Role of transcriptional bursts in cellular oscillations.

Genetic oscillators are present in the cells of many organisms and control several biological processes. The common feature of such oscillators is the presence of a protein which represses the transcription of its own gene. Recently, it has been shown that for many genes transcription is not a continuous process, but that it proceeds in bursts. We study here the relationship between bursty transcription and the robustness of protein oscillations. We concentrate on the temporal profile of mRNA production by studying regimes where this profile changes but the amount of mRNA produced is kept fixed. For systems with different degrees of cooperativity we show that in general bursts are associated with more robust oscillations, but when they are too short and intense they can have the opposite effect. In other words, we show that, in terms of the regularity of the oscillations generated, there is an optimal value for the intensity of the bursts.

Effects of time-delayed feedback on the properties of self-sustained oscillators.

Most self-sustained oscillations in biological systems and in technical applications are based on a feedback loop, and it is usually important to know how they will react when an external oscillatory force is applied. Here we investigate the effects that the introduction of a time delay in the feedback can have in the entrainment properties of self-sustained oscillators. To do this, we derive analytic expressions for the periodic trajectories and their asymptotic stability, for a generic external oscillatory force. This allows us to show that, for large quality factors, the resonance frequency does not depend on the feedback delay. When the external force is harmonic, it is shown that the largest entrainment range does not correspond to the time delay that gives the maximal response of the unforced oscillator. In fact, that delay gives the shortest entrainment range.

Epidemic thresholds for bipartite networks.

It is well known that sexually transmitted diseases (STD) spread across a network of human sexual contacts. This network is most often bipartite, as most STD are transmitted between men and women. Even though network models in epidemiology have quite a long history now, there are few general results about bipartite networks. One of them is the simple dependence, predicted using the mean field approximation, between the epidemic threshold and the average and variance of the degree distribution of the network. Here we show that going beyond this approximation can lead to qualitatively different results that are supported by numerical simulations. One of the new features, that can be relevant for applications, is the existence of a critical value for the infectivity of each population, below which no epidemics can arise, regardless of the value of the infectivity of the other population.

Backbone structure of the Edwards-Anderson spin-glass model.

We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.

Directed transport induced by α-stable Lévy noises in weakly asymmetric periodic potentials.

We study the motion of a particle in spatially periodic potentials with broken mirror symmetry under the influence of white α-stable Lévy noises. We consider both time-independent and fluctuating potentials. We focus on cases in which the spatial asymmetry of the potential is due not to a difference between the distances from an absolute minimum to the absolute maximum on its left and to the absolute maximum on its right but only to the curvatures of the potential profiles. The analysis is performed using the fractional Fokker-Planck formalism. Consistent results from Langevin simulations are also presented. We analyze the influence of the symmetry properties of the potentials in combination with the fluctuating characteristics of the system in the determination of the current. We find different situations in which both the absolute value and the direction of the current depend not only on the properties of the potential but also on the parameters characterizing the α-stable Lévy noise. Among other features, we analyze the case of supersymmetric potentials. In particular, we show that a static supersymmetric potential produces no current, and we analyze the conditions for observing a nonvanishing current when the potential fluctuates between different supersymmetric profiles.

Relationship between clustering coefficient and the success of cooperation in networks.

In recent years the prisoner's dilemma has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such a structure is usually assumed to be given by a graph. In general, the success of cooperative strategies is associated with the possibility of forming globular clusters, which in turn depends on a feature of the network that is measured by its clustering coefficient. In this work we study the dependence of the success of cooperation on this coefficient for regular networks. Additionally, for both stochastic and deterministic dynamics we show that there is a strong dependence on the initial composition of the population. This hints at the existence of several different mechanisms that could promote or hinder cluster expansion. We have studied in detail some of these mechanisms by concentrating on completely ordered networks (large clustering coefficient) or completely random networks (vanishing clustering coefficient).

A model for the emergence of adaptive subsystems.

We investigate the interaction of learning and evolution in a changing environment. A stable learning capability is regarded as an emergent adaptive system evolved by natural selection of genetic variants. We consider the evolution of an asexual population. Each genotype can have 'fixed' and 'flexible' alleles. The former express themselves as synaptic connections that remain unchanged during ontogeny and the latter as synapses that can be adjusted through a learning algorithm. Evolution is modelled using genetic algorithms and the changing environment is represented by two optimal synaptic patterns that alternate a fixed number of times during the 'life' of the individuals. The amplitude of the change is related to the Hamming distance between the two optimal patterns and the rate of change to the frequency with which both exchange roles. This model is an extension of that of Hinton and Nowlan in which the fitness is given by a probabilistic measure of the Hamming distance to the optimum. We find that two types of evolutionary pathways are possible depending upon how difficult (costly) it is to cope with the changes of the environment. In one case the population loses the learning ability, and the individuals inherit fixed synapses that are optimal in only one of the environmental states. In the other case a flexible subsystem emerges that allows the individuals to adapt to the changes of the environment. The model helps us to understand how an adaptive subsystem can emerge as the result of the tradeoff between the exploitation of a congenital structure and the exploration of the adaptive capabilities practised by learning.

Statistical mechanics of learning with soft margin classifiers.

We study the typical learning properties of the recently introduced soft margin classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of statistical mechanics. We derive analytically the behavior of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin support vector machine and is very close to that of a Bayesian classifier.

A model for the interaction of learning and evolution.

We present a simple model in order to discuss the interaction of the genetic and behavioral systems throughout evolution. This considers a set of adaptive perceptrons in which some of their synapses can be updated through a learning process. This framework provides an extension of the well-known Hinton and Nowlan model by blending together some learning capability and other (rigid) genetic effects that contribute to the fitness. We find a halting effect in the evolutionary dynamics, in which the transcription of environmental data into genetic information is hindered by learning, instead of stimulated as is usually understood by the so-called Baldwin effect. The present results are discussed and compared with those reported in the literature. An interpretation is provided of the halting effect.

Generalization properties of finite-size polynomial support vector machines

The learning properties of finite-size polynomial support vector machines are analyzed in the case of realizable classification tasks. The normalization of the high-order features acts as a squeezing factor, introducing a strong anisotropy in the patterns distribution in feature space. As a function of the training set size, the corresponding generalization error presents a crossover, more or less abrupt depending on the distribution's anisotropy and on the task to be learned, between a fast-decreasing and a slowly decreasing regime. This behavior corresponds to the stepwise decrease found by Dietrich et al. [Phys. Rev. Lett. 82, 2975 (1999)] in the thermodynamic limit. The theoretical results are in excellent agreement with the numerical simulations.