A study of generalized closed set in the closure space

2022 ◽  
Author(s):  
Neeran Tahir Abd Alameer ◽  
Shahad Safy Hussein
Keyword(s):  
Author(s):  
U.D. Tapi ◽  
Bhagyashri A. Deole

A Čech closure space (X, u) is a set X with Čech closure operator u: P(X) → P(X) where P(X) is a power set of X, which satisfies u𝝓=𝝓, A ⊆uA for every A⊆X, u (A⋃B) = uA⋃uB, for all A, B ⊆ X. Many properties which hold in topological space hold in closure space as well. A topological space X is strongly connected if and only if it is not a disjoint union of countably many but more than one closed set. If X is strongly connected, and Ei‟s are nonempty disjoint closed subsets of X, then X≠ E1∪E2∪. We further extend the concept of strongly connectedness in closure space. The aim of this paper is to introduce and study the concept of strongly connectedness in closure space.


2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran

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.


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

Author(s):  
BINGZHANG MA ◽  
K. J. HARRISON

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.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Clara Borrelli ◽  
Paolo Bestagini ◽  
Fabio Antonacci ◽  
Augusto Sarti ◽  
Stefano Tubaro

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.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adam Goodwin ◽  
Sanket Padmanabhan ◽  
Sanchit Hira ◽  
Margaret Glancey ◽  
Monet Slinowsky ◽  
...  

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.


2021 ◽  
Vol 11 (2) ◽  
pp. 150-166
Author(s):  
Hanin Rayes ◽  
Ghada Al-Malky ◽  
Deborah Vickers

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.


Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1225
Author(s):  
Ria Gupta ◽  
Ananga Kumar Das

New generalizations of normality in Čech closure space such as π-normal, weakly π-normal and κ-normal are introduced and studied using canonically closed sets. It is observed that the class of κ-normal spaces contains both the classes of weakly π-normal and almost normal Čech closure spaces.


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