Related papers: Asymptotic Robustness in Biochemical Systems
The functioning of many biochemical networks is often robust -- remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly…
In this essay, we investigate some relations between Chemical Reaction Networks (CRN) and Mathematical Epidemiology (ME) and report on several pleasant surprises which we had simply by putting these two topics together. Firstly, we propose…
Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…
The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
A biological system achieve homeostasis when there is a regulated quantity that is maintained within a narrow range of values. Here we consider homeostasis as a phenomenon of network dynamics. In this context, we improve a general theory…
Cells attach to their environment by means of focal adhesions, which are molecular complexes that exhibit the remarkable ability to adapt to mechanical load by changing their size. Drawing from the biomolecular mechanisms underlying this…
Anomalous Hall crystals (AHCs) are exotic phases of matter that simultaneously break continuous translation symmetry and exhibit the quantum anomalous Hall effect. AHCs have recently been proposed to explain the observation of an integer…
Biochemical oscillations are ubiquitous in nature and allow organisms to properly time their biological functions. In this paper, we consider minimal Markov state models of nonequilibrium biochemical networks that support oscillations. We…
Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, the…
We consider Activated Random Walk (ARW), a model which generalizes the Stochastic Sandpile, one of the canonical examples of self organized criticality. Informally ARW is a particle system on $\mathbb{Z}$ with mass conservation. One starts…
A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…
Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
This paper theoretically investigates the closed-loop performance of active disturbance rejection control (ADRC) on a third-order linear plant with relative degree 3, subject to a class of exogenous disturbances. While PID control cannot be…