The compartmentalization of distinct templates in protocells and the exchange of templates between them (migration) are key elements of a modern scenario for prebiotic evolution. Here we use the diffusion approximation of population genetics to study
analytically the steady-state properties of such prebiotic scenario. The coexistence of distinct template types inside a protocell is achieved by a selective pressure at the protocell level (group selection) favoring protocells with a mixed template composition. In the degenerate case, where the templates have the same replication rate, we find that a vanishingly small migration rate suffices to eliminate the segregation effect of random drift and so to promote coexistence. In the non-degenerate case, a small migration rate greatly boosts coexistence as compared with the situation where there is no migration. However, increase of the migration rate beyond a critical value leads to the complete dominance of the more efficient template type (homogeneous regime). In this case, we find a continuous phase transition separating the homogeneous and the coexistence regimes, with the order parameter vanishing linearly with the distance to the transition point.
Establishing the conditions that guarantee the spreading or the sustenance of altruistic traits in a population is the main goal of intergroup selection models. Of particular interest is the balance of the parameters associated to group size, migrati
on and group survival against the selective advantage of the non-altruistic individuals. Here we use Kimuras diffusion model of intergroup selection to determine those conditions in the case the group survival probability is a nonlinear non-decreasing function of the proportion of altruists in a group. In the case this function is linear, there are two possible steady states which correspond to the non-altruistic and the altruistic phases. At the discontinuous transition line separating these phases there is a non-ergodic coexistence phase. For a continuous concave survival function, we find an ergodic coexistence phase that occupies a finite region of the parameter space in between the altruistic and the non-altruistic phases, and is separated from these phases by continuous transition lines. For a convex survival function, the coexistence phase disappears altogether but a bistable phase appears for which the choice of the initial condition determines whether the evolutionary dynamics leads to the altruistic or the non-altruistic steady state.
Cross-situational word learning is based on the notion that a learner can determine the referent of a word by finding something in common across many observed uses of that word. Here we propose an adaptive learning algorithm that contains a parameter
that controls the strength of the reinforcement applied to associations between concurrent words and referents, and a parameter that regulates inference, which includes built-in biases, such as mutual exclusivity, and information of past learning events. By adjusting these parameters so that the model predictions agree with data from representative experiments on cross-situational word learning, we were able to explain the learning strategies adopted by the participants of those experiments in terms of a trade-off between reinforcement and inference. These strategies can vary wildly depending on the conditions of the experiments. For instance, for fast mapping experiments (i.e., the correct referent could, in principle, be inferred in a single observation) inference is prevalent, whereas for segregated contextual diversity experiments (i.e., the referents are separated in groups and are exhibited with members of their groups only) reinforcement is predominant. Other experiments are explained with more balanced doses of reinforcement and inference.
Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selecti
ve pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steady-state probability density of protocell compositions.
An explanation for the acquisition of word-object mappings is the associative learning in a cross-situational scenario. Here we present analytical results of the performance of a simple associative learning algorithm for acquiring a one-to-one mappin
g between $N$ objects and $N$ words based solely on the co-occurrence between objects and words. In particular, a learning trial in our learning scenario consists of the presentation of $C + 1 < N$ objects together with a target word, which refers to one of the objects in the context. We find that the learning times are distributed exponentially and the learning rates are given by $ln{[frac{N(N-1)}{C + (N-1)^{2}}]}$ in the case the $N$ target words are sampled randomly and by $frac{1}{N} ln [frac{N-1}{C}] $ in the case they follow a deterministic presentation sequence. This learning performance is much superior to those exhibited by humans and more realistic learning algorithms in cross-situational experiments. We show that introduction of discrimination limitations using Webers law and forgetting reduce the performance of the associative algorithm to the human level.
The categorization of emotion names, i.e., the grouping of emotion words that have similar emotional connotations together, is a key tool of Social Psychology used to explore peoples knowledge about emotions. Without exception, the studies following
that research line were based on the gauging of the perceived similarity between emotion names by the participants of the experiments. Here we propose and examine a new approach to study the categories of emotion names - the similarities between target emotion names are obtained by comparing the contexts in which they appear in texts retrieved from the World Wide Web. This comparison does not account for any explicit semantic information; it simply counts the number of common words or lexical items used in the contexts. This procedure allows us to write the entries of the similarity matrix as dot products in a linear vector space of contexts. The properties of this matrix were then explored using Multidimensional Scaling Analysis and Hierarchical Clustering. Our main findings, namely, the underlying dimension of the emotion space and the categories of emotion names, were consistent with those based on peoples judgments of emotion names similarities.
We study analytically a variant of the one-dimensional majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors opinions. The individuals are fixed in the sites of a ring of size $L$ and can interact
with their nearest neighbors only. The interesting feature of this model is that it exhibits an infinity of spatially heterogeneous absorbing configurations for $L to infty$ whose statistical properties we probe analytically using a mean-field framework based on the decomposition of the $L$-site joint probability distribution into the $n$-contiguous-site joint distributions, the so-called $n$-site approximation. To describe the broken-ergodicity steady state of the model we solve analytically the mean-field dynamic equations for arbitrary time $t$ in the cases n=3 and 4. The asymptotic limit $t to infty$ reveals the mapping between the statistical properties of the random initial configurations and those of the final absorbing configurations. For the pair approximation ($n=2$) we derive that mapping using a trick that avoids solving the full dynamics. Most remarkably, we find that the predictions of the 4-site approximation reduce to those of the 3-site in the case of expectations involving three contiguous sites. In addition, those expectations fit the Monte Carlo data perfectly and so we conjecture that they are in fact the exact expectations for the one-dimensional majority-vote model.
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Jose F. Fontanari
, Marie-Claude Bonniot-Cabanac
, Michel Cabanac andn Leonid I. Perlovsky
2012
Cognitive dissonance is the stress that comes from holding two conflicting thoughts simultaneously in the mind, usually arising when people are asked to choose between two detrimental or two beneficial options. In view of the well-established role of
emotions in decision making, here we investigate whether the conventional structural models used to represent the relationships among basic emotions, such as the Circumplex model of affect, can describe the emotions of cognitive dissonance as well. We presented a questionnaire to 34 anonymous participants, where each question described a decision to be made among two conflicting motivations and asked the participants to rate analogically the pleasantness and the intensity of the experienced emotion. We found that the results were compatible with the predictions of the Circumplex model for basic emotions.
The existence of juxtaposed regions of distinct cultures in spite of the fact that peoples beliefs have a tendency to become more similar to each others as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we s
tudy an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model -- Axelrods model -- we found that these opinion domains are unstable to the effect of a thermal-like noise.
We investigate the performance of a variant of Axelrods model for dissemination of culture - the Adaptive Culture Heuristic (ACH) - on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size $F$ by a B
oolean Binary Perceptron. In this heuristic, $N$ agents, characterized by binary strings of length $F$ which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable $F/N^{1/4}$ so that the number of agents must increase with the fourth power of the problem size, $N propto F^ 4$, to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with $F^ 6$ which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean Binary Perceptron, given a fixed probability of success.
