arXiv research

Non-local GNNs improve performance on disassortative graphs.

Weather2vec learns representations to adjust for non-local confounding in air pollution studies.

This paper improves image super-resolution by integrating cross-scale non-local attention.

We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal boundaries are smooth. This can be viewed as a non-local version of the Almgren-…

The study examines hypersurfaces close to constant mean curvature and their proximity to spheres.

Deep learning has shown its great promise in various biomedical image segmentation tasks. Existing models are typically based on U-Net and rely on an encoder-decoder architecture with stacked local operators to aggregate long-range information gradually. However, only using the local operators limits the efficiency and…

Study of Dirac equation with non-local nonlinearity on spheres.

We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positi…

It is argued that the enlargement of the gauge group found in non-commutative gauge theory is more fundamentally thought of as a consequence of the non-locality of the construction and that it was already encountered in an earlier discussion of a non-local gauge theory.

3D Axial-Attention improves lung nodule classification accuracy.

In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

The ability to witness non-local correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scena…

We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic type, there ex…

In this paper, we study CAT(0) spaces with non-locally connected boundary. We give some condition of a CAT(0) space whose boundary is not locally connected.

In this paper, we study global existence and blow up properties to $L^p$ norm preserving non-local heat flows. We first study two kinds of $L^p$ norm preserving non-local flows and prove that these flows have the global solutions. Finally, we give a example to show that one kind of this heat flow may blow up in $L^{\in…

Two local learning rules are investigated to avoid weight transport in neural networks.

MFNs parameterize non-local interactions through matrix equivariant functions, improving graph neural network performance.

Regularization plays a crucial role in machine learning models, especially for deep neural networks. The existing regularization techniques mainly rely on the i.i.d. assumption and only consider the knowledge from the current sample, without the leverage of the neighboring relationship between samples. In this work, we…

Road extraction from very high resolution satellite (VHR) images is one of the most important topics in the field of remote sensing. In this paper, we propose an efficient Non-Local LinkNet with non-local blocks that can grasp relations between global features. This enables each spatial feature point to refer to all ot…

Finite volume ends found in quaternionic Kähler manifolds.

Study non-local isoperimetric energies on spheres using a Riemannian autocorrelation function.

Gradients help find global optima in complex functions.

Proposes a graph dynamics prior for more accurate relational inference.

Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…

Scientific discovery is limited by hypothesis redundancy, and hybrid methods can exploit non-local exploration.

In this paper, we consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\infty} sense as time goes into infinity.

This article addresses the two significant aspects of Ozsváth and Szabó's knot Floer cube of resolutions that differentiate it from Khovanov and Rozansky's HOMFLY-PT chain complex: (1) the use of twisted coefficients and (2) the appearance of a mysterious non-local ideal. Our goal is to facilitate progress on Rasmussen…

It is shown that the qc Yamabe problem has a solution on any compact qc manifold which is non-locally qc equivalent to the standard 3-Sasakian sphere. Namely, it is proved that on a compact non-locally spherical qc manifold there exists a qc conformal qc structure with constant qc scalar curvature

Paper proposes an active learning method for surgical workflow recognition using long-range temporal dependency.

Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into the NLM framework. This general optimization framework, called Non-Local Patch Regression (NLPR), contains NLM as a spe…

New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.

Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS) that results in focal injury to the grey and white matter. The presence of white matter lesions biases morphometric analyses such as registration, individual longitudinal measurements and tissue segmentation for brain v…

Study finds non-uniqueness in sphere metrics with constant fractional curvature.

We study conformal metrics on $R^3$, i.e., metrics of the form $g_u=e^{2u}|dx|^2$, which have constant $Q$-curvature and finite volume. This is equivalent to studying the non-local equation $(-Δ)^\frac32 u = 2 e^{3u}$ in $R^3$ $V:=\int_{\mathbb{R}^3}e^{3u}dx<\infty,$ where $V$ is the volume of $g_u$. Adapting a te…

New examples show non-locally-flat PL-disk bounds in rational homology balls but not in integer homology balls.

We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat $\mathbb{R}^4$. We show how all such connections lie in the orbit of the flat connection on $\mathbb{R}^4$ under the action of non-local symmetries of the self-dual Yang-Mills …

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at ea…

Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programmin…

Deep learning model predicts traffic flows across entire network for multiple steps ahead.

We solve the $σ_2$-Yamabe problem for a non locally conformally flat manifold of dimension $n>8$.

This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…

Softmax is found ineffective for NL block, leading to improved performance.

We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.

The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to in…

Combines local and global samplers for efficient sampling.

Paper presents a novel approach for global feature aggregation in Graph Neural Networks.