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4.0
Jun 30, 2018
06/18
by
Caihua Chen; Shiqian Ma; Junfeng Yang
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In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ convergence rate result (under certain measure) of the proposed general inertial proximal point method. We then show that the...
Topics: Mathematics, Optimization and Control
Source: http://arxiv.org/abs/1407.8238
8
8.0
Jun 30, 2018
06/18
by
Cédric M. Campos; J. M. Sanz-Serna
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We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefully, may be accepted. We present experiments that clearly indicate that the additional work per sample carried out in the extra chance approach clearly pays in terms of the quality of the samples generated.
Topics: Probability, Mathematics, Numerical Analysis
Source: http://arxiv.org/abs/1407.8107
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5.0
Jun 30, 2018
06/18
by
Franziska Jahnke; Jochen Koenigsmann
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Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply...
Topics: Mathematics, Logic, Commutative Algebra
Source: http://arxiv.org/abs/1407.8156
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7.0
Jun 30, 2018
06/18
by
Javad Noorbakhsh; David Schwab; Allyson Sgro; Thomas Gregor; Pankaj Mehta
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Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves...
Topics: Nonlinear Sciences, Quantitative Biology, Mathematics, Pattern Formation and Solitons, Cell...
Source: http://arxiv.org/abs/1407.8210
8
8.0
Jun 30, 2018
06/18
by
Jennifer Hom
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Ozsvath-Stipsicz-Szabo recently defined a one-parameter family, upsilon of K at t, of concordance invariants associated to the knot Floer complex. We compare their invariant to the {-1, 0, 1}-valued concordance invariant epsilon, which is also associated to the knot Floer complex. In particular, we give an example of a knot K with upsilon uniformly equal to zero but epsilon non-zero.
Topics: Mathematics, Geometric Topology
Source: http://arxiv.org/abs/1407.8200
4
4.0
Jun 30, 2018
06/18
by
Ji Oon Lee; Kevin Schnelli
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We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for the matrix entries of $W$ and we choose $V$ so that the eigenvalues of $W$ and $V$ are typically of the same order. For a large class of diagonal matrices $V$ we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom...
Topics: Probability, Mathematics
Source: http://arxiv.org/abs/1407.8015
4
4.0
Jun 30, 2018
06/18
by
John D. Jakeman; Michael S. Eldred; Khachik Sargsyan
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In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets that have more terms in important dimensions and limits the number of unimportant terms that increase mutual coherence and thus degrade the performance of $\ell_1$-minimization. The important features and the accuracy of basis selection are demonstrated with a...
Topics: Mathematics, Numerical Analysis, Computing Research Repository
Source: http://arxiv.org/abs/1407.8093
4
4.0
Jun 30, 2018
06/18
by
Jonathan L. Gross; Michal Kotrbčík; Timothy Sun
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We derive a quadratic-time algorithm for the genus distribution of any 3-regular, biconnected series-parallel graph, which we extend to any biconnected series-parallel graph of maximum degree at most 3. Since the biconnected components of every graph of treewidth 2 are series-parallel graphs, this yields, by use of bar-amalgamation, a quadratic-time algorithm for every graph of treewidth at most 2 and maximum degree at most 3.
Topics: Mathematics, Discrete Mathematics, Computing Research Repository, Combinatorics
Source: http://arxiv.org/abs/1407.8031
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3.0
Jun 30, 2018
06/18
by
Karel Dekimpe; Jonas Deré
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Every expanding map on a closed manifold is topologically conjugate to an expanding map on an infra-nilmanifold, but not every infra-nilmanifold admits an expanding map. In this article we give a complete algebraic characterization of the infra-nilmanifolds admitting an expanding map. We show that, just as in the case of Anosov diffeomorphisms, the existence of an expanding map depends only on the rational holonomy representation of the infra-nilmanifold. A similar characterization is also...
Topics: Mathematics, Dynamical Systems
Source: http://arxiv.org/abs/1407.8106
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6.0
Jun 30, 2018
06/18
by
Sherry Chu; Benjamin Landon; Jane Panangaden
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Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of [Breuer-Ryckman-Simon]....
Topics: Mathematics, Spectral Theory, Mathematical Physics
Source: http://arxiv.org/abs/1407.8127
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5.0
Jun 30, 2018
06/18
by
Wang Cong; Jaume Llibre; Xiang Zhang
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In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincar\'e's one \cite{Po}, the Furta's one, part of Chen's ones, and the Shi's one. The key point in the proof of our main results is that functionally independence of generalized rational functions implies the...
Topics: Mathematics, Classical Analysis and ODEs, Dynamical Systems
Source: http://arxiv.org/abs/1407.7948
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10.0
Jun 30, 2018
06/18
by
Yixuan Xie; Jinhong Yuan; Qifu; Sun
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We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They are constructed based on multi-weight circulant matrix generated from idempotent polynomial, which is obtained from a quadratic residue set. The proposed Type-II stabilizer codes are of quasi-cyclic (QC) structure and code length $N=pk$, where $k$ is the size...
Topics: Mathematics, Computing Research Repository, Information Theory
Source: http://arxiv.org/abs/1407.8249
