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On entropy and optimal coding cost for stochastic language

Fundamenta Informaticae 1998年第2-3期36卷 285-305页

作者： Zhiltsova, Larissa Chair of Computer Science Nizhni Novgorod State Pedagogical University 1 Uljanova St. Nizhni Novgorod 603600 Russia

We investigate questions, relating to optimal binary coding of a language, for which a probability distribution is given on its words (for a stochastic language). As optimal we understand the coding, which gives minimum of mathematical expectation of a length of the coded word, or minimum of the coding cost. For any stochastic language with a finite value of the entropy we establish lower and upper bounds of the optimal coding cost, dependent only on the entropy, and we prove their unimprovability. For any stochastic context-free language with unique derivation it is found necessary and sufficient condition of existence of finite values of the optimal coding cost and the entropy. Also an effective method of calculation of the entropy is found for the case when the considered condition holds.

关键词： stochastic language context-free grammar entropy optimal coding optimal Probability distribution context-free grammars entropy Stochastic Language computational methods

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Gaussian channels and the optimal coding

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Journal of Multivariate Analysis 1975年第1期5卷 106-118页

作者： Hitsuda, Masuyuki Ihara, Shunsuke Department of Mathematics Nagoya Institute of Technology Nagoya Japan Department of Mathematics Ehime University Matsuyama Japan

For the Gaussian channel Y(t) = Φ(ξ(s), Y(s);s ≦ t) + X(t), the mutual information I(ξ, Y) between the message ξ(·) and the output Y(·) is evaluated, where X(·) is a Gaussian noise. Furthermore, th... 详细信息

关键词： canonical representation of Gaussian processes Gaussian channel mutual information optimal coding reproducing kernel Hilbert space

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optimal redundancy in computations from random oracles

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2018年 92卷 1-8页

作者： Barmpalias, George Lewis-Pye, Andrew Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China London Sch Econ Dept Math Columbia HouseHoughton St London WC2A 2AE England

It is a classic result in algorithmic information theory that every infinite binary sequence is computable from an infinite binary sequence which is random in the sense of Martin-Lof. If the computation of the first n bits of a sequence requires n + g(n) bits of the random oracle, then g is the redundancy of the computation. We devise a new coding method that achieves optimal logarithmic redundancy. For any computable non-decreasing function g such that Sigma(i) 2(-g(i)) is bounded we show that there is a coding process that codes any given infinite binary sequence into a Martin-Lof random infinite binary sequence with redundancy g. This redundancy bound is known to be the best possible. (C) 2017 Elsevier Inc. All rights reserved.

关键词： optimal coding Algorithmic randomness Minimal redundancy Random codes Algorithmic information theory

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optimal representation in average using Kolmogorov complexity

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THEORETICAL COMPUTER SCIENCE 1998年第1-2期200卷 261-287页

作者： Rivals, E Delahaye, JP Deutsch Krebsforschungszentrum D-69120 Heidelberg Germany Univ Lille 1 UA 369 CNRS Lab Informat Fondamentale Lille F-59655 Villeneuve Dascq France

One knows from the Algorithmic Complexity Theory' [2-5, 8, 14] that a word is incompressible on average. For words of pattern x(m), it is natural to believe that providing x and m is an optimal average representation. On the contrary, for words like x circle plus y (i.e., the bit to bit x or between x and y), providing x and y is not an optimal description on average. In this work, we sketch a theory of average optimal representation that formalizes natural ideas and operates where intuition does not suffice. First, we formulate a definition of K-optimality on average for a pattern, then demonstrate results that corroborate intuitive ideas, and give worthy insights into the best compression in more complex cases. (C) 1998-Elsevier Science B.V. All rights reserved.

关键词： optimal coding compression Kolmogorov complexity information theory

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The role of glyclinergic interneurons in the dorsal column nuclei

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NEUROCOMPUTING 2004年 58卷 1049-1055页

作者： Sánehez, E Aguilar, J Rivadulla, C Canedo, A Univ Santiago de Compostela Fac Fis GSI Dept Elect & Ciencias Computac Santiago De Compostela 15782 Spain Univ Santiago de Compostela Fac Med Dept Fisiol Santiago De Compostela Spain Univ A Coruna Escola Univ Fisioterapia Dept Med Coruna 15006 Spain

The aim of this paper is to provide new insights about the circuitry and the role of the dorsal column nuclei (DCN) in processing somatosensory information. The presence of glycinergic cells, a second type of DCN interneurons in addition to well-known GABAergic interneurons, opens the door to more complex interactions between cuneate cells as well as to a new hypothesis about the computational implications of such interactions. The research posed here fits in a broader context in the field of the sensory systems and deals with the general issue on the role of subcortical structures (i.e the thalamus) in processing sensory information. (C) 2004 Elsevier B.V. All rights reserved.

