Related papers: Stochastic simulation of binary annihilation react…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schr\"odinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which…
Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
We have calculated accurate quantum reactive and elastic cross-sections for the prototypical barrierless reaction D$^{+}$ + H$_2$($v$=0, $j$=0) using the hyperspherical scattering method. The considered kinetic energy ranges from the…
In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we…
Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
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…
Anderson, Craciun, and Kurtz have proved that a stochastically modelled chemical reaction system with mass-action kinetics admits a stationary distribution when the deterministic model of the same system with mass-action kinetics admits an…
We propose a $\tau$-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional $\tau$-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing…
We consider stochastic population processes that are almost surely absorbed at the origin within finite time. Our interest is in the quasistationary distribution, $\boldsymbol{u}$, and the expected time, $\tau$, from quasistationarity to…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
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…
Multistability of mesoscopic, driven biochemical reaction systems has implications to a wide range of cellular processes. Using several simple models, we show that one class of bistable chemical systems has a deterministic counterpart in…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…