383 research outputs found
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
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
Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz
We apply the maximum entropy principle to construct the natural invariant
density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel
function reconstruction technique that is based on the solution of Hausdorff
moment problem via maximizing Shannon entropy, we estimate the invariant
density and the Lyapunov exponent of nonlinear maps in one-dimension from a
knowledge of finite number of moments. The accuracy and the stability of the
algorithm are illustrated by comparing our results to a number of nonlinear
maps for which the exact analytical results are available. Furthermore, we also
consider a very complex example for which no exact analytical result for
invariant density is available. A comparison of our results to those available
in the literature is also discussed.Comment: 16 pages including 6 figure
A Convergent Method for Calculating the Properties of Many Interacting Electrons
A method is presented for calculating binding energies and other properties
of extended interacting systems using the projected density of transitions
(PDoT) which is the probability distribution for transitions of different
energies induced by a given localized operator, the operator on which the
transitions are projected. It is shown that the transition contributing to the
PDoT at each energy is the one which disturbs the system least, and so, by
projecting on appropriate operators, the binding energies of equilibrium
electronic states and the energies of their elementary excitations can be
calculated. The PDoT may be expanded as a continued fraction by the recursion
method, and as in other cases the continued fraction converges exponentially
with the number of arithmetic operations, independent of the size of the
system, in contrast to other numerical methods for which the number of
operations increases with system size to maintain a given accuracy. These
properties are illustrated with a calculation of the binding energies and
zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain,
which is compared with analytic results for this system and extrapolations from
finite rings of spins.Comment: 30 pages, 4 figures, corrected pd
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
The smallest eigenvalue of Hankel matrices
Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive
measure with moments of any order. We study the large N behaviour of the
smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential
decay to zero for any measure with compact support. For general determinate
moment problems the decay to 0 of lambda_N can be arbitrarily slow or
arbitrarily fast. In the indeterminate case, where lambda_N is known to be
bounded below by a positive constant, we prove that the limit of the n'th
smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity
with n. The special case of the Stieltjes-Wigert polynomials is discussed
Symptomatic hypogammaglobulinemia in infancy and childhood – clinical outcome and in vitro immune responses
BACKGROUND: Symptomatic hypogammaglobulinemia in infancy and childhood (SHIC), may be an early manifestation of a primary immunodeficiency or a maturational delay in the normal production of immunoglobulins (Ig). We aimed to evaluate the natural course of SHIC and correlate in vitro lymphoproliferative and secretory responses with recovery of immunoglobulin values and clinical resolution. METHODS: Children, older than 1 year of age, referred to our specialist clinic because of recurrent infections and serum immunoglobulin (Ig) levels 2 SD below the mean for age, were followed for a period of 8 years. Patient with any known familial, clinical or laboratory evidence of cellular immunodeficiency or other immunodeficiency syndromes were excluded from this cohort. Evaluation at 6- to 12-months intervals continued up to 1 year after resolution of symptoms. In a subgroup of patients, in vitro lymphocyte proliferation and Ig secretion in response to mitogens was performed. RESULTS: 32 children, 24 (75%) males, 8 (25%) females, mean age 3.4 years fulfilled the inclusion criteria. Clinical presentation: ENT infections 69%, respiratory 81%, diarrhea 12.5%. During follow-up, 17 (53%) normalized serum Ig levels and were diagnosed as transient hypogammaglobulinemia of infancy (THGI). THGI patients did not differ clinically or demographically from non-transient patients, both having a benign clinical outcome. In vitro Ig secretory responses, were lower in hypogammaglobulinemic, compared to normal children and did not normalize concomitantly with serum Ig's in THGI patients. CONCLUSIONS: The majority of children with SHIC in the first decade of life have THGI. Resolution of symptoms as well as normalization of Ig values may be delayed, but overall the clinical outcome is good and the clinical course benign
Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to
the temperature variations in the cosmic microwave background
radiation; can be observed in all directions around us. A standard
but idealised model of this effect leads to an infinite set of moment-like
equations: the integral of with respect to k ()
is equal to a given constant, , for . Here, P is the
power spectrum of the primordial density variations, is a spherical
Bessel function and y is a positive constant. It is shown how to solve these
equations exactly for ~. The same solution can be recovered, in
principle, if the first ~m equations are discarded. Comparisons with classical
moment problems (where is replaced by ) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late
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
Evaluation of effective resistances in pseudo-distance-regular resistor networks
In Refs.[1] and [2], calculation of effective resistances on distance-regular
networks was investigated, where in the first paper, the calculation was based
on the stratification of the network and Stieltjes function associated with the
network, whereas in the latter one a recursive formula for effective
resistances was given based on the Christoffel-Darboux identity. In this paper,
evaluation of effective resistances on more general networks called
pseudo-distance-regular networks [21] or QD type networks \cite{obata} is
investigated, where we use the stratification of these networks and show that
the effective resistances between a given node such as and all of the
nodes belonging to the same stratum with respect to
(, belonging to the -th stratum with respect
to the ) are the same. Then, based on the spectral techniques, an
analytical formula for effective resistances such that
(those nodes , of
the network such that the network is symmetric with respect to them) is given
in terms of the first and second orthogonal polynomials associated with the
network, where is the pseudo-inverse of the Laplacian of the network.
From the fact that in distance-regular networks,
is satisfied for all nodes
of the network, the effective resistances
for ( is diameter of the network which
is the same as the number of strata) are calculated directly, by using the
given formula.Comment: 30 pages, 7 figure
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