Comparing the Medvedev and Turing degrees of Π01 classes

2014 ◽  
Vol 25 (8) ◽  
pp. 1649-1668
Author(s):  
TAKAYUKI KIHARA
Keyword(s):  
Turing Degrees ◽  
Cantor Space ◽  
Closed Set ◽  
Medvedev Lattice ◽  
Π01 Classes

Every co-c.e. closed set (Π01 class) in Cantor space is represented by a co-c.e. tree. Our aim is to clarify the interaction between the Medvedev and Muchnik degrees of co-c.e. closed subsets of Cantor space and the Turing degrees of their co-c.e. representations. Among other results, we present the following theorems: if v and w are different c.e. degrees, then the collection of the Medvedev (Muchnik) degrees of all Π01 classes represented by v and the collection represented by w are also different; the ideals generated from such collections are also different; the collections of the Medvedev and Muchnik degrees of all Π01 classes represented by incomplete co-c.e. sets are upward dense; the collection of all Π01 classes represented by K-trivial sets is Medvedev-bounded by a single Π01 class represented by an incomplete co-c.e. set; and the Π01 classes have neither nontrivial infinite suprema nor infima in the Medvedev lattice.

On the ranked points of a Π10 set

1989 ◽  
Vol 54 (3) ◽  
pp. 975-991 ◽  
Author(s):  
Douglas Cenzer ◽  
Rick L. Smith
Keyword(s):  
Baire Space ◽  
High Rank ◽  
Joint Work ◽  
Cantor Space ◽  
Closed Set ◽  
Applied Logic ◽  
Rank One ◽  
Author Paper

AbstractThis paper continues joint work of the authors with P. Clote, R. Soare and S. Wainer (Annals of Pure and Applied Logic, vol. 31 (1986), pp. 145–163). An element x of the Cantor space 2ω is said have rank α in the closed set P if x is in Dα(P)/Dα + 1(P), where Dα is the iterated Cantor-Bendixson derivative. The rank of x is defined to be the least α such that x has rank a in some set. The main result of the five-author paper is that for any recursive ordinal λ + n (where λ is a limit and n is finite), there is a point with rank λ + n which is Turing equivalent to O(λ + 2n) All ranked points constructed in that paper are singletons. We now construct a ranked point which is not a singleton. In the previous paper the points of high rank were also of high hyperarithmetic degree. We now construct points with arbitrarily high rank. We also show that every nonrecursive RE point is Turing equivalent to an RE point of rank one and that every nonrecursive point is Turing equivalent to a hyperimmune point of rank one. We relate Clote's notion of the height of a singleton in the Baire space with the notion of rank. Finally, we show that every hyperimmune point x is Turing equivalent to a point which is not ranked.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals Unavoidable subprojections in union-closed set systems of infinite breadth

2021 ◽  
Vol 94 ◽  
pp. 103311
Author(s):  
Yemon Choi ◽  
Mahya Ghandehari ◽  
Hung Le Pham
Keyword(s):  
Closed Set ◽  
Set Systems

REFLEXIVITY INDEX AND IRRATIONAL ROTATIONS

2021 ◽  
pp. 1-13
Author(s):  
BINGZHANG MA ◽  
K. J. HARRISON
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Irrational Rotations ◽  
Index 2

Abstract We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.

scholarly journals Synthetic speech detection through short-term and long-term prediction traces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Clara Borrelli ◽  
Paolo Bestagini ◽  
Fabio Antonacci ◽  
Augusto Sarti ◽  
Stefano Tubaro
Keyword(s):  
Deep Learning ◽  
Speech Processing ◽  
Synthetic Speech ◽  
Opinion Formation ◽  
Closed Set ◽  
Speech Detection ◽  
Open Set ◽  
Technological Advances ◽  
Speech Generation ◽  
Long Term Prediction

AbstractSeveral methods for synthetic audio speech generation have been developed in the literature through the years. With the great technological advances brought by deep learning, many novel synthetic speech techniques achieving incredible realistic results have been recently proposed. As these methods generate convincing fake human voices, they can be used in a malicious way to negatively impact on today’s society (e.g., people impersonation, fake news spreading, opinion formation). For this reason, the ability of detecting whether a speech recording is synthetic or pristine is becoming an urgent necessity. In this work, we develop a synthetic speech detector. This takes as input an audio recording, extracts a series of hand-crafted features motivated by the speech-processing literature, and classify them in either closed-set or open-set. The proposed detector is validated on a publicly available dataset consisting of 17 synthetic speech generation algorithms ranging from old fashioned vocoders to modern deep learning solutions. Results show that the proposed method outperforms recently proposed detectors in the forensics literature.

scholarly journals Mosquito species identification using convolutional neural networks with a multitiered ensemble model for novel species detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adam Goodwin ◽  
Sanket Padmanabhan ◽  
Sanchit Hira ◽  
Margaret Glancey ◽  
Monet Slinowsky ◽  
...  
Keyword(s):  
Neural Networks ◽  
Species Identification ◽  
Convolutional Neural Networks ◽  
Novel Species ◽  
Novelty Detection ◽  
Mosquito Species ◽  
Image Database ◽  
Closed Set ◽  
Open Set

AbstractWith over 3500 mosquito species described, accurate species identification of the few implicated in disease transmission is critical to mosquito borne disease mitigation. Yet this task is hindered by limited global taxonomic expertise and specimen damage consistent across common capture methods. Convolutional neural networks (CNNs) are promising with limited sets of species, but image database requirements restrict practical implementation. Using an image database of 2696 specimens from 67 mosquito species, we address the practical open-set problem with a detection algorithm for novel species. Closed-set classification of 16 known species achieved 97.04 ± 0.87% accuracy independently, and 89.07 ± 5.58% when cascaded with novelty detection. Closed-set classification of 39 species produces a macro F1-score of 86.07 ± 1.81%. This demonstrates an accurate, scalable, and practical computer vision solution to identify wild-caught mosquitoes for implementation in biosurveillance and targeted vector control programs, without the need for extensive image database development for each new target region.

scholarly journals The Development of a Paediatric Phoneme Discrimination Test for Arabic Phonemic Contrasts

2021 ◽  
Vol 11 (2) ◽  
pp. 150-166
Author(s):  
Hanin Rayes ◽  
Ghada Al-Malky ◽  
Deborah Vickers
Keyword(s):  
Closed Set ◽  
Retest Reliability ◽  
Response Options ◽  
Phoneme Discrimination ◽  
Significant Difference ◽  
Age Appropriate ◽  
Hearing Children ◽  
Test Retest Reliability ◽  
Development And Validation ◽  
Arabic Speaking

Objective: The aim of this project was to develop the Arabic CAPT (A-CAPT), a Standard Arabic version of the CHEAR auditory perception test (CAPT) that assesses consonant perception ability in children. Method: This closed-set test was evaluated with normal-hearing children aged 5 to 11 years. Development and validation of the speech materials were accomplished in two experimental phases. Twenty-six children participated in phase I, where the test materials were piloted to ensure that the selected words were age appropriate and that the form of Arabic used was familiar to the children. Sixteen children participated in phase II where test–retest reliability, age effects, and critical differences were measured. A computerized implementation was used to present stimuli and collect responses. Children selected one of four response options displayed on a screen for each trial. Results: Two lists of 32 words were developed with two levels of difficulty, easy and hard. Assessment of test–retest reliability for the final version of the lists showed a strong agreement. A within-subject ANOVA showed no significant difference between test and retest sessions. Performance improved with increasing age. Critical difference values were similar to the British English version of the CAPT. Conclusions: The A-CAPT is an appropriate speech perception test for assessing Arabic-speaking children as young as 5 years old. This test can reliably assess consonant perception ability and monitor changes over time or after an intervention.

scholarly journals THE n-r.e. DEGREES: UNDECIDABILITY AND Σ1 SUBSTRUCTURES

2012 ◽  
Vol 12 (01) ◽  
pp. 1250005 ◽  
Author(s):  
MINGZHONG CAI ◽  
RICHARD A. SHORE ◽  
THEODORE A. SLAMAN
Keyword(s):  
Turing Degrees ◽  
First Order ◽  
Global Properties

We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].

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