income distribution an adaptive heterogeneous model abstract in this communication an adaptive process is introduced into a many agent model for closed economic system in order to establish general features of income distribution in this new version agents are able to modify their exchange parameter i of resources through an adaptive process the conclusions indicate that assuming an instantaneous learning behavior of all agents a distribution for income is reproduced while a frozen behavior establishes a pareto s distribution for income with an exponent 0 94 0 02 a third case occurs when a heterogeneous inertia behavior is introduced leading us to a distribution at the low income regime and a power law decay for the large income values with an exponent 2 05 0 05 this method enables investigation of the resources flux in the economic environment and produces also bounding values for the gini index comparable with data evidences

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

stochastic multiplicative processes for financial markets abstract we study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets we find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated levy like distribution and the cross correlation between relative updated wealths is the origin of the nontrivial properties of returns including the power law distribution with exponent outside the stable levy regime and the long range persistence of volatility correlations

theoretical analysis and simulations of the generalized lotka volterra model the dynamics of generalized lotka volterra systems is studied by theoretical techniques and computer simulations these systems describe the time evolution of the wealth distribution of individuals in a society as well as of the market values of firms in the stock market the individual wealths or market values are given by a set of time dependent variables w i i 1 dots n the equations include a stochastic autocatalytic term representing investments a drift term representing social security payments and a time dependent saturation term due to the finite size of the economy the w i mathrm mathrm s turn out to exhibit a power law distribution of the form p w ensuremath sim w ensuremath 1 ensuremath ensuremath alpha it is shown analytically that the exponent ensuremath alpha can be expressed as a function of one parameter which is the ratio between the constant drift component social security and the fluctuating component investments this result provides a link between the lower and upper cutoffs of this distribution namely between the resources available to the poorest and those available to the richest in a given society the value of ensuremath alpha is found to be insensitive to variations in the saturation term which represent the expansion or contraction of the economy the results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power law distribution with 1l ensuremath alpha l2

master equation for a kinetic model of a trading market and its analytic solution we analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income m distribution p m in the model has a power law tail with pareto index nu exactly equal to unity confirming the earlier numerical studies on this model the analysis starts with the development of a master equation for the time development of p m precise solutions are then obtained in some special cases

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

training neural nets with the reactive tabu search in this paper the task of training subsymbolic systems is considered as a combinatorial optimization problem and solved with the heuristic scheme of the reactive tabu search rts an iterative optimization process based on a modified local search component is complemented with a meta strategy to realize a discrete dynamical system that discourages limit cycles and the confinement of the search trajectory in a limited portion of the search space the possible cycles are discouraged by prohibiting i e making tabu the execution of moves that reverse the ones applied in the most recent part of the search the prohibition period is adapted in an automated way the confinement is avoided and a proper exploration is obtained by activating a diversification strategy when too many configurations are repeated excessively often the rts method is applicable to nondifferentiable functions is robust with respect to the random initialization and effective in continuing the search after local minima three tests of the technique on feedforward and feedback systems are presented

a perturbation based variable neighborhood search heuristic for solving the vehicle routing problem with simultaneous pickup and delivery with time limit abstract the vehicle routing problem with simultaneous pickup and delivery with time limit vrpspdtl is a variant of the basic vehicle routing problem where the vehicles serve delivery as well as pick up operations of the clients under time limit restrictions the vrpspdtl determines a set of vehicle routes originating and terminating at a central depot such that the total travel distance is minimized for this problem we propose a mixed integer mathematical optimization model and a perturbation based neighborhood search algorithm combined with the classic savings heuristic variable neighborhood search and a perturbation mechanism the numerical results show that the proposed method produces superior solutions for a number of well known benchmark problems compared to those reported in the literature and reasonably good solutions for the remaining test problems

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

on the estimation of the power law exponent in the mean field bouchaud mezard model abstract in this article our primary objective is to develop an estimator of the power law exponent based on the observable individual wealth in the mean field bouchaud mezard model as a result a simple and strongly consistent estimator of the power law exponent in the mean field bouchaud mezard model has been established and performs well on simulated data

on the convergence of the lms algorithm with adaptive learning rate for linear feedforward networks we consider the problem of training a linear feedforward neural network by using a gradient descent like lms learning algorithm the objective is to find a weight matrix for the network by repeatedly presenting to it a finite set of examples so that the sum of the squares of the errors is minimized kohonen showed that with a small but fixed learning rate or stepsize some subsequences of the weight matrices generated by the algorithm will converge to certain matrices close to the optimal weight matrix in this paper we show that by dynamically decreasing the learning rate during each training cycle the sequence of matrices generated by the algorithm will converge to the optimal weight matrix we also show that for any given 0 the lms algorithm with decreasing learning rates will generate an optimal weight matrix i e a matrix of distance at most away from the optimal matrix after o 1 training cycles this is in contrast to 1 log 1 training cycles needed to generate an optima

fokker planck equation of distributions of financial returns and power laws abstract our purpose is to relate the fokker planck formalism proposed by friedrich et al phys rev lett 84 2000 5224 for the distribution of stock market returns to the empirically well established power law distribution with an exponent in the range 3 5 we show how to use friedrich et al s formalism to predict that the distribution of returns is indeed asymptotically a power law with an exponent that can be determined from the kramers moyal coefficients determined by friedrich et al however with their values determined for the u s dollar german mark exchange rates the exponent predicted from their theory is found to be around 12 in disagreement with the often quoted value between 3 and 5 this could be explained by the fact that the large asymptotic value of 12 does not apply to real data that lie still far from the stationary state of the fokker planck description another possibility is that power laws are inadequate the mechanism for the power law is based on the presence of multiplicative noise across time scales which is different from the multiplicative noise at fixed time scales implicit in the arch models developed in the finance literature

