Influence Of Random Fluctuations Research Articles

Stochastic Modeling of Bacterial Population Growth with Antimicrobial Resistance

In this paper we consider a stochastic model of bacterial population growth with antimicrobial resistance under the influence of random fluctuations. We analyze the model for the problem of persistence and extinction of bacterial cells. This analysis shows asymptotic extinction and conditional persistence for growing population. Moreover, we perform computer simulations in order to illustrate the model behavior. The model results have important implications for the eradication of bacterial cells and the emergence of resistance.

ON MODELLING WATER QUALITY WITH STOCHASTIC DIFFERENTIAL EQUATIONS

AbstractBased on biochemical kinetics, a stochastic model to characterize wastewater treatment plants and dynamics of river water quality under the influence of random fluctuations is proposed in this paper. This model describes the interaction between dissolved oxygen (DO) and biochemical oxygen demand (BOD), and is in the form of stochastic differential equations driven by multiplicative Gaussian noises. The stochastic persistence problem for the model of the system is analysed. Further, a numerical simulation of the stationary probability distributions of BOD and OD by approximations of the stochastic process solution is presented. These results have implications for the prediction and control of pollutants.

Improvement of Strain Measurement Accuracy and Resolution by Dual-Slope-Assisted Chaotic Brillouin Optical Correlation Domain Analysis

A dual-slope-assisted chaotic Brillouin optical correlation domain analysis (DSA-CBOCDA) technique is proposed to improve the measurement accuracy and resolution for static and dynamic strain sensing. By using the gain ratio obtained from two slopes of the Brillouin gain spectrum (BGS), the influence of random fluctuation in chaotic pump power on the measurement result is alleviated. Compared with the previous single-slope-assisted CBOCDA, the measurement accuracy of the DSA-CBOCDA is improved from 25.0 μϵ to 3.9 μϵ for the static strain, and from 28.5 μϵ to 6.2 μϵ for the dynamic strain. Meanwhile, the static strain resolution of 10 μϵ and dynamic strain resolution of 15 μϵ are verified in the experiment. Moreover, the dynamic strain measurement range of 800 μϵ for the proposed DSA-CBOCDA system is also experimentally confirmed, which is approximately fivefold larger than the current DSA-based Brillouin sensing system.

Tumor Stabilization Induced by T-Cell Recruitment Fluctuations

The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated immune response for which chaotic and periodic oscillations coexist together with stable tumor dynamics. A thorough parametric analysis of the noise-induced transition from this oscillatory regime to complete tumor dominance is carried out. A hysteresis phenomenon is uncovered, which stabilizes the tumor at its carrying capacity and drives the healthy and the immune cell populations to their extinction. Furthermore, it is shown that near a crisis bifurcation, such transitions occur under weak noise intensities. Finally, the corresponding noise-induced chaos-order transformation is analyzed and discussed in detail.

Impact of Discretization Units on the Modelling Efficiency of Currency Exchange Rate in Binary Representation

Exchange rate course trajectory can be visualised in a binary representation. Binarization algorithm involves transformation of a course represented by tic data into a respective binary string. Each exchange rate increase by one discretization unit is assigned a binary value 1, and a respective decrease is assigned a 0. Properties and character of the exchange rate course in binary representation, that is, for example, influence of random fluctuations (noise) or relationship between current changes and historical data, are dependent on the appointed discretization unit. In the article a statistical analysis of an exchange rate trajectory for AUD/NZD currency pair in binary representation with different discretization units is presented. The analysis was performed in order to verify possible application of binary representation to create prediction systems based on binary representation state model (BRSM). Data used in performed research consisted of tick data for AUD/NZD from a five-year time period 2012–2017.

Viral dynamics of an HIV stochastic model with cell-to-cell infection, CTL immune response and distributed delays.

Recent studies have demonstrated that both virus-to-cell infection and cell-to-cell transmission play an important role in the process of HIV infection. In this paper, stochastic perturbation is introduced into HIV model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and three distributed delays. The stochastic integro-delay differential equations is transformed into a degenerate stochastic differential equations. Through rigorous analysis of the model, we obtain the solution is unique, positive and global. By constructing appropriate Lyapunov functions, the existence of the stationary Markov process is derived when the critical condition is bigger than one. Furthermore, the extinction of the virus for sufficiently big noise intensity is established. Numerically, we investigate that the small noise intensity of fluctuations could help to sustain the number of virions and CTL immune response within a certain range, while the big noise intensity may be beneficial to the extinction of the virus. We also examine that the influence of random fluctuations on model dynamics may be more significant than that of the delay.

Elementary bifurcations for a simple dynamical system under non-Gaussian Lévy noises

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation or P-bifurcation, for stochastic differential equations with non-Gaussian Lévy noises.

Influence of Random Fluctuations in the Λ‐Effect on Meridional Flow and Differential Rotation

We present a mean field model based on the approach taken by Rempel (astro-ph/0604451) in order to investigate the influence of stochastic fluctuations in the Reynolds stresses on meridional flow and differential rotation. The stochastic fluctuations found in the meridional flow pattern directly resemble the stochastic fluctuations of the Reynolds stresses, while the stochastic fluctuations in the differential rotation are smaller by almost two orders of magnitude. It is further found that the correlation length and time scale of the stochastic fluctuations have only a weak influence on meridional flow, but a significant influence on the magnitude of variations in the differential rotation. We analyze the energy fluxes within the model to estimate time scales for the replenishment of differential rotation and meridional flow. We find that the time scale for the replenishment of differential rotation (~10 years) is nearly four orders of magnitude longer than the time scale for the replenishment of meridional flow, which explains the differences in the response to stochastic fluctuations of the Reynolds stress found for both flow fields.

Computer-simulation investigation of nonlinear transport dynamics in a compensated semiconductor during low-temperature electric breakdown

The possibility of chaotic behavior of the current in a partially compensated semiconductor during low-temperature electrical breakdown is explored by computer simulation. The influence of random fluctuations in the parameters or the variables of the mathematical model, as well as the effect of some weak periodic disturbances of the current density in the semiconductor, are discussed. As a result, various pictures of chaotic oscillations of the current are obtained, including a transition to a chaotic regime through period doubling, which is characteristic of the Feigenbaum scenario.

The significance of digital gene expression profiles.

Genes differentially expressed in different tissues, during development, or during specific pathologies are of foremost interest to both basic and pharmaceutical research. "Transcript profiles" or "digital Northerns" are generated routinely by partially sequencing thousands of randomly selected clones from relevant cDNA libraries. Differentially expressed genes can then be detected from variations in the counts of their cognate sequence tags. Here we present the first systematic study on the influence of random fluctuations and sampling size on the reliability of this kind of data. We establish a rigorous significance test and demonstrate its use on publicly available transcript profiles. The theory links the threshold of selection of putatively regulated genes (e.g., the number of pharmaceutical leads) to the fraction of false positive clones one is willing to risk. Our results delineate more precisely and extend the limits within which digital Northern data can be used.

Partition of phase and magnitude contributions in residual variance analysis

This paper presents a method that can decompose the total residual variance between the observations and numerical model predictions into two components: one due to the pure magnitude differences and the other due to the spatial and temporal mismatches, or the so‐called “phase errors.” Quantitative separation of these two components makes it possible to explicitly estimate their individual contributions to residual variabilities in numerical model predictions. The influence of random fluctuations in the data on residual variance between the observed and predicted fields has been simulated and discussed. It is found that random fluctuations on the average increase the residual variance through essentially the artificial phase errors which they create. The major impact of random fluctuations, however, occurs when the true observed and predicted fields are nearly in phase. Assuming the signal‐to‐noise ratio to be greater than 4.5, the simulation results suggest that for the proportion Q of the residual sum of squares attributable to spatial and temporal mismatches to exceed 0.71, it would strongly suggest that a real (spatial and/or temporal) phase error may exist. In numerical modeling, large Q coupled with large residual variance but small mean residual is often a reflection of compensating errors arising from physical discrepancies such as inaccurate simulation of dynamic transport or improper source allocations. Thus this method provides an additional tool to diagnose the underlying problems of model predictions.

Influence of random fluctuations on delayed bifurcations. II. The cases of white and colored additive and multiplicative noise.

The influence of noise on the delay of a bifurcation point in the presence of a swept control parameter has been investigated theoretically, by digital simulation and by analog electronic experiment. The results obtained in an earlier paper [N. G. Stocks, R. Mannella, and P. V. E. McClintock, Phys. Rev. A 40, 5361 (989)] have thereby been extended and complemented. In particular, exact analytic expressions have been derived for the time-dependent probability densities P(x,t), and these have been used to obtain the mean first-passage time t*MFPT for x^2(t) to reach a threshold under the influence of Gaussian fluctuations, in several contexts: additive external white noise, additive external exponentially correlated noise, additive internal white noise, additive internal exponentially correlated noise, multiplicative white and colored noise. Based on Zeghlache, Mandel, and Van den Broeck's [Phys. Rev. A 40, 286 (989)] alternative definition of the bifurcation time t*moment in terms of the evolution of the second moment [x^2(t)], an expression is derived for t*moment for the general case of combined additive and multiplicative noises. The calculations are tested by comparison with the results of analog experiments and digital simulations, with which they are shown to be in excellent agreement.

The Curie temperature of multilayer films with aperiodic compositional modulation

The influence of random fluctuations in modulation amplitude, thickness of layers, and width of interdiffusion zones on the Curie temperature of compositionally modulated magnetic films is studied in the molecular field approximation. The Curie temperature has been found to be most sensitive to the fluctuations in the modulation amplitude, which give rise to some kind of localized magnetism in the film. >

Influence of random fluctuations on delayed bifurcations: The case of additive white noise.

The influence of additive white noise on the delay of a bifurcation point in the presence of a swept control parameter has been studied by analog experiment and digital simulation. Measurements of the time taken for the second moment [x^2(t)] to reach a given threshold are in excellent agreement with the calculations of Zeghlache, Mandel, and Van den Broeck [Phys, Rev. A 40, 286 (1989)). It is demonstrated, however, that the mean first-passage time (MFPT) for x^2(t) to attain the same threshold, corresponding to the quantity that is usually determined in laser experiments, can be markedly different. It may be either larger or smaller, depending on the conditions under which the measurements are made. A calculation of the MFPT is presented and shown to be in excellent agreement with the experimental measurements and to reduce, in the relevant limit, to the theoretical results previously published by Torrent and San Miguel [Phys. Rev. A 38, 245 (1988)].

On the deterministic and stochastic stability of dissipative magnetohydrodynamic equilibria

The deterministic and stochastic stability of stationary equilibria of dissipative magnetohydrodynamics is discussed using the direct Liapunov method. The influence of random fluctuations on the stability is studied using three stochastic models.

Kinetics of the adsorption of a mixture of two substances from a flux

1. The kinetics of the adsorption of a mixture of two substances (1 and 2), when the limiting step of the process is external mass exchange, and adsorption occurs on an adsorbent initially saturated with component 2, was considered. 2. The case of displacement desorption (substance 2 is absent in the flux) was also investigated. 3. The influence of random fluctuations of the concentration of the displacing component on the process of displacement desorption was considered. It was shown that these fluctuations slow down the indicated process.

Experimental study of random fluctuation effects on spinodal-like decomposition of Al-15 at.% Zn

The influence of random fluctuations upon the kinetics of decomposition of an Al-15 at.%Zn alloy has been observed at −45°C by absolute small angle X-ray scattering measurements. Although the alloy at that temperature should be inside the spinodal, the experimental results show important deviations from the predictions of Cahn's theory, mainly in the high wavenumber region, as was already observed in previous similar studies. A correction was introduced following Cook's scheme to allow for random fluctuations, but agreement with theoretical predictions does not follow; instead, new inconsistencies appear. A new reformulation of the theory by de Fontaine and Cook, which takes into account both fluctuations and the lattice of the solid solution, allows an interpretation of the results consistent with theoretical predictions and previous experimental results. However, it should be noted that the second composition derivative of the free energy at the experiment temperature cannot be obtained by extrapolation of the high temperature data.