scholarly journals Structural Characteristics of Two-Sender Index Coding

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 615 ◽  
Author(s):  
Chandra Thapa ◽  
Lawrence Ong ◽  
Sarah Johnson ◽  
Min Li
Keyword(s):  
Graph Coloring ◽  
Side Information ◽  
Structural Characteristics ◽  
A Priori ◽  
Index Coding ◽  
Multiple Receivers ◽  
Normal Graph

This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori, known as side-information, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called two-sender unicast index coding (TSUIC). The main goal is to find the shortest aggregate normalized codelength, which is expressed as the optimal broadcast rate. In this work, firstly, for a given TSUIC problem, we form three independent sub-problems each consisting of the only subset of the messages, based on whether the messages are available only in one of the senders or in both senders. Then, we express the optimal broadcast rate of the TSUIC problem as a function of the optimal broadcast rates of those independent sub-problems. In this way, we discover the structural characteristics of TSUIC. For the proofs of our results, we utilize confusion graphs and coding techniques used in single-sender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graph-coloring approach that is different from the normal graph coloring, which we call two-sender graph coloring, and propose a way of grouping the vertices to analyze the number of colors used. We further determine a class of TSUIC instances where a certain type of side-information can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders.

scholarly journals The Effect of Motion Time of a Scots Pine Single Seed on Mobile Optoelectronic Grader Efficiency: A Mathematical Patterning

Inventions ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 55 ◽  
Author(s):  
Arthur Novikov ◽  
Michael Drapalyuk ◽  
Olga Dornyak ◽  
Vladimir Zelikov ◽  
Vladan Ivetić
Keyword(s):  
Mathematical Modeling ◽  
Scots Pine ◽  
Structural Characteristics ◽  
A Priori ◽  
High Energy ◽  
Radius Of Curvature ◽  
Optical Scheme ◽  
Single Seed ◽  
Research Problems ◽  
Forest Seeds

Research Highlights: Forest owners will be able to solve the problem of testing and selection of viable forest seeds on location and save financial, time, and material resources. The possibility of integrating non-destructive quality control and separation functions in a single portable apparatus is extremely promising. The speed of the contemporary optoelectronic grader is limited by the speed of the slowest component—the mechanical system. Background and Objectives: The technological process of forest seed establishment and design of optoelectronic graders is based on a priori mathematical modeling of structural characteristics, taking into account these criteria. Known models of industrial photoseparators are expensive and have a high energy and material consumption not applicable in the field. Laboratory seed analyzers are characterized by a long time exposure, and the overall size and level of climatic performance do not allow them to be used in the field. Consequently, for small amounts of seed treatment, it is necessary to orient the seeds one by one and ensure clear and rapid coordinated actions of optoelectronic and mechanical systems. The main goal of this research is to increase the efficiency of grading forest seeds by patterning the speed of the mobile device. We will answer the following questions. What are effective geometric parameters for the seed pipe? What factors affect the speed of a single seed’s movement? Materials and Methods: This study is based on mathematical modeling, taking into account the basic principles of mechanics, using MatLab software. Results: A mechanical model of a single Scots pine seed’s motion in different zones of the seed pipe is designed, taking into account air resistance. The effective height of the seed pipe, taking into account the response time of optoelectronic grader systems, is determined. Conclusions: The time and speed of single seed movement through grader systems depends on the seed pipe’s height and radius of curvature. Other things being equal, through the use of the same optical scheme with a microprocessor to solve various problems, the compactness of the photodetector scheme allows, if necessary, to upgrade the grader to solve research problems and for use in forestry.

scholarly journals Local graph coloring and index coding

2013 ◽  
Author(s):  
Karthikeyan Shanmugam ◽  
Alexandros G. Dimakis ◽  
Michael Langberg
Keyword(s):  
Graph Coloring ◽  
Index Coding ◽  
Local Graph

Chromatic Zagreb and irregularity polynomials of graphs

2020 ◽  
pp. 2150061
Author(s):  
Smitha Rose ◽  
Sudev Naduvath
Keyword(s):  
Graph Coloring ◽  
Recent Literature ◽  
Structural Characteristics ◽  
Vertex Coloring ◽  
Proper Vertex

Graph coloring is an assignment of colors, labels or weights to elements of a graph subject to certain constraints. Coloring the vertices of a graph in such a way that adjacent vertices are having different colors is called proper vertex coloring. A proper vertex coloring using minimum parameters of colors is studied extensively in recent literature. In this paper, we define new coloring related polynomials, called chromatic Zagreb polynomials and chromatic irregularity polynomials, in terms of minimal parameter coloring and structural characteristics of graphs such as distances and degrees of vertices.

scholarly journals Quality of Health Information on Acute Myocardial Infarction and Stroke in the World Wide Web

2014 ◽  
Vol 27 (2) ◽  
pp. 223 ◽  
Author(s):  
Ana Bastos ◽  
Dagmara Paiva ◽  
Ana Azevedo
Keyword(s):  
Myocardial Infarction ◽  
Acute Myocardial Infarction ◽  
Health Information ◽  
Structural Characteristics ◽  
A Priori ◽  
Web Pages ◽  
Search Terms ◽  
Internet Explorer ◽  
Information Coverage

<p><strong>Introduction:</strong> The quality of health information in the Internet may be low. This is a concerning issue in cardiovascular diseases which warrant patient self-management. We aimed to assess the quality of Portuguese websites as a source of health information on acute myocardial infarction and stroke.<br /><strong>Material and Methods:</strong> We used the search terms ‘enfarte miocardio’ and ‘acidente vascular cerebral’ (Portuguese terms for myocardial infarction and stroke) on Google®, on April 5th and 7th 2011, respectively, using Internet Explorer®. The first 200 URL retrieved in each search were independently visited and Portuguese websites in Portuguese language were selected. We analysed and classified 121 websites for structural characteristics, information coverage and accuracy of the web pages with items defined a priori, trustworthiness in general according to the Health on the Net Foundation and regarding treatments using the DISCERN instrument (48 websites).<br /><strong>Results:</strong> Websites were most frequently commercial (49.5%), not exclusively dedicated to acute myocardial infarction/ stroke (94.2%), and with information on medical facts (59.5%), using images, video or animation (60.3%). Websites’ trustworthiness was low. None of the websites displayed the Health on the Net Foundation seal. Acute myocardial infarction/ stroke websites differed in information coverage but the accuracy of the information was acceptable, although often incomplete.<br /><strong>Conclusion:</strong> The quality of information on acute myocardial infarction/ stroke in Portuguese websites was acceptable. Trustworthiness was low, impairing users’ capability of identifying potentially more reliable content.</p>

scholarly journals Index Coding With Side Information

2011 ◽  
Vol 57 (3) ◽  
pp. 1479-1494 ◽  
Author(s):  
Ziv Bar-Yossef ◽  
Yitzhak Birk ◽  
T. S. Jayram ◽  
Tomer Kol
Keyword(s):  
Side Information ◽  
Index Coding
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