scholarly journals Markov Processes Involving q-Stirling Numbers

1997 ◽  
Vol 6 (2) ◽  
pp. 165-178 ◽  
Author(s):  
D. CRIPPA ◽  
K. SIMON ◽  
P. TRUNZ
Keyword(s):  
Markov Process ◽  
Normal Distribution ◽  
Markov Processes ◽  
Random Graphs ◽  
Transition Probabilities ◽  
Analysis Of Algorithms ◽  
Random Variables ◽  
Stirling Numbers ◽  
Time Dependent

In this paper we consider the Markov process defined byP1,1=1, Pn,[lscr ]=(1−λn,[lscr ]) ·Pn−1,[lscr ] +λn,[lscr ]−1 ·Pn−1,[lscr ]−1for transition probabilities λn,[lscr ]=q[lscr ] and λn,[lscr ]=qn−1. We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of q-Stirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution. We also show that these Markov processes describe some parameters related to the study of random graphs as well as to the analysis of algorithms.

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs

Comparison and Analysis of Algorithms Used for Detecting Slums in Satellite Images

2019 ◽  
Author(s):  
Pallavi Saindane ◽  
Gayatri Ganapathy ◽  
Neha Prabhavalkar ◽  
Nilesh Bhatia ◽  
Aishwarya Vaidya
Keyword(s):  
Satellite Images ◽  
Analysis Of Algorithms ◽  
Comparison And Analysis

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

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