Tuesday, June 16th, 2009

Time	Event
8:21a	Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres. (arXiv:0906.2 Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres. (arXiv:0906.2230v1 [math.SG]) Authors: Maksim Maydanskiy, Paul Seidel We construct open symplectic manifolds which are convex at infinity ("Liouville manifolds") and which are diffeomorphic, but not symplectically isomorphic, to cotangent bundles T^*S^{n+1}, for any n+1 \geq 3. These manifolds are constructed as total spaces of Lefschetz fibrations, where the fibre and all but one of the vanishing cycles are fixed. We show that almost any choice of the last vanishing cycle leads to a nonstandard symplectic structure (those choices which yield standard T^*S^{n+1} can be exactly determined). read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Every graph has an embedding in $S^3$ containing no non-hyperbolic knot. (arXiv:0906.2229v1 [math.GT Every graph has an embedding in $S^3$ containing no non-hyperbolic knot. (arXiv:0906.2229v1 [math.GT]) Authors: Erica Flapan, Hugh Howards In contrast with knots, whose properties depend only on their extrinsic topology in $S^3$, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in $S^3$ . For example, it was shown in [2] that every embedding of the complete graph $K_7$ in $S^3$ contains a non-trivial knot. Later in it was shown that for every $m \in N$, there is a complete graph $K_n$ such that every embedding of $K_n$ in $S_3$ contains a knot $Q$ whose minimal crossing number is at least $m$. Thus there are arbitrarily complicated knots in every embedding of a sufficiently large complete graph in $S^3$. We prove here the contrasting result that every graph has an embedding in $S^3$ such that every non-trivial knot in that embedding is hyperbolic. Our theorem implies that every graph has an embedding in $S^3$ which contains no composite or satellite knots. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Exotic symplectic manifolds from Lefschetz fibrations. (arXiv:0906.2224v1 [math.SG]) Exotic symplectic manifolds from Lefschetz fibrations. (arXiv:0906.2224v1 [math.SG]) Authors: Maksim Maydanskiy In this paper we construct, in all odd complex dimensions, pairs of Liouville domains W_0 and W_1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W_0 is symplectically very similar to the cotangent bundle itself, W_1 is more unusual. We use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W_1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Geodesic rewriting systems and pregroups. (arXiv:0906.2223v1 [math.GR]) Geodesic rewriting systems and pregroups. (arXiv:0906.2223v1 [math.GR]) Authors: Volker Diekert, Andrew J. Duncan, Alexei Miasnikov In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent and then systems in which the length reducing rules lead to geodesics. Combining these properties we arrive at our main object of study which we call geodesically perfect rewriting systems. We show that these are well-behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Homologically thin, non-quasi-alternating links. (arXiv:0906.2222v1 [math.GT]) Homologically thin, non-quasi-alternating links. (arXiv:0906.2222v1 [math.GT]) Authors: Joshua Greene We exhibit the first examples of links which are homologically thin but not quasi-alternating. To show that they are not quasi-alternating, we argue that none of their branched double-covers bounds a negative definite 4-manifold with non-torsion H_1. Using this method, we also complete the determination of the quasi-alternating pretzel links. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Rank-Sparsity Incoherence for Matrix Decomposition. (arXiv:0906.2220v1 [math.OC]) Rank-Sparsity Incoherence for Matrix Decomposition. (arXiv:0906.2220v1 [math.OC]) Authors: Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo, Alan S. Willsky Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the $\ell_1$ norm and the nuclear norm of the components. We develop a notion of \emph{rank-sparsity incoherence}, expressed as an uncertainty principle between the sparsity pattern of a matrix and its row and column spaces, and use it to characterize both fundamental identifiability as well as (deterministic) sufficient conditions for exact recovery. Our analysis is geometric in nature, with the tangent spaces to the algebraic varieties of sparse and low-rank matrices playing a prominent role. When the sparse and low-rank matrices are drawn from certain natural random ensembles, we show that the sufficient conditions for exact recovery are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition problems. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	On intersections of conjugacy classes and Bruhat cells. (arXiv:0906.2254v1 [math.RT]) On intersections of conjugacy classes and Bruhat cells. (arXiv:0906.2254v1 [math.RT]) Authors: Kei Yuen Chan, Jiang-Hua Lu, Simon Kai Ming To For a connected complex semi-simple Lie group $G$ and a fixed pair $(B, B^-)$ of opposite Borel subgroups of $G$, we determine when the intersection of a conjugacy class $C$ in $G$ and a double coset $BwB^-$ is non-empty, where $w$ is in the Weyl group $W$ of $G$. