1,720,967 research outputs found
Numerical methods for retrieving aerosol size distributions from optical measurements of solar radiation.
No full textA stochastic model for interacting neurons in the olfactory bulb
No full textWe focus on interacting neurons organized in a block-layered network devoted to the information processing from the sensory system to the brain. Specifically, we consider the firing activity of olfactory sensory neurons, periglomerular, granule and mitral cells in the context of the neuronal activity of the olfactory bulb. We propose and investigate a stochastic model of a layered and modular network to describe the dynamic behavior of each prototypical neuron, taking into account both its role (excitatory/inhibitory) and its location within the network. We adopt specific Gauss-Markov processes suitable to provide reliable estimates of the firing activity of the different neurons, given their linkages. Furthermore, we study the impact of selective excitation/inhibition on the information transmission by means of simulations and numerical estimates obtained through a Volterra integral approach
Linked Gauss-Diffusion processes for modeling a finite-size neuronal network
No full textA Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages is considered to describe the firing activity of neurons interacting in a (2 × 2)-size feed-forward network. In the subthreshold regime and under the assumption that no more than one spike is exchanged between coupled neurons, the stochastic evolution of the neuronal membrane voltage is subject to random jumps due to interactions in the network. Linked Gauss-Diffusion processes are proposed to describe this dynamics and to provide estimates of the firing probability density of each neuron. To this end, an iterated integral equation-based approach is applied to evaluate numerically the first passage time density of such processes through the firing threshold. Asymptotic approximations of the firing densities of surrounding neurons are used to obtain closed-form expressions for the mean of the involved processes and to simplify the numerical procedure. An extension of the model to an (N × N)-size network is also given. Histograms of firing times obtained by simulations of the LIF dynamics and numerical firings estimates are compared
Turing patterns in a reaction–diffusion system modeling hunting cooperation
No full textA reaction–diffusion system governing the prey–predator interaction with hunting cooperation is investigated. Definitive boundedness of solutions is proved via the existence of positive invariants and attractive sets. Linear stability of the coexistence equilibria is performed and conditions guaranteeing the occurrence of Turing instability are found. Numerical simulations on the obtained results are provided
Analysis of a model for waterborne diseases with Allee effect on bacteria
No full textA limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown
A fractional PDE for first passage time of time-changed Brownian motion and its numerical solution
No full textWe show that the First-Passage-Time probability distribution of a Lévy time-changed Brownian motion with drift is solution of a time fractional advection-diffusion equation subject to initial and boundary conditions; the Caputo fractional derivative with respect to time is considered. We propose a high order compact implicit discretization scheme for solving this fractional PDE problem and we show that it preserves the structural properties (non-negativity, boundedness, time monotonicity) of the theoretical solution, having to be a probability distribution. Numerical experiments confirming such findings are reported. Simulations of the sample paths of the considered process are also performed and used to both provide suitable boundary conditions and to validate the numerical results
Nonlinear stability and numerical simulations for a reaction-diffusion system modelling Allee effect on predators
No full textA reaction-diffusion system governing the prey-predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown
On the dynamics of an intraguild predator-prey model
No full textAn intraguild predator-prey model with a carrying capacity proportional to the biotic resource, is generalized by introducing a Holling type II functional response. The longtime behavior of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. The existence of biologically meaningful equilibria (boundary and internal equilibria) has been investigated. Linear and nonlinear stability conditions for biologically meaningful equilibria are performed. Finally, numerical simulations on different regimes of coexistence and extinction of the involved populations have been shown
Comparing Some Simulation Strategies for First Passage Times of Time-Changed Brownian Motion
No full textThe first passage time of a time-changed Brownian motion through a given boundary is investigated by means of three simulation methods. The time-changed process is constructed by composing the Brownian motion with the inverse of an α-stable subordinator process. We implement a path simulation algorithm and two variants of the hazard rate simulation algorithm. The two variants are based on different expressions for the hazard rate of the time-changed process. Results obtained by applying the different strategies are graphically compared and discussed
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