Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Exploring synonymous codon usage preferences of disulfide-bonded and non-disulfide bonded cysteines in the E-coli genome

High-quality data about protein structures and their gene sequences are essential to the understanding of the relationship between protein folding and protein coding sequences. Firstly we constructed the EcoPDB database, which is a high-quality database of Escherichia coli genes and their corresponding PDB structures. Based on EcoPDB, we presented a novel approach based on information theory to investigate the correlation between cysteine synonymous codon usages and local amino acids flanking cysteines, the correlation between cysteine synonymous codon usages and synonymous codon usages of local amino acids flanking cysteines, as well as the correlation between cysteine synonymous codon usages and the disulfide bonding states of cysteines in the E. coli genome. The results indicate that the nearest neighboring residues and their synonymous codons of the C-terminus have the greatest influence on the usages of the synonymous codons of cysteines and the usage of the synonymous codons has a specific correlation with the disulfide bond formation of cysteines in proteins. The correlations may result from the regulation mechanism of protein structures at gene sequence level and reflect the biological function restriction that cysteines pair to form disulfide bonds. The results may also be helpful in identifying residues that are important for synonymous codon selection of cysteines to introduce disulfide bridges in protein engineering and molecular biology. The approach presented in this paper can also be utilized as a complementary computational method and be applicable to analyse the synonymous codon usages in other model organisms. (c) 2005 Elsevier Ltd. All rights reserved.

Practical limitations in optical entanglement purification

Entanglement purification protocols play an important role in the distribution of entangled systems, which is necessary for various quantum information processing applications. We consider the effects of photodetector efficiency and bandwidth, channel loss and mode mismatch on the operation of an optical entanglement purification protocol. We derive necessary detector and mode-matching requirements to facilitate practical operation of such a scheme, without having to resort to destructive coincidence-type demonstrations.

CHAMADAS PROMOCIONAIS: INFORMAÇÃO E PERSUASÃO NOS INTERVALOS COMERCIAIS DA TV RECORD

As chamadas promocionais são consideradas como um comercial da emissora. Através delas, o conteúdo da programação é divulgado para persuadir o público a assistir os programas. Esta investigação identificou que o uso de apelos verbais e visuais, aproxima as chamadas da linguagem publicitária. No entanto, as semelhanças com a publicidade não se dão no momento da exibição das peças. Baseando-se no conceito de redundância proposto pela Teoria da Informação e na Teoria da Aprendizagem da Mensagem, de Carl Hovland, a pesquisa realizou um estudo de caso das duas primeiras temporadas de A FAZENDA, exibidas na Rede Record de Televisão. Pôde-se concluir que as chamadas do reality show não foram exibidas de acordo com os conceitos publicitários de GRP, cobertura e frequência, desperdiçando o espaço dos breaks e causando superexposição das mensagens autopromocionais.

Tighter decoding reliability bound for Gallager's error-correcting code

Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.

Statistical mechanics of typical set decoding

The performance of "typical set (pairs) decoding" for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.

Weight vs magnetization enumerator for Gallager codes

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (¸M), rather than on the weight enumerator (¸W) presented recently in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Critical noise levels for LDPC decoding

We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator , rather than on the weight enumerator employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Magnetization enumerator for LDPC codes - a statistical physics approach

We propose a method based on the magnetization enumerator to determine the critical noise level for Gallager type low density parity check error correcting codes (LDPC). Our method provides an appealingly simple interpretation to the relation between different decoding schemes, and provides more optimistic critical noise levels than those reported in the information theory literature.

Evaluating zero error noise thresholds by replica method for Gallager code ensembles

The replica method, developed in statistical physics, is employed in conjunction with Gallager's methodology to accurately evaluate zero error noise thresholds for Gallager code ensembles. Our approach generally provides more optimistic evaluations than those reported in the information theory literature for sparse matrices; the difference vanishes as the parity check matrix becomes dense.

Density evolution for multistage CDMA multiuser detector

An analytical framework to analyze the stage-by-stage detection dynamics of the multistage CDMA multiuser detector is presented. The density evolution idea is applied to analyze the multistage detector. Message distribution is treated basically by a Gaussian approximation, but interstage correlation of messages is systematically taken into account, which turns out to provide significant improvement.