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

asmo dan algorithm for adaptive spline modelling of observation data nonlinear system identification by modelling the underlying relationships in observation data is an important application area for artificial neural networks and other learning paradigms splines have been used for scattered data interpolation but the applications have mainly been restricted to low dimensional input spaces this paper describes asmod a new learning paradigm for higher dimensional data 3 based on b spline interpolation the models can be trained online and a method for step wise model refinement is applied during model training for gradually increasing the modelling capability until the desired or best possible accuracy is obtained for every refinement step a number of possible refinement actions are evaluated and the one that gives the highest improvement of the model accuracy is chosen the model structure is hence adapted to the modelling problem giving a model of small size and high accuracy asmod has very efficient implementations on serial computers the scheme has been

fractal fluctuations in cardiac time series human heart rate controlled by complex feedback mechanisms is a vital index of systematic circulation however it has been shown that beat to beat values of heart rate fluctuate continually over a wide range of time scales herein we use the relative dispersion the ratio of the standard deviation to the mean to show by systematically aggregating the data that the correlation in the beat to beat cardiac time series is a modulated inverse power law this scaling property indicates the existence of long time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal we argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

a trade investment model for distribution of wealth econophysics provides a strategy for understanding the potential mechanisms underlying the anomalous distribution of wealth found in real societies we present a computational nonlinear stochastic model for the distribution of wealth that depends upon three parameters and two mechanisms trade and investment to avoid economic paradoxes the trade mechanism is assumed to be related to the poorer trader s wealth and to statistically advantage the poorer of the two traders the two mechanisms together are shown to generate a distribution that reproduces the full range of the empirical wealth distribution and not only the inverse power law tail that pareto found in western societies at the end of the 19th century

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

diffusion entropy and waiting time statistics of hard x ray solar flares we show at work a technique of scaling detection based on evaluating the shannon entropy of the diffusion process obtained by converting the time series under study into trajectories this method called diffusion entropy affords information that cannot be derived from the direct evaluation of waiting times we apply this method to the analysis of the distribution of time distance t between two nearest neighbor solar flares this traditional part of the analysis is based on the direct evaluation of the distribution function c t or of the probability c t that no time distance smaller than a given t is found we adopt the paradigm of the inverse power law behavior and we focus on the determination of the inverse power index m without ruling out different asymptotic properties that might be revealed at larger scales with the help of richer statistics we then use the de method with three different walking rules and we focus on the regime of transition to scaling this regime of transition and the value of the scaling parameter itself d depends on the walking rule adopted a property of interest to shed light on the slow process of transition from dynamics to thermodynamics often occurring under anomalous statistical conditions with the first two rules the transition regime occurs throughout a large time interval and the information contained in the time series is transmitted to a great extent to it as well as to the scaling regime by using the third rule on the contrary the same information is essentially conveyed to the scaling regime which in fact emerges very quickly after a fast transition process we show that the de method not only causes to emerge the long range correlation with a given m 3 and so a basin of attraction different from the ordinary gaussian one but it also reveals the presence of memory effects induced by the time dependence of the solar flare rate when this memory is annihilated by shuffling the scaling parameter d is shown to fit the theoretically expected function of m all this leads us to the compelling conclusion that m52 13860 01

the gompertz pareto income distribution abstract this work analyzes the gompertz pareto distribution gpd of personal income formed by the combination of the gompertz curve representing the overwhelming majority of the economically less favorable part of the population of a country and the pareto power law which describes its tiny richest part equations for the lorenz curve gini coefficient and the percentage share of the gompertzian part relative to the total income are all written in this distribution we show that only three parameters determined by linear data fitting are required for its complete characterization consistency checks are carried out using income data of brazil from 1981 to 2007 and they lead to the conclusion that the gpd is consistent and provides a coherent and simple analytical tool to describe personal income distribution data

a theoretical comparison of batch mode on line cyclic and almost cyclic learning we study and compare different neural network learning strategies batch mode learning online learning cyclic learning and almost cyclic learning incremental learning strategies require less storage capacity than batch mode learning however due to the arbitrariness in the presentation order of the training patterns incremental learning is a stochastic process whereas batch mode learning is deterministic in zeroth order i e as the learning parameter spl eta tends to zero all learning strategies approximate the same ordinary differential equation for convenience referred to as the ideal behavior using stochastic methods valid for small learning parameters spl eta we derive differential equations describing the evolution of the lowest order deviations from this ideal behavior we compute how the asymptotic misadjustment measuring the average asymptotic distance from a stable fixed point of the ideal behavior scales as a function of the learning parameter and the number of training patterns knowing the asymptotic misadjustment we calculate the typical number of learning steps necessary to generate a weight within order spl epsiv of this fixed point both with fixed and time dependent learning parameters we conclude that almost cyclic learning learning with random cycles is a better alternative for batch mode learning than cyclic learning learning with a fixed cycle

some asymptotic results for learning in single hidden layer feedforward network models abstract we investigate the properties of a recursive estimation procedure the method of back propagation for a class of nonlinear regression models single hidden layer feedforward network models recently developed by cognitive scientists the results follow from more general results for a class of recursive m estimators obtained using theorems of ljung 1977 and walk 1977 for the method of stochastic approximation conditions are given ensuring that the back propagation estimator converges almost surely to a parameter value that locally minimizes expected squared error loss provided the estimator does not diverge and that the back propagation estimator is asymptotically normal when centered at this minimizer this estimator is shown to be statistically inefficient and a two step procedure that has efficiency equivalent to that of nonlinear least squares is proposed practical issues are illustrated by a numerical example involving approximation of the henon map