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Search · four archives
22 papers · ranked by Valyu relevance
Patrick R. Conrad, Mark Girolami, Simo Särkkä, Andrew Stuart + 1 more
'Konstantinos Zygalakis'] In this paper, we present a formal quantification of uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the finite-dimensional approximation of an unknown and…
Raphael Kruse, Yue Wu
This paper contains an error analysis of two randomized explicit Runge-Kutta schemes for ordinary differential equations (ODEs) with timeirregular coefficient functions. In particular, the methods are applicable to ODEs of Carath´eodory type, whose coefficient functions are only integrable with respect to the time…
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…
Mahmood Saghaei
Background Typically, randomization software should allow users to exert control over the different aspects of randomization including block design, provision of unique identifiers and control over the format and type of program output. While some of these characteristics have been addressed by available software, none…
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…
Jonathan Oesterle, Nicholas Krämer, Philipp Hennig, Philipp Berens
Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic…
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…
Zhimin Hong, Zaizai Yan, Jiao Yan, Guido Germano
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this…
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.
Qiang Ji
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and Markov chain Monte Carlo to sample a probability distribution…
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…
Luciana De Micco, Maximiliano Antonelli, Osvaldo Anibal Rosso, Luca Faes
'Luca Faes'] The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step…
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…
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…
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…
Ljubomir Buturović
We developed a machine learning method for subgroup analyses of randomized controlled trials (RCT), and applied it to the results of the SPRINT RCT for treatment of hypertension. To date, the subgroup analyses mostly focused on detecting associations between certain factors and outcome, in the hope that the results…
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…
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…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…