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Cell fate decisions in multicellular organisms are precisely coordinated, leading to highly reproducible macroscopic outcomes of developmental processes. The origins of this reproducibility can be found at the molecular level during the…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
Genomic expression depends critically both on the ability of regulatory proteins to locate specific target sites on a DNA within seconds and on the formation of long lived (many minutes) complexes between these proteins and the DNA.…
Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns…
Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…
We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by $x$ and $v$ respectively, we consider two different resetting protocols - (i) complete…
We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of ``stochastic feedback''. We illustrate this approach by considering the neuroautonomic regulation of the heart…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the…
Using an analytically solvable stochastic model, we study the properties of a simple genetic circuit consisting of multiple copies of an self-regulating gene. We analyse how the variation in gene copy number and the mutations changing the…
An important step towards understanding the mechanistic basis of the central dogma is the quantitative characterization of the dynamics of nucleic-acid-bound molecular motors in the context of the living cell, where a crowded cytoplasm as…
During the initiation stage of protein synthesis, a ribosomal initiation complex (IC) is assembled on a messenger RNA (mRNA) template. In bacteria, the speed and accuracy of this assembly process are regulated by the complementary…
Engineering genetic networks to be both predictable and robust is a key challenge in synthetic biology. Synthetic circuits must reliably function in dynamic, stochastic and heterogeneous environments, and simple circuits can be studied to…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform…
Controlling large swarms of robotic agents presents many challenges including, but not limited to, computational complexity due to a large number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the…
We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and…
It is promising but challenging to design flocking control for a robot swarm to autonomously follow changing patterns or shapes in a optimal distributed manner. The optimal flocking control with dynamic pattern formation is, therefore,…
This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of…