the securities investment industry, has focused primarily on the portfolio level, where property selection and allocation factors are the two primary attributes of total return that can be parsed and benchmarked. In the case of real estate investments, property-level investment functions such as operational management and asset transaction execution, which are not captured by a traditional attribution analysis, also play a major role in the overall investment returns. During the past two decades a system to drill the investment performance attribution down to a deeper level, separating the asset "selection" component into further breakouts, including income return and components of the capital return (cash flow change and yield change), have been propounded by influential firms such as the Investment Property Databank (IPD) based in the UK. In a 2003 article David Geltner proposed a system for property-level performance attribution (PPA) based on the since-inception IRR of each individual property investment. This thesis furthered Geltner's work on PPA by an in depth exploration of the application of the IRR-Based Property-Level Performance Attribution analysis based on a large-scale, real-world-based ca, by Tony Feng., S.M.in Real Estate Development