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The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Important workloads, such as machine learning and graph analytics applications, heavily involve sparse linear algebra operations. These operations use sparse matrix compression as an effective means to avoid storing zeros and performing…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
Molecular discovery within the vast chemical space remains a significant challenge due to the immense number of possible molecules and limited scalability of conventional screening methods. To approach chemical space exploration more…
The model of chemical reaction networks is among the oldest and most widely studied and used in natural science. The model describes reactions among abstract chemical species, for instance $A + B \to C$, which indicates that if a molecule…
Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or…
There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in…
Placing signal templates (grid points) as efficiently as possible to cover a multi-dimensional parameter space is crucial in computing-intensive matched-filtering searches for gravitational waves, but also in similar searches in other…
This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations.…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
Quantum computing has recently exhibited great potentials in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such…
A new algorithm, "HiER-leap", is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or…
Numerous algorithms and parallelisations have been developed for short-range particle simulations; however, none are optimally performant for all scenarios. Such a concept led to the prior development of the particle simulation library…
This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et…
Over the billions of years since the Big Bang, the lives, deaths and afterlives of stars have enriched the Universe in the heavy elements that make up so much of ourselves and our world. This review summarizes the methods used to evolve…
We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The…