GRAPH ZETA FUNCTION AND DIMENSION OF COMPLEX NETWORK

2007 ◽  
Vol 21 (11) ◽  
pp. 639-644 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Zeta Function ◽  
Complex Network ◽  
System Behavior ◽  
Mathematical Properties ◽  
Scaling Property ◽  
Definition Of

In a recent paper we had defined the dimension of a complex network in terms of the scaling property of the volume. The question assumes significance because the dependence of system behavior on dimension is an important topic in statistical mechanics. Hence we consider the definition in more detail, and we propose a more widely applicable definition in this work. This definition has good mathematical properties, and it is based on the definition of a zeta function for complex networks.

DEFINING DIMENSION OF A COMPLEX NETWORK

2007 ◽  
Vol 21 (06) ◽  
pp. 321-326 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Regular Lattices ◽  
Extensive Property ◽  
Definition Of

An important question in statistical mechanics is the dependence of model behavior on the dimension of the system. In this paper, we discuss extending the definition of dimension from regular lattices to complex networks. We use the definition to study how the extensive property of the power law potential exponent depends on dimension.

VULNERABILITY AND FALL OF EFFICIENCY IN COMPLEX NETWORKS: A NEW APPROACH WITH COMPUTATIONAL ADVANTAGES

2009 ◽  
Vol 19 (02) ◽  
pp. 727-735 ◽  
Author(s):  
S. BOCCALETTI ◽  
R. CRIADO ◽  
J. PELLO ◽  
M. ROMANCE ◽  
M. VELA-PÉREZ
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
New Approach ◽  
And Performance ◽  
Definition Of

An efficient and computationally advantageous definition of vulnerability of a complex network is introduced, through which one is able to overcome a series of practical difficulties encountered by the measurements used so far to quantify a network's security and stability under the effects of failures, attacks or disfunctions. By means of this approach, we prove a series of theorems that allow to gather information on the ranking of the nodes of a network with respect to their strategic importance in order to preserve the functioning and performance of the network as a whole.

scholarly journals A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion

2021 ◽  
Vol 18 (6) ◽  
pp. 9253-9263
Author(s):  
Fu Tan ◽  
◽  
Bing Wang ◽  
Daijun Wei
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Structural Properties ◽  
Complex Network ◽  
Repulsive Force ◽  
Nonextensive Statistical Mechanics ◽  
Entropy Measurement ◽  
Structural Entropy ◽  
Degree Structure ◽  
The Difference

<abstract><p>The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.</p></abstract>

Information on evolutionary age in redundancy of complex network

2019 ◽  
Vol 33 (27) ◽  
pp. 1950331
Author(s):  
Shiguo Deng ◽  
Henggang Ren ◽  
Tongfeng Weng ◽  
Changgui Gu ◽  
Huijie Yang
Keyword(s):  
Principal Component Analysis ◽  
Complex Networks ◽  
Metabolic Network ◽  
Complex Network ◽  
Cellular Networks ◽  
Topological Structure ◽  
Quantitative Measure ◽  
Principal Component ◽  
Evolutionary Information ◽  
Local Patterns

Evolutionary processes of many complex networks in reality are dominated by duplication and divergence. This mechanism leads to redundant structures, i.e. some nodes share most of their neighbors and some local patterns are similar, called redundancy of network. An interesting reverse problem is to discover evolutionary information from the present topological structure. We propose a quantitative measure of redundancy of network from the perspective of principal component analysis. The redundancy of a community in the empirical human metabolic network is negatively and closely related with its evolutionary age, which is consistent with that for the communities in the modeling protein–protein network. This behavior can be used to find the evolutionary difference stored in cellular networks.

scholarly journals CNFE-SE: a novel approach combining complex network-based feature engineering and stacked ensemble to predict the success of intrauterine insemination and ranking the features

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sima Ranjbari ◽  
Toktam Khatibi ◽  
Ahmad Vosough Dizaji ◽  
Hesamoddin Sajadi ◽  
Mehdi Totonchi ◽  
...  
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Semen Quality ◽  
Intrauterine Insemination ◽  
Machine Learning Algorithms ◽  
Semen Parameters ◽  
Feature Engineering ◽  
Operating Characteristics ◽  
Scoring Method ◽  
Novel Approach

