Consistent Digital Line Segments

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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 ...

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

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 are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

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 ...

We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

Popular clustering algorithms based on usual distance functions (e.g., the Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances and violation of neighborhood structure have advers ...

Consistent Digital Line Segments

Chattez avec Graph Search

On Linear Interpolation in the Latent Space of Deep Generative Models

A dependence of the cost of fast controls for the heat equation on the support of initial datum

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

Model order reduction of flow based on a modular geometrical approximation of blood vessels

UCLID-Net: Single View Reconstruction in Object Space

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

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

Coordinate Difference Matrices

On Perfect Clustering of High Dimension, Low Sample Size Data