Related papers: Modeling delay in genetic networks: From delay bir…
Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed…
Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…
Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
The expression of genes usually follows a two-step procedure. First, a gene (encoded in the genome) is transcribed resulting in a strand of (messenger) RNA. Afterwards, the RNA is translated into protein. Classically, this gene expression…
Delays in protein synthesis cause a confounding effect when constructing Gene Regulatory Networks (GRNs) from RNA-sequencing time-series data. Accurate GRNs can be very insightful when modelling development, disease pathways, and drug…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the…
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…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
A method to direct evaluation of expectations for Langevin systems (stochastic differential equations) is proposed. The method is based on a birth-death process which is derived using combinations of dummy variables and It{\^o} formula. As…
We show that simple stochastic models of genome evolution lead to power law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation Models (BDIM), represent a special class of balanced…
Time-varying delays adversely affect the performance of networked control sys-tems (NCS) and in the worst-case can destabilize the entire system. Therefore, modelling network delays is important for designing NCS. However, modelling…
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay…
To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…
We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…