zero lag synchronization and multiple time delays in two coupled chaotic systems zero lag synchronization zls between two chaotic systems coupled by a portion of their signal is achieved for restricted ratios between the delays of the self feedback and the mutual coupling we extend this scenario to the case of a set of multiple self feedbacks n d i and a set of multiple mutual couplings n c j we demonstrate both analytically and numerically that zls can be achieved when ensuremath sum l i n d i ensuremath sum m j n c j 0 where l i m j mathbb z results which were mainly derived for bernoulli maps and exemplified with simulations of the lang kobayashi differential equations indicate that zls can be achieved for a continuous range of mutual coupling delay this phenomenon has an important implication in the possible use of zls in communication networks

distributivity equations in the class of semi t operators recently the distributivity equations have been discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this study we present the solutions to distributivity between semi t operators previous results related to the distributivity between nullnorms and between semi t operators and semi nullnorms can be obtained as simple corollaries

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

hyperchaos in the generalized rossler system introduced as a model for hyperchaos the generalized r ossler system of dimension n is obtained by linearly coupling n ensuremath 3 additional degrees of freedom to the original r ossler equation under variation of a single control parameter it is able to exhibit the chaotic hierarchy ranging from fixed points via limit cycles and tori to chaotic and finally hyperchaotic attractors through the help of a mode transformation we reveal a structural symmetry of the generalized r ossler system the latter will allow us to interpret the number shape and location in phase space of the observed coexisting attractors within a common scheme for arbitrary odd dimension n the appearance of hyperchaos is explained in terms of interacting coexisting attractors in a second part we investigate the lyapunov spectra and related properties of the generalized r ossler system as a function of the dimension n we find scaling properties which are not similar to those found in homogeneous spatially extended systems indicating that the high dimensional chaotic dynamics of the generalized r ossler system fundamentally differs from spatiotemporal chaos if the time scale is chosen properly though a universal scaling function of the lyapunov exponents is found which is related to the real part of the eigenvalues of an unstable fixed point

information cascade with marginal stability in a network of chaotic elements abstract a newly discovered cascade process of clusters is studied in a network of chaotic elements it is shown that the splitting of clusters and the synchronization of elements are balanced in a class of partially ordered states where marginal stability is sustained over an interval of the bifurcation parameters the partition information creation in bit space shows an avalanche process of information which leads to the anomalous behavior of power spectra roughly fitted by a power law form of the wavenumber lyapunov spectra have accumulation at null exponents analogous with those studied in fluid turbulence models

intrinsic stochasticity with many degrees of freedom we study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior some concepts of fully developed turbulence are discussed in relation to this model we also develop an approach based on lyapunov exponent measurements numerical results on the distribution of lyapunov numbers and the power spectrum of the associated lyapunov vectors are presented and briefly discussed

practical criterion for delay estimation using random perturbations many systems contain an internal time delay which significantly influences their dynamical properties methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied addressing this problem we demonstrate that it is sufficient to analyze the system s response to short correlated external disturbances or internal noise following this idea it is shown for linear and nonlinear systems as well as for periodic dynamics that the delay can be estimated by analyzing the correlation function this method covers the case of strong noise and multiple delays

coexistence of exponentially many chaotic spin glass attractors a chaotic network of size n with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated for a load p n 1 where p stands for the number of stored patterns the chaotic network functions as an associative memory of 2p attractors with macroscopic basin of attractions which decrease with at finite a chaotic spin glass phase exists where the number of distinct chaotic attractors scales exponentially with n each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the n chaotic units or freezing with respect to the p patterns results are supported by large scale simulations of networks composed of bernoulli map units and mackey glass time delay differential equations

the distributive equations for idempotent uninorms and nullnorms the distributive equations only involving idempotent uninorms and nullnorms are investigated the following two cases are proved i as for a nullnorm with an idempotent uninorm having distributivity the necessary and sufficient conditions are given ii as for an idempotent uninorm with a nullnorm having distributivity the necessary and sufficient conditions are given also

delay differential equation versus 1d map application to chaos control abstract theoretical and experimental results on the control of chaotic motion in an electronic circuit modeled by a delay differential equation are presented the model is derived from a nonlinear optical system with time delay feedback our control method is based on pyragas approach and applied to the infinite dimensional system generalized mean floquet multipliers and mean lyapunov exponents related to delay differential equations are introduced in order to compare a discrete time approximation with the continuous time equation this control method is also used to find the so called isomers related to harmonic periodic solutions predicted by ikeda and matsumoto

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

power spectra and dynamical invariants for delay differential and difference equations abstract the mackey glass and ikeda delay differential equations ddes are models of feedback systems in which attractor dimension is proportional to the delay power spectra from these models are investigated analytically and numerically as the delay increases much beyond the system response time an exponentially decaying spectrum with a near periodic superimposed modulation appears it is shown that each peak in this modulation is associated with a mode of oscillation predicted by linear stability analysis around the fixed point the number of such modes within a characteristic autocorrelation time of the solution agrees with the lyapunov dimension of the attractor the disappearance of this modulation at higher delay values is also explained the decay rate of the spectrum in the mid to high frequency range is found to agree with the sum of the positive lyapunov exponents i e with the metric entropy realistic models with a distribution of delays display similar spectra as their memory kernel narrows into a delta function for very large delay the dde approaches an infinite dimensional continuous time difference equation ctde with each point on a delay interval evolving independently and according to a chaotic discrete time map ctde spectra which have many features of finite delay dde spectra can be computed analytically if the spectrum of this map is known for constant initial functions they have a 1 f 2 form at low frequencies our analysis suggests that the spectrum of the chaotic map is at the origin of the peak shapes in dde spectra at low frequency our findings highlight the relevance of the linear prrperties of ddes to the characterization of their nonlinear properties

high dimensional chaos in delayed dynamical systems abstract we introduce a general class of iterative delay maps to model high dimensional chaos in dynamical systems with delayed feedback the class includes as particular cases systems with a linear local dynamics we report analytic and numerical results on the scaling laws of lyapunov spectra with a number of degrees of freedom invariant measure is computed through a self consistent frobenius perron formalism which allows also a recalculation of the maximum lyapunov exponent in good agreement with the one measured directly

numerical test for hyperbolicity of chaotic dynamics in time delay systems we develop a numerical test of hyperbolicity of chaotic dynamics in time delay systems the test is based on the angle criterion and includes computation of angle distributions between expanding contracting and neutral manifolds of trajectories on the attractor three examples are tested for two of them previously predicted hyperbolicity is confirmed the third one provides an example of a time delay system with nonhyperbolic chaos

shape adaptive radial basis functions radial basis functions for discrimination and regression have been used with some success in a wide variety of applications here we investigate the optimal choice for the form of the basis functions and present an iterative strategy for obtaining the function in a regression context using a conjugate gradient based algorithm together with a nonparametric smoother this is developed in a discrimination framework using the concept of optimal scaling results are presented for a range of simulated and real data sets

modularity conditions between overlap grouping function and uni nullnorm or null uninorm abstract overlap and grouping functions as two kinds of special continuous commutative aggregation functions have wide applications in image processing and classification modularity conditions between the class of overlap grouping functions satisfying o 1 e e g 0 e e and special classes of uninorms and those of another special class of overlap grouping functions over nullnorms have been studied in 49 in this paper we extend these results to any overlap grouping function moreover we study the modularity conditions between overlap grouping functions and uni nullnorms null uninorms which are the generalization of uninorms nullnorms

a note on left and right distributivity equations for semi t operators and uninorms abstract dryga et al showed that lemma 3 3 i in 5 is false by a counterexample see example 2 in 4 for details the goal of this short note is to indicate that example 2 in 4 is wrong and lemma 3 3 i in 5 is valid

