A complexity dichotomy for poset constraint satisfaction

In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free $\leq$-formulas. An instance of Poset-SAT($\Phi$) consists of finitely many variables $x_1,\ldots,x_n$ and formulas $\phi_i(x_{i_1},\ldots,x_{i_k})$ with $\phi_i \in \Phi$; the question is whether this input is satisfied by any partial order on $x_1,\ldots,x_n$ or not. We show that every such problem is NP-complete or can be solved in polynomial time, depending on $\Phi$. All Poset-SAT problems can be formalized as constraint satisfaction problems on reducts of the random partial order. We use model-theoretic concepts and techniques from universal algebra to study these reducts. In the course of this analysis we establish a dichotomy that we believe is of independent interest in universal algebra and model theory.Comment: 29 page

Representation Growth in positive characteristic and conjugacy classes of maximal subgroups

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n is bounded by a low degree polynomial in n. As a consequence, we show that the number of conjugacy classes of maximal subgroups of a finite almost simple group G is at most O(log|G|).Comment: 25 page

The Largest Irreducible Representations of Simple Groups

Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non-abelian simple group can be bounded in terms of the smaller degrees. We also study the asymptotic behavior of this largest degree for finite groups of Lie type. Moreover, we show that for groups of Lie type, the Steinberg character has largest degree among all unipotent characters.Comment: 34 page

Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to thin samples with low refractive-index contrasts. More recent works have shown the benefit of adopting nonlinear models. They account for multiple scattering and reflections, improving the quality of reconstruction. To reduce the complexity and memory requirements of these methods, we derive an explicit formula for the Jacobian matrix of the nonlinear Lippmann-Schwinger model which lends itself to an efficient evaluation of the gradient of the data- fidelity term. This allows us to deploy efficient methods to solve the corresponding inverse problem subject to sparsity constraints

"Racial Preferences in a Small Urban Housing Market: A Spatial Econometric Analysis of Microneighborhoods in Kingston, New York"

This paper use spatial econometric models to test for racial preferences in a small urban housing market. Identifying racial preferences is difficult when unobserved neighborhood amenities vary systematically with racial composition. We adopt three strategies to redress this problem: (1) we focus on housing price differences across microneighborhoods in the small and relatively homogenous city of Kingston, New York; (2) we introduce GIS-based spatial amenity variables as controls in the hedonic regressions; and (3) we use spatial error and lag models to explicitly account for the spatial dependence of unobserved neighborhood amenities. Our simple OLS estimates agree with the consensus in the literature that black neighborhoods have lower housing prices. However, racial price discounts are no longer significant when we account for the spatial dependence of errors. Our results suggest that price discounts in black neighborhoods are caused not by racial preferences but by the demand for amenities that are typically not found in black neighborhoods.Housing; Race; Neighborhood Amenities; Spatial Econometrics Commonwealth of Independent States