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The order type of a point set in $R^d$ maps each $(d{+}1)$-tuple of points to its orientation (e.g., clockwise or counterclockwise in $R^2$). Two point sets $X$ and $Y$ have the same order type if there exists a mapping $f$ from $X$ to $Y$…
We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed…
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…
Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the…
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…
This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We give an approximate algorithm of computing holonomic systems of linear differential equations for definite integrals with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…
In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals (STOs) is presented. The proposed…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…