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4.0

Jun 30, 2018
06/18

by
Akitoshi Kawamura; Yusuke Kobayashi

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Suppose we want to patrol a fence (line segment) using k mobile agents with given speeds v_1, ..., v_k so that every point on the fence is visited by an agent at least once in every unit time period. Czyzowicz et al. conjectured that the maximum length of the fence that can be patrolled is (v_1 + ... + v_k)/2, which is achieved by the simple strategy where each agent i moves back and forth in a segment of length v_i/2. We disprove this conjecture by a counterexample involving k = 6 agents. We...

Topics: Multiagent Systems, Computing Research Repository, Computational Geometry, Robotics

Source: http://arxiv.org/abs/1407.8194

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5.0

Jun 30, 2018
06/18

by
Alejandro Edera; Yanela Strappa; Facundo Bromberg

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Markov networks are models for compactly representing complex probability distributions. They are composed by a structure and a set of numerical weights. The structure qualitatively describes independences in the distribution, which can be exploited to factorize the distribution into a set of compact functions. A key application for learning structures from data is to automatically discover knowledge. In practice, structure learning algorithms focused on "knowledge discovery" present...

Topics: Computing Research Repository, Data Structures and Algorithms, Learning

Source: http://arxiv.org/abs/1407.8088

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4.0

Jun 30, 2018
06/18

by
Chia-Yu Hsieh; YunKyong Hyon; Hijin Lee; Tai-Chia Lin; Chun Liu

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In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system is more complicated than the original PNP system but with the same equilibrium states. Using Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system....

Topics: Mathematics, Analysis of PDEs, Mathematical Physics

Source: http://arxiv.org/abs/1407.8245

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6.0

Jun 30, 2018
06/18

by
Kanishka Perera; Marco Squassina; Yang Yang

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In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev embedding.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.8061

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6.0

Jun 30, 2018
06/18

by
Richard Baraniuk; Simon Foucart; Deanna Needell; Yaniv Plan; Mary Wootters

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Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they may be a result of extreme quantization. In one-bit compressed sensing it has recently been shown that the number of one-bit measurements required for signal estimation mirrors that of unquantized compressed sensing. Indeed, $s$-sparse signals in $\mathbb{R}^n$...

Topics: Mathematics, Computing Research Repository, Information Theory, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1407.8246

4
4.0

Jun 30, 2018
06/18

by
Yanyong Hong

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Fix a positive integer number $r$. A class of $r$-dim Lie conformal superalgebras named $r$-dim $i$-linear Lie conformal superalgebras are studied for $1\leq i \leq r$. We present an equivalent characterization of this class of Lie conformal superalgebras in $r$ dimension. Moreover, by this equivalent characterization, several constructions and examples are given.

Topics: Quantum Algebra, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.8240

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3.0

Jun 30, 2018
06/18

by
Yaping Yang; Gufang Zhao

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We introduce for each quiver $Q$ and each algebraic oriented cohomology theory $A$, the cohomological Hall algebra (CoHA) of $Q$, as the $A$-homology of the moduli of representations of the preprojective algebra of $Q$. This generalizes the $K$-theoretic Hall algebra of commuting varieties defined by Schiffmann-Vasserot. We construct an action of the preprojective CoHA on the $A$-homology of Nakajima quiver varieties. We compare this with the action of the Borel subalgebra of Yangian when $A$...

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.7994

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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

7
7.0

Jun 30, 2018
06/18

by
Yuan Zhu; Siyun Tang

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In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional K{\"o}tter-Vardy algorithm, new algorithm needs interpolation for two smaller multiplicity matrixes, due to the corresponding factorization algorithm for re-constructing codewords.

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.8069