Extended Abstracts Spring 2013

A better understanding of convection is crucial for reducing the intrinsic errors present in climate models [4]. Many atmospheric processes related to precipitation have large scale correlations in time and space, which are the result of the coupling between several non-linear mechanisms with different temporal and spatial characteristic scales. Despite the diversity of individual rain events, a recent array of statistical measures presents surprising statistical regularities giving support to the hypothesis that atmospheric convection and precipitation may be a real-world example of Self-Organised Criticality (SOC) [2, 16].

Power-law distributions contain precious information about a large variety of physical processes [10]. Although there are sound theoretical grounds for these distributions, the empirical evidence giving support to power laws has been traditionally weak.

The most intriguing and celebrated empirical law in quantitative linguistics is Zipf’s law [6], which in one of its forms states that the distribution of word frequencies in a text follows a power law with exponent γ ∼ 2. At least in a qualitative sense, the fulfillment of Zipf’s law is astonishing, being valid no matter the author, style, or language [4–6]. An important problem of Zipf’s law is the variation of the exponent γ among different samples. Although the dependence of γ with system size was firstly acknowledged by Zipf himself [6], and later on other authors have confirmed it [1, 2], few systematic studies on these dependence have been performed. This can be formulated within the framework of (directed) networks, where words (types) are nodes, and consecutive appearances of word tokens increase the weight w _ij of a link between the two nodes by an amount equal to one. In this way, the frequency of a word is equivalent to the strength \(s_{i} =\sum _{j}w_{\mathit{ij}}\) of its corresponding node.

Ecosystems are often described as food webs: networks in which nodes are species and links stand for predation. The research in the field of these ecological networks is becoming more and more relevant given the increasing pressure the ecosystems are facing, which makes the study of their topology specially interesting due to its interconnection with the dynamical processes taking place in it. The concept of the ecological niche of a species has been discussed for a long time. The term was originally used to refer to a species habitat or ecological role. It was then re-defined by Hutchinson as a position in a multi-dimensional hyperspace—each dimension being some biologically relevant magnitude [2].

The main purpose of this study is to model the population dynamics in a eukaryotic cell culture. Besides providing an insight into the important aspects of modelling at different scales and the relation between these models, the study is supposed to allow the prediction of the time profile of the total population size within an admissible tolerance.

We explore the effects of different forms of structural stress on the robustness of metabolic networks and we use two different kinds of randomization methods [4, 5]. We also explore the effects of single and multiple gene knockouts in the metabolic network of a genome-reduced bacterium.

The phenomenon of Stochastic Amplification comes out to describe the oscillations of a community of interacting individuals, as for example, the fluctuations of two species in a prey-predator system. It has been put forward in the context of Theoretical Ecology [7] and Epidemiology [1], giving a simple explanation to the temporal patterns found in nature. In a nutshell, the phenomenon operates as follow: when the system is poised nearby a stable fixed point of the dynamics, noise can amplify some specific frequencies and produce quasi-oscillations.

Our aim is to study the evolutionary properties of a model of the genotype-phenotype. The relation between genotype and phenotype is very complicated. Such complexity is a consequence of the fact that the phenotype emerges from networks of interactions between genes and their products, which regulate gene expression and give rise to non-linear, high-dimensional dynamical systems. In addition, these gene regulatory networks (GRNs) are shaped by evolution by natural selection.

The formation of spatio-temporal patterns is one of the most important forms of collective electrical activity of neural networks. Such forms of activity have been detected experimentally in different neural structures, including the structures in visual [4] and somatosensory [11] cortex, in the temporal lobe [7], in the inferior olives [5], etc. Modeling of the network structure and dynamics can be a possible way of identifying mechanisms of the pattern appearance and disappearance in such large-scale systems.

Single molecule manipulation experiments are becoming increasingly important, for they aim at understanding the mechanical properties of molecules such as nucleic acids and proteins. Here, in particular, we are interested in DNA stretching experiments [13]. We present a model that reproduces the main features observed when pulling DNA, namely the elastic elongation at small forces, the resistance to bending and the enthalpic response to strong stretching forces [1, 5].

The physical modelization of biomolecules requires a careful choice of the scale of work depending on the problem we wish to study. All-atom simulations allow an accurate description of the system but within small time scales and severe size limitations subject to the available computational power. Coarse-grained models gather groups of atoms in point particles simplifying greatly the system but keeping the essence of the important interactions in the problem of study. At this level, the free energy landscape (FEL) of the system appears as a powerful tool to extract relevant information from a system with a high number of degrees of freedom.

Quenched disorder has a dramatic effect on both the statics and the dynamics of phase transitions [5, 7,10]. An argument by Imry and Ma explains why symmetries, in low dimensional systems, cannot be spontaneously broken in the presence of quenched random fields [9]. In a nutshell, the argument is as follows. Suppose a discrete symmetry (e.g., Z ₂ or up-down) was actually spontaneously broken in a d-dimensional system and imagine a region of linear size L with a majority of random fields opposing the broken-symmetry state.

It has recently been shown [1, 5] that there might be a strong relation between the statistics of the acoustic emission AE detected during the compression of porous materials in the lab and the statistics of real earthquakes. In this extended abstract we discuss details of this comparison and what would be the consequences if the two phenomena turn out to be in the same universality class.

We refer to sexually transmitted diseases as the illnesses caused by pathogens which are transmitted mostly via sexual contacts. Although STDs are a very heterogenous set of diseases, there is a common property closely related to their dissemination: the spread of STDs over the population is not homogenous, but it depends on the sexual habits of the population. More precisely, population splits in two groups: those who have a risky sexual behaviour and those who take care during sexual contacts, which is known as the core.

One of the main difficulties in the modeling and numerical simulation of the spread of an infectious disease in wildlife resides in properly taking into account the heterogeneities of the landscape. Forests, plains and mountains present different levels of hospitality, while large interstates, lakes and major waterways can provide strong natural barriers to the epidemic spread. A canonical approach has been to discretize both population and geography into geopolitical units and consider the movement of individuals from unit to unit [4]. This approach, however, does not well represent the biological realities of animal movement, since animals do not move at the scale of geopolitical units. We combine a standard SEI epidemiological model with a diffusion process to account for movement as a continuous process across a continuous region [1]. This results in a system of parabolic reaction-diffusion equations with nonlinear reaction term. Landscape heterogeneities are accounted for by including in the computational domain the significant geographical features of the area. We discretize the resulting model in time by an IMEX scheme and in space by finite elements. To show the effectiveness of the method, we present numerical simulation for rabies epidemics among raccoons in New York State.

In marine microbial biosystems, high magnitude variations in abundance and an unstable dynamics, such as planktonic blooms alternating with extended periods of low abundances, are quite common. In many cases, such blooms are immediate consequences of seasonal variations in temperature, light and other conditions. However, variations in abundance, which are not directly associated with seasonal forcing, are also common; Anderson and May [1] provided numerous examples of observations, where irregular explosions in abundance of clearly non-seasonal nature.

Viruses can amplify their genomes following different replication modes (RMs) ranging from the stamping machine replication (SMR) model to the geometric replication (GR) model. Different RMs are expected to produce different evolutionary and dynamical outcomes in viral quasi-species due to differences in the mutations accumulation rate. Theoretical and computational models revealed that while SMR may provide RNA viruses with mutational robustness, GR may confer a dynamical advantage against genomes degradation. Here, recent advances in the investigation of the RM in positive-sense single-stranded RNA viruses are reviewed. Dynamical experimental quantification of Turnip mosaic virus RNA strands, together with a nonlinear mathematical model, indicated the SMR model for this pathogen. The same mathematical model for natural infections is here further analyzed, and we prove that the interior equilibrium involving coexistence of both positive and negative viral strands is globally asymptotically stable.

The theory and applications of singularly perturbed systems of differential equations, traditionally connected with the problems of fluid dynamics and nonlinear mechanics, has been developed intensively and the methods are applied actively to the solution of a wide range of problems from other areas of natural science. This can be explained by the fact that such singularly perturbed systems appear naturally in the process of modelling various processes, that are characterized by slow and fast motions simultaneously. In many cases it is necessary to consider the behaviour of the system as a whole and not of separate trajectories, and to investigate the system by means of a qualitative analysis. This is what is done in this talk. In the present talk asymptotic and geometrical techniques of analysis are combined for the investigation of singularly perturbed systems. The essence of this approach consists in separating out the slow motions of the system under investigation. Then the order of the differential system decreases, but the reduced system, of lesser order, inherits the essential elements of the qualitative behaviour of the original system in the corresponding domain when the slow integral manifold is attracting. The construction of simplified models is achieved and these simpler models reflect the behaviour of the original models to a high order of accuracy. A mathematical justification of this method can be given by means of the theory of integral manifolds for singularly perturbed systems Note that the pioneering papers were published during the period 1957–1970 by K. Zadiraka [4], V. Fodchuk and Y. Baris, who followed on the work of N. Bogolyubov and Y. Mitropolsky. The existence of slow integral manifolds, stable, unstable and conditionally stable, occur in these papers.

Aquatic microorganisms are responsible for a variety of biogeochemical cycles that fuel our planet [5, 6]. In particular, viruses that could infect all marine organisms (from bacteria to whales) play a key role in marine systems [7]. Virus are the most abundant biological particles, ca. 10⁷ ml⁻¹ in surface waters Suttle 2007 and a large proportion are bacteriophages which together with protists are the main source of microbial mortality (viral shunt) returning dissolved nutrients and organic matter from lysed bacteria to the water column [3, 14] and contributing to the recycling production of the systems; see Fig. 1. Viruses are mostly considered as killers, releasing from 20 to 300 virus particles per host-cell [2, 17]. However they can insert part of their genome in the chromosome of the prokaryotic host or in the chloroplast, mitochondrial or nuclear genetic systems in the eukaryotic algae host.