scholarly journals Caveats: Numerical Requirements in Graph Theory Based Quantitation of Tissue Architecture

2000 ◽  
Vol 21 (2) ◽  
pp. 59-69 ◽  
Author(s):  
J. Sudbø ◽  
R. Marcelpoil ◽  
A. Reith
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Oral Mucosa ◽  
Voronoi Diagram ◽  
Structural Features ◽  
Grey Level ◽  
Tissue Architecture ◽  
Cell Nuclei ◽  
Centre Of Gravity ◽  
Number Of Cells

Graph theory based methods represent one approach to an objective and reproducible structural analysis of tissue architecture. By these methods, neighborhood relations between a number of objects (e.g., cells) are explored and inherent to these methods are therefore certain requirements as to the number of objects to be included in the analysis. However, the question of how many objects are required to achieve reproducible values in repeated computations of proposed structural features, has previously not been adressed specifically.After digitising HE stained slides and storing them as grey level images, cell nuclei were segmented and their geometrical centre of gravity were computed, serving as the basis for construction of the Voronoi diagram (VD) and its subgraphs. Variations in repeated computations of structural features derived from these graphs were related to the number of cell nuclei included in the analysis.We demonstrate a large variation in the values of the structural features from one computation to another in one and the same section when only a limited number of cells (100–500) are included in the analysis. This variation decreased with increasing number of cells analyzed. The exact number of cells required to achieve reproducible values differ significantly between tissues, but not between separate cases of similar lesions. There are no significant differences between normal and malignantly changed tissues in oral mucosa with respect to how many cells must be included.For graph theory based analysis of tissue architecture, care must be taken to include an adequate number of objects; for some of the structural features we have tested, more than 3000 cells.

scholarly journals New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas

2000 ◽  
Vol 21 (2) ◽  
pp. 71-86 ◽  
Author(s):  
J. Sudbø ◽  
R. Marcelpoil ◽  
A. Reith
Keyword(s):  
Pilot Study ◽  
Oral Mucosa ◽  
Voronoi Diagram ◽  
Tongue Cancer ◽  
Ccd Camera ◽  
Structural Features ◽  
Grey Level ◽  
Tissue Architecture ◽  
Cell Nuclei ◽  
Cervical Carcinomas

An adequate reproducibility in the description of tissue architecture is still a challenge to diagnostic pathology, sometimes with unfortunate prognostic implications. To assess a possible diagnostic and prognostic value of quantitiative tissue architecture analysis, structural features based on the Voronoi Diagram (VD) and its subgraphs were developed and tested.A series of 27 structural features were developed and tested in a pilot study of 30 cases of prostate cancer, 10 cases of cervical carcinomas, 8 cases of tongue cancer and 8 cases of normal oral mucosa. Grey level images were acquired from hematoxyline‐eosine (HE) stained sections by a charge coupled device (CCD) camera mounted on a microscope connected to a personal computer (PC) with an image array processor. From the grey level images obtained, cell nuclei were automatically segmented and the geometrical centres of cell nuclei were computed. The resulting 2‐dimensional (2D) swarm of pointlike seeds distributed in a flat plane was the basis for construction of the VD and its subgraphs. From the polygons, triangulations and arborizations thus obtained, 27 structural features were computed as numerical values. Comparison of groups (normal vs. cancerous oral mucosa, cervical and prostate carcinomas with good and poor prognosis) with regard to distribution in the values of the structural features was performed with Student's t‐test.We demonstrate that some of the structural features developed are able to distinguish structurally between normal and cancerous oral mucosa (P=0.001), and between good and poor outcome groups in prostatic (P=0.001) and cervical carcinomas (P=0.001).We present results confirming previous findings that graph theory based algorithms are useful tools for describing tis‐ sue architecture (e.g., normal versus malignant). The present study also indicates that these methods have a potential for prognostication in malignant epithelial lesions.

scholarly journals Logistics management of the rail connections using graph theory: the case of a public transportation company on the example of Koleje Dolnośląskie S.A.

