CM points and weight 3/2 modular forms.

The theta correspondence has been an important tool in the theory of automorphic forms with plentiful applications to arithmetic questions. In this paper, we consider a specific theta lift for an isotropic quadratic space V over Q of signature (1, 2). The theta kernel we employ associated to the lift has been constructed by Kudla-Millson (e.g., [29, 30]) in much greater generality for O(p, q) (U(p, q)) to realize generating series of cohomo-logical intersection numbers of certain, ’special ’ cycles in locally symmetric spaces of orthogonal (unitary) type as holomorphic Siegel (Hermitian) mod-ular forms. In our case for O(1, 2), the underlying locally symmetric space M is a modular curve, and the special cycles, parametrized by positive in-tegers N, are the classical CM points Z(N); i.e., quadratic irrationalities of discriminant −N in the upper half plane. We survey the results of [16] and of our joint work with Bruinier [12] on using this particular theta kernel to define lifts of various kinds of functions F on the underlying modular curve M. The theta lift is given b

Provider Opinions on Frequent Mental Health Hospitalizations

Frequent mental health hospitalizations are contingent on many variables. The purpose of this study was to gather provider opinions on frequent mental health hospitalizations. A qualitative design was utilized; ten providers participated in this study which explored factors of frequent mental health hospitalizations. Data were analyzed using content analysis. The findings indicated that all providers view medication management as a precipitating factor to psychiatric hospitalization. Findings indicate that support at discharge will greatly influence the success of the patron. The findings of this study indicate further need for education and advocacy in mental health. Findings suggest that stigma and limited community resources are key variables to frequent mental health hospitalizations. This study parallels data from previous research on this subject; however, patient opinions on frequent mental health hospitalizations are still absent

Provider Opinions on Frequent Mental Health Hospitalizations

Frequent mental health hospitalizations are contingent on many variables. The purpose of this study was to gather provider opinions on frequent mental health hospitalizations. A qualitative design was utilized; ten providers participated in this study which explored factors of frequent mental health hospitalizations. Data were analyzed using content analysis. The findings indicated that all providers view medication management as a precipitating factor to psychiatric hospitalization. Findings indicate that support at discharge will greatly influence the success of the patron. The findings of this study indicate further need for education and advocacy in mental health. Findings suggest that stigma and limited community resources are key variables to frequent mental health hospitalizations. This study parallels data from previous research on this subject; however, patient opinions on frequent mental health hospitalizations are still absent

Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms

The purpose of this paper is to generalize the relation between intersection numbers of cycles in locally symmetric spaces of orthogonal type and Fourier coefficients of Siegel modular forms to the case where the cycles have local coefficients. Now the correspondence will involve vector-valued Siegel modular forms

Traces of CM values of modular functions

Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also study the theta lift for the weight 0 Eisenstein series for SL2() and realize a certain generating series of arithmetic intersection numbers as the derivative of Zagier's Eisenstein series of weight 3/2. This recovers a result of Kudla, Rapoport and Yang

Structured learning of assignment models for neuron reconstruction to minimize topological errors

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Structured learning provides a powerful framework for empirical risk minimization on the predictions of structured models. It allows end-to-end learning of model parameters to minimize an application specific loss function. This framework is particularly well suited for discrete optimization models that are used for neuron reconstruction from anisotropic electron microscopy (EM) volumes. However, current methods are still learning unary potentials by training a classifier that is agnostic about the model it is used in. We believe the reason for that lies in the difficulties of (1) finding a representative training sample, and (2) designing an application specific loss function that captures the quality of a proposed solution. In this paper, we show how to find a representative training sample from human generated ground truth, and propose a loss function that is suitable to minimize topological errors in the reconstruction. We compare different training methods on two challenging EM-datasets. Our structured learning approach shows consistently higher reconstruction accuracy than other current learning methods.Peer ReviewedPostprint (author's final draft

Charge and momentum transfer in supercooled melts: Why should their relaxation times differ?

The steady state values of the viscosity and the intrinsic ionic-conductivity of quenched melts are computed, in terms of independently measurable quantities. The frequency dependence of the ac dielectric response is estimated. The discrepancy between the corresponding characteristic relaxation times is only apparent; it does not imply distinct mechanisms, but stems from the intrinsic barrier distribution for $\alpha$-relaxation in supercooled fluids and glasses. This type of intrinsic ``decoupling'' is argued not to exceed four orders in magnitude, for known glassformers. We explain the origin of the discrepancy between the stretching exponent $\beta$, as extracted from $\epsilon(\omega)$ and the dielectric modulus data. The actual width of the barrier distribution always grows with lowering the temperature. The contrary is an artifact of the large contribution of the dc-conductivity component to the modulus data. The methodology allows one to single out other contributions to the conductivity, as in ``superionic'' liquids or when charge carriers are delocalized, implying that in those systems, charge transfer does not require structural reconfiguration.Comment: submitted to J Chem Phy