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Jun 29, 2018
06/18

by
Tilen Marc

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Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article we settle the structure of mirror graphs by characterizing them as precisely the Cayley graphs of the finite Coxeter groups or equivalently the tope graphs of reflection arrangements - well understood and classified structures. We provide a polynomial...

Topics: Combinatorics, Discrete Mathematics, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1609.00591

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Jun 29, 2018
06/18

by
Seungsang Oh; Sangyop Lee

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A set of vertices in a graph is called independent if no two vertices of the set are connected by an edge. In this paper we use the state matrix recursion algorithm, developed by Oh, to enumerate independent vertex sets in a grid graph and even further to provide the generating function with respect to the number of vertices. We also enumerate bipartite independent vertex sets in a grid graph. The asymptotic behavior of their growth rates is presented.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1609.00515

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Jun 29, 2018
06/18

by
Marc Glen; Sergey Kitaev; Artem Pyatkin

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A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy$ is an edge in $E$. It is known that any word-representable graph $G$ is $k$-word-representable for some $k$, that is, there exists a word $w$ representing $G$ such that each letter occurs exactly $k$ times in $w$. The minimum such $k$ is called $G$'s representation number. A crown graph $H_{n,n}$ is a graph obtained from the complete...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1609.00674

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Jun 29, 2018
06/18

by
Miroslav Olšák

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An equational condition is a set of equations in an algebraic language, and an algebraic structure satisfies such a condition if it possesses terms that meet the required equations. We find a single nontrivial equational condition which is implied by any nontrivial idempotent equational condition.

Topics: Logic, Mathematics

Source: http://arxiv.org/abs/1609.00531

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Jun 29, 2018
06/18

by
I. M. Verloop

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We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00563

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Jun 29, 2018
06/18

by
Bohdan Maslowski; Jana Šnupárková

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A stochastic affine evolution equation with bilinear noise term is studied where the driving process is a real-valued fractional Brownian motion. Stochastic integration is understood in the Skorokhod sense. Existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00582

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Jun 29, 2018
06/18

by
Bojan Basrak; Hrvoje Planinic; Philippe Soulier

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We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. By going beyond the existing asymptotic theory, we are able to prove a new...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00687

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Jun 29, 2018
06/18

by
Zhenan Wang

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Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form d_tu = div (A\nabla u) + f (t, x, u;w) + g_i(t, x, u;w)\dot{w}^i_t. We will also show that the solution of the above equation will be almost surely strictly positive if the initial condition is non-negative and not identically vanishing.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00769

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Jun 29, 2018
06/18

by
Per Alexandersson

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In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand--Tsetlin polytopes. Several of the counterexamples are too large to be discovered via a brute-force computer search. We also show that the multiset of hooks in a Young diagram is not enough information to determine the Ehrhart polynomial for an associated order polytope. This is somewhat counter-intuitive to the fact that the multiset of hooks always determine the leading...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1609.00647

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Jun 29, 2018
06/18

by
Peter Frankl; Vojtech Rödl; Andrzej Ruciński

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In 1965 Erd\H os conjectured that for all $k\ge2$, $s\ge1$ and $n\ge k(s+1)$, an $n$-vertex $k$-uniform hypergraph $\F$ with $\nu(\F)=s$ cannot have more than \newline $\max\{\binom{sk+k-1}k,\;\binom nk-\binom{n-s}k\}$ edges. It took almost fifty years to prove it for triple systems. In 2012 we proved the conjecture for all $s$ and all $n\ge4(s+1)$. Then {\L}uczak and Mieczkowska (2013) proved the conjecture for sufficiently large $s$ and all $n$. Soon after, Frankl proved it for all $s$. Here...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1609.00530

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Jun 29, 2018
06/18

by
Svante Janson

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A survey is given of some Chernoff type bounds for the tail probabilities P(X-EX > a) and P(X-EX < a) when X is a random variable that can be written as a sum of indicator variables that are either independent or negatively related. Most bounds are previously known and some comparisons are made. This paper was written in 1994, but was never published because I had overlooked some existing papers containing some of the inequalities. Because of some recent interest in one of the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00533

