arXiv research

Study on ruled surfaces over elliptic curves with unique foliations and parallelizable 4-webs.

We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply a recently found in [AGL] the linearizability conditions for 4-webs in the plane to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is …

The abstract discusses maximal rank 4-webs formed by confocal conics and their properties.

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is lineari…

We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web …

Geodesic flows on surfaces have specific fractional-linear integrals related to constant cross-ratios.

Geodesic flows with specific integrals are linked to special 4-webs.

New model for rational tropical points using $\mathfrak{sp}_4$-webs and measures.

Study of $\mathfrak{sp}_4$-webs on surfaces, proving cluster algebra structure.

Proof of orientable 3-manifolds parallelizability using knot theory.

Study on the Kodaira dimension of real parallelizable manifolds with almost complex structures.

New proof shows 3D shapes can be continuously deformed.

The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry. Two remarkable li…

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

Proves Nakai webs have rank 0 or 1, provides examples.

Regularities and stability shown for a specific type of complex parallelizable manifolds.

The paper explores algebraic and geometric structures on parallelizable manifolds.

A 4-manifold is parallelizable if its Stiefel-Whitney and Pontryagin classes vanish.

Study homogenizes equations on parallelizable manifolds using tensor localization and periodicity.

Modified BFGS and LBFGS++ libraries boost performance for non-parallelizable functions.

Study on special metrics and deformations of solvmanifolds.

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…

Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty).$ Using this flow, we outline a simple proof of the Poincare Conjecture.

We show that if $M$ is an orientable 4-dimensional infrasolvmanifold and either $β=β_1(M;\mathbb{Q})\geq2$ or $M$ is a $\mathbb{S}ol_0^4$- or a $\mathbb{S}ol_{m,n}^4$-manifold (with $m\not=n$) then $M$ is parallelizable. There are non-parallelizable examples with $β=1$ for each of the other solvable Lie geometries $\ma…

Study finds infinite families of Sasaki-Einstein metrics on spheres.

Study the rank of Nijenhuis tensor on parallelizable almost complex manifolds.

The paper proposes a parallelizable clustering method for multivariate data.

New 4D shapes can't be opened like books.

We show that if a compact, oriented 4-manifold admits a coassociative-free immersion into the Euclidean 7-space then its Euler characteristic and signature vanish. Moreover, in the spin case the Gauss map is contractible, so that the immersed manifold is parallelizable. The proof makes use of homotopy theory in particu…

We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.

Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are approximated by Gaussian sampling. These approaches are of particular interest …

The study generalizes Blaschke curvature for higher-dimensional webs and identifies infinite classes of isomorphism.

pLSTM tackles long-range language modeling and computer vision tasks with parallelizable linear source transition mark networks.

We find d - 2 relative differential invariants for a d-web, d \geq 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f (x,y) and g_4 (x,y),...,g_d (x,y), then necessary and sufficient c…

The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.

We give various results and applications using the connection $(E,\nabla)$ associated with a $d$-web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They cast some new lights on the connection and its construction, both conceptually an…

We propose a new model for unsupervised document embedding. Leading existing approaches either require complex inference or use recurrent neural networks (RNN) that are difficult to parallelize. We take a different route and develop a convolutional neural network (CNN) embedding model. Our CNN architecture is fully par…

Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.

Let $G$ be a simply connected solvable Lie group with a lattice $Γ$ and the Lie algebra $\g$ and a representation $ρ:G\to GL(V_ρ)$ whose restriction on the nilradical is unipotent. Consider the flat bundle $E_ρ$ given by $ρ$. By using "many" characters $\{α\}$ of $G$ and "many" flat line bundles $\{E_α\}$ over $G/Γ$, w…

After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.

EigenGame reinterprets PCA as a game to find eigenvectors.

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections.

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type. More precise…

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.

Proposes SVM-based Deep Stacking Network for improved deep learning.

MSLs use parallelizable root-finding for efficient ODE and PDE solutions.

The well-known fact that $S^1$, $S^3$ and $S^7$ are parallelizable manifolds admitting flat connections is revisited. The role of torsion in the construction of those flat connections is made explicit, and the possibilities allowed by different metric signatures are examined. A necessary condition for parallelizability…

The paper explores $p$-Kähler structures on complex manifolds and their properties.