3,080 research outputs found
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(), where is a given set of
quantifier-free -formulas. An instance of Poset-SAT() consists of
finitely many variables and formulas
with ; the question is
whether this input is satisfied by any partial order on or
not. We show that every such problem is NP-complete or can be solved in
polynomial time, depending on . 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
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