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4.0

Jun 29, 2018
06/18

by
Anatolii A. Puhalskii

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We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate of the probability that the portfolio exceeds the benchmark or to maximise the decay rate that the portfolio falls short. The other criterion concerns the growth rate of the risk-sensitive utility of wealth which has to be either minimised, for the risk-averse...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.00587

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Jun 29, 2018
06/18

by
Mirko Rösner

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We determine the parahoric restriction of non-cuspidal irreducible smooth representations of GSp(4,F) for a local non-archimedean number field F.

Topics: Representation Theory, Mathematics

Source: http://arxiv.org/abs/1609.00625

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Jun 29, 2018
06/18

by
Yi Lin

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In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic $d\delta$-lemma for any such foliations with the (transverse) $s$-Lefschetz property. As transversely symplectic foliations include many geometric structures, such as contact manifolds, co-symplectic manifolds, symplectic orbifolds, and symplectic quasi-folds as special examples, our work provides a unifying treatment of symplectic Hodge theory in these geometries....

Topics: Mathematics, Symplectic Geometry

Source: http://arxiv.org/abs/1609.00773

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Jun 29, 2018
06/18

by
Amar Kumar Banerjee; Rahul Mondal

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In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to study the idea of I-sequentially compactness [3] in the sense of double sequences.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1609.00571

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Jun 29, 2018
06/18

by
Mohammad Arshad Rahman; Shubham Karnamwat

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We propose an estimation technique for the flexible Bayesian quantile regression in ordinal (FBQROR) models --- an ordinal quantile regression where the error is assumed to follow a generalized asymmetric Laplace (GAL) distribution. The GAL distribution allows to fix specific quantiles while simultaneously letting the mode, skewness and tails to vary; a characteristic nonexistent in the asymmetric Laplace (AL) distribution since a single parameter defines both the quantile and the skewness. We...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1609.00710

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Jun 29, 2018
06/18

by
Erwan Hingant; Romain Yvinec

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We present a survey on the results on a particular coagulation-fragmentation model given by the Becker-D\"oring equations. For both the deterministic and stochastic versions, we include well-posedness, long-time behavior, convergence rate towards equilibrium, coarsening and relation to transport equations, time-dependent properties, metastability and classical nucleation theory. All along this survey, we highlight recent results and open questions.

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1609.00697

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Jun 29, 2018
06/18

by
Matthew M. Lin; Chun-Yueh Chiang

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This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a discrete-type flow depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00581

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Jun 29, 2018
06/18

by
Hiromu Tanaka

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We show that there exist Mori fibre spaces whose total spaces are klt but bases are not. We also construct Mori fibre spaces which have relatively non-trivial torsion line bundles.

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1609.00574

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Jun 29, 2018
06/18

by
Chunmei Su; Zhiping Li

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The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient $\det \nabla u$ is required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known that the constraint can often cause serious difficulties in both theoretical analysis and numerical computation, especially when the material is subject to large deformations. In this paper, we derive a set of sufficient and necessary conditions for the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00617

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Jun 29, 2018
06/18

by
Mark Gross; Bernd Siebert

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This contribution to the 2015 AMS Summer Institute in Algebraic Geometry (Salt Lake City) announces a general mirror construction. This construction applies to log Calabi-Yau pairs (X,D) with maximal boundary D or to maximally unipotent degenerations of Calabi-Yau manifolds. The new ingredient is a notion of "punctured Gromov-Witten invariant", currently in progress with Abramovich and Chen. The mirror to a pair (X,D) is constructed as the spectrum of a ring defined using the...

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1609.00624

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Jun 29, 2018
06/18

by
Will Brian

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Given a countable graph, we say a set $A$ of its vertices is \emph{universal} if it contains every countable graph as an induced subgraph, and $A$ is \emph{weakly universal} if it contains every finite graph as an induced subgraph. We show that, for almost every graph on $\mathbb N$, $(1)$ every set of positive upper density is universal, and $(2)$ every set with divergent reciprocal sums is weakly universal. We show that the second result is sharp (i.e., a random graph on $\mathbb N$ will...

