1,720,967 research outputs found
Banach spaces and descriptive set theory: selected topics
No full textThis volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective
Uniformity norms, their weaker versions, and applications
Get PDFWe show that, under some mild hypotheses, the Gowers uniformity norms (both
in the additive and in the hypergraph setting) are essentially equivalent to
certain weaker norms which are easier to understand. We present two
applications of this equivalence: a variant of the Koopman--von Neumann
decomposition, and a proof of the relative inverse theorem for the Gowers
-norm using a norm-type pseudorandomness condition
Forbidden sparse intersections
Get PDFLet be a positive integer, let ,
and let be a nonnegative integer. We prove that if
are two families whose cross
intersections forbid -- that is, they satisfy for
every and every -- then, setting
, we have the subgaussian bound where and denote the
-biased and -biased measures on respectively
Anticoncentration and Berry--Esseen bounds for random tensors
Get PDFWe obtain estimates for the Kolmogorov distance to appropriately chosen
gaussians, of linear functions of random
tensors which are symmetric and
exchangeable, and whose entries have bounded third moment and vanish on
diagonal indices. These estimates are expressed in terms of intrinsic (and
easily computable) parameters associated with the random tensor
and the given coefficients , and they are optimal in various regimes.
The key ingredient -- which is of independent interest -- is a combinatorial
CLT for high-dimensional tensors which provides quantitative non-asymptotic
normality under suitable conditions, of statistics of the form where
is a deterministic
real tensor, and is a random permutation uniformly distributed on the
symmetric group . Our results extend, in any dimension ,
classical work of Bolthausen who covered the one-dimensional case, and more
recent work of Barbour/Chen who treated the two-dimensional case.Comment: Probability Theory and Related Fields 187 (2023), 317-38
Contributions to non-smooth and multivalued analysis
No full textΗ Πλειότιμη Ανάλυση είναι ένα μείγμα από διαφορετικά μαθηματικά πεδία, όπως η τοπολογία, η θεωρία μέτρου, η περιγραφική συνολοθεωρία και η μη-γραμμική ανάλυση. Η ανάγκη για τη μελέτη απεικονήσεων οι οποίες παίρνουν ως τιμές σύνολα, τις οποίες και καλούμε πλειότιμες συναρτήσεις, αναγνωρίστηκε από τις αρχές του εικοστού αιώνα και πολλοί αξιόλογοι μαθηματικοί όπως οι Hausdorff, Vietoris, Hahn και Kura- towski (για να αναφέρουμε μερικούς) έκαναν κάποιες αρχικές έρευνες. Σήμερα η Πλειότιμη Ανάλυση έχει εξελιχθεί σε ένα ώριμο, αυτόνομο πεδίο μαθηματικής δραστηριότητας, με τις δικές της μεθόδους, τεχνικές και εργαλεία και με πολλές εφαρμογές. Επιπλέον η Πλειότιμη Ανάλυση έχει μεγάλη σχέση με τη Μη Λεία Ανάλυση. Άλλωστε δεν είναι σύμπτωση ότι η πραγματική έκρηξη της Πλειότιμης Ανάλυσης έγινε όταν εμφανίστηκε η Μη Λεία Ανάλυση. Από τότε τα δύο πεδία είναι στενά συνδεδεμένα και παρέχουν το ένα στο άλλο καινούργια εργαλεία, ιδέες και αποτελέσματα. Η Μη Λεία Ανάλυση είναι η ανάπτυξη αναλυτικών εργαλείων και μεθόδων για τη μελέτη μη παραγωγίσιμων συναρτήσεων. Από τις πρώτες και πιο γνωστές τέτοιες προσπάθειες ήταν το υποδιαφορικό της κυρτής ανάλυσης του Rockafellar. Η μεγάλη ανάπτυξη όμως της Μη Λείας Ανάλυσης έγινε με το υποδιαφορικό του Clarke για τις τοπικά Lipschitz πραγματικές συναρτήσεις το 1973. Ο εξαιρετικός λογισμός του και οι πολύ ικανοποιητικές αναλυτικές του ιδιότητες, του επέτρεψαν να διαδοθεί αμέσως και να χρησιμοποιηθεί σε ένα ευρύτατο φάσμα προβλημάτων, αντικαθιστώντας με μεγάλη επιτυχία την έννοια της παραγώγου. Δυστυχώς, όμως, το υποδιαφορικό του Clarke δεν ήταν πανάκεια. Ήδη, από τις αρχές της δεκαετίας του '90, έγινε σαφές ότι το υποδιαφορικό του Clarke ήταν εξαιρετικά παθολογικό για μια μεγάλη κλάση συναρτήσεων (παραπέμπουμε στις εργασίες των Preise [51] και Jouini [30]). Συγκεκριμένα υπάρχουν υπεραριθμήσιμες, διακριτές μεταξύ τους, Lipschitz συναρτήσεις f : R —> R για τις οποίες θcf(x) = [0,1] για κάθε x ∈ R. Είναι σαφές ότι για αυτές τις συναρτήσεις το υποδιαφορικό του Clarke δεν παρέχει καμία ουσιαστική πληροφορία. Σε μία πρόσφατη εργασία οι Borwein, Moors και Wang επέκτειναν αυτά τα αποτελέσματα σε γενικούς χώρους Banach, κάνοντας χρήση του θεωρήματος κατηγορίας του Baire. […
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
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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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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