Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Role of generalized and episode specific memories in the word frequency effect in recognition

Frequency, recency, and type of prior exposure to very low-and high-frequency words were manipulated in a 3-phase (i.e., familiarization training, study, and test) design. Increasing the frequency with which a definition for a very low-frequency word was provided during familiarization facilitated the word's recognition in both yes-no (Experiment 1) and forced-choice paradigms (Experiment 2). Recognition of very low-frequency words not accompanied by a definition during familiarization first increased, then decreased as familiarization frequency increased (Experiment I). Reasons for these differences were investigated in Experiment 3 using judgments of recency and frequency. Results suggested that prior familiarization of a very low-frequency word with its definition may allow a more adequate episodic representation of the word to be formed during a subsequent study trial. Theoretical implications of these results for current models of memory are discussed.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Febrile seizures and generalized epilepsy associated with a mutation in the Na+-channel beta 1 subunit gene SCN1B

Febrile seizures affect approximately 3% of all children under six years of age and are by far the most common seizure disorder(1). A small proportion of children with febrile seizures later develop ongoing epilepsy with afebrile seizures(2). Segregation analysis suggests the majority of cases have complex inheritance(3) but rare families show apparent autosomal dominant: inheritance. Two putative loci have been mapped (FEB1 and FEB2), but specific genes have not yet been identified(4,5). We recently described a clinical subset, termed generalized epilepsy with febrile seizures plus (GEFS(+)), in which many family members have seizures with fever that may persist beyond six years of age or be associated with afebrile generalized seizures(6). We now report linkage, in another large GEFS(+) family, to chromosome region 19q13.1 and identification of a mutation in the voltage-gated sodium (Na+)-channel beta 1 subunit gene (SCN1B). The mutation changes a conserved cysteine residue disrupting a putative disulfide bridge which normally maintains an extracellular immunoglobulin-like fold. Go-expression of the mutant pr subunit with a brain Na+-channel alpha subunit in Xenopus laevis oocytes demonstrates that the mutation interferes with the ability of the subunit to modulate channel-gating kinetics consistent with a loss-of-function allele. This observation develops the theme that idiopathic epilepsies are a family of channelopathies and raises the possibility of involvement of other Na+-channel subunit genes in febrile seizures and generalized epilepsies with complex inheritance patterns.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

Risk premiums and benefit measures for generalized-expected-utility theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave.

Localizing the relativistic electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density (rho(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive energy states. A suitable spin operator can be diagonalized at the same time.

Neuronal sodium-channel alpha 1-subunit mutations in generalized epilepsy with febrile seizures plus

Generalized epilepsy with febrile seizures plus (GEFS+) is a familial epilepsy syndrome characterized by the presence of febrile and afebrile seizures. The first gene, GEFS1, was mapped to chromosome 19q and was identified as the sodium-channel beta1-subunit, SCN1B. A second locus on chromosome 2q, GEFS2, was recently identified as the sodium-channel alpha1-subunit, SCN1A. Single-stranded conformation analysis (SSCA) of SCN1A was performed in 53 unrelated index cases to estimate the frequency of mutations in patients with GEFS+. No mutations were found in 17 isolated cases of GEFS+. Three novel SCN1A mutations-D188V, V1353L, and I1656M-were found in 36 familial cases; of the remaining 33 families, 3 had mutations in SCN1B. On the basis of SSCA, the combined frequency of SCN1A and SCN1B mutations in familial cases of GEFS+ was found to be 17%.

Truncation of the GABA(A)-receptor gamma 2 subunit in a family with generalized epilepsy with febrile seizures plus

Recent findings from studies of two families have shown that mutations in the GABA(A)-receptor gamma2 subunit are associated with generalized epilepsies and febrile seizures. Here we describe a family that has generalized epilepsy with febrile seizures plus (GEFS(+)), including an individual with severe myoclonic epilepsy of infancy, in whom a third GABA(A)-receptor gamma2-subunit mutation was found. This mutation lies in the intracellular loop between the third and fourth transmembrane domains of the GABA(A)-receptor gamma2 subunit and introduces a premature stop codon at Q351 in the mature protein. GABA sensitivity in Xenopus laevis oocytes expressing the mutant gamma2(Q351X) subunit is completely abolished, and fluorescent-microscopy studies have shown that receptors containing GFP-labeled gamma2(Q351X) protein are retained in the lumen of the endoplasmic reticulum. This finding reinforces the involvement of GABA(A) receptors in epilepsy.

Generalized epilepsy with febrile seizures plus: Mutation of the sodium channel subunit SCN1B

Generalized epilepsy with febrile seizures plus (GEFS(+)) is an important childhood genetic epilepsy syndrome with heterogeneous phenotypes, including febrile seizures (FS) and generalized epilepsies of variable severity. Forty unrelated GEFS(+) and FS patients were screened for mutations in the sodium channel beta-subunits SCN1B and SCN2B, and the second GEFS(+) family with an SCN1B mutation is described here. The family had 19 affected individuals: 16 with typical GEFS(+) phenotypes and three with other epilepsy phenotypes. Site-specific mutation within SCN1B remains a rare cause of GEFS(+), and the authors found no evidence to implicate SCN2B in this syndrome.