arXiv research

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-…

Non-local GNNs improve performance on disassortative graphs.

Machine learning detects non-local correlations in complex scenarios.

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.

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.

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

Non-local U-Net improves biomedical image segmentation with fewer parameters and faster computation.

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 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…

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.

NL-LinkNet improves road extraction from satellite images with fewer parameters and faster training.

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

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

New method fills MS lesions more realistically and naturally.

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

Finite volume ends found in quaternionic Kähler manifolds.

Gradients help find global optima in complex functions.

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…

The paper studies curvature and topology of conformally flat manifolds with non-local curvature constraints.

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…

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.

Paper proves well-posedness of PDE for option pricing in a complex market model.

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

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

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…

3D Axial-Attention improves lung nodule classification accuracy.

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…

Bayesian detector improves defect detection on rough surfaces.

Solution to qc Yamabe problem on non-spherical quaternionic contact manifolds.

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

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…

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…

Deep Local-Global network improves lung nodule malignancy prediction.

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

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

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

SCRAM accelerates image attention computation to O(n log(n)) from O(n^2).

Study on birational rigidity and stability of hypersurfaces and complete intersections, proving non-locally closed property.

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

Study shows non-locally-flat concordance elements in knot theory.

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

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