EIGENTIME IDENTITY OF THE WEIGHTED KOCH NETWORKS

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850042 ◽  
Author(s):  
YU SUN ◽  
JIAHUI ZOU ◽  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
HUALONG TANG ◽  
...  
Keyword(s):  
Transition Matrix ◽  
Small World ◽  
Laplacian Matrix ◽  
Block Matrix ◽  
The Other ◽  
Small World Networks ◽  
Eigenvalues And Eigenvectors ◽  
Two Factors ◽  
Analytical Research ◽  
Definition Of

The eigenvalues of the transition matrix of a weighted network provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to biased walks. Although various dynamical processes have been investigated in weighted networks, analytical research about eigentime identity on such networks is much less. In this paper, we study analytically the scaling of eigentime identity for weight-dependent walk on small-world networks. Firstly, we map the classical Koch fractal to a network, called Koch network. According to the proposed mapping, we present an iterative algorithm for generating the weighted Koch network. Then, we study the eigenvalues for the transition matrix of the weighted Koch networks for weight-dependent walk. We derive explicit expressions for all eigenvalues and their multiplicities. Afterwards, we apply the obtained eigenvalues to determine the eigentime identity, i.e. the sum of reciprocals of each nonzero eigenvalues of normalized Laplacian matrix for the weighted Koch networks. The highlights of this paper are computational methods as follows. Firstly, we obtain two factors from factorization of the characteristic equation of symmetric transition matrix by means of the operation of the block matrix. From the first factor, we can see that the symmetric transition matrix has at least [Formula: see text] eigenvalues of [Formula: see text]. Then we use the definition of eigenvalues and eigenvectors to calculate the other eigenvalues.

APPLICATION OF THE SZNAJD SOCIOPHYSICS MODEL TO SMALL-WORLD NETWORKS

2001 ◽  
Vol 12 (10) ◽  
pp. 1537-1544 ◽  
Author(s):  
A. S. ELGAZZAR
Keyword(s):  
Time Series ◽  
Fixed Point ◽  
Time Series Analysis ◽  
Fixed Points ◽  
Small World ◽  
Small World Networks ◽  
Opinion Formation ◽  
Series Analysis ◽  
Definition Of ◽  
Simple Definition

The Sznajd model for the opinion formation is generalized to small-world networks. This generalization destroyed the stalemate fixed point. Then a simple definition of leaders is included. No fixed points are observed. This model displays some interesting aspects in sociology. The model is investigated using time series analysis.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

Real-World Networks Are Not Always Fast Mixing

2020 ◽  
Author(s):  
Yi Qi ◽  
Wanyue Xu ◽  
Liwang Zhu ◽  
Zhongzhi Zhang
Keyword(s):  
Real World ◽  
Transition Matrix ◽  
Mixing Time ◽  
Real Life ◽  
Small World ◽  
Design Of Algorithms ◽  
Scale Free ◽  
Analytical Research ◽  
Second Largest Eigenvalue ◽  
Recursive Relations

Abstract The mixing time of random walks on a graph has found broad applications across both theoretical and practical aspects of computer science, with the application effects depending on the behavior of mixing time. It is extensively believed that real-world networks, especially social networks, are fast mixing with their mixing time at most $O(\log N)$ where $N$ is the number of vertices. However, the behavior of mixing time in the real-life networks has not been examined carefully, and exactly analytical research for mixing time in models mimicking real networks is still lacking. In this paper, we first experimentally evaluate the mixing time of various real-world networks with scale-free small-world properties and show that their mixing time is much higher than anticipated. To better understand the behavior of the mixing time for real-world networks, we then analytically study the mixing time of the Apollonian network, which is simultaneously scale-free and small-world. To this end, we derive the recursive relations for all eigenvalues, especially the second largest eigenvalue modulus of the transition matrix, based on which we deduce a lower bound for the mixing time of the Apollonian network, which approximately scales sublinearly with $N$. Our results indicate that real-world networks are not always fast mixing, which has potential implications in the design of algorithms related to mixing time.

DISTANCE PREFERENCES SMALL-WORLD COMMUNICATION TOPOLOGY FOR AGENT NETWORK

2010 ◽  
Vol 24 (11) ◽  
pp. 1489-1499
Author(s):  
ZHENGPING WU ◽  
RENMING WANG
Keyword(s):  
Communication Networks ◽  
Path Length ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Average Path Length ◽  
Small World Networks ◽  
Network Parameter ◽  
Communication Topology ◽  
Multi Agent

In multi-agent system (MAS), the communication topology of agent network plays a very important role in its collaboration. Small-world networks are the networks with high local clustering and small average path length, and the communication networks of MAS can be analyzed within the frame of small-world topology. Yet the real multiagent communication networks are abundant and the classical WS small-world model is not suitable for all cases. In this paper, two new small-world network models are presented. One is based on random graph substrate and local nodes preference reconnection and the other is based on regular graph substrate and long-range nodes preference reconnection. The characteristic of the network parameter such as the clustering coefficients, average path length, and eigenvalue λ2 and λn of the Laplacian matrix for these two models and WS model is studied. The consensus problem that based on these three models is also studied. An example is given and the conclusions are made in the end.

