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

dynamics of interacting neural networks the dynamics of interacting perceptrons is solved analytically for a directed flow of information the system runs into a state which has a higher symmetry than the topology of the model a symmetry breaking phase transition is found with increasing learning rate in addition it is shown that a system of interacting perceptrons which is trained on the history of its minority decisions develops a good strategy for the problem of adaptive competition known as the bar problem or minority game

playing the hypothesis testing minority game in the maximal reduced strategy space abstract hypothesis testing minority game hmg is a variant of the standard minority game mg that models the inertial behavior of agents in the market in the earlier study of our group we find that agents cooperate better in hmg than in the standard mg when strategies are picked from the full strategy space here we continue to study the behavior of hmg when strategies are chosen from the maximal reduced strategy space surprisingly we find that unlike the standard mg the level of cooperation in hmg depends strongly on the strategy space used in addition a novel intermittency dynamics is also observed in the minority choice time series in a certain parameter range in which the orderly phases are characterized by a variety of periodic dynamics remarkably all these findings can be explained by the crowd anticrowd theory

stochastic decision making in the minority game abstract a discussion is presented of the effects of stochasticity in the decision making of agents in the minority game both simulational and analytic results are reported and discussed for both additive and multiplicative noise as a function of the ratio d of information dimension to number of agents a phase transition separates a low d non ergodic phase from a high d ergodic phase for additive noise the critical dc is temperature independent but for multiplicative noise dc t decreases with t additive noise does not affect the asymptotic behaviour for d dc but is relevant below dc multiplicative noise has consequence for all d

dynamical solution of the on line minority game we solve the dynamics of the on line minority game mg with general types of decision noise using generating functional techniques a la de dominicis and the temporal regularization procedure of bedeaux et al the result is a macroscopic dynamical theory in the form of closed equations for correlation and response functions defined via an effective continuous time single trader process which are exact in both the ergodic and in the non ergodic regime of the mg our solution also explains why although one cannot formally truncate the kramers moyal expansion of the process after the fokker planck term upon doing so one still finds the correct solution that the previously proposed diffusion matrices for the fokker planck term are incomplete and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions

structure generating mechanisms in agent based models abstract the emergence of dynamical structures in multi agent systems is analysed three different mechanisms are identified namely 1 sensitive dependence in the agent dynamics and convex coupling 2 sensitive dependence and extremal dynamics and 3 interaction through a collectively generated field the dynamical origin of the emergent structures is traced back either to a modification by interaction of the lyapunov spectrum or to multistable dynamics

nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

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

minority game with peer pressure abstract to study the interplay between global market choice and local peer pressure we construct a minority game like econophysical model in this so called networked minority game model every selfish player uses both the historical minority choice of the population and the historical choice of one s neighbors in an unbiased manner to make decision results of numerical simulation show that the level of cooperation in the networked minority game differs remarkably from the original minority game as well as the prediction of the crowd anticrowd theory we argue that the deviation from the crowd anticrowd theory is due to the negligence of the effect of a four point correlation function in the effective hamiltonian of the system

relevance of memory in minority games by considering diffusion on de bruijn graphs we study in detail the dynamics of the histories in the minority game a model of competition between adaptative agents such graphs describe the structure of the temporal evolution of m bit strings each node standing for a given string i e a history in the minority game we show that the frequency of visit of each history is not given by 1 2 m in the limit of large m when the transition probabilities are biased consequently all quantities of the model do significantly depend on whether the histories are real or uniformly and randomly sampled we expose a self consistent theory of the case of real histories which turns out to be in very good agreement with numerical simulations

a minority game with bounded recall this paper studies a repeated minority game with public signals symmetric bounded recall and pure strategies we investigate both public and private equilibria of the game with fixed recall size we first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de bruijn graph then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases we also show that private equilibria behave badly a private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff

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

the quasi periodic time sequence of the population in minority game abstract we observe that a quasi periodic structure appears in the time sequence of population in the minority game when the amount of information to all agents is limited the structure disappears when the amount of information is about the size the number of agents the system then enters a phase with standard deviation smaller than that of a random process we show that these phenomena are the consequences of using best strategies by agents

generating functional analysis of batch minority games with arbitrary strategy numbers both the phenomenology and the theory of minority games mg with more than two strategies per agent are different from those of the conventional and extensively studied case s 2 mgs with s 2 exhibit nontrivial statistics of the frequencies with which the agents select from their available decision making strategies with far reaching implications in the few theoretical mg studies with s 2 published so far these statistics could not be calculated analytically this prevented solution even in ergodic stationary states equations for order parameters could only be closed approximately using simulation data here we carry out a generating functional analysis of fake history batch mgs with arbitrary values of s and give an analytical solution of the strategy frequency problem this leads to closed equations for order parameters in the ergodic regime exact expressions for strategy selection statistics and phase diagrams our results find perfect confirmation in numerical simulations

the cokernel of the johnson homomorphisms of the automorphism group of a free metabelian group in this paper we determine the cokernel of the k th johnson homomorphisms of the automorphism group of a free metabelian group for k 2 and n 4 as a corollary we obtain a lower bound on the rank of the graded quotient of the johnson filtration of the automorphism group of a free group furthermore by using the second johnson homomorphism we determine the image of the cup product map in the rational second cohomology group of the ia automorphism group of a free metabelian group and show that it is isomorphic to that of the ia automorphism group of a free group which is already determined by pettet finally by considering the kernel of the magnus representations of the automorphism group of a free group and a free metabelian group we show that there are non trivial rational second cohomology classes of the ia automorphism group of a free metabelian group which are not in the image of the cup product map

multichoice minority game dynamics and global cooperation abstract in the original two choice minority game mg selfish players cooperate with each other even though direct communication is not allowed moreover there is a periodic dynamics in the mg whenever the strategy space size is much smaller than the number of strategies at play do these phenomena persist if every player has n c 2 choices where all player s strategies are picked from a reduced strategy space we answer this question by studying a multichoice minority game model known as mg n c s numerical simulation shows that these two models have very similar global cooperative behaviors nevertheless unlike in the mg periodic dynamics does not always appear in the mg n c s even when the strategy space size is much smaller than the number of strategies at play

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

the full strategy minority game abstract the full strategy minority game f s m g is an instance of the minority game m g which includes a single copy of every potential agent in this work we explicitly solve the f s m g thanks to certain symmetries of this game furthermore by considering the m g as a statistical sample of the f s m g we compute approximated values of the key variable 2 n in the symmetric phase for different versions of the m g as another application we prove that our results can be easily modified in order to handle certain kinds of initial biased strategy scores in particular when the bias is introduced at the agents level we also show that the f s m g verifies a strict period two dynamics i e period two dynamics satisfied with probability 1 giving to the best of our knowledge the first example of an instance of the m g for which this feature can be analytically proved thanks to this property it is possible to compute in a simple way the probability that a general instance of the m g breaks the period two dynamics for the first time in a given simulation

order and disorder in the local evolutionary minority game abstract we study a modification of the evolutionary minority game emg in which agents are placed in the nodes of a regular or a random graph a neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision scheme depending upon the options made in her immediate neighborhood we name this model the local evolutionary minority game lemg we report numerical results for the topologies of a ring a torus and a random graph changing the size of the neighborhood we focus our discussion in a one dimensional system and perform a detailed comparison of the results obtained from the random relaxation dynamics of the lemg and from a linear chain of interacting spin like variables with temperature we provide a physical interpretation of the surprising result that in the lemg a better coordination a lower frustration is achieved if agents base their actions on local information we show how the lemg can be regarded as a model that gradually interpolates between a fully ordered antiferromagnetic like system and a fully disordered system that can be assimilated to a spin glass

el farol revisited this article is concerned with the global behavior of agents in the el farol bar problem in particular we discuss global attendance in terms of its mean and variance and show that there is a strong dependence of both on the externally imposed comfort level we present a possible interpretation for the observed behavior and propose that the mean attendance converges to the perceived threshold value as opposed to the actually imposed one

