scholarly journals USING THE METHOD OF BUILDING OF OPTIMAL HAMILTONIAN CYCLE FOR INVESTIGATION OF SEASONAL CHANGES IN MACROPHYTOBENTOS (ON EXAMPLE OF THE VOSTOK BAY, JAPAN SEA)

2019 ◽  
Vol 197 ◽  
pp. 233-238
Author(s):  
B. I. Semkin ◽  
L. I. Varchenko
Keyword(s):  
Hamiltonian Cycle ◽  
Higher Plants ◽  
Similarity Index ◽  
Japan Sea ◽  
Hamiltonian Cycles ◽  
Vostok Bay ◽  
Dice Coefficient ◽  
Jaccard Similarity ◽  
Species Lists ◽  
Cyclic Changes

Method of building of optimal Hamiltonian cycle is proposed for study of cyclic changes in species composition of macrophytobenthos in the Vostok Bay. Compiled lists of macroalgae and higher plants are composed for each month. Requirements for the species lists comparing are established. The optimal Hamiltonian cycles for the lists without permanent species are different from those for the complete lists because of higher values of the measures of difference, particularly in winter. The Sørensen–Dice coefficient, Jaccard similarity index, or equivalent measures are recommended to use for assessment of the differences between the species lists.

A simple way to improve multivariate analyses of paleoecological data sets

Paleobiology ◽  
2015 ◽  
Vol 41 (3) ◽  
pp. 377-386 ◽  
Author(s):  
John Alroy
Keyword(s):  
Cluster Analysis ◽  
Sample Size ◽  
Similarity Index ◽  
The United States ◽  
Data Sets ◽  
Distance Metric ◽  
Dice Coefficient ◽  
Data Set ◽  
Principal Coordinates ◽  
Species Lists

AbstractMultivariate methods such as cluster analysis and ordination are basic to paleoecology, but the messy nature of fossil occurrence data often makes it difficult to recover clear patterns. A recently described faunal similarity index based on the Forbes coefficient improves results when its complement is employed as a distance metric. This index involves adding terms to the Forbes equation and ignoring one of the counts it employs (that of species found in neither of the samples under consideration). Analyses of simulated data matrices demonstrate its advantages. These matrices include large and small samples from two partially overlapping species pools. In a cluster analysis, the widely used Dice coefficient and the Euclidean distance metric both create groupings that reflect sample size, the Simpson index suggests large differences that do not exist, and the corrected Forbes index creates groupings based strictly on true faunal overlap. In a principal coordinates analysis (PCoA) the Forbes index almost removes the sample-size signal but other approaches create a second axis strongly dominated by sample size. Meanwhile, species lists of late Pleistocene mammals from the United States capture biogeographic signals that standard ordination methods do recover, but the adjusted Forbes coefficient spaces the points out more sensibly. Finally, when biome-scale lists for living mammals are added to the data set and extinct species are removed, correspondence analysis misleadingly separates out the biome lists, and PCoA based on the Dice coefficient places them to the edge of the cloud of fossil assemblage data points. PCoA based on the Forbes index places them in more reasonable positions. Thus, only the adjusted Forbes index is able to recover true biological patterns. These results suggest that the index may be useful in analyzing not only paleontological data sets but any data set that includes species lists having highly variable lengths.

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

scholarly journals Genetic structure and gene flow of Eugenia dysenterica natural populations

2005 ◽  
Vol 40 (10) ◽  
pp. 975-980 ◽  
Author(s):  
Maria Imaculada Zucchi ◽  
José Baldin Pinheiro ◽  
Lázaro José Chaves ◽  
Alexandre Siqueira Guedes Coelho ◽  
Mansuêmia Alves Couto ◽  
...  
Keyword(s):  
Gene Flow ◽  
Genetic Variability ◽  
Pearson Correlation ◽  
Natural Populations ◽  
Similarity Index ◽  
Genetic Distances ◽  
Strong Positive Correlation ◽  
Randomly Amplified Polymorphic Dna ◽  
Jaccard Similarity ◽  
Eugenia Dysenterica

This study was carried out to assess the genetic variability of ten "cagaita" tree (Eugenia dysenterica) populations in Southeastern Goiás. Fifty-four randomly amplified polymorphic DNA (RAPD) loci were used to characterize the population genetic variability, using the analysis of molecular variance (AMOVA). A phiST value of 0.2703 was obtained, showing that 27.03% and 72.97% of the genetic variability is present among and within populations, respectively. The Pearson correlation coefficient (r) among the genetic distances matrix (1 - Jaccard similarity index) and the geographic distances were estimated, and a strong positive correlation was detected. Results suggest that these populations are differentiating through a stochastic process, with restricted and geographic distribution dependent gene flow.

scholarly journals Semi-Degree Threshold for Anti-Directed Hamiltonian Cycles

10.37236/3610 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Louis DeBiasio ◽  
Theodore Molla
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Hamiltonian Cycles ◽  
Alternate Direction ◽  
Degree Conditions

In 1960 Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$, then $D$ contains a directed Hamiltonian cycle. For directed graphs one may ask for other orientations of a Hamiltonian cycle and in 1980 Grant initiated the problem of determining minimum degree conditions for a directed graph $D$ to contain an anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even $n$, if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $\frac{n}{2}+1$, then $D$ contains an anti-directed Hamiltonian cycle. In fact, we prove the stronger result that $\frac{n}{2}$ is sufficient unless $D$ is one of two counterexamples. This result is sharp.

An abundance- and morphology-based similarity index

Paleobiology ◽  
2021 ◽  
pp. 1-18
Author(s):  
Daniel G. Dick ◽  
Marc Laflamme
Keyword(s):  
River Flow ◽  
Similarity Index ◽  
Ecological Gradients ◽  
Jaccard Similarity ◽  
Real World Data ◽  
Large Component ◽  
Morphological Gradient ◽  
Random Samples ◽  
Similarity Indices ◽  
General Method

Abstract Classic similarity indices measure community resemblance in terms of incidence (the number of shared species) and abundance (the extent to which the shared species are an equivalently large component of the ecosystem). Here we describe a general method for increasing the amount of information contained in the output of these indices and describe a new “soft” ecological similarity measure (here called “soft Chao-Jaccard similarity”). The new measure quantifies community resemblance in terms of shared species, while accounting for intraspecific variation in abundance and morphology between samples. We demonstrate how our proposed measure can reconstruct short ecological gradients using random samples of taxa, recognizing patterns that are completely missed by classic measures of similarity. To demonstrate the utility of our new index, we reconstruct a morphological gradient driven by river flow velocity using random samples drawn from simulated and real-world data. Results suggest that the new index can be used to recognize complex short ecological gradients in settings where only information about specimens is available. We include open-source R code for calculating the proposed index.

An Attempt to Estimate the Noises in Homeopathic Pathogenetic Trials by Employing the Jaccard Similarity Index and Noise Index

Homeopathy ◽  
2021 ◽  
Author(s):  
Kurian Poruthukaren
Keyword(s):  
Placebo Group ◽  
Hepatitis C ◽  
Intervention Group ◽  
Similarity Index ◽  
Signs And Symptoms ◽  
Piper Methysticum ◽  
Common Elements ◽  
Jaccard Similarity ◽  
Noise Index ◽  
Trial Drug

Abstract Background The critical task of researchers conducting double-blinded, randomized, placebo-controlled homeopathic pathogenetic trials is to segregate the signals from the noises. The noises are signs and symptoms due to factors other than the trial drug; signals are signs and symptoms due to the trial drug. Unfortunately, the existing tools (criteria for a causal association of symptoms only with the tested medicine, qualitative pathogenetic index, quantitative pathogenetic index, pathogenic index) have limitations in analyzing the symptoms of the placebo group as a comparator, resulting in inadequate segregation of the noises. Hence, the Jaccard similarity index and the Noise index are proposed for analyzing the symptoms of the placebo group as a comparator. Methods The Jaccard similarity index is the ratio of the number of common elements among the placebo and intervention groups to the aggregated number of elements in these groups. The Noise index is the ratio of common elements among the placebo and intervention group to the total elements of the intervention group. Homeopathic pathogenetic trials of Plumbum metallicum, Piper methysticum and Hepatitis C nosode were selected for experimenting with the computation of the Jaccard similarity index and the Noise index. Results Jaccard similarity index calculations show that 8% of Plumbum metallicum's elements, 10.7% of Piper methysticum's elements, and 19.3% of Hepatitis C nosode's elements were similar to the placebo group when elements of both the groups (intervention and placebo) were aggregated. Noise index calculations show that 10.7% of Plumbum metallicum's elements, 13.9% of Piper methysticum's elements and 25.7% of Hepatitis C nosode's elements were similar to those of the placebo group. Conclusion The Jaccard similarity index and the Noise index might be considered an additional approach for analyzing the symptoms of the placebo group as a comparator, resulting in better noise segregation in homeopathic pathogenetic trials.