self organizing radial basis function network for real time approximation of continuous time dynamical systems real time approximators for continuous time dynamical systems with many inputs are presented these approximators employ a novel self organizing radial basis function rbf network which varies its structure dynamically to keep the prescribed approximation accuracy the rbfs can be added or removed online in order to achieve the appropriate network complexity for the real time approximation of the dynamical systems and to maintain the overall computational efficiency the performance of this variable structure rbf network approximator with both gaussian rbf grbf and raised cosine rbf rcrbf is analyzed the compact support of rcrbf enables faster training and easier output evaluation of the network than that of the network with grbf the proposed real time self organizing rbf network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme especially for higher order dynamical systems the uniform ultimate boundedness of the approximation error is proved using the second method of lyapunov

localized behavior in the lyapunov vectors for quasi one dimensional many hard disk systems we introduce a definition of a localization width whose logarithm is given by the entropy of the distribution of particle component amplitudes in the lyapunov vector different types of localization widths are observed for example a minimum localization width where the components of only two particles are dominant we can distinguish a delocalization associated with a random distribution of particle contributions a delocalization associated with a uniform distribution and a delocalization associated with a wavelike structure in the lyapunov vector using the localization width we show that in quasi one dimensional systems of many hard disks there are two kinds of dependence of the localization width on the lyapunov exponent index for the larger exponents one is exponential and the other is linear differences due to these kinds of localizations also appear in the shapes of the localized peaks of the lyapunov vectors the lyapunov spectra and the angle between the spatial and momentum parts of the lyapunov vectors we show that the krylov relation for the largest lyapunov exponent ensuremath lambda ensuremath sim ensuremath ensuremath rho mathrm ln ensuremath rho as a function of the density ensuremath rho is satisfied apart from a factor in the same density region as the linear dependence of the localization widths is observed it is also shown that there are asymmetries in the spatial and momentum parts of the lyapunov vectors as well as in their x and y components

generating functional approach to space and time dependent colored noise a stochastic model for time and space dependent colored noise is suggested based on the following assumptions 1 the noise field is generated by a random number of point events corresponding to a correlated point process 2 the contributions of the different events to the noise field are additive each contribution being a random function selected from the same probability density functional an analytical treatment of the noise field described by these assumptions is possible the generating functional of the noise field as well as the corresponding cumulants can be computed exactly all cumulants are explicitly evaluated when the contribution of an event is given by a diffusion equation a detailed analysis of the asymptotic behavior is made for time homogeneous and translationally invariant processes a gaussian random field colored in space and time emerges for very frequent independent events of very small intensities provided that the central moments of the contribution of an event to the noise field are finite and fast decreasing in space the correlations among events lead to corrections of the gauss limit law however the cumulants of the random fields are also finite if the central moments of an event are slowly decreasing in space a different type of asymptotic behavior occurs the cumulants of the noise field become infinite and the resulting field is described by a non gaussian stable law of the l evy type the theory may be applied to the study of stochastic gravitational fluctuations in galactic systems to the analysis of concentration fluctuations for diffusion processes in disordered systems and for the analysis of the influence of environmental fluctuations in continuum mechanics and electrodynamics

functional approximation by feed forward networks a least squares approach to generalization this paper considers a least squares approach to function approximation and generalization the particular problem addressed is one in which the training data are noiseless and the requirement is to define a mapping that approximates the data and that generalizes to situations in which data samples are corrupted by noise in the input variables the least squares approach produces a generalizer that has the form of a radial basis function network for a finite number of training samples the finite sample approximation is valid provided that the perturbations due to noise on the expected operating conditions are large compared to the sample spacing in the data space in the other extreme of small noise perturbations a particular parametric form must be assumed for the generalizer it is shown that better generalization will occur if the error criterion used in training the generalizer is modified by the addition of a specific regularization term this is illustrated by an approximator that has a feedforward architecture and is applied to the problem of point source location using the outputs of an array of receivers in the focal plane of a lens

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

asymptotic theory of multidimensional chaos a delay differential equation u t u t f u t 1 0 t and its generalization are investigated in the limit 0 when the attractor s dimension increases infinitely it is shown that a number of statistical characteristics are asymptotically independent of as for the attractor it can be regarded as a direct product ofo 1 equivalent subattractors their statistical characteristics being asymptotically independent of the results enable one to predict some characteristics of the attractor with fractal dimensiond 1 for the case 1 when they are inaccessible numerically the approach developed seems to be applicable for a wide class of spatiotemporal systems

sublattice synchronization of chaotic networks with delayed couplings synchronization of chaotic units coupled by their time delayed variables is investigated analytically a type of cooperative behavior is found sublattice synchronization although the units of one sublattice are not directly coupled to each other they completely synchronize without time delay the chaotic trajectories of different sublattices are only weakly correlated but not related by generalized synchronization nevertheless the trajectory of one sublattice is predictable from the complete trajectory of the other one the spectra of lyapunov exponents are calculated analytically in the limit of infinite delay times and phase diagrams are derived for different topologies

on the structure of uninorms on bounded lattices abstract uninorms are a generalization of triangular norms and triangular conorms with a neutral element in the interior of a bounded lattice in this study we present two methods to construct uninorms from a given triangular norm and triangular conorm on bounded lattices under some constraints as a by product of these methods we obtain new types of idempotent uninorms with a neutral element on bounded lattices in addition some illustrative examples for the constructions of uninorms on bounded lattices are provided

distributivity and conditional distributivity for s uninorms abstract the distributivity condition plays an essential role in the framework of fuzzy connectives this paper studies both regular and conditional distributivity equations for s uninorms and gives the characterizations of distributivity equations between some binary aggregation operators and s uninorms in u min moreover we describe t norms t uninorms and semi t operators that are conditional distributive over s uninorms

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

semi t operators on bounded lattices abstract we study semi t operators on bounded lattices and show the existence of semi t operators using the fact that there exist some pseudo t norms and pseudo t conorms on the arbitrary fixed bounded lattice l as a by product some constructive approaches to semi t operators are discussed using these approaches we obtain the least semi t operators and the greatest semi t operators on bounded lattices a partial order relation is also defined based on the semi t operator and some properties of this relation are examined

synchronization of noisy delayed feedback systems with delayed coupling synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied using as an example circular chains of three and four delayed coupled ikeda oscillators it is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling and an analytic estimate of the sufficient coupling is given the sufficiency condition is compared with numerical computations and typical effects of noise on the exact and some generalized types of synchronization are illustrated

reduced hyperbf networks regularization by explicit complexity reduction and scaled rprop based training hyper basis function hyperbf networks are generalized radial basis function neural networks where the activation function is a radial function of a weighted distance such generalization provides hyperbf networks with high capacity to learn complex functions which in turn make them susceptible to overfitting and poor generalization moreover training a hyperbf network demands the weights centers and local scaling factors to be optimized simultaneously in the case of a relatively large dataset with a large network structure such optimization becomes computationally challenging in this paper a new regularization method that performs soft local dimension reduction in addition to weight decay is proposed the regularized hyperbf network is shown to provide classification accuracy competitive to a support vector machine while requiring a significantly smaller network structure furthermore a practical training to construct hyperbf networks is presented hierarchal clustering is used to initialize neurons followed by a gradient optimization using a scaled version of the rprop algorithm with a localized partial backtracking step experimental results on seven datasets show that the proposed training provides faster and smoother convergence than the regular rprop algorithm

on the associativity functional equation abstract let a b be any bounded closed real interval the class of all continuous nondecreasing associative functions m a b 2 a b fulfilling the boundary conditions m a a a and m b b b is described

corrigendum corrigendum to the distributivity condition for uninorms and t operators fuzzy sets and systems 128 2002 209 225 in this paper the study of the distributivity equation involving uninorms in u given in fuzzy sets and systems 128 2002 209 225 is revised two wrong propositions in the mentioned reference are corrected and their right versions are proved

