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Optimal information processing in peripheral sensory systems has been associated in several examples to the signature of a critical or near critical state. Furthermore, cortical systems have also been described to be in a critical state in both wake and anesthetized experimental models, both {\it in vitro} and {\it in vivo}. We investigate whether a similar signature characterizes the internal representations (IR) of a multilayer (deep) spiking artificial neural network performing computationally simple but meaningful cognitive tasks, using a methodology inspired in the biological setup, with cortical implanted electrodes in rats, either freely behaving or under different levels of anesthesia. The increase of the characteristic time of the decay of the correlation of fluctuations of the IR, found when the network input changes, are indications of a broad-tailed distribution of IR fluctuations. The broad tails are present even when the network is not yet capable of performing the classification tasks, either due to partial training or to the effect of a low dose of anesthesia in a simple model. However, we don't find enough evidence of power law distributions of avalanche size and duration. We interpret the results from a renormalization group perspective to point out that despite having broad tails, this is not related to a critical transition but rather similar to fluctuations driven by the reversal of the magnetic field in a ferromagnetic system. Another example of persistent correlation of fluctuations of a non critical system is constructed, where a particle undergoes Brownian motion on a slowly varying potential.

Basede on a study of the modern presidencial democracies in South America, we present a statistical mechanics exploration of the collective, coordinated action of political actors in the legislative chamber that may result on the impeachment of the executive. By representing the legislative political actors with neurla networks, we observed that the larger the effective number of presidential-agenda items are treated, the smaller the chances for a cross-party dialogue, which, if combined with a decrement in the president's public approval rating, could trigger an impeachment process., Comment: 40 pages and 5 figures

Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi's idea and calculate analytically a complexity index for two systems of Ising spins with parallel update dynamics, the homogeneous and a modular infinite range models. Using the information geometry formulation of integrated information theory, we calculate the geometric integrated information index, $\phi_G(\Pi)$ for a fixed partition $\Pi$ with $K$ components and $\Phi=$max$_\Pi\phi_G(\Pi)$ for $K=2$ or $3$. For systems in the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest (largest) component is above (resp. below) its critical temperature. The effects of partitioning are taken into account by introducing site dilution., Comment: 23 pages, 4 figures

We study the interaction of agents, where each one consists of an associative memory neural network trained with the same memory patterns and possibly different reinforcement-unlearning dreaming periods. Using replica methods, we obtain the rich equilibrium phase diagram of the coupled agents. It shows phases such as the student-professor phase, where only one network benefits from the interaction while the other is unaffected; a mutualism phase, where both benefit; an indifferent phase and an insufficient phase, where neither are benefited nor impaired; a phase of amensalism where one is unchanged and the other is damaged. In addition to the paramagnetic and spin glass phases, there is also one we call the reinforced delusion phase, where agents concur without having finite overlaps with memory patterns. For zero coupling constant, the model becomes the reinforcement and removal dreaming model, which without dreaming is the Hopfield model. For finite coupling and a single memory pattern, it becomes a Mattis version of the Ashkin-Teller model. In addition to the analytical results, we have explored the model with Monte Carlo simulations., Comment: 23 pages , 4 figures

A neural network with a learning algorithm optimized by information theory entropic dynamics is used to build an agent dubbed Homo Entropicus. The algorithm can be described at a macroscopic level in terms of aggregate variables interpretable as quantitative markers of proto-emotions. We use systems of such interacting neural networks to construct a framework for modeling societies that show complex emergent behavior. A few applications are presented to investigate the role the interactions of opinions about multidimensional issues and trust on the information source play on the state of the agent society. These include the case of a class of $N$ agents learning from a fixed teacher; two dynamical agents; panels of three agents modeling the interactions that occur in decisions of the US Court of Appeals, where we quantify how politically biased are the agents, how trustful of other agents-judges of other parties, how much the agents follow a common understanding of the law. Finally we address under which conditions ideological polarization follows or precedes affective polarization in large societies and how simpler versions of the learning algorithm may change these relations., Comment: 16 pages, 13 figures

