scholarly journals Butterfly Triple System Algorithm Based on Graph Theory

2021 ◽  
Vol 21 (No.1) ◽  
pp. 27-49
Author(s):  
Raja'i Mohammad Aldiabat ◽  
Haslinda Ibrahim ◽  
Sharmila Karim
Keyword(s):  
Graph Theory ◽  
Special Reference ◽  
Complete Graph ◽  
Triple System ◽  
Design Theory ◽  
Combinatorial Design ◽  
Algorithm Development ◽  
Cycle System ◽  
New Type ◽  
Insight Into

In combinatorial design theory, clustering elements into a set of three elements is the heart of classifying data. This article will provide insight into formulating algorithm for a new type of triple system, called a Butterfly triple system. Basically, in this algorithm development, a starter of cyclic near-resolvable ((v-1)/2)-cycle system of the 2-fold complete graph 2K_v is employed to construct the starter of cyclic ((v-1)/2)-star decomposition of 2K_v. These starters were then decomposed into triples and classified as a starter of a cyclic Butterfly triple system. The obtained starter set generated a triple system of order A special reference for case 𝑣𝑣 ≡ 9 (mod 12) was presented to demonstrate the development of the Butterfly triple system.

scholarly journals Removing Symmetry in Circulant Graphs and Point-Block Incidence Graphs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 166
Author(s):  
Josephine Brooks ◽  
Alvaro Carbonero ◽  
Joseph Vargas ◽  
Rigoberto Flórez ◽  
Brendan Rooney ◽  
...  
Keyword(s):  
Graph Theory ◽  
Design Theory ◽  
Difficult Problem ◽  
Combinatorial Design ◽  
Surprising Result ◽  
Cyclic Structure ◽  
Circulant Graphs ◽  
Minimum Number ◽  
Automorphism Of A Graph

An automorphism of a graph is a mapping of the vertices onto themselves such that connections between respective edges are preserved. A vertex v in a graph G is fixed if it is mapped to itself under every automorphism of G. The fixing number of a graph G is the minimum number of vertices, when fixed, fixes all of the vertices in G. The determination of fixing numbers is important as it can be useful in determining the group of automorphisms of a graph-a famous and difficult problem. Fixing numbers were introduced and initially studied by Gibbons and Laison, Erwin and Harary and Boutin. In this paper, we investigate fixing numbers for graphs with an underlying cyclic structure, which provides an inherent presence of symmetry. We first determine fixing numbers for circulant graphs, showing in many cases the fixing number is 2. However, we also show that circulant graphs with twins, which are pairs of vertices with the same neighbourhoods, have considerably higher fixing numbers. This is the first paper that investigates fixing numbers of point-block incidence graphs, which lie at the intersection of graph theory and combinatorial design theory. We also present a surprising result-identifying infinite families of graphs in which fixing any vertex fixes every vertex, thus removing all symmetries from the graph.

The Subaltern Speak- A Study On The Culture Of The Arunachalis With Special Reference To Mamang Dai’s The Legends Of Pensam

2019 ◽  
Vol 5 (4) ◽  
pp. 14-20
Author(s):  
Ms. Cheryl Antonette Dumenil ◽  
Dr. Cheryl Davis
Keyword(s):  
Special Reference ◽  
Small World ◽  
Natural World ◽  
Arunachal Pradesh ◽  
North East India ◽  
North East ◽  
Shared History ◽  
History Of ◽  
And Gender ◽  
Insight Into

North- East India is an under veiled region with an awe-inspiring landscape, different groups of ethnic people, their culture and heritage. Contemporary writers from this region aspire towards a vision outside the tapered ethnic channel, and they represent a shared history. In their writings, the cultural memory is showcased, and the intensity of feeling overflows the labour of technique and craft. Mamang Dai presents a rare glimpse into the ecology, culture, life of the tribal people and history of the land of the dawn-lit mountains, Arunachal Pradesh, through her novel The Legends of Pensam. The word ‘Pensam’ in the title means ‘in-between’,  but it may also be interpreted as ‘the hidden spaces of the heart’. This is a small world where anything can happen. Being adherents of the animistic faith, the tribes here believe in co-existence with the natural world along with the presence of spirits in their forests and rivers. This paper attempts to draw an insight into the culture and gender of the Arunachalis with special reference to The Legends of Pensam by Mamang Dai.

