相关论文: An algebraic approach to product-form stationary d…
Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally…
In a previous paper we determined one dimensional distributions of a stationary field with linear regressions and quadratic conditional variances under a linear constraint on the coefficients of the quadratic expression. In this paper we…
Conditional belief networks introduce stochastic binary variables in neural networks. Contrary to a classical neural network, a belief network can predict more than the expected value of the output $Y$ given the input $X$. It can predict a…
This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the…
In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…
Nonlinear Markov chains with finite state space have been introduced in Kolokoltsov (2010). The characteristic property of these processes is that the transition probabilities do not only depend on the state, but also on the distribution of…
Owing to exhibiting phase transitions, we investigate the local convergence near a stationary distribution for distribution dependent stochastic differential equations. By linearizing the nonlinear Markov semigroup associated with the…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…
Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when one truncates an infinite state Markov chain…
We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…
We establish a generalized work theorem for stochastic chemical reaction networks (CRNs). By using a compensated Poisson jump process, we identify a martingale structure in a generalized entropy defined relative to an auxiliary backward…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
In order to fully exploit the potential of molecular communication (MC) for intra-body communication, practically implementable cellular receivers are an important long-term goal. A variety of receiver architectures based on chemical…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…