We study spreading dynamics of a reaction diffusion process in a special class of heterogeneous graphs with Poissonian degree distribution and composed of both local and long range links. The behavior of the spreading dynamics on such networks are investigated by relating them to the topological features of graphs. We find that the degree of assortativity can give just some indication about the large scale behavior of the spreading dynamics while a detailed description of the process can be addressed by introducing new, more appropriate, topological quantities linked to the distance between nodes. (C) 2016 Published by Elsevier B.V.

We investigate front propagation in systems with diffusive and subdiffusive behavior. The scaling behavior of moments of the diffusive problem, both in the standard and in the anomalous cases, is not enough to determine the features of the reactive front. In fact, the shape of the bulk of the probability distribution of the transport process, which determines the diffusive properties, is important just for preasymptotic behavior of front propagation, while the precise shape of the tails of the probability distribution determines asymptotic behavior of front propagation.

A nullomer is an oligomer that does not occur as a subsequence in a given DNA sequence, i.e. it is an absent word of that sequence. The importance of nullomers in several applications, from drug discovery to forensic practice, is now debated in the literature. Here, we investigated the nature of nullomers, whether their absence in genomes has just a statistical explanation or it is a peculiar feature of genomic sequences. We introduced an extension of the notion of nullomer, namely high order nullomers, which are nullomers whose mutated sequences are still nullomers. We studied different aspects of them: comparison with nullomers of random sequences, CpG distribution and mean helical rise. In agreement with previous results we found that the number of nullomers in the human genome is much larger than expected by chance. Nevertheless antithetical results were found when considering a random DNA sequence preserving dinucleotide frequencies. The analysis of CpG frequencies in nullomers and high order nullomers revealed, as expected, a high CpG content but it also highlighted a strong dependence of CpG frequencies on the dinucleotide position, suggesting that nullomers have their own peculiar structure and are not simply sequences whose CpG frequency is biased. Furthermore, phylogenetic trees were built on eleven species based on both the similarities between the dinucleotide frequencies and the number of nullomers two species share, showing that nullomers are fairly conserved among close species. Finally the study of mean helical rise of nullomers sequences revealed significantly high mean rise values, reinforcing the hypothesis that those sequences have some peculiar structural features. The obtained results show that nullomers are the consequence of the peculiar structure of DNA (also including biased CpG frequency and CpGs islands), so that the hypermutability model, also taking into account CpG islands, seems to be not sufficient to explain nullomer phenomenon. Finally, high order nullomers could emphasize those features that already make simple nullomers useful in several applications.

We present a solution based on a suitable combination of heuristics and parallel processing techniques for finding the best allocation of the financial assets of a pension fund, taking into account all the specific rules of the fund. We compare the values of an objective function computed with respect to a large set (thousands) of possible scenarios for the evolution of the Net Asset Value (NAV) of the share of each asset class in which the financial capital of the fund is invested. Our approach does not depend neither on the model used for the evolution of the NAVs nor on the objective function. In particular, it does not require any linearization or similar approximations of the problem. Although we applied it to a situation in which the number of possible asset classes is limited to few units (six in the specific case), the same approach can be followed also in other cases by grouping asset classes according to their features.

We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider strong anomalous diffusion characterized by the moment behaviour <(x(t)(q)> similar to t(qv)(q), where v(q) is a non constant function, and we discuss its consequences. Even in the apparently simple case v(2) = 1/2, strong anomalous diffusion may correspond to non trivial features, such as non Gaussian probability distribution and peculiar scaling of large order moments.

In order to study the possibility to discriminate between random and natural amino acid sequences, we introduce different measures of association between pairs of amino acids in a sequence, and apply them to a dataset of 1047 natural protein sequences and 10,470 random sequences, carefully generated in order to preserve the relative length and amino acid distribution of the natural proteins. We analyze the multidimensional measures with machine learning techniques and show that, to a reasonable extent, natural protein sequences can be differentiated from random ones. (C) 2015 Elsevier Ltd. All rights reserved. Casual mutations and natural selection have driven the evolution of protein amino acid sequences that we observe at present in nature. The question about which is the dominant force of proteins evolution is still lacking of an unambiguous answer. Casual mutations tend to randomize protein sequences while, in order to have the correct functionality, one expects that selection mechanisms impose rigid constraints on amino acid sequences. Moreover, one also has to consider that the space of all possible amino acid sequences is so astonishingly large that it could be reasonable to have a well tuned amino acid sequence indistinguishable from a random one.

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.

Casual mutations and natural selection have driven the evolution of protein amino acid sequences that we observe at present in nature. The question about which is the dominant force of proteins evolution is still lacking of an unambigu- ous answer. Casual mutations tend to randomize protein sequences while, in order to have the correct functionality, one expects that selection mechanisms impose rigid contraints on amino acid sequences. Moreover, one also has to consider that the space of all possible amino acid sequences is so astonishingly large that it could be reasonable to have a well tuned amino acid sequence in- distinguishable from a random one. In order to study the possibility to discriminate between random and natural amino acid sequences, we introduce different measures of association between pairs of amino acids in a sequence, and apply them to a dataset of 1, 047 nat- ural protein sequences and 10, 470 random sequences, carefully generated in order to preserve the relative length and amino acid distribution of the natu- ral proteins. We analize the multidimensional measures with machine learning techniques and show that, to a reasonable extent, natural protein sequences can be differentiated from random ones

This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.

This contribution aims at introducing the topics of this book. We start with a brief historical excursion on the developments from the law of large numbers to the central limit theorem and large deviations theory. The same topics are then presented using the language of probability theory. Finally, some applications of large deviations theory in physics are briefly discussed through examples taken from statistical mechanics, dynamical and disordered systems.

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate vf in a shear flow increases with compressibility intensity ?, following the relation ?vf??2. Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case. The effect has been quantitatively measured, and it turns out to be generally small. For the cellular flow, two extreme cases have been investigated, with the whole perturbation situated either in the center of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behavior in the two cases. The enhancing remains modest and is always less than 20%.

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t)~tdl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channel.

We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the population dies at fixed rate. In the former it grows either with the logistic or with an Allee effect type dynamics, where the population has to overcome a threshold to glow. We study the conditions for successful invasions and the speed of the invasion process, which is numerically and analytically investigated in several limits. Generically advection enhances the downstream invasion speed but decreases the population size of the invading species, and can even inhibit the invasion process. Remarkably, however, the rate of population increase, which quantifies the invasion efficiency, is maximized by an optimal advection velocity. In models with Allee effect, differently from the logistic case, above a critical unfavorable patch size the population localizes in a favorable patch, being unable to invade the habitat. However, we show that advection, when intense enough, may activate the invasion process.

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, $M(t)$. At variance with pure diffusive processes, characterized by the spectral dimension, $d_s$, for reaction spreading the important quantity is found to be the connectivity dimension, $d_l$. Numerical data, in agreement with analytical estimates based on the features of $n$ independent random walkers on the graph, show that $M(t) \sim t^{d_l}$. In the case of Erd\"{o}s-Renyi random graphs, the reaction-product is characterized by an exponential growth $M(t) \sim e^{\alpha t}$ with $\alpha$ proportional to $\ln \lra{k}$, where $\lra{k}$ is the average degree of the graph.

The problem of asymptotic features of front propagation in stirred media is addressed for laminar and turbulent velocity fields. In particular we consider the problem in two dimensional steady and unsteady cellular flows in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case we provide an analytical approximation for the front speed, vf, as a function of the stirring intensity, U, in good agreement with the numerical results. In the unsteady (time-periodic) case, albeit the Lagrangian dynamics is chaotic, chaos in the front dynamics is relevant only for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front. In addition we study front propagation of reactive fields in systems whose diffusive behavior is anomalous. The features of the front propagation depend, not only on the scaling exponent ?, which characterizes the diffusion properties, ((x(t) - x(0))2 ~ t2?), but also on the detailed shape of the probability distribution of the diffusive process.

We have developed a rat brain organotypic culture model, in which tissue slices contain cortex-subventricular zone-striatum regions, to model neuroblast activity in response to in vitro ischemia. Neuroblast activation has been described in terms of two main parameters, proliferation and migration from the subventricular zone into the injured cortex. We observed distinct phases of neuroblast activation as is known to occur after in vivo ischemia. Thus, immediately after oxygen/glucose deprivation (6-24 hours), neuroblasts reduce their proliferative and migratory activity, whereas, at longer time points after the insult (2 to 5 days), they start to proliferate and migrate into the damaged cortex. Antagonism of ionotropic receptors for extracellular ATP during and after the insult unmasks an early activation of neuroblasts in the subventricular zone, which responded with a rapid and intense migration of neuroblasts into the damaged cortex (within 24 hours). The process is further enhanced by elevating the production of the chemoattractant SDf-1alpha and may also be boosted by blocking the activation of microglia. This organotypic model which we have developed is an excellent in vitro system to study neurogenesis after ischemia and other neurodegenerative diseases. Its application has revealed a SOS response to oxygen/glucose deprivation, which is inhibited by unfavorable conditions due to the ischemic environment. Finally, experimental quantifications have allowed us to elaborate a mathematical model to describe neuroblast activation and to develop a computer simulation which should have promising applications for the screening of drug candidates for novel therapies of ischemia-related pathologies.

We present an analysis of the dynamics of the term structure of interest rates based on the study of the time evolution of the parameters of a variation of the Nelson-Siegel model. The results show that it is extremely difficult to find a relation between the evolution of the term structure and the behavior of macroeconomic variables different from the official interest rate. (c) 2007 Elsevier B.V. All rights reserved

An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon, and front propagation, focusing on differences with respect to the continuous case. We introduce a renormalized reaction rate depending both on the interaction radius and the particle density, and we relate it to macroscopic observables (e.g., front speed and front thickness) of the system.