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):  
Author(s):  
Matthew de Brecht ◽  
Masanori Kobayashi ◽  
Hiroo Tokunaga ◽  
Akihiro Yamamoto
Keyword(s):  

2020 ◽  
Author(s):  
Yemon Choi ◽  
Mahya Ghandehari ◽  
Hung Le Pham

AbstractWe continue the study of the AMNM property for weighted semilattices that was initiated in Choi (J Aust Math Soc 95(1):36–67, 2013. 10.1017/S1446788713000189). We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this “filter stability” property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in loc. cit., and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.


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.


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 9 (2) ◽  
pp. 1-19
Author(s):  
Z. Li ◽  
A. Vetta

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the items form a hereditary set system. We present a simple algorithm that allocates each agent a bundle of items whose value is at least 0.3666 times the maximin share of the agent. This improves upon the current best known guarantee of 0.2 due to Ghodsi et al. The analysis of the algorithm is almost tight; we present an instance where the algorithm provides a guarantee of at most 0.3738. We also show that the algorithm can be implemented in polynomial time given a valuation oracle for each agent.


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.


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