arXiv research

Improved upper bound for mass partitioning problem using Gray codes.

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

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

The paper proves stability for contact groupoids and deformations.

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.

Unlike traditional programs (such as operating systems or word processors) which have large amounts of code, machine learning tasks use programs with relatively small amounts of code (written in machine learning libraries), but voluminous amounts of data. Just like developers of traditional programs debug errors in the…

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…

In this work, a deep learning-based quantization scheme for log-likelihood ratio (L-value) storage is introduced. We analyze the dependency between the average magnitude of different L-values from the same quadrature amplitude modulation (QAM) symbol and show they follow a consistent ordering. Based on this we design a…

In this paper, a neural network-aided bit-interleaved coded modulation (NN-BICM) receiver is designed to mitigate the nonlinear clipping distortion in the LDPC coded direct currentbiased optical orthogonal frequency division multiplexing (DCOOFDM) systems. Taking the cross-entropy as loss function, a feed forward netwo…

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…

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.

Though deep neural networks have achieved state-of-the-art performance in visual classification, recent studies have shown that they are all vulnerable to the attack of adversarial examples. Small and often imperceptible perturbations to the input images are sufficient to fool the most powerful deep neural networks. Va…

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

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.

Minimalistic unsupervised learning with sparse manifold transform achieves SOTA performance.

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.

Detects project management anti-patterns using code and issue data.

Proposes FMS for more efficient neural network hyperparameter optimization.

We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods. Our approach does not need to know the details of the structured likelihood model and can scale up to a large number of observations. Furthermore, we show that…

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…

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…

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.

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.

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…

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…

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…