Search results for " graph"
showing 10 items of 1277 documents
A Novel Approach of a Low-Cost UWB Microwave Imaging System with High Resolution Based on SAR and a New Fast Reconstruction Algorithm for Early-Stage…
2022
In this article, a new efficient and robust approach—the high-resolution microwave imaging system—for early breast cancer diagnosis is presented. The core concept of the proposed approach is to employ a combination of a newly proposed delay-and-sum (DAS) algorithm and the specific absorption rate (SAR) parameter to provide high image quality of breast tumors, along with fast image processing. The new algorithm enhances the tumor response by altering the parameter referring to the distance between the antenna and the tumor in the conventional DAS matrices. This adjustment entails a much clearer reconstructed image with short processing time. To achieve these aims, a high directional Vivaldi …
Inferring networks from high-dimensional data with mixed variables
2014
We present two methodologies to deal with high-dimensional data with mixed variables, the strongly decomposable graphical model and the regression-type graphical model. The first model is used to infer conditional independence graphs. The latter model is applied to compute the relative importance or contribution of each predictor to the response variables. Recently, penalized likelihood approaches have also been proposed to estimate graph structures. In a simulation study, we compare the performance of the strongly decomposable graphical model and the graphical lasso in terms of graph recovering. Five different graph structures are used to simulate the data: the banded graph, the cluster gr…
Structure of eigenvectors of random regular digraphs
2018
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we study the structure of the kernel of submatrices of $M-z\,{\rm Id}$, formed by removing a subset of rows. We show that with large probability the kernel consists of two non-intersecting types of vectors, which we call very steep and gradual with many levels. As a corollary, we show, in particular, that every eigenvector of $M$, except for constant multiples of $(1,1,\dots,1)$, possesses a weak delocalization property: its level sets have cardin…
Spatial Search by Quantum Walk is Optimal for Almost all Graphs.
2015
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erd\"os-Renyi random graphs, i.e.\ graphs of $n$ vertices where each edge exists with probability $p$, search by CTQW is \textit{almost surely} optimal as long as $p\geq \log^{3/2}(n)/n$. Consequently, we show that quantum spatial search is in fact optimal for \emph{almost all} graphs, meaning that the fraction of graphs of $n$ vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by provin…
Homogeneous actions on the random graph
2018
We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.
From time series to complex networks: the visibility graph
2008
In this work we present a simple and fast computational method, the visibility algorithm , that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach cha…
Information Functionals and the Notion of (Un)Certainty: Random Matrix Theory - Inspired Case
2007
Information functionals allow one to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the “minimum information” assumption, which is a classic concept (R. Balian, 1968) in the random matrix theory. We put special emphasis on generic level (eigenvalue) spacing distributions and the degree of their randomness, or alternatively — information/organization deficit.
Growth, percolation, and correlations in disordered fiber networks
1997
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
Spatial graphs and Convolutive Models
2020
In the last two decades, many complex systems have benefited from the use of graph theory, and these approaches have shown robust applicability in the field of finance, computer circuits and in biological systems. Large scale models of brain systems make also a great use of random graph models. Graph theory can be instrumental in modeling the connectivity and spatial distribution of neurons, through a characterization of the relative topological properties. However, all approaches in studying brain function have been so far limited to use experimental constraints obtained at a macroscopic level (e.g. fMRI, EEG, MEG, DTI, DSI). In this contribution, we present a microscopic use (i.e. at the …
Joint Topology and Radio Resource Optimization for Device-to-Device Based Mobile Social Networks
2018
In this paper, we consider a joint topology and radio resource optimization for device-to-device (D2D) based mobile social networks. The considered social network is an interest based which is modeled as a d -intersection binomial random graph. The Radio network is also modeled as a random graph where an edge between any two distinct nodes is activated with a certain probability that is equivalent to the probability of exceeding a certain signal to interference ratio for that link. The entire network is then modeled as an intersection graph between the social and radio induced graphs. Thereafter, network topology is optimized such that enabled social edges satisfy certain network connectivi…