Search results for "graphs"
showing 10 items of 126 documents
Chevalley cohomology for aerial Kontsevich graphs
2013
Let $T_{\operatorname{poly}}(\mathbb{R}^d)$ denote the space of skew-symmetric polyvector fields on $\mathbb{R}^d$, turned into a graded Lie algebra by means of the Schouten bracket. Our aim is to explore the cohomology of this Lie algebra, with coefficients in the adjoint representation, arising from cochains defined by linear combination of aerial Kontsevich graphs. We prove that this cohomology is localized at the space of graphs without any isolated vertex, any "hand" or any "foot". As an application, we explicitly compute the cohomology of the "ascending graphs" quotient complex.
Quantum synchronisation and clustering in chiral networks
2022
We study the emergence of synchronisation in a chiral network of harmonic oscillators. The network consists of a set of locally incoherently pumped harmonic oscillators coupled pairwise in cascade with travelling field modes. Such cascaded coupling leads to feedback-less dissipative interaction between the harmonic oscillators of the pair which can be described in terms of an effective pairwise hamiltonian a collective pairwise decay. The network is described mathematically in terms of a directed graph. By analysing geometries of increasing complexity we show how the onset of synchronisation depends strongly on the network topology, with the emergence of synchronised communities in the case…
Maintaining Dynamic Minimum Spanning Trees: An Experimental Study
2010
AbstractWe report our findings on an extensive empirical study on the performance of several algorithms for maintaining minimum spanning trees in dynamic graphs. In particular, we have implemented and tested several variants of the polylogarithmic algorithm by Holm et al., sparsification on top of Frederickson’s algorithm, and other (less sophisticated) dynamic algorithms. In our experiments, we considered as test sets several random, semi-random and worst-case inputs previously considered in the literature together with inputs arising from real-world applications (e.g., a graph of the Internet Autonomous Systems).
Riesz transform and vertical oscillation in the Heisenberg group
2023
We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…
Root cause analysis of large scale application testing results
2015
In this paper we present a new root cause analysis algorithm for discovering the most likely causes of the differences found in testing results of two versions of the same software. The problematic points in test and environment attribute hierarchies are presented to the user in compact way which in turn allows to save time on test result processing. We have proven that for clearly separated problem causes our algorithm gives exact solution. Practical application of described method is discussed.
Architettura barocca nella Sicilia orientale e progettazione del restauro: la conservazione della facciata della Chiesa di Santa Maria delle Stelle a…
2010
La tavola mostra alcuni elaborati estratti dal progetto di restauro della chiesa di Santa Maria delle Stelle a Comiso (RG), uno degli esempi più rappresentativi d'architettura barocca nella Sicilia orientale.
Graph-based minimal path tracking in the skeleton of the retinal vascular network
2012
This paper presents a semi-automatic framework for minimal path tracking in the skeleton of the retinal vascular network. The method is based on the graph structure of the vessel network. The vascular network is represented based on the skeleton of the available segmented vessels and using an undirected graph. Significant points on the skeleton are considered nodes of the graph, while the edge of the graph is represented by the vessel segment linking two neighboring nodes. The graph is represented then in the form of a connectivity matrix, using a novel method for defining vertex connectivity. Dijkstra and Floyd-Warshall algorithms are applied for detection of minimal paths within the graph…
3D Map Computation from Historical Stereo Photographs of Florence
2018
The analysis of early photographic sources is fundamental for documenting and understanding the evolution of a city so rich in history and art as Florence. Indeed, by the 1860s several photographers used to work in town, and their images (often obtained through stereoscopic set-ups) can help us to reconstruct Florence in 3D as it was by the time of the Italian unification. The first and most delicate part of such reconstruction process is the computation of disparity maps from the historical stereo pairs. This is a very challenging task for fully-automatic computer vision algorithms, since XIX century photographs are affected by several problems—ranging from superficial damages to asynchron…
The rank of random regular digraphs of constant degree
2018
Abstract Let d be a (large) integer. Given n ≥ 2 d , let A n be the adjacency matrix of a random directed d -regular graph on n vertices, with the uniform distribution. We show that the rank of A n is at least n − 1 with probability going to one as n grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of A n .
The smallest singular value of a shifted $d$-regular random square matrix
2017
We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let $$C_1<d< c n/\log ^2 n$$ and let $$\mathcal {M}_{n,d}$$ be the set of all $$n\times n$$ square matrices with 0 / 1 entries, such that each row and each column of every matrix in $$\mathcal {M}_{n,d}$$ has exactly d ones. Let M be a random matrix uniformly distributed on $$\mathcal {M}_{n,d}$$ . Then the smallest singular value $$s_{n} (M)$$ of M is greater than $$n^{-6}$$ with probability at least $$1-C_2\log ^2 d/\sqrt{d}$$ , where c, $$C_1$$ , and $$C_2$$ are absolute positive constants independent of any other parameter…