Concept
Maximal and minimal elements
Related publications (33)
From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem
Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based ...
2024On the number of regions of piecewise linear neural networks
Michaël Unser, Alexis Marie Frederic Goujon
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
2024Early 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 Ltd2023On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls
Daniel Kuhn, Zhi Chen, Wolfram Wiesemann
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...
2022On complete reducibility of tensor products of simple modules over simple algebraic groups
Let G be a simply connected simple algebraic group over an al- gebraically closed field k of characteristic p > 0. The category of rationalG-modules is not semisimple. We consider the question of when the tensorproduct of two simple G-modules L(λ) and L(μ) ...
2021AKSEL: Fast Byzantine SGD
Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Sébastien Louis Alexandre Rouault
Modern machine learning architectures distinguish servers and workers. Typically, a d-dimensional model is hosted by a server and trained by n workers, using a distributed stochastic gradient descent (SGD) optimization scheme. At each SGD step, the goal is ...
Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik2021A simple proof for a forbidden subposet problem
The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)
ELECTRONIC JOURNAL OF COMBINATORICS2020Multiplicative combinatorial properties of return time sets in minimal dynamical systems
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove t ...
2019Almost tiling of the Boolean lattice with copies of a poset
Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...
ELECTRONIC JOURNAL OF COMBINATORICS2018Data-Driven Chance Constrained Programs over Wasserstein Balls
Daniel Kuhn, Zhi Chen, Wolfram Wiesemann
We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed ...
2018