Search results for "graphs"
showing 10 items of 126 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Intégrer la connectivité paysagère dans la séquence ERC : une approche par la quantité d'habitat atteignable
2019
Des engagements nationaux, européens et internationaux ont été pris pour maintenir et restaurer la connectivité entre habitats naturels face à la perte et à la fragmentation de ces habitats. Dans le même temps, les politiques environnementales dans différents pays mettent en oeuvre la séquence Eviter-Réduire-Compenser (ERC) pour atteindre l’objectif d’absence de perte nette de biodiversité (PPN). La séquence ERC a pour principe d’évaluer l’ensemble des impacts écologiques d’un aménagement, mais les critères et indicateurs permettant de quantifier les impacts sur la connectivité paysagère ne sont pas satisfaisants. Nous proposons une démarche opérationnelle pour évaluer les impacts environne…
Online Scheduling of Task Graphs on Hybrid Platforms
2018
Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous \(4\sqrt{m/k}\)-competitive online algorithm [2], where m is the number of CPUs and k the number of GPUs (\(m\ge k\)). We prove that no online algorithm can have a competitive ratio …
Robust link prediction in criminal networks: A case study of the Sicilian Mafia
2020
Abstract Link prediction exercises may prove particularly challenging with noisy and incomplete networks, such as criminal networks. Also, the link prediction effectiveness may vary across different relations within a social group. We address these issues by assessing the performance of different link prediction algorithms on a mafia organization. The analysis relies on an original dataset manually extracted from the judicial documents of operation “Montagna”, conducted by the Italian law enforcement agencies against individuals affiliated with the Sicilian Mafia. To run our analysis, we extracted two networks: one including meetings and one recording telephone calls among suspects, respect…
Graph-theoretical derivation of brain structural connectivity
2020
Brain connectivity at the single neuron level can provide fundamental insights into how information is integrated and propagated within and between brain regions. However, it is almost impossible to adequately study this problem experimentally and, despite intense efforts in the field, no mathematical description has been obtained so far. Here, we present a mathematical framework based on a graph-theoretical approach that, starting from experimental data obtained from a few small subsets of neurons, can quantitatively explain and predict the corresponding full network properties. This model also changes the paradigm with which large-scale model networks can be built, from using probabilisti…
Having your cake and eating it: Faster responses with reduced muscular activation while learning a temporal interval
2019
International audience; We examined how motor responses to a stimulus evolve as individuals learn to predict when a stimulus will appear, by comparing responses to a regular versus irregular stimulus train. The study was conducted with two groups of adults — one responded to the regular appearance of a visual stimulus every 3 s (R group) and the second responded to the irregular presentation of the same stimulus (IR group) at intervals varying between 2 and 4 s. Participants responded to the appearance of the stimulus by bending over to press a button that was slightly out of reach. This whole body reach requires muscular activation at the ankles. Over the course of 50 consecutive responses…
The Metabolic Building Blocks of a Minimal Cell
2020
This article belongs to the Section Evolutionary Biology.
Molecular Diversity Required for the Formation of Autocatalytic Sets
2019
Systems chemistry deals with the design and study of complex chemical systems. However, such systems are often difficult to investigate experimentally. We provide an example of how theoretical and simulation-based studies can provide useful insights into the properties and dynamics of complex chemical systems, in particular of autocatalytic sets. We investigate the issue of the required molecular diversity for autocatalytic sets to exist in random polymer libraries. Given a fixed probability that an arbitrary polymer catalyzes the formation of other polymers, we calculate this required molecular diversity theoretically for two particular models of chemical reaction systems, and then verify …
Accuracy combining different brands of implants and abutments
2013
Objective: To evaluate the vertical misfit between different brands of dental implants and prosthetic abutments, with or without mechanical torque, and to study their possible combination. Study design: Five different brands of implant were used in the study: Biofit (Castemaggiore, Italy), Bioner S.A. (Barcelona, Spain), 3i Biomet (Palm Beach, U.S.A.), BTI (Alava, Spain) and Nobel Biocare (Göteborg, Sweden), with standard 4.1 mm heads and external hexagons, and their respective machined prosthetic abutments. The implant-to- abutment fit/misfit was evaluated at four points (vestibular, lingual/palatine, mesial and distal) between implants and abutments of the same brand and different brands,…