identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

evolutionary minority game with heterogeneous strategy distribution abstract we present detailed numerical results for a modified form of the so called minority game which provides a simplified model of a competitive market each agent has a limited set of strategies and competes to be in a minority an evolutionary rule for strategy modification is included to mimic simple learning the results can be understood by considering crowd formation within the population

statistical properties of german dax and chinese indices abstract we investigate statistical properties of the german dax and chinese indices including the volatility distribution autocorrelation function dfa function and return volatility correlation function with both the daily data and minutely data at the minutely time scale the chinese indices may show irregular dynamic behavior at the daily time scale the volatility distribution autocorrelation function and dfa function of the chinese indices are qualitatively similar to those of the german dax while the return volatility correlation function exhibits an anti leverage effect different from the leverage effect of the german dax

an optimal control approach to the optical flow problem abstract the optical flow problem is reduced to an optimal control problem governed by a linear parabolic equation having the unknown velocity field the optical flow as drift term this model is derived from a new assumption that is the brightness intensity is conserved on a moving pattern driven by a gaussian stochastic process the optimality conditions are deduced by a passage to the limit technique in an approximating optimal control problem introduced for a regularization purpose finally the controller uniqueness is addressed

minority games diversity cooperativity and the concept of intelligence abstract in this paper we revisit some minority games formed by two different types of agents there are some games where the differences of power processing among the agents are fundamental for achieving success in other games which are characterized by a dynamical phase transition the results can only be explained by cooperative intelligence and diversity in both cases the concept of informational efficiency plays an important role in the understanding of the dynamics finally aiming to explain the results of these games we try to make a link among diversity informational efficiency and the concept of intelligence

an image multiresolution representation for lossless and lossy compression we propose a new image multiresolution transform that is suited for both lossless reversible and lossy compression the new transformation is similar to the subband decomposition but can be computed with only integer addition and bit shift operations during its calculation the number of bits required to represent the transformed image is kept small through careful scaling and truncations numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity in addition we propose entropy coding methods that exploit the multiresolution structure and can efficiently compress the transformed image for progressive transmission up to exact recovery the lossless compression ratios are among the best in the literature and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods

survival probabilities in time dependent random walks we analyze the dynamics of random walks in which the jumping probabilities are periodic time dependent functions in particular we determine the survival probability of biased walkers who are drifted towards an absorbing boundary the typical lifetime of the walkers is found to decrease with an increment in the oscillation amplitude of the jumping probabilities we discuss the applicability of the results in the context of complex adaptive systems

volatility clustering and scaling for financial time series due to attractor bubbling a microscopic model of financial markets is considered consisting of many interacting agents spins with global coupling and discrete time heat bath dynamics similar to random ising systems the interactions between agents change randomly in time in the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on off intermittency resembling the empirical financial time series with volatility clustering for a proper choice of the model parameters the probability distributions of returns exhibit power law tails with scaling exponents close to the empirical ones

modeling interactions of trading volumes in financial dynamics abstract a dynamic herding model with interactions of trading volumes is introduced at time t an agent trades with a probability which depends on the ratio of the total trading volume at time t 1 to its own trading volume at its last trade the price return is determined by the volume imbalance and number of trades the model can reproduce the power law distributions of the trading volume number of trades and price return and the probable relation between them the exponents are tunable by adjusting the values of the parameters but show slight deviation from those revealed in empirical studies moreover the time series generated are long range correlated we demonstrate that the results are rather robust and do not depend on the particular form of the trading probability

mixed population minority game with generalized strategies we present a quantitative theory based on crowd effects for the market volatility in a minority game played by a mixed population below a critical concentration of generalized strategy players we find that the volatility in the crowded regime remains above the random coin toss value regardless of the temperature controlling strategy use our theory yields good agreement with numerical simulations

the minority game with different payoff functions crowd anticrowd theory abstract the crowd anticrowd theory is applied to explain the features observed in a class of the minority game using different payoff functions simulations results using both the full strategy space and a reduced strategy space reveal that the standard deviation sd in the number of agents making a particular decision over time as a function of the agents memory size m does not depend on the explicit form of the payoff function the robustness of the results is explained in terms of the general features in strategy selection among the agents in different regimes of m while different payoff functions may affect the popularity of a particular strategy the strategy selection is found to be insensitive to the choice of payoff functions the crowd anticrowd cancellation effect leads to a minimum in sd at an intermediate value of m separating the small m regime characterized by crowd behavior and the large m regime characterized by random coin toss behavior of the agents

