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One important question that interests those who work in chemical reaction network theory (CRNT) is this: Does the system obtained from a reaction network admit a positive equilibrium and if it does, can there be more than one within a…
We propose a new approach to study the long time dynamics of the wave kinetic equation in the statistical description of acoustic turbulence. The approach is based on rewriting the discrete version of the wave kinetic equation in the form…
Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving,…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…
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,…
Stochastic model checking is a technique for analyzing systems that possess probabilistic characteristics. However, its scalability is limited as probabilistic models of real-world applications typically have very large or infinite state…
Swarm robotics has potential for a wide variety of applications, but real-world deployments remain rare due to the difficulty of predicting emergent behaviors arising from simple local interactions. Traditional engineering approaches design…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology. When chemical species and reaction rates in a reaction system have different orders of magnitude, the associated…
The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
The numerical computation of equilibrium reward gradients for Markov chains appears in many applications for example within the policy improvement step arising in connection with average reward stochastic dynamic programming. When the state…
The Chemical Reaction Network (CRN) is a well-studied model that describes the interaction of molecules in well-mixed solutions. In 2014, Qian and Winfree [22] proposed the abstract surface chemical reaction network model (sCRN), which…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
The model of chemical reaction networks is among the oldest and most widely studied and used in natural science. The model describes reactions among abstract chemical species, for instance $A + B \to C$, which indicates that if a molecule…
To implement deep learning models on edge devices, model compression methods have been widely recognized as useful. However, it remains unclear which model compression methods are effective for Structured State Space Sequence (S4) models…