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on $W$ and an involution $\mc \in W$ associated to $C$. We study properties of the elements $\mc$. For $G = SL(n+1, \Cset)$, we describe $\mc$ explicitly for every conjugacy class $C$, and for the case when $w \in W$ is an involution, we also give an explicit answer to when $C \cap (BwB)$ is non-empty. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Perfect Matchings in Claw-free Cubic Graphs. (arXiv:0906.2261v1 [math.CO]) Perfect Matchings in Claw-free Cubic Graphs. (arXiv:0906.2261v1 [math.CO]) Authors: Sang-il Oum Lovasz and Plummer conjectured that there exist a fixed positive constant c such that every cubic n-vertex graph with no cutedge has at least 2^(cn) perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove that every claw-free cubic n-vertex graph with no cutedge has more than 2^(n/18) perfect matchings, thus verifying the conjecture for claw-free graphs. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Coexistence in stochastic spatial models. (arXiv:0906.2293v1 [math.PR]) Coexistence in stochastic spatial models. (arXiv:0906.2293v1 [math.PR]) Authors: Rick Durrett In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363--394], and that we explain in this paper is that this can be determined by examining the mean-field ODE. There are a number of rigorous results in support of this picture, but we will state nine challenging and important open problems, most of which date from the 1990's. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Remarks on global existence of classical solution to multi-dimensional compressible Euler-Poisson eq Remarks on global existence of classical solution to multi-dimensional compressible Euler-Poisson equations with geometrical symmetry. (arXiv:0906.2290v1 [math.AP]) Authors: Satoshi Masaki We give a necessary and sufficient condition for the global existence of the classical solution to the Cauchy problem of the compressible Euler-Poisson equations with radial symmetry. We introduce a new quantity which describes the balance between the initial velocity of the flow and the strength of the force governed by Poisson equation. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Existence of projective variety with arbitrary set of characteristic numbers. (arXiv:0906.2287v1 [ma Existence of projective variety with arbitrary set of characteristic numbers. (arXiv:0906.2287v1 [math.AG]) Authors: A. Y. Buryak It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Zade gave a definition of Chern characteristic numbers of singular compact complex analytic varieties. We prove that there exists a singular projective variety with arbitrary set of characteristic numbers. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvatur A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. (arXiv:0906.2280v1 [math.ST]) Authors: Aldéric Joulin The purpose of this paper is to extend the investigation of Poisson-type deviation inequalities started by Joulin (Bernoulli 13 (2007) 782--798) to the empirical mean of positively curved Markov jump processes. In particular, our main result generalizes the tail estimates given by Lezaud (Ann. Appl. Probab. 8 (1998) 849--867, ESAIM Probab. Statist. 5 (2001) 183--201). An application to birth--death processes completes this work. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Some Computations on Hilbert Type Matrices. (arXiv:0906.2279v1 [math.CA]) Some Computations on Hilbert Type Matrices. (arXiv:0906.2279v1 [math.CA]) Authors: Ruiming Zhang In this note, we present the determinant, the inverse and a lower bound for the smallest eigenvalue for some generalized Hilbert matrices associated with some power moment problems read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Multifractal scaling of products of birth--death processes. (arXiv:0906.2277v1 [math.ST]) Multifractal scaling of products of birth--death processes. (arXiv:0906.2277v1 [math.ST]) Authors: Vo V. Anh, Nikolai N. Leonenko, Narn-Rueih Shieh We investigate the scaling properties of products of the exponential of birth--death processes with certain given marginal discrete distributions and covariance structures. The conditions on the mean, variance and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We provide four illustrative examples of Poisson, Pascal, binomial and hypergeometric distributions. We establish the corresponding log-Poisson, log-Pascal, log-binomial and log-hypergeometric scenarios for the limiting processes, including their R\'{e}nyi functions and dependence properties. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Estimating the joint distribution of independent categorical variables via model selection. (arXiv:0 Estimating the joint distribution of independent categorical variables via model selection. (arXiv:0906.2275v1 [math.ST]) Authors: C. Durot, E. Lebarbier, A.