We study maximum entropy mechanisms of information exchange between agents modeled by neural networks and the macroscopic states of a society of such agents in a few situations. Mathematical quantification of surprise, distrust of other agents and confidence about its opinion emerge as essential ingredients in the entropy based learning dynamics. Learning is shown to be driven by surprises, i.e. the receptor agent is confronted with the concurring opinion of a distrusted agent or with a trusted agent's disagreeing opinion. Attribution of blame for the surprise derives from measures of distrust of the receiver towards the emitter agent and the receiver's confidence about its own opinion. The dynamics proceeds by changes of mainly one or the other: the receptor opinion about the issue or the distrust about the emitter. A society with $N$ agents exchanging binary opinions about a set of issues show rich behavior which depend on the complexity of the agenda. For small sets the society reaches a steady state polarized into antagonistic factions, where balanced norms such as "the friend of an enemy is an enemy" are strictly satisfied. For larger sets of issues, societies can persist for a long time in spin-glass like states. There are two types of frustration: ideological and affective, with dynamical annealing properties depending on the complexity of the set of questions under discussion, leading to the lack of sharply defined parties for long transients.

Empirical evidence suggests that social structure may have changed from hierarchical to egalitarian and back along the evolutionary line of humans. We model a society subject to competing cognitive and social navigation constraints. The theory predicts that the degree of hierarchy decreases with encephalization and increases with group size. Hence hominin groups may have been driven from a phase with hierarchical order to a phase with egalitarian structures by the encephalization during the last two million years, and back to hierarchical due to fast demographical changes during the Neolithic. The dynamics in the perceived social network shows evidence in the egalitarian phase of the observed phenomenon of Reverse Dominance. The theory also predicts for modern hunter-gatherers in mild climates a trend towards an intermediate hierarchy degree and a phase transition for harder ecological conditions. In harsher climates societies would tend to bemore egalitarian if organized in small groups but more hierarchical if in large groups. The theoretical model permits organizing the available data in the cross-cultural record (Ethnographic Atlas, N=248 cultures) where the symmetry breaking transition can be clearly seen., Comment: 23 pages, 8 figures

We study source localization from high dimensional M/EEG data by extending a multiscale method based on Entropic inference devised to increase the spatial resolution of inverse problems. This method is used to construct informative prior distributions in a manner inspired in the context of fMRI (Amaral et al 2004). We construct a set of renormalized lattices that approximate the cortex region where the source activity is located and address the related problem of defining the relevant variables in a coarser scale representation of the cortex. The priors can be used in conjunction with other Bayesian methods such as the Variational Bayes method (VB, Sato et al 2004). The central point of the algorithm is that it uses a posterior obtained at a coarse scale to induce a prior at the next finer scale stage of the problem. We present results which suggest, on simulated data, that this way of including prior information is a useful aid for the source location problem. This is judged by the rate and magnitude of errors in source localization. Better convergence times are also achieved. We also present results on public data collected during a face recognition task.

Within an agent-based model where moral classifications are socially learned, we ask if a population of agents behaves in a way that may be compared with conservative or liberal positions in the real political spectrum. We assume that agents first experience a formative period, in which they adjust their learning style acting as supervised Bayesian adaptive learners. The formative phase is followed by a period of social influence by reinforcement learning. By comparing data generated by the agents with data from a sample of 15000 Moral Foundation questionnaires we found the following. 1. The number of information exchanges in the formative phase correlates positively with statistics identifying liberals in the social influence phase. This is consistent with recent evidence that connects the dopamine receptor D4-7R gene, political orientation and early age social clique size. 2. The learning algorithms that result from the formative phase vary in the way they treat novelty and corroborative information with more conservative-like agents treating it more equally than liberal-like agents. This is consistent with the correlation between political affiliation and the Openness personality trait reported in the literature. 3. Under the increase of a model parameter interpreted as an external pressure, the statistics of liberal agents resemble more those of conservative agents, consistent with reports on the consequences of external threats on measures of conservatism. We also show that in the social influence phase liberal-like agents readapt much faster than conservative-like agents when subjected to changes on the relevant set of moral issues. This suggests a verifiable dynamical criterium for attaching liberal or conservative labels to groups., Comment: 31 pages, 5 figures

The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighborhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents even when disagreeing. We consider a family of learning algorithms parametrized by \delta, that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter \delta at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustains less opinion diversity. We discuss predictions of the model and propose possible experimental tests., Comment: 13 pags, 9 figures

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ at high-T, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a toy model of hard rods on a 1-dimensional ring.

The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on linear public goods games. This emphasis led to the conclusion that even modest levels of migration would pose a serious problem to the spread of altruism in group structured populations. Here we challenge this conclusion, by analyzing evolution in a framework which allows for complex group interactions and random migration among groups. We conclude that contingent forms of strong altruism can spread when rare under realistic group sizes and levels of migration. Our analysis combines group-centric and gene-centric perspectives, allows for arbitrary strength of selection, and leads to extensions of Hamilton's rule for the spread of altruistic alleles, applicable under broad conditions., Comment: 5 pages, 2 figures. Supplementary material with 50 pages and 26 figures

A framework for the mathematical modeling of evolution in group structured populations is introduced. The population is divided into a fixed large number of groups of fixed size. From generation to generation, new groups are formed that descend from previous groups, through a two-level Fisher-Wright process, with selection between groups and within groups and with migration between groups at rate $m$. When $m=1$, the framework reduces to the often used trait-group framework, so that our setting can be seen as an extension of that approach. Our framework allows the analysis of previously introduced models in which altruists and non-altruists compete, and provides new insights into these models. We focus on the situation in which initially there is a single altruistic allele in the population, and no further mutations occur. The main questions are conditions for the viability of that altruistic allele to spread, and the fashion in which it spreads when it does. Because our results and methods are rigorous, we see them as shedding light on various controversial issues in this field, including the role of Hamilton's rule, and of the Price equation, the relevance of linearity in fitness functions and the need to only consider pairwise interactions, or weak selection. In this paper we analyze the early stages of the evolution, during which the number of altruists is small compared to the size of the population. We show that during this stage the evolution is well described by a multitype branching process. The driving matrix for this process can be obtained, reducing the problem of determining when the altruistic gene is viable to a comparison between the leading eigenvalue of that matrix, and the fitness of the non-altruists before the altruistic gene appeared. This leads to a generalization of Hamilton's condition for the viability of a mutant gene., Comment: Complete abstract in the paper. 71 pages, 20 figures

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals as obtained by survey studies of social psychology., Comment: 11 pages, 4 figures, 2 C codes, to appear in Advances in Complex Systems

We study opinion dynamics in a population of interacting adaptive agents voting on a set of complex multidimensional issues. We consider agents which can classify issues into for or against. The agents arrive at the opinions about each issue in question using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean Perceptron to state its opinion. If there is no internal clock, so the update occurs with asynchronously exchanged information among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society thorn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. The curious result is that it is learning from those that hold the same opinions that drives the emergence of factions. This results follows from the fact that factions are prevented by not learning at all from those agents that hold the same opinion. If the number of issues is large, the dynamics becomes trapped and the society does not evolve into factions and a distribution of moderate opinions is observed. We also study the less realistic, but technically simpler synchronous case showing that global consensus is a fixed point. However, the approach to this consensus is glassy in the limit of large societies if agents adapt even in the case of agreement., Comment: 16 pages, 10 figures, revised version

We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concepts of one of the presented algorithms is analysed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking based on our results is also presented., Comment: 8 pages, 6 figures

We employ the Bayesian framework to define a cointegration measure aimed to represent long term relationships between time series. For visualization of these relationships we introduce a dissimilarity matrix and a map based on the Sorting Points Into Neighborhoods (SPIN) technique, which has been previously used to analyze large data sets from DNA arrays. We exemplify the technique in three data sets: US interest rates, monthly inflation rates and gross domestic product growth rates., Comment: 13 pages, 8 figures, extended version submitted to Physica A

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $\tau$ near but below the repetitive firing critical current, $\tau \simeq C (I_c-I)^{-\Delta}$. For both the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent is independent of the numerical integration time step and that both systems belong to the same universality class, with $\Delta = 1/2$. For appropriately chosen parameters, the FitzHugh-Nagumo model presents the same generic transient behavior, but the critical region is significantly smaller. We propose an experiment that may reveal nontrivial critical exponents in the squid axon., Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev. E

