Related papers: Pseudo-Random Fluctuations, Stochastic Cooperativi…
A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…
Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…
Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
Nonlinear systems driven by noise and periodic forces with more than one frequency exhibit the phenomenon of Ghost Stochastic Resonance (GSR) found in a wide and disparate variety of fields ranging from biology to geophysics. The common…
We prove that complex networks of interactions have the capacity to regulate and buffer unpredictable fluctuations in production events. We show that non-bursty network-driven activation dynamics can effectively regulate the level of…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…
A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…
Gas-fired generators, with their ability to quickly ramp up and down their electricity production, play an important role in managing renewable energy variability. However, these changes in electricity production translate into variability…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
This paper considers adiabatic reduction in both discrete and continuous models of stochastic gene expression. In gene expression models, the concept of bursting is a production of several molecules simultaneously and is generally…
The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the…