scholarly journals A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Points

10.37236/578 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Weiwen Gu
Keyword(s):  
Oriented Graph ◽  
Decomposition Algorithm ◽  
Adjacency Graph ◽  
Connected Graphs ◽  
Marked Points ◽  
Adjacency Graphs ◽  
Mutation Type

In this paper we consider an oriented version of adjacency graphs of triangulations of bordered surfaces with marked points. We develop an algorithm that determines whether a given oriented graph is an oriented adjacency graph of a triangulation. If a given oriented graph corresponds to many triangulations, our algorithm finds all of them. As a corollary we find out that there are only finitely many oriented connected graphs with non-unique associated triangulations. We also discuss a new algorithm which determines whether a given quiver is of finite mutation type. This algorithm is linear in the number of nodes and is more effective than the previously known one.

scholarly journals Contiguity: Contig adjacency graph construction and visualisation

2015 ◽  
Author(s):  
Mitchell J Sullivan ◽  
Nouri L Ben Zakour ◽  
Brian M Forde ◽  
Mitchell Stanton-Cook ◽  
Scott A Beatson
Keyword(s):  
De Novo ◽  
Reference Sequence ◽  
De Bruijn Graph ◽  
Interactive Software ◽  
Graph Exploration ◽  
Adjacency Graph ◽  
Highly Sensitive ◽  
Long Read ◽  
Genome Assemblies ◽  
Adjacency Graphs

Contiguity is an interactive software for the visualization and manipulation of de novo genome assemblies. Contiguity creates and displays information on contig adjacency which is contextualized by the simultaneous display of a comparison between assembled contigs and reference sequence. Where scaffolders allow unambiguous connections between contigs to be resolved into a single scaffold, Contiguity allows the user to create all potential scaffolds in ambiguous regions of the genome. This enables the resolution of novel sequence or structural variants from the assembly. In addition, Contiguity provides a sequencing and assembly agnostic approach for the creation of contig adjacency graphs. To maximize the number of contig adjacencies determined, Contiguity combines information from read pair mappings, sequence overlap and De Bruijn graph exploration. We demonstrate how highly sensitive graphs can be achieved using this method. Contig adjacency graphs allow the user to visualize potential arrangements of contigs in unresolvable areas of the genome. By combining adjacency information with comparative genomics, Contiguity provides an intuitive approach for exploring and improving sequence assemblies. It is also useful in guiding manual closure of long read sequence assemblies. Contiguity is an open source application, implemented using Python and the Tkinter GUI package that can run on any Unix, OSX and Windows operating system. It has been designed and optimized for bacterial assemblies. Contiguity is available at http://mjsull.github.io/Contiguity .

scholarly journals The hull number of an oriented graph

2003 ◽  
Vol 2003 (36) ◽  
pp. 2265-2275 ◽  
Author(s):  
Gary Chartrand ◽  
John Frederick Fink ◽  
Ping Zhang
Keyword(s):  
Connected Graph ◽  
Oriented Graph ◽  
Connected Graphs

We present characterizations of connected graphsGof ordern≥2for whichh+(G)=n. It is shown that for every two integersnandmwith1≤n−1≤m≤(n2), there exists a connected graphGof ordernand sizemsuch that for each integerkwith2≤k≤n, there exists an orientation ofGwith hull numberG.

Modification of Algorithm of Directed Graph Paths Decomposition with Schedule

2021 ◽  
Vol 11 (2) ◽  
pp. 51-58
Author(s):  
I.A. Zolotarev ◽  
V.A. Rasskazova
Keyword(s):  
Directed Graph ◽  
Original Problem ◽  
Oriented Graph ◽  
Additional Constraint ◽  
Decomposition Algorithm ◽  
Transport Networks ◽  
Complex Topology ◽  
Balance Parameter

This study aims to refinement of the oriented graph paths decomposition algorithm. An additional constraint on the balance parameter is considered to take into account the locomotive departure schedule. Also new rule to compute Ns parameters is given. An example of the operation of the oriented graph paths decomposition algorithm with the schedule is given. The scientific and practical novelty of the work lies in a significant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

A Graph and Matrix Based Approach for Stamping Operation Sequencing for Progressive Die Design

2011 ◽  
Vol 421 ◽  
pp. 564-569
Author(s):  
Chang Yong Chu
Keyword(s):  
Die Design ◽  
Graph Colouring ◽  
Operation Sequencing ◽  
Adjacency Graph ◽  
Fully Integrated ◽  
Cad System ◽  
System A ◽  
Joint Operations ◽  
Adjacency Graphs

