Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution

A class of integrable boundary terms for the eight-state supersymmetric U model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1998 Elsevier Science B.V.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].

An investigation of pretend play, mental state terms and false belief understanding: In search of a metarepresentational link

The aim of this study was to investigate the association between false belief comprehension, the exhibition of pretend play and the use of mental state terms in pre-school children. Ferry children, aged between 36 and 54 months were videotaped engaging in free play with each parent. The exhibit-ion of six distinct acts of pretend play and the expression of 16 mental sr:ate terms were coded during play. Each child was also administered a pantomime task and three standard false belief casks. Reliable associations were also found between false belief performance and the pretence categories of object substitution and role assignment, and the exhibition of imaginary object pantomimes. Moreover, the use of mental state terms was positively correlated with false belief and the pretence categories of object substitution, imaginary play and role assignment, and negatively correlated with the exhibition of body part object pantomimes. These findings indicate that the development of a mental state lexicon and some, bur not all, components of pretend play are dependent on the capacity for metarepresentational cognition.

Interpretation of the reversible inhibition of adenosine deaminase by small cosolutes in terms of molecular crowding

Published results on the inhibitory effects of small cosolutes on adenosine deamination by adenosine deaminase [Kurz. L. C.. Weitkamp, E., and Frieden, C. (1987) Biochemistry 26, 3027-3032; Dzingeleski, G., and Wolfenden, R. (1993) Biochemistry 32, 9143 -9147] have been reexamined. Results for sucrose, dioxane, methanol, and ethanol are shown to be qualitatively consistent with thermodynamic interpretation in terms of molecular crowding effects arising from the occurrence of a minor increase in enzyme volume and/or asymmetry during the kinetic reaction-a conformational transition that could be either preexisting or ligand induced. Direct evidence for the existence of the putative isomeric transition is provided by active enzyme gel chromatography on Sephadex G-100, which demonstrates a negative dependence of enzyme elution volume upon substrate concentration and is therefore consistent with substrate-mediated conformational changes that favor a larger (or more asymmetric) isomeric state of the enzyme. There are thus experimental grounds for adopting the present description of the inhibitory effects of unrelated cosolutes on the kinetics of adenosine deamination by adenosine deaminase in terms of thermodynamic nonideality.

Analysis of thermodynamic non-ideality in terms of protein solvation

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical-mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation. parameter delta are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein-protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected. (C) 2001 Elsevier Science B.V. All rights reserved.

GONOME: measuring correlations between GO terms and genomic positions

Background: Current methods to find significantly under- and over-represented gene ontology (GO) terms in a set of genes consider the genes as equally probable balls in a bag, as may be appropriate for transcripts in micro-array data. However, due to the varying length of genes and intergenic regions, that approach is inappropriate for deciding if any GO terms are correlated with a set of genomic positions. Results: We present an algorithm - GONOME - that can determine which GO terms are significantly associated with a set of genomic positions given a genome annotated with (at least) the starts and ends of genes. We show that certain GO terms may appear to be significantly associated with a set of randomly chosen positions in the human genome if gene lengths are not considered, and that these same terms have been reported as significantly over-represented in a number of recent papers. This apparent over-representation disappears when gene lengths are considered, as GONOME does. For example, we show that, when gene length is taken into account, the term development is not significantly enriched in genes associated with human CpG islands, in contradiction to a previous report. We further demonstrate the efficacy of GONOME by showing that occurrences of the proteosome-associated control element (PACE) upstream activating sequence in the S. cerevisiae genome associate significantly to appropriate GO terms. An extension of this approach yields a whole-genome motif discovery algorithm that allows identification of many other promoter sequences linked to different types of genes, including a large group of previously unknown motifs significantly associated with the terms 'translation' and 'translational elongation'. Conclusion: GONOME is an algorithm that correctly extracts over-represented GO terms from a set of genomic positions. By explicitly considering gene size, GONOME avoids a systematic bias toward GO terms linked to large genes. Inappropriate use of existing algorithms that do not take gene size into account has led to erroneous or suspect conclusions. Reciprocally GONOME may be used to identify new features in genomes that are significantly associated with particular categories of genes.

T-Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j -> infinity limit of the corresponding transfer matrix with spin-j (i.e., (2j + I)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian. (c) 2006 Elsevier B.V. All rights reserved.