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

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

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

mesoscopic approach to minority games in herd regime abstract we study minority games in efficient regime by incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of the state of the game using this approach the game can be represented as a markov process with substantially reduced number of states with explicitly computable probabilities for any payoff the finiteness of the number of states is proved interesting features of an extensive random variable called aggregated demand viz its strong inhomogeneity and presence of patterns in time can be easily interpreted using markov theory and quenched disorder approach we can explain important macroscopic characteristics of the game behavior of variance per capita and predictability of the aggregated demand we prove that in the case of linear payoff many attractors in the state space are possible

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

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

generalized strategies in the minority game we show analytically how the fluctuations i e standard deviation ensuremath sigma in the minority game can decrease below the random coin toss limit if the agents use more general stochastic strategies this suppression of ensuremath sigma results from a cancellation between the actions of a crowd in which agents act collectively and make the same decision and those of an anticrowd in which agents act collectively by making the opposite decision to the crowd

continuum time limit and stationary states of the minority game we discuss in detail the derivation of stochastic differential equations for the continuum time limit of the minority game we show that all properties of the minority game can be understood by a careful theoretical analysis of such equations in particular i we confirm that the stationary state properties are given by the ground state configurations of a disordered soft spin system ii we derive the full stationary state distribution iii we characterize the dependence on initial conditions in the symmetric phase and iv we clarify the behavior of the system as a function of the learning rate this leaves us with a complete and coherent picture of the collective behavior of the minority game strikingly we find that the temperaturelike parameter which is introduced in the choice behavior of individual agents turns out to play the role at the collective level of the inverse of a thermodynamic temperature

the minority game with interactions we partially modify the rules of the minority game mg by introducing some degree of local information in the game which is only available for some agents called the interacting agents our work shows that for small values of the new parameter of the model the fraction of interacting agents there is an improvement of the use of the resources with respect to the mg while as this number grows the response of the system changes and ends up behaving worst than the usual mg

intermittency in an interacting generalization of the geometric brownian motion model we propose a minimal interacting generalization of the geometric brownian motion model which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons for sufficiently strong interactions such systems may have many meta stable states transitions between meta stable states are associated with macroscopic reorganizations of the system which can be triggered by random external forcing such a system will exhibit intermittent dynamics within a large part of its parameter space we propose market dynamics as a possible application of this model in which case random external forcing would correspond to the arrival of important information the emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

how to attain maximum profit in minority game what is the physical origin of player cooperation in minority game and how to obtain maximum global wealth in minority game we answer the above questions by studying a variant of minority game from which players choose among nc alternatives according to strategies picked from a restricted set of strategy space our numerical experiment concludes that player cooperation is the result of a suitable size of sampling in the available strategy space hence the overall performance of the game can be improved by suitably adjusting the strategy space size

three phases of the minority game we define three phases of the minority game according to the value 2m n 2m n the ratio of the number of entries in a strategy to the number of agents the time sequence of the population in one room has distinct feature in different phase it shows quasi periodic structure in the first phase where c2 c2 the system is able to reach its best performance in reducing the population variance the crucial factor which hinders the system to reach its best performance in the first and second phases is the number of agents who switch strategy at the same time when c2 c2 the constraint that bound 2m predictions in a strategy is small so that too many agents will switch to a better strategy simultaneously as a result they form a majority group and are more likely to lose we give analytical approximate formulas for the population variance in the first and third phases we have also determined the phase changing point c1 c1

quantifying complexity in the minority game abstract a lempel ziv complexity measure is introduced into the theory of a minority game in order to capture some features that volatility one of the central quantities in this model of interacting agents is not able to extracted solely from the binary string of outcomes of the game complexity offers new and valuable information on collective behavior of players also we show that an expression for volatility may be included in the analytical expression for complexity

minority game a mean field like approach abstract we calculate the standard deviation of n 1 n 0 the difference of the number of agents choosing between the two alternatives of the minority game our approach is based on two approximations we use the whole set of possible strategies rather than only those distributed between the agents involved in a game moreover we assume that a period two dynamics discussed by previous authors is appropriate within the range of validity of our work with these approximations we introduce a set of states of the system and are able to replace time averages by ensemble averages over these states our results show a very good agreement with simulations results for most part of the informationally efficient phase

generating functional analysis of the dynamics of the batch minority game with random external information we study the dynamics of the batch minority game with random external information using generating functional techniques introduced by de dominicis the relevant control parameter in this model is the ratio a5 p n of the number p of possible values for the external information over the number n of trading agents in the limit n we calculate the location a c of the phase transition signaling the onset of anomalous response and solve the statics for a a c exactly the temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times for a a c the stationary state is shown to be nonunique for a 0 we analyze our equations in leading order in a and find asymptotic solutions with diverging volatility s5o a 21 2 as regularly observed in simulations but also asymptotic solutions with vanishing volatility s5o a 1 2 the former however are shown to emerge only if the agents initial strategy valuations are below a specific critical value

diffusion and localization of relative strategy scores in the minority game we study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase alpha equiv p n gtrsim 1 of the basic minority game using sign payoff with n agents holding two strategies over p histories we formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent s strategies to quantify the correlation between the attendance and the distribution of strategies the relative score x in mathbb z of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities leading either to a static and asymmetric exponential distribution centered at x 0 for fickle agents or to diffusion with a positive or negative drift for frozen agents in terms of scaled coordinates x sqrt n and t n the distributions are uniquely given by alpha and in quantitative agreement with direct simulations of the game as the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic minority game in the asymmetric phase

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

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

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

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

directional filtering transform for image intra frame compression while directional adaption is introduced into traditional transforms different orders of two 1 d transforms will result in different results of one 2 d transform based upon an anisotropic image model this paper analyzes the effect of transform orders in terms of theoretical coding gain our results reveal that the transform orders have little effect on the coding gain with full decomposition good directional modes and good interpolation however in practical compression schemes since high pass bands are not decomposed fully because of the consideration on complexity different transform orders have different coding performances which can be solved by an adaptive transform order motivated by our analyzed results a directional filtering transform dft in order to distinguish from the common usage on dft is proposed in this paper to better exploit correlations among samples in h 264 intraframe coding it provides an evenly distributed set of prediction modes with an adaptive transform order both interblock and intrablock correlations are exploited in this scheme experimental results in h 264 intraframe coding demonstrate its superiority both objectively and subjectively

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

direction adaptive discrete wavelet transform for image compression we propose a direction adaptive dwt da dwt that locally adapts the filtering directions to image content based on directional lifting with the adaptive transform energy compaction is improved for sharp image features a mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions the analysis indicates that the proposed da dwt is more effective than other lifting based approaches experimental results report a gain of up to 2 5 db in psnr over the conventional dwt for typical test images subjectively the reconstruction from the da dwt better represents the structure in the image and is visually more pleasing

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

translation invariant directional framelet transform combined with gabor filters for image denoising this paper is devoted to the study of a directional lifting transform for wavelet frames a nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising then the directionality of the lifting based tight frame is explicitly discussed followed by a specific translation invariant directional framelet transform tidft the tidft has two framelets 1 2 with vanishing moments of order two and one respectively which are able to detect singularities in a given direction set it provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction in addition an adaptive block wise orientation estimation method based on gabor filters is presented instead of the conventional minimization of residuals furthermore the tidft is utilized to exploit the capability of image denoising incorporating the map estimator for multivariate exponential distribution consequently the tidft is able to eliminate the noise effectively while preserving the textures simultaneously experimental results show that the tidft outperforms some other frame based denoising methods such as contourlet and shearlet and is competitive to the state of the art denoising approaches

a 2 d orientation adaptive prediction filter in lifting structures for image coding lifting style implementations of wavelets are widely used in image coders a two dimensional 2 d edge adaptive lifting structure which is similar to daubechies 5 3 wavelet is presented the 2 d prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image consequently the prediction domain is allowed to rotate spl plusmn 45 spl deg in regions with diagonal gradient the gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction and no multiplications are required

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

the quasi periodicity of the minority game revisited abstract we analyze two well known related aspects regarding the sequence of minority sides from the minority game m g in its symmetric phase period two dynamics and quasi periodic behavior we also study the sequence of minority sides in a general way within a graph theoretical framework in order to analyze the outcome dynamics of the mg it is useful to define the m g p r i o r namely an m g with a new choosing rule of the strategy to play which takes into account both prior preferences and game information in this way each time an agent is undecided because two of her best strategies predict different choices while being equally successful so far she selects her a priori favorite strategy to play instead of performing a random tie break as in the m g this new choosing rule leaves the generic behavior of the model unaffected and simplifies the game analysis furthermore interesting properties arise which are only partially present in the m g like the quasi periodic behavior of the sequence of minority sides which turns out to be periodic for the m g p r i o r

statistical mechanics of the mixed majority minority game with random external information we study the asymptotic macroscopic properties of the mixed majority minority game modelling a population in which two types of heterogeneous adaptive agents namely fundamentalists driven by differentiation and trend followers driven by imitation interact the presence of a fraction f of trend followers is shown to induce a a significant loss of informational efficiency with respect to a pure minority game in particular an efficient unpredictable phase exists only for f 1 2 we solve the model by means of an approximate static replica theory and by a direct dynamical generating functional technique the two approaches coincide and match numerical results convincingly

image reconstruction using matched wavelet estimated from data sensed compressively using partial canonical identity matrix this paper proposes a joint framework wherein lifting based separable image matched wavelets are estimated from compressively sensed images and are used for the reconstruction of the same matched wavelet can be easily designed if full image is available also compared with the standard wavelets as sparsifying bases matched wavelet may provide better reconstruction results in compressive sensing cs application since in cs application we have compressively sensed images instead of full images existing methods of designing matched wavelets cannot be used thus we propose a joint framework that estimates matched wavelets from compressively sensed images and also reconstructs full images this paper has three significant contributions first a lifting based image matched separable wavelet is designed from compressively sensed images and is also used to reconstruct the same second a simple sensing matrix is employed to sample data at sub nyquist rate such that sensing and reconstruction time is reduced considerably third a new multi level l pyramid wavelet decomposition strategy is provided for separable wavelet implementation on images that leads to improved reconstruction performance compared with the cs based reconstruction using standard wavelets with gaussian sensing matrix and with existing wavelet decomposition strategy the proposed methodology provides faster and better image reconstruction in cs application

from naive to sophisticated behavior in multiagents based financial market models the behavior of physical complexity and mutual information function of the outcome of a model of heterogeneous inductive rational agents inspired by the el farol bar problem and the minority game is studied the first magnitude is a measure rooted in the kolmogorov chaitin theory and the second a measure related to shannon s information entropy extensive computer simulations were done as a result of which is proposed an ansatz for physical complexity of the type c l l and the dependence of the exponent from the parameters of the model is established the accuracy of our results and the relationship with the behavior of mutual information function as a measure of time correlation of agents choice are discussed

multifractal features of financial markets abstract we study the tick dynamical behavior of three assets in financial markets the kospi the won dollar and yen dollar exchange rates using the rescaled range r s analysis the multifractal hurst exponents with long run memory effect can be obtained from those assets and we discuss whether there exists the crossover or not for the hurst exponents at characteristic time scales particularly we find that the probability distribution of returns approaches to a lorentz distribution different from gaussian properties

replica symmetry breaking in the minority game we extend and complete recent work concerning the analytic solution of the minority game nash equilibria ne of the game have been found to be related to the ground states of a disordered hamiltonian with replica symmetry breaking rsb signalling the presence of a large number of ne here we study the number of ne both analytically and numerically we then analyse the stability of the recently obtained replica symmetric solution and in the region where it becomes unstable derive the solution within one step rsb approximation we are finally able to draw a detailed phase diagram of the model

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

dynamics of a spherical minority game we present an exact dynamical solution of a spherical version of the batch minority game mg with random external information the control parameters in this model are the ratio of the number of possible values for the public information over the number of agents and the radius of the spherical constraint on the microscopic degrees of freedom we find a phase diagram with three phases two without anomalous response an oscillating versus a frozen state and a further frozen phase with divergent integrated response in contrast to standard mg versions we can also calculate the volatility exactly our study reveals similarities between the spherical and the conventional mg but also intriguing differences numerical simulations confirm our analytical results

generating functional analysis of minority games with inner product strategy definitions we use generating functional methods to solve the so called inner product versions of the minority game mg with fake and or real market histories by generalizing the theory developed recently for look up table mgs with real histories the phase diagrams of the look up table and inner product mg versions are generally found to be identical with the exception of inner product mgs where histories are sampled linearly which are found to be structurally critical however we encounter interesting differences both in the theory where the role of the history frequency distribution in look up table mgs is taken over by the eigenvalue spectrum of a history covariance matrix in inner product mgs and in the static and dynamic phenomenology of the models our theoretical predictions are supported by numerical simulations

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

effective history length of the minority game it is known that the memory is relevant in the symmetric phase of the minority game in our previous work we have successfully explained the quasi periodic behavior of the game in the symmetric phase with the help of the probability theory based on this explanation we are able to determine how the history length affects the variance of the system in this paper by using some particular types of fake history such as periodic type and random type we determine how efficient the history length has been used in the standard game furthermore the analysis on the effective history length strongly supports the result we proposed previously that there are three distinct phases in the minority game r 2007 elsevier b v all rights reserved

design of low complexity high performance wavelet filters for image analysis this paper addresses the construction of a family of wavelets based on halfband polynomials an algorithm is proposed that ensures maximum zeros at for a desired length of analysis and synthesis filters we start with the coefficients of the polynomial and then use a generalized matrix formulation method to construct the filter halfband polynomial the designed wavelets are efficient and give acceptable levels of peak signal to noise ratio when used for image compression furthermore these wavelets give satisfactory recognition rates when used for feature extraction simulation results show that the designed wavelets are effective and more efficient than the existing standard wavelets

deterministic dynamics in the minority game the minority game mg behaves as a stochastically disturbed deterministic system due to the coin toss invoked to resolve tied strategies averaging over this stochasticity yields a description of the mg s deterministic dynamics via mapping equations for the strategy score and global information the strategy score map contains both restoring force and bias terms whose magnitudes depend on the game s quenched disorder approximate analytical expressions are obtained and the effect of market impact is discussed the global information map represents a trajectory on a de bruijn graph for small quenched disorder a eulerian trail represents a stable attractor it is shown analytically how antipersistence arises the response to perturbations and different initial conditions is also discussed

weighted adaptive lifting based wavelet transform for image coding in this paper a new weighted adaptive lifting wal based wavelet transform is presented the proposed wal approach is designed to solve the problems existing in the previous adaptive directional lifting adl approach such as mismatch between the predict and update steps interpolation favoring only horizontal or vertical direction and invariant interpolation filter coefficients for all images the main contribution of the proposed approach consists of two parts one is the improved weighted lifting which maintains the consistency between the predict and update steps as far as possible and preserves the perfect reconstruction at the same time another is the directional adaptive interpolation which improves the orientation property of the interpolated image and adapts to statistical property of each image experimental results show that the proposed wal based wavelet transform for image coding outperforms the conventional lifting based wavelet transform up to 3 06 db in psnr and significant improvement in subjective quality is also observed compared with the adl based wavelet transform up to 1 22 db improvement in psnr is reported