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 Spatiotemporal Graph Imaging Associated with Multilevel Atomic Excitations

Proceedings ◽  
2020 ◽  
Vol 67 (1) ◽  
pp. 16
Author(s):  
Abu Mohamed Alhasan
Keyword(s):  
Transition Matrix ◽  
Graph Model ◽  
Connectivity Matrix ◽  
Image Model ◽  
Atomic Systems ◽  
Image Entropy ◽  
The Matrix ◽  
Multiple Levels ◽  
Atomic Excitations ◽  
Value Decomposition

In this paper, we establish a graph imaging technique to manifest local stabilization within atomic systems of multiple levels. Specifically, we address the interrelation between local stabilization and image entropy. As an example, we consider the mutual interaction of two pair of pulses propagating in a double-Λ configuration. Thus, we have two different sets of two pulses that share the same shape and phase, initially. The first (second) set belongs to lower (upper) -Λ subsystems, respectively. The configuration of two pair of pulses is considered as a dynamical graph model with four nodes. The dynamic transition matrix describes the connectivity matrix in the static graph model. It is to be emphasized that the graph and its image have the same transition matrix. In particular, the graph model exposes the stabilization in terms of the singular-value decomposition of energies for the transition matrix, that is, irrespectively of the structure of the transition matrix. The image model of the graph displays the details of the matrix structure in terms of row and column probabilities. Therefore, it enables one to study conditional probabilities and mutual information inherent in the network of the graph. Furthermore, the graph imaging provides the main row/column contribution to the transition matrix in terms of image entropy. Our results show that image entropy exposes spatial dependence, which is irrelevant to graph entropy.

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

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.

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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