1,721,017 research outputs found
△Y-EXCHANGES AND THE CONWAY–GORDON THEOREMS
No full text Conway–Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on seven vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 modulo 2. In this paper, we give a Conway–Gordon type theorem for any graph which is obtained from the complete graph on six or seven vertices by a finite sequence of △Y-exchanges. </jats:p
A refinement of the Conway–Gordon theorems
No full textAbstractIn 1983, Conway–Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 modulo 2. In this article, we give integral lifts of the Conway–Gordon theorems above in terms of the square of the linking number and the second coefficient of the Conway polynomial. As applications, we give alternative topological proofs of theorems of Brown–Ramírez Alfonsín and Huh–Jeon for rectilinear spatial complete graphs which were proved by computational and combinatorial methods
Converses to generalized Conway--Gordon type congruences
Full text linkIt is known that for every spatial complete graph on vertices, the
summation of the second coefficients of the Conway polynomials over the
Hamiltonian knots is congruent to modulo , where if , and if . In particular the case of
is famous as the Conway--Gordon theorem. In this paper,
conversely, we show that every integer is realized as the
summation of the second coefficients of the Conway polynomials over the
Hamiltonian knots in some spatial complete graph on vertices.Comment: 11 pages, 7 figure
Conway–Gordon problem for reduced complete spatial graphs
No full textКораблёв Филипп Глебович – доцент кафедры компьютерной топологии и алгебры, Челябинский государственный университет; Лаборатория квантовой топологии, Челябинский государственный университет; заведующий отделом алгоритмической топологии, Институт математики и механики им. Н.Н.Красовского Уральского отделения Российской академии наук.
E-mail: [email protected]
Казаков Александр Андреевич – преподаватель кафедры компьютерной топологии и алгебры, Челябинский государственный университет.
E-mail: [email protected]. Korablev Philipp Glebovich is Associate Professor, Department of Computer Topology and Algebra, Laboratory of Quantum Topology,
Chelyabinsk State University; Head of Mathematician of Algorithmic Topology Department, Institute of Mathematics and Mechanics, Ural
Branch of Russian Academy of Sciences.
E-mail: [email protected]
Kazakov Alexander Andreevich is Lecturer, Department of Computer Topology and Algebra, Chelyabinsk State University.
E-mail: [email protected]Работа посвящена исследованию графов, вложенных в трёхмерное пространство, которые получаются из полных графов удалением нескольких
рёбер, инцидентных одной вершине. Для всех таких графов вводится аналог функции Конвея–Гордона ω2 . Доказывается, что её значение равно нулю для всех графов, полученных из полных графов с не менее, чем восемью
вершинами. Также приводятся примеры графов с шестью вершинами, для
которых значение этой функции равно единице. This paper is devoted to 3D embeddable graphs, which are obtained from full spatial graphs by removing
several edges incident to one vertex. For all such graphs we introduce the analogue of Conway-Gordon function ω2. We prove that its value is zero for all spatial graphs obtained from full graphs with no less than eight vertices. There are examples of graphs with six vertices, where the value of this function is equal to unity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Knots and links in spatial graphs
No full textM.Phil.In this thesis, we study the intrinsic knottedness and linkedness of spatial graphs.In the first chapter, we introduce Conway and Gordon’s work. By considering spatial graph invariants under crossing move, they showed that K₆ is intrinsically linked and K₇ is intrinsically knotted.In the second and third chapter, we present Taniyama’s and Motohashi’s work on graph homology and graph homotopy, as well as various spatial graph invariants under those equivalence relations.In the fourth chapter, we give an overview to the current study of Conway Gordon type formula. We present results from Nikkuni, Taniyama, Hashimoto and O’Donnol about Conway-Gordon type formula for K₆,K₇,K₃,₃,₁,K₃,₃,₁,₁, as well as the Petersen family, the K₇ family and the K₃,₃,₁,₁ family. We also generalized Nikunni’s proof to obtain Conway-Gordon type formula for Kₙ(n ≥ 7). These formula are proved by considering graph homology invariants and graph homotopy invariants introduced in chapter 2 and 3. These formula give insights to how the intrinsic knottedness and linkedness of spatial graph are related.在本論文中，我們研究了空間圖的內在打結和鏈接性。在第一章中，我們介紹了Conway和Gordon的工作。通過考慮交叉移動下的空間圖不變量，他們表明K₆是內在鏈接的，K₇是內在打結的。在第二章和第三章中，我們介紹了Taniyama和Motohashi關於圖同調和圖同倫，以及這些等價關係下的各種空間圖不變量的工作。在第四章中，我們概述了Conway-Gordon型公式的當前研究。我們提供來自Nikkuni，Taniyama，Hashimoto和O’Donnol的關於Conway-Gordon型公式的結果，包括K₆,K₇,K₃,₃,1,K₃,₃,₁,₁，以及Petersen家族，K₇家族和K₃,₃,₁,₁家族的Conway-Gordon型公式。 我們還推廣了Nikunni的證明 ， 以獲得 Kn(n ≥ 7)的 Conway-Gordon型公式。這些公式是通過考慮第二章和第三章中介紹的圖同調不變量和圖同倫不變量來證明的。這些公式提示了關於空間圖的內在打結與鏈接如何相關。Kung, Man Kit.Thesis M.Phil. Chinese University of Hong Kong 2018.Includes bibliographical references (leaves 66-68).Abstracts also in Chinese.Title from PDF title page (viewed on 13, August, 2020)
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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