-S. Tocquet Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial sequence. A new estimator for this mean is proposed that is nonparametric, non-asymptotic and implementable even for large sequences. It is a penalized least-squares estimator based on wavelets, with a penalization term inspired by papers of Birg\'{e} and Massart. The estimator is proved to satisfy an oracle inequality and to be adaptive in the minimax sense over a class of Besov bodies. The method is embedded in a general framework which allows us to recover also an existing method for segmentation. Beyond theoretical results, a simulation study is reported and an application on real data is provided. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Zero-cycles on varieties over p-adic fields and Brauer groups. (arXiv:0906.2273v2 [math.AG]) Zero-cycles on varieties over p-adic fields and Brauer groups. (arXiv:0906.2273v2 [math.AG]) Authors: Shuji Saito, Kanetomo Sato In this paper, we study the Brauer-Manin pairing of smooth proper varieties over local fields, and determine the $p$-adic part of the kernel of one side. We also compute the $A_0$ of a potentially rational surface which splits over a wildly ramified extension. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Portfolio optimization when expected stock returns are determined by exposure to risk. (arXiv:0906.2 Portfolio optimization when expected stock returns are determined by exposure to risk. (arXiv:0906.2271v1 [math.ST]) Authors: Carl Lindberg It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the difficulty of estimating expected returns accurately. In this paper, we modify the $n$ stock Black--Scholes model by introducing a new parametrization of the drift rates. We solve Markowitz' continuous time portfolio problem in this framework. The optimal portfolio weights correspond to keeping $1/n$ of the wealth invested in stocks in each of the $n$ Brownian motions. The strategy is applied out-of-sample to a large data set. The portfolio weights are stable over time and obtain a significantly higher Sharpe ratio than the classical $1/n$ strategy. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	On the Expectations of Maxima of Sets of Independent Random Variables. (arXiv:0906.2270v1 [math.PR]) On the Expectations of Maxima of Sets of Independent Random Variables. (arXiv:0906.2270v1 [math.PR]) Authors: D. V. Tokarev, K. A. Borovkov Let $X^1, ..., X^k$ and $Y^1, ..., Y^m$ be jointly independent copies of random variables $X$ and $Y$, respectively. For a fixed total number $n$ of random variables, we aim at maximising $M(k,m):= E \max \{X^1, ..., X^k, Y^1, >..., Y^{m} \}$ in $k = n-m\ge 0$, which corresponds to maximising the expected lifetime of an $n$-component parallel system whose components can be chosen from two different types. We show that the lattice $\{M(k,m): k, m\ge 0\}$ is concave, give sufficient conditions on $X$ and $Y$ for M(n,0) to be always or ultimately maximal and derive a bound on the number of sign changes in the sequence $M(n,0)-M(0,n)$, $n\ge 1$. The results are applied to a mixed population of Bienayme-Galton-Watson processes, with the objective to derive the optimal initial composition to maximise the expected time to extinction. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Toward optimal multistep forecasts in non-stationary autoregressions. (arXiv:0906.2266v1 [math.ST]) Toward optimal multistep forecasts in non-stationary autoregressions. (arXiv:0906.2266v1 [math.ST]) Authors: Ching-Kang Ing, Jin-Lung Lin, Shu-Hui Yu This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expressions not only characterize how the prediction errors are influenced by the model orders, prediction methods, values of parameters and unit roots, but also inspire us to construct some new predictor selection criteria that can ultimately choose the best combination of the model order and prediction method with probability 1. Finally, simulation analysis confirms the satisfactory finite sample performance of the newly proposed criteria. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$. Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$. (arXiv:0906.2262v1 [math.MG]) Authors: R.N. Karasev In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21a	Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution. (arXiv:0906.2217v1 [math.PR Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution. (arXiv:0906.2217v1 [math.PR]) Authors: Shui Feng, Fuqing Gao The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $\alpha$ and $\theta$, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the two-parameter Poisson-Dirichlet distribution and the corresponding homozygosity when $\theta$ approaches infinity, and the large deviation principle is established for the two-parameter Poisson-Dirichlet distribution when both $\alpha$ and $\theta$ approach zero. read more at math updates on arXiv.org rss2lj (Comment on this)

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