scholarly journals Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 916 ◽  
Author(s):  
Mikołaj Morzy ◽  
Tomasz Kajdanowicz

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properties. In this paper we investigate the usefulness of the concept of graph energy in the context of large, complex networks. We show that when graph energies are applied to local egocentric networks, the values of these energies correlate strongly with vertex centrality measures. In particular, for some generative network models graph energies tend to correlate strongly with the betweenness and the eigencentrality of vertices. As the exact computation of these centrality measures is expensive and requires global processing of a network, our research opens the possibility of devising efficient algorithms for the estimation of these centrality measures based only on local information.

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.


2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.


2003 ◽  
Vol 3 (3) ◽  
pp. 193-202
Author(s):  
K. Chen ◽  
L.-A. Wu

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.


Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 184 ◽  
Author(s):  
Qing Li ◽  
Steven Liang

Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estimates non-zero singular values (i.e., fault component) accurately and (2) it maintains the convexity of the proposed objective cost function (OCF) by restricting the parameters of the non-convex regularization. Specifically, the AHNPR model is expressed as the L1-norm minus a generalized Huber function, which avoids the underestimation weakness of the L1-norm regularization. Furthermore, the convexity of the proposed OCF is proved via the non-diagonal characteristic of the matrix BTB, meanwhile, the non-zero singular values of the OCF is solved by the forward–backward splitting (FBS) algorithm. Last, the proposed method is validated by the simulated signal and vibration signals of tapered bearing. The results demonstrate that the proposed approach can identify weak fault information from the raw vibration signal under severe background noise, that the non-convex penalty regularization can induce sparsity of the singular values more effectively than the typical convex penalty (e.g., L1-norm fused lasso optimization (LFLO) method), and that the issue of underestimating sparse coefficients can be improved.


2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.


2018 ◽  
Vol 3 (1) ◽  
pp. 2 ◽  
Author(s):  
Suzana Fong

Hyper-raising consists in raising a DP from an embedded finite clause into the matrix clause. HR introduces a phase problem: the embedded clause is finite, which is supposed to be impervious to raising. This can be overcome by postulating A-features at the C of the the embedded clause. They trigger the movement of the subject to [Spec, CP]. Being at the edge of a phase, it is visible to a matrix probe. If successful, this analysis provides support for the claim that syntactic positions are not inherently A or A-bar; they can be defined featurally instead.


Author(s):  
K. Oliinyk

The article examines the specificity of existence of the renewed mystery genre as a meta genre in the twentieth century. The main literary study views on the definition of ancient and medieval / Christian ritual mystery are analyzed. The beginning of the twentieth century was full of a general feeling of catastrophe and tragic hopelessness. In artistic terms, the consequence of this was the activation of Christian issues, motives, plots, religious genres (miracles, morality and mystery). The most universal from the point of view of the ideological message and content for the writers of the twentieth century. was the matrix of the medieval mystery, which retained the ritual basis in its primary structure. This made it possible for the multilevel organization of the action and the space for it. The genre of medieval mystery is being modified, it ceases to be a purely form of religious action and acquires the quality of a meta genre. There is a transition from the religious sphere to the secular one, and the aesthetic one is replacing the didactic load. Mystery begins to exist on the edge of genres as a synthetic formation, showing intentions to “help” other genres. A large number of dramatic works of the twentieth century. ("Forest Song" by Lesia Ukrainka, "Iconostasis of Ukraine" by Vіra Vovk) comes close to the mystery, using its archetypal components: the ideas of faith in the absolute beginning, governing the eternal rotation of life and death, world order and harmony, death and rebirth, transformations of the human soul, chosenness and initiation associated with trials, sacrifice, deepening into mysticism. Such works are a certain imitation with elements of mythological or religious subjects. So, the twentieth century, actualizes a certain involvement of the semantic content of dramas to the mysteries, bringing the mystery to the level of the meta genre.


2021 ◽  
Vol 4 ◽  
Author(s):  
Monica Billio ◽  
Roberto Casarin ◽  
Michele Costola ◽  
Matteo Iacopini

Networks represent a useful tool to describe relationships among financial firms and network analysis has been extensively used in recent years to study financial connectedness. An aspect, which is often neglected, is that network observations come with errors from different sources, such as estimation and measurement errors, thus a proper statistical treatment of the data is needed before network analysis can be performed. We show that node centrality measures can be heavily affected by random errors and propose a flexible model based on the matrix-variate t distribution and a Bayesian inference procedure to de-noise the data. We provide an application to a network among European financial institutions.


2014 ◽  
Vol 1008-1009 ◽  
pp. 1176-1179
Author(s):  
Hai Dong ◽  
Heng Bao Xin

In this paper, an approach of fuzzy Petri nets (FPN) is proposed to simulate the fault spreading and diagnosis of hydraulic pump. First, the fuzzy production rules and the definition of FPN were briefly introduced. Then, its knowledge reasoning process and the matrix operations based on an algorithm were conducted, which makes full use of its parallel reasoning ability and makes it simpler and easier to implement. Finally, a case of hydraulic pump fault diagnosis with FPN was presented in detail, for illustrating the interest of the proposed modeling and analysis algorithm.


Author(s):  
Тарас Гриценко ◽  
Жанна Передера ◽  
Анна Теряева

В работе рассматривается возможность формирования в банковском секторе среды, в которой сотрудники смогут самостоятельно реализовывать цифровые инициативы для развития компании и самообучения. Обоснована необходимость её наличия. Проведен анализ соответствия поставленной проблемы российским и мировым трендам на основе изучения федеральных программ и оценок рейтинговых агентств. В результате исследования разработан бизнес-процесс реализации цифровых инициатив, про-веден конкурентный анализ его преимуществ и недостатков перед традиционным подходом к обучению. The article discusses the possibility of forming in the banking business an environment in which employees will be able to in-dependently implement digital initiatives for the development of the company and self-learning. The necessity of its presence is grounded. The analysis of compliance of the problem with the trends in Russia and the world based on the study of Federal programs and ratings agencies. To attract new staff with the necessary knowledge, banks have a number of tools - business classes, sponsorship programs, mentoring, hackathons, man-agement fights, case-championships, etc. It has been revealed that new professionals with technical skills can solve complex problems and generate products. But it’s difficult for them to dive into the banking sector, study its features and offer their own solutions to problems. It was also revealed that the company is interested in product results that are practice oriented. Com-bining product results and training is only possible by creating an environment in which they can discuss their ideas, find sup-port and implement them. As a result, a business process for the implementation of digital initiatives has been formed, a competi-tive analysis of its advantages and disadvantages over the tradi-tional approach to training has been conducted. strategies. The leading method of research is the definitions according grouping to the principles of the matrix method. It was revealed that the economic security concept is disclosed using factors freely com-bined into three groups (includes: sustainability, protection of interests, ensuring sovereignty), and the most common definitions are built using words-markers: state, security, advantage, process. One of the main study results is an algorithm for constructing the definition of the economic security concept, which allows to model and refine the definition of the concept based on the initial categories, consider-ing the economic context. The author's definition is also formulated, which reflects the interrelation of such components as the protection of interests, the impact of threats, the stability preservation, inde-pendence, ensuring development, self-adaptation and self-reproduction.


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