scholarly journals DISTRIBUTED ALGORITHMS FOR BUILDING HAMILTONIAN CYCLES IN k-ARY n-CUBES AND HYPERCUBES WITH FAULTY LINKS

2007 ◽  
Vol 08 (03) ◽  
pp. 253-284 ◽  
Author(s):  
IAIN A. STEWART
Keyword(s):  
Distributed Algorithms ◽  
Distributed Algorithm ◽  
Hamiltonian Cycle ◽  
Sequential Algorithm ◽  
Hamiltonian Cycles ◽  
Cube Formula

We derive a sequential algorithm Find-Ham-Cycle with the following property. On input: k and n (specifying the k-ary n-cube [Formula: see text]); F, a set of at most 2n − 2 faulty links; and v , a node of [Formula: see text], the algorithm outputs nodes v + and v − such that if Find-Ham-Cycle is executed once for every node v of [Formula: see text] then the node v + (resp. v −) denotes the successor (resp. predecessor) node of v on a fixed Hamiltonian cycle in [Formula: see text] in which no link is in F. Moreover, the algorithm Find-Ham-Cycle runs in time polynomial in n and log k. We also obtain a similar algorithm for an n-dimensional hypercube with at most n − 2 faulty links. We use our algorithms to obtain distributed algorithms to embed Hamiltonian cycles k-ary n-cubes and hypercubes with faulty links; our hypercube algorithm improves on a recently-derived algorithm due to Leu and Kuo, and our k-ary n-cube algorithm is the first distributed algorithm for embedding a Hamiltonian cycle in a k-ary n-cube with faulty links.

scholarly journals Complexity of Hamiltonian Cycle Reconfiguration

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 140 ◽  
Author(s):  
Asahi Takaoka
Keyword(s):  
Hamiltonian Cycle ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Interval Graph ◽  
Unit Interval ◽  
Chordal Graphs ◽  
Hamiltonian Cycles ◽  
Permutation Graph ◽  
Proper Subclass ◽  
Chordal Bipartite Graphs

The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained from C i − 1 by a switch for each i with 1 ≤ i ≤ t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time.

KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7 INTO ℝ3

2012 ◽  
Vol 21 (14) ◽  
pp. 1250132 ◽  
Author(s):  
YOUNGSIK HUH
Keyword(s):  
Complete Graph ◽  
Hamiltonian Cycle ◽  
Hamiltonian Cycles ◽  
Intrinsic Properties ◽  
Linear Embedding

In 1983 Conway and Gordon proved that any embedding of the complete graph K7 into ℝ3 contains at least one nontrivial knot as its Hamiltonian cycle. After their work knots (also links) are considered as intrinsic properties of abstract graphs, and numerous subsequent works have been continued until recently. In this paper, we are interested in knotted Hamiltonian cycles in linear embedding of K7. Concretely it is shown that any linear embedding of K7 contains at most three figure-8 knots.

scholarly journals Feasible Bases for a Polytope Related to the Hamilton Cycle Problem

2021 ◽  
Author(s):  
Thomas Kalinowski ◽  
Sogol Mohammadian
Keyword(s):  
Decision Process ◽  
Network Flow ◽  
Hamiltonian Cycle ◽  
Hamilton Cycle ◽  
Hamiltonian Cycles ◽  
Combinatorial Interpretation ◽  
Full Characterization ◽  
Computational Support ◽  
Markov Decision ◽  
Flow Polytope

We study a certain polytope depending on a graph G and a parameter β ∈ (0,1) that arises from embedding the Hamiltonian cycle problem in a discounted Markov decision process. Literature suggests a conjecture a lower bound on the proportion of feasible bases corresponding to Hamiltonian cycles in the set of all feasible bases. We make progress toward a proof of the conjecture by proving results about the structure of feasible bases. In particular, we prove three main results: (1) the set of feasible bases is independent of the parameter β when the parameter is close to one, (2) the polytope can be interpreted as a generalized network flow polytope, and (3) we deduce a combinatorial interpretation of the feasible bases. We also provide a full characterization for a special class of feasible bases, and we apply this to provide some computational support for the conjecture.

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