scholarly journals Nakade — a graph theoretic concept in Go

2001 ◽  
Vol 235 (1-3) ◽  
pp. 385-397
Author(s):  
Tomoki Nakamigawa
Keyword(s):  
Graph Theoretic ◽  
Theoretic Concept

Robustness of Regular Caterpillars

2017 ◽  
Vol 28 (07) ◽  
pp. 835-841 ◽  
Author(s):  
Aysun Aytaç ◽  
Zeynep Nihan Odabaş Berberler
Keyword(s):  
Computer Networks ◽  
Network Topology ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept

Robustness of the network topology is a key aspect in the design of computer networks. Vertex residual closeness is a new graph-theoretic concept defined as a measure of network robustness. In this model, edges are perfectly reliable and the vertices fail independently of each other. In this paper, vertex residual closeness of paths and regular caterpillars are calculated by giving an insight of how to evaluate the vertex residual closeness of path-like graphs.

scholarly journals Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

2016 ◽  
Author(s):  
Jochen Kursawe ◽  
Rémi Bardenet ◽  
Jeremiah J. Zartman ◽  
Ruth E. Baker ◽  
Alexander G. Fletcher
Keyword(s):  
Cell Tracking ◽  
Positional Information ◽  
Large Cell ◽  
Field Of View ◽  
Maximum Common Subgraph ◽  
Graph Theoretic ◽  
Epithelial Tissues ◽  
Theoretic Concept ◽  
Tissue Size ◽  
Epithelial Sheets

AbstractTracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterising cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a ‘maximum common subgraph’ to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as photoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell-cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues.

Link-Centre and Indexes of a Kinematic Chain

1992 ◽  
Author(s):  
V. P. Agrawal ◽  
J. N. Yadav ◽  
C. R. Pratap
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Input Output ◽  
Function Generator ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
Optimum Selection ◽  
Theoretic Concept ◽  
Selection Of

Abstract A new graph theoretic concept of link-centre of a kinematic chain is introduced. The link-centre of a kinematic chain is defined as a subset of set of links of the kinematic chain using a hierarchy of criteria based on distance concept. A number of structural invariants are defined for a kinematic chain which may be used for identification and classification of kinematic chains and mechanisms. An algorithm is developed on the basis of the concept of distance and the link-centre for optimum selection of input, output and fixed links in a multi-degree-of-freedom function generator.

scholarly journals Cache Transition Systems for Graph Parsing

2018 ◽  
Vol 44 (1) ◽  
pp. 85-118 ◽  
Author(s):  
Daniel Gildea ◽  
Giorgio Satta ◽  
Xiaochang Peng
Keyword(s):  
Transition System ◽  
Tree Decomposition ◽  
Dependency Parsing ◽  
Semantic Parsing ◽  
Fixed Size ◽  
Transition Systems ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
The Relationship

Motivated by the task of semantic parsing, we describe a transition system that generalizes standard transition-based dependency parsing techniques to generate a graph rather than a tree. Our system includes a cache with fixed size m, and we characterize the relationship between the parameter m and the class of graphs that can be produced through the graph-theoretic concept of tree decomposition. We find empirically that small cache sizes cover a high percentage of sentences in existing semantic corpora.

Network robustness and residual closeness

2018 ◽  
Vol 52 (3) ◽  
pp. 839-847
Author(s):  
Aysun Aytaç ◽  
Zeynep Nihan Odabaş Berberler
Keyword(s):  
Complex Networks ◽  
Interconnection Networks ◽  
Network Reliability ◽  
Central Issue ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
Individual Nodes

A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of residual closeness as a measure of network robustness which provides a much fuller characterization of the network.

Vulnerability Measures of Transformation Graph Gxy+

2015 ◽  
Vol 26 (06) ◽  
pp. 667-675 ◽  
Author(s):  
Aysun Aytaç ◽  
Tufan Turaci
Keyword(s):  
Communication Networks ◽  
Network Topology ◽  
Interconnection Networks ◽  
Network Reliability ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
System Robustness ◽  
The Cost ◽  
Cost Of Construction

Several factors have to be taken into account in the design of large interconnection networks. Optimal design is important both to achieve good performance and to reduce the cost of construction and maintenance. Practical communication networks are exposed to failures of network components. Failures between nodes and connections happen and it is desirable that a network is robust in the sense that a limited number of failures does not break down the whole system. Robustness of the network topology is a key aspect in the design of computer networks. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of domination and strong-weak domination numbers of the transformation graph Gxy+ as a measure of network robustness.