2018 ◽  
Vol 10 (3) ◽  
pp. 7-22
Author(s):  
Paweł Sobczak ◽  
Ewa Stawiarska ◽  
Judit Oláh ◽  
József Popp ◽  
Tomas Kliestik
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Public Transportation ◽  
Transportation Networks ◽  
Logistics Management ◽  
Simulation Methods ◽  
Southern Poland ◽  
Transport Services ◽  
Network Simulations ◽  
Simulation Results

Abstract The main purpose of the paper was the structural analysis of the connections network used by a railway carrier Koleje Dolnośląskie S.A. operating in southern Poland. The analysis used simulation methods. The analysis and simulation were based on graph theory, which is successfully used in analysing a wide variety of networks (social, biological, computer, virtual and transportation networks). The paper presents indicators which allow judging the analysed connections network according to an appropriate level of transport services. Simulation results allowed proposing some modifications for the improvement of the analysed connections network. The paper also demonstrates that graph theory and network simulations should be used as tools by transportation companies during the stage of planning a connections network.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

Geology, Structural Analysis, and Paragenesis of the Arrow Uranium Deposit, Western Athabasca Basin, Saskatchewan, Canada: Implications for the Development of the Patterson Lake Corridor

2020 ◽  
Author(s):  
Sean Hillacre ◽  
Kevin Ansdell ◽  
Brian McEwan
Keyword(s):  
Structural Analysis ◽  
Uranium Deposit ◽  
Regional Scale ◽  
Structural Features ◽  
White Mica ◽  
Uranium Mineralization ◽  
Fault System ◽  
Thin Sections ◽  
Athabasca Basin ◽  
Quartz Veins

Abstract Recent significant discoveries of uranium mineralization in the southwestern Athabasca basin, northern Saskatchewan, Canada, have been associated with a series of geophysical conductors along a NE- to SW-trending structural zone, termed the Patterson Lake corridor. The Arrow deposit (indicated mineral resource: 256.6 Mlb U3O8; grade 4.03% U3O8) is along this trend, hosted exclusively in basement orthogneisses of the Taltson domain, and is the largest undeveloped uranium deposit in the basin. This study is the first detailed analysis of a deposit along this corridor and examines the relationships between the ductile framework and brittle reactivation of structures, mineral paragenesis, and uranium mineralization. Paragenetic information from hundreds of drill core samples and thin sections was integrated with structural analysis utilizing over 18,000 measurements of various structural features. The structural system at Arrow is interpreted as a partitioned, strike-slip–dominated, brittle-ductile fault system of complex Riedel-style geometry. The system developed along subvertical, NE- to SW-trending dextral high-strain zones formed syn- to post-D3 deformation, which were the focus of extensive premineralization metasomatism (quartz flooding, sericitization, chloritization), within the limb domain of a regional-scale fold structure. These zones evolved through post-Athabasca dextral and sinistral reactivation events, creating brittle fault linkages and dilation zones, allowing for hydrothermal fluid migration and resulting uraninite precipitation and associated alteration (white mica, chlorite, kaolinite, hematite, quartz veins). This study of the structural context of Arrow is important as it emphasizes that protracted reactivation of deep-seated structures and their subsidiaries was a fundamental control on uranium mineralization in the southwestern Athabasca basin.

Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

2014 ◽  
Vol 592-594 ◽  
pp. 1165-1169
Author(s):  
Preeti Gulia ◽  
V.P. Singh
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Reliable Method ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Mobility Test ◽  
Structural Problems ◽  
Algebraic Test

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.

Studies of the aggregation of an amyloidogenic α-synuclein peptide fragment

2005 ◽  
Vol 33 (5) ◽  
pp. 1113-1115 ◽  
Author(s):  
J. Madine ◽  
A.J. Doig ◽  
A. Kitmitto ◽  
D.A. Middleton
Keyword(s):  
Structural Analysis ◽  
Characteristic Feature ◽  
Neurodegenerative Disorders ◽  
Lewy Bodies ◽  
Structural Features ◽  
Full Length ◽  
Peptide Fragment ◽  
Structural Investigations ◽  
Detailed Structural Analysis ◽  
Β Sheet