Topics: Combinatorics, Logic, Mathematics

Source: http://arxiv.org/abs/1609.00744

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Jun 29, 2018
06/18

by
Yi Lin; Xiangdong Yang

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Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation whose basic cohomology satisfies the Hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic $d\delta$-lemma in this setting. As an application, we show that there exists a natural Frobenius manifold structure on the equivariant basic cohomology of the given foliation. In particular, this result provides a class of new examples of $dGBV$-algebras...

Topics: Mathematics, Symplectic Geometry

Source: http://arxiv.org/abs/1609.00774

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Jun 29, 2018
06/18

by
Goo Ishikawa

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In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basic theory and known studies on frontals in several geometric problems from singularity theory viewpoints. In particular, in this paper, we try to give some of detailed proofs and related ideas, which were omitted in the original papers, to the basic and important results related to frontals.

Topics: Differential Geometry, Mathematics

Source: http://arxiv.org/abs/1609.00488

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Jun 29, 2018
06/18

by
Dmitry N. Kozlov

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In this paper we define a family of topological spaces, which vastly generalizes the higher-dimensional Dunce hats. Our definition is purely combinatorial, and is phrased in terms of identifications of boundary simplices of an n-simplex. By virtue of construction, the obtained spaces may be indexed by words, and they automatically carry the structure of a $\Delta$-complex. As our main result, we completely determine the homotopy type of these spaces. In fact, somewhat surprisingly, we are able...

Topics: Combinatorics, Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1609.00505

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Jun 29, 2018
06/18

by
Shen Zeng; Frank Allgöwer

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In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear optimal centroid stabilization. In the former problem, the considered cost functional integrates squared synchronization error and input, and in the latter, the considered cost functional integrates squared sum of the states and input. Our...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1609.00655

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Jun 29, 2018
06/18

by
A. Chambolle; B. Merlet; L. Ferrari

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In this paper we consider the branched transportation problem in 2D associated with a cost per unit length of the form $1 + \alpha m$ where $m$ denotes the amount of transported mass and $\alpha > 0$ is a fixed parameter (notice that the limit case $\alpha = 0$ corresponds to the classical Steiner problem). Motivated by the numerical approximation of this problem, we introduce a family of functionals $(\{F_\epsilon\}_{\epsilon>0})$ which approximate the above branched transport energy. We...

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1609.00519

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Jun 29, 2018
06/18

by
Jürgen Herzog; Ayesha Asloob Qureshi; Akihiro Shikama

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It is shown that for large classes of posets $P$ and $Q$, the defining ideal $J_{P,Q}$ of an isotonian algebras is generated by squarefree binomials. Within these classes, those posets are classified for which $J_{P,Q}$ is quadratically generated.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1609.00595

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Jun 29, 2018
06/18

by
Tao Yin; Liwei Xu

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We consider the finite element method solving a fluid-solid interaction (FSI) problem in two dimensions. The original problem is reduced to an equivalent nonlocal boundary value problem through an exact Dirichlet-to-Neumann (DtN) mapping defined on an artificial boundary enclosing the solid. The solvability results are established for the corresponding variational problem and its modified form resulting from truncation of the DtN mapping. Regarding to the numerical solutions, we derive a priori...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00583

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Jun 29, 2018
06/18

by
Marius Tarnauceanu; Mihai-Silviu Lazorec

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In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some particular classes of groups. A criterion for a finite group to be an Iwasawa group is also presented.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1609.00476

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Jun 29, 2018
06/18

by
Matthieu Romagny; Gabriel Zalamansky

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We define the notion of complexity of a flat groupoid in algebriac spaces. We prove a descent theorem along quotients by groupoid of complexity one. We then proceed to construct quotient of groupoids by subgroupoids of complexity one.

