Pedro A. Pury

Statistical keyword detection in literary corpora

Abstract.Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means of statistical information referring to the spatial use of the words. Shannons entropy of information is used as a tool for automatic keyword extraction. By using The Origin of Species by Charles Darwin as a representative text sample, we show the performance of our detector and compare it with another proposals in the literature. The random shuffled text receives special attention as a tool for calibrating the ranking indices.

Mean first-passage and residence times of random walks on asymmetric disordered chains

An algebraic derivation is presented which yields the exact solution of the mean first-passage and mean residence times of a one-dimensional asymmetric random walk for quenched disorder. Two models of disorder are analytically treated. Both absorbing–absorbing and reflecting–absorbing boundaries are considered. Particularly, the interplay between asymmetry and disorder is studied.

Survival and residence times in disordered chains with bias

We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on the exact expansion of the backward master equation in cumulants. The dependence on the initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorders. Application to thermally activated processes is also developed.

Biomarkers of Progression after HIV Acute/Early Infection: Nothing Compares to CD4+ T-cell Count?

Progression of HIV infection is variable among individuals, and definition disease progression biomarkers is still needed. Here, we aimed to categorize the predictive potential of several variables using feature selection methods and decision trees. A total of seventy-five treatment-naïve subjects were enrolled during acute/early HIV infection. CD4+ T-cell counts (CD4TC) and viral load (VL) levels were determined at enrollment and for one year. Immune activation, HIV-specific immune response, Human Leukocyte Antigen (HLA) and C-C chemokine receptor type 5 (CCR5) genotypes, and plasma levels of 39 cytokines were determined. Data were analyzed by machine learning and non-parametric methods. Variable hierarchization was performed by Weka correlation-based feature selection and J48 decision tree. Plasma interleukin (IL)-10, interferon gamma-induced protein (IP)-10, soluble IL-2 receptor alpha (sIL-2Rα) and tumor necrosis factor alpha (TNF-α) levels correlated directly with baseline VL, whereas IL-2, TNF-α, fibroblast growth factor (FGF)-2 and macrophage inflammatory protein (MIP)-1β correlated directly with CD4+ T-cell activation (p < 0.05). However, none of these cytokines had good predictive values to distinguish “progressors” from “non-progressors”. Similarly, immune activation, HIV-specific immune responses and HLA/CCR5 genotypes had low discrimination power. Baseline CD4TC was the most potent discerning variable with a cut-off of 438 cells/μL (accuracy = 0.93, κ-Cohen = 0.85). Limited discerning power of the other factors might be related to frequency, variability and/or sampling time. Future studies based on decision trees to identify biomarkers of post-treatment control are warrantied.

Multifractal spectra of mean first-passage-time distributions in disordered chains.

The multifractal characterization of the distribution over disorder of the mean first-passage time in a finite chain is revisited. Both, absorbing-absorbing and reflecting-absorbing boundaries are considered. Two models of dichotomic disorder are compared and our analysis clarifies the origin of the multifractality. The phenomenon is only present when the diffusion is anomalous.

Diffusion and annihilation of a particle on a disordered chain

We present an effective-medium approximation to a diffusion model of a particle in a one dimensional medium, that can be annihilated. This approximation is compared with results based on a multistate continuous-time random walk. The mean-square displacement and the annihilation rate in Laplace transformed form are computed in both schemes. We also analyse the small- and largetime asymptotic behavior of the effective hopping and annihilation probabilities per unit time. The effectivemedium approximation results are in full agreement with those of the multistate continuous-time random walk scheme only under a linear approximation of the square root that appears in the Greens function for a homogeneous medium.

Lifetime of a target in the presence of N independent walkers

We study the survival probability of an immobile target in the presence of N independent diffusing walkers. We address the problem of the Mean Target Lifetime and its dependence on the number and initial distribution of the walkers when the trapping is perfect or imperfect. We consider the diffusion on lattices and in the continuous space and we address the bulk limit corresponding to a density of diffusing particles and only one isolated trap. Also, we use intermittent motion for the optimization of search strategies.

Random walk on a 2D anisotropic percolation network

We have studied the variance of a random walk on 2D anisotropic random percolation networks. The problem has been worked out by introducing a generalization of the effective medium approximation. A set of coupled non-linear self-consistent equations must be solved to find the effective rates in each direction. Here we have solved a particular 2D model in its dc-limit. Monte Carlo simulations have been made to show the agreement with our theoretical predictions.

The waiting time problem

The traditional waiting time problem of a passenger arriving at a bus stop is considered. Giving a pausing time density (statistics of the buses arriving at the bus stop) the passenger waiting time density is calculated. A monoparametric family of pausing time densities is used which gives for a value of the parameter the Poissonian case, obtaining the well known waiting time paradox. Periodic sequence of events is obtained for a limit value of the parameter; in this case the averaged mean value of the waiting time is one half the time between successive events, as one should expect. From the expression of the waiting time density Fellers theorem for ongoing renewal processes is derived. Pathological pausing time densities are mentioned.