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This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Complex systems can be advantageously modeled by formal reaction systems (RS), a.k.a. chemical reaction networks in chemistry. Reaction-based models can indeed be interpreted in a hierarchy of semantics, depending on the question at hand,…
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…
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…
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural…
Reinforcement learning (RL) under changing environment models many real-world applications via nonstationary Markov Decision Processes (MDPs), and hence gains considerable interest. However, theoretical studies on nonstationary MDPs in the…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
In this paper, we study various theoretical properties of a class of prioritized inverse kinematics (PIK) solutions that can be considered as a class of (output regulation or tracking) control laws of a dynamical system with prioritized…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
In this paper, we provide a detailed theoretical analysis of the numerical scheme introduced in J. Comput. Phys. 436 (2021) 110253 for the reaction kinetics of a class of chemical reaction networks that satisfies detailed balance condition.…
State space truncation methods are widely used to approximate solutions of the chemical master equation. While most methods of this kind focus on truncating the state space directly, in this work we propose modifying the underlying chemical…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of…
Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a…
Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as…
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…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…