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1609.00516

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Jun 29, 2018
06/18

by
Paul Arnaud Songhafouo Tsopméné; Victor Turchin

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The current paper is the second one of our project, which is an investigation of spaces of high dimensional string links. In the first one we showed that when the dimensions are in the stable range, the rational homology and homotopy of these latter spaces can be calculated as the homology of a direct sum of certain finite colored graph-complexes that we described explicitly. In this paper we compute the generating function of the Euler characteristics of the summands in the homological and...

Topics: Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1609.00778

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Jun 29, 2018
06/18

by
Eric A. Carlen; Raffaelle Esposito; Joel L. Lebowitz; Rossana Marra; Clement Mouhot

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We continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in earlier work, we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not...

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1609.00580

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Jun 29, 2018
06/18

by
L. Dykes; S. Noschese; L. Reichel

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Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block Toeplitz matrix with Toeplitz blocks also have been developed. This paper is concerned with preconditioning of linear systems of equations with a symmetric block Toeplitz matrix with symmetric Toeplitz blocks that stem from the discretization of a linear ill-posed...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00573

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Jun 29, 2018
06/18

by
Yaguang Yang

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Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally efficient and algorithms demonstrated efficiency in computation do not have a good or any polynomial bound. Todd raised a question in 2002: "Can we find a theoretically and practically efficient way to reoptimize?" This paper is an effort to close the...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1609.00694

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Jun 29, 2018
06/18

by
Dmitry Ostrovsky

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A multiple integral representation of single and joint moments of the total mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy [$\textit{Comm. Math. Phys.}$ ${\bf 236}$: 449-475, 2003] is derived. The covariance structure of the total mass of the measure is shown to be logarithmic. A generalization of the Selberg integral corresponding to single moments of the limit measure is proposed and shown to satisfy a recurrence relation. The joint moments of the limit...

Topics: Probability, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1609.00666

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Jun 29, 2018
06/18

by
Payam Bahiraei; Rasool Hafezi

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In this paper, we study the category $\mathbb{C}(\text{Rep}(\mathcal{Q}, \mathcal{G}))$ of complexes of representations of quiver $\mathcal{Q}$ with values in a Grothendieck category $\mathcal{G}$. We develop a method for constructing some model structures on $\mathbb{C}(\text{Rep}(\mathcal{Q}, \mathcal{G}))$ based on componentwise notion. Moreover we also show that these model structures are monoidal. As an application of these model structure we introduce some descriptions of the derived...

Topics: Representation Theory, Mathematics

Source: http://arxiv.org/abs/1609.00712

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Jun 29, 2018
06/18

by
Thomas Führer; Norbert Heuer; Ernst P. Stephan

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We derive and analyze discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We present different symmetric and non-symmetric formulations where optimal test functions are only used for the PDE part of the problem, not the boundary conditions. For the symmetric case and lowest order approximations, we provide a simple a posteriori error estimate. In a second part, we apply our technique to the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00765

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Jun 29, 2018
06/18

by
Rene Marczinzik

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The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. In \cite{Yam}, Yamagata stated the stronger conjecture that the dominant dimension of a non-selfinjective finite dimensional algebra is bounded by a function depending on the number of simple modules of that algebra. With a view towards those conjectures, new bounds on dominant dimensions seem desirable. We give a new approach to bounds on the dominant dimension of...

Topics: Representation Theory, Mathematics

Source: http://arxiv.org/abs/1609.00588

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Jun 29, 2018
06/18

by
Ilya Kossovskiy; Bernhard Lamel; Ming Xiao

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We provide regularity results for CR-maps between real hypersurfaces in complex spaces of different dimension with a Levi-degenerate target. We address both the real-analytic and the smooth case. Our results allow immediate applications to the study of proper holomorphic maps between Bounded Symmetric Domains.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1609.00652

