Related papers: A Simple Noise Model with Memory for Biological Sy…

This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…

We study the effects of propagation delays on the stochastic dynamics of bumps in neural fields with multiple layers. In the absence of noise, each layer supports a stationary bump. Using linear stability analysis, we show that delayed…

Extensive studies have shown that deep learning models are vulnerable to adversarial and natural noises, yet little is known about model robustness on noises caused by different system implementations. In this paper, we for the first time…

The phenomena of stochasticity in biochemical processes have been intriguing life scientists for the past few decades. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others.…

With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable to the typical relaxation time of the channel environment. We introduce a model of a bosonic…

We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…

Human history leaves fingerprints in human languages. Little is known over language evolution and its study is of great importance. Here, we construct a simple stochastic model and compare its results to statistical data of real languages.…

We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any…

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…

Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…

Large language models readily memorize arbitrary training instances, such as label noise, yet they perform strikingly well on reasoning tasks. In this work, we investigate how language models memorize label noise, and why such memorization…

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…

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus…

Generative diffusion models have emerged as leading models in speech and image generation. However, in order to perform well with a small number of denoising steps, a costly tuning of the set of noise parameters is needed. In this work, we…

Synaptic integration is a prominent aspect of neuronal information processing. The detailed mechanisms that modulate synaptic inputs determine the computational properties of any given neuron. We study a simple model for the summation of…

We study a dephasing channel with memory, described by a Hamiltonian model in which the system-environment interaction is described by a stochastic process. We propose a useful way to describe the channel uses correlations. Moreover, we…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and…

Stochastic models for collections of interacting populations have crucial roles in scientific fields such as epidemiology and ecology, yet the standard approach to extending an ordinary differential equation model to a Markov chain does not…