Related papers: Path integrals for stochastic hybrid reaction-diff…
In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump…
By returning to the underlying discrete time formalism, we relate spurious results in coherent state path integral calculations to the high frequency structure of their propagators. We show how to modify the standard expressions for…
We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system on a one dimensional domain. The domain has two subregions which share a single common boundary. Each of…
Chemical reaction networks offer a natural nonlinear generalisation of linear Markov jump processes on a finite state-space. In this paper, we analyse the dynamical large deviations of such models, starting from their microscopic version,…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
The path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet…
Systems driven by Brownian motion are ubiquitous. A prevailing challenge is inferring, from data, the diffusion and kinetic parameters that describe these stochastic processes. In this work, we investigate a multi-state diffusion process…
As computational chemistry methods evolve, dynamic effects have been increasingly recognized to govern chemical reaction pathways in both organic and inorganic systems. Here, we introduce a committor-based workflow that integrates a…
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We describe a new path integral approach to strongly correlated fermion systems, considering the Hubbard model as a specific example. Our approach is based on the introduction of spin-particle-hole coherent states which generalize the…
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random…