Obstacles For Splitting Multidimensional Necklaces

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In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get m ...

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-n ...

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

Tonality is one of the most central theoretical concepts for the analysis of Western classical music. This study presents a novel approach for the study of its historical development, exploring in particular the concept of mode. Based on a large dataset of ...

We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in al ...

We show that the finitely generated simple left orderable groups G(rho) constructed by the first two authors in Hyde and Lodha [Finitely generated infinite simple groups of homeomorphisms of the real line. Invent. Math. (2019), doi:10.1007/s00222-01900880- ...

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

In this article we explain the essence of the interrelation described in [PNAS 118, 15 (2021)] on how to write explicit interpolation formula for solutions of the Klein-Gordon equation by using the recent Fourier pair interpolation formula of Viazovska and ...

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve the Euclidean st ...

Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...

Obstacles For Splitting Multidimensional Necklaces

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On Generalizations of Some Distance Based Classifiers for HDLSS Data

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Neural-network quantum states for periodic systems in continuous space

Realizing doubles: a conjugation zoo

Exploring the foundations of tonality: statistical cognitive modeling of modes in the history of Western classical music

Experimental Observation and Spin Texture of Dirac Node Arcs in Tetradymite Topological Metals

Uniformly perfect finitely generated simple left orderable groups

On Linear Interpolation in the Latent Space of Deep Generative Models

Hyperbolic Fourier series

UCLID-Net: Single View Reconstruction in Object Space

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms