arXiv research

Study Killing forms on negatively curved manifolds, introducing generalized vector cross products.

Defines cross product for m vectors in n-dimensional spaces.

In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.

The connection between Hitchin's stable forms and vector cross products is observed. Using this correspondence, we construct new examples of non-Kahler Calabi-Yau 3-folds and manifolds with G2-structure of class W3. We also generalize and refine results of Calabi and Gray in the paracomplex setting.

Proposes a novel approach using vector cross product to preserve directional edges in directed graphs.

Research decouples Lie algebroids using bicocycle double cross product theory.

The paper extends a theorem to Lie-Rinehart algebras and provides new decompositions of universal enveloping algebras.

Harmonic unit normal sections studied for Grassmannians induced by cross products.

Many classical objects on a surface S can be interpreted as cross-ratio functions on the circle at infinity of the universal covering. This includes closed curves considered up to homotopy, metrics of negative curvature considered up to isotopy and, in the case of interest here, tangent vectors to the Teichmüller space…

In this paper we study the geometry of manifolds with vector cross product and its complexification. First we develop the theory of instantons and branes and study their deformations. For example they are (i) holomorphic curves and Lagrangian submanifolds in symplectic manifolds and (ii) associative submanifolds and co…

Two constructions of Chern character for equivariant vector bundles in noncommutative geometry.

Proposes using entity embedding vectors to improve Gaussian Process models for knowledge transfer across cell lines.

The paper proves a generalization of complex structures on knot spaces.

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.

Copulas model cross-product effects in intraday power markets.

The GANs are generative models whose random samples realistically reflect natural images. It also can generate samples with specific attributes by concatenating a condition vector into the input, yet research on this field is not well studied. We propose novel methods of conditioning generative adversarial networks (GA…

Researchers create spectral triples for twisted crossed products using Kasparov's external product.

Global geometric expressions derived for manifold embeddings.

Isomorphism found between filtered calculus and crossed products.

We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross product. We present a system of partial differential equations for an unknown vect…

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimiza…

Paper finds conditions for finite-dimensional vector spaces of cross-sections.

New dynamics derived from Lie groups using 2nd order tangent groups.

The present article provides a study of $2-$Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a $2-$Killing vector field on a warped product manifold to be parallel are obtained. Moreover, …

Study characterizes 2-Killing vector fields on complex spacetimes.

PRISM-VQ combines financial priors with vector quantization for better stock prediction.

Study of symplectic cross-ratios in moduli spaces of line configurations.

Let $G$ be a finite group. Noncommutative geometry of unital $G$-algebras is studied. A geometric structure is determined by a spectral triple on the crossed product algebra associated with the group action. This structure is to be viewed as a representative of a noncommutative orbifold. Based on a study of classical o…

We generalize the natural cross ratio on the ideal boundary of a rank one symmetric spaces, or even $\mathrm{CAT}(-1)$ space, to higher rank symmetric spaces and (non-locally compact) Euclidean buildings - we obtain vector valued cross ratios defined on simplices of the building at infinity. We show several properties …

We construct a gauge fixed action for topological membranes on $G_2$-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on $M\times S^1$ the theory naturally reduces…

Defines complex manifolds on commutative Banach algebras and studies continuous families of compact complex manifolds.

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. …

To compare entities of differing types and structural components, the artificial neural network paradigm was used to cross-compare structural components between heterogeneous documents. Trainable weighted structural components were input into machine-learned activation functions of the neurons. The model was used for m…

The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…

Let $\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\mathfrak{g}$ as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: ${\mathcal H}{\mathcal L}^{2}_{\mathfrak{g}} \, (…

The paper studies conformal Ricci solitons in warped product spaces.

The paper generalizes product inequalities for random vectors and their applications.

Study on Gaussian ensemble of matrix products with mixed moments computed.

Explores tensor products in hyperdimensional computing.

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product.…

Warped product metrics are a class of Riemannian metrics on cross products $B \times F$ which have been well studied and provide a rich set of examples. In this paper we consider shrinking gradient Ricci solitons which are warped product metrics. We prove that if the curvature of the metric is bounded and the base $B$ …

Study Nijenhuis operators on homogeneous spaces related to C*-algebras.

Study relative commutants in von Neumann algebras using contraction notions.

This work merges 3-anchored bundles into 3-Lie algebroids.

Given a fiber bundle $Z \to M \to B$ and a flat vector bundle $E \to M$ with a compatible action of a discrete group $G$, and regarding $B / G$ as the non-commutative space corresponding to the crossed product algebra, we construct an analytic torsion form as a non-commutative deRham differential form. We show that our…

The paper studies regular contact manifolds and their products.

Two formulas for Chern classes of tensor products of vector bundles are presented.

E-commerce sales forecast using LSTM with cross-series information.