You Can't Get There from Here—an Algorithmic Approach to Eulerian and Hamiltonian Circuits

1987 ◽  
Vol 80 (2) ◽  
pp. 95-148
Author(s):  
Joan H. Shyers
Keyword(s):  
Hamiltonian Circuit ◽  
Algorithmic Approach ◽  
Starting Point ◽  
Eulerian Circuit ◽  
Hamiltonian Circuits

Suppose you are in charge of the routing for a road crew whose job is to paint yellow lines down the center of all highways in a given section of the country. Your first task is to organize their travels to find a route that takes the crew over each section of the highway exactly once and returns them to their starting point. Such a route is an Eulerian circuit. Now suppose that the towns being served by these highways will pay the workers only on completion of the entire job. Your second task is to find a route that will take them through each town exactly once, again returning them to their starting point. This kind of route is a Hamiltonian circuit.

scholarly journals Some new theoretical work on Half Butterfly Method for Hamiltonian circuit in complete graph

MATEMATIKA ◽  
2017 ◽  
Vol 33 (1) ◽  
pp. 113 ◽  
Author(s):  
Maizon Mohd Darus ◽  
Haslinda Ibrahim ◽  
Sharmila Karim
Keyword(s):  
Complete Graph ◽  
Theoretical Work ◽  
New Method ◽  
Complete Graphs ◽  
Hamiltonian Circuit ◽  
Hamiltonian Circuits

A new method to construct the distinct Hamiltonian circuits in complete graphs is called Half Butterfly Method. The Half Butterfly method used the concept of isomorphism in developing the distinct Hamiltonian circuits. Thus some theoretical works are presented throughout developing this method.

scholarly journals Detection of Hamiltonian circuits in a directed graph

1982 ◽  
Vol 24 (2) ◽  
pp. 234-242 ◽  
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Directed Graph ◽  
Algebraic Method ◽  
Necessary Condition ◽  
Search Procedure ◽  
Hamiltonian Circuit ◽  
Hamiltonian Circuits

AbstractA simple algebraic method is presented to determine the necessary condition for the existence of a Hamiltonian circuit in a directed graph of n vertices. A search procedure is then introduced to identify any or all of the existing Hamiltonian circuits. The procedure is based upon finding a set of edges which will then be candidates for being parts of circuits of length n at any vertex of the graph.

scholarly journals Chemical Formula Encryption - using Hamiltonian Circuits and Graph Valued Functions

2019 ◽  
Vol 8 (12) ◽  
pp. 4843-4846
Keyword(s):  
Graph Theory ◽  
Line Graphs ◽  
Chemical Formula ◽  
Hamiltonian Graphs ◽  
Algorithmic Approach ◽  
Practical Applications ◽  
Convenient Tool ◽  
Wide Range ◽  
Encryption And Decryption ◽  
Hamiltonian Circuits

The ever expanding nature of graph theory has made it a convenient tool for a wide range of practical applications. This study prescribes an algorithmic approach of cryptographic decoding of chemical formula using Jump graphs and Line graphs. Hamiltonian graphs are used as the key for encryption and decryption.

scholarly journals Some graph properties of the optimised degree six 3-modified chordal ring network

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Stephen Lim Een-Chien ◽  
R. N. Farah ◽  
M. Othman
Keyword(s):  
Optical Networks ◽  
Linear Array ◽  
Graph Model ◽  
Distributed Network ◽  
Circulant Graph ◽  
Ring Network ◽  
Hamiltonian Circuit ◽  
Graph Properties ◽  
Eulerian Circuit ◽  
Chordal Ring

The interconnection topology of a parallel or distributed network is pivotal in ensuring good system performance. It can be modelled by a graph, where its edges represent the links between processor nodes represented by vertices. One such graph model that has gained attention by researchers since its founding is the chordal ring, based on an undirected circulant graph. This paper discusses the degree six 3-modified chordal ring, CHR6o3, and presents its graph theoretical properties of symmetry and Hamiltonicity. CHR6o3 is shown to be asymmetric, and can be decomposed into similar subgraphs, each consisting of only one type of node in its class if ring links are ignored. These properties aid both the development of a routing scheme and also determining lower bounds for its chromatic number. Conditions for the existence of a Hamiltonian Circuit within CHR6o3 are also discussed. The existence of a Hamiltonian Circuit within a network simplifies parallel processing as the processors can be arranged to work on a task in a linear array. An Eulerian Circuit was shown to exist in CHR6o3. The existence of an Eulerian Circuit plays a role in routing in optical networks.

