math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveThree fermions with six single particle states can be entangled in two inequivalent ways. (arXiv:0806.4076v1 quant-ph CROSS LISTED)- (Found June 29, 2008 ) Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single...http://arxiv.org/abs/0806.4076 Link invariants, the chromatic polynomial and the Potts model. (arXiv:0806.3484v1 math.CO CROSS LISTED)- (Found June 29, 2008 ) We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we define the chromatic algebra, whose Markov trace is the chromatic polynomial chi_Q of an associated graph, and we give applications of this new algebraic approach to the...http://arxiv.org/abs/0806.3484 Information In The Non-Stationary Case. (arXiv:0806.3978v1 q-bio.NC CROSS LISTED)- (Found June 29, 2008 ) Information estimates such as the direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or..http://arxiv.org/abs/0806.3978 Bounds of some real (complex) solution of a finite system of polynomial equations with rational coefficients. (arXiv:math0702558v70 math.AC UPDATED)- (Found June 29, 2008 ) We discuss two conjectures. (I) For each x_1,...,x_n in R (C) there exist y_1,...,y_n in R (C) such that forall i in 1,...,n y_i leq 22n-2 forall i in 1,...,n (x_i=1 Rightarrow y_i=1) forall i,j,k in 1,...,n (x_i+x_j=x_k Rightarrow y_i+y_j=y_k) forall i,j,k in 1,...,n (x_i cdot x_j=x_k Rightarrow y_i cdot y_j=y_k) (II) Let G be an additive subgroup of C. Then for each x_1,...,x_n in G there exist y_1,...,y_n in G cap Q such that forall i in 1,...,n y_i leq 2n-1 forall i in 1,...,n...http://arxiv.org/abs/math/0702558 Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data. (arXiv:math0702326v2 ma- (Found June 29, 2008 ) It has been recently shown that nonparametric estimators of the additive regression function could be obtained in the presence of right censoring by coupling the marginal integration method with initial kernel-type Inverse Probability of Censoring Weighted estimators of the multivariate regression function citeDebbarhViallon3. In this paper, we get the exact rate of strong uniform consistency for such estimators. Our uniform limit laws especially lead to the construction of asymptotic...http://arxiv.org/abs/math/0702326 Estimation for almost periodic processes. (arXiv:math0607802v2 math.ST UPDATED)- (Found June 29, 2008 ) Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration if the locations of the lines are known. Here methods for estimating the intercepts of the lines of spectral concentration in the Gaussian case are given under appropriate conditions. The methods determine rates of convergence sufficiently fast as the sample...http://arxiv.org/abs/math/0607802 Moduli Spaces for Principal Bundles in Arbitrary Characteristic. (arXiv:math0506511v4 math.AG UPDATED)- (Found June 29, 2008 ) In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.http://arxiv.org/abs/math/0506511 A Special Class of Rank 10 and 11 Coxeter Groups. (arXiv:hep-th0610278v4 UPDATED)- (Found June 29, 2008 ) In the course of investigating regular subalgebras of E(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E(10) was uncovered (hep-th0606123). These Coxeter groups all share the property that their Coxeter graphs have incidence index 3, i.e. that each node is incident to three and only three single lines. Furthermore, the Coxeter exponents are either 2 or 3, but never infinity. We...http://arxiv.org/abs/hep-th/0610278 Failure of microcausality in noncommutative field theories. (arXiv:0802.0997v2 hep-th UPDATED)- (Found June 29, 2008 ) We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:phistarphi:(x)$ as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator O(x),O(y) and prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an...http://arxiv.org/abs/0802.0997 Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases. (arXiv:0802.069- (Found June 29, 2008 ) This is a continuation of the papers 4 of Bleher and Fokin and 5 of Bleher and Liechty, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large $n$ asymptotics of $Z_n$ on the critical line between these two phases.http://arxiv.org/abs/0802.0690 |