相关论文: Kahler: An Implementation of Discrete Exterior Cal…

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. However, so far, the emphasis has been on batch techniques. It is only recently, that online adaptive techniques…

Dealing with asymmetry in the architecture opens a plethora of questions from the perspective of scheduling task-parallel applications, and there exist early attempts to address this problem via ad-hoc strategies embedded into a runtime…

Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler characteristic as a measure, these objects record rich geometric…

Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of…

We present version 3.4 of the CalcHEP software package which is designed for effective evaluation and simulation of high energy physics collider processes at parton level. The main features of CalcHEP are the computation of Feynman…

Optimization over the embedded submanifold defined by constraints $c(x) = 0$ has attracted much interest over the past few decades due to its wide applications in various areas. Plenty of related optimization packages have been developed…

In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Central to this is the construction of a (non-linear) Dirac…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

In recent years, there has been increasing interest in network diffusion models and related problems. The most popular of these are the independent cascade and linear threshold models. Much of the recent experimental work done on these…

Training modern deep learning models is increasingly constrained by GPU memory and compute limits. While Randomized Numerical Linear Algebra (RandNLA) offers proven techniques to compress these models, the lack of a unified,…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Sharp $L^\infty$ estimates are obtained for general classes of fully non-linear PDE's on non-K\"ahler manifolds, complementing the theory developed earlier by the authors in joint work with F. Tong for the K\"ahler case. The key idea is…

Let M be a hypercomplex Hermitian manifold, (M,I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction produces a canonical nowhere degenerate…

This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…

We present Kosmulator, a modular and vectorised Python framework designed to accelerate the statistical testing of cosmological models. As the theoretical landscape expands beyond standard $\Lambda$CDM, implementing new expansion histories…

We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…

A standard practice in extragalactic population studies is the fitting of parametric models to galaxy images. From such fits, key structural parameters of galaxies such as total flux and effective radius (size) can be extracted. One of the…

This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…