相关论文: Coarse graining of master equations with fast and …

In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…

We investigate the multi-chain version of the Chemical Master Equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a…

We consider two different ways of representing stochastic matrices by bi-stochastic ones acting on a larger probability space, referred to as ``dilation by uniform coarse graining" and ``environmental dilation". The latter is motivated by…

Two crucial for the breakdown of the master equation arguments are put forward. The first one is related to the violence of a fundamental requirement to the notion of state (thermodynamical) variable, namely: a state variable is defined…

This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…

For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…

In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…

This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment…

We consider chemical reaction networks taken with mass action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop…

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…

We present a novel reformulation of nonsmooth differential equations with state jumps which enables their easier simulation and use in optimal control problems without the need of using integer variables. The main idea is to introduce an…

We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. We distill entanglement from such states by projecting n copies of…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…

We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum…

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two…

We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focussing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form.…

Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows…