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Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
The Gene Regulatory Network (GRN) of biological cells governs a number of key functionalities that enables them to adapt and survive through different environmental conditions. Close observation of the GRN shows that the structure and…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
The Unfolded Protein Response is the cell mechanism for maintaining the balance of properly folded proteins in the endoplasmic reticulum , the specialized cellular compartment. Although it is largely studied from a biological point of view,…
Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data…
In this technical note we calculate the dynamics of a linear feedback model of progression in the cell cycle in the case that the cells are organized into k=3 clusters. We examine the dynamics in detail for a specific subset of parameters…
This paper proposes a data-driven approach to design a feedforward Neural Network (NN) controller with a stability guarantee for plants with unknown dynamics. We first introduce data-driven representations of stability conditions for Neural…
Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For…
A new method for stability assessment of inverter-based microgrids is presented in this paper. It leverages the notion of critical clusters -- a localized group of inverters with parameters having the highest impact on the system stability.…
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…
Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the…
The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. In 2000, Elowitz and Leibler showed that by rational design of the reaction network, and using existing…
Determining a stability domain, i.e. a set of equilibria for which a dynamical system remains stable, is a core problem in control. When dealing with controlled systems, the problem is generally transformed into a robustness analysis…
The Newton-Raphson Controller, established on the output prediction and the Newton-Raphson algorithm, is shown to be effective in a variety of control applications. Although the stability condition of the controller for linear systems has…