scholarly journals Spectral and Dynamic Consequences of Network Specialization

2020 ◽  
Vol 30 (06) ◽  
pp. 2050091
Author(s):  
Leonid Bunimovich ◽  
D. J. Passey ◽  
Dallas Smith ◽  
Benjamin Webb
Keyword(s):  
Global Stability ◽  
Small World ◽  
Machine Learning Algorithms ◽  
Network Growth ◽  
Hierarchical Topology ◽  
Topological Evolution ◽  
Topological Features ◽  
Standard Notion ◽  
Rigorous Study ◽  
Small World Property

One of the hallmarks of real networks is the ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the function(s) they perform. A recent model of network growth based on this notion of specialization has been able to reproduce some of the most well-known topological features found in real-world networks including right-skewed degree distributions, the small world property, modular as well as hierarchical topology, etc. Here we describe how specialization under this model also effects the spectral properties of a network. This allows us to give the conditions under which a network is able to maintain its dynamics as its topology evolves. Specifically, we show that if a network is intrinsically stable, which is a stronger version of the standard notion of global stability, then the network maintains this type of dynamics as the network evolves. This is one of the first steps toward unifying the rigorous study of the two types of dynamics exhibited by networks. These are the dynamics of a network, which is the topological evolution of the network’s structure, modeled here by the process of network specialization, and the dynamics on a network, which is the changing state of the network elements, where the type of dynamics we consider is global stability. The main examples we apply our results to are recurrent neural networks, which are the basis of certain types of machine learning algorithms.

scholarly journals Specialization Models of Network Growth

2018 ◽  
Vol 7 (3) ◽  
pp. 375-392 ◽  
Author(s):  
L A Bunimovich ◽  
D C Smith ◽  
B Z Webb
Keyword(s):  
Power Law ◽  
Network Topology ◽  
Real World ◽  
Degree Distribution ◽  
Small World ◽  
Hierarchical Network ◽  
Network Growth ◽  
Complex Tasks ◽  
Small World Property ◽  
Law Degree

AbstractOne of the most important features observed in real networks is that, as a network’s topology evolves so does the network’s ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain subnetworks begin to specialize the function(s) they perform. Herein, we introduce a class of models of network growth based on this notion of specialization and show that as a network is specialized using this method its topology becomes increasingly sparse, modular and hierarchical, each of which are important properties observed in real networks. This procedure is also highly flexible in that a network can be specialized over any subset of its elements. This flexibility allows those studying specific networks the ability to search for mechanisms that describe their growth. For example, we find that by randomly selecting these elements a network’s topology acquires some of the most well-known properties of real networks including the small-world property, disassortativity and a right-skewed degree distribution. Beyond this, we show how this model can be used to generate networks with real-world like clustering coefficients and power-law degree distributions, respectively. As far as the authors know, this is the first such class of models that can create an increasingly modular and hierarchical network topology with these properties.

STOCHASTIC EVOLVING MODEL FOR COMPLEX NETWORKS

2004 ◽  
Vol 18 (23) ◽  
pp. 1157-1164 ◽  
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI ◽  
JIN MIN KIM
Keyword(s):  
Control Parameter ◽  
Small World ◽  
Network Size ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Hierarchical Topology ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
High Degree

We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We obtain the various values of degree exponent γ in the range 2<γ≤3 by adjusting the parameter p and find that the degree exponent decreases logarithmically with p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln ( ln N) with nonzero p, where N is the network size.

scholarly journals Can recurrence networks show small-world property?

2016 ◽  
Vol 380 (35) ◽  
pp. 2718-2723 ◽  
Author(s):  
Rinku Jacob ◽  
K.P. Harikrishnan ◽  
R. Misra ◽  
G. Ambika
Keyword(s):  
Small World ◽  
Small World Property

scholarly journals Models And Mining Of On-Line Social Networks

2021 ◽  
Author(s):  
Yanhua Tian
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Spectral Expansion ◽  
On Line ◽  
Simulation Results ◽  
Small World Property ◽  
P Type ◽  
Law Degree

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

Experimental Characterization of Electroplated CBN Grinding Wheel Wear: Topology Evolution and Interfacial Toughness

2014 ◽  
Author(s):  
Tianyu Yu ◽  
Ashraf F. Bastawros ◽  
Abhijit Chandra
Keyword(s):  
Grinding Wheel ◽  
Activation Process ◽  
Time To Failure ◽  
Wheel Surface ◽  
Wheel Wear ◽  
Modeling Framework ◽  
Topological Evolution ◽  
Pull Out ◽  
Topological Features ◽  
Cbn Grinding Wheel

The wear rate of a grinding wheel directly affects the workpiece surface integrity and tolerances. This paper summarizes a combined experimental-modeling framework for life cycle prediction of an electroplated Cubic Boron Nitride (CBN) grinding wheel, typically utilized in nickel-based superalloy grinding. The paper presents an experimental framework to facilitate the formulation of a micro-mechanics based modeling framework. The presented work investigates the topological evolution of the grinding wheel surface and mechanisms of grit failure via depth profiling, digital microscopy and scanning electron microscopy. The results are used to elucidate the statistical evolution of the grinding wheel surface. Different modes of grit failure, including grit attritious wear, fracture and pull out haven been identified. The analysis of the surface topological features indicates a unique grit activation process, leading to a non-uniform spatial distribution of the grit wear. Additionally, single grit pull out experiment has been conducted to assess the residual strength of the grit-wheel interface and the associated state of damage percolation. The experimental results can be utilized in developing a life expectancy model for the CBN grinding wheel to assess the grit mean time to failure as well as grit surface topological evolution as a function of the process parameters.

scholarly journals Disentangling network topology and pathogen spread

2021 ◽  
Author(s):  
Maria Perez-Ortiz ◽  
Petru Manescu ◽  
Fabio Caccioli ◽  
Delmiro Fernandez-Reyes ◽  
Parashkev Nachev ◽  
...  
Keyword(s):  
Network Topology ◽  
Large Scale ◽  
Social Contact ◽  
Small World ◽  
Pathogen Transmission ◽  
Stochastic Simulations ◽  
Equal Weight ◽  
Topological Features ◽  
Network Metrics ◽  
The Impact

How do we best constrain social interactions to prevent the transmission of communicable respiratory diseases? Indiscriminate suppression, the currently accepted answer, is both unsustainable long term and implausibly presupposes all interactions to carry equal weight. Transmission within a social network is determined by the topology of its graphical structure, of which the number of interactions is only one aspect. Here we deploy large-scale numerical simulations to quantify the impact on pathogen transmission of a set of topological features covering the parameter space of realistic possibility. We first test through a series of stochastic simulations the differences in the spread of disease on several classes of network geometry (including highly skewed networks and small world). We then aim to characterise the spread based on the characteristics of the network topology using regression analysis, highlighting some of the network metrics that influence the spread the most. For this, we build a dataset composed of more than 9000 social networks and 30 topological network metrics. We find that pathogen spread is optimally reduced by limiting specific kinds of social contact -- unfamiliar and long range -- rather than their global number. Our results compel a revaluation of social interventions in communicable diseases, and the optimal approach to crafting them.

A Review of Recent Advances and Research on Drug Target Identification Methods

2019 ◽  
Vol 20 (3) ◽  
pp. 209-216 ◽  
Author(s):  
Yang Hu ◽  
Tianyi Zhao ◽  
Ningyi Zhang ◽  
Ying Zhang ◽  
Liang Cheng
Keyword(s):  
Machine Learning ◽  
Computational Methods ◽  
Drug Target ◽  
Drug Targets ◽  
Target Identification ◽  
Machine Learning Algorithms ◽  
Topological Features ◽  
Drug Target Identification ◽  
Incomplete Datasets ◽  
Optimal Set

Background:From a therapeutic viewpoint, understanding how drugs bind and regulate the functions of their target proteins to protect against disease is crucial. The identification of drug targets plays a significant role in drug discovery and studying the mechanisms of diseases. Therefore the development of methods to identify drug targets has become a popular issue.Methods:We systematically review the recent work on identifying drug targets from the view of data and method. We compiled several databases that collect data more comprehensively and introduced several commonly used databases. Then divided the methods into two categories: biological experiments and machine learning, each of which is subdivided into different subclasses and described in detail.Results:Machine learning algorithms are the majority of new methods. Generally, an optimal set of features is chosen to predict successful new drug targets with similar properties. The most widely used features include sequence properties, network topological features, structural properties, and subcellular locations. Since various machine learning methods exist, improving their performance requires combining a better subset of features and choosing the appropriate model for the various datasets involved.Conclusion:The application of experimental and computational methods in protein drug target identification has become increasingly popular in recent years. Current biological and computational methods still have many limitations due to unbalanced and incomplete datasets or imperfect feature selection methods

Sign in / Sign up

Export Citation Format

Share Document