scholarly journals Physically feasible decomposition of Engino® toy models: A graph-theoretic approach

2018 ◽  
Vol 30 (2) ◽  
pp. 278-297
Author(s):  
E. N. ANTONIOU ◽  
A. ARAÚJO ◽  
M. D. BUSTAMANTE ◽  
A. GIBALI
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Study Group ◽  
Theoretic Approach ◽  
European Study ◽  
Graph Theoretic ◽  
European Study Group ◽  
Graph Theoretic Approach ◽  
Assembly Instructions ◽  
Algorithmic Procedure

During the 125th European Study Group with Industry held in Limassol, Cyprus, 5–9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets – the Engino® toy sets – consisting of a number of building blocks, which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilizing the blocks present in the set; however, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper, we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well-established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which a series of step-by-step assembly instructions can be recovered, is proposed.

scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2020 ◽  
Author(s):  
Tanvir Singh ◽  
V.P. Agrawal
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2021 ◽  
Author(s):  
Tanvir Singh
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Abstract Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

scholarly journals A Graph-Theoretic Approach to Wilf's Conjecture

10.37236/9106 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Shalom Eliahou
Keyword(s):  
Graph Theory ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Theoretic Approach ◽  
Primitive Elements ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Wilf’S Conjecture ◽  
Open Question

Let $S \subseteq \mathbb{N}$ be a numerical semigroup with multiplicity $m = \min(S \setminus \{0\})$ and conductor $c=\max(\mathbb{N} \setminus S)+1$. Let $P$ be the set of primitive elements of $S$, and let $L$ be the set of elements of $S$ which are smaller than $c$. A longstanding open question by Wilf in 1978 asks whether the inequality $|P||L| \ge c$ always holds. Among many partial results, Wilf's conjecture has been shown to hold in case $|P| \ge m/2$ by Sammartano in 2012. Using graph theory in an essential way, we extend the verification of Wilf's conjecture to the case $|P| \ge m/3$. This case covers more than $99.999\%$ of numerical semigroups of genus $g \le 45$.

scholarly journals Input-to-state stability of multi-group stochastic coupled systems with time-varying delay

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2109-2121
Author(s):  
Xiaoling Zou ◽  
Jiacheng Xu
Keyword(s):  
Graph Theory ◽  
Coupled Oscillators ◽  
Coupled Systems ◽  
Theoretic Approach ◽  
Time Varying ◽  
Systematic Method ◽  
Graph Theoretic ◽  
Time Varying Delay ◽  
Graph Theoretic Approach ◽  
Varying Delay

We investigate the issue of p-th moment exponentially input-to-state stability (pMEISS) of multi-group stochastic coupled systems with time-varying delay (MSCSTD) in this paper. By means of results from graph theory, we develop a systematic method that allows one to construct a proper Lyapunov function for MSCSTD. More specifically, two kinds of sufficient criteria, which are called Lyapunov-type and coefficient-type respectively, are derived to ensure pMEISS for MSCSTD by using the graph-theoretic approach. To make results more understandable, we apply them to a typical stochastic coupled oscillators with control inputs.

A Graph-Theoretic Approach to Comparing and Integrating Genetic, Physical and Sequence-Based Maps

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2235-2247
Author(s):  
Immanuel V Yap ◽  
David Schneider ◽  
Jon Kleinberg ◽  
David Matthews ◽  
Samuel Cartinhour ◽  
...  
Keyword(s):  
Directed Graph ◽  
Source Material ◽  
Complete Picture ◽  
Theoretic Approach ◽  
Research Groups ◽  
Genome Coverage ◽  
Graph Theoretic ◽  
Novel Approach ◽  
Graph Theoretic Approach ◽  
Locus Order

AbstractFor many species, multiple maps are available, often constructed independently by different research groups using different sets of markers and different source material. Integration of these maps provides a higher density of markers and greater genome coverage than is possible using a single study. In this article, we describe a novel approach to comparing and integrating maps by using abstract graphs. A map is modeled as a directed graph in which nodes represent mapped markers and edges define the order of adjacent markers. Independently constructed graphs representing corresponding maps from different studies are merged on the basis of their common loci. Absence of a path between two nodes indicates that their order is undetermined. A cycle indicates inconsistency among the mapping studies with regard to the order of the loci involved. The integrated graph thus produced represents a complete picture of all of the mapping studies that comprise it, including all of the ambiguities and inconsistencies among them. The objective of this representation is to guide additional research aimed at interpreting these ambiguities and inconsistencies in locus order rather than presenting a “consensus order” that ignores these problems.

scholarly journals Study of the Concrete Production Process -A graph theoretic approach

2020 ◽  
Vol 1706 ◽  
pp. 012115
Author(s):  
P Sangeetha ◽  
M Shanmugapriya ◽  
R Sundareswaran ◽  
K Sowmya ◽  
S Srinidhi
Keyword(s):  
Production Process ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Concrete Production
Sign in / Sign up

Export Citation Format

Share Document