math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveSparse permutation invariant covariance estimation. (arXiv:0801.4837v2 math.ST UPDATED)- (Found June 29, 2008 ) The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension $p$ and sample size $n$ are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a...http://arxiv.org/abs/0801.4837 On line arrangements with applications to 3-nets. (arXiv:0704.0469v3 math.AG UPDATED)- (Found June 29, 2008 ) We start by showing a one-to-one correspondence between arrangements of d lines in $P2$, and lines in $Pd-2$. We apply this to classify (3,q)-nets on $P2$ over the complex numbers for all 2<=q<=6. For the new case q=6, we have a priori twelve possible combinatorial cases, but we obtain that only nine of them are realizable over the complex numbers. We give equations for the lines defining these nets. We also construct a three dimensional family of (3,8)-nets corresponding to the...http://arxiv.org/abs/0704.0469 Spectral and scattering theory for space-cutoff $P(varphi)_2$ models with variable metric. (arXiv:0806.4377v1 math-ph)- (Found June 29, 2008 ) We consider space-cutoff $P(varphi)_2$ models with a variable metric of the form H= dG(omega)+ int_rrg(x):P(x, varphi(x)):d x, on the bosonic Fock space $L2(rr)$, where the kinetic energy $omega= h12$ is the square root of a real second order differential operator h= Da(x)D+ c(x), where the coefficients $a(x), c(x)$ tend respectively to 1 and $m_infty2$ at $infty$ for some $m_infty>0$. The interaction term $int_rrg(x):P(x, varphi(x)):d x$ is defined using a bounded below polynomial in...http://arxiv.org/abs/0806.4377 Online data processing: comparison of Bayesian regularized particle filters. (arXiv:0806.4242v1 math.ST)- (Found June 29, 2008 ) The aim of this paper is to compare three regularized particle filters in an online data processing context. We carry out the comparison in terms of hidden states filtering and parameters estimation, considering a Bayesian paradigm and a univariate stochastic volatility model. We discuss the use of an improper prior distribution in the initialization of the filtering procedure and show that the regularized Auxiliary Particle Filter (APF) outperforms the regularized Sequential Importance...http://arxiv.org/abs/0806.4242 On Border Basis and Groebner Basis Schemes. (arXiv:0802.2793v2 math.AC UPDATED)- (Found June 29, 2008 ) Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing zero-dimensional ideals when the coefficients are inexact. And in this situation they show a clear advantage with respect to Groebner bases which, nevertheless, can also be used in the study of Hilbert schemes, since they provide tools for constructing...http://arxiv.org/abs/0802.2793 A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions. (arXiv:0803.0402v2- (Found June 29, 2008 ) In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estimator. Example estimators are considered to highlight how this measure compliments recent influence analysis. Importantly, we also show how a sample based version of this measure can be used to accurately and efficiently detect influential observations in practice.http://arxiv.org/abs/0803.0402 Conserved Quantities and the Algebra of Braid Excitations in Quantum Gravity. (arXiv:0805.0453v2 hep-th UPDATED)- (Found June 29, 2008 ) We derive conservation laws from interactions of braid-like excitations of embedded framed spin networks in Quantum Gravity. We also demonstrate that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, in which the set of actively-interacting braids is a subalgebra.http://arxiv.org/abs/0805.0453 C, P, and T of Braid Excitations in Quantum Gravity. (arXiv:0805.1265v2 hep-th UPDATED)- (Found June 29, 2008 ) We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T.http://arxiv.org/abs/0805.1265 WDVV solutions from orthocentric polytopes and Veselov systems. (arXiv:0805.3245v2 hep-th UPDATED)- (Found June 29, 2008 ) N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. For U=0 one remains with the WDVV equation which suggests an ansatz for F in terms of a set of covectors to be found. One approach constructs such covectors from suitable polytopes, another method solves Veselov's vee-conditions in terms of deformed Coxeter..http://arxiv.org/abs/0805.3245 Differentiability of stochastic flow of reflected Brownian motions. (arXiv:0806.0119v2 math.PR UPDATED)- (Found June 29, 2008 ) We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for reflected Brownian motion. The method of proof is based on excursion theory and analysis of the deterministic Skorokhod equation.http://arxiv.org/abs/0806.0119 |