José F. Fontanari

ERROR THRESHOLD IN FINITE POPULATIONS

A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage disequilibrium at the population level is neglected. In particular, for the single-sharp-peak replication landscape we investigate the dependence of the error threshold on the population size and find that the replication accuracy at threshold increases linearly with the reciprocal of the population size for sufficiently large populations. Furthermore, in the deterministic limit our formulation yields the exact steady-state of the quasispecies model, indicating then the population composition is a random combination of the molecules.

Language and cognition integration through modeling field theory: category formation for symbol grounding

Neural Modeling Field Theory is based on the principle of associating lower-level signals (e.g., inputs, bottom-up signals) with higher-level concept-models (e.g. internal representations, categories/concepts, top-down signals) avoiding the combinatorial complexity inherent to such a task. In this paper we present an extension of the Modeling Field Theory neural network for the classification of objects. Simulations show that (i) the system is able to dynamically adapt when an additional feature is introduced during learning, (ii) that this algorithm can be applied to the classification of action patterns in the context of cognitive robotics and (iii) that it is able to classify multi-feature objects from complex stimulus set. The use of Modeling Field Theory for studying the integration of language and cognition in robots is discussed.

Evolving Compositionality in Evolutionary Language Games

Evolutionary language games have proved a useful tool to study the evolution of communication codes in communities of agents that interact among themselves by transmitting and interpreting a fixed repertoire of signals. Most studies have focused on the emergence of Saussurean codes (i.e., codes characterized by an arbitrary one-to-one correspondence between meanings and signals). In this contribution, we argue that the standard evolutionary language game framework cannot explain the emergence of compositional codes-communication codes that preserve neighborhood relationships by mapping similar signals into similar meanings-even though use of those codes would result in a much higher payoff in the case that signals are noisy. We introduce an alternative evolutionary setting in which the meanings are assimilated sequentially and show that the gradual building of the meaning-signal mapping leads to the emergence of mappings with the desired compositional property.

2008 Special Issue: How language can help discrimination in the Neural Modelling Fields framework

The relationship between thought and language and, in particular, the issue of whether and how language influences thought is still a matter of fierce debate. Here we consider a discrimination task scenario to study language acquisition in which an agent receives linguistic input from an external teacher, in addition to sensory stimuli from the objects that exemplify the overlapping categories that make up the environment. Sensory and linguistic input signals are fused using the Neural Modelling Fields (NMF) categorization algorithm. We find that the agent with language is capable of differentiating object features that it could not distinguish without language. In this sense, the linguistic stimuli prompt the agent to redefine and refine the discrimination capacity of its sensory channels.

A game theoretical approach to the evolution of structured communication codes

Structured meaning-signal mappings, i.e., mappings that preserve neighborhood relationships by associating similar signals with similar meanings, are advantageous in an environment where signals are corrupted by noise and sub-optimal meaning inferences are rewarded as well. The evolution of these mappings, however, cannot be explained within a traditional language evolutionary game scenario in which individuals meet randomly because the evolutionary dynamics is trapped in local maxima that do not reflect the structure of the meaning and signal spaces. Here we use a simple game theoretical model to show analytically that when individuals adopting the same communication code meet more frequently than individuals using different codes—a result of the spatial organization of the population—then advantageous linguistic innovations can spread and take over the population. In addition, we report results of simulations in which an individual can communicate only with its K nearest neighbors and show that the probability that the lineage of a mutant that uses a more efficient communication code becomes fixed decreases exponentially with increasing K. These findings support the mother tongue hypothesis that human language evolved as a communication system used among kin, especially between mothers and offspring.

2009 Special Issue: Cross-situational learning of object-word mapping using Neural Modeling Fields

The issue of how children learn the meaning of words is fundamental to developmental psychology. The recent attempts to develop or evolve efficient communication protocols among interacting robots or virtual agents have brought that issue to a central place in more applied research fields, such as computational linguistics and neural networks, as well. An attractive approach to learning an object-word mapping is the so-called cross-situational learning. This learning scenario is based on the intuitive notion that a learner can determine the meaning of a word by finding something in common across all observed uses of that word. Here we show how the deterministic Neural Modeling Fields (NMF) categorization mechanism can be used by the learner as an efficient algorithm to infer the correct object-word mapping. To achieve that we first reduce the original on-line learning problem to a batch learning problem where the inputs to the NMF mechanism are all possible object-word associations that could be inferred from the cross-situational learning scenario. Since many of those associations are incorrect, they are considered as clutter or noise and discarded automatically by a clutter detector model included in our NMF implementation. With these two key ingredients--batch learning and clutter detection--the NMF mechanism was capable to infer perfectly the correct object-word mapping.

FINITE-SIZE SCALING OF THE ERROR THRESHOLD TRANSITION IN FINITE POPULATIONS

The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model exhibits a first-order transition at , where Q is the probability of exact replication of a molecule of length , and a is the selective advantage of the master string. For sufficiently large population size, N, we show that in the critical region the characteristic time for the vanishing of the master strings from the population is described very well by the scaling assumption , where is an a-dependent scaling function.

Probabilistic analysis of the number partitioning problem

Given a sequence of N positive real numbers , the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of over the two sets is minimized. In the case in which the s are statistically independent random variables uniformly distributed in the unit interval, this NP-complete problem is equivalent to the problem of finding the ground state of an infinite-range, random antiferromagnetic Ising model. We employ the annealed approximation to derive analytical lower bounds to the average value of the difference for the best constrained and unconstrained partitions in the large N limit. Furthermore, we calculate analytically the fraction of metastable states, i.e. states that are stable against all single spin flips, and found that it vanishes like .

Multifractal analysis of DNA walks and trails

The characterization of the long-range order and fractal properties of DNA sequences has proved a difficult though rewarding task mainly due to the mosaic character of DNA consisting of many interwoven patches of various lengths with different nucleotide constitutions. We apply here a recently proposed generalization of the detrended fluctuation analysis method to show that the DNA walk construction, in which the DNA sequence is viewed as a time series, exhibits a monofractal structure regardless of the existence of local trends in the series. In addition, we point out that the monofractal structure of the DNA walks carries over to an apparently alternative graphical construction given by the projection of the DNA walk into the d spatial coordinates, termed DNA trails. In particular, we calculate the fractal dimension D(t) of the DNA trails using a well-known result of fractal theory linking D(t) to the Hurst exponent H of the corresponding DNA walk. Comparison with estimates obtained by the standard box-counting method allows the evaluation of both finite-length and local trends effects.

Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a mean-field approximation to the pure model proposed by Bouchaud and MŽzard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP.