We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are correlated, forcing their convergence to the same, possibly random, limit. Random walks of this form have been introduced in the context of urn models and in stochastic algorithms. We also propose an application to opinion dynamics in a random network evolving via preferential attachment. We study, in particular, random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. Under certain conditions, synchronization is faster than convergence.

We consider a system of urns of Pólya type, containing balls of two colors; the reinforcement of each urn depends on both the content of the urn and the average content of all urns. We show that the urns synchronize almost surely, in the sense that the fraction of balls of a given color converges almost surely as time tends to ∞ to the same limit for all urns. A normal approximation for a large number of urns is also obtained.

The multidimensionality of chronic pain forces us to look beyond isolated assessment such as pain intensity, which does not consider multiple key parameters, particularly in post-operative Persistent Spinal Pain Syndrome (PSPS-T2) patients. Our ambition was to produce a novel Multi-dimensional Clinical Response Index (MCRI), including not only pain intensity but also functional capacity, anxiety-depression, quality of life and quantitative pain mapping, the objective being to achieve instantaneous assessment using machine learning techniques. Two hundred PSPS-T2 patients were enrolled in the real-life observational prospective PREDIBACK study with 12-month follow-up and received various treatments. From a multitude of questionnaires/scores, specific items were combined, as exploratory factor analyses helped to create a single composite MCRI; using pairwise correlations between measurements, it appeared to more accurately represent all pain dimensions than any previous classical score. It represented the best compromise among all existing indexes, showing the highest sensitivity/specificity related to Patient Global Impression of Change (PGIC). Novel composite indexes could help to refine pain assessment by informing the physician’s perception of patient condition on the basis of objective and holistic metrics, and also by providing new insights regarding therapy efficacy/patient outcome assessments, before ultimately being adapted to other pathologies.

Persistent Spinal Pain Syndrome Type 2 (PSPS-T2), (Failed Back Surgery Syndrome), dramatically impacts on patient quality of life, as evidenced by Health-Related Quality of Life (HRQoL) assessment tools. However, the importance of functioning, pain perception and psychological status in HRQoL can substantially vary between subjects. Our goal was to extract patient profiles based on HRQoL dimensions in a sample of PSPS-T2 patients and to identify factors associated with these profiles. Two classes were clearly identified using a mixture of mixed effect models from a clinical data set of 200 patients enrolled in “PREDIBACK”, a multicenter observational prospective study including PSPS-T2 patients with one-year follow-up. We observed that HRQoL was more impacted by functional disability for first class patients (n = 136), and by pain perception for second class patients (n = 62). Males that perceive their work as physical were more impacted by disability than pain intensity. Lower education level, lack of adaptive coping strategies and higher pain intensity were significantly associated with HRQoL being more impacted by pain perception. The identification of such classes allows for a better understanding of HRQoL dimensions and opens the gate towards optimized health-related quality of life evaluation and personalized pain management.

Abstract. Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are discrete time Markov chains on lattice with finite single-cell states whose distinguishing feature is the parallel character of the updating rule. We study the ground states of the Hamiltonian and the low-temperature phase diagram of the related Gibbs measure naturally associated with a class of reversible PCA, called the cross PCA. In such a model the updating rule of a cell depends indeed only on the status of the five cells forming a cross centered at the original cell itself. In particular, it depends on the value of the center spin (self-interaction). The goal of the paper is that of investigating the role played by the self-interaction parameter in connection with the ground states of the Hamiltonian and the low-temperature phase diagram of the Gibbs measure associated with this particular PCA.Pacs: 05.50.+q; 64.60.De

For a general attractive Probabilistic Cellular Automata on S Z d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {−1, +1} Z d , with a naturally associated Gibbsian potential ϕ, we prove that a (spatial-) weak mixing condition (WM) for ϕ implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition. REPRINT,

Summary Helicotylenchus microlobus is considered to be a junior synonym of H. pseudorobustus by several authors while others consider it as valid. To clarify the status of both species, 39 samples collected from various countries were subjected to statistical analyses that showed they could be grouped into six groups. Topotypes of H. pseudorobustus and H. microlobus belong to two different groups. However, samples in the other groups were morphologically intermediate between these two groups. Characters used in the past to uphold the validity of H. microlobus were variable and overlapping from group to group. The 28 samples studied are identified as H. pseudorobustus. Helicotylenchus microlobus, H. bradys and H. phalerus are confirmed as junior synonyms of H. pseudorobustus. There was no complete congruence between the morphological groups and molecular groups proposed by other authors. For these, two MOTU (Molecular Operational Taxonomic Unit) are accepted within H. pseudorobustus.

We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and harmonic oscillator. By unfolding of the spectrum of such matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe Poissonian behavior in the integrable case and Wignerian behavior in the chaotic case. We present numerical evidence that the action matrix of the stadium billiard displays GOE behavior and give an explanation for it. The findings present evidence for universality of level fluctuations -known from quantum chaos -also to hold in classical physics. [7] states that in time-reversal invariant quantum systems with fully chaotic classical counterpart, the energy level spacing distribution is the same as that obtained from random matrices of a certain symmetry (Gaussian orthogonal ensembles GOE), resulting in a Wignerian distribution. This paper is about classical chaos occuring widely in nature, for example in astro physics, meteorology and dynamics of the atmosphere, fluid and ocean dynamics, climate change, chemical reactions, biology, physiology, neuroscience, or medicine. Traditionally, classical chaos is described by tools of nonlinear dynamics like Lyapunov exponents, Kolmogorov-Sinai entropy and phase space portraits (Poincaré sections). In this work we present evidence that fully chaotic classical systems show univer-