Abstract Background Intrauterine Insemination (IUI) outcome prediction is a challenging issue which the assisted reproductive technology (ART) practitioners are dealing with. Predicting the success or failure of IUI based on the couples' features can assist the physicians to make the appropriate decision for suggesting IUI to the couples or not and/or continuing the treatment or not for them. Many previous studies have been focused on predicting the in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) outcome using machine learning algorithms. But, to the best of our knowledge, a few studies have been focused on predicting the outcome of IUI. The main aim of this study is to propose an automatic classification and feature scoring method to predict intrauterine insemination (IUI) outcome and ranking the most significant features. Methods For this purpose, a novel approach combining complex network-based feature engineering and stacked ensemble (CNFE-SE) is proposed. Three complex networks are extracted considering the patients' data similarities. The feature engineering step is performed on the complex networks. The original feature set and/or the features engineered are fed to the proposed stacked ensemble to classify and predict IUI outcome for couples per IUI treatment cycle. Our study is a retrospective study of a 5-year couples' data undergoing IUI. Data is collected from Reproductive Biomedicine Research Center, Royan Institute describing 11,255 IUI treatment cycles for 8,360 couples. Our dataset includes the couples' demographic characteristics, historical data about the patients' diseases, the clinical diagnosis, the treatment plans and the prescribed drugs during the cycles, semen quality, laboratory tests and the clinical pregnancy outcome. Results Experimental results show that the proposed method outperforms the compared methods with Area under receiver operating characteristics curve (AUC) of 0.84 ± 0.01, sensitivity of 0.79 ± 0.01, specificity of 0.91 ± 0.01, and accuracy of 0.85 ± 0.01 for the prediction of IUI outcome. Conclusions The most important predictors for predicting IUI outcome are semen parameters (sperm motility and concentration) as well as female body mass index (BMI).

scholarly journals Connecting complex networks to nonadditive entropies

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. M. de Oliveira ◽  
Samuraí Brito ◽  
L. R. da Silva ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Energy Distribution ◽  
Complex Networks ◽  
Wide Class ◽  
Scale Invariant ◽  
Nonlocal Effects ◽  
Geometric Problem ◽  
Exponential Factor ◽  
Research Areas ◽  
Quasi Stationary State

AbstractBoltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

Evaluation of invulnerability of scale-free networks using total information of local sub-graph

2018 ◽  
Vol 29 (08) ◽  
pp. 1850075
Author(s):  
Tingyuan Nie ◽  
Xinling Guo ◽  
Mengda Lin ◽  
Kun Zhao
Keyword(s):  
Mutual Information ◽  
Complex Network ◽  
Fundamental Problem ◽  
The Self ◽  
Practical Significance ◽  
Scale Free ◽  
Total Information ◽  
Scale Free Networks ◽  
Influential Nodes ◽  
Definition Of

The quantification for the invulnerability of complex network is a fundamental problem in which identifying influential nodes is of theoretical and practical significance. In this paper, we propose a novel definition of centrality named total information (TC) which derives from a local sub-graph being constructed by a node and its neighbors. The centrality is then defined as the sum of the self-information of the node and the mutual information of its neighbor nodes. We use the proposed centrality to identify the importance of nodes through the evaluation of the invulnerability of scale-free networks. It shows both the efficiency and the effectiveness of the proposed centrality are improved, compared with traditional centralities.

scholarly journals Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Haipeng Peng ◽  
Lixiang Li ◽  
Jürgen Kurths ◽  
Shudong Li ◽  
Yixian Yang
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Complex Network ◽  
Parameter Optimization ◽  
Ant Algorithm ◽  
Structure Parameters ◽  
Topology Identification ◽  
Unknown Structure ◽  
Swarm Algorithm ◽  
Scientific Fields

Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.

scholarly journals On the Geometrical Representation of Classical Statistical Mechanics

2018 ◽  
Author(s):  
Georgios C. Boulougouris
Keyword(s):  
Statistical Mechanics ◽  
Parametric Representation ◽  
Gauss Map ◽  
Inner Product ◽  
Necessary And Sufficient Condition ◽  
Thermodynamic State ◽  
Classical Statistical Mechanics ◽  
Geometrical Representation ◽  
Definition Of ◽  
Necessary And Sufficient

In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by “properly transformed probability Euclidian vectors” that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state “close” to equilibrium is described by a triplet that represent the “infinitesimal volume” of the points, the Euclidian probability vector at equilibrium that points on a hypersphere of equilibrium thermodynamic state and a Euclidian vector a vector on the tangent bundle of the hypersphere. The necessary and sufficient condition for such representation is expressed as an invertibility condition on the proposed transformation. Finally, the relation of the proposed geometric representation, to similar approaches introduced under the context of differential geometry, information geometry, and finally the Ruppeiner and the Weinhold geometries, is discussed. It turns out that in the case of thermodynamic equilibrium, the proposed representation can be considered as a Gauss map of a parametric representation of statistical mechanics.

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