A Graph-Theoretic Approach to the Evolution of Cahokia

1991 ◽  
Vol 56 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Peter Peregrine
Keyword(s):  
Mississippi River ◽  
Theoretic Approach ◽  
River Drainage ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Theoretic Concept

Many researchers have linked the evolution of the prehistoric center Cahokia to its location near the confluence of the Mississippi, Missouri, and Illinois rivers. It is possible to evaluate this idea mathematically through the graph-theoretic concept of centrality. The analysis suggests that Cahokia was located at the point of highest centrality in the Mississippi River drainage.

Extremal Results on Vertex and Link Residual Closeness

2021 ◽  
pp. 1-21
Author(s):  
Bo Zhou ◽  
Zhenan Li ◽  
Haiyan Guo
Keyword(s):  
Computer Networks ◽  
Network Topology ◽  
Network Robustness ◽  
Unicyclic Graphs ◽  
Graph Theoretic ◽  
Theoretic Concept

Robustness of the network topology is a key aspect in the design of computer networks. Vertex (Link, respectively) residual closeness is a new graph-theoretic concept defined as a measure of network robustness due to the failure of individual vertices (links, respectively). In this paper, we identify the trees and unicyclic graphs with the first a few smallest vertex residual closeness, and determine the graphs that minimize or maximize the vertex (link, respectively) residual closeness over some classes of graphs.

scholarly journals Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

2016 ◽  
Vol 13 (124) ◽  
pp. 20160725 ◽  
Author(s):  
Jochen Kursawe ◽  
Rémi Bardenet ◽  
Jeremiah J. Zartman ◽  
Ruth E. Baker ◽  
Alexander G. Fletcher
Keyword(s):  
Cell Tracking ◽  
Positional Information ◽  
Large Cell ◽  
Field Of View ◽  
Maximum Common Subgraph ◽  
Graph Theoretic ◽  
Epithelial Tissues ◽  
Theoretic Concept ◽  
Tissue Size ◽  
Epithelial Sheets

Tracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterizing cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a ‘maximum common subgraph’ to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as phototoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell–cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues.

scholarly journals A Construction of Uniquely $n$-Colorable Digraphs with Arbitrarily Large Digirth

10.37236/4823 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Michael Severino
Keyword(s):  
Chromatic Number ◽  
Graph Coloring ◽  
Independent Set ◽  
Directed Cycle ◽  
Circular Chromatic Number ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
Vertex Set ◽  
Large Girth

A natural digraph analogue of the graph-theoretic concept of an `independent set' is that of an `acyclic set', namely a set of vertices not spanning a directed cycle. Hence a digraph analogue of a graph coloring is a decomposition of the vertex set into acyclic sets and we say a digraph is uniquely $n$-colorable when this decomposition is unique up to relabeling. It was shown probabilistically in [A. Harutyunyan et al., Uniquely $D$-colorable digraphs with large girth, Canad. J. Math., 64(6): 1310-1328, 2012] that there exist uniquely $n$-colorable digraphs with arbitrarily large girth. Here we give a construction of such digraphs and prove that they have circular chromatic number $n$. The graph-theoretic notion of `homomorphism' also gives rise to a digraph analogue. An acyclic homomorphism from a digraph $D$ to a digraph $H$ is a mapping $\varphi: V(D) \rightarrow V(H)$ such that $uv \in A(D)$ implies that either $\varphi(u)\varphi(v) \in A(H)$ or $\varphi(u)=\varphi(v)$, and all the `fibers' $\varphi^{-1}(v)$, for $v \in V(H)$, of $\varphi$ are acyclic. In this language, a core is a digraph $D$ for which there does not exist an acyclic homomorphism  from $D$ to a proper subdigraph of itself. Here we prove some basic results about digraph cores and construct highly chromatic cores without short cycles.

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