Factorial Structure of the Death Concern Scale

1976 ◽  
Vol 38 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Leo Klug ◽  
Marvin Boss
Keyword(s):  
College Students ◽  
Negative Evaluation ◽  
The Other ◽  
Factorial Structure ◽  
Factor Analyses ◽  
Definition Of Death ◽  
Two Factors ◽  
Single Score ◽  
Item Scores ◽  
Definition Of

Dickstein's (1972) 30-item Death Concern Scale was developed as a measure of the extent to which an individual consciously contemplates death and evaluates it negatively. Scoring procedures provide a single score as a measure of death concern. Dickstein's definition of death concern and an examination of the items support the authors' contention that two aspects of death concern are being measured. Factor analyses of the item scores of 671 college students indicated the presence of two distinct factors in the Death Concern Scale. One factor represented Dickstein's “conscious contemplation of death” component, the other the “negative evaluation” component. The results of the factor analyses corroborated the subjective judgments of 5 independent judges and the authors of this article. It is suggested that the usefulness of this instrument may be enhanced by the utilization of separate scores for each of these two factors.

scholarly journals The Evaluation of the Number and the Entropy of Spanning Trees on Generalized Small-World Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Raihana Mokhlissi ◽  
Dounia Lotfi ◽  
Joyati Debnath ◽  
Mohamed El Marraki ◽  
Noussaima EL Khattabi
Keyword(s):  
Complex Networks ◽  
Spanning Tree ◽  
Decomposition Method ◽  
Spanning Trees ◽  
Small World ◽  
Theoretical Computer Science ◽  
The Other ◽  
Small World Networks ◽  
Theoretical Computer ◽  
Number Of Spanning Trees

Spanning trees have been widely investigated in many aspects of mathematics: theoretical computer science, combinatorics, so on. An important issue is to compute the number of these spanning trees. This number remains a challenge, particularly for large and complex networks. As a model of complex networks, we study two families of generalized small-world networks, namely, the Small-World Exponential and the Koch networks, by changing the size and the dimension of the cyclic subgraphs. We introduce their construction and their structural properties which are built in an iterative way. We propose a decomposition method for counting their number of spanning trees and we obtain the exact formulas, which are then verified by numerical simulations. From this number, we find their spanning tree entropy, which is lower than that of the other networks having the same average degree. This entropy allows quantifying the robustness of the networks and characterizing their structures.

SYNCHRONIZABILITY OF COMPLEX NETWORKS WITH COMMUNITY STRUCTURE

2012 ◽  
Vol 23 (04) ◽  
pp. 1250029 ◽  
Author(s):  
MAHDI JALILI
Keyword(s):  
Community Structure ◽  
Real World ◽  
Order Parameter ◽  
Small World ◽  
Laplacian Matrix ◽  
Small World Networks ◽  
Scale Free ◽  
Community Connections ◽  
Scale Free Networks ◽  
Kuramoto Oscillators

Many real-world networks show community structure characterized by dense intra-community connections and sparse inter-community links. In this paper we investigated the synchronization properties of such networks. In this work we constructed such networks in a way that they consist of a number of communities with scale-free or small-world structure. Furthermore, with a probability, the intra-community connections are rewired to inter-community links. Two synchronizability measures were considered as the eigenratio of the Laplacian matrix and the phase order parameter obtained for coupled nonidentical Kuramoto oscillators. We found a power-law relation between the eigenratio and the inter-community rewiring probability in which as the rewiring probability increased, the eigenratio decreased, and hence, the synchronizability enhanced. The phase order parameter also increased by increasing the rewiring probability. Also, small-world networks with community structure showed better synchronization properties as compared to scale-free networks with community structure.

scholarly journals ENVIRONMENTAL RECLAMATION AS STRATEGY FOR SUSTAINABILITY

2016 ◽  
Vol 13 (27) ◽  
pp. 109-133
Author(s):  
Adriano Bressane ◽  
Admilson Írio Ribeiro ◽  
Gerson Araujo de Medeiros
Keyword(s):  
Public Policy ◽  
Environmental Change ◽  
The Other ◽  
Brazilian Legislation ◽  
Environmental Recovery ◽  
Environmental Public Policy ◽  
Analytical Research ◽  
The Moment ◽  
Multidisciplinary Perspective ◽  
Definition Of

The environmental change by the society is recurring and has been intensified since the first civilizations. However, the lack of conservationist practices has caused the emergence of degraded areas, whose recovery is fundamental for the sustainability. In this context, this paper aims at analyzing the environmental recovery as a public policy strategy supported in the Brazilian legislation. As methodology, a documental and analytical research was developed on the regulations, discussed at a multidisciplinary perspective, from the view of legal and engineering specialists, from the agricultural and environmental areas. As a result, it was identified a collection of rules pointing at a significant commitment on the definition of guidelines. On the other hand, this meaningful quantity of legal mechanisms, associated to misalignment, may cause damages to its effectiveness. In conclusion, we can consider that environmental reclamation is widely regulated, and it represents one of the main strategies of the environmental public policy adopted in Brazil. Nevertheless, it still requires advances to combine harmoniously practical and theoretical-conceptual aspects. Thus, considering the moment that Brazil is consolidating a new Forestry Code, we hope that the achieved outcomes can contribute to the debate and mobilization about the environmental reclamation as a strategy for sustainability. 

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

Factor Structure of the Hellenic WISC-III for Children with Learning Disabilities

2018 ◽  
Vol 9 (03) ◽  
pp. 20445-20451
Author(s):  
Adam A ◽  
Kiosseoglou G ◽  
Abatzoglou G ◽  
Papaligoura Z.
Keyword(s):  
Learning Disabilities ◽  
Factor Structure ◽  
Factor Model ◽  
The Other ◽  
Clinical Value ◽  
Reasoning Abilities ◽  
Picture Arrangement ◽  
Factorial Model ◽  
Verbal Subtest ◽  
Two Factors

The present research aims to examine the factor structure of the Hellenic WISC-III in a sample of 50 children with learning disabilities. The results show the existence of a factorial model with two factors, one aggregating the Comprehension verbal subtest with four performance subtests and the other the Picture Arrangement performance subtest with four verbal subtests. This two-factor model includes loadings in two factors that relate to the sequencing abilities and the verbal reasoning abilities of children. These findings assert the clinical value of the intelligence evaluation in these children.

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