Related papers: simode: R Package for statistical inference of ord…
The R package optimParallel provides a parallel version of the gradient-based optimization methods of optim(). The main function of the package is optimParallel(), which has the same usage and output as optim(). Using optimParallel() can…
A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all…
In this paper, to begin with, we review six different analytical methods which are widely used to derive symmetries, integrating factors, multipliers, Darboux polynomials and integrals of second order nonlinear ordinary differential…
Missing data on response variables are common in clinical studies. Corresponding to the uncertainty of missing mechanism, theoretical frameworks on controlled imputation have been developed. In practice, it is recommended to conduct a…
Differential privacy (DP) is the state-of-the-art framework for guaranteeing privacy for individuals when releasing aggregated statistics or building statistical/machine learning models from data. We develop the open-source R package DPpack…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
The numerical availability of statistical inference methods for a modern and robust analysis of longitudinal- and multivariate data in factorial experiments is an essential element in research and education. While existing approaches that…
This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…
There exist excellent codes for an efficient numerical treatment of stiff and differential-algebraic problems. Let us mention {\sc Radau5} which is based on the $3$-stage Radau IIA collocation method, and its extension to problems with…
Background: Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, and healthcare informatics. They are used to simulate complex dynamic…
The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…
Sum of Ranking Differences (SRD) is a relatively novel, non-para-metric statistical procedure that has become increasingly popular recently. SRD compares solutions via a reference by applying a rank transformation on the input and…
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some…
We propose a physical analogy between finding the solution of an ordinary differential equation (ODE) and a $N$ particle problem in statistical mechanics. It uses the fact that the solution of an ODE is equivalent to obtain the minimum of a…