A hierarchical system of learning automata that can learn die globally optimal path

Systems of learning automata have been studied by various researchers to evolve useful strategies for decision making under uncertainity. Considered in this paper are a class of hierarchical systems of learning automata where the system gets responses from its environment at each level of the hierarchy. A classification of such sequential learning tasks based on the complexity of the learning problem is presented. It is shown that none of the existing algorithms can perform in the most general type of hierarchical problem. An algorithm for learning the globally optimal path in this general setting is presented, and its convergence is established. This algorithm needs information transfer from the lower levels to the higher levels. Using the methodology of estimator algorithms, this model can be generalized to accommodate other kinds of hierarchical learning tasks.

Theory For The Anomalous Hall Constant Of Mixed-Valence Systems

We show that the large anomalous Hall constants of mixed-valence and Kondo-lattice systems can be understood in terms of a simple resonant-level Fermi-liquid model. Splitting of a narrow, orbitally unquenched, spin-orbit split, f resonance in a magnetic field leads to strong skew scattering of band electrons. We interpret both the anomalous signs and the strong temperature dependence of Hall mobilities in CeCu2Si2, SmB6, and CePd3 in terms of this theory.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.

A Hierarchical System of Learning Automata

A learning automaton operating in a random environment updates its action probabilities on the basis of the reactions of the environment, so that asymptotically it chooses the optimal action. When the number of actions is large the automaton becomes slow because there are too many updatings to be made at each instant. A hierarchical system of such automata with assured c-optimality is suggested to overcome that problem.The learning algorithm for the hierarchical system turns out to be a simple modification of the absolutely expedient algorithm known in the literature. The parameters of the algorithm at each level in the hierarchy depend only on the parameters and the action probabilities of the previous level. It follows that to minimize the number of updatings per cycle each automaton in the hierarchy need have only two or three actions.

Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Thermodynamic scaling theory for impurities in metals

A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

A cooperative game of a pair of learning automata

A cooperative game played in a sequential manner by a pair of learning automata is investigated in this paper. The automata operate in an unknown random environment which gives a common pay-off to the automata. Necessary and sufficient conditions on the functions in the reinforcement scheme are given for absolute monotonicity which enables the expected pay-off to be monotonically increasing in any arbitrary environment. As each participating automaton operates with no information regarding the other partner, the results of the paper are relevant to decentralized control.

Fluctuation Theory Of The Specific-Heat Of Normal Liquid-3He

The measured specific heat of normal liquid 3He shows a plateau for 0.15<1 K; below 0.15 K and above 1 K, it rises linearly with temperature. However, the slope on the high-temperature side is very much reduced compared with the free-Fermi-gas value. We explain these features through a microscopic, thermal spin- and density-fluctuation model. The plateau is due to spin fluctuations which have a low characteristic energy in 3He. Because of the low compressibility, the density fluctuations are highly suppressed; this leads to a reduced slope for CV(T) for high temperatures.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.