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In this paper, a single-species stochastic population model is considered in the presence of density-dependent proportional harvesting. The stochastic model is considered to include the effects of fluctuation in the predation rate and environmental variability. Coloured cross-correlated Gaussian coloured noises are used to generate stochastic fluctuations. Steady-state probability distribution function and stationary potential are determined using the approximate Fokker–Planck equation. Phenomenological bifurcation analysis and mean first passage time have been computed. The average population density in the outbreak state is calculated using normalised probability distribution of the outbreak state. The species outbreak control strategy has been proposed. The key observations of this study are the negative cross-correlation strength-induced noise enhanced stability (NES) phenomenon and the environmental stochasticity-induced resonant activation (RA) phenomenon. Bistable to monostable phase regime shift is observed to depend on the environmental stochasticity whereas monostable to bistatble phase regime shift is observed to depend on correlation time of the environmental stochasticity. [ABSTRACT FROM AUTHOR]

In this work, we highlight the influence of the material uncertainties (magnetic permeability, electric conductivity of a Mn-Zn ferrite core, and electric permittivity of wire insulation) on the RLC parameters of a wound inductor extracted from the finite element method. To that end, the finite element method is embedded in a Monte Carlo simulation. We show that considering mentioned different material properties as real random variables, leads to significant variations in the distributions of the RLC parameters.

The paper introduces a new approach to kriging based multi-objective optimization by utilizing a local probability of improvement as the infill sampling criterion and the nearest neighbor check to ensure diversification and uniform distribution of Pareto fronts. The proposed method is computationally fast and linearly scalable to higher dimensions.

Diatoms are microalgae encased in highly structured and regular frustules of porous silica. A long-standing biological question has been the function of these frustules, with hypotheses ranging from them acting as photonic light absorbers to being particle filters. While it has been observed that the girdle band pores of the frustule of Coscinodiscus sp. resemble those of a hydrodynamic drift ratchet, we show using scaling arguments and numerical simulations that they cannot act as effective drift ratchets. Instead, we present evidence that frustules are semi-active filters. We propose that frustule pores simultaneously repel viruses while promoting uptake of ionic nutrients via a recirculating, electroosmotic dead-end pore flow, a new mechanism of "hydrodynamic immunity". [ABSTRACT FROM AUTHOR]

Modern trends in physiology, psychology and cognitive neuroscience suggest that noise is an essential component of brain functionality and self-organization. With adequate noise the brain as a complex dynamical system can easily access different ordered states and improve signal detection for decision-making by preventing deadlocks. Using a stochastic sensitivity function approach, we analyze how sensitive equilibrium points are to Gaussian noise in a bistable energy model often used for qualitative description of visual perception. The probability distribution of noise-induced transitions between two coexisting percepts is calculated at different noise intensity and system stability. Stochastic squeezing of the hysteresis range and its transition from positive (bistable regime) to negative (intermittency regime) are demonstrated as the noise intensity increases. The hysteresis is more sensitive to noise in the system with higher stability. [ABSTRACT FROM AUTHOR]

The stochastic direct simulation method is a numerical scheme for approximating the solutions of ordinary differential equations by path simulations of certain associated Markov jump processes. Its particular features make it suitable especially when applied to ODE systems originating from the spatial discretization of PDEs. The present paper provides further improvements to this basic method, which are based on the predictor–corrector principle. They are made possible by the fact that in its context a full path of the jump process is computed. With this full set of data one can perform either Picard iterations, Runge–Kutta steps, or a combination, with the goal of increasing the order of convergence. The improved method is applied to standard test problems such as a reaction–diffusion equation modeling a combustion process in 1D and 2D as well as to the radiation–diffusion equations, a system of two partial differential equations in two space dimensions which is very demanding from the computational point of view. Further optimization aspects which are also discussed in this paper are related to the efficient implementation of sampling algorithms based on Huffman trees. [ABSTRACT FROM AUTHOR]

Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and furthermore the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods. We initially study with care two special networks, namely the open triplet and closed triangle, for which we can obtain analytical results. We then explore numerically the exactness of moment closures for a wide range of larger motifs, thus gaining understanding of the factors that introduce errors in the approximations, in particular the presence of a random duration of the infectious period and the presence of overlapping triangles in a network. We also derive a simpler and more intuitive proof than previously available concerning the known result that pair-based moment closure is exact for the Markovian SIR model on tree-like networks under pure initial conditions. We also extend such a result to all infectious models, Markovian and non-Markovian, in which susceptibles escape infection independently from each infected neighbour and for which infectives cannot regain susceptible status, provided the network is tree-like and initial conditions are pure. This works represent a valuable step in enriching intuition and deepening understanding of the assumptions behind moment closure approximations and for putting them on a more rigorous mathematical footing. [ABSTRACT FROM AUTHOR]

A new statistical method to study repair mechanism of individual cells exposed to ionizing radiation is presented. The method is based on deviations from the Poisson distribution of observed chromosome aberrations and allows to determine the efficiency of repair mechanisms of individual cells. On basis of the dose-effect curves and the chi-square analysis, the ratio between the variance and the mean value of the observed aberration distribution could be calculated and related to the efficiency of the cellular repair mechanisms. The method has been tested on human lymphocytes and CHO-K1 cells exposed to different radiation species. In the case of high-linear energy transfer ion irradiation a correction due to Neyman A statistics has been introduced. [ABSTRACT FROM AUTHOR]

A large number of studies have recently been carried out on the early signatures of regime shifts in a number of dynamical systems, e.g., ecosystems, the climate, fish and wildlife populations, financial markets, complex diseases and gene circuits. The underlying model in most cases is that of the fold-bifurcation in which a sudden regime shift occurs at a bifurcation point. The shift involves a discontinuous jump from one type of stable steady state to another. The dynamics of natural systems have both deterministic and stochastic components. The early signatures of abrupt regime shifts include the critical slowing down as a transition point is approached, rising variance and the lag-1 autocorrelation function, increased skewness of the steady-state probability distribution and the ratio of two mean first passage times for the exits from the stable steady states as the bifurcation point is approached. Noise-induced regime shifts are also possible for which the vicinity of the bifurcation point is not essential. In this paper, we review examples of regime shifts in natural systems and the associated early signatures. We further discuss how such approaches provide useful insights on a cell biological process involving the fold-bifurcation. [ABSTRACT FROM AUTHOR]

The process of gene regulation is comprised of intrinsically random events resulting in large cell-to-cell variability in mRNA and protein numbers. With gene expression being the central dogma of molecular biology, it is essential to understand the origin and role of these fluctuations. An intriguing observation is that the number of mRNA present in a cell are not only random and small but also that they are produced in bursts. The gene switches between an active and an inactive state, and the active gene transcribes mRNA in bursts. Transcriptional noise being bursty, so are the number of proteins and the subsequent gene expression levels. It is natural to ask the question: what is the reason for the bursty mRNA dynamics? And can the bursty dynamics be shown to be entropically favorable by studying the reaction kinetics underlying the gene regulation mechanism? The dynamics being an out-of-equilibrium process, the fluctuation theorem for entropy production in the reversible reaction channel is discussed. We compute the entropy production rate for varying degrees of burstiness. We find that the reaction parameters that maximize the burstiness simultaneously maximize the entropy production rate. [ABSTRACT FROM AUTHOR]

Noise has been traditionally viewed as undesirable in biology, resulting in disorder, distortion, and disruption, and ultimately as something that needs to be filtered and removed. More recently, it has been shown that noise can also be beneficial. We briefly review historical developments pertaining to noise in biological physics, and some of the current research in the field of molecular and cellular biophysics. [ABSTRACT FROM AUTHOR]

Intermittent transport is frequently observed in nature and has been proven to accelerate search processes at both the macroscopic (e.g., animals looking for food) and microscopic scale (e.g., protein-DNA interactions). In living cells, active transport of membrane proteins (e.g., membrane receptors) or intracellular vesicles (organelles) has been extensively studied as an example of intermittent behavior. The intermittent stochastic process is commonly analyzed in terms of first-passage probabilities. Here we derive exact occupation probabilities of intermittent active transport, making such analysis available for image correlation spectroscopy techniques. The power of this new theoretical framework is demonstrated on intracellular trafficking of lipid/DNA nanoparticles in living cells for which we were allowed to quantify switching time scales.

The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x -direction are allowed only when the y coordinate of the particle is zero. Here, we propose an extension for the comb model via Langevin-like equations driven by fractional Gaussian noises (long-range correlated). By carrying out computer simulations, we show that the correlations in the y -direction affect the diffusive behavior in the x -direction in a non-trivial fashion, resulting in a quite rich diffusive scenario characterized by usual, superdiffusive or subdiffusive scaling of second moment in the x -direction. We further show that the long-range correlations affect the probability distribution of the particle positions in the x -direction, making their tails longer when noise in the y -direction is persistent and shorter for anti-persistent noise. Our model thus combines and allows the study/analysis of the interplay between different mechanisms of anomalous diffusion (geometric constraints and long-range correlations) and may find direct applications for describing diffusion in complex systems such as living cells.