Related papers: Herding model and 1/f noise
We study macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be alpha-stable whenever they are delta-correlated (white). For the case of…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of…
Gene expression is inherently a noisy process which manifests as cell-to-cell variability in time evolution of proteins. Consequently, events that trigger at critical threshold levels of regulatory proteins exhibit stochasticity in their…
We develop a microscopic transport theory in a randomly driven fermionic model with and without linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of…
We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window $[t_w,t_w+t_m]$, namely the observation started after a waiting time…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…
We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the…
We consider Hilbert-valued evolution equations driven by H\"{o}lder paths with H\"{o}lder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be…
Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We…
We study the information transfer model for biological evolution with several kinds of fitness function. The system is stimulated to volve into a stationary state, depending on the fitness function and on the dimension of the lattice formed…
Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^\alpha$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of…
Fractional killing in response to drugs is a hallmark of non-genetic cellular heterogeneity. Yet how individual lineages evade drug treatment, as observed in bacteria and cancer cells, is not quantitatively understood. We analyse a…
We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the $q$-th power of the number of the…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
In systems with weak ergodicity breaking, the equivalence of time averages and ensemble averages is known to be broken. We study here the computation of the power spectrum from realizations of a specific process exhibiting 1/f^beta noise,…
In this paper it is demonstrated that a 1/f power spectrum appears in the process originated by the superposition of many similar single-sided RTN processes with the same relaxation time. The non-relaxed regime, the Gaussian nature and the…
In the classic herding model, agents receive private signals about an underlying binary state of nature, and act sequentially to choose one of two possible actions, after observing the actions of their predecessors. We investigate what…
We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state…
We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled…