相关论文: Supporting Proving and Discovering Geometric Inequ…

Existing LiDAR semantic segmentation models often suffer from decreased accuracy when exposed to adverse weather conditions. Recent methods addressing this issue focus on enhancing training data through weather simulation or universal…

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…

In this paper, we apply the so-called Alexandrov-Bakelman-Pucci (ABP) method to establish some geometric inequalities. We first prove a logarithmic Sobolev inequality for closed $n$-dimensional minimal submanifolds $\Sigma$ of $\mathbb…

Since Knowledge Graphs are often incomplete, link prediction methods are adopted for predicting missing facts. Scalable embedding based solutions are mostly adopted for this purpose, however, they lack comprehensibility, which may be…

We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for…

In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an…

Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric…

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…

In this paper, we propose a fast and convergent algorithm to solve unassigned distance geometry problems (uDGP). Technically, we construct a novel quadratic measurement model by leveraging $\ell_0$-norm instead of $\ell_1$-norm in the…

We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…

The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…

This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…

Dataset biases are notoriously detrimental to model robustness and generalization. The identify-emphasize paradigm appears to be effective in dealing with unknown biases. However, we discover that it is still plagued by two challenges: A,…

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…

Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered…

Finding the best mathematical equation to deal with the different challenges found in complex scenarios requires a thorough understanding of the scenario and a trial and error process carried out by experts. In recent years, most…