Maximum entropy and the problem of moments: A stable algorithm

We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an optimal solution can be constructed iteratively. We demonstrate the performance and stability of our algorithm with several tests on numerically difficult functions. We then consider an electronic structure application, the electronic density of states of amorphous silica and study the convergence of Fermi level with increasing number of moments.Comment: 4 pages including 3 figure

Coherent states of a charged particle in a uniform magnetic field

The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.Comment: 2 eps figure

Cellular Automata and Ultra-Discrete Painlev\'e Equations

Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the Painlev\'e equations organizing themselves into a coalescence cascade and possessing special solutions. A necessary condition for the integrability of cellular automata is also presented.Comment: 8 pages, plainTeX, 2 figure

Vector Continued Fractions using a Generalised Inverse

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically.Comment: Published form - minor change

Real-variables characterization of generalized Stieltjes functions

We obtain a characterization of generalized Stieltjes functions of any order \lambda > 0 in terms of inequalities for their derivatives on (0,\infty). When \lambda=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.Comment: LaTeX2e, 9 pages. Version 2 contains some improvements in the exposition suggested by a referee. To be published in Expositiones Mathematica

Generating GHZ state in 2m-qubit spin network

We consider a pure 2m-qubit initial state to evolve under a particular quantum me- chanical spin Hamiltonian, which can be written in terms of the adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques such as spectral dis- tribution and stratification associated with the graphs, employed in [1, 2], a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an explicit formula is given for the suitable coupling strengths of the hamiltonian, so that a maximally entangled state can be generated between antipodes of the network. By using some known multipartite entanglement measures, the amount of the entanglement of the final evolved state is calculated, and finally two examples of four qubit and six qubit states are considered in details.Comment: 22 page

Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory

The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present paper, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the quantum probability theory, we investigate quantum central limit theorem for continuous-time quantum walks on odd graphs.Comment: 19 page, 1 figure

Pertussis infection in fully vaccinated children in day-care centers, Israel.

We tested 46 fully vaccinated children in two day-care centers in Israel who were exposed to a fatal case of pertussis infection. Only two of five children who tested positive for Bordetella pertussis met the World Health Organization's case definition for pertussis. Vaccinated children may be asymptomatic reservoirs for infection

Densities of States, Moments, and Maximally Broken Time-Reversal Symmetry

Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic limit point-wise in energy with increasing numbers of moments. In this work the moment problem is further constrained by minimal lifetimes or maximal breaking of time-reversal symmetry, to yield approximate densities of states with point-wise macroscopic limits. This is applied numerically to models with one and two finite bands with various singularities, as well as to a model with infinite band-width, and the results are compared with the maximum entropy approximation where possible.Comment: Accepted for publication in Physical Review