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Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…

We propose to apply to the detection of Gravitational Waves a new method developed for the spectral analysis of noisy time-series of damped oscillators. From the Pad\'e Approximations of the time-series Z-transform, a Jacobi Matrix…

We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian orthogonal ensemble (Cartan class B$|$DI) and the ensemble of…

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…

This paper investigates the enhancement of spatial resolution in Sentinel-2 bands that contain spectral information using advanced super-resolution techniques by a factor of 2. State-of-the-art CNN models are compared with enhanced GAN…

We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…

We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping…

Earth observation with small satellites serves a wide range of relevant applications. However, significant advances in sensor technology (e.g., higher resolution, multiple spectrums beyond visible light) in combination with challenging…

Geometric deep learning is an emerging technique in Artificial Intelligence (AI) driven cheminformatics, however the unique implications of different Graph Neural Network (GNN) architectures are poorly explored, for this space. This study…

Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations…

In this paper, we propose to estimate the invariant subspace across heterogeneous multiple networks using a novel bias-corrected joint spectral embedding algorithm. The proposed algorithm recursively calibrates the diagonal bias of the sum…

Dense image alignment from RGB-D images remains a critical issue for real-world applications, especially under challenging lighting conditions and in a wide baseline setting. In this paper, we propose a new framework to learn a pixel-wise…

We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac-Weyl problem exactly, we show that the imaginary part of the barrier renders the…

Multiplicative noise makes stochastic dynamics depend on how the white-noise limit is interpreted. In multidimensional systems with matrix-valued noise amplitudes $\sigma(x)$, this dependence includes a local Jacobian contribution that is…

Spatial transcriptomics (ST) measures mRNA expression while preserving spatial organization, but multi-slice analysis faces two coupled difficulties: large non-rigid deformations across slices and inter-slice batch effects when alignment…

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a…

Critical applications in areas such as medicine, robotics and autonomous systems require compact (i.e., memory efficient), uncertainty-aware neural networks suitable for edge and other resource-constrained deployments. We study compact…

Accurately registering in-vivo two-photon and ex-vivo fluorescence micro-optical sectioning tomography images of individual neurons is critical for structure-function analysis in neuroscience. This task is profoundly challenging due to a…

Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix…