310 research outputs found

    Group completion and units in I-spaces

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    The category of I-spaces is the diagram category of spaces indexed by finite sets and injections. This is a symmetric monoidal category whose commutative monoids model all E-infinity spaces. Working in the category of I-spaces enables us to simplify and strengthen previous work on group completion and units of E-infinity spaces. As an application we clarify the relation to Gamma-spaces and show how the spectrum of units associated with a commutative symmetric ring spectrum arises through a chain of Quillen adjunctions.Comment: v3: 43 pages. Minor revisions, accepted for publication in Algebraic and Geometric Topolog

    Derived logarithmic geometry I

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    Contains fulltext : 163271.pdf (preprint version ) (Open Access

    POSIX lexing with derivatives of regular expressions (proof pearl)

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    Brzozowski introduced the notion of derivatives for regular expressions. They can be used for a very simple regular expression matching algorithm. Sulzmann and Lu cleverly extended this algorithm in order to deal with POSIX matching, which is the underlying disambiguation strategy for regular expressions needed in lexers. Sulzmann and Lu have made available on-line what they call a “rigorous proof” of the correctness of their algorithm w.r.t. their specification; regrettably, it appears to us to have unfillable gaps. In the first part of this paper we give our inductive definition of what a POSIX value is and show (i) that such a value is unique (for given regular expression and string being matched) and (ii) that Sulzmann and Lu’s algorithm always generates such a value (provided that the regular expression matches the string). We also prove the correctness of an optimised version of the POSIX matching algorithm. Our definitions and proof are much simpler than those by Sulzmann and Lu and can be easily formalised in Isabelle/HOL. In the second part we analyse the correctness argument by Sulzmann and Lu and explain why the gaps in this argument cannot be filled easily.Postprin

    Logarithmic topological Hochschild homology of topological K-theory spectra

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    In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand into the p-local complex connective K-theory spectrum, equipped with suitable log structures, is a formally log THH-etale map, and compute the V(1)-homotopy of their logarithmic topological Hochschild homology spectra. As an application, we recover Ausoni's computation of the V(1)-homotopy of the ordinary THH of ku.Comment: v3: 32 pages; slightly revised. Accepted for publication in J. Eur. Math. Soc. (JEMS

    Impact of the learners diversity and combination method on the generation of heterogeneous classifier ensembles

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    Ensembles of classifiers is a proven approach in machine learning with a wide variety of research works. The main issue in ensembles of classifiers is not only the selection of the base classifiers, but also the combination of their outputs. According to the literature, it has been established that much is to be gained from combining classifiers if those classifiers are accurate and diverse. However, it is still an open issue how to define the relation between accuracy and diversity in order to define the best possible ensemble of classifiers. In this paper, we propose a novel approach to evaluate the impact of the diversity of the learners on the generation of heterogeneous ensembles. We present an exhaustive study of this approach using 27 different multiclass datasets and analysing their results in detail. In addition, to determine the performance of the different results, the presence of labelling noise is also considered.This work has been supported under projects PEAVAUTO-CM-UC3M–2020/00036/001, PID2019-104793RB-C31, and RTI2018-096036-B-C22, and by the Region of Madrid’s Excellence Program, Spain (EPUC3M17)

    Implementation of Two Layers Type Theory in Dedukti and Application to Cubical Type Theory

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    International audienceIn this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be expressed by the rewrite rules of Dedukti. As an alternative, 2 Layer Type Theories are variants of Martin-Lf Type Theory where all or part of the definitionalequality can be represented in terms of a so-called external equality. We propose to split the encodingby giving an encoding of 2 Layer Type Theories (2LTT) in Dedukti, and a partial encoding of CTTin 2LTT
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