arXiv subjects

Nestor Caticha

Publications and source records attributed to Nestor Caticha.

At least 19 recordsLinked to original sources

arXiv2024

Rebellions and Impeachments in a Neural Network Society

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.

physics.soc-ph↗

arXiv2024

Internal Representations in Spiking Neural Networks, criticality and the Renormalization Group

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.

physics.bio-ph↗

arXiv2023

Integrated Information, a Complexity Measure for optimal partitions

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, $ϕ_G(Π)$ for a fixed partition $Π$ with $K$ components and $Φ=$max$_Πϕ_G(Π)$ 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.

cond-mat.stat-mech↗

arXiv2023

Interacting Dreaming Neural Networks

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.

cond-mat.stat-mech↗

arXiv2021

Homo Entropicus, the emotional agent and societies of Neural Networks

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.

physics.soc-ph↗

arXiv2021

Frustration, glassy behavior and dynamical annealing in societies of Neural Networks

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.

physics.soc-ph↗

arXiv2016

Phase transition from egalitarian to hierarchical societies driven by competition between cognitive and social constraints

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.

physics.soc-ph↗

arXiv2015

Backward Renormalization Priors and the Cortical Source Localization Problem with EEG or MEG

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.

q-bio.QM↗

arXiv2015

For whom will the Bayesian agents vote?

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.

physics.soc-ph↗

arXiv2013

Moral foundations in an interacting neural networks society

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 δ, 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 δat 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.

physics.soc-ph↗

arXiv2013

Temperature Integration: an efficient procedure for calculation of free energy differences

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.

cond-mat.stat-mech↗

arXiv2012

Altruism can proliferate through group/kin selection despite high random gene flow

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.

q-bio.PE↗

arXiv2011

Agent-based Social Psychology: from Neurocognitive Processes to Social Data

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.

physics.soc-ph↗

arXiv2011

Two-level Fisher-Wright framework with selection and migration: An approach to studying evolution in group structured populations

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.

q-bio.PE↗

arXiv2009

Opinion Dynamics of Learning Agents: Does Seeking Consensus Lead to Disagreement?

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.

physics.soc-ph↗

arXiv2007

Online Learning in Discrete Hidden Markov Models

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.

stat.ML↗

arXiv2007

Long Term Economic Relationships From Cointegration Maps

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.

physics.soc-ph↗

arXiv2007

Scaling law for the transient behavior of type-II neuron models

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $τ$ near but below the repetitive firing critical current, $τ\simeq C (I_c-I)^{-Δ}$. 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 $Δ= 1/2$. 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.

q-bio.NC↗