RESOURCE NETWORKS WITH LIMITATIONS ON VERTEX CAPACITIES

2017 ◽  
Author(s):  
Людмила Жилякова ◽  
Liudmila Zhilyakova
Keyword(s):  
Graph Model ◽  
Discrete Mathematics ◽  
Dynamic Graph ◽  
Resource Network ◽  
Limited Bandwidth ◽  
Inhomogeneous Markov Chain ◽  
Storage Resource ◽  
Resource Networks ◽  
Research Students ◽  
Vertex Capacities

Work is continuation of studies whose results are published in the monograph "Theory of resource networks" — M.: RIOR: INFRA-M, 2017. The resource network is a dynamic graph model in which vertices at discrete time homogeneous resource exchange through channels with limited bandwidth capabilities. At each step, the vertices give the resource to one of the two rules with the threshold switch, depending on its quantity. In the original model all the vertices have an unlimited capacity. Ie can take and store an arbitrary amount of the resource. In the model proposed in the present work, the vertices, the storage resource (attractors) have limitations on capacity. This creates the possibility of accumulation of the resource in the set of vertices, called secondary attractors. Investigated the inhomogeneous Markov chain generated by the process of redistribution of the resource. The book is intended for specialists in graph theory and operations research, students, masters and post-graduate students studying in various areas of discrete mathematics and computer science.

scholarly journals Graph Entropy Associated with Multilevel Atomic Excitation

Proceedings ◽  
2020 ◽  
Vol 46 (1) ◽  
pp. 9
Author(s):  
Abu Mohamed Alhasan
Keyword(s):  
Hyperfine Structure ◽  
Transition Matrix ◽  
Graph Model ◽  
Connectivity Matrix ◽  
Dynamic Graph ◽  
Short Pulses ◽  
Atomic Excitation ◽  
Energy Concept ◽  
Metal Atoms ◽  
Spatiotemporal Behavior

A graph-model is presented to describe multilevel atomic structure. As an example, we take the double Λ configuration in alkali-metal atoms with hyperfine structure and nuclear spin I = 3 / 2 , as a graph with four vertices. Links are treated as coherence. We introduce the transition matrix which describes the connectivity matrix in static graph-model. In general, the transition matrix describes spatiotemporal behavior of the dynamic graph-model. Furthermore, it describes multiple connections and self-looping of vertices. The atomic excitation is made by short pulses, in order that the hyperfine structure is well resolved. Entropy associated with the proposed dynamic graph-model is used to identify transitions as well as local stabilization in the system without invoking the energy concept of the propagated pulses.

scholarly journals Flows in strongly regular periodic dynamic resource networks

2021 ◽  
Vol 31 (3) ◽  
pp. 458-470
Author(s):  
V.A. Skorokhodov ◽  
D.O. Sviridkin
Keyword(s):  
Resource Allocation ◽  
Limit State ◽  
Dynamic Networks ◽  
Dynamic Network ◽  
Limit States ◽  
Resource Network ◽  
Strongly Regular ◽  
Dynamic Resource ◽  
Resource Networks ◽  
Time Resource

This paper is devoted to studying the processes of resource allocation in dynamic resource networks. In such networks, the capacities of the arcs depend on time. Resource allocation in the network occurs in discrete time. The resource of each vertex is distributed only between adjacent vertices according to some rules. The study of the processes of resource redistribution in such networks is carried out. The main goal is to develop methods for finding the limit state (distribution) of a resource in a dynamic resource network. It is shown that the approach based on the construction of an auxiliary network is also applicable to reduce the problem of resource allocation in a dynamic network to a similar problem in an auxiliary network. Theorems on the existence of a limit state on an auxiliary graph are proved for strongly regular periodic dynamical networks. To find the limit states, one can use the approaches which are developed for the shortest path problem in dynamic networks.

scholarly journals Transportation, Germs, Culture: A Dynamic Graph Model of 2019-nCoV Spread

2020 ◽  
Author(s):  
Xiaofei Yang ◽  
Tun Xu ◽  
Peng Jia ◽  
Han Xia ◽  
Li Guo ◽  
...  
Keyword(s):  
Graph Model ◽  
Emergency Situation ◽  
Contributing Factors ◽  
Dynamic Graph ◽  
Model And Simulation ◽  
Health Authorities ◽  
Public Health Authorities ◽  
Precise Prediction ◽  
Novel Coronavirus ◽  
Major Factors

Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China1. There are more than one hundred cases outside of China, affecting a dozen of countries globally2. The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed3. Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days 4,5. However, major factors such as transportation and cultural customs have not been weighed enough. Our model is not set out for precise prediction of the number of infected cases, rather, it is meant for a glance of the dynamics under a public epidemic emergency situation and of different contributing factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

scholarly journals Transportation, germs, culture: a dynamic graph model of COVID-19 outbreak

2020 ◽  
Vol 8 (3) ◽  
pp. 238-244
Author(s):  
Xiaofei Yang ◽  
Tun Xu ◽  
Peng Jia ◽  
Han Xia ◽  
Li Guo ◽  
...  
Keyword(s):  
Graph Model ◽  
Dynamic Graph

Transportation, Germs, Culture: A Dynamic Graph Model of COVID-19 Outbreak

2020 ◽  
Author(s):  
Xiaofei Yang ◽  
Tun Xu ◽  
Peng Jia ◽  
Han Xia ◽  
Li Guo ◽  
...  
Keyword(s):  
Graph Model ◽  
Dynamic Graph

User-centered recommendation using US-ELM based on dynamic graph model in E-commerce

2017 ◽  
Vol 10 (4) ◽  
pp. 693-703 ◽  
Author(s):  
Linlin Ding ◽  
Baishuo Han ◽  
Shu Wang ◽  
Xiaoguang Li ◽  
Baoyan Song
Keyword(s):  
Graph Model ◽  
Dynamic Graph ◽  
User Centered
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