Related papers: Efficient implementation of the hybrid method for …
The effective Hamiltonian method is a powerful tool for simulating large-scale systems across a wide range of temperatures. However, previous methods for constructing effective Hamiltonian models suffer from key limitations: some require to…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any…
Stochastic variance reduced optimization methods are known to be globally convergent while they suffer from slow local convergence, especially when moderate or high accuracy is needed. To alleviate this problem, we propose an optimization…
Dose-finding trials are a key component of the drug development process and rely on a statistical design to help inform dosing decisions. Triallists wishing to choose a design require knowledge of operating characteristics of competing…
Stochastic HYPE is a novel process algebra that models stochastic, instantaneous and continuous behaviour. It develops the flow-based approach of the hybrid process algebra HYPE by replacing non-urgent events with events with…
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…
Efficient hybrid DFT simulations of solid state materials would be extremely beneficial for computational chemistry and materials science, but is presently bottlenecked by difficulties in computing Hartree-Fock (HF) exchange with plane wave…
The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects…
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
Reaction systems are a computational model inspired by the bio-chemical reactions that happen inside biological cells. They have been and currently are studied for their many nice theoretical properties. They are also a useful modeling tool…
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…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be…
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…