approximation of nonlinear systems with radial basis function neural networks a technique for approximating a continuous function of n variables with a radial basis function rbf neural network is presented the method uses an n dimensional raised cosine type of rbf that is smooth yet has compact support the rbf network coefficients are low order polynomial functions of the input a simple computational procedure is presented which significantly reduces the network training and evaluation time storage space is also reduced by allowing for a nonuniform grid of points about which the rbfs are centered the network output is shown to be continuous and have a continuous first derivative when the network is used to approximate a nonlinear dynamic system the resulting system is bounded input bounded output stable for the special case of a linear system the rbf network representation is exact on the domain over which it is defined and it is optimal in terms of the number of distinct storage parameters required several examples are presented which illustrate the effectiveness of this technique

left and right distributivity equations for semi t operators and uninorms abstract recently the distributivity equation for different kind of operators has become a focus of research as the crucial tool in the numerous applications as utility and optimization theory or integration theory the main purpose of this paper is to study the distributivity equations between two special classes of aggregation operators namely semi t operators and uninorms without the commutativity assumption of semi t operators it is necessary to consider the left and the right distributivity conditions separately in both cases the obtained solutions are significantly different

synchronization of chaotic networks with time delayed couplings an analytic study networks of nonlinear units with time delayed couplings can synchronize to a common chaotic trajectory although the delay time may be very large the units can synchronize completely without time shift for networks of coupled bernoulli maps analytic results are derived for the stability of the chaotic synchronization manifold for a single delay time chaos synchronization is related to the spectral gap of the coupling matrix for networks with multiple delay times analytic results are obtained from the theory of polynomials finally the analytic results are compared with networks of iterated tent maps and lang kobayashi equations which imitate the behavior of networks of semiconductor lasers

the distributivity equations for semi t operators over uninorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we describe the solutions of distributivity for semi t operators over uninorms previous results about distributivity for nullnorms over uninorms can be obtained as a corollary

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

on distributive laws of uninorms over overlap and grouping functions overlap and grouping functions as two new classes of special binary aggregation functions have been investigated by several authors for applications in image processing decision making classification and fuzzy community detection problems on the other hand after aczel studied the distributive law between two operations the distributive laws among particular binary aggregation functions become an interesting and natural research area in this paper we continue to discuss this topic for uninorms and overlap and grouping functions first we give some basic properties for the distributive law of uninorms over overlap functions second we study this distributive law when the uninorms belong to one of the usual classes e g mathcal u min mathcal u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 finally we investigate the distributive law of uninorms over grouping functions by an analogous way

fluctuations of lyapunov vectors in large volume limit and the information flow configuration in space time dynamics abstract the fluctuation of lyapunov vectors in r n for large n and in the infinite dimensional limit are studied in the context of entropy balance from dynamical system theory the density of the fluctuation yields the information flow configuration ifc which captures the interaction of degrees of freedom dof in information flow terms generally the ifc can be extended or localized the study of these cases leads to the local formulation of entropy balance for a dof two examples of coupled map lattice are given to demonstrate the approach based on the numerical data we conjecture that a locally balance imbalance configuration of the extended localized ifc implies absence presence of pattern in the spatially extended system moreover for dissipative dynamics the localization for the largest and smallest exponents can take place in a fixed spatial domain which describes a stronger version fluctuation dissipation principle derived by ruelle 1982 in viscous turbulence flow some of its implications are discussed

distributivity between uninorms and nullnorms recently the distributivity equation was investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms generally the assumption of associativity is not necessary in consideration of distributivity equation moreover if we omit commutativity assumption consideration of the left and right distributivity conditions is reasonable previous results about distributivity between uninorms and nullnorms can be obtained as simple corollaries

a hopf like equation and perturbation theory for differential delay equations we extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations because the phase spaces of differential delay equations are infinite dimensional phase space densities for these systems are functionals we derive a hopf like functional differential equation governing the evolution of these densities the functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory a necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given finally we show that the evolution equation for the density functional is the fourier transform of the infinite dimensional version of the kramers moyal expansion

