arXiv research

The paper proves stability for contact groupoids and deformations.

In this article we introduce a higher dimensional analogue of Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability for Engel manifolds.

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…

The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.

We define the thin fundamental Gray 3-groupoid $S_3(M)$ of a smooth manifold $M$ and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps $S_3(M) \to C(H)$, where $H$ is a 2-crossed module of Lie groups and $C(H)$ is the Gray 3-groupoid naturally constructed f…

The aim of this paper is to describe a large class of Hermitian Gray manifolds.

We give an expository about compactification of heteorotic superstrings with torsion on generalized Calabi-Gray manifolds.

The aim of this research is the study of Gray curvature identities, introduced by Alfred Gray in \cite{kn:Gra76} for the class of almost hermitian manifolds. As known till now, there is no equivalent for the class of almost contact manifolds. For this purpose we use the Boohby-Wang fibration and the warped manifolds co…

We give a parameterization of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid using Jacobi's elliptic functions. This parameterization avoids some problems present in the original depiction of these surfaces.

In this paper we determine the Gray-Hervella classes of the compatible almost complex structures on the twistor spaces of oriented Riemannian four-manifolds considered by G. Deschamps

In the $3$-gauge theory, a $3$-connection is given by a $1$-form $A$ valued in the Lie algebra $\mathfrak g$, a $2$-form $B$ valued in the Lie algebra $\mathfrak h$ and a $3$-form $C$ valued in the Lie algebra $\mathfrak l$, where $(\mathfrak g,\mathfrak h, \mathfrak l)$ constitutes a differential $2$-crossed modu…

A lightweight framework improves convergence and stability of PINNs for complex PDEs.

Harmonic almost complex structures on specific Lie groups and solvmanifolds identified.

Study of complex structures on product twistor spaces for 4D manifolds.

We characterize quasi Kähler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related with the third Gray identity and in the almost Kähler case implies the integrability. Our main tool is the existence of generalized holomorphic f…

Improved upper bound for mass partitioning problem using Gray codes.

Unified view of geometries with parallel skew torsion via submersions.

The paper extends Gray's result to quaternion-Kähler manifolds.

We classify, up to a local isometry, all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost Kahler 4-manifolds satisfy the third curvature condition of A. Gr…

The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray mo…

Characterizes a class of almost Hermitian 4-manifolds using integral identities.

The aim of this paper is to describe Kahler surfaces which admit an opposite almost Hermitian structure satisfying the first Gray condition

Recent studies have highlighted that deep neural networks (DNNs) are vulnerable to adversarial attacks, even in a black-box scenario. However, most of the existing black-box attack algorithms need to make a huge amount of queries to perform attacks, which is not practical in the real world. We note one of the main reas…

We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. …

We give a description of Gray AC^{\perp} manifolds $(M,g)$ whose Ricci tensor has two eigenvalues of multiplicity 1 and dim M-1.

Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian foliations of any open subset of $\mathbb{P}^n$ of codimension one. As a consequence …

Gray-box attack improves on white-box methods for trading agents.

Data-driven approach learns effective equations for phase field interfaces.

The aim of this paper is to classify bi-Hermitian compact surfaces $(M,g)$ whose Ricci tensor $ρ$ satisfies the relation $\nabla_Xρ(X,X) =\frac13Xτg(X,X)$.

Study of contact-complex Riemannian submersions in various manifold classes.

This paper defines systematic value investing as an empirical optimization problem. Predictive modeling is introduced as a systematic value investing methodology with dynamic and optimization features. A predictive modeling process is demonstrated using financial metrics from Gray & Carlisle and Buffett & Clark. A 31-y…

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and com…

A. Gray presented an interesting $O\left( n\right)$ invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what con…

The structure of nearly Kähler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces ov…

This paper presents a useful method to achieve classification in satellite imagery. The approach is based on pixel level study employing various features such as correlation, homogeneity, energy and contrast. In this study gray-scale images are used for training the classification model. For supervised classification, …

In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.

New method finds 198,846 toric-colorable seeds of Picard number 5.

NMF and PCC linked, improving data denoising and feature stability.

We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions.

Extends RCNNs to handle hypercomplex-valued data.

Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between the three components (R,G,B) of a pixel, and the global relations describing edge…

The aim of this paper is to give examples of compact neutral 4-manifolds $(M,g)$ whose Ricci tensor $ρ$ satisfies the relation $\nabla_Xρ(X,X) =\frac13Xτg(X,X)$. We present also a family of new Einstein bi-Hermitian neutral metrics on ruled surfaces of genus $g>1$.

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.

We determine the space of algebraic pseudo-Hermitian Kähler-Weyl curvature tensors and the space of para-Hermitian Kähler-Weyl curvature tensors in dimension 4 and show that every algebraic possibility is geometrically realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds and for para-Hermitian…

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26\% w.r.t. to QAM.

For G_2-manifolds the Fernández-Gray class X_1+X_4 is shown to consist of the union of the class X_4 of G_2-manifolds locally conformal to parallel G_2-structures and that of conformal transformations of nearly parallel or weak holonomy G_2-manifolds of type X_1. The analogous conclusion is obtained for Gray-Hervella c…

We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant *-scalar curvature which satisfies the Kaehl…

A {\em blink} is a plane graph with a bipartition (black, gray) of its edges. Subtle classes of blinks are in 1-1 correspondence with closed, oriented and connected 3-manifolds up to orientation preserving homeomorphisms \cite{lins2013B}. Switching black and gray in a blink $B$, giving $-B$, reverses the manifold orien…