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian S\~ao Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20 minutes to 160 days. At time scales shorter than 20 minutes we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics., Comment: 20 pages, 9 figures, to appear in Physica A

We analyse a period spanning 35 years of activity in the Sao Paulo Stock Exchange Index (IBOVESPA) and show that the Heston model with stochastic volatility is capable of explaining price fluctuations for time scales ranging from 5 minutes to 100 days with a single set of parameters. We also show that the Heston model is inconsistent with the observed behavior of the volatility autocorrelation function. We deal with the latter inconsistency by introducing a slow time scale to the model. The fact that the price dynamics in a period of 35 years of macroeconomical unrest may be modeled by the same stochastic process is evidence for a general underlying microscopic market dynamics., Comment: 11 pages, 8 figures, subimitted

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that generates examples. In opposition to concentrating on final results, which would be the natural aim while designing good learning algorithms, we study the evolution process and pay particular attention to the temporal order of appearance of functional structures responsible for the improvements in the learning process, as measured by the generalization capabilities of the resulting algorithms. The effect of such appearances can be described as dynamical phase transitions. The concepts of phenotypic and genotypic entropies, which serve to describe the distribution of fitness in the population and the distribution of symbols respectively, are used to monitor the dynamics. In different runs the phase transitions might be present or not, with the system finding out good solutions, or staying in poor regions of algorithm space. Whenever phase transitions occur, the sequence of appearances are the same. We identify combinations of variables and operators which are useful in measuring experience or performance in rule extraction and can thus implement useful annealing of the learning schedule., Comment: 11 pages, 11 figures, 2 tables

In this paper we pose the question: After gathering N data points, at what value of the control parameter should the next measurement be done? We propose an on-line algorithm which samples optimally by maximizing the gain in information on the parameters to be measured. We show analytically that the information gain is maximum for those potential measurements whose outcome is most unpredictable, i.e. for which the predictive distribution has maximum entropy. The resulting algorithm is applied to exponential analysis., Comment: Presented at MaxEnt 2000, the 20th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2000, Gif-sur-Yvette, France) To be published in the Proceedings, Ali Mohammad-Djafari Ed

Relations between the off thermal equilibrium dynamical process of on-line learning and the thermally equilibrated off-line learning are studied for potential gradient descent learning. The approach of Opper to study on-line Bayesian algorithms is extended to potential based or maximum likelihood learning. We look at the on-line learning algorithm that best approximates the off-line algorithm in the sense of least Kullback-Leibler information loss. It works by updating the weights along the gradient of an effective potential different from the parent off-line potential. The interpretation of this off equilibrium dynamics holds some similarities to the cavity approach of Griniasty. We are able to analyze networks with non-smooth transfer functions and transfer the smoothness requirement to the potential., Comment: 08 pages, submitted to the Journal of Physics A

We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent teacher of the same architecture is analyzed. The best possible generalization ability is determined exactly, through the use of a variational method. The constructive variational method also suggests a learning algorithm. It depends, however, on some unavailable quantities, such as the present performance of the student. The construction of estimators for these quantities permits the implementation of a very effective, highly adaptive algorithm. Several other algorithms are also studied for comparison with the optimal bound and the adaptive algorithm, for different types of time evolution of the rule., Comment: 24 pages, 8 figures, to appear in Machine Learning Journal

We study the problem of determining the Hamiltonian of a fully connected Ising Spin Glass of $N$ units from a set of measurements, whose sizes needs to be ${\cal O}(N^2)$ bits. The student-teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with arbitrary couplings. The set of measurements consists of data about the local minima of the rugged energy landscape. We compare simulations and analytical approximations for the resulting learning curves obtained by using different algorithms., Comment: 5 pages, 1 figure, to appear in Physica A

We study the online dynamics of learning in fully connected soft committee machines in the student-teacher scenario. The locally optimal modulation function, which determines the learning algorithm, is obtained from a variational argument in such a manner as to maximise the average generalisation error decay per example. Simulations results for the resulting algorithm are presented for a few cases. The symmetric phase plateaux are found to be vastly reduced in comparison to those found when online backpropagation algorithms are used. A discussion of the implementation of these ideas as practical algorithms is given.