Related papers: Accurate and efficient explicit approximations of …
In this work, we develop a method for rational approximation of the Fourier transform (FT) based on the real and imaginary parts of the complex error function \[ w(z) = e^{-z^2}(1 - {\rm{erf}}(-iz)) = K(x,y) + iL(x,y), \qquad z = x + iy, \]…
The C library \texttt{libkww} provides functions to compute the Kohlrausch-Williams-Watts function, i.e.\ the Laplace-Fourier transform of the stretched (or compressed) exponential function $\exp(-t^\beta)$ for exponents $\beta$ between 0.1…
We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…
Optimal power flow (OPF) is a key tool for planning and operations in energy grids. The line-flow constraints, generator loading effect, piece-wise cost functions, emission, and voltage quality cost make the optimization model non-convex…
The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known…
Error bound condition has recently gained revived interest in optimization. It has been leveraged to derive faster convergence for many popular algorithms, including subgradient methods, proximal gradient method and accelerated proximal…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
A jump-diffusion process along with a particle scheme is devised as an accurate and efficient particle solution to the Boltzmann equation. The proposed process (hereafter Gamma-Boltzmann model) is devised to match the evolution of all…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can…
We start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known beta function of Novikov et…
We investigate the log-concavity on the half-line of the Wright function $\phi(-\alpha,\beta,-x),$ in the probabilistic setting $\alpha\in (0,1)$ and $\beta \ge 0.$ Applications are given to the construction of generalized entropies…
The full width at half maximum (FWHM) is a useful quantity for characterizing the bandwidth of unimodal functions. However, a closed-form expression for the FWHM of gamma-shaped functions-i.e. functions that are shaped like the gamma…
Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from…
The Willmore flow is well known problem from the differential geometry. It minimizes the Willmore functional defined as integral of the mean-curvature square over given manifold. For the graph formulation, we derive modification of the…
Full-waveform inversion is a cutting-edge methodology for recovering high-resolution subsurface models. However, one of the main conventional full-waveform optimization problems challenges is cycle-skipping, usually leading us to an…
An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…
This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally…