1,720,958 research outputs found
Decision Algorithms for Ostrowski-Automatic Sequences
Full text linkWe extend the notion of automatic sequences to a broader class, the Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions about such sequences that can be expressed as predicates in first-order logic.
In Chapter 1, we begin with topics and ideas that are preliminary to this work, including a small introduction to non-standard positional numeration systems and the relationship between words and automata. In Chapter 2, we define the theoretical foundations for recognizing addition in a generalized Ostrowski numeration system and formalize the general theory that develops our decision procedure. Next, in Chapter 3, we show how to implement these ideas in practice, and provide the implementation as an integration to the automatic theorem-proving software package -- Walnut.
Further, we provide some applications of our work in Chapter 4. These applications span several topics in combinatorics on words, including repetitions, pattern-avoidance, critical exponents of special classes of words, properties of Lucas words, and so forth. Finally, we close with open problems on decidability and higher-order numeration systems and discuss future directions for research
Statistical Foundations for Learning on Graphs
No full textGraph Neural Networks are one of the most popular architectures used to solve classification problems on data where entities have attribute information accompanied by relational information. Among them, Graph Convolutional Networks and Graph Attention Networks are two of the most popular GNN architectures.
In this thesis, I present a statistical framework for understanding node classification on feature-rich relational data. First, I use the framework to study the generalization error and the effects of existing neural network architectures, namely, graph convolutions and graph attention on the Contextual Stochastic Block Model in the regime where the average degree of a node is at least order log squared n in the number of nodes n.
Second, I propose a notion of asymptotic local optimality for node classification tasks and design a GNN architecture that is provably optimal in this notion, for the sparse regime, i.e., average degree O(1).
In the first part, I present a rigorous theoretical understanding of the effects of graph convolutions in neural networks through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model.
First, I identify two quantities corresponding to the signal from the two sources of information: the graph, and the node features, followed by a result that shows that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of up to one over square root of the expected degree of a node.
Second, I show that with a slightly stronger graph density, two graph convolutions improve this factor to up to 1/sqrt{n}, where n is the number of nodes in the graph.
This set of results provides both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a neural network, concluding that the performance is mutually similar for all combinations of the placement.
In the second part, the analysis of graph attention is provided, where the main result states that in a well-defined ``hard'' regime, every attention mechanism fails to distinguish the intra-class edges from the inter-class edges. In addition, if the signal in the node attributes is sufficiently weak, graph attention convolution cannot perfectly classify the nodes even if the intra-class edges are separable from the inter-class edges.
In the third part, I study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is O(1) in the number of nodes, in the fixed-dimensional asymptotic regime, i.e., the dimension of the feature data is fixed while the number of nodes is large. Such graphs are typically known to be locally tree-like. Here, I introduce a notion of Bayes optimality for node classification tasks, called asymptotic local Bayes optimality, and compute the optimal classifier according to this criterion for a fairly general statistical data model with arbitrary distributions of the node features and edge connectivity. The optimal classifier is implementable using a message-passing graph neural network architecture. This is followed by a result that precisely computes the generalization error of this optimal classifier, and compares its performance statistically against existing learning methods on a well-studied data model with naturally identifiable signal-to-noise ratios (SNRs). We find that the optimal message-passing architecture interpolates between a standard MLP in the regime of low graph signal and a typical graph convolutional layer in the regime of high graph signal. Furthermore, I provide a corresponding non-asymptotic result that demonstrates the practical potential of the asymptotically optimal classifier
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
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
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