scholarly journals Centered Polygonal Lacunary Graphs: A Graph Theoretic Approach to p-Sequences of Centered Polygonal Lacunary Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1021 ◽  
Author(s):  
Keith Sullivan ◽  
Drew Rutherford ◽  
Darin J. Ulness
Keyword(s):  
Three Dimensional ◽  
Special Role ◽  
Theoretic Approach ◽  
Scaling Properties ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Condensed Graphs ◽  
Dimensional Graph ◽  
Insight Into

This work is on the nature and properties of graphs which arise in the study of centered polygonal lacunary functions. Such graphs carry both graph-theoretic properties and properties related to the so-called p-sequences found in the study of centered polygonal lacunary functions. p-sequences are special bounded, cyclic sequences that occur at the natural boundary of centered polygonal lacunary functions at integer fractions of the primary symmetry angle. Here, these graphs are studied for their inherent properties. A ground-up set of planar graph construction schemes can be used to build the numerical values in p-sequences. Further, an associated three-dimensional graph is developed to provide a complementary viewpoint of the p-sequences. Polynomials can be assigned to these graphs, which characterize several important features. A natural reduction of the graphs original to the study of centered polygonal lacunary functions are called antipodal condensed graphs. This type of graph provides much additional insight into p-sequences, especially in regard to the special role of primes. The new concept of sprays is introduced, which enables a clear view of the scaling properties of the underling centered polygonal lacunary systems that the graphs represent. Two complementary scaling schemes are discussed.

scholarly journals On a matching distance between rooted phylogenetic trees

2013 ◽  
Vol 23 (3) ◽  
pp. 669-684 ◽  
Author(s):  
Damian Bogdanowicz ◽  
Krzysztof Giaro
Keyword(s):  
Asymptotic Behavior ◽  
Metric Space ◽  
Phylogenetic Trees ◽  
Perfect Matching ◽  
Minimum Weight ◽  
Theoretic Approach ◽  
Popular Method ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Insight Into

Abstract The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs, the values of similarity between clusters are transformed to the final MC-score of the dissimilarity of trees. The analyzed properties give insight into the structure of the metric space generated by MC, its relations with the Matching Split (MS) distance of unrooted trees and asymptotic behavior of the expected distance between binary n-leaf trees selected uniformly in both MC and MS (Θ(n3/2)).

A Graph-theoretic Approach to the Identification of Three-dimensional Patterns of Amino Acid Side-chains in Protein Structures

1994 ◽  
Vol 243 (2) ◽  
pp. 327-344 ◽  
Author(s):  
Peter J. Artymiuk ◽  
Andrew R. Poirrette ◽  
Helen M. Grindley ◽  
David W. Rice ◽  
Peter Willett
Keyword(s):  
Amino Acid ◽  
Protein Structures ◽  
Three Dimensional ◽  
Side Chains ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Amino Acid Side Chains

scholarly journals Stability Analysis of a Multigroup SEIR Epidemic Model with General Latency Distributions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Nan Wang ◽  
Jingmei Pang ◽  
Jinliang Wang
Keyword(s):  
Epidemic Model ◽  
Classical Method ◽  
Theoretic Approach ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Latency Distributions ◽  
The Given

The global stability of a multigroup SEIR epidemic model with general latency distribution and general incidence rate is investigated. Under the given assumptions, the basic reproduction numberℜ0is defined and proved as the role of a threshold; that is, the disease-free equilibriumP0is globally asymptotically stable ifℜ0≤1, while an endemic equilibriumP*exists uniquely and is globally asymptotically stable ifℜ0>1. For the proofs, we apply the classical method of Lyapunov functionals and a recently developed graph-theoretic approach.

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

scholarly journals The distribution of myosin II in Dictyostelium discoideum slug cells.

1991 ◽  
Vol 115 (5) ◽  
pp. 1267-1274 ◽  
Author(s):  
S Eliott ◽  
P H Vardy ◽  
K L Williams
Keyword(s):  
Cell Motility ◽  
Dictyostelium Discoideum ◽  
Immunofluorescence Microscopy ◽  
Molecular Genetic ◽  
Myosin Ii ◽  
Three Dimensional ◽  
Homogeneous Distribution ◽  
Multicellular Development ◽  
Insight Into

While the role of myosin II in muscle contraction has been well characterized, less is known about the role of myosin II in non-muscle cells. Recent molecular genetic experiments on Dictyostelium discoideum show that myosin II is necessary for cytokinesis and multicellular development. Here we use immunofluorescence microscopy with monoclonal and polyclonal antimyosin antibodies to visualize myosin II in cells of the multicellular D. discoideum slug. A subpopulation of peripheral and anterior cells label brightly with antimyosin II antibodies, and many of these cells display a polarized intracellular distribution of myosin II. Other cells in the slug label less brightly and their cytoplasm displays a more homogeneous distribution of myosin II. These results provide insight into cell motility within a three-dimensional tissue and they are discussed in relation to the possible roles of myosin II in multicellular development.

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