Crystal structure images of large gold clusters and growing crystals by HRTEM

1984 ◽  
Vol 42 ◽  
pp. 428-429
Author(s):  
L.R. Wallenberg ◽  
J.-O. Bovin ◽  
G. Schmid
Keyword(s):  
Crystal Structure ◽  
Nucleation And Growth ◽  
Close Packing ◽  
Gold Clusters ◽  
Molecular Weight Determination ◽  
Growth Mechanisms ◽  
Starting Point ◽  
Different Types ◽  
Nucleation And Growth Mechanisms ◽  
Points Of View

Metallic clusters are interesting from various points of view, e.g. as a mean of spreading expensive catalysts on a support, or following heterogeneous and homogeneous catalytic events. It is also possible to study nucleation and growth mechanisms for crystals with the cluster as known starting point.Gold-clusters containing 55 atoms were manufactured by reducing (C6H5)3PAuCl with B2H6 in benzene. The chemical composition was found to be Au9.2[P(C6H5)3]2Cl. Molecular-weight determination by means of an ultracentrifuge gave the formula Au55[P(C6H5)3]Cl6 A model was proposed from Mössbauer spectra by Schmid et al. with cubic close-packing of the 55 gold atoms in a cubeoctahedron as shown in Fig 1. The cluster is almost completely isolated from the surroundings by the twelve triphenylphosphane groups situated in each corner, and the chlorine atoms on the centre of the 3x3 square surfaces. This gives four groups of gold atoms, depending on the different types of surrounding.

Two isoprenylated flavonoids from Dorstenia psilurus activate AMPK, stimulate glucose uptake, inhibit glucose production and lower glycemia

2019 ◽  
Vol 476 (24) ◽  
pp. 3687-3704 ◽  
Author(s):  
Aphrodite T. Choumessi ◽  
Manuel Johanns ◽  
Claire Beaufay ◽  
Marie-France Herent ◽  
Vincent Stroobant ◽  
...  
Keyword(s):  
Glucose Uptake ◽  
Human Cancer ◽  
Glucose Production ◽  
Liver Mitochondria ◽  
New Drugs ◽  
Structural Isomer ◽  
Rat Liver Mitochondria ◽  
Ionization Mass ◽  
Ampk Activation ◽  
Starting Point

Root extracts of a Cameroon medicinal plant, Dorstenia psilurus, were purified by screening for AMP-activated protein kinase (AMPK) activation in incubated mouse embryo fibroblasts (MEFs). Two isoprenylated flavones that activated AMPK were isolated. Compound 1 was identified as artelasticin by high-resolution electrospray ionization mass spectrometry and 2D-NMR while its structural isomer, compound 2, was isolated for the first time and differed only by the position of one double bond on one isoprenyl substituent. Treatment of MEFs with purified compound 1 or compound 2 led to rapid and robust AMPK activation at low micromolar concentrations and increased the intracellular AMP:ATP ratio. In oxygen consumption experiments on isolated rat liver mitochondria, compound 1 and compound 2 inhibited complex II of the electron transport chain and in freeze–thawed mitochondria succinate dehydrogenase was inhibited. In incubated rat skeletal muscles, both compounds activated AMPK and stimulated glucose uptake. Moreover, these effects were lost in muscles pre-incubated with AMPK inhibitor SBI-0206965, suggesting AMPK dependency. Incubation of mouse hepatocytes with compound 1 or compound 2 led to AMPK activation, but glucose production was decreased in hepatocytes from both wild-type and AMPKβ1−/− mice, suggesting that this effect was not AMPK-dependent. However, when administered intraperitoneally to high-fat diet-induced insulin-resistant mice, compound 1 and compound 2 had blood glucose-lowering effects. In addition, compound 1 and compound 2 reduced the viability of several human cancer cells in culture. The flavonoids we have identified could be a starting point for the development of new drugs to treat type 2 diabetes.

Overview of Current Approaches to Aural Rehabilitation for Adults With Cochlear Implants

2020 ◽  
Vol 5 (5) ◽  
pp. 1175-1187
Author(s):  
Rachel Glade ◽  
Erin Taylor ◽  
Deborah S. Culbertson ◽  
Christin Ray
Keyword(s):  
Health Care ◽  
Clinical Practice ◽  
Cochlear Implants ◽  
Practice Patterns ◽  
The United States ◽  
Care Providers ◽  
Aural Rehabilitation ◽  
Starting Point ◽  
Clinical Models ◽  
Hearing Health

Purpose This clinical focus article provides an overview of clinical models currently being used for the provision of comprehensive aural rehabilitation (AR) for adults with cochlear implants (CIs) in the Unites States. Method Clinical AR models utilized by hearing health care providers from nine clinics across the United States were discussed with regard to interprofessional AR practice patterns in the adult CI population. The clinical models were presented in the context of existing knowledge and gaps in the literature. Future directions were proposed for optimizing the provision of AR for the adult CI patient population. Findings/Conclusions There is a general agreement that AR is an integral part of hearing health care for adults with CIs. While the provision of AR is feasible in different clinical practice settings, service delivery models are variable across hearing health care professionals and settings. AR may include interprofessional collaboration among surgeons, audiologists, and speech-language pathologists with varying roles based on the characteristics of a particular setting. Despite various existing barriers, the clinical practice patterns identified here provide a starting point toward a more standard approach to comprehensive AR for adults with CIs.

Indirect Assessment of Attitudes with Response-Time-Based Measures

2006 ◽  
Vol 37 (3) ◽  
pp. 131-139 ◽  
Author(s):  
Juliane Degner ◽  
Dirk Wentura ◽  
Klaus Rothermund
Keyword(s):  
Social Cognitive ◽  
Incremental Validity ◽  
Self Report ◽  
Small Scale ◽  
Implicit Measures ◽  
Scale Theory ◽  
Starting Point ◽  
Self Reports ◽  
Predicting Behavior ◽  
Social Cognitive Theories

Abstract: We review research on response-latency based (“implicit”) measures of attitudes by examining what hopes and intentions researchers have associated with their usage. We identified the hopes of (1) gaining better measures of interindividual differences in attitudes as compared to self-report measures (quality hope); (2) better predicting behavior, or predicting other behaviors, as compared to self-reports (incremental validity hope); (3) linking social-cognitive theories more adequately to empirical research (theory-link hope). We argue that the third hope should be the starting point for using these measures. Any attempt to improve these measures should include the search for a small-scale theory that adequately explains the basic effects found with such a measure. To date, small-scale theories for different measures are not equally well developed.

The Solidarity of Distance1

2005 ◽  
Vol 36 (3) ◽  
pp. 103-115 ◽  
Author(s):  
Robert A. Wicklund
Keyword(s):  
Physical Contact ◽  
Emotional Distance ◽  
Starting Point ◽  
Shared Emotions ◽  
Common Goals ◽  
Full Interaction ◽  
The Individual ◽  
Social Incompetence

Abstract: Solidarity in the classic sense pertains to a cohesion among humans that entails physical contact, shared emotions, and common goals or projects. Characteristic cases are to be found among families, close friends, or co-workers. The present paper, in contrast, treats a phenomenon of the solidarity of distance, a solidarity based in fear of certain others and in incompetence to interact with them. The starting point for this analysis is the person who is motivated to interact with others who are unfamiliar or fear-provoking. Given that the fear and momentary social incompetence do not allow a full interaction to ensue, the individual will move toward solidarity with those others on a symbolic level. In this manner the motivation to approach the others is acted upon while physical and emotional distance is retained.

A Starting Point for Inquiry Into Inquiry

PsycCRITIQUES ◽  
2006 ◽  
Vol 51 (4) ◽  
Author(s):  
Joseph L. Polman
Keyword(s):  
Starting Point
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