Related papers: YAM2: Yet another library for the $M_2$ variables …
Computer algebra systems play an important role in science as they facilitate the development of new theoretical models. The resulting symbolic equations are often implemented in a compiled programming language in order to provide fast and…
In this paper, we present a new approach to linearizing zero-one quadratic minimization problem which has many applications in computer science and communications. Our algorithm is based on the observation that the quadratic term of…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…
Standard approaches to tackle high-dimensional supervised classification problem often include variable selection and dimension reduction procedures. The novel methodology proposed in this paper combines clustering of variables and feature…
This research explores the application of quadratic polynomials in Python for advanced data analysis. The study demonstrates how quadratic models can effectively capture nonlinear relationships in complex datasets by leveraging Python…
The common exact diagonalization-based techniques to solving tight-binding models suffer from O(N^2) and O(N^3) scaling with respect to model size in memory and CPU time, hindering their applications in large tight-binding models. On the…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
Automatic design of organic materials requires black-box optimization in a vast chemical space. In conventional molecular design algorithms, a molecule is built as a combination of predetermined fragments. Recently, deep neural network…
Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to…
The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Many computer vision pipelines involve dynamic programming primitives such as finding a shortest path or the minimum energy solution in a tree-shaped probabilistic graphical model. In such cases, extracting not merely the best, but the set…
Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…