scholarly journals Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 86 ◽  
Author(s):  
C. Martínez-Martínez ◽  
J. Méndez-Bermúdez
Keyword(s):  
Numerical Simulations ◽  
Network Model ◽  
Information Entropy ◽  
Spectral Properties ◽  
Random Network ◽  
Tight Binding ◽  
Network Connectivity ◽  
Network Size ◽  
Random Networks ◽  
Scaling And Universality

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivity α , and the losses-and-gain strength γ . Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i γ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ ≡ ξ ( N , α , γ ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ < 0.1 ( 10 < ξ ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1 < ξ < 10 . Moreover, to extend the applicability of our findings, we demonstrate that for fixed ξ , the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.

scholarly journals Computational Properties of General Indices on Random Networks

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1341 ◽  
Author(s):  
R. Aguilar-Sánchez ◽  
I. F. Herrera-González ◽  
J. A. Méndez-Bermúdez ◽  
José M. Sigarreta
Keyword(s):  
Matrix Theory ◽  
Random Network ◽  
Scaling Law ◽  
Network Models ◽  
Network Size ◽  
Topological Indices ◽  
Random Networks ◽  
Theory Approach ◽  
Complexity Measures ◽  
Computational Properties

We perform a detailed (computational) scaling study of well-known general indices (the first and second variable Zagreb indices, M1α(G) and M2α(G), and the general sum-connectivity index, χα(G)) as well as of general versions of indices of interest: the general inverse sum indeg index ISIα(G) and the general first geometric-arithmetic index GAα(G) (with α∈R). We apply these indices on two models of random networks: Erdös–Rényi (ER) random networks GER(nER,p) and random geometric (RG) graphs GRG(nRG,r). The ER random networks are formed by nER vertices connected independently with probability p∈[0,1]; while the RG graphs consist of nRG vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidean distance is less or equal than the connection radius r∈[0,2]. Within a statistical random matrix theory approach, we show that the average values of the indices normalized to the network size scale with the average degree k of the corresponding random network models, where kER=(nER−1)p and kRG=(nRG−1)(πr2−8r3/3+r4/2). That is, X(GER)/nER≈X(GRG)/nRG if kER=kRG, with X representing any of the general indices listed above. With this work, we give a step forward in the scaling of topological indices since we have found a scaling law that covers different network models. Moreover, taking into account the symmetries of the topological indices we study here, we propose to establish their statistical analysis as a generic tool for studying average properties of random networks. In addition, we discuss the application of specific topological indices as complexity measures for random networks.

Traffic dynamics on multilayer networks with two logical layers

2021 ◽  
pp. 2150109
Author(s):  
Jinlong Ma ◽  
Zhichao Sun ◽  
Yongqiang Zhang ◽  
Xiangyang Xu ◽  
Ruimei Zhao ◽  
...  
Keyword(s):  
Network Model ◽  
Random Network ◽  
Physical Layer ◽  
Random Networks ◽  
Scale Free Network ◽  
Multilayer Networks ◽  
Traffic Dynamics ◽  
Scale Free ◽  
Traffic Capacity ◽  
Free Network

In order to study traffic dynamics on multilayer networks, it is of great significance to build a network model which can more exactly reflect the actual network layered structure characteristics. In this paper, a three-layer network model in which two logical layers are mapped on one physical layer is established, and the traffic capacities of three kinds of multilayer networks with different combinations of logical layers are compared. Simulation results show that when the physical layer is the same random network, the network whose logical layers are two random networks has the optimal traffic capacity, the network with one random network and one scale-free network in the logical layers has the better traffic capacity than the network whose logical layers are two scale-free networks.

scholarly journals Sublinear domination and core–periphery networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marios Papachristou
Keyword(s):  
Network Model ◽  
Power Law ◽  
Real World ◽  
Random Network ◽  
Small World ◽  
The Core ◽  
Entire Network

AbstractIn this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

scholarly journals Simulations of disks in binary systems using parallelized SPH to reach extreme spatial resolution

2003 ◽  
Vol 208 ◽  
pp. 427-428
Author(s):  
D. Molteni ◽  
F. Fauci ◽  
G. Gerardi ◽  
M. A. Valenza
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Numerical Simulations ◽  
Spatial Resolution ◽  
Spectral Properties ◽  
Binary Systems ◽  
Compact Star ◽  
Close Binary ◽  
Gas Transfer ◽  
Set Up

Results of 3D numerical simulations of the gas transfer in close binary systems show that it is possible the production of accretion streams having low specific angular momentum in a region close to the accreting star. These streams are mainly placed above the orbital disc. The eventual formation of such bulges and shock heated flows is interesting in the context of advection dominated solutions and for the explanation of spectral properties of the Black Hole candidates in binary systems. We set up a parallelized version of 3D S.P.H. code, using domain decomposion. with increasing spatial resolution around the compact star.

