84,552 research outputs found
Nonresonance conditions for arrangements
We prove a vanishing theorem for the cohomology of the complement of a
complex hyperplane arrangement with coefficients in a complex local system.
This result is compared with other vanishing theorems, and used to study Milnor
fibers of line arrangements, and hypersurface arrangements.Comment: LaTeX, 10 page
Proof of some asymptotic results for a model equation for low Reynolds number flow
A two-point boundary value problem in the interval [Δ, â], Δ > 0 is studied. The problem contains additional parameters α â„ 0, ÎČ â„ 0, 0 †U 0; for α = 0 an explicit construction shows that no solution exists unless k > 1. A special method is used to show uniqueness. For Δ â 0, k â„ 1, various results had previously been obtained by the method of matched asymptotic expansions. Examples of these results are verified rigorously using the integral representation. For k < 1, the problem is shown not to be a layer-type problem, a fact previously demonstrated explicitly for k = 0. If k is an integer â„ 0 the intuitive understanding of the problem is aided by regarding it as spherically symmetric in k + 1 dimensions. In the present study, however, k may be any real number, even negative
Microscopic chaos from Brownian motion?
A recent experiment on Brownian motion has been interpreted to exhibit direct
evidence for microscopic chaos. In this note we demonstrate that virtually
identical results can be obtained numerically using a manifestly
microscopically nonchaotic system.Comment: 3 pages, 1 figure, Comment on P. Gaspard et al, Nature vol 394, 865
(1998); rewritten in a more popular styl
Assessing Bias in Regression Estimates Using Monte Carlo Simulations: Examples in Criminal Justice Research
Can we trust published results? Problems with bias in reported results: âDo social scientists even know anything?â Failed replications (ârepligateâ). Inaccurate inferences about important relationships (Type I and Type II errors). Inaccurate power analyses for future studies. To avoid these problems, researchers need tools to rigorously evaluate statistical models. The Monte Carlo method is one tool that can be used to evaluate bias in model estimateshttps://digitalscholarship.unlv.edu/gcua_symposium/1008/thumbnail.jp
Consumption, Happiness, and Climate Change
In this article, we explore the implications of this literature for understanding the relationship between climate change policies and consumption. We identify a number of ways in which accounting for the implications of the new happiness literature could lead to laws and policies that influence consumption in ways that increase the prospects for reducing greenhouse gas emissions in developed and developing countries. We do not examine every nuance of the growing happiness literature, but we provide a brief introduction and observations that we hope will stimulate further efforts by academicians and policymakers.happiness, life satisfaction, subjective well-being
Algebraic Properties of Valued Constraint Satisfaction Problem
The paper presents an algebraic framework for optimization problems
expressible as Valued Constraint Satisfaction Problems. Our results generalize
the algebraic framework for the decision version (CSPs) provided by Bulatov et
al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties
and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP
languages to weighted algebras. We show that the difficulty of VCSP depends
only on the weighted variety generated by the associated weighted algebra.
Paralleling the results for CSPs we exhibit a reduction to cores and rigid
cores which allows us to focus on idempotent weighted varieties. Further, we
propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the
hardness direction and verify that it agrees with known results for VCSPs on
two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny
2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author
Comparing persistence diagrams through complex vectors
The natural pseudo-distance of spaces endowed with filtering functions is
precious for shape classification and retrieval; its optimal estimate coming
from persistence diagrams is the bottleneck distance, which unfortunately
suffers from combinatorial explosion. A possible algebraic representation of
persistence diagrams is offered by complex polynomials; since far polynomials
represent far persistence diagrams, a fast comparison of the coefficient
vectors can reduce the size of the database to be classified by the bottleneck
distance. This article explores experimentally three transformations from
diagrams to polynomials and three distances between the complex vectors of
coefficients.Comment: 11 pages, 4 figures, 2 table
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