Two graphs are introduced to describe the precedence and cluster constraints among stamping operations, i.e., operation precedence graph and operation adjacency graph. A graph colouring algorithm clusters the operations based on both the precedence and adjacency graphs to form joint operations. A joint operation matrix is then generated. A matrix based algorithm is presented to iteratively order the joint operations to generate the final sequence according to the index of priority for each operation. The algorithm is implemented in C++ and is fully integrated with SolidWorks CAD system. A case study is presented to illustrate the algorithm.

scholarly journals The Decomposition Algorithm for Skew-Symmetrizable Exchange Matrices

10.37236/2447 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Weiwen Gu
Keyword(s):  
Decomposition Algorithm ◽  
Symmetric Matrices ◽  
Combinatorial Algorithm ◽  
Median Graph ◽  
The One ◽  
Mutation Type

Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admit unfoldings to skew-symmetric matrices. We develop a combinatorial algorithm that determines if a given skew-symmetrizable matrix is of such type. This algorithm generalizes the one in Weiwen Gu's Decomposition Algorithm for Median Graph of Triangulation of a Bordered 2D Surface. As a corollary, we use this algorithm to determine if a given skew-symmetrizable matrix has finite mutation type.

scholarly journals New Graphs of Finite Mutation Type

10.37236/863 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Harm Derksen ◽  
Theodore Owen
Keyword(s):  
Directed Graph ◽  
Symmetric Matrix ◽  
Cluster Algebras ◽  
Symmetric Matrices ◽  
Finite Graphs ◽  
Isomorphism Classes ◽  
Geometric Type ◽  
Symmetrizable Matrices ◽  
Marked Points ◽  
Mutation Type

To a directed graph without loops or $2$-cycles, we can associate a skew-symmetric matrix with integer entries. Mutations of such skew-symmetric matrices, and more generally skew-symmetrizable matrices, have been defined in the context of cluster algebras by Fomin and Zelevinsky. The mutation class of a graph $\Gamma$ is the set of all isomorphism classes of graphs that can be obtained from $\Gamma$ by a sequence of mutations. A graph is called mutation-finite if its mutation class is finite. Fomin, Shapiro and Thurston constructed mutation-finite graphs from triangulations of oriented bordered surfaces with marked points. We will call such graphs "of geometric type". Besides graphs with $2$ vertices, and graphs of geometric type, there are only 9 other "exceptional" mutation classes that are known to be finite. In this paper we introduce 2 new exceptional finite mutation classes.

scholarly journals Contiguity: Contig adjacency graph construction and visualisation

2015 ◽  
Author(s):  
Mitchell J Sullivan ◽  
Nouri L Ben Zakour ◽  
Brian M Forde ◽  
Mitchell Stanton-Cook ◽  
Scott A Beatson
Keyword(s):  
De Novo ◽  
Reference Sequence ◽  
De Bruijn Graph ◽  
Interactive Software ◽  
Graph Exploration ◽  
Adjacency Graph ◽  
Highly Sensitive ◽  
Long Read ◽  
Genome Assemblies ◽  
Adjacency Graphs

Contiguity is an interactive software for the visualization and manipulation of de novo genome assemblies. Contiguity creates and displays information on contig adjacency which is contextualized by the simultaneous display of a comparison between assembled contigs and reference sequence. Where scaffolders allow unambiguous connections between contigs to be resolved into a single scaffold, Contiguity allows the user to create all potential scaffolds in ambiguous regions of the genome. This enables the resolution of novel sequence or structural variants from the assembly. In addition, Contiguity provides a sequencing and assembly agnostic approach for the creation of contig adjacency graphs. To maximize the number of contig adjacencies determined, Contiguity combines information from read pair mappings, sequence overlap and De Bruijn graph exploration. We demonstrate how highly sensitive graphs can be achieved using this method. Contig adjacency graphs allow the user to visualize potential arrangements of contigs in unresolvable areas of the genome. By combining adjacency information with comparative genomics, Contiguity provides an intuitive approach for exploring and improving sequence assemblies. It is also useful in guiding manual closure of long read sequence assemblies. Contiguity is an open source application, implemented using Python and the Tkinter GUI package that can run on any Unix, OSX and Windows operating system. It has been designed and optimized for bacterial assemblies. Contiguity is available at http://mjsull.github.io/Contiguity .

Methyl-CpG-binding protein 2 (MECP2) mutation type is associated with bone disease severity in Rett syndrome

2019 ◽  
Author(s):  
Carla Caffarelli ◽  
Tomai Pitinca Maria Dea ◽  
Valentina Francolini ◽  
Roberto Canitano ◽  
felice Claudio De ◽  
...  
Keyword(s):  
Disease Severity ◽  
Rett Syndrome ◽  
Bone Disease ◽  
Binding Protein ◽  
Mecp2 Mutation ◽  
Mutation Type

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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