Search results for "stochastic"
showing 10 items of 1018 documents
Cancer growth dynamics: stochastic models and noise induced effects
2009
In the framework of the Michaelis‐Menten (MM) reaction kinetics, we analyze the cancer growth dynamics in the presence of the immune response. We found the coexistence of noise enhanced stability (NES) and resonant activation (RA) phenomena which act in an opposite way with respect to the extinction of the tumor. The role of the stochastic resonance (SR) in the case of weak cancer therapy has been analyzed. The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a Monte Carlo approach. We analyzed the effects of a targeted therapy on the evolutionary dynamics of normal, first‐mutant and cancerous cell populations. We show how …
The grass is always greener on the other side of the fence: the effect of misperceived signalling in a network formation process
2007
Social and economic networks are becoming increasingly popular in the last ten years, because of both the application of game theory to the network formation processes4, and the study of stochastic processes that fit the statistical properties of real world social networks.5 In the very recent years there have also been attempts to combine the contribution of these two streams of research, trying to find strategic models whose equilibria resemble the empirical data.6 A well known source of debate in the game theoretical approach is the incompatibility between stability and efficiency: in most of the models Nash equilibria are actually not the network architectures that maximize the overall …
Inclusion of Instantaneous Influences in the Spectral Decomposition of Causality: Application to the Control Mechanisms of Heart Rate Variability
2021
Heart rate variability is the result of several physiological regulation mechanisms, including cardiovascular and cardiorespiratory interactions. Since instantaneous influences occurring within the same cardiac beat are commonplace in this regulation, their inclusion is mandatory to get a realistic model of physiological causal interactions. Here we exploit a recently proposed framework for the spectral decomposition of causal influences between autoregressive processes [2] and generalize it by introducing instantaneous couplings in the vector autoregressive model (VAR). We show the effectiveness of the proposed approach on a toy model, and on real data consisting of heart period (RR), syst…
Structural Analyses in the Study of Anxiety and Anxiety-Related Behaviour
2016
According to the latest Diagnostic and Statistical Manual of Mental Disorders, 5th edition, anxiety encompasses various conditions sharing an excessive sense of fear and/or apprehension for no evident reason and related behavioural disturbances (Association, 2013). The association of such a gloomy symptomatology, with the great diffusion in the general population, explains the critical impact of anxiety disorders on inter-personal relationships and job-related activities (Greenberg et al.,1999; Wittchen & Hoyer, 2001; Keeley & Storch, 2009). Hence, anxiety disorders represent an important and consistent topic of discussion, not only in terms of underlying neuro-psychological processes but, …
Parallel translations, Newton flows and Q-Wiener processes on the Wasserstein space
2022
- We extend the definition of Lott’s Levi-Civita connection to the Wasserstein space of probability measures having density and divergence. We give an extension of a vector field defined along an absolutely curve onto the whole space so that parallel translations can be introduced as done in differential geometry. In the case of torus, we prove the well-posedness of Lott’s equation for parallel translations.- We prove the well-posedness of the Newton flow equation on the Wasserstein space and show the connections between the relaxed Newton flow equation and the Keller-Segel equation.- We establish an intrinsic formalism for Itô stochastic calculus on the Wasserstein space throughout three k…
Role of noise in a market model with stochastic volatility
2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES ef…
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
2005
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …
Stochastic analysis of a non-local fractional viscoelastic beam forced by Gaussian white noise
2017
Recently, a displacement-based non-local beam model has been developed and the relative finite element (FE) formulation with closed-form expressions of the elastic and fractional viscoelastic matrices has also been obtained. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non-local fractional viscoelastic beam, forced by a Gaussian white noise. In this context, by taking into account the mass of the beam, the system of coupled fractional differential equations ruling the beam motion can be decoupled with the method of the fractional order state variable expansion and statistics of the motion of the beam can be readily…
Stochastic dynamic analysis of fractional viscoelastic systems
2011
A method is presented to compute the non-stationary response of single-degree-of-freedom structural systems with fractional damping. Based on an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion is reverted to a set of coupled linear equations involving additional half oscillators, the number of which depends on the discretization of the fractional derivative operator. In this context, it is shown that such a set of oscillators can be given a proper fractal representation, with a Mandelbrot dimension depending on the fractional derivative order a. It is then seen that the response second-order statistics of the derived set of c…
An approximate technique for determining in closed-form the response transition probability density function of diverse nonlinear/hysteretic oscillat…
2019
An approximate analytical technique is developed for determining, in closed form, the transition probability density function (PDF) of a general class of first-order stochastic differential equations (SDEs) with nonlinearities both in the drift and in the diffusion coefficients. Specifically, first, resorting to the Wiener path integral most probable path approximation and utilizing the Cauchy–Schwarz inequality yields a closed-form expression for the system response PDF, at practically zero computational cost. Next, the accuracy of this approximation is enhanced by proposing a more general PDF form with additional parameters to be determined. This is done by relying on the associated Fokke…