Search results for " Graph theory"
showing 10 items of 26 documents
Social Network Analysis of Sicilian Mafia Interconnections
2019
In this paper, we focus on the study of Sicilian Mafia organizations through Social Network Analysis. We analyse datasets reflecting two different Mafia Families, based on examinations of digital trails and judicial documents, respectively. The first dataset includes the phone calls logs among suspected individuals. The second one is based on police traces of meeting that have taken place among different types of criminals. Our breakthrough is twofold. First in the method followed to generate these new datasets. Second, in the method used to carry out a quantitative phenomena investigation that are hard to evaluate. Our networks are weighted ones, with each weight catching the frequency of …
Robust Graph Topology Learning and Application in Stock Market Inference
2019
In many applications, there are multiple interacting entities, generating time series of data over the space. To describe the relation within the set of data, the underlying topology may be used. In many real applications, not only the signal/data of interest is measured in noise, but it is also contaminated with outliers. The proposed method, called RGTL, infers the graph topology from noisy measurements and removes these outliers simultaneously. Here, it is assumed that we have no information about the space graph topology, while we know that graph signal are sampled consecutively in time and thus the graph in time domain is given. The simulation results show that the proposed algorithm h…
Free Minor Closed Classes and the Kuratowski theorem
2009
Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.
Graph Topology Learning and Signal Recovery Via Bayesian Inference
2019
The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…
Quasi *-Algebras of Operators in Rigged Hilbert Spaces
2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …
Topologies on Partial O*-Algebras
2002
In this chapter, we introduce some basic locally convex topologies on partial O*-algebras and we establish general properties of these topologies. In Section 4.1, we compare the graph topologies induced by different O-families on the same domain (and the corresponding families of bounded subsets). In the case where the domain D M of an O-family M is a (quasi-) Frechet space, the structure of bounded subsets in D M can be described in a rather explicit way. Section 4.2 and Section 4.3 are devoted to the topologization of (partial) O*-algebras. Section 4.2 deals with locally convex topologies, the so-called uniform topologies τ u , τ u , τ * u and quasiuniform topologies τ qu , and Section 4.…
Daži trīssakarīgi grafi un to saimes bez Hamiltona cikliem
2013
These manuscripts (in Latvian) contain examples of graphs without Hamiltonian cycles. See the flower snark J5 on the page 13. The date here 1.6.78.
Random Feature Approximation for Online Nonlinear Graph Topology Identification
2021
Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments con…
Joint Graph Learning and Signal Recovery via Kalman Filter for Multivariate Auto-Regressive Processes
2018
In this paper, an adaptive Kalman filter algorithm is proposed for simultaneous graph topology learning and graph signal recovery from noisy time series. Each time series corresponds to one node of the graph and underlying graph edges express the causality among nodes. We assume that graph signals are generated via a multivariate auto-regressive processes (MAR), generated by an innovation noise and graph weight matrices. Then we relate the state transition matrix of Kalman filter to the graph weight matrices since both of them can play the role of signal propagation and transition. Our proposed Kalman filter for MAR processes, called KF-MAR, runs three main steps; prediction, update, and le…
Social network analysis: the use of graph distances to compare artificial and criminal networks
2021
Aim: Italian criminal groups become more and more dangerous spreading their activities into new sectors. A criminal group is made up of networks of hundreds of family gangs which extended their influence across the world, raking in billions from drug trafficking, extortion and money laundering. We focus in particular on the analysis of the social structure of two Sicilian crime families and we used a Social Network Analysis approach to study the social phenomena. Starting from a real criminal network extracted from meetings emerging from the police physical surveillance during 2000s, we here aim to create artificial models that present similar properties. Methods: We use specific tools of s…