Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Uso de ODR en las comunidades de desarrollo de software libre

La revolució del programari lliure ha estat i és un dels fenòmens més imprevisibles i de major abast que han sorgit des del desenvolupament de les Tecnologies de la Informació. No obstant això és un fenomen que, a causa de pròpia construcció social i distribuïda, està intrínsecament unit a la noció de conflicte, la manifestació del qual més notòria és la bifurcació o fork. En el present treball analitzem els diferents tipus de conflictes i els mecanismes habitualment emprats per a la resolució dels mateixos, i si formen part dels denominats mètodes alternatius de resolució de controvèrsies en Línia o ODR o si són part d'una categoria diferent i separada.

Distribution of events of positive selection and population differentiation in a metabolic pathway: the case of asparagine N-glycosylation

Background: Asparagine N-Glycosylation is one of the most important forms of protein post-translational modification in eukaryotes. This metabolic pathway can be subdivided into two parts: an upstream sub-pathway required for achieving proper folding for most of the proteins synthesized in the secretory pathway, and a downstream sub-pathway required to give variability to trans-membrane proteins, and involved in adaptation to the environment andinnate immunity. Here we analyze the nucleotide variability of the genes of this pathway in human populations, identifying which genes show greater population differentiation and which genes show signatures of recent positive selection. We also compare how these signals are distributed between the upstream and the downstream parts of the pathway, with the aim of exploring how forces of population differentiation and positive selection vary among genes involved in the same metabolic pathway but subject to different functional constraints. Results:Our results show that genes in the downstream part of the pathway are more likely to show a signature of population differentiation, while events of positive selection are equally distributed among the two parts of the pathway. Moreover, events of positive selection arefrequent on genes that are known to be at bifurcation points, and that are identified as beingin key position by a network-level analysis such as MGAT3 and GCS1.Conclusions: These findings indicate that the upstream part of the Asparagine N-Glycosylation pathway has lower diversity among populations, while the downstream part is freer to tolerate diversity among populations. Moreover, the distribution of signatures of population differentiation and positive selection can change between parts of a pathway, especially between parts that are exposed to different functional constraints. Our results support the hypothesis that genes involved in constitutive processes can be expected to show lower population differentiation, while genes involved in traits related to the environment should show higher variability. Taken together, this work broadens our knowledge on how events of population differentiation and of positive selection are distributed among different parts of a metabolic pathway.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex time-dependent behavior does not break the basic, single-roll structure.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Spontaneous mirror symmetry breaking in the limited enantioselective autocatalysis model: abyssal hydrotermal vents as scenario for the emergence of chirality in prebiotic chemistry

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an ade- quate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temper- ature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role. Key Words: Homochirality Prebiotic chemistry.

A subcritical instability of wave-driven alongshore currents

The development of shear instabilities of a wave-driven alongshore current is investigated. In particular, we use weakly nonlinear theory to investigate the possibility that such instabilities, which have been observed at various sites on the U.S. coast and in the laboratory, can grow in linearly stable flows as a subcritical bifurcation by resonant triad interaction, as first suggested by Shrira eta/. [1997]. We examine a realistic longshore current profile and include the effects of eddy viscosity and bottom friction. We show that according to the weakly nonlinear theory, resonance is possible and that these linearly stable flows may exhibit explosive instabilities. We show that this phenomenon may occur also when there is only approximate resonance, which is more likely in nature. Furthermore, the size of the perturbation that is required to trigger the instability is shown in some circumstances to be consistent with the size of naturally occurring perturbations. Finally, we consider the differences between the present case examined and the more idealized case of Shrira et a/. [ 1997]. It is shown that there is a possibility of coupling between triads, due to the richer modal structure in more realistic flows, which may act to stabilize the flow and act against the development of subcritical bifurcations. Extensive numerical tests are called for.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Distribution of events of positive selection and population differentiation in a metabolic pathway: the case of asparagine N-glycosylation

Asparagine N-Glycosylation is one of the most important forms of protein post-translational modification in eukaryotes. This metabolic pathway can be subdivided into two parts: an upstream sub-pathway required for achieving proper folding for most of the proteins synthesized in the secretory pathway, and a downstream sub-pathway required to give variability to trans-membrane proteins, and involved in adaptation to the environment and innate immunity. Here we analyze the nucleotide variability of the genes of this pathway in human populations, identifying which genes show greater population differentiation and which genes show signatures of recent positive selection. We also compare how these signals are distributed between the upstream and the downstream parts of the pathway, with the aim of exploring how forces of population differentiation and positive selection vary among genes involved in the same metabolic pathway but subject to different functional constraints. Our results show that genes in the downstream part of the pathway are more likely to show a signature of population differentiation, while events of positive selection are equally distributed among the two parts of the pathway. Moreover, events of positive selection are frequent on genes that are known to be at bifurcation points, and that are identified as being in key position by a network-level analysis such as MGAT3 and GCS1. These findings indicate that the upstream part of the Asparagine N-Glycosylation pathway has lower diversity among populations, while the downstream part is freer to tolerate diversity among populations. Moreover, the distribution of signatures of population differentiation and positive selection can change between parts of a pathway, especially between parts that are exposed to different functional constraints. Our results support the hypothesis that genes involved in constitutive processes can be expected to show lower population differentiation, while genes involved in traits related to the environment should show higher variability. Taken together, this work broadens our knowledge on how events of population differentiation and of positive selection are distributed among different parts of a metabolic pathway.

Block structured dynamics and neuronal coding

When certain control parameters of nervous cell models are varied, complex bifurcation structures develop in which the dynamical behaviors available appear classified in blocks, according to criteria of dynamical likelihood. This block structured dynamics may be a clue to understand how activated neurons encode information by firing spike trains of their action potentials.