Few distinct distances implies no heavy lines or circles

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We prove that a geometrically integral smooth projective 3-fold (Formula presented.) with nef anti-canonical class and negative Kodaira dimension over a finite field (Formula presented.) of characteristic (Formula presented.) and cardinality (Formula prese ...

Morton's knots are a family of space curves to which there is no plane simultaneously tangent in three distinct points. This property enables a physical instance to roll on a plane while having at most two contact points with it. These knots are not smooth ...

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

A method for optimizing at least one of a geometry, an implantation procedure, and/or stimulation protocol of one or more electrodes for an electrical stimulation of a target structure in a nervous system of a living being by a computer device, the method ...

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. They also enable building of dat ...

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible ...

The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, th ...

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat c ...

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 ...

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...

Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with re ...

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

Nonparametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these issues in the de ...

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

Few distinct distances implies no heavy lines or circles

Chat with Graph Search

Rational points on 3-folds with nef anti-canonical class over finite fields

Smooth-Rolling Knots

Unlabeled Principal Component Analysis and Matrix Completion

Incorporating Projective Geometry into Deep Learning

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Cochains are all you need

Geometric Learning: Leveraging differential geometry for learning and control

A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

Enhancement of brain atlases with region-specific coordinate systems: flatmaps and barrel column annotations

Koopman analysis of the periodic Korteweg-de Vries equation

New SIDH Countermeasures for a More Efficient Key Exchange

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

Neural-network quantum states for periodic systems in continuous space

Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

Reduced order modelling of nonaffine problems on parameterized NURBS multipatch geometries

An unrefinement algorithm for planar THB-spline parameterizations

Localization errors of the stochastic heat equation

Inference and Computation for Sparsely Sampled Random Surfaces

Reduced representations of complexes, signals, and multifiltrations