arXiv research

New method fills MS lesions more realistically and naturally.

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

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…

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

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

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep learning architectures work for specific inverse problems. To address these issu…

3D Axial-Attention improves lung nodule classification accuracy.

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-…

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

We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with possibly non locally Lipschitz functions. We characterize the points where this Lip…

Non-local GNNs improve performance on disassortative graphs.

The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.

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

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

New kernels capture both local and non-local interactions efficiently.

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.

Deep learning systems have become ubiquitous in many aspects of our lives. Unfortunately, it has been shown that such systems are vulnerable to adversarial attacks, making them prone to potential unlawful uses. Designing deep neural networks that are robust to adversarial attacks is a fundamental step in making such sy…

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.

Study shows that dimension of Dolbeault harmonic forms is not always equal to B- on certain 4-manifolds.

A new GCN variant tackles large eigengaps in dense graphs and hypergraphs.

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

In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying asset prices over some predetermined time interval. The mathematical model for the …

New birth-death dynamics accelerates convergence in neural networks.

We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that McMullen's polytope algebra is a subalgebra of the (partial) convolution algebra …

We give necessary conditions for certain real analytic tube generic submanifolds in C^n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in C^n. During the proof, we show that the local CR automorphism group of a minimal, finitely n…

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…

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…

NESTA accelerates neural networks by compressing Hamming weights.

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.

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …

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

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.

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.

Corrected graph convolutions improve node classification on graphs.

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…

FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.

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

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.

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…