arXiv research

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.

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 …

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

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 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.

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.

We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in 3-space.

New fault-tolerant quantum gates for homological LDPC codes with constant or almost-constant rate.

New approach for learning large Bayesian networks using feature clustering and compression.

We prove that no $14$-connected (resp. $30$-connected) stably parallelizable manifold $N^{30}$ (resp. $N^{62}$) of dimension $30$ (resp. $62$) with the Arf-Kervaire invariant 1 can be smoothly embedded into $\mathbb{R}^{36}$ (resp. $\mathbb{R}^{83}$).

New method solves robust matrix completion using nonlinear equations.

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Pa…

Computes Picard groups of complex parallelizable manifolds.

We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / Γ$, where $G$ is a complex connected Lie group and $Γ$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_ρ$ associated to any irreducible representa…

We prove that the stable moduli space of $(n-1)$-connected, $n$-parallelizable, $(2n+1)$-dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq 7$. The main novel ingredient is a version of the cobordism category incorporating surgery data in the form of Lagrangian subspaces.

We consider the stable ruled surface $S_1$ over an elliptic curve. There is a unique foliation on $S_1$ transverse to the fibration. The minimal self-intersection sections also define a 2-web. We prove that the 4-web defined by the fibration, the foliation and the 2-web is locally parallelizable.

ParaRNN improves RNN interpretability and parallelizability for time-dependent data.

MACE uses higher-order messages to create fast, accurate force fields.

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 …

TempoPFN models for zero-shot time series forecasting using synthetic data.