1,720,974 research outputs found
A guide to F-automatic sets
Full text linkA self-contained introduction to the theory of F-automatic sets is given. Building on [Bell, Moosa, F-sets and finite automata, Journal de théorie des nombres de Bordeaux, 2019], contributions are made to both the foundations of this theory and to questions of a model-theoretic nature.
Suppose Γ is an abelian group and F : Γ → Γ is an injective endomorphism. If (Γ, F) admits a "spanning set" then the notion of an F-automatic set can be defined. It is shown that this notion is independent of the spanning set chosen. A characterization of the existence of a spanning set is given in terms of certain functions on Γ, called "height functions". It is shown that if Γ is finitely generated then (Γ, F) admits a spanning set if and only if no eigenvalue of the matrix of F lies in the complex unit disk.
A notion of sparsity among F-automatic sets, called F-sparsity, is studied. Outstanding questions from [Bell, Moosa, F-sets and finite automata, Journal de théorie des nombres de Bordeaux, 2019] are resolved, including independence from the spanning set chosen and closure under set summation. In addition, it is shown that sparsity can be characterized in terms of another natural class of functions introduced here, called "length functions".
Model-theoretic tameness properties of F-automatic sets are studied. In the case where Γ is finitely generated, a combinatorial description is given of the stable F-sparse sets in terms of the F-sets introduced in [Moosa, Scanlon, F-structures and integral points on semiabelian varieties over finite fields, American Journal of Mathematics, 2004]. When Γ = ℤ, this description is extended to a characterization of the stable F-automatic sets. It is shown that if A ⊆ Γ is F-sparse then (Γ, +, A) is NIP. Automatic methods are used to show that the following structures have NIP theories: (ℤ, +, d^ℕ, ×↾d^ℕ) for d ≥ 2, (_p[t], +, t^ℕ, ×↾t^ℕ) for prime p ≥ 9, and (ℤ, +, <, d^ℕ) for d ≥ 2. (Here d^ℕ = {1, d, d^2, ...}, and likewise with t^ℕ.
The Logarithmic Derivative and Model-Theoretic Analysability in Differentially Closed Fields
Full text linkThis thesis deals with internal and analysable types, mainly in the context of the stable theory of differentially closed fields. Two main problems are dealt with: the construction of types analysable in the constants with specific properties, and a criterion for a given analysable type to be actually internal to the constants.
For analysable types, the notion of canonical analyses is introduced. A type has a canonical analysis if all its analyses of shortest length are interalgebraic. Given a finite sequence of ranks, it is constructed, in the theory of differentially closed field, a type analysable in the constants such that it admits a canonical analysis and each step of the analysis is of the given rank. The construction of such a type starts from the well-known example of δ(logδx)=0, whose generic type is analysable in the constants in 2 steps but is not internal to the constants. Along the way, techniques for comparing analyses in stable theories are developed, including in particular the notions of analyses by reductions and by coreductions.
The property of the logδ function is further studied when the following question is raised: given a type internal to the constants, is its preimage under logδ, which is 2-step analysable in the constants, ever internal to the constants? The question is answered positively, and a criterion for when the preimage is indeed internal is proposed. Partial results are proven for this conjectured criterion, namely the cases where the group of automorphisms (the binding group) of the given internal type is additive, multiplicative, or trivial. In particular, the conjecture is resolved for generic types of equations of the form δx=f(x) where f is a rational function over the constants. It is discovered that the related problem where logδ is replaced by δ is significantly different, and the analogue of the conjecture fails in this case.
Also included in this thesis are two examples asked for in the literature: internality of a particular twisted D-group, and a 2-step analysable set with independent fibres
On internality and the canonical base property
No full textThis thesis contributes to the understanding of almost internality with respect to invariant families of types in a superstable theory of finite Lascar rank and was motivated by the so-called canonical base property (in short, CBP).Influenced by work of Chatzidakis and Moosa-Pillay, we study two weakenings of the CBP, namely transfer of internality to intersections, resp. to quotients, with respect to invariant families of types of Lascar rank one. Transfer of internality to intersections is a special case of transfer to quotients. We prove that transfer of internality to quotients with respect to the family of all minimal types already implies the CBP.We give an alternative presentation of the uncountably categorical counterexample to the CBP produced by Hrushovski, Palacin and Pillay as an additive cover of the complex numbers. We prove that this structure does not even transfer internality to intersections with respect to the unique (up to non-orthogonality) strongly minimal set, giving another reason for the failure of the CBP.Furthermore, we begin a structural study of groups of finite Lascar rank definable in theories which transfer internality to quotients and obtain as a consequence infinitely many new additive covers of the complex numbers without the CBP
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
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
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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