A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper studies geometrical objects in time-dependent Hamiltonian systems.
Paper presents techniques to classify UWB SAR imagery, distinguishing targets from clutter.
Introduces pqc structures, generalizing para 3-Sasakian geometry.
Introduces tensor product for quiver representations and applies to stable bundles and character varieties.
In this paper we establish an analogue of the classical Lichnerowicz' theorem giving a sharp lower bound of the first non-zero eigenvalue of the sub-Laplacian on a compact seven-dimensional quaternionic contact manifold, assuming a lower bound of the qc-Ricci tensor, torsion tensor and its distinguished covariant deriv…
Computes Finsler geometry curvature using anisotropic connections.
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize our approach of multi-time Hamilton geometry. In this direction, we firstly intro…
The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain as particular cases the Lagrange, Finsler and, for trivial nonlinear connections,…
Extends RT TQFT to include surface defects and line defects.
We show that there are isometrically nonequivalent Robertson-Walker metrics which have the same set of geodesics. While one of these metrics satisfies the Einstein equations of pure dust without a cosmological constant, all the other describe pure dust with additional energy momentum tensor of cosmological constant typ…
New characterisation of geodesics in various geometries yields conserved quantities.
We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension genera…
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
We developed a perturbation model for affine gravity theories.
The paper construct a suitable generalized metrical multi-time Lagrange geometrical model for both gravitational and electromagnetic fields, in a general setting. In this construction, the gravitational potentials are described by a distinguished vertical metrical tensor of the form .
Study of Langevin dynamics for tensor PCA recovery in high dimensions.
The notions of the interior and truncated connections of a nonholonomic manifold are introduced. A class of extended truncated connections is distinguished. For the case of a contact space with a Finsler metric, it is shown that there exists a unique extended truncated connection that satisfies additional properties. T…
Interactive platform for knot invariant computation and identification.
New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.
New invariant from Viro's gl(1|1) polynomial distinguishes lens spaces.
In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection DΓ(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by DΓ(N), and then we analyze th…
The study finds obstructions to certain Riemannian metrics using Lorentzian geometry.
We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to "negative frequencies":…
Classifies 4D metric Lie algebras with parallel skew-symmetric tensors.
Formulae track evolution of angular momentum and center of mass at null infinity.
Unified approach to tensor PCA and related problems using tensor cumulants.
We compute the full holonomy group of compact Lorentzian manifolds with parallel Weyl tensor, which are neither conformally flat nor locally symmetric, for the case where the fundamental group is contained in a distinguished subgroup G of the isometry group of the universal cover. To prove this, we show that every such…
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from inherent misuse of objects and for finding natural formulations of various objects…
Identifies all type D^k spacetimes in arbitrary dimensions.
The geometric constructions are elaborated on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also ind…
Geometric GNNs improve graph discrimination through GWL.
The paper describes a new type of Kähler surfaces and their properties.
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation. The latter is based on a correspondence between first order differential calcu…
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity e…
TQFT invariants are either easy or hard to compute, depending on the TQFT type.
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
SMPI recovers tensor spikes from noisy data with improved performance.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
The paper explores conditions for Randers metrics to have compatible linear connections.
We investigate parallel submanifolds of a Riemannian symmetric space . The special case of a symmetric submanifold has been investigated by many authors before and is well understood. We observe that there is an intrinsic property of the second fundamental form which distinguishes full symmetric submanifolds from ar…
The ``Links-Gould invariant'' is a two-variable Laurent polynomial invariant of oriented (1,1) tangles, which is derived from the representation of the braid generator associated with the one-parameter family of four dimensional representations with highest weights (0,0|a) of the quantum superalgebra U_q[gl(2|1)]. We u…
We introduce and study in detail an invariant of (1,1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra U_q[gl(2|1)], will be referred to as the Links-Gould invariant. We find that our invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (de…
New skein categories for non-semisimple settings, extending existing theory.
Researchers describe the metric structure of compact ECS manifolds.
Derives curvature conditions for spatial isotropy without field equations.
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…
We give a computer free proof of the Deligne, Cohen and deMan formulas for the dimensions of the irreducible -modules appearing in the tensor powers of , where ranges over the exceptional complex simple Lie algebras. We give additional dimension formulas for the exceptional series, as well as uniform dimensio…