26 papers · ranked by Valyu relevance
Shuze Liu, Shuhang Chen, Shangtong Zhang
Stochastic approximation is a class of algorithms that update a vector iteratively, incrementally, and stochastically, including, e.g., stochastic gradient descent and temporal difference learning. One fundamental challenge in analyzing a stochastic approximation algorithm is to establish its stability, i.e., to show…
Xiaochi Qian, Zixuan Xie, Xinyu Liu, Shangtong Zhang
Approximation and Reinforcement Learning with Markovian Noise Authors: ['Xiaochi Qian' 'Zixuan Xie' 'Xinyu Liu' 'Shangtong Zhang'] This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms…
Gang Wang, Bingcong Li, Georgios B. Giannakis
Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the underlying stochastic noise sequence. Building upon a carefully designed multistep…
Chen Wang
There is an increasing need in solving high-dimensional optimization problems under nondeterministic environment. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for solving high-dimensional optimization problems where the analytical formula cannot…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Giorgos Minas, David A Rand
In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these…
Christoph Zimmer, Sven Sahle
Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the ‘multiple…
José Augusto Fontenele Magalhães, Muhammad Fuady Emzir, Francesco Corona
In order to characterise the dynamics of a biochemical system such as the chemostat, we consider a differential description of the evolution of its state under environmental fluctuations. We present solutions to the filtering problem for a chemostat subjected to geometric Brownian motion. Under this modelling…
James Holehouse, Augustinas Sukys, Ramon Grima
We derive an approximate closed-form solution to the chemical master equation describing the Michaelis-Menten reaction mechanism of enzyme action. In particular, assuming that the probability of a complex dissociating into enzyme and substrate is significantly larger than the probability of a product formation event…
Fern Y. Hunt, Roldan Pozo
We present scalable first hitting time methods for finding a collection of nodes that enables the fastest time for the spread of consensus in a network. That is, given a graph G = (V, E) and a natural number k, these methods find k vertices in G that minimize the sum of hitting times (expected number of steps of random…
Davoud Mirzaei
| Contents | 1 | Deterministic vs. | Stochastic | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |…
Richard M. Jiang, Fredrik Wrede, Prashant Singh, Andreas Hellander + 1 more
'Linda R. Petzold'] Background Approximate Bayesian Computation (ABC) has become a key tool for calibrating the parameters of discrete stochastic biochemical models. For higher dimensional models and data, its performance is strongly dependent on having a representative set of summary statistics. While regression-based…
Ignacio A. Rodriguez-Brenes, Dominik Wodarz, Natalia L. Komarova
Spatial stochastic simulations of evolutionary processes are computationally expensive. Here, based on spatially explicit decoupling approximations (SEDA) introduced in [1], we derive a deterministic approximation to a spatial stochastic birth-death process in the presence of two types: the less advantageous resident…
Authors not listed
Molecular Polariton is becoming one of the leading directions to control a multitude of chemical and physical processes, such as charge transfer, selective bond breaking, and excited state dynamics. Accurately and efficiently simulating polariton properties under the collective coupling regimes (between $N$ molecules…
Migran N. Gevorkyan, Tatyana R. Velieva, Anna V. Korolkova, Dmitry S. Kulyabov + 1 more
'Dmitry S. Kulyabov' 'L. A. Sevastyanov'] As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker–Planck equation)…
Riccardo Mannella, Aneta Stefanovska, Philip C.E. Stamp, Mark Dykman + 2 more
The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and…
Lucy Ham, Megan A. Coomer, Michael P. H. Stumpf
Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly…
Pier Paolo Poir, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Muhammad Zafarullah Baber, Wael W. Mohammed, Nauman Ahmed, Muhammad Sajid Iqbal
'Muhammad Sajid Iqbal'] In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This…
Sukanta Nayak, Snehashish Chakraverty
In this paper an alternative approach to solve uncertain Stochastic Differential Equation (SDE) is proposed. This uncertainty occurs due to the involved parameters in system and these are considered as Triangular Fuzzy Numbers (TFN). Here the proposed fuzzy arithmetic in [2] is used as a tool to handle Fuzzy Stochastic…
Oskar Weser, Kai Guther, Khaldoon Ghanem, Giovanni Li Manni
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction…
Marcin Kamiński, Rafał Leszek Ossowski, Nikolai Leonenko
In this study, we introduce Shannon entropy as a key metric for assessing concentration variability in diffusion processes. Shannon entropy quantifies the uncertainty or disorder in the spatial distribution of diffusing particles, providing a novel perspective on diffusion dynamics. This proposed approach enables a…
Michelle Rudolph-Lilith
Many physical systems exhibit random or stochastic components which shape or even drive their dynamic behavior. The stochastic models and equations describing such systems are typically assessed numerically, with a few exceptions allowing for a mathematically more rigorous treatment in the framework of stochastic…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Aryan Deshwal, Cory Simon, Janardhan Rao Doppa
Given a gas storage or separation task, we wish to search a library of nanoporous materials (NPMs) for the one with the optimal adsorption property. The high cost of measuring the adsorption property of an NPM, whether in the lab or a simulation, precludes exhaustive search. We explain, demonstrate, and advocate…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…