关键词： dorsal column nuclei somatosensory system computational models optimal coding

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Convergence criteria for genetic algorithms

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SIAM JOURNAL ON COMPUTING 2000年第1期30卷 269-282页

作者： Greenhalgh, D Marshall, S Univ Strathclyde Dept Stat & Modeling Sci Glasgow G1 1XH Lanark Scotland Univ Strathclyde Dept Elect & Elect Engn Glasgow G1 1XW Lanark Scotland

In this paper we discuss convergence properties for genetic algorithms. By looking at the effect of mutation on convergence, we show that by running the genetic algorithm for a sufficiently long time we can guarantee convergence to a global optimum with any specified level of confidence. We obtain an upper bound for the number of iterations necessary to ensure this, which improves previous results. Our upper bound decreases as the population size increases. We produce examples to show that in some cases this upper bound is asymptotically optimal for large population sizes. The final section discusses implications of these results for optimal coding of genetic algorithms.

关键词： genetic algorithms convergence criteria upper bounds probability optimal coding

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How a well-adapted immune system is organized

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2015年第19期112卷 5950-5955页

作者： Mayer, Andreas Balasubramanian, Vijay Mora, Thierry Walczak, Aleksandra M. Univ Paris 06 Phys Theor Lab F-75005 Paris France Univ Paris 06 CNRS Lab Phys Stat F-75005 Paris France Ecole Normale Super F-75005 Paris France Univ Penn Dept Phys & Astron Philadelphia PA 19104 USA CUNY Grad Ctr Initiat Theoret Sci New York NY 10016 USA

The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from the frequency of encounters;individuals exposed to the same infections will have sparse repertoires that are largely different, but nevertheless exploit cross-reactivity to provide the same coverage of antigens;and the optimal repertoires can be reached via the dynamics of competitive binding of antigens by receptors and selective amplification of stimulated receptors. Our results follow from a tension between the statistics of pathogen detection, which favor a broader receptor distribution, and the effects of cross-reactivity, which tend to concentrate the optimal repertoire onto a few highly abundant clones. Our predictions can be tested in high-throughput surveys of receptor and pathogen diversity.

关键词： immune repertoires optimal coding repertoire diversity competitive exclusion jamming

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Population coding under normalization

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VISION RESEARCH 2010年第22期50卷 2223-2232页

作者： Ringach, Dario L. Univ Calif Los Angeles David Geffen Sch Med Jules Stein Eye Inst Dept Neurobiol Los Angeles CA 90095 USA Univ Calif Los Angeles David Geffen Sch Med Jules Stein Eye Inst Dept Psychol Los Angeles CA 90095 USA

A common computation in visual cortex is the divisive normalization of responses by a pooled signal of the activity of cells within its neighborhood From a geometrical point of view normalization constraints the population response to high-contrast stimuli to lie on the surface of a high-dimensional sphere Here we study the implications this constraint imposes on the representation of a circular variable such as the orientation of a visual stimulus New results are derived for the infinite dimensional case of a homogeneous populations of neurons with identical tuning curves but different orientation preferences An important finding is that the ability of the population to discriminate between any two orientations depends exclusively on the Fourier amplitude spectrum of the orientation tuning curve We also study the problem of encoding by a finite set of neurons A central result is that under normalization optimal encoding can be achieved by a finite number of neurons with heterogeneous tuning curves In other words increasing the number of neurons in the population does not always allow for an improved population code These results are used to estimate the number of neurons involved in the coding of orientation at one position in the visual field If the cortex were to code orientation optimally we find that a small number (similar to 4) of neurons should suffice (C) 2010 Elsevier Ltd All rights reserved

关键词： Normalization Gain control Population coding optimal coding Visual cortex Electrostatic potential Thomson problem Minimum energy

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STUDY AND APPLICATIONS OF AN INFORMATIONAL MEASURE OF DEPENDENCE IN SURVIVAL MODELS

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METHODS OF INFORMATION IN MEDICINE 1992年第4期31卷 275-283页

作者： ELHASNAOUI, A JAIS, JP Laboratoire de Biostatistique et Informatique Médicale Hôpital Necker Paris France.

In survival models, when the factor of interest is a continuous variable or is expressed through a group of several variables, the classical measures of risk, i. e. relative risk and odds ratio, are not appropriate and there is no standard measure of dependence between survival and the considered factor. The Information Gain has been proposed by Linfoot (1957) and Kent (1983), giving any parametric model as a generalization of the squared product-moment correlation coefficient of the linear regression model with normal errors. By using simulation methods, we studied the statistical properties of the information gain as a measure of dependence, in the particular case of survival regression models. We suggest several efficient applications of this informational concept to some classical problems of regression analysis and prognostic analysis. Our ideas are illustrated through an example on the prognosis of idiopathic dilated cardiomyopathy.

关键词： INFORMATION GAIN MEASURE OF DEPENDENCE SURVIVAL MODELS PROGNOSTIC ANALYSIS optimal coding

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ON THE CAPACITY OF THE CONTINUOUS-TIME GAUSSIAN-CHANNEL WITH FEEDBACK

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JOURNAL OF MULTIVARIATE ANALYSIS 1980年第3期10卷 319-331页

作者： IHARA, S Department of Mathematics Ehime University Matsuyama 790 Japan

We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the covariance functions of the input processes, is imposed on the input processes. It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback.

关键词： 94A15 60G15 60G35 94A40 Gaussian channel with feedback capacity of channel optimal coding canonical representation of Gaussian process

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