The deposition of α-syn (α-synuclein) fibrils in Lewy bodies is a characteristic feature of individuals with neurodegenerative disorders. A peptide comprising the central residues 71–82 of α-syn [α-syn(71–82)] is capable of forming β-sheet-rich, amyloid-like fibrils with similar morphologies to fibrils of the full-length protein, providing a useful model of pathogenic α-syn fibrils that is suitable for detailed structural analysis. We have studied the morphology and gross structural features of α-syn(71–82) fibrils formed under different conditions in order to obtain reliable conditions for producing fibrils for further structural investigations. The results indicate that the rate of aggregation and the morphology of the fibrils formed are sensitive to pH and temperature.

scholarly journals Understanding Structural Features of Microbial Lipases–-An Overview

2008 ◽  
Vol 3 ◽  
pp. ACI.S551 ◽  
Author(s):  
John Geraldine Sandana Mala ◽  
Satoru Takeuchi
Keyword(s):  
Structural Analysis ◽  
Candida Rugosa ◽  
Structural Data ◽  
Data Bank ◽  
Candida Rugosa Lipase ◽  
Structural Features ◽  
X Ray Crystallography ◽  
Versatile Tool ◽  
Microbial Lipases

The structural elucidations of microbial lipases have been of prime interest since the 1980s. Knowledge of structural features plays an important role in designing and engineering lipases for specific purposes. Significant structural data have been presented for few microbial lipases, while, there is still a structure-deficit, that is, most lipase structures are yet to be resolved. A search for ‘lipase structure’ in the RCSB Protein Data Bank ( http://www.rcsb.org/pdb/ ) returns only 93 hits (as of September 2007) and, the NCBI database ( http://www.ncbi.nlm.nih.gov ) reports 89 lipase structures as compared to 14719 core nucleotide records. It is therefore worthwhile to consider investigations on the structural analysis of microbial lipases. This review is intended to provide a collection of resources on the instrumental, chemical and bioinformatics approaches for structure analyses. X-ray crystallography is a versatile tool for the structural biochemists and is been exploited till today. The chemical methods of recent interests include molecular modeling and combinatorial designs. Bioinformatics has surged striking interests in protein structural analysis with the advent of innumerable tools. Furthermore, a literature platform of the structural elucidations so far investigated has been presented with detailed descriptions as applicable to microbial lipases. A case study of Candida rugosa lipase (CRL) has also been discussed which highlights important structural features also common to most lipases. A general profile of lipase has been vividly described with an overview of lipase research reviewed in the past.

scholarly journals Structural analysis of disordered dimer packings

Soft Matter ◽  
2021 ◽  
Vol 17 (39) ◽  
pp. 8877-8890
Author(s):  
Esma Kurban ◽  
Adrian Baule
Keyword(s):  
Structural Analysis ◽  
Structural Features ◽  
Density Peak

We identify structural features that accompany the formation of the density peak in jammed disordered packings of dimer shaped particles.

scholarly journals Structural Analysis in Transit System Using Network Theory Case of Guadalajara, Mexico

Urban Science ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 87
Author(s):  
Orlando Barraza ◽  
Miquel Estrada
Keyword(s):  
Structural Analysis ◽  
Network Theory ◽  
Planning Process ◽  
Structural Features ◽  
Transport Network ◽  
Structural Elements ◽  
Transit System ◽  
Transit Network ◽  
Network Properties ◽  
In Transit

Structural analysis in a transit network is a key aspect used to evaluate in a planning process. In this sense, the use of network science was applied in this work to generate a framework of the main structural features of a transport network. In this case, an alternative transport network in Guadalajara, Mexico was taken as an example. The network properties selected were grade of accessibility, spatial friction, and vulnerability. In the case of the grade of accessibility, this propriety makes reference to the efficiency of the travel time that the network gives due to its structural features. The spatial friction measures how direct in terms of distance the trips that the network provides are, and the vulnerability relates to the ease with which the network can comprise its performance by affectations to their nodes or links. In this sense, this work presents a detailed methodology and a set of open-source tools that can be used to measure these key structural elements for decision making.

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