Concept

Sigma additivité

Publications associées (18)

Early decoding of walking tasks with minimal set of EMG channels

Silvestro Micera, Francesco Iberite, Federica Barberi, Eugenio Anselmino

Objective. Powered lower-limb prostheses relying on decoding motor intentions from non-invasive sensors, like electromyographic (EMG) signals, can significantly improve the quality of life of amputee subjects. However, the optimal combination of high decod ...

IOP Publishing Ltd2023

Correspondence functors and duality

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

Deterministic error bounds for kernel-based learning techniques under bounded noise

Colin Neil Jones, Paul Scharnhorst, Emilio Maddalena

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

2021

Sparse non-negative super-resolution - simplified and stabilised

Armin Eftekhari, Hemant Tyagi

We consider the problem of non-negative super-resolution, which concerns reconstructing a non-negative signal x = Sigma(k )(i=1)a(i)delta(ti) from m samples of its convolution with a window function phi(s - t), of the form y(s(j)) = Sigma(k)(i=1) a(i) phi( ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Dynamic Optimization of Reaction Systems via Exact Parsimonious Input Parameterization

Dominique Bonvin, Diogo Filipe Mateus Rodrigues

This paper discusses the use of parsimonious input parameterization for the dynamic optimization of reaction systems. This parameterization is able to represent the optimal inputs with only a few parameters. In the context of batch, semibatch, and continuo ...

AMER CHEMICAL SOC2019

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Volkan Cevher, Marwa El Halabi

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinato ...

2017

Families with no s pairwise disjoint sets

Andrei Kupavskii

For integers n >= s >= 2 let e (n, s) denote the maximum of vertical bar F vertical bar, where F is a family of subsets of an n- element set and F contains no s pairwise disjoint members. Half a century ago, solving a conjecture of Erd. os, Kleitman determ ...

Wiley2017

Small subset sums

Gergely Ambrus

Let parallel to.parallel to be a norm in R-d whose unit ball is B. Assume that V subset of B is a finite set of cardinality n, with Sigma(v is an element of V) v = 0. We show that for every integer k with 0

Elsevier Science Inc2016

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

The algebra of essential relations on a finite set

Jacques Thévenaz, Serge Bouc

Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential rel ...

Walter de Gruyter2016

Double-Normal Pairs In Space

János Pach

A double-normal pair of a finite set S of points that spans R-d is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair {p, q} is strict if S \ {p,q} lies i ...

London Mathematical Society, Cambridge2015

The monoid algebra of all relations on a finite set

Jacques Thévenaz, Serge Bouc

We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra. ...

2015

Metastability of reversible condensed zero range processes on a finite set

Johel Beltran Ramirez

Let r : S x S -> R+ be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For alpha > 1, let g : N -> R+ be given by g(0) = 0, g(1) = 1, g(k) = (k/k - 1)(alpha), k >= 2. Consider a zero ra ...

2012

Overlap properties of geometric expanders

The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...

De Gruyter2011

Tangencies between families of disjoint regions in the plane

János Pach

Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...

2010

Convexly independent subsets of the Minkowski sum of planar point sets

János Pach, Friedrich Eisenbrand, Thomas Rothvoss

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...

American Mathematical Society2008