A reduction principle for Fourier coefficients of automorphic forms

In this paper we analyze a general class of Fourier coefficients of automorphic forms on reductive adelic groups $\mathbf{G}(\mathbb{A}_\mathbb{K})$ and their covers. We prove that any such Fourier coefficient is expressible through integrals and sums involving 'Levi-distinguished' Fourier coefficients. By the latter we mean the class of Fourier coefficients obtained by first taking the constant term along the nilradical of a parabolic subgroup, and then further taking a Fourier coefficient corresponding to a $\mathbb{K}$-distinguished nilpotent orbit in the Levi quotient. In a follow-up paper we use this result to establish explicit formulas for Fourier expansions of automorphic forms attached to minimal and next-to-minimal representations of simply-laced reductive groups.Comment: 35 pages. v2: Extended results and paper split into two parts with second part appearing soon. New title to reflect new focus of this part. v3: Minor corrections and updated reference to the second part that has appeared as arXiv:1908.08296. v4: Minor corrections and reformulation

Electronic Health Records and Support For Primary Care Teamwork

This study examined primary care practices' experiences using electronic health records (EHRs) as they strive to function as teams in patientcentered medical homes (PCMHs). We identify how EHRs facilitate and pose challenges to teamwork and how practices overcame such challenges. We describe solutions and identify opportunities to improve care processes as well as EHR functionalities and policies, to support teamwork

Eulerianity of Fourier coefficients of automorphic forms

We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.Comment: 28 pages. v2: Clarified connection to Fourier-Jacobi coefficients and references added. v3: Minor correction

Hundreds of scholars have signed a statement defending the international institutions that Trump has attacked

In July, forty-two international relations scholars published a statement in the New York Times which argued that President Trump needed to do more to preserve the post World War II international order. David A. Lake and Peter Gourevitch led the effort to publish the statement and argue why the president should consider their points of view

Stable individual variation in ventral spotting patterns in Phyllomedusa trinitatis (Anura: Phyllomedusidae) and other Phyllomedusa species: a minimally invasive method for recognizing individuals

Variação individual estável no padrão de manchas ventrais em Phyllomedusa trinitatis (Anura: Phyllomedusidae) e em outras espécies de Phyllomedusa: um método minimamente invasivo para o reconhecimento de indivíduos. Descrevemos aqui um padrão distintivo de “ilhas” e pontos brancos individualmente variáveis nas superfícies ventrais das regiões da garganta e do antebraço de machos e fêmeas de Phyllomedusa trinitatis. Crucialmente, a partir de indivíduos criados em cativeiro relatamos que esses padrões são ontogeneticamente estáveis. Usamos esses padrões para reconhecer pererecas individuais em populações de 60 ou mais indivíduos. O exame das superfícies ventrais de outras espécies de Phyllomedusa em espécimes de museus e de relatos publicados sugere que o uso desses padrões fornece um método de reconhecimento minimamente invasivo e geralmente útil nesse gênero. Descobrimos que espécies anteriormente classifcadas como Phyllomedusa, mas agora consideradas pertencentes a diferentes gêneros, não possuem esses padrões.Stable individual variation in ventral spotting patterns in Phyllomedusa trinitatis (Anura: Phyllomedusidae) and other Phyllomedusa species: a minimally invasive method for recognizing individuals. We describe a distinctive pattern of individually variable white ‘islands’ and dots on the ventral surfaces of the throat and forearm regions of male and female Phyllomedusa trinitatis. Crucially, we report from captive-reared individuals that these patterns are ontogenetically stable. We have used these patterns to recognize individual frogs in populations of 60 and more. Examination of the ventral surfaces of other Phyllomedusa species in museum specimens and from published accounts suggests that use of these patterns provides a generally useful, minimally invasive recognition method in this genus. We fnd that species previously classed as Phyllomedusa but now regarded as belonging to different genera lack these patterns

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Acromegaly, Mr Punch and caricature.

The origin of Mr Punch from the Italian Pulcinella of the Commedia dell'arte is well known but his feature, large hooked nose, protruding chin, kyphosis and sternal protrusion all in an exaggerated form also suggest the caricature of an acromegalic. This paper looks at the physical characteristics of acromegaly, the origin of Mr Punch and the development of caricature linking them together in the acromegalic caricature that now has a life of its own

Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

In this paper we analyze Fourier coefficients of automorphic forms on adelic split simply-laced reductive groups $G(\mathbb{A})$. Let $\pi$ be a minimal or next-to-minimal automorphic representation of $G(\mathbb{A})$. We prove that any $\eta\in \pi$ is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro--Shalika formula for cusp forms on $GL_n$. We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient in terms of these Whittaker coefficients. A consequence of our results is the non-existence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for $G$ of type $D_5$ and $E_8$ with a view towards applications to scattering amplitudes in string theory

Legitimacy gaps, taxpayer conflict, and the politics of austerity in the UK

Following the 2008 financial crisis, fiscal deficit reduction has become the name of the game for many Western states. This article uses focus group data to explore the legitimation of austerity in the United Kingdom. It is argued that fiscal consolidation speaks to real concerns citizens have over unfair redistribution to supposed ‘undeserving’ groups. The undeserving rich and poor are stigmatised during times of austerity since they are assumed to take more than they give from the public purse—leaving taxpayers, the assumption goes, to pick up the bill. By speaking to this legitimacy gap between prudent normative expectations and the lived experiences of state profligacy, fiscal consolidation can appear to speak to the interests of ‘the taxpayer’—a group conceptualised as a sense of group position that arises from collective sense-making rather than a pre-given constituency