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

minority game with arbitrary cutoffs we study a model of a competing population of n adaptive agents with similar capabilities repeatedly deciding whether to attend a bar with an arbitrary cutoff l decisions are based upon past outcomes the agents are only told whether the actual attendance is above or below l for l n 2 the game reproduces the main features of challet and zhang s minority game as l is lowered however the mean attendances in different runs tend to divide into two groups the corresponding standard deviations for these two groups are very different this grouping effect results from the dynamical feedback governing the game s time evolution and is not reproduced if the agents are fed a random history

an approximation theory for the identification of nonlinear distributed parameter systems an abstract approximation framework for the identification of nonlinear distributed parameter systems is developed inverse problems for nonlinear systems governed by strongly maximal monotone operators satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified are treated convergence of galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original infinite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analogue of the trotter kato approximation result for semigroups of bounded linear operators the nonlinear theory developed here is shown to subsume an existing linear theory as a special case it is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead an application of the theory to a quas

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

cooperative behavior in evolutionary snowdrift game with bounded rationality abstract an evolutionary snowdrift game sg that incorporates bounded rationality and limited information in the evolutionary process is proposed and studied based on sg in a well mixed population and defining the winning action at a turn to be the one that gets a higher payoff the most recent m winning actions can be used as a public information based on which the competing agents decide their next actions this defines a strategy pool from which each agent picks a number of strategies as their tool in adapting to the competing environment the payoff parameter r in sg serves to set the maximum number of winners per turn due to the bounded rationality and limited information the cooperative frequency shows steps and plateaux as a function of r and these features tend to be smoothed out as m increases these features are results of an interplay between a restricted subset of m bit histories that the system can visit at a value of r and the limited capacity that agents can adapt the standard deviation in the number of agents taking the cooperative action is also studied for general values of r our model generates a realization of the binary agent resource model the idea of introducing bounded rationality into a two person game to realize the minority game or binary agent resource model could be a useful tool for future research

reversible intraframe compression of medical images the performance of several reversible intraframe compression methods is compared by applying them to angiographic and magnetic resonance mr images reversible data compression involves two consecutive steps decorrelation and coding the result of the decorrelation step is presented in terms of entropy because huffman coding generally approximates these entropy measures within a few percent coding has not been investigated separately it appears that a hierarchical decorrelation method based on interpolation hint outperforms all other methods considered the compression ratio is around 3 for angiographic images of 8 9 b pixel but is considerably less for mr images whose noise level is substantially higher

low entropy image pyramids for efficient lossless coding an efficient image source coding technique gives good compression performance at low computational complexity this research introduces an efficient coding technique based on pyramid coding that involves transforming an image into an equivalent lower entropy form prior to lossless coding the proposed method is also a multiresolution technique that facilitates progressive image transmission

error estimates for the numerical identification of a variable coefficient error estimates are derived for the approximate identification of an unknown transmissivity coefficient in a partial differential equation describing a model problem in groundwater now the approximation scheme considered determines the coefficient by least squares fitting of the observed pressure data 1 introduction in this paper we wish to present an error analysis of a common numerical scheme used in the identification of parameters in distributed systems specifically we shall concern ourselves here with a model problem in groundwater flow the problem is to identify a spatially varying transmissivity coefficient a x from observations of the piezometric head u x in a two dimensional static aquifer s where a and u are related by the equations 1 div avw ins2

on the minority game analytical and numerical studies abstract we investigate further several properties of the minority game we have recently introduced we explain the origin of the phase transition and give an analytical expression of 2 n in the n 2 m region the ability of the players to learn a given payoff is also analyzed and we show that the darwinian evolution process tends to a self organized state in particular the lifetime distribution is a power law with exponent 2 furthermore we study the influence of identical players on their gain and on the systems performance finally we show that large brains always take advantage of small brains

