相关论文: Kahler: An Implementation of Discrete Exterior Cal…
We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds $M$, by generalizing the twistor $\mathbb{P}^{1}$ to a more general complex manifold $Q$. The resulting manifold $X$ is complex if and only…
We present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…
High dimensional sampling is an important computational tool in statistics and other computational disciplines, with applications ranging from Bayesian statistical uncertainty quantification, metabolic modeling in systems biology to volume…
In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations…
In the era of diminishing returns from Moores Law, heterogeneous computing systems have emerged as a vital approach to enhance computational efficiency. This paper introduces a novel MLIR-based dialect, named hyper, designed to optimize…
Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems. Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\mathbb{R}^n$, while many…
In the first part of this paper we begin the study of polysymplectic manifolds, and of their relationship with PDE's. This notion provides a generalization of symplectic manifolds which is very well suited for the geometric study of PDE's…
The pyglaf reasoner takes advantage of circumscription to solve computational problems of abstract argumentation frameworks. In fact, many of these problems are reduced to circumscription by means of linear encodings, and a few others are…
We introduce a novel, efficient framework for clustering data on high-dimensional, non-Euclidean manifolds that overcomes the computational challenges associated with standard intrinsic methods. The key innovation is the use of the…
We introduce CaMEL (Case Marker Extraction without Labels), a novel and challenging task in computational morphology that is especially relevant for low-resource languages. We propose a first model for CaMEL that uses a massively…
We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions…
Exterior calculus with its three operations meet, join and hodge star complement, is used for the representation of fermion-hole systems and for fermionic analogues of logical gates. Two different schemes that implement fermionic quantum…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on…
Given a smooth manifold $M$ (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential…
We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it…
A Hermitian metric on a complex manifold is called strong K\"ahler with torsion (SKT) if its fundamental 2-form $\omega$ is $\partial \bar \partial$-closed. We review some properties of strong KT metrics also in relation with symplectic…
Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…