Related papers: Computing with reaction networks at input-independ…
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
The notion of Reactive Turing machine (RTM) was proposed as an orthogonal extension of Turing machines with interaction. RTMs are used to define the notion of executable transition system in the same way as Turing machines are used to…
For many data-processing applications, a comprehensive set of efficient operations for the management of priority values is required. Indexed priority queues are particularly promising to satisfy this requirement by design. In this work, we…
An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and…
In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the…
Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is…
This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…
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…
Chemical reaction networks (CRNs) model systems where molecules interact according to a finite set of reactions such as $A + B \to C$, representing that if a molecule of $A$ and $B$ collide, they disappear and a molecule of $C$ is produced.…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific…
A variety of natural phenomena comprises a huge number of competing reactions and short-lived intermediates. Any study of such processes requires the discovery and accurate modeling of their underlying reaction network. However, this task…
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…
Molecular computation based on chemical reaction networks (CRNs) has emerged as a promising paradigm for designing programmable biochemical systems. However, the implementation of complex computations still requires excessively large and…
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…
Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $\mathsf{Q}$, since $\exp…
Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges…
Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed,…