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

left and right distributivity equations in the class of semi t operators abstract the issue of distributivity is crucial for many different theoretical areas such as the utility theory and the integration theory also this problem is of high interest for modelling some practical situations from e g fields of economics and social sciences thus recently the distributivity equations have been studied for different classes of aggregation operators by a significant number of researchers the focus of this paper in particular is on solving the left and the right distributivity equations between semi t operators

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

patterns of chaos synchronization small networks of chaotic units which are coupled by their time delayed variables are investigated in spite of the time delay the units can synchronize isochronally i e without time shift moreover networks cannot only synchronize completely but can also split into different synchronized sublattices these synchronization patterns are stable attractors of the network dynamics different networks with their associated behaviors and synchronization patterns are presented in particular we investigate sublattice synchronization symmetry breaking spreading chaotic motifs synchronization by restoring symmetry and cooperative pairwise synchronization of a bipartite tree

multiobjective evolutionary optimization of the size shape and position parameters of radial basis function networks for function approximation this paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks rbfnns in order to approach target functions from a set of input output pairs the procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process these new operators are based on two well known matrix transformations singular value decomposition svd and orthogonal least squares ols which have been used to define new mutation operators that produce local or global modifications in the radial basis functions rbfs of the networks the individuals in the population in the evolutionary procedure after analyzing the efficiency of the different operators we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the rbfnns

conditional distributivity of continuous semi t operators over disjunctive uninorms with continuous underlying t norms and t conorms abstract the issue of conditional distributivity which is also known as restricted distributivity is crucial for many different areas such as utility theory and integration theory in the present study we focus on this specific form of distributivity for continuous semi t operators with respect to disjunctive uninorms with continuous underlying t norms and t conorms this study extends previous research by focusing on a much wider class of uninorms

study of a high dimensional chaotic attractor the nature of a very high dimensional chaotic attractor in an infinite dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high dimensional attractor in the phase space we introduce two complementary bases from which the attractor is observed one the lyapunov basis composed of the lyapunov vectors and the another the fourier basis composed of the fourier modes we introduce the exterior subspaces on the basis of the lyapunov vectors and observe the chaotic motion projected onto these exteriors it is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor the origin of such a phenomenon is attributed to more fundamental features of our attractor which become manifest when the attractor is observed from the lyapunov basis a counterpart of the phenomenon can be observed also on the fourier basis because there is a statistical one to one correspondence between the lyapunov vectors and the fourier modes in particular a statistical property of the high pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor

a characterization of idempotent nullnorms nullnorms are generalization of triangular norms and conorms with a zero element anywhere in the unit interval nullnorms are built up from triangular norms and triangular conorms if nullnorm is idempotent then it is composed of a minimum and a maximum the idea of this paper is to find minimal assumptions on an operation in order to get an idempotent nullnorm

distributivity between semi t operators and semi nullnorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this paper we describe the solutions of distributivity between semi t operators and semi nullnorms previous results about distributivity between nullnorms can be obtained as simple corollaries

stochastic gradient identification of polynomial wiener systems analysis and application this paper presents analytical numerical and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial type nonlinear system with memory for noisy output observations the analysis includes the computation of the stationary points the mean square error surface and the stability regions of the algorithm for gaussian data convergence of the mean is studied using l sub 2 and euclidian norms monte carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise an application is presented for the identification of a nonlinear time delayed feedback system

uninorms on bounded lattices with the underlying t norms and t conorms abstract uninorms are a generalization of the concepts of triangular norms t norms and triangular conorms t conorms that admit a neutral element as any element in a bounded lattice in this study we discuss the characterization of uninorms on bounded lattices we introduce some new constructions for uninorms on bounded lattices which are derived from both t norms and t conorms in particular two idempotent uninorms on bounded lattices are obtained we also provide some corresponding examples to help understand the structure of these new classes of uninorms in addition we provide an answer to the open problem proposed by cayli 2019 14