Related papers: A modified Next Reaction Method for simulating che…
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…
High-density microfluidics is becoming an important experimental platform for studying complex biological systems such as synthetic gene regulatory networks, molecular biocomputating of engineered cells, distributing rapid point-of-care…
We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
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…
We develop a broadly-applicable computational method for the automatic exploration of the bimolecular multi-reaction mechanism. The current methodology mainly involves the high-energy Born-Oppenheimer molecular dynamics (BOMD) simulation…
Understanding the mechanisms of explosions is important for minimizing devastating hazards. Due to the complexity of real chemistry, a single-step reaction mechanism is usually used for theoretical and numerical studies. The purpose of this…
The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
Understanding molecular structure, dynamics, and reactivity requires bridging processes that occur across widely separated time scales. Conventional molecular dynamics simulations provide atomistic resolution, but their femtosecond time…
Let $X$ be a chemical reaction process, modeled as a multi-dimensional continuous-time jump process. Assume that at given times $0< t_1 < \cdots <t_n$, linear combinations $v_i = L_i X(t_i),\, i=1,\dots ,n$ are observed for given matrices…
Chemical reaction network is an important method for modeling and exploring complex biological processes, bio-chemical interactions and the behavior of different dynamics in system biology. But, formulating such reaction kinetics takes…
This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such…
Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy…
We describe a new computational method for the numerically stable particle-based simulation of open-boundary flows, including volume conserving chemical reactions. The novel method is validated for the case of heterogeneous catalysis…
Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background,…
Chemical kinetic mechanisms can be represented by sets of elementary reactions that are easily translated into mathematical terms using physicochemical relationships. The schematic representation of reactions captures the interactions…