arXiv research

New methods connect low-loss points on neural network surfaces.

Improved method for numerical conformal mappings on complex domains.

Method counts connected 2D stratifolds with singular curves and components.

New method proves Jones Polynomial's connect sum property.

Direct method finds Yang-Mills connections for SO(3) bundles.

LOCUS separates brain network connectivity matrices efficiently.

The paper proves hyperbolic groups are semistable and their boundaries are linearly connected.

New method for linear connections in ODEs with constraints.

Defines annulus complex of handlebodies and proves its connectivity.

Method estimates network connectivity and dimensionality from multiple networks.

We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We prove some basic results concerning completeness of Cartan connections. We provide…

The paper characterizes simply connected quandles using cocycles with prime values.

We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.

The paper explores connections between braids, links, and cobordisms using algebraic methods.

Estimation of reliable whole-brain connectivity is a crucial step towards the use of connectivity information in quantitative approaches to the study of neuropsychiatric disorders. When estimating brain connectivity a challenge is imposed by the paucity of time samples and the large dimensionality of the measurements. …

Proposes a method to enhance graph models by injecting unseen connections.

Clarifies connections between Nyström and SVGP methods for scalable GPs.

The past few years have witnessed the fast development of different regularization methods for deep learning models such as fully-connected deep neural networks (DNNs) and Convolutional Neural Networks (CNNs). Most of previous methods mainly consider to drop features from input data and hidden layers, such as Dropout, …

Reduces constructing multiplicative connections to simpler tasks.

Proves rotational symmetry for Serrin-type problems in doubly connected domains.

Method flattens complex surfaces with consistent density and shape.

Method proves connection stability of vector fields on noncompact manifolds.

Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant connections on algebroids. This has fundamental consequences for the theory of numeri…

Study finds PLI functional connectivity feature superior for depression recognition.

Two novel algorithms for conformal parameterization of multiply-connected surfaces.

We present a hybrid method for latent information discovery on the data sets containing both text content and connection structure based on constrained low rank approximation. The new method jointly optimizes the Nonnegative Matrix Factorization (NMF) objective function for text clustering and the Symmetric NMF (SymNMF…

Paper connects risk consistency to L_p consistency for broader loss functions.

Learning-based link scheduling improves network performance in millimeter-wave multi-connectivity.

Paper finds non-positive Weyl connections on Lie groups, confirming a conjecture.

We proved a uniqueness theorem of tangent connections for a Yang-Mills connection with an isolated singularity with a quadratic growth of the curvature at the singularity. We also obtained controls over the rate of the asymptotic convergence of the connection to the tangent connection under assumptions that the connect…

Skip connections are an essential component of current state-of-the-art deep neural networks (DNNs) such as ResNet, WideResNet, DenseNet, and ResNeXt. Despite their huge success in building deeper and more powerful DNNs, we identify a surprising security weakness of skip connections in this paper. Use of skip connectio…

This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…

DCGANs generate drainage networks quickly from samples.

The paper extends affine connection results to singular warped and twisted products.

eDCF estimates intrinsic dimension using local connectivity.

In this paper, a frequency coefficient based on the Sen-Shorrocks-Thon (SST) poverty index notion is proposed. The clustering SST index can be used as the method for determination of the connection between similar neighbor sub-clusters. Consequently, connections can reveal existence of natural homogeneous. Through esti…

It is well-known that a torsion-free linear connection on a light-like manifold $(M,g)$ compatible with the degenerate metric $g$ exists if and only if $Rad(TM)$ is a Killing distribution. In case of existence, there is an infinitude of connections with none distinguished. We propose a method to single out connections …

Improved graph-based connectivity estimation using heat modelling.

We propose a novel denoising framework for task functional Magnetic Resonance Imaging (tfMRI) data to delineate the high-resolution spatial pattern of the brain functional connectivity via dictionary learning and sparse coding (DLSC). In order to address the limitations of the unsupervised DLSC-based fMRI studies, we u…

A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic model-based dynamic neural network structure optimization that considers the probabilit…

In this paper, we discuss some aspects of the averaging method for Poisson connections on foliated manifolds with symmetry generalizing the previous results on the Hannay-Berry connections on fibrations due to \cite{Mn-88,MaMoRa-90} which play an important role in the normal form theory for Hamiltonian systems of adiab…

Development of stock networks is an important approach to explore the relationship between different stocks in the era of big-data. Although a number of methods have been designed to construct the stock correlation networks, it is still a challenge to balance the selection of prominent correlations and connectivity of …

We construct several natural connections and Dirac type operators on a general metric contact manifold which are more sensitive to the geometric background. In the special case of CR manifolds these connections are also compatible with the CR structure and include among them the Webster connection. We also describe sev…

Improved matching for multiple objects using a novel reweighting method.

A new method for faster optimization on statistical manifolds.

The paper studies conformal and projective structures using 2-frame bundles.

We introduce a method in differential geometry to study the derivative operators of Siegel modular forms. By determining the coefficients of the invariant Levi-Civita connection on a Siegel upper half plane, and further by calculating the expressions of the differential forms under this connection, we get a non-holomor…

In our previous work, we have defined a nonlinear connection of Finsler manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method easier and more useful in applications, moving frame (vielbein) $θ^a={e^a}_μdx^μ$ formalism for the nonlinear connection is newly considered. We derive formulae to calculat…