scholarly journals Breakout Group Allocation Schedules and the Social Golfer Problem with Adjacent Group Sizes

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 13
Author(s):  
Alice Miller ◽  
Matthew Barr ◽  
William Kavanagh ◽  
Ivaylo Valkov ◽  
Helen C. Purchase
Keyword(s):  
Design Theory ◽  
Teaching Experience ◽  
Combinatorial Design ◽  
Breakout Group ◽  
Online Resource ◽  
The Social ◽  
Adjacent Group ◽  
Group Allocation ◽  
Novel Variation ◽  
The Ideal

The current pandemic has led schools and universities to turn to online meeting software solutions such as Zoom and Microsoft Teams. The teaching experience can be enhanced via the use of breakout rooms for small group interaction. Over the course of a class (or over several classes), the class will be allocated to breakout groups multiple times over several rounds. It is desirable to mix the groups as much as possible, the ideal being that no two students appear in the same group in more than one round. In this paper, we discuss how the problem of scheduling balanced allocations of students to sequential breakout rooms directly corresponds to a novel variation of a well-known problem in combinatorics (the social golfer problem), which we call the social golfer problem with adjacent group sizes. We explain how solutions to this problem can be obtained using constructions from combinatorial design theory and how they can be used to obtain good, balanced breakout room allocation schedules. We present our solutions for up to 50 students and introduce an online resource that educators can access to immediately generate suitable allocation schedules.

The Optimization Simulated Analysis of Permanent Magnet Linear Synchronous Motor

2011 ◽  
Vol 101-102 ◽  
pp. 538-542
Author(s):  
Hai Jun Tan ◽  
Mei Qin Zhang ◽  
Cheng Tang ◽  
Lei Li
Keyword(s):  
Permanent Magnet ◽  
Design Theory ◽  
Synchronous Motor ◽  
Electromagnetic Analysis ◽  
Positioning Accuracy ◽  
Finite Element Software ◽  
Transient Electromagnetic ◽  
Linear Synchronous Motor ◽  
New Type ◽  
Simulated Analysis

Permanent magnet linear synchronous motor (PMLSM) is a new type of motor with high positioning accuracy. This paper introduces the related design theory of PMLSM with the utilization of finite element software. we refer to the sample transient electromagnetic analysis, firstly. And then get the Thrust fluctuation map and compare to its winding back EMF curve and other related graphs. Through altering of the thickness, air gap length, junior core’s structure and size and other parameters, we finally conclude the designed requirements will be eventually fulfilled this optimization.

scholarly journals A Bacterial Microcompartment Is Used for Choline Fermentation byEscherichia coli536

2018 ◽  
Vol 200 (10) ◽  
Author(s):  
Taylor I. Herring ◽  
Tiffany N. Harris ◽  
Chiranjit Chowdhury ◽  
Sujit Kumar Mohanty ◽  
Thomas A. Bobik
Keyword(s):  
Electron Microscopy ◽  
Heart Disease ◽  
Gene Cluster ◽  
Transcriptional Regulator ◽  
Human Gut ◽  
Content Type ◽  
E Coli ◽  
Bacterial Microcompartment ◽  
New Type ◽  
Insight Into

ABSTRACTBacterial choline degradation in the human gut has been associated with cancer and heart disease. In addition, recent studies found that a bacterial microcompartment is involved in choline utilization byProteusandDesulfovibriospecies. However, many aspects of this process have not been fully defined. Here, we investigate choline degradation by the uropathogenEscherichia coli536. Growth studies indicatedE. coli536 degrades choline primarily by fermentation. Electron microscopy indicated that a bacterial microcompartment was used for this process. Bioinformatic analyses suggested that the choline utilization (cut) gene cluster ofE. coli536 includes two operons, one containing three genes and a main operon of 13 genes. Regulatory studies indicate that thecutXgene encodes a positive transcriptional regulator required for induction of the maincutoperon in response to choline supplementation. Each of the 16 genes in thecutcluster was individually deleted, and phenotypes were examined. ThecutX,cutY,cutF,cutO,cutC,cutD,cutU, andcutVgenes were required for choline degradation, but the remaining genes of thecutcluster were not essential under the conditions used. The reasons for these varied phenotypes are discussed.IMPORTANCEHere, we investigate choline degradation inE. coli536. These studies provide a basis for understanding a new type of bacterial microcompartment and may provide deeper insight into the link between choline degradation in the human gut and cancer and heart disease. These are also the first studies of choline degradation inE. coli536, an organism for which sophisticated genetic analysis methods are available. In addition, thecutgene cluster ofE. coli536 is located in pathogenicity island II (PAI-II536) and hence might contribute to pathogenesis.

scholarly journals A Structural-Thermal Model of the Karkonosze Pluton (Sudetes Mountains, SW Poland) for Hot Dry Rock (HDR) Geothermal Use

2016 ◽  
Vol 61 (4) ◽  
pp. 917-935 ◽  
Author(s):  
Wiesław Bujakowski ◽  
Antoni Barbacki ◽  
Maciej Miecznik ◽  
Leszek Pająk ◽  
Robert Skrzypczak
Keyword(s):  
Central Area ◽  
Tectonic Activity ◽  
Fluid Migration ◽  
Geothermal Resources ◽  
Radiogenic Heat ◽  
Cycle System ◽  
The Earth ◽  
Binary Cycle ◽  
Sw Poland ◽  
Insight Into

Abstract The main objective of this study was to develop a spatial temperature distribution of the Karkonosze Pluton to indicate optimum locations for HDR systems at drillable depth. HDR geothermal technology makes it possible to extract heat from the Earth in areas where no hydro-geothermal resources are present. To produce electricity in a binary cycle, system temperatures of > 100°C are usually required. In this paper, the authors have analysed the potential opportunities for applying HDR technology in the area of the Karkonosze Pluton, which is regarded as an optimum location for the application of the HDR concept (due to the potential for stimulation offered by the mechanical properties of the granites, radiogenic heat production, modern tectonic activity, and the thickness of the pluton). The model used in the analysis, which takes into account a hypothetical assessment of the manner and paths of fluid migration within the pluton, provides an insight into the spatial distribution of subsurface temperatures. It thus allows the location of relatively shallow high-temperature zones, which are optimal for the efficient application of HDR technology, to be identified. With respect to this technology, the Szklarska Poręba area and the NE part of the pluton seem to be better targets than the Cieplice central area, where the model indicated much lower temperatures (e.g. at a depth of 5,000 m, estimated temperatures in the vicinity of Szklarska Poręba were about 185°C and in the vicinity of Cieplice they were about 140°C).

scholarly journals The Study of the Theoretical Size and Node Probability of the Loop Cutset in Bayesian Networks

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1079 ◽  
Author(s):  
Jie Wei ◽  
Yufeng Nie ◽  
Wenxian Xie
Keyword(s):  
Probability Theory ◽  
Graph Theory ◽  
Bayesian Inference ◽  
Bayesian Networks ◽  
Numerical Simulations ◽  
Complete Graph ◽  
Upper Bound ◽  
Numerical Algorithms ◽  
Theoretical Research ◽  
Theoretical Results

Pearl’s conditioning method is one of the basic algorithms of Bayesian inference, and the loop cutset is crucial for the implementation of conditioning. There are many numerical algorithms for solving the loop cutset, but theoretical research on the characteristics of the loop cutset is lacking. In this paper, theoretical insights into the size and node probability of the loop cutset are obtained based on graph theory and probability theory. It is proven that when the loop cutset in a p-complete graph has a size of p − 2 , the upper bound of the size can be determined by the number of nodes. Furthermore, the probability that a node belongs to the loop cutset is proven to be positively correlated with its degree. Numerical simulations show that the application of the theoretical results can facilitate the prediction and verification of the loop cutset problem. This work is helpful in evaluating the performance of Bayesian networks.

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