arXiv research

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

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.

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.

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…

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

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…

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

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.

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…

The paper proposes a method to precisely decompose confounders and estimate treatment effects.

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.

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…

Research shows continual learning challenges in confounded datasets.

Statistical learning on biological data can be challenging due to confounding variables in sample collection and processing. Confounders can cause models to generalize poorly and result in inaccurate prediction performance metrics if models are not validated thoroughly. In this paper, we propose methods to control for …

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

Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treat…

Detect hidden confounding in observational data using multiple environments.

Machine learning confound removal biases results, leading to misleading predictions.

KRCD detects unobserved confounders in nonlinear observational data.

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…

Study identifies conditions for proxy adjustment in confounded binary treatment outcomes.

New method estimates policy performance under unobserved confounding.

Consistent estimator derived for confounding strength in observational data.

A new method uses randomized trials to estimate the strength of unobserved confounding.

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…

This paper tackles confounding biases in data augmentation.

New method recovers latent confounders from high-dimensional proxy variables.

Proposes tests to control confounding bias in predictive models.

New method tackles confounded bandit problems with dual instrumental variables.

New approach for causal inference with interdependent, time-varying latent confounders.

Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders, while some constraint-based methods can present them. This paper proposes a causal f…

Estimating the individual treatment effect (ITE) from observational data is essential in medicine. A central challenge in estimating the ITE is handling confounders, which are factors that affect both an intervention and its outcome. Most previous work relies on the unconfoundedness assumption, which posits that all th…