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Jun 29, 2018
06/18

by
Minwoo Chae; Stephen G. Walker

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It has been an open problem [Saad (2003)] to find an iterative method that can solve an arbitrary sparse linear system $Ax = b$ in an efficient way (i.e. guaranteed convergence at geometric rate). We propose a novel iterative algorithm which can be applied to a large sparse linear system and guarantees convergence for any consistent (i.e. it has a solution) linear system. Moreover, the algorithm is highly stable, fast, easy to code and does not require further constraints on $A$ other than that...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.00670

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Jun 29, 2018
06/18

by
Senping Luo; Juncheng Wei; Wenming Zou

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We classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: $(-\Delta)^s u=|u|^{p-1}u$ in $\mathbb{R}^n$ for $2

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1609.00705

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Jun 29, 2018
06/18

by
Livio Flaminio; Krzysztof Frączek; Joanna Kułaga-Przymus; Mariusz Lemańczyk

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Let $ G $ be a connected, simply connected nilpotent Lie group and $ \Gamma < G $ a lattice. We prove that each ergodic diffeomorphism $ \phi(x\Gamma)=uA(x)\Gamma $ on the nilmanifold $ G/\Gamma $, where $ u\in G $ and $ A:G\to G $ is a unipotent automorphism satisfying $ A(\Gamma)=\Gamma $, enjoys the property of asymptotically orthogonal powers (AOP). Two consequences follow: (i) Sarnak's conjecture on M\"obius orthogonality holds in every uniquely ergodic model of an ergodic affine...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1609.00699

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Jun 29, 2018
06/18

by
Diana Davis; W. Patrick Hooper

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We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almost every ray of light is dense in a region of a particular form: the regions are infinite area and consists of the plane with a periodic family of triangles removed. We also completely describe initial conditions for periodic and drift-periodic light rays.

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1609.00772

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Jun 29, 2018
06/18

by
Grechkoseeva Mariya

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We say that a finite almost simple $G$ with socle $S$ is admissible (with respect to the spectrum) if $G$ and $S$ have the same sets of orders of elements. Let $L$ be a finite simple linear or unitary group of dimension at least three over a field of odd characteristic. We describe admissible almost simple groups with socle $L$. Also we calculate the orders of elements of the coset $L\tau$, where $\tau$ is the inverse-transpose automorphism of $L$.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1609.00518

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Jun 29, 2018
06/18

by
Seungsang Oh

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Lomonaco and Kauffman introduced a knot mosaic system to give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot $n$--mosaic is an $n \times n$ array of 11 mosaic tiles representing a knot or a link diagram by adjoining properly that is called suitably connected. The total number of knot $n$--mosaics is denoted by $D_n$ which is known to...

Topics: Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1609.00517

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Jun 29, 2018
06/18

by
Bram Petri

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We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.

Topics: Differential Geometry, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1609.00632

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Jun 29, 2018
06/18

by
Nik. A. Tyurin

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In previous papers we define certain Lagrangian shadows of ample divisors in algebraic varieties. In the present brief note an existence condition is discussed for these Lagrangian shadows.

Topics: Mathematics, Algebraic Geometry, Symplectic Geometry

Source: http://arxiv.org/abs/1609.00633

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Jun 29, 2018
06/18

by
Johan Taflin

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Let $f$ be a holomorphic endomorphism of $\mathbb P^k$ of degree $d.$ For each quasi-attractor of $f$ we construct a finite set of currents with attractive behaviors. To every such an attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of $\mathbb P^k.$ As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of $\log...

Topics: Complex Variables, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1609.00605

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Jun 29, 2018
06/18

by
Min Lee; Jens Marklof

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Einsiedler, Mozes, Shah and Shapira [Compos. Math. 152 (2016), 667-692] prove an equidistribution theorem for rational points on expanding horospheres in the space of d-dimensional Euclidean lattices, with d>2. Their proof exploits measure classification results, but provides no insight into the rate of convergence. We pursue here an alternative approach, based on harmonic analysis and Weil's bound for Kloosterman sums, which in dimension d=3 yields an effective estimate on the rate of...

Topics: Number Theory, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1609.00525