arXiv research

Geometric approach combines asset returns and investor views for better portfolio optimization.

Survey on conservation laws for geometric PDEs.

Geometric deep learning predicts knot invariants.

From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspe…

Integrates rough geometric forms on manifolds.

New theory connects geometry without relying on connections.

Introduces a new geometric method for optimal experimental design.

Geometric programming approach for traffic equilibrium problems.

A new method for group invariant machine learning using geometric projections.

I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous thermo--statistical--geometrical formalisms, (pseudo-)Riemannian [Weinhold 1975; Ruppeiner 1979] as well a…

Tensor approach simplifies Euclidean space descriptions.

A novel geometric algebra-based KG embedding framework improves link prediction.

GDB bridges geometric states with improved accuracy and generality.

Geometric mechanics approach to constrained and floating multibody systems using Hamel's equations.

Deep learning models complex multivariate extremes using geometric shapes.

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the…

We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particular…

We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…

We give a more geometric approach to an algorithm for deciding whether two hyperbolic 3-manifolds are homeomorphic. We also give a more algebraic approach to the homeomorphism problem for geometric, but non-hyperbolic, 3-manifolds.

Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive method to determine the quantizing dimension in Zador's theorem is provided. A geom…

Flexible approach for normal approximations in geometric and topological statistics.

Investigates fluid flow perturbations using geometric theory.

Geometric method improves uncertainty estimation in real-time.

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 or within a vector manifold framework, here we define geometric calculus directl…

We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.

New approach combines geometric and probabilistic methods to estimate manifold dimension in high-dimensional data.

Geometric tempering fails for Langevin dynamics, proving convergence limits.

Paper formalizes multi-dimensional FSD using geometric methods.

Combines topological and geometric approaches to data analysis.

Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noi…

Geometric Graph Alignment enhances IoT intrusion detection using NID data.

New approach for uniform estimates in complex equations.

Extends geometric approach to model non-stationary extremal dependence.

Solves geometric Cauchy problem for submanifolds with constant rank.

Geometric vector perceptrons improve protein structure learning.

Equations of motion of low-energy string effective actions can be conveniently described in terms of generalized geometry and Levi-Civita connections on Courant algebroids. This approach is used to propose and prove a suitable version of the Kaluza-Klein-like reduction. Necessary geometrical tools are recalled.

New proofs for curvature problems using a viscosity approach.

The commuting vector fields approach, devised for strichartz estimates in [13], was developed for proving the local well-posedness in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by Klainerman and Rodnianski. Via this approach they obtained the l…

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

Variational approach to basic manifold structures.

This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely man…

New geometric proof of convex function differentiability and approximation.

We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …

Study of control problems on Carnot groups with SO(3) symmetry using geometric algebra.

Extends potential theory to Carnot groups, estimating Hausdorff dimension.

Geometric cohomology model uses co-oriented maps to define a product structure.

Transforms curves and surfaces for efficient geometric analysis.

Geometric approach to moment maps in complex geometry.