arXiv research

The paper proposes a novel tensor-based method for non-parametric density estimation.

The study introduces new tensors for almost Finsler manifolds and analyzes their properties.

Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebr…

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called character…

It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such a manifold a fundamental tensor by the metric and by the covariant derivative of…

Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…

We define the notion of characteristic classes for supermanifolds endowed with a homological vector field $Q$. These take values in the cohomology of the Lie derivative operator $L_Q$ acting on arbitrary tensor fields. We formulate a classification theorem for intrinsic characteristic classes and give their explicit de…

Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.

Bounding characteristic numbers of Riemannian manifolds via volume.

The study connects conic connections and torsion-free principal connections on G-structures.

Certain curvature conditions for stability of Einstein manifolds with respect to the Einstein-Hilbert action are given. These conditions are given in terms of quantities involving the Weyl tensor and the Bochner tensor. In dimension six, a stability criterion involving the Euler characteristic is given.

A $Q$-manifold $M$ is a supermanifold endowed with an odd vector field $Q$ squaring to zero. The Lie derivative $L_Q$ along $Q$ makes the algebra of smooth tensor fields on $M$ into a differential algebra. In this paper, we define and study the invariants of $Q$-manifolds called characteristic classes. These take value…

The paper explores conditions for homothetic Killing vectors on spacetime hypersurfaces.

Enhances tensor regression for interpretability and performance.

We give an algebraic characterization of the possible characteristic tensors of an infinitesimally homogeneous affine manifold with G-structure.

New method compresses non-Gaussian distributions exponentially.

Solves characteristic problem in general relativity for null data.

Proposes a method to recover sparse tensors with covariate info.

We study symmetric Killing 2-tensors on Riemannian manifolds and show that several additional conditions can be realised only for Sasakian manifolds and Euclidean spheres. In particular we show that (three)-Sasakian manifolds can also be characterized by properties of the symmetric products of their characteristic 1-fo…

The study shows that nonpositively curved 4-manifolds with zero Euler characteristic have degenerating Ricci curvature.

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and $φ$-sectional curvature of indefinite almost $\…

New model analyzes customer churn with tensor completion and binary data.

Paper improves MVSC using tensor low-rank modeling.

Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.

We apply the Atiyah-Singer index theorem and tensor products of elliptic complexes to the cohomology of transitive Lie algebroids. We prove that the Euler characteristic of a representation of a transitive Lie algebroid $A$ over a compact manifold $M$ vanishes unless $A=TM$, and prove a general Künneth formula. As appl…

Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors θwith an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators on the basis of S or A realized by differentiable tensor fields in a na…

Tensor Regression tackles high-dimensional data analysis.

The Finsleroid-Finsler space is constructed over an underlying Riemannian space by the help of a scalar $g(x)$ and an input 1-form $b$ of unit length. Explicit form of the entailed tensors, as well as the respective spray coefficients, is evaluated. The involutive case means the framework in which the characteristic sc…

Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such manifolds, namely, vanishing of the Euler characteristic and real Pontryagin classe…

A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the present work, solutions of the projective parameter's ODE are characterized with…

Paper proposes a novel MTL framework for personalized modeling of diverse individuals.

We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism \s of the tensor product T\otimes T' of the tangent bundle T with the cotangent bundle T'. To such a curvature type tensor \s one associates the fir…

Paper uses tensor completion to estimate HVAC fan power baselines.

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor networks. The graph underlying these networks is given by the triangulation of a mani…

We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…

The Weyl functional is analyzed on 4-manifolds with positive scalar curvature.

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexio…

Any 7-dimensional cocalibrated G_2-manifold admits a unique connection $\nabla$ with skew symmetric torsion. We study these manifolds under the additional condition that the $\nabla$-Ricci tensor vanishes. In particular, we describe their geometry in case of a maximal number of $\nabla$-parallel vector fields.

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations …

We solve the equivalence problem for the orthogonally separable webs on the three-sphere under the action of the isometry group. This continues a classical project initiated by Olevsky in which he solved the corresponding canonical forms problem. The solution to the equivalence problem together with the results by Olev…

The vast majority of current machine learning algorithms are designed to predict single responses or a vector of responses, yet many types of response are more naturally organized as matrices or higher-order tensor objects where characteristics are shared across modes. We present a new machine learning algorithm BaTFLE…

Study on 3D manifolds with circulant structures and their properties.

Paper introduces a new method for efficient portfolio risk quantification.

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

A new Riemannian manifold with skew-circulant structures and its associated locally conformal Kähler manifold are studied.

Study $p$-brane Galilean and Carrollian geometries via intrinsic torsion.

New SDEs from affine and polynomial perspectives for path-dependent processes.