How to realize "a sense of humour" in computers ?
Computer model of a "sense of humour" suggested previously [arXiv:0711.2058, 0711.2061, 0711.2270] is raised to the level of a realistic algorithm.
cs.CL↗
arXiv subjects
I. M. Suslov
Publications and source records attributed to I. M. Suslov.
Can a Computer Laugh ?
A computer model of "a sense of humour" suggested previously [arXiv:0711.2058,0711.2061], relating the humorous effect with a specific malfunction in information processing, is given in somewhat different exposition. Psychological aspects of humour are elaborated more thoroughly. The mechanism of laughter is formulated on the more general level. Detailed discussion is presented for the higher levels of information processing, which are responsible for a perception of complex samples of humour. Development of a sense of humour in the process of evolution is discussed.
cs.CL↗
Symmetry Theory of the Anderson Transition
We prove the Vollhardt and Wolfle hypothesis that the irreducible vertex U_{kk'}(q) appearing in the Bethe--Salpeter equation contains a diffusion pole (with the observable diffusion coefficient D(ω,q)) in the limit k+k'\to 0. The presence of a diffusion pole in U_{kk'}(q) makes it possible to represent the quantum "collision operator" L as a sum of a singular operator L_{sing}, which has an infinite number of zero modes, and a regular operator L_{reg} of a general form. Investigation of the response of the system to a change in L_{reg} leads to a self-consistency equation, which replaces the rough Vollhardt-Wolfle equation. Its solution shows that D(0,q) vanishes at the transition point simultaneously for all q. The spatial dispersion of D(ω,q) at ω\to 0 is found to be \sim 1 in relative units. It is determined by the atomic scale, and it has no manifestations on the scale q \sim ξ^{-1} associated with the correlation length ξ. The values obtained for the critical exponent s of the conductivity and the critical exponent νof the localization length in a d-dimensional space, s=1 (d>2) and ν=1/(d-2) (2 4), agree with all reliably established results. With respect to the character of the change in the symmetry, the Anderson transition is found to be similar to the Curie point of an isotropic ferromagnet with an infinite number of components. For such a magnet, the critical exponents are known exactly and they agree with the exponents indicated above. This suggests that the symmetry of the critical point has been established correctly and that the exponents have been determined exactly.
cond-mat.dis-nn↗
High orders of perturbation theory: are renormalons significant?
According to Lipatov, the high orders of perturbation theory are determined by saddle-point configurations (instantons) of the corresponding functional integrals. According to t'Hooft, some individual large diagrams, renormalons, are also significant and they are not contained in the Lipatov contribution. The history of the conception of renormalons is presented, and the arguments in favor of and against their significance are discussed. The analytic properties of the Borel transforms of functional integrals, Green functions, vertex parts, and scaling functions are investigated in the case of ϕ^4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of ϕ^4 theory.
hep-ph↗
Computer Model of a "Sense of Humour". I. General Algorithm
A computer model of a "sense of humour" is proposed. The humorous effect is interpreted as a specific malfunction in the course of information processing due to the need for the rapid deletion of the false version transmitted into consciousness. The biological function of a sense of humour consists in speeding up the bringing of information into consciousness and in fuller use of the resources of the brain.
q-bio.NC↗
Computer Model of a "Sense of Humour". II. Realization in Neural Networks
The computer realization of a "sense of humour" requires the creation of an algorithm for solving the "linguistic problem", i.e. the problem of recognizing a continuous sequence of polysemantic images. Such algorithm may be realized in the Hopfield model of a neural network after its proper modification.
q-bio.NC↗
On the Critical Exponents for the Λ-Transition in Liquid Helium
The use of a new method for summing divergent series makes it possible to significantly increase the accuracy of determining the critical exponents from the field theoretical renormalization group. The exponent value ν=0.6700\pm 0.0006 for the λ-transition in liquid helium is in good agreement with the experiment, but contradicts the last theoretical results based on using high-temperature series, the Monte Carlo method, and their synthesis.
cond-mat.stat-mech↗
Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the existence of nonanalytic contributions in the RG functions. The situation is analysed in this work using a new algorithm for summing divergent series that makes it possible to analyse dependence of the results for the critical exponents on the expansion coefficients for RG functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonities or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in RG functions.
cond-mat.stat-mech↗
Diffusion Poles and the Anderson Transition
In the recent series of papers (cond-mat/0402471, cond-mat/0403618, cond-mat/0407618, cond-mat/0501586), Janis and Kolorenc discussed the role of the diffision poles in the Anderson transition theory. Their picture contradicts the general principles and is shown below to be completely misleading. Correct setting of the problem is given and the contemporary situation is discussed. The critical remarks are given on the relation of the diffusion coefficient with multifractality of the wave functions.
cond-mat.dis-nn↗
Anderson Transition and Generalized Lyapunov Exponents (comment on comment by P.Markos, L.Schweitzer and M.Weyrauch, cond-mat/0402068)
The generalized Lyapunov exponents describe the growth of the second moments for a particular solution of the quasi-1D Schroedinger equation with initial conditions on the left end. Their possible application in the Anderson transition theory became recently a subject for controversy in the literature. The approach to the problem of the second moments advanced by Markos et al (cond-mat/0402068) is shown to be trivially incorrect. The difference of approaches by Kuzovkov et al (cond-mat/0212036, cond-mat/0501446) and the present author (cond-mat/0504557, cond-mat/0512708) is discussed.
cond-mat.dis-nn↗
Anderson transition: numerical vs analytical results (comment on the review article by P.Markos cond-mat/0609580)
In the recent review article, P.Markos admits that practically all numerical results on the critical behavior near the Anderson transition are in conflict with analytical expectations, but no serious discussion of this fact is given. The aim of the present comment is to give an analysis of the arising situation.
cond-mat.dis-nn↗
Analytical realization of finite-size scaling for Anderson localization: Is there transition in the 2D case?
Roughly half of numerical investigations of the Anderson transition are based on consideration of an associated quasi-1D system and postulation of one-parameter scaling for the minimal Lyapunov exponent. If this algorithm is taken seriously, it leads to unumbiguous prediction of the 2D phase transition. The transition is of the Kosterlitz-Thouless type and occurs between exponential and power law localization (Pichard and Sarma, 1981). This conclusion does not contradict numerical results if the raw data are considered. As for interpretation of these data in terms of one-parameter scaling, such interpretation is inadmissible: the minimal Lyapunov exponent does not obey any scaling. A scaling relation is valid not for minimal, but for some effective Lyapunov exponent, whose dependence on parameters is determined by scaling itself. If finite-size scaling is based on the effective Lyapunov exponent, existence of the 2D transition becomes not definite, but still rather probable. Interpretation of the results in terms of the Gell-Mann -- Low equation is also given.
cond-mat.dis-nn↗
Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point is splitted into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990). The possibility of restoring the conventional picture still exists but requires a radical reinterpretetion of the raw numerical data.
cond-mat.dis-nn↗
Gell-Mann - Low Function in QED for the arbitrary coupling constant
The Gell-Mann -- Low function β(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as β_\infty g^αwith α\approx 1, β_\infty\approx 1.
hep-ph↗
Gell-Mann - Low Function for QCD in the strong-coupling limit
The Gell-Mann - Low function β(g) in QCD (g=g0^2/16π^2 where g0 is the coupling constant in the Lagrangian) is shown to behave in the strong-coupling region as β_\infty g^αwith α\approx -13, β_\infty\sim 10^5.
hep-ph↗
Renormalons and the Renormalization Scheme
The possibility is discussed that existence of renormalon singularities is not the internal property of the specific field theory but depends on the renormalization scheme.
hep-ph↗
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in ϕ^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.
hep-ph↗
Renormalons and Analytic Properties of the βfunction
The presence or absense of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann - Low function β(g) and some other functions. A constructive criterion for the absense of singularities consists in the proper behavior of the βfunction and its Borel image B(z) at infinity, β(g)\sim g^αand B(z)\sim z^αwith α\le 1. This criterion is probably fulfilled for the ϕ^4 theory, QED and QCD, but is violated in the O(n)-symmetric sigma model with n\to\infty.
hep-ph↗