Ubiraci P.C. Neves

Shannon entropy applied to the analysis of event-related fMRI time series.

Event-related functional magnetic resonance imaging (ER-fMRI) refers to the blood oxygen level-dependent (BOLD) signal in response to a short stimulus followed by a long period of rest. These paradigms have become more popular in the last few years due to some advantages over standard block techniques. Most of the analysis of the time series generated in such exams is based on a model of specific hemodynamic response function. In this paper we propose a new method for the analysis of ER-fMRI based in a specific aspect of information theory: the entropy of a signal using the Shannon formulation, which makes no assumption about the shape of the response. The results show the ability to discriminate between activated and resting cerebral regions for motor and visual stimuli. Moreover, the results of simulated data show a more stable pattern of the method, if compared to typical algorithms, when the signal to noise ratio decreases.

Non-extensive entropy and the extraction of BOLD spatial information in event-related functional MRI.

Functional magnetic resonance imaging (fMRI) data analysis has been carried out recently in the framework of information theory, by means of the Shannon entropy. As a natural extension, a method based on the generalized Tsallis entropy was developed to the analysis event-related (ER-fMRI), where a brief stimulus is presented, followed by a long period of rest. The new technique aims for spatial localization neuronal activity due to a specific task. This method does not require a priori hypothesis of the hemodynamic response function (HRF) shape and the linear relation between BOLD responses with the presented task. Numerical simulations were performed so as to determine the optimal values of the Tsallis q parameter and the number of levels, L. In order to avoid undesirable divergences of the Tsallis entropy, only positive q values were studied. Results from simulated data (with L = 3) indicated that, for q = 0.8, the active brain areas are detected with the highest performance. Moreover, the method was tested for an in vivo experiment and demonstrated the ability to discriminate active brain regions that selectively responded to a bilateral motor task.

Series expansion of the directed percolation probability

Using a transfer-matrix technique the authors obtain extended series expansion of the percolation probability for the directed site percolation problem on the square lattice. Their approach reveals a previously unsuspected connection between his problem and the enumeration of the number of ways of dissecting a ball. They show that the method can also be used to determine a series expansion for the mean cluster size. An analysis based on Pade approximants gives estimates of the critical threshold and also of the critical exponent beta .

Tsallis information measure applied to the analysis of EEG signals in a model of the somatosensory system

Abstract The collective behavior of cortical neurons during processes of reorganization after amputation of a digit in a realistic computational model of the somatosensory system is studied with Tsallis entropy measure. The presence of transient events and significant alterations into the level of entropy associated with the reorganization processes in the simulated cortical area during and after the organization of new representational areas show that the application of this kind of analysis may provide interesting insights into the analysis of reorganization processes in cortical areas by means of extracellular field potentials recordings.

Topology, dynamics and finite size effects of a kinetic growth model

Ramified polymerization is studied through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities. The polymer configuration is identified with a bond tree in order to examine its topology. The fractal dimensions of clusters are obtained at criticality. Simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents. In regard to finite size effects, a fourth-order cumulant technique is employed to estimate the critical branching probability bc and the critical exponents ν and β. Finally, for the case when impurities are not present, the surface roughness is described in terms of the Hurst exponents.

Finite-size scaling and damage spreading in Ising systems with multispin interactions

We investigate two-dimensional Ising systems with multispin interactions of three- (m=3) and four-body terms (m=4). The application of a new type of finite-size algorithm of de Oliveira allow us to clearly distinguish a first-order transition (in the m=4 case) from a continuous one (in the m=3 one). We also study the damage spreading in these systems. In this study, a dynamical phenomenon is observed to occur at a critical point separating a chaotic phase from a frozen one. However, the width of the interval where this transition happens does not yield a conclusive evidence about the order of the phase transition.

Monte Carlo simulations for a kinetic growth model

We simulate a kinetic growth model on the square lattice using a Monte Carlo approach in order to study ramified polymerization with short-distance attractive interactions between monomers. The phase boundary separating finite from infinite growth regimes is obtained in the (T,b) space, where T is the reduced temperature and b is the branching probability. In the thermodynamic limit, we extrapolate the temperature below which the phase is found to be always infinite. We also observe the occurrence of a roughening transition at the polymer surface.

The branched polymer growth model revisited

The branched polymer growth model (BPGM) has been employed to study the kinetic growth of ramified polymers in the presence of impurities. In this article, the BPGM is revisited on the square lattice and a subtle modification in its dynamics is proposed in order to adapt it to a scenario closer to reality and experimentation. This new version of the model is denominated the adapted branched polymer growth model (ABPGM). It is shown that the ABPGM preserves the functionalities of the monomers and so recovers the branching probability b as an input parameter which effectively controls the relative incidence of bifurcations. The critical locus separating infinite from finite growth regimes of the ABPGM is obtained in the (b,c) space (where c is the impurity concentration). Unlike the original model, the phase diagram of the ABPGM exhibits a peculiar reentrance.

Event-Related Functional MRI and Information Theory

Functional magnetic resonance imaging (fMRI) has become one of the main tools for non-invasive assessment of normal human brain functions. Most of the analysis that have been done thus far, either in the clinical environment or for research purposes, have made use of block paradigms, that involves periods of activation alternated with periods of rest. Nevertheless, in the last few years event-related fMRI (ER-fMRI) has become an alternative approach to infer about human brain functions. It consists basically of the presentation of a series of short stimuli, for further following of the brain activation patterns, translated by variations in brain hemoglobin state, resulting in local image contrast changes [1]. Recently, event-related paradigms, also called single trial paradigms, have become more extensively applied to cognitive experiments [2]. Classically the analysis of ER time series is based on the computation of the covariance between the observed averaged signal and an artificial hemodynamic response function. However, choosing the right reference function can become a significant problem. In fact, separate cortical regions can exhibit very different hemodynamic responses, varying its shape and amplitude [3]. Besides the conventional algorithms for analysis of fMRI block paradigms, such as cross correlation and student-t test, here we propose a new technique for analysis of event-related fMRI time series, based on an information measurement dependent on time. The results of the two methods are then compared in a standard visual and motor experiment. More specifically, the method consists in the computation of the Shannon entropy derived from the image time series, generated in a typical ER visual and motor paradigms. The maximum and minimum of the entropies were interpreted based on the temporal evolution of the probability distribution of the states of the system. For the calculation of the entropy dependent on time» one can define the states accessible to the system as the amplitude levels of a signal within a time interval (window) centered at time /. The Shannon entropy is then calculated as [4]:

Persistent agents in Axelrod's social dynamics model

Axelrods model of social dynamics has been studied under the effect of external media. Here we study the formation of cultural domains in the model by introducing persistent agents. These are agents whose cultural traits are not allowed to change but may be spread through local neighborhood. In the absence of persistent agents, the system is known to present a transition from a monocultural to a multicultural regime at some critical Q (number of traits). Our results reveal a dependence of critical Q on the occupation probability p of persistent agents and we obtain the phase diagram of the model in the -plane. The critical locus is explained by the competition of two opposite forces named here barrier and bonding effects. Such forces are verified to be caused by non-persistent agents which adhere (adherent agents) to the set of traits of persistent ones. The adherence (concentration of adherent agents) as a function of p is found to decay for constant Q. Furthermore, adherence as a function of Q is found to decay as a power law with constant p.