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New characterizations of partition functions using connection matrices
Get PDFIn this thesis we expand upon a line of research pioneered by Freedman, Lovász and Schrijver, and Szegedy, that uses algebraic methods to characterize families of partition functions. We introduce two new types of partition functions: skew partition functions and mixed partition functions. We give two algebraic characterizations of skew partition functions and we show that a mixed partition functions satisfy certain algebraic relationships that are related to the invariant of the symmetric group and to the invariant theory of the Orthosymplectic Supergroup. We furthermore give a characterization of real-valued partition functions for 3-graphs and for virtual link diagrams in terms of positive semidefiniteness of the associated connection matrices
Partition functions: Zeros, unstable dynamics and complexity
Get PDFThis thesis considers the complexity of approximating the partition functions of the ferromagnetic Ising model and of the hard-core model (independence polynomial) within the class of bounded degree graphs. It is known that the absence of zeros essentially implies that approximation is easy. In this thesis the inverse is proved: the presence of zeros implies that approximation is #P hard. The most important step of the proof is relating both the "zero parameters" and the "#P hard parameters" to the set of parameters around which a related set of functions, namely the occupation ratios, behaves chaotically. The first two chapters contain the proof of the main theorem for the ferromagnetic Ising model and the independence polynomial respectively. Chapters 3 and 4 concern the set of zeros of the independence polynomial for bounded degree graphs. In Chapter 3 it is shown that zeros of Cayley trees are not extremal within the set of zeros of all bounded degree graphs, something that was previously conjectured. In Chapter 4 a very precise description of the set of zeros is given as the degree bound goes to infinity
Applications of representation theory in discrete mathematics
Get PDFIn this thesis we present two new applications of the representation theory of finite groups in discrete mathematics. The first application is in coding theory. We further develop the theory of upper bounds for error-correcting codes and mixed binary/ternary codes, thereby expanding upon the work of Gijswijt et al. and Brouwer et al. We consider semidefinite programs based on quadruples of codewords and apply a symmetry reduction to obtain an optimization problem of polynomial size. This enables us to solve the semidefinite program with the aid of the computer for several values of n (the length of the words), q (the size of the alphabet) and d (the distance). The second application of representation theory is concerned with the enumeration of local flows in embedded graphs. We extend the domain of the surface Tutte polynomial of Goodall et al. to include non-orientable embedded graphs and show that this invariant for embedded graphs contains for every finite group G the number of nowhere-identity local G-flows and the number of nowhere-identity local G-tensions as evaluations. We prove that for an embedded graph nowhere-identity local tensions correspond with proper colorings of a covering of the embedded graph, thereby generalizing coloring-flow duality for planar graphs. The surface Tutte polynomial also specializes to a trivariate polynomial for signed graphs. We show that this polynomial has a universal property, which we finally use to give combinatorial interpretations of several of its evaluations
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Compact orbit spaces in Hilbert spaces and limits of edge-colouring models
No full textLet be a group of orthogonal transformations of a real Hilbert space . Let and
be bounded -stable subsets of . Let be the seminorm on defined by , for . We show that if is weakly compact and the orbit space is compact for each , then the orbit space is compact when ||\cdot||_R$.
As a consequence we derive the existence of limits of edge-colouring models which answers a
question posed by Lov\'asz. It forms the edge-colouring counterpart of the graph limits of Lov\'asz and
Szegedy, which can be seen as limits of vertex-colouring models. In the terminology of de la Harpe and Jones, vertex- and edge-colouring models are called ‘spin models’ and ‘vertex models’ respectively
Variations on the Author
Get PDF“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
Get PDFWe 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
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