Search · four archives
Search · four archives
21 papers · ranked by Valyu relevance
Fabio V. Difonzo, Paweł Przybyłowicz, Yue Wu, Xinheng Xie
In this paper we investigate the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with the right-hand side functions f = f(t, x, z) that are Lipschitz continuous with respect to x but only H¨older continuous with respect to (t, z). We give a construction of the randomized…
Chuan-gang Kang, Heng Zhou
The Kaczmarz method is an iterative projection scheme for solving consistent system Ax = b. It is later extended to the inconsistent and ill-posed linear problems. But the classical Kaczmarz method is sensitive to the correlation of the adjacent equations. In order to reduce the impact of correlation on the convergence…
Inês A. Ferreira, Juan A. Acebrón, José Monteiro
The Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single equation, resulting in minimal computational work per iteration. Second, solving…
Guanjie Wang, Qifeng Liao
We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the stochastic Galerkin method, such that the cost of solvers for the Galerkin system is significantly reduced. To reduce the main cost of…
Matteo Croci, Massimiliano Fasi, Nicholas J. Higham, Theo Mary + 1 more
'Mantas Mikaitis'] Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to x. This rounding mode was first proposed for use in computer arithmetic in the…
Nicolas L. Guidotti, Per-Gunnar Martinsson, Juan A. Acebrón, José Monteiro
'José Monteiro'] Abstract. Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement can quickly become overwhelming as the basis grows…
Haochen Jiang, Dongdong Liu, Xianping Wu, Yang Xu
Motivated by the randomized sketch to solve a variety of problems in scientific computation, we improve both the maximal weighted residual Kaczmarz method and the randomized block average Kaczmarz method using two new randomized sketch techniques. Besides, convergence analyses of the proposed methods are provided.…
Daniel Kressner, Bor Plestenjak
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to…
Haoze He, Daniel Kressner
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.
H. Robert Frost
We have developed a new, and analytically novel, single sample gene set testing method called Reconstruction Set Test (RESET). RESET quantifies gene set importance at both the sample-level and for the entire dataset based on the ability of set genes to reconstruct values for all measured genes. RESET addresses four…
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…
Thomas Lynn, Julio Ottino, Richard Lueptow, Paul Umbanhowar
Cut-and-shuffle mixing is an instructive candidate system with which to assess the potential of machine learning (ML) as an approach to solve difficult mixing problems. We focus on a specific subset of cut-and-shuffle systems, the one-dimensional interval exchange transform. This class of mixing operations is well…
Chenghua Duan, Chun Liu, Xingye Yue
We propose a numerical method to uniformly handle the random genetic drift model for pure drift with or without natural selection and mutation. For pure drift and natural selection case, the Dirac δ singularity will develop at two boundary ends and the mass lumped at the two ends stands for the fixation probability.…
Oleksandr Sverdlov, Yevgen Ryeznik, Volodymyr Anisimov, Olga M. Kuznetsova + 4 more
'Olga M. Kuznetsova' 'Ruth Knight' 'Kerstine Carter' 'Sonja Drescher' 'Wenle Zhao'] Background The design of a multi-center randomized controlled trial (RCT) involves multiple considerations, such as the choice of the sample size, the number of centers and their geographic location, the strategy for recruitment of…
Muhammad Azeem, Javid Shabbir, Najma Salahuddin, Sundus Hussain + 2 more
In social surveys, the randomized response technique can be considered a popular method for collecting reliable information on sensitive variables. Over the past few decades, it has been a common practice that survey researchers develop new randomized response techniques and show their improvement over previous models.…
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…
James M. Osborne
In recent years, multi–cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi–cellular modelling tools and to…
Junya Watanabe
Theory predicts that the additive genetic covariance (G) matrix determines a population’s short-term (in)ability to respond to directional selection—evolvability in the Hansen–Houle sense—which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining…
Sumedh S Nagrale, Alik S Widge
The use of Deep Brain Stimulation (DBS) on the ventral capsule/ventral striatum (VCVS) has therapeutic potential for patients with refractory psychiatric disorders, but clinical success is impeded by the need for a time-consuming and trial-and-error process when setting the parameters, this process relying on…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Christopher Myers, Ken Miyazaki, Thomas Trepl, Christine Isborn + 1 more
GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure…