Unbiased interpretation of noisy single molecular motor recordings remains a challenging task. To address this issue, we have developed robust algorithms based on hidden Markov models (HMMs) of motor proteins. The basic algorithm, called variable-stepsize HMM (VS-HMM), was introduced in the previous article. It improves on currently available Markov-model based techniques by allowing for arbitr...

Abstract The numerical treatment of an atmospheric chemical scheme, which contains 56 species, is discussed in this paper. This scheme often used studies air pollution levels different domains, as, for example, Europe, by large-scale environmental models containing additionally two other important physical processes—transport pollutants the atmosphere (advection) and diffusion phenomena. We sha...

This paper investigates iterated Runge-Kutta methods of high order designed in such a way that the right-hand side evaluations can be computed in parallel. Using stepsize control based on embedded formulas a highly efficient code is developed. On parallel computers, the 8th-order mode of this code is more efficient than the DOPR18 implementation of the formulas of Prince and Dormand. The lOth-o...

In this article, we consider the iterated Runge–Kutta (IRK) method which is an iteration method based on a predictor–corrector scheme for the solution of ordinary differential equations. The method uses embedded formulae to control the stepsize. We present different algorithms of the IRK method on distributed memory multiprocessors using appropriate communication primitives. The theoretical per...

We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of Dassl and a modified version, including stepsize control based on...

Inverter-based resources (IBRs) are required to provide dynamic voltage support (DVS) during dips enhance the low-voltage ride-through capability. In this paper, a model-free control method is developed achieve optimal DVS (ODVS) without relying on knowledge of grid parameters. Delving into optimum trajectory ODVS problem, it found that current constraint and maximum active power IBRs both bind...

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The uses variable stepsize which is updated at each iteration and based some previous iterates. convergence analysis of the proposed discussed under mild assumptions. case where bifunction strongly pseudomonotone, $R$-linear rate formulated. A fundamental experiment...

This paper proposes a new inertial triple-projection algorithm for solving the split feasibility problem. The process of projections is divided into three parts. Each part adopts different variable stepsize to obtain its projection point, which from existing extragradient methods. Flexible rules are employed selecting stepsizes and technique used improving convergence. Convergence results prove...

This paper derives a new class of general linear methods (GLMs) intended for the solution of stiff ordinary differential equations (ODEs) on parallel computers. Although GLMs were introduced by Butcher in the 1960s, the task of deriving formulas from the class with properties suitable for specific applications is far from complete. This paper is a contribution to that work. Our new methods have...

In this short note is studied the observer introduced in [1] and [5]. The relationship between the Lipschitz constant and the measurement stepsize is exhibited. For second order system, we evaluate the authorized measurement stepsize.