Related papers: Variable elimination in post-translational modific…

This paper addresses a structural design problem in control systems, and explicitly takes into consideration the possible application to large-scale systems. More precisely, we aim to determine and characterize the minimum number of…

A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…

We analyze the solutions, on single network instances, of a recently introduced class of constraint-satisfaction problems (CSPs), describing feasible steady states of chemical reaction networks. First, we show that the CSPs generalize the…

In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…

A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a comprehensive description of biochemical networks by considering individual atoms and…

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…

We provide a short supplement to the paper "MAPK networks and their capacity for multistationarity due to toric steady states" by P\'erez Mill\'an and Turjanski. We show that the capacity for toric steady states in the three networks…

Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…

We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are…

A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the…

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…

Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…

The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…

Biological organisms are open, adaptve systems that can respond to changes in environment in specific ways. Adaptation and response can be posed as an optimization problem, with a tradeoff between the benefit obtained from a response and…

Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give…