arXiv research

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

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.

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…

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

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

We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local potential. We then consider the fractional perimeter in half-spaces. We prove the exis…

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…

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-…

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…

Non-local GNNs improve performance on disassortative graphs.

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

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.

Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result becomes false for some arbitrarily small, smooth perturbations of the potential.

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…

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…

We present an alternative local definition of the writhe of a self-avoiding closed loop which differs from the traditional non-local definition by an integer. When studying dynamics this difference is immaterial. We employ a formula due to Aldinger, Klapper and Tabor for the change in writhe and propose a set of local,…

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.

Study examines how insurance affects households prone to proportional losses, especially those near poverty.

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic Kähler non locally hyper paraKähler manifolds. Then we examine, as an example, the c…

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

We establish some a priori geometric relations on stable minimal surfaces lying inside three-manifolds with scalar curvature uniformly bounded below. The relations are based on a slight generalization of a formula due to Castillon. We apply it to prove non-local rigidity results in the particular sense that they expres…

New method fills MS lesions more realistically and naturally.

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.

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…

New curve flow preserves area and converges to a circle.

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.

Study a flow preserving area of plane curves, ending in a circle.

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

Study proves existence and properties of shrinkers in area-preserving curve-shortening flow.

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

We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us …

The paper analyzes Laplacian pyramids for extending and denoising discrete functions.

Study the boundary operator property on simplicial complexes, proving essential properties for Hodge theory.

New birth-death dynamics accelerates convergence in neural networks.

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.

Study covers of surfaces, showing types and properties.

Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, ther…