Related papers: Alpha shapes and optimal transport on the sphere

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…

This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical…

We describe linear and nonlinear transport across a single impurity Anderson model quantum dot with intermediate coupling to the leads, i.e., with tunnel coupling of the order of the thermal energy k_B T. The coupling is large enough that…

We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…

In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…

In calculations of transport quantities, such as the electrical conductivity, thermal conductivity, Seebeck, Peltier, Nernst, Ettingshausen, Righi-Leduc, or Hall coefficients, sums over the Brillouin zone of wave-vector derivatives of the…

Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…

Graph neural networks (GNNs) are designed to extract latent patterns from graph-structured data, making them particularly well suited for crystal representation learning. Here, we propose a GNN model tailored for estimating electronic…

Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of…

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…

Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the…

This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…

We investigate Turing's notion of an A-type artificial neural network. We study a refinement of Turing's original idea, motivated by work of Teuscher, Bull, Preen and Copeland. Our A-types can process binary data by accepting and outputting…

Optimization of neural network (NN) significantly influenced by the transfer function used in its active nodes. It has been observed that the homogeneity in the activation nodes does not provide the best solution. Therefore, the…

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an…

We propose a graph-oriented attention-based explainability method for tabular data. Tasks involving tabular data have been solved mostly using traditional tree-based machine learning models which have the challenges of feature selection and…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation…

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is…