minority game with sk interactions a batch minority game with fake random history and additional sk like quenched interaction is introduced and analysed a mixing parameter quantifies the admixture and dictates the relative dominance of the two contributions if 0 agent decisions are based on their strategies and point scores alone as in the pure minority game whereas for 0 the agents also communicate with each other directly and update their points accordingly keeping the minority game dynamics in which the agents points are updated in parallel at each time step the aim is to understand what happens if instead of simply using the normal strategy based decisions the agents also take account of an effective field generated by the other agents it is shown that the sk interaction introduces a noise term which is broader than that in the normal minority game and which furthermore kills the normal phase transition it is also shown that the same effect would occur if instead of an sk interaction gaussian distributed quenched random fields are added by calculating order parameters in the time translational invariant phase we show that the system is persistent in a ergodic phase both simulational and analytical results are presented

the hamming distance in the minority game abstract we investigate different versions of the minority game a toy model for agents buying and selling a commodity the hamming distance between the strategies used by agents to make decisions is introduced as an analytical tool to determine several properties of these models the success rate of the agents in an adaptive version of the game is compared with the rate from a stochastic version it is shown numerically and analytically that the adaptive process is inefficient increasing the success rate of the unused strategies while decreasing the success rate of the strategies used by the agents the agents do not do as well as if they were forced to use only one strategy permanently a version of the game in which the agents strategies evolve is also analysed using the notion of distance the agents evolve into a state in which they are all using one strategy which is again the state that yields the maximum success rate

existence results for inverse problems associated with a nonlinear parabolic equation this paper deals with the determination of a pair p u in the nonlinear parabolic equation ut u p x f u 0 with initial and boundary conditions u x 0 0 u 0 t g from the overspecified data u t q the problem is reduced to a nonlinear operator equation and solved by taking advantage of a fixed point theory in ordered banach spaces similarly another form of overspecified data is considered

failsafe modes in incomplete minority game abstract we make a failsafe extension to the incomplete minority game model give a brief analysis on how incompleteness will effect system efficiency simulations that limited incompleteness in strategies can improve the system efficiency among three failsafe modes the back to best mode brings most significant improvement and keeps the system efficiency in a long range of incompleteness a simple analytic formula has a trend which matches simulation results the immg model is used to study the effect of distribution and we find that there is one junction point in each series of curves at which system efficiency is not influenced by the distribution of incompleteness when p i p i c the concentration of incompleteness weakens the effect on the other side of p i c concentration will be helpful when p i is close to zero agents using incomplete strategies have on average better profits than those using standard strategies and the back to best agents have a wider range of p i to win

microscopic models for long ranged volatility correlations we propose a general interpretation for long range correlation effects in the activity and volatility of financial markets this interpretation is based on the fact that the choice between active and inactive strategies is subordinated to random walk like processes we numerically demonstrate our scenario in the framework of simplified market models such as the minority game model with an inactive strategy or a more sophisticated version that includes some price dynamics we show that real market data can be surprisingly well accounted for by these simple models

memory effect and multifractality of cross correlations in financial markets abstract we introduce an instantaneous and an average instantaneous cross correlation function to detect the temporal cross correlations between individual stocks based on the daily data of the united states and the chinese stock markets the memory effect of the instantaneous cross correlations is investigated by applying the detrended fluctuation analysis dfa where the dfa exponents can be partly explained by the correlation function from the common sense long range memory is observed for the average instantaneous cross correlations and persists up to a month magnitude of timescale for the united states stock market and half a month magnitude of timescale for the chinese stock market in addition multifractal nature is investigated by a multifractal detrended fluctuation analysis

estimation of parameters in two dimensional transport equations a general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two dimensional transport equations the parameter estimation problem is first cast as an abstract infinite dimensional minimization problem then a sequence of approximate finite dimensional minimization problems is defined which yields a sequence of parameter estimates since convergence results relating the approximate problems to the full infinite dimensional problem are presented in 6 and 17 this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data the technique is also applied to the analysis of actual biological data from an insect dispersal experiment in which the movement of cabbage root flies in the presence of a cabbage crop was studied

simultaneous identification of the spatio temporal dependent heat transfer coefficient and spatially dependent heat flux using an mcgm in a parabolic system abstract this paper aims to simultaneously identify the spatio temporal dependent heat transfer coefficient x t and the spatially dependent heat flux q x in a parabolic system the simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with tikhonov regularization the differentiability of the solution and adjoint equations are investigated to obtain the gradient formulae and determine the step lengths respectively to illustrate the efficiency accuracy and robustness of the proposed algorithm numerical results are investigated using the modified conjugate gradient method mcgm

irrelevance of memory in the minority game by means of extensive numerical simulations we show that all the distinctive features of the minority game introduced by challet and zhang physica a 256 514 1998 are completely independent of the memory of the agents the only crucial requirement is that all the individuals must possess the same information irrespective of whether this information is true or false

fluctuations in multiplicative systems with jumps fluctuation properties of the langevin equation including a multiplicative power law noise and a quadratic potential are discussed the noise has the l evy stable distribution if this distribution is truncated the covariance can be derived in the limit of large time it falls exponentially covariance in the stable case studied for the cauchy distribution exhibits a weakly stretched exponential shape and can be approximated by the simple exponential the dependence of that function on system parameters is determined then we consider a dynamics which involves the above process and obeys the generalized langevin equation the same as for the gaussian case the resulting distributions possess power law tails which fall similarly to those for the driving noise whereas central parts can assume the gaussian shape moreover a process with the covariance 1 t at large time is constructed and the corresponding dynamical equation is solved diffusion properties of systems for both covariances are discussed

effect of imitation in evolutionary minority game on small world networks abstract the system performance in an evolutionary minority game with imitation on small world networks is studied numerical results show that system performance positively correlates with the clustering coefficients the domain structure of the agents strategies can be used to give a qualitative explanation for it we also find that the time series of the reduced variance 2 n could have a phasic evolution from a metastable state two crowds are formed but the distribution of their probabilities does not peak at p 0 and p 1 to a s t e a d y s t a t e the two crowds evolve into a crowd and an anticrowd with the distribution of their probabilities peaking at p 0 and p 1

effects of dynamic response time in an evolving market abstract considering the time scales of global information and personal reaction we study the role of dynamic response time in the evolution of collective behavior in an evolving market the insensitiveness to the market information makes the population cluster around a kind of extreme behavior in which they always follow what happened last time while a sensitive population tends to self segregate into opposing groups the average success rate r among all the agents is found to have a nonmonotonic dependence on the time scale parameter q there exists a critical value below above which r decreases increases with the rise of q theoretical analyses demonstrate that the higher efficiency found in the market with an insensitive population is related to its predictability in such a predictable market the agents following current prediction have a higher winning probability than those rejecting it analytical calculations are in good agreement with numerical data

space frequency quantization for wavelet image coding a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree structured quantization related to spatial structures has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation this paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder we consider zerotree quantization zeroing out tree structured sets of wavelet coefficients and the simplest form of scalar quantization a single common uniform scalar quantizer applied to all nonzeroed coefficients and we formalize the problem of optimizing their joint application we develop an image coding algorithm for solving the resulting optimization problem despite the basic form of the two quantizers considered the resulting algorithm demonstrates coding performance that is competitive often outperforming the very best coding algorithms in the literature

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

time dependent random walks and the theory of complex adaptive systems motivated by novel results in the theory of complex adaptive systems we analyze the dynamics of random walks in which the jumping probabilities are time dependent we determine the survival probability in the presence of an absorbing boundary for an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities on the other hand a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability we use the results to reveal the underlying dynamics responsible for the phenomenon of self segregation and clustering observed in the evolutionary minority game

time series analysis for minority game simulations of financial markets the minority game mg model introduced recently provides promising insights into the understanding of the evolution of prices indices and rates in the financial markets in this paper we perform a time series analysis of the model employing tools from statistics dynamical systems theory and stochastic processes using benchmark systems and a financial index for comparison several conclusions are obtained about the generating mechanism for this kind of evolution the motion is deterministic driven by occasional random external perturbation when the interval between two successive perturbations is sufficientlylarge one can find low dimensional chaos in this regime however the full motion of the mg model is found to be similar to that of the first differences of the sp500 index stochastic nonlinear and unit root stationary

segregation in a competing and evolving population abstract we conducted a study on a recently proposed model in which an odd number of agents are competing to be in the minority in the model the agents have one strategy in hand which is to follow the most recent history each agent is also assigned a value p which is the probability that an agent will follow the trend evolution is introduced through the modification of the value of p when the performance of an agent becomes unsatisfactory we present numerical results for the distribution of p values in the population as well as the average duration between modifications at a given p for different values of the parameters in the model agents who either always follow the trend or always act opposite to the trend tend to out perform the cautious agents in this study we also point out the difference between the present model and a slightly modified model in which a strategy is randomly assigned to every agent initially

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

theory of networked minority games based on strategy pattern dynamics we formulate a theory of agent based models in which agents compete to be in a winning group the agents may be part of a network or not and the winning group may be a minority group or not an important feature of the present formalism is its focus on the dynamical pattern of strategy rankings and its careful treatment of the strategy ties which arise during the system s temporal evolution we apply it to the minority game with connected populations expressions for the mean success rate among the agents and for the mean success rate for agents with k neighbors are derived we also use the theory to estimate the value of connectivity p above which the binary agent resource system with high resource levels makes the transition into the high connectivity state

effect of imitation in a competing and evolving population in different situations abstract the effect of imitation in a competing and evolving population in different situations is studied agents in the population are repeatedly competing to be in a minority and they have a common strategy each agent has a parameter p characterizing the probability that he is following the prediction of the common strategy agents are lined up in a one dimensional chain with periodic boundary condition imitation is allowed among nearest neighboring agents numerical results show that the phase transition appears when the prize to fine ratio r is smaller than a given value the strategy distribution of the population turns into a symmetric inverted u shape consequently imitation is harmful in a sense of enhancement in the overall performance of the population

statistical mechanics of socio economic systems with heterogeneous agents we review the statistical mechanics approach to the study of the emerging collective behaviour of systems of heterogeneous interacting agents the general framework is presented through examples in such contexts as ecosystem dynamics and traffic modelling we then focus on the analysis of the optimal properties of large random resource allocation problems and on minority games and related models of speculative trading in financial markets discussing a number of extensions including multi asset models majority games and models with asymmetric information finally we summarize the main conclusions and outline the major open problems and limitations of the approach

inverse statistics in economics the gain loss asymmetry abstract inverse statistics in economics is considered we argue that the natural candidate for such statistics is the investment horizons distribution this distribution of waiting times needed to achieve a predefined level of return is obtained from often detrended historic asset prices such a distribution typically goes through a maximum at a time called the optimal investment horizon since this defines the most likely waiting time for obtaining a given return by considering equal positive and negative levels of return we report on a quantitative gain loss asymmetry most pronounced for short horizons it is argued that this asymmetry reflects the market dynamics and we speculate over the origin of this asymmetry

some extensions of radial basis functions and their applications in artificial intelligence abstract radial basis functions have recently found interesting applications in artificial intelligence and in particular in the problem of learning to perform a particular task from a set of examples however in many practical cases the radial basis functions method cannot be applied in a straight forward manner because it does not take into account some features that are typical of the problem of learning from examples in this paper we show some extensions of the standard theory introduced in order to deal with a large number of examples and with problems in which different variables play very different roles we present some examples and also point out some open problems

crowd anticrowd theory of the minority game abstract the minority game is a simple yet highly non trivial agent based model for a complex adaptive system here we provide an explanation of the game s fluctuations which is both intuitive and quantitative and which applies over the entire parameter range of interest the physical idea behind our theory is to describe the interplay between crowds of like minded agents and their anticorrelated partners anticrowds

effects of imitation in a competing and evolving population abstract we propose and study a modified version of the evolutionary minority game consisting of a competing population agents in the population are repeatedly competing to be in a minority and they have a common strategy each agent has a parameter p characterizing the probability that she is following the prediction of the common strategy agents are lined up in a one dimensional chain with periodic boundary condition imitation is allowed among nearest neighboring agents numerical results show that the agents evolve into a state in which they self segregate into opposite groups characterized by extreme behavior and imitation leads to considerable enhancement in the overall performance of the population

the estimation of l diffusion coefficients in the parabolic equations abstract the estimation of diffusion coefficients having only l bounds in parabolic equations is considered existence is obtained within a more general class of parabolic operators by means of g convergence the corresponding semi discrete problems are related to the original problem

comparative performance of pyramid data structures for progressive image transmission a review of various pyramid data structures for progressive image transmission focusing on the steps involved in forming the pyramid and the performance comparisons is presented the simple mean pyramid its variants including the truncated mean reduced sum difference reduced difference and s transform pyramids and the more general laplacian pyramid are discussed it is also shown that the use of an interpolation function improves the quality of the full resolution approximations both objectively and subjectively

minority games with score dependent and agent dependent payoffs score dependent and agent dependent payoffs of the strategies are introduced into the standard minority game the intrinsic periodicity is consequently removed and the stylized facts arise such as long range volatility correlations and fat tails in the distribution of the returns the agent dependence of the payoffs is essential in producing the long range volatility correlations the new payoffs lead to a better performance in the dynamic behavior nonlocal in time and can coexist with the inactive strategy we also observe that the standard deviation ensuremath sigma 2 n is significantly reduced thus the efficiency of the system is distinctly improved based on this observation we give a qualitative explanation for the long range volatility correlations

theory of the evolutionary minority game we present a theory describing a recently introduced model of an evolving adaptive system in which agents compete to be in the minority the agents themselves are able to evolve their strategies over time in an attempt to improve their performance the theory explicitly demonstrates the self interaction or market impact that agents in such systems experience

statistical properties of the attendance time series in the minority game abstract we study the statistical properties of the attendance time series corresponding to the number of agents making a particular decision in the minority game mg we focus on the analysis of the probability distribution and the autocorrelation function of the attendance over a time interval in the efficient phase of the game in this regime both the probability distribution and the autocorrelation function are shown to have similar behaviour for time differences corresponding to multiples of 2 2m which is twice the number of possible history bit strings in a mg with agents making decisions based on the most recent m outcomes of the game

crowd effects and volatility in markets with competing agents abstract we present analytic and numerical results for two models namely the minority model and the bar attendance model which offer simple paradigms for a competitive marketplace both models feature heterogeneous agents with bounded rationality who act using inductive reasoning we find that the effects of crowding are crucial to the understanding of the macroscopic fluctuations or volatility in the resulting dynamics of these systems

approximate periodic solutions of a nonlinear parabolic system and an identification problem this work continues our study in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 on the identification problem for the coefficients for the lower order terms in a parabolic system through its approximate periodic solutions different from the work in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 our system now is nonlinear and the coefficients to be detected are from the first order term from the application point of view we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain the existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper

statistical analysis of the evolutionary minority game with different capacities abstract in this paper we consider the evolutionary minority game with different capacities with the increase of capacity level 1 the probability n of room1 with n agents changes from one normal distribution to two normal distributions and back to one normal distribution again when room2 is the basic strategy the probability of room1 with n agents is a small normal distribution and when room1 is the basic strategy the probability of room1 with n agents is a large normal distribution we calculate the integral of the normal distributions and explain the characters in the figures for instance the room with more capacity represents the interest of the majority and the room has more probability to win

image interpolation for progressive transmission by using radial basis function networks investigates the application of a radial basis function network rbfn to hierarchical image coding for progressive transmission the rbfn is then used to generate an interpolated image from the subsampled version an efficient method of computing the network parameters is developed for reduction in computational and memory requirements the coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly quantization error effects introduced at one stage are considered in decoding images at the following stages thus allowing lossless progressive transmission

trading model with pair pattern strategies abstract a simple trading model based on pair pattern strategy space with holding periods is proposed power law behavior is observed for the return variance 2 the price impact h and the predictability k for both models with linear and square root impact functions the sum of the traders wealth displays a positive value for the model with a square root price impact function and a qualitative explanation is given based on the observation of the conditional excess demand a u the cumulative wealth distribution also obeys a power law behavior with an exponent close to that of real markets an evolutionary trading model is further proposed the elimination mechanism effectively changes the behavior of traders and a power law behavior is observed in the measure of zero return distribution p r 0 the trading model with other types of traders e g traders with the mg s strategies and producers are also carefully studied

generating functional analysis of minority games with real market histories it is shown how the generating functional method of de dominicis can be used to solve the dynamics of the original version of the minority game mg in which agents observe real as opposed to fake market histories here one again finds exact closed equations for correlation and response functions but now these are defined in terms of two connected effective non markovian stochastic processes a single effective agent equation similar to that of the fake history models and a second effective equation for the overall market bid itself the latter is absent in fake history models the result is an exact theory from which one can calculate from first principles both the persistent observables in the mg and the distribution of history frequencies

