Publications related to Affine plane (incidence geometry)

Spatial analysis of 10-year predicted risk and incident atherosclerotic cardiovascular disease: the CoLaus cohort

Stéphane Joost, Idris Guessous, David Nicolas De Ridder, Guillaume Jordan

Whether cardiovascular risk scores geographically aggregate and inform on spatial development of atherosclerotic cardiovascular diseases (ASCVD) remains unknown. Our aim is to determine the spatial distribution of 10-year predicted cardiovascular risk and ...

2024

Finite Littlestone Dimension Implies Finite Information Complexity

Michael Christoph Gastpar, Aditya Pradeep, Ido Nachum

We prove that every online learnable class of functions of Littlestone dimension d admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of ...

2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

An Input–Output Parametrization of Stabilizing Controllers: Amidst Youla and System Level Synthesis

Maryam Kamgarpour, Luca Furieri

This letter proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances ...

2019

Homology of the three flag Hilbert Scheme

Daniele Boccalini

We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing ...

EPFL2016

Decomposition of Multiple Packings with Subquadratic Union Complexity

János Pach, Bartosz Maria Walczak

Suppose k is a positive integer and X is a k-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most k sets. Suppose there is a function f(n) = o(n(2)) with the property that any ...

Cambridge Univ Press2016

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exis ...

Tech Univ Braunschweig2014

Tangent-based manifold approximation with locally linear models

Pascal Frossard, Sofia Karygianni

In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...

Elsevier2014

On The Convergence Of The Affine Hull Of The Chvatal-Gomory Closures

Yuri Faenza, Marco Di Summa

Given an integral polyhedron P subset of R-n and a rational polyhedron Q subset of R-n containing the same integer points as P, we investigate how many iterations of the Chvatal-Gomory closure operator have to be performed on Q to obtain a polyhedron conta ...

Siam Publications2013

Affine plane (incidence geometry)

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Spatial analysis of 10-year predicted risk and incident atherosclerotic cardiovascular disease: the CoLaus cohort

Finite Littlestone Dimension Implies Finite Information Complexity

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

An Input–Output Parametrization of Stabilizing Controllers: Amidst Youla and System Level Synthesis

Homology of the three flag Hilbert Scheme

Decomposition of Multiple Packings with Subquadratic Union Complexity

Signal structure: from manifolds to molecules and structured sparsity

Deciding Conditional Termination

Tangent-based manifold approximation with locally linear models

On The Convergence Of The Affine Hull Of The Chvatal-Gomory Closures

Finite Littlestone Dimension Implies Finite Information Complexity

Decomposition of Multiple Packings with Subquadratic Union Complexity

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Deciding Conditional Termination

Signal structure: from manifolds to molecules and structured sparsity

On The Convergence Of The Affine Hull Of The Chvatal-Gomory Closures

Spatial analysis of 10-year predicted risk and incident atherosclerotic cardiovascular disease: the CoLaus cohort

Homology of the three flag Hilbert Scheme

Tangent-based manifold approximation with locally linear models

An Input–Output Parametrization of Stabilizing Controllers: Amidst Youla and System Level Synthesis