Related papers: Alpha shapes and optimal transport on the sphere

Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…

We consider a PDE approach to numerically solving the optimal transportation problem on the sphere. We focus on both the traditional squared geodesic cost and a logarithmic cost, which arises in the reflector antenna design problem. At each…

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

We examine how conformal boundaries encode energy transport coefficients -- namely transmission and reflection probabilities -- of corresponding conformal interfaces in symmetric orbifold theories. These constitute a large class of…

For every Gaussian kernel density estimator $f(x)=\sum_i a_i \exp(-\lVert x-x_i\rVert^2/2h^2)$ associated to a point cloud $\mathcal{D}=\{x_1,...,x_N\}\subset \mathbb{R}^d$, we define a nested family of closed subspaces…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

During the past decades, approximate Kohn-Sham density-functional theory schemes garnered many successes in computational chemistry and physics; yet the performance in the prediction of spin state energetics is often unsatisfactory. By…

We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…

The Kinematic Theory of rapid movements, and its associated Sigma-Lognormal, model 2D spatiotemporal trajectories. It is constructed mainly as a temporal overlap of curves between virtual target points. Specifically, it uses an arc and a…

We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…

Transfer learning has drawn growing attention with the target of improving statistical efficiency of one study (dataset) by digging information from similar and related auxiliary studies (datasets). In the article, we consider transfer…

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with…

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…

In this short note, we consider the problem of prescribing the Gauss curvature and image of the Gauss map for the graph of a function over a domain in Euclidean space. The prescription of the image of the Gauss map turns this into a second…

This paper investigates how Transformer language models (LMs) fine-tuned for acceptability classification capture linguistic features. Our approach uses the best practices of topological data analysis (TDA) in NLP: we construct directed…

An efficient computational methodology is used to explore charge transport properties in chemically-modified (and randomly disordered) graphene-based materials. The Hamiltonians of various complex forms of graphene are constructed using…

A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many…