Related papers: The Dimensional Recurrence and Analyticity Method …

Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…

We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not…

This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the…

In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the PDE residual in the least-squares sense as the loss function…

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…

This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…

Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed,…

Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…

We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…

Discrete de Rham (DDR) methods provide non-conforming but compatible approximations of the continuous de Rham complex on general polytopal meshes. Owing to the non-conformity, several challenges arise in the analysis of these methods. In…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

Optimizing discrete phase shifts in large-scale reconfigurable intelligent surfaces (RISs) is challenging due to their non-convex and non-linear nature. In this letter, we propose a heuristic-integrated deep reinforcement learning (DRL)…

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…

We evaluate the phase-space integrals that arise in double real emission diagrams for semi-inclusive deep-inelastic scattering at next-to-next-to-leading order (NNLO) in QCD. Utilizing the reverse unitarity technique, we convert these…

This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while…

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…