Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise

Dynamics of a single anisotropic particle under various resetting protocols

We study analytically the dynamics of an anisotropic particle subjected to different stochastic resetting schemes in two dimensions. The Brownian motion of shape-asymmetric particles in two dimensions results in anisotropic diffusion at short times, while the late-time transport is isotropic due to rotational diffusion. We show that the presence of orientational resetting promotes the anisotropy to late times. When the spatial and orientational degrees of freedom are reset, we find that a non-trivial spatial probability distribution emerges in the steady state that is determined by the initial orientation, particle asymmetry and the resetting rate. When only spatial degrees of freedom are reset while the orientational degree of freedom is allowed to evolve freely, the steady state is independent of the particle asymmetry. When only particle orientation is reset, the late-time probability density is given by a Gaussian with an effective diffusion tensor, including off-diagonal terms, determined by the resetting rate. Generally, the coupling between the translational and rotational degrees of freedom, when combined with stochastic resetting, gives rise to unique behavior at late times not present in the case of symmetric particles. Considering recent developments in experimental implementations of resetting, our results can be useful for the control of asymmetric colloids, for example in self-assembly processes.

Stochastic response analysis of a birhythmic oscillator under Poisson white noise excitation via path integration method

This paper investigates the stochastic response of a classical model of the birhythmic Van der Pol oscillator under Poisson white noise excitation. The improved path integration (PI) method is comprehensively derived in this paper and the probability density of the system is calculated using this method. Monte Carlo simulations are employed to validate the accuracy of the improved PI method. The findings reveal that the nonlinear parameters of the system significantly influence the mechanism by which Poisson white noise impacts the birhythmic oscillator. For the stationary response, we compare the effects of Gaussian white noise and Poisson white noise at equivalent intensities, and specifically analyze the mechanisms of two key parameters of Poisson white noise. This analysis offers general insights into the mechanisms by which Poisson noise impacts the birhythmic oscillator. For transient response, the occurrence time of birhythmicity, along with the system's probability distribution at different moments, are influenced by random perturbations, yet the nonlinear parameters of the system remain pivotal factors. This study provides a perspective for investigating the dynamic behavior of birhythmic oscillators under discontinuous stochastic disturbances.

Understanding the Target Search by Multiple Transcription Factors on Nucleosomal DNA

The association of multiple Transcription Factors (TFs) in the cis-regulatory region is imperative for developmental changes in eukaryotes. The underlying process is exceedingly complex, and it is not at all clear what orchestrates the overall search process by multiple TFs. In this study, by developing a theoretical model based on a discrete-state stochastic approach, we investigated the target search mechanism of multiple TFs on nucleosomal DNA. Experimental kinetic rate constants of different TFs are taken as input to estimate the Mean-First-Passage time to recognize the binding motifs by two TFs on a dynamic nucleosome model. The theory systematically analyzes when the TFs search their binding motifs hierarchically and when simultaneously by proceeding via the formation of a protein-protein complex. Our results, validated by extensive Monte Carlo simulations, elucidate the molecular basis of the complex target search phenomenon of multiple TFs on nucleosomal DNA.

Time-averaging and nonergodicity of reset geometric Brownian motion with drift

How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Δ)≠TAMSD(Δ) and Variance(Δ)≠TAMSD(Δ) at short lag times Δ and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Δ/T≪1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.

Scheduling control method of Internet of things data uplink based on TS algorithm

In order to ensure the efficiency of link scheduling control and improve the accuracy and energy efficiency of scheduling control, a scheduling control method for Internet of things data uplink based on TS algorithm is proposed.The principle of tabu search algorithm is analyzed, and the scheduling control function of Internet of things data uplink is constructed. Tabu search algorithm is used to solve the scheduling control problem of Internet of things data uplink, and realize the scheduling control of Internet of things data uplink.The experimental results show that the scheduling control energy efficiency of the proposed method is as high as 10.4 bit/j, the link scheduling control packet loss rate of the proposed method is only 1.4%, and the scheduling control energy efficiency is as high as 10.4 bit/j, which can effectively improve the scheduling control accuracy and energy efficiency.

Kinetic origin of nucleosome invasion by pioneer transcription factors

Recently, a cryo-electron microscopy study has captured different stages of nucleosome breathing dynamics that show partial unwrapping of DNA from histone core to permit transient access to the DNA sites by transcription factors. In practice, however, only a subset of transcription factors named pioneer factors can invade nucleosomes and bind to specific DNA sites to trigger essential DNA metabolic processes. We propose a discrete-state stochastic model that considers the interplay of nucleosome breathing and protein dynamics explicitly and estimate the mean time to search the target DNA sites. It is found that the molecular principle governing the search process on nucleosome is very different compared to that on naked DNA. The pioneer factors minimize their search times on nucleosomal DNA by compensating their nucleosome association rates by dissociation rates. A fine balance between the two presents a tradeoff between their nuclear mobility and error associated with the search process.