The Structure of Ion-Implanted Amorphous Silicon

1998 ◽  
Vol 540 ◽  
Author(s):  
J. M. Gibson ◽  
J-Y. Cheng ◽  
P. Voyles ◽  
M.M.J. TREACY ◽  
D.C. Jacobson
Keyword(s):  
Amorphous Silicon ◽  
Network Model ◽  
Random Network ◽  
Amorphous Semiconductors ◽  
Range Order ◽  
Medium Range Order ◽  
Medium Range ◽  
Large Heat ◽  
Continuous Random Network ◽  
Ion Implanted

AbstractUsing fluctuation microscopy, we show that ion-implanted amorphous silicon has more medium-range order than is expected from the continuous random network model. From our previous work on evaporated and sputtered amorphous silicon, we conclude that the structure is paracrystalline, i.e. it possesses crystalline-like order which decays with distance from any point. The observation might pose an explanation for the large heat of relaxation that is evolved by ion-implanted amorphous semiconductors.

Evaluation of effective thermal conductivity of unsaturated granular materials using random network model

Geothermics ◽  
2017 ◽  
Vol 67 ◽  
pp. 76-85 ◽  
Author(s):  
Chulho Lee ◽  
Li Zhuang ◽  
Dongseop Lee ◽  
Seokjae Lee ◽  
In-Mo Lee ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Network Model ◽  
Random Network

Estimation of Effective Thermal and Mechanical Properties of Particulate Thermal Interface Materials (TIMs) by a Random Network Model

2017 ◽  
Author(s):  
Pavan Kumar Vaitheeswaran ◽  
Ganesh Subbarayan
Keyword(s):  
Mechanical Properties ◽  
Network Model ◽  
Thermal Stresses ◽  
Volume Fraction ◽  
Random Network ◽  
Thermal Interface Materials ◽  
Thermal And Mechanical Properties ◽  
Thermal Interface ◽  
Classical Models ◽  
Interface Materials

Particulate thermal interface materials (TIMs) are commonly used to transport heat from chip to heat sink. While high thermal conductance is achieved by large volume loadings of highly conducting particles in a compliant matrix, small volume loadings of stiff particles will ensure reduced thermal stresses in the brittle silicon device. Developing numerical models to estimate effective thermal and mechanical properties of TIM systems would help optimize TIM performance with respect to these conflicting requirements. Classical models, often based on single particle solutions or regular arrangement of particles, are insufficient as real-life TIM systems contain a distriubtion of particles at high volume fractions, where classical models are invalid. In our earlier work, a computationally efficient random network model was developed to estimate the effective thermal conductivity of TIM systems [1,2]. This model is extended in this paper to estimate the effective elastic modulus of TIMs. Realistic microstructures are simulated and analyzed using the proposed method. Factors affecting the modulus (volume fraction and particle size distribution) are also studied.

scholarly journals Stochastic Models of Emerging Infectious Disease Transmission on Adaptive Random Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Navavat Pipatsart ◽  
Wannapong Triampo ◽  
Charin Modchang
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Random Network ◽  
Network Models ◽  
Transmission Probability ◽  
Stochastic Simulations ◽  
Random Networks ◽  
Cumulative Number ◽  
Network Adaptation ◽  
Infectious Disease Dynamics

We presented adaptive random network models to describe human behavioral change during epidemics and performed stochastic simulations of SIR (susceptible-infectious-recovered) epidemic models on adaptive random networks. The interplay between infectious disease dynamics and network adaptation dynamics was investigated in regard to the disease transmission and the cumulative number of infection cases. We found that the cumulative case was reduced and associated with an increasing network adaptation probability but was increased with an increasing disease transmission probability. It was found that the topological changes of the adaptive random networks were able to reduce the cumulative number of infections and also to delay the epidemic peak. Our results also suggest the existence of a critical value for the ratio of disease transmission and adaptation probabilities below which the epidemic cannot occur.

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