genetic learning of fuzzy cognitive maps fuzzy cognitive maps fcms are a very convenient simple and powerful tool for simulation and analysis of dynamic systems they were originally developed in 1980 by kosko and since then successfully applied to numerous domains such as engineering medicine control and political affairs their popularity stems from simplicity and transparency of the underlying model at the same time fcms are hindered by necessity of involving domain experts to develop the model since human experts are subjective and can handle only relatively simple networks maps there is an urgent need to develop methods for automated generation of fcm models this study proposes a novel learning method that is able to generate fcm models from input historical data and without human intervention the proposed method is based on genetic algorithms and requires only a single state vector sequence as an input the paper proposes and experimentally compares several different design alternatives of genetic optimization and thoroughly tests and discusses the best design extensive benchmarking tests which involve 200 fcms with varying size and density of connections performed on both synthetic and real life data quantifies the performance of the development method and emphasizes its suitability

duality between the trigonometric bcn sutherland system and a completed rational ruijsenaars schneider van diejen system we present a new case of duality between integrable many body systems where two systems live on the action angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other one our investigation utilizes an idea that was exploited previously to provide group theoretic interpretation for several dualities discovered originally by ruijsenaars in the group theoretic framework one applies hamiltonian reduction to two abelian poisson algebras of invariants on a higher dimensional phase space and identifies their reductions as action and position variables of two integrable systems living on two different models of the single reduced phase space taking the cotangent bundle of u 2n as the upstairs space we demonstrate how this mechanism leads to a new dual pair involving the bcn trigonometric sutherland system thereby we generalize earlier results pertaining to the an trigonometric sutherland system as well as a recent work by pusztai on the hyperbolic bcn sutherland system

colored noise induced chaotic array synchronization the effect of a time correlated gaussian noise on one dimensional arrays consisting of diffusively coupled chaotic cells is analyzed a resonance effect between the time scale of the chaotic attractor and the colored gaussian noise has been found as well depending on the number of cells coupling and noise strength an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation these nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior

lax representation of the hyperbolic van diejen dynamics with two coupling parameters in this paper we construct a lax pair for the classical hyperbolic van diejen system with two independent coupling parameters built upon this construction we show that the dynamics can be solved by a projection method which in turn allows us to initiate the study of the scattering properties as a consequence we prove the equivalence between the first integrals provided by the eigenvalues of the lax matrix and the family of van diejen s commuting hamiltonians also at the end of the paper we propose a candidate for the lax matrix of the hyperbolic van diejen system with three independent coupling constants

a study of network dynamics the dynamics of a discrete time neural network model are investigated first a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states the steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters summary statistics are presented to give gross measures of the model s temporal activity in parameter space second a detailed study of the dynamics of a particular network is described complex dynamical behavior is observed including hopf bifurcations the ruelle takens newhouse route to chaos showing mode locking at rational winding numbers and the destruction of an invariant torus and the period doubling route to chaos

differential equations in the spectral parameter we determine all the potentialsv x for the schrodinger equation 2 v x k2 such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formb k k o x o for each suchv x we determine the algebra of all possible operatorsb and the corresponding functions x

quantum versus classical integrability in calogero moser systems calogero moser systems are classical and quantum integrable multiparticle dynamics defined for any root system the quantum calogero systems having 1 q2 potential and a confining q2 potential and the sutherland systems with 1 sin2q potentials have integer energy spectra characterized by the root system various quantities of the corresponding classical systems e g minimum energy frequencies of small oscillations the eigenvalues of the classical lax pair matrices etc at the equilibrium point of the potential are investigated analytically as well as numerically for all root systems to our surprise most of these classical data are also integers or they appear to be quantized to be more precise these quantities are polynomials of the coupling constant s with integer coefficients the close relationship between quantum and classical integrability in calogero moser systems deserves fuller analytical treatment which would lead to better understanding of these systems and of integrable systems in general

relativistic toda systems we present and study poincare invariant generalizations of the galilei invariant toda systems the classical nonperiodic systems are solved by means of an explicit action angle transformation

action angle maps and scattering theory for some finite dimensional integrable systems i the pure soliton case we construct an action angle transformation for the calogero moser systems with repulsive potentials and for relativistic generalizations thereof this map is shown to be closely related to the wave transformations for a large classl of hamiltonians and is shown to have remarkable duality properties all dynamics inl lead to the same scattering transformation which is obtained explicitly and exhibits a soliton structure an auxiliary result concerns the spectral asymptotics of matrices of the formm exp td ast it pertains to diagonal matricesd whose diagonal elements have pairwise different real parts and to matricesm for which certain principal minors are non zero

adaptive stochastic resonance in noisy neurons based on mutual information noise can improve how memoryless neurons process signals and maximize their throughput information such favorable use of noise is the so called stochastic resonance or sr effect at the level of threshold neurons and continuous neurons this work presents theoretical and simulation evidence that 1 lone noisy threshold and continuous neurons exhibit the sr effect in terms of the mutual information between random input and output sequences 2 a new statistically robust learning law can find this entropy optimal noise level and 3 the adaptive sr effect is robust against highly impulsive noise with infinite variance histograms estimate the relevant probability density functions at each learning iteration a theorem shows that almost all noise probability density functions produce some sr effect in threshold neurons even if the noise is impulsive and has infinite variance the optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases simulations further show that the sr effect persists for several sigmoidal neurons and for gaussian radial basis function neurons

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions abstract starting from the hyperoctahedral multivariate hypergeometric function of heckman and opdam associated with the b c n root system we arrive via partial confluent limits in the sense of oshima and shimeno at solutions of the eigenvalue equations for the quantum toda chain with one sided boundary perturbations of poschl teller type and for the hyperbolic quantum calogero sutherland system in a morse potential with the aid of corresponding degenerations of the bispectral dual difference equations for the heckman opdam hyperoctahedral hypergeometric function it is deduced that the eigensolutions in question are holomorphic in the spectral variable

on the duality between the hyperbolic sutherland and the rational ruijsenaars schneider models we consider two families of commuting hamiltonians on the cotangent bundle of the group and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic sutherland and of the rational ruijsenaars schneider lax matrices respectively the duality symplectomorphism between these two integrable models that was constructed by ruijsenaars using direct methods can then be interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group

poisson lie interpretation of trigonometric ruijsenaars duality a geometric interpretation of the duality between two real forms of the complex trigonometric ruijsenaars schneider system is presented the phase spaces of the systems in duality are viewed as two different models of the same reduced phase space arising from a suitable symplectic reduction of the standard heisenberg double of u n the collections of commuting hamiltonians of the systems in duality are shown to descend from two families of free hamiltonians on the double which are dual to each other in a poisson lie sense our results give rise to a major simplification of ruijsenaars proof of the crucial symplectomorphism property of the duality map

nonlinear dynamic elements with noisy sinusoidal forcing enhancing response via nonlinear coupling we consider a network of nonlinear dynamic elements with nonlinear global coupling subject to noise and a time periodic signal the system response characterized by its signal to noise ratio is computed via approximate analytic techniques and precise numerical simulations we find that cooperative effects arising from the noise and coupling lead to an enhancement of the response of the network over that of a single element

double coset decompositions of reductive lie groups arising from two involutions g 0 h g and g 0 l g here g g g g g for an automorphism of g and f0 denote the connected component of f containing the identity e for a lie group f in 8 we gave standard representatives of double coset decompositions h g l for some typical triples g h l by only using algebraic method as the most elementary example we studied the case g h l gl n if gl p if gl n p if gl r if gl n r if for an arbitrary field if we also studied in 8 other examples related to quadratic forms on vector spaces over the fields ir c and ih in this paper we assume that g is a reductive lie group and we will describe the structure of the double coset decomposition h g l for an arbitrary g h l first we study the compact case section 3 and next the noncompact case section 4 in section 3 we assume that the semisimple part gs of g is compact gs is the analytic subgroup of g for gs g g when g gs and

difference equation for the heckman opdam hypergeometric function and its confluent whittaker limit abstract we present an explicit difference equation for the heckman opdam hypergeometric function associated with root systems via a confluent hypergeometric limit an analogous difference equation is obtained for the class one whittaker function diagonalizing the open quantum toda chain

trigonometric sutherland systems and their ruijsenaars duals from symplectic reduction beside its usual interpretation as a system of n indistinguishable particles moving on the circle the trigonometric sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line and these three physically distinct systems are in duality with corresponding variants of the rational ruijsenaars schneider system we explain that the three duality relations first obtained by ruijsenaars in 1995 arise naturally from the kazhdan kostant sternberg symplectic reductions of the cotangent bundles of the group u n and its covering groups u 1 su n and r su n respectively this geometric interpretation enhances our understanding of the duality relations and simplifies ruijsenaars original direct arguments that led to their discovery

a new model in the calogero ruijsenaars family hamiltonian reduction is used to project a trivially integrable system on the heisenberg double of su n n to obtain a system of ruijsenaars type on a suitable quotient space this system possesses bcn symmetry and is shown to be equivalent to the standard three parameter bcn hyperbolic sutherland model in the cotangent bundle limit

self duality and scattering map for the hyperbolic van diejen systems with two coupling parameters with an appendix by s ruijsenaars in this paper we construct global action angle variables for a certain two parameter family of hyperbolic van diejen systems following ruijsenaars ideas on the translation invariant models the proposed action angle variables come from a thorough analysis of the commutation relation obeyed by the lax matrix whereas the proof of their canonicity is based on the study of the scattering theory as a consequence we show that the van diejen system of our interest is self dual with a factorized scattering map also in an appendix by s ruijsenaars a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented this result is of crucial importance in our scattering theoretical analysis

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

noise enhanced fisher information in parallel arrays of sensors with saturation this paper investigates stochastic resonance in parallel arrays of uncoupled saturating devices the fisher information is used to demonstrate the possibility of noise improved parameter estimation for arbitrary parametric signals especially it is shown that improvement by noise always occurs in these arrays for any configuration of the input signal even in optimal configuration the results contribute to establish stochastic resonance in parallel uncoupled arrays as a general mechanism of enhancement by noise which can occur in wide classes of nonlinearities and for various information processing tasks it can supplement other mechanisms of stochastic resonance that take place in isolated nonlinearities but generally in restricted configurations of the input signal

noise sensitivity of phase synchronization time in stochastic resonance theory and experiment recent numerical and heuristic arguments have revealed that the average phase synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation in particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value here we present an explicit formula for the average phase synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals we also provide experimental evidence for the cusplike behavior by using a bistable microelectronic circuit system