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

enhanced winnings in a mixed ability population playing a minority game we study a mixed population of adaptive agents with small and large memories competing in a minority game if the agents are sufficiently adaptive we find that the average winnings per agent can exceed that obtainable in the corresponding pure populations in contrast to the pure population the average success rate of the large memory agents can be greater than 50 the present results are not reproduced if the agents are fed a random history thereby demonstrating the importance of memory in this system

boolean game on scale free networks abstract inspired by the local minority game we propose a network boolean game and investigate its dynamical properties on scale free networks the system can self organize to a stable state with better performance than the random choice game although only the local information is available to each agent by introducing the heterogeneity of local interactions we find that the system will achieve the best performance when each agent s interaction frequency is linearly correlated with its information capacity generally the agents with more information gain more than those with less information while in the optimal case each agent almost has the same average profit in addition we investigate the role of irrational factor and find an interesting symmetrical behavior

persistence probabilities of the german dax and shanghai index abstract we present a relatively detailed analysis of the persistence probability distributions in financial dynamics compared with the auto correlation function the persistence probability distributions describe dynamic correlations nonlocal in time universal and non universal behaviors of the german dax and shanghai index are analyzed and numerical simulations of some microscopic models are also performed around the fixed point z 0 0 the interacting herding model produces the scaling behavior of the real markets

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

a generalized dynamic herding model with feed back interactions abstract a dynamic feed back interaction is introduced to the eguiluz zimmermann model phys rev lett 85 2000 5659 in application to financial dynamics transmission of information at time t is supposed to depend on the variation of the financial index at t 1 the generated time series is strongly correlated in time at criticality both static and dynamic behavior are investigated

dynamics of the time horizon minority game abstract we present numerical and analytic results for a new version of the minority game mg in which strategy performance is recorded over a finite time horizon the dynamics of this time horizon minority game thmg exhibit many distinct features from the mg and depend strongly on whether the participants are fed real or random history strings the thmg equations are equivalent to a markov chain and yield exact analytic results for the volatility given a specific realization for the quenched strategy disorder

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

statistical mechanics of systems with heterogeneous agents minority games we study analytically a simple game theoretical model of heterogeneous interacting agents we show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz such a stationary state differs from the nash equilibrium where each agent maximizes her own utility the latter turns out to be characterized by a replica symmetry broken structure numerical results fully agree with our analytical findings

parameter identification for a class of abstract nonlinear parabolic distributed parameter systems this paper studies the parameter identification problem of nonlinear abstract parabolic distributed parameter systems via variational method 1 based on the fundamental optimal control theory and the transposition method studied in 2 the existence of optimal parameter is proved and the necessary condition for the optimal parameter is established

a reduced laplacian pyramid for lossless and progressive image communication the laplacian pyramid lp is appropriate for lossy image compression conversely the reduced difference pyramid rdp having as many data as pixels gives a better performance with lossless encoding a reduced lp is designed by discarding the anti aliasing filter and adopting a half band interpolator thus retaining three over four of the lp coefficients lossless coding outperforms both lp and rdp especially when dealing with medical images

shedding light on el farol abstract we mathematize el farol bar problem and transform it into a workable model we find general conditions on the predictor space under which the convergence of the average attendance to the resource level does not require any intelligence on the side of the agents secondly specializing to a particular ensemble of continuous strategies yields a model similar to the minority game statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model on the basis of its phase diagram

an augmented lagrangian method for parameter identifications in parabolic systems the identification of parameters in parabolic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation

the parameter estimation problem for parabolic equations and discontinuous observation operators parameter estimation problems are studied for a class of linear autonomous parabolic partial differential equations with various fit to data criteria which may be discontinuous with respect to the state variable we analyze the convergence of galerkin schemes approximating the optimization problems and generalize results to higher dimensional problems an example is then presented for the case of point observation fit to data criteria in higher dimensions finally discretization of coefficients is discussed for identification problems with variable coefficients

economic fluctuations and anomalous diffusion we quantify the relation between trading activity measured by the number of transactions n deltat and the price change g deltat for a given stock over a time interval t t deltat to this end we analyze a database documenting every transaction for 1000 u s stocks for the two year period 1994 1995 we find that price movements are equivalent to a complex variant of classic diffusion where the diffusion constant fluctuates drastically in time we relate the analog for stock price fluctuations of the diffusion constant known in economics as the volatility to two microscopic quantities i the number of transactions n deltat in deltat which is the analog of the number of collisions and ii the variance w 2 deltat of the price changes for all transactions in deltat which is the analog of the local mean square displacement between collisions our results are consistent with the interpretation that the power law tails of p g deltat are due to p w deltat and the long range correlations in g deltat are due to n deltat

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed