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We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
A method is presented for the evaluation of integrals on tetrahedra where the integrand has an integrable singularity at one vertex. The approach uses a transformation to spherical polar coordinates which explicitly eliminates the…
The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a…
A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…
We present a family of modified Hermite integrators of arbitrary order possessing superior behaviour for the integration of Keplerian and near-Keplerian orbits. After recounting the derivation of Hermite N-body integrators of arbitrary…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction…
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving Schr\"o{}dinger equation. In order to pass the information among grids we use the values of the fields only at the contact…
Gray-box optimization leverages the information available about the mathematical structure of an optimization problem to design efficient search operators. Efficient hill climbers and crossover operators have been proposed in the domain of…
This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…
The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…
The combination of linear transformations and non-linear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic…
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [Numer. Algorithms, 99:921-948, 2025] for a parabolic-parabolic interface problem. We modify the first step of the scheme so that several…
This paper presents a detailed theoretical review of the amplification process in Josephson Parametric Amplifiers (JPAs), which are crucial for quantum-limited signal amplification in superconducting circuits. The paper begins by outlining…
High-gain optical parametric amplification is an important nonlinear process used both as a source of coherent infrared light and as a source of nonclassical light. In this work, we experimentally demonstrate an approach to optical…
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational…
Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning…