scholarly journals Classification of Metaplectic Fusion Categories

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2102
Author(s):  
Eddy Ardonne ◽  
Peter E. Finch ◽  
Matthew Titsworth
Keyword(s):  
Equivalence Classes ◽  
Modular Systems ◽  
Fusion Categories ◽  
Number Of Classes ◽  
Explicit Expressions

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for so(2p+1)2. These categories describe non-abelian anyons dubbed ‘metaplectic anyons’. We obtain explicit expressions for all the F- and R-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes.

scholarly journals Classification of pointed fusion categories of dimension p3 up to weak Morita Equivalence

2020 ◽  
pp. 2140008
Author(s):  
Kevin Maya ◽  
Adriana Mejía Castaño ◽  
Bernardo Uribe
Keyword(s):  
Complete Classification ◽  
Global Dimension ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Fusion Categories ◽  
Dimension Formula ◽  
Equivalent Categories

We give a complete classification of pointed fusion categories over [Formula: see text] of global dimension [Formula: see text] for [Formula: see text] any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension [Formula: see text] and we determine which of these equivalence classes have equivalent categories of modules.

scholarly journals Vegetation of Croatia: Phytosociological classification of the high-rank syntaxa

2017 ◽  
Vol 76 (2) ◽  
pp. 200-224 ◽  
Author(s):  
Željko Škvorc ◽  
Nenad Jasprica ◽  
Antun Alegro ◽  
Sanja Kovačić ◽  
Jozo Franjić ◽  
...  
Keyword(s):  
Vascular Plants ◽  
High Rank ◽  
Vegetation Diversity ◽  
Central European ◽  
Floristic Richness ◽  
Level Of Knowledge ◽  
European Method ◽  
Number Of Classes ◽  
Rich Countries

AbstractCroatia is among the most ecologically diverse and floristically rich countries in Europe, with a great variety of communities. The vegetation elaboration according to the standard central European method was initiated in Croatia at the beginning of the 20thcentury. In previous overviews of Croatian vegetation, the number of classes and alliances was underrepresented in relation to the country’s floristic richness. Furthermore, the level of knowledge and the amount of available data varied greatly among the various types of vegetation. The aims of this paper are mainly to compile a stabile syntaxonomic list of classes, orders and alliances dominated by vascular plants in Croatia and to adjust Croatian vegetation to the new European syntaxonomic system (EuroVegChecklist). It introduces a consistent description of high-rank syntaxa in Croatian. In conclusion, the vegetation of Croatia comprises 66 classes, 121 orders and 201 alliances. The number of syntaxa shows vegetation diversity that is rather high compared to most other European countries; this is related to the high floristic richness and endemism. The list points out the obvious problems and gaps in our knowledge of vegetation in Croatia and can serve as a baseline for the future vegetation studies.

scholarly journals Classification of fused links

2016 ◽  
Vol 25 (14) ◽  
pp. 1650076 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Symmetric Group ◽  
Equivalence Classes ◽  
One To One ◽  
Text Component

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of [Formula: see text]-component fused links is in one-to-one correspondence with the set of elements of the abelization [Formula: see text] up to conjugation by elements from the symmetric group [Formula: see text].

scholarly journals Classification of Hyperspectral Reflectance Images With Physical and Statistical Criteria

2020 ◽  
Vol 12 (14) ◽  
pp. 2335 ◽  
Author(s):  
Alexandre Alakian ◽  
Véronique Achard
Keyword(s):  
Classification Algorithms ◽  
Type Ii ◽  
Spectral Indices ◽  
Shape Features ◽  
Hyperspectral Reflectance ◽  
Roof Tile ◽  
Dark Green ◽  
Number Of Classes ◽  
Statistical Criteria

A classification method of hyperspectral reflectance images named CHRIPS (Classification of Hyperspectral Reflectance Images with Physical and Statistical criteria) is presented. This method aims at classifying each pixel from a given set of thirteen classes: unidentified dark surface, water, plastic matter, carbonate, clay, vegetation (dark green, dense green, sparse green, stressed), house roof/tile, asphalt, vehicle/paint/metal surface and non-carbonated gravel. Each class is characterized by physical criteria (detection of specific absorptions or shape features) or statistical criteria (use of dedicated spectral indices) over spectral reflectance. CHRIPS input is a hyperspectral reflectance image covering the spectral range [400–2500 nm]. The presented method has four advantages, namely: (i) is robust in transfer, class identification is based on criteria that are not very sensitive to sensor type; (ii) does not require training, criteria are pre-defined; (iii) includes a reject class, this class reduces misclassifications; (iv) high precision and recall, F 1 score is generally above 0.9 in our test. As the number of classes is limited, CHRIPS could be used in combination with other classification algorithms able to process the reject class in order to decrease the number of unclassified pixels.

scholarly journals A classification of intersection type systems

2002 ◽  
Vol 67 (1) ◽  
pp. 353-368
Author(s):  
M. W. Bunder
Keyword(s):  
Type Systems ◽  
Equivalence Classes ◽  
Type Assignment ◽  
Emptiness Problem ◽  
Intersection Types

AbstractThe first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η). but without (ΛI).The aim of this paper is to classify intersection type systems lacking some of (ΛI), (ΛE) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants.This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants.

scholarly journals Illiteracy Classification Using K Means-Naïve Bayes Algorithm

2018 ◽  
Vol 2 (3) ◽  
pp. 153 ◽  
Author(s):  
Muhammad Firman Aji Saputra ◽  
Triyanna Widiyaningtyas ◽  
Aji Prasetya Wibawa
Keyword(s):  
Error Rate ◽  
Naive Bayes ◽  
Research Result ◽  
Naïve Bayes ◽  
Optimal Number ◽  
Testing Method ◽  
The World ◽  
Bayes Algorithm ◽  
Number Of Classes

Illiteracy is an inability to recognize characters, both in order to read and write. It is a significant problem for countries all around the world including Indonesia. In Indonesia, illiteracy rate is generally set as an indicator to see whether or not education in Indonesia is successful. If this problem is not going to be overcome, it will affect people’s prosperity. One system that has been used to overcome this problem is prioritizing the treatment from areas with the highest illiteracy rate and followed by areas with lower illiteracy rate. The method is going to be a way easier to be applied if it is supported by classification process. Since the classification process needs a class, and there has not been any fine classification of illiteracy rate, there is needed a clustering process before classification process. This research is aimed to get optimal number of classes through clustering process and know the result of illiteracy classification process. The clustering process is conducted by using k means algorithm, and for the classification process is conducted by using Naïve Bayes algorithm. The testing method used to assess the success of classification process is 10-fold method. Based on the research result, it can be concluded that the optimal illiteracy classes are three classes with the classification accuracy value of 96.4912% and error rate value of 3.5088%. Whereas the classification with two classes get the accuracy value of 93.8596% and error rate value of 6.1404%. And for the classification with five classes get the accuracy value of 90.3509% and error rate value of 9.6491%.

scholarly journals Potential and Use of the Googlenet Ann for the Purposes of Inland Water Ships Classification

2020 ◽  
Vol 27 (4) ◽  
pp. 170-178
Author(s):  
Katarzyna Bobkowska ◽  
Izabela Bodus-Olkowska
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Video Recording ◽  
Inland Water ◽  
Video Cameras ◽  
Image Repository ◽  
Ship Recognition ◽  
Number Of Classes ◽  
Classification Quality

AbstractThis article presents an analysis of the possibilities of using the pre-degraded GoogLeNet artificial neural network to classify inland vessels. Inland water authorities monitor the intensity of the vessels via CCTV. Such classification seems to be an improvement in their statutory tasks. The automatic classification of the inland vessels from video recording is a one of the main objectives of the Automatic Ship Recognition and Identification (SHREC) project. The image repository for the training purposes consists about 6,000 images of different categories of the vessels. Some images were gathered from internet websites, and some were collected by the project’s video cameras. The GoogLeNet network was trained and tested using 11 variants. These variants assumed modifications of image sets representing (e.g., change in the number of classes, change of class types, initial reconstruction of images, removal of images of insufficient quality). The final result of the classification quality was 83.6%. The newly obtained neural network can be an extension and a component of a comprehensive geoinformatics system for vessel recognition.

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