Motivated by a model for neural networks with adaptation and fatigue, we study a conservative fragmentation equation that describes the density probability of neurons with an elapsed time s after its last discharge. In the linear setting, we extend an argument by Laurençot and Perthame to prove exponential decay to the steady state. This extension allows us to handle coefficients that have a large variation rather than constant coefficients.
View Article and Find Full Text PDFA population׳s survival depends on its ability to adapt to constraints impinging upon it. As such, adaptation is at the heart of an increasing number of theoretical models. In this paper, we propose a bottom-up evolutionary model to explore the relationship between individual evolutionary dynamics and population-level survival.
View Article and Find Full Text PDFA broad range of mortality patterns has been documented across species, some even including decreasing mortality over age. Whether there exist a common denominator to explain both similarities and differences in these mortality patterns remains an open question. The disposable soma theory, an evolutionary theory of aging, proposes that universal intracellular trade-offs between maintenance/lifespan and reproduction would drive aging across species.
View Article and Find Full Text PDFCommuting data is increasingly used to describe population mobility in epidemic models. However, there is little evidence that the spatial spread of observed epidemics agrees with commuting. Here, using data from 25 epidemics for influenza-like illness in France (ILI) as seen by the Sentinelles network, we show that commuting volume is highly correlated with the spread of ILI.
View Article and Find Full Text PDFCharacterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states.
View Article and Find Full Text PDFIt is well established that individuals age differently. Yet the nature of these inter-individual differences is still largely unknown. For humans, two main hypotheses have been recently formulated: individuals may experience differences in aging rate or aging timing.
View Article and Find Full Text PDFTheoretical works have shed light on the impact of natural selection in shaping phenotypes and genotypes. Wagner's canalization model (Wagner, 1996) is one of the well-established models which describe emergent properties of evolving gene networks. In this paper, we propose a deeper theoretical understanding of this well-studied model and we extend its conclusions by characterizing new emergent properties of evolving networks.
View Article and Find Full Text PDFWe introduce a method for systematically reducing the dimension of biophysically realistic neuron models with stochastic ion channels exploiting time-scales separation. Based on a combination of singular perturbation methods for kinetic Markov schemes with some recent mathematical developments of the averaging method, the techniques are general and applicable to a large class of models. As an example, we derive and analyze reductions of different stochastic versions of the Hodgkin Huxley (HH) model, leading to distinct reduced models.
View Article and Find Full Text PDFThe assessment of the variability of neuronal spike timing is fundamental to gain understanding of latency coding. Based on recent mathematical results, we investigate theoretically the impact of channel noise on latency variability. For large numbers of ion channels, we derive the asymptotic distribution of latency, together with an explicit expression for its variance.
View Article and Find Full Text PDFIEEE Trans Neural Netw
June 2010
In irreducible excitatory networks of analog graded-response neurons, the trajectories of most solutions tend to the equilibria. We derive sufficient conditions for such networks to be globally asymptotically stable. When the network possesses several locally stable equilibria, their location in the phase space is discussed and a description of their attraction basin is given.
View Article and Find Full Text PDFWe complement the study of the asymptotic behaviour of the dynamical threshold neuron model with delay, introduced by Gopalsamy and Leung, by providing a description of the dynamics of the system in the remaining parameters range. We characterize the regions of "harmless" delays and those in which delay-induced oscillations appear.
View Article and Find Full Text PDFThe reasons for the seasonality and annual changes in the impact of influenza epidemics remain poorly understood. We investigated the covariations between a major component of climate, namely the El Niño Southern Oscillation (ENSO), and indicators of the impact of influenza, as measured by morbidity, excess mortality and viral subtypes collected in France during the period 1971-2002. We show that both the circulating subtype and the magnitude of ENSO are associated with the impact of influenza epidemics.
View Article and Find Full Text PDFDetermining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes.
View Article and Find Full Text PDFJamming avoidance responses (JARs) are exhibited by pairs of pulse type electric fish that discharge with similar frequencies whenever their individual pulses are about to coincide: responses consist of the transient shortenings in inter-discharge intervals in the fish with the higher frequency. This study describes and models novel forms of JARs observed in sexually mature male or female Brachyhypopomus pinnicaudatus. One novel JAR was observed in male-female pairs in their natural habitat.
View Article and Find Full Text PDFInfluenza epidemics occur once a year during the winter in temperate areas. Little is known about the similarities between epidemics at different locations. We have analyzed pneumonia and influenza deaths from 1972 to 1997 in the United States, France, and Australia to examine the correlation over space and time between the three countries.
View Article and Find Full Text PDFThe squid giant axon is the canonical experimental membrane prototype for the study of action potential generation. This work is concerned with Clay's model for this preparation, which implements the nonlinear dependence of sodium and potassium currents on voltage, a multicompartmental description of sodium channel kinetics that takes into account the dependence between activation and inactivation, revised potassium activation function, and potassium accumulation in the axoplasm and its uptake by glial cells. This model accounts better than the standard Hodgkin-Huxley (HH) model for the response of squid giant axons to various stimuli.
View Article and Find Full Text PDFThe behavior of neural networks may be influenced by transmission delays and many studies have derived constraints on parameters such as connection weights and output functions which ensure that the asymptotic dynamics of a network with delay remains similar to that of the corresponding system without delay. However, even when the delay does not affect the asymptotic behavior of the system, it may influence other important features in the system's dynamics such as the boundary of the basin of attraction of the stable equilibria. In order to better understand such effects, we study the dynamics of a system constituted by two neurons interconnected through delayed excitatory connections.
View Article and Find Full Text PDFThe Nucleus Tractus Solitarius (NTS) of the brainstem contains a neural circuit with only excitatory connections displaying a spontaneous activity involved in the control of respiration. A model of a network with random connections is presented and is used to investigate a possible mechanism of spontaneous activity generation consisting of the amplification of a low-background activity by the excitatory connections. First, the steady states of the network model and its ability to amplify the activity are studied.
View Article and Find Full Text PDFNeuronal adaptation as well as interdischarge interval correlations have been shown to be functionally important properties of physiological neurons. We explore the dynamics of a modified leaky integrate-and-fire (LIF) neuron, referred to as the LIF with threshold fatigue, and show that it reproduces these properties. In this model, the postdischarge threshold reset depends on the preceding sequence of discharge times.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
October 2002
Based upon numerical evidence, Ruan et al. [J. Ruan, L.
View Article and Find Full Text PDFJ Comput Neurosci
March 2003
The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes-the excitable, bistable, and oscillatory ones.
View Article and Find Full Text PDFWhen n types of univalent ligands are competing for the binding to m types of protein sites, the determination of the system composition at equilibrium reduces to the solving of a non-linear system of n equations in C = [0; 1](n). We present an iterative method to solve such a system. We show that the sequence presented here is always convergent, regardless of the initial value in C.
View Article and Find Full Text PDFWe studied the combined influence of noise and constant current stimulations on the Hodgkin-Huxley neuron model through time and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of the linearized Hodgkin-Huxley system.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
December 1999
Spike timing precision in response to a subthreshold stimulation can be enhanced by noise in ensembles of neurons [X. Pei, L. Wilkens, and F.
View Article and Find Full Text PDFPhys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics
November 1999
In systems at phase transitions, two phases of the same substance may coexist for a long time before one of them dominates. We show that a similar phenomenon occurs in systems with delayed feedback, where short-term stable oscillatory patterns can also have very long lifetimes before vanishing into constant or periodic steady states.
View Article and Find Full Text PDF