scholarly journals Wilf-Classification of Mesh Patterns of Short Length

10.37236/4678 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Ísak Hilmarsson ◽  
Ingibjörg Jónsdóttir ◽  
Steinunn Sigurðardóttir ◽  
Lína Viðarsdóttir ◽  
Henning Ulfarsson
Keyword(s):  
Upper Bound ◽  
Short Length ◽  
Actual Number ◽  
Automatic Methods

This paper starts the Wilf-classification of mesh patterns of length 2. Although there are initially 1024 patterns to consider we introduce automatic methods to reduce the number of potentially different Wilf-classes to at most 65. By enumerating some of the remaining classes we bring that upper-bound further down to 56. Finally, we conjecture that the actual number of Wilf-classes of mesh patterns of length 2 is 46.

scholarly journals A Convolutional Network for the Classification of Sleep Stages

Proceedings ◽  
2018 ◽  
Vol 2 (18) ◽  
pp. 1174 ◽  
Author(s):  
Isaac Fernández-Varela ◽  
Elena Hernández-Pereira ◽  
Vicente Moret-Bonillo
Keyword(s):  
Sleep Medicine ◽  
Sleep Stages ◽  
Kappa Index ◽  
Night Sleep ◽  
Convolutional Network ◽  
Sleep Study ◽  
Convolutional Networks ◽  
Sleep Studies ◽  
Automatic Methods

The classification of sleep stages is a crucial task in the context of sleep medicine. It involves the analysis of multiple signals thus being tedious and complex. Even for a trained physician scoring a whole night sleep study can take several hours. Most of the automatic methods trying to solve this problem use human engineered features biased for a specific dataset. In this work we use deep learning to avoid human bias. We propose an ensemble of 5 convolutional networks achieving a kappa index of 0.83 when classifying 500 sleep studies.

Supervised Adaptive Hamming Net for Classification of Multiple-Valued Patterns

1997 ◽  
Vol 08 (02) ◽  
pp. 181-200
Author(s):  
Cheng-An Hung ◽  
Sheng-Fuu Lin
Keyword(s):  
Upper Bound ◽  
Incremental Learning ◽  
Arbitrary Sequence ◽  
Input Output ◽  
Multiple Valued Logic

A Supervised Adaptive Hamming Net (SAHN) is introduced for incremental learning of recognition categories in response to arbitrary sequence of multiple-valued or binary-valued input patterns. The binary-valued SAHN derived from the Adaptive Hamming Net (AHN) is functionally equivalent to a simplified ARTMAP, which is specifically designed to establish many-to-one mappings. The generalization to learning multiple-valued input patterns is achieved by incorporating multiple-valued logic into the AHN. In this paper, we examine some useful properties of learning in a P-valued SAHN. In particular, an upper bound is derived on the number of epochs required by the P-valued SAHN to learn a list of input-output pairs that is repeatedly presented to the architecture. Furthermore, we connect the P-valued SAHN with the binary-valued SAHN via the thermometer code.

scholarly journals DENSE CODING WITH MULTIPARTITE QUANTUM STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 415-428 ◽  
Author(s):  
DAGMAR BRUß ◽  
MACIEJ LEWENSTEIN ◽  
ADITI SEN(DE) ◽  
UJJWAL SEN ◽  
GIACOMO MAURO D'ARIANO ◽  
...  
Keyword(s):  
Quantum State ◽  
Upper Bound ◽  
Arbitrary Number ◽  
Information Transfer ◽  
Quantum States ◽  
Dense Coding ◽  
Joint Operations ◽  
Single Receiver

We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.

scholarly journals COMPARISON OF AUTOMATIC AND SEMI-AUTOMATIC METHODS FOR CLASSIFICATION OF SIDE SCAN SONAR IMAGERY

2019 ◽  
Vol 37 (1) ◽  
pp. 1
Author(s):  
Tiago Rafael de Barros Pereira ◽  
Helenice Vital ◽  
André Giskard Aquino da Silva ◽  
Cecília Alves de Oliveira
Keyword(s):  
Maximum Likelihood ◽  
Remote Sensing Data ◽  
Automated Classification ◽  
Side Scan Sonar ◽  
Swath Bathymetry ◽  
Seafloor Classification ◽  
Automatic Methods ◽  
Acoustic Remote Sensing ◽  
Occurrence Matrix

ABSTRACT. The main scope of this paper is the analysis of seafloor classification using acoustic remote sensing data. These data were acquired in a hydroacoustic survey of bathymetry and sonography using an interferometric swath bathymetry system. The study area is a sector of the internal northeast Brazilian shelf adjacent to the Ponta Negra beach - Natal (RN). The objective of the work is to identify and draw the different textural patterns, which characterize the seafloor of the study area. In addition, two approaches for textural classification of sonograms were compared and evaluated, which were: Automatic Gray Level Co-occurrence Matrix (GLCM) classification available in SonarWiz software; and the semi-automatic Maximum Likelihood, available in ArcGIS software. The comparison tested the capacity for identifying and drawing the textural patterns distribution. The automated classification identified 4 patterns while on the semi-automated 5 patterns were identified. It was made the correlation between the textural patterns found in each classification, besides the correlation between textural patterns and the levels of intensity of reflectance presents on the sonogram.Keywords: sonography, textural classification, textural patterns, hydroacoustic. RESUMO. Este trabalho foi realizado a partir da análise de dados geofísicos adquiridos em levantamento hidroacústico de batimetria e sonografia utilizando um sonar interferométrico EdgeTech 4600. A área de estudo é uma porção da plataforma interna do nordeste brasileiro adjacente Natal (RN). O objetivo deste trabalho é identificar e delimitar os diferentes padrões texturais que caracterizam o substrato marinho da área de estudo. Adicionalmente, são avaliadas e comparadas duas abordagens distintas de classificação textural de sonogramas, sendo elas: a classificação automática GLCM disponível no software SonarWiz, e a classificação semi-automática máxima verossimilhança (Maximum Likelihood) disponível no software ArcGIS. A comparação foi realizada com base na capacidade de identificação e delimitação da distribuição dos padrões texturais. A utilização da classificação automática identificou 4 padrões, enquanto que, na classificação semi-automática 6 padrões foram identificados. Foi feita a correlação entre os padrões texturais encontrados em cada classificação, além da correlação entre os padrões texturais e os níveis de intensidade de reflectância presente no sonograma.Palavras-chave: sonografia, classificação textural, padrões de textura, hidroacústica.

scholarly journals On the Number of Similar Instances of a Pattern in a Finite Set

10.37236/4972 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Bernardo M. Ábrego ◽  
Silvia Fernández-Merchant ◽  
Daniel J. Katz ◽  
Levon Kolesnikov
Keyword(s):  
Arithmetic Progression ◽  
Finite Subset ◽  
Upper Bound ◽  
Point Subset ◽  
Finite Set ◽  
Equilateral Triangles ◽  
Optimal Configurations ◽  
Full Classification ◽  
General Method

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is shown to be no more than $\lfloor{(4 n-1)(n-1)/18}\rfloor$. The number of $k$-term arithmetic progressions that lie within an $n$-point subset of the line is shown to be at most $(n-r)(n+r-k+1)/(2 k-2)$, where $r$ is the remainder when $n$ is divided by $k-1$. This upper bound is achieved when the $n$ points themselves form an arithmetic progression, but for some values of $k$ and $n$, it can also be achieved for other configurations of the $n$ points, and a full classification of such optimal configurations is given. These results are achieved using a new general method based on ordering relations.

Groups Admitting only Finitely Many Nilpotent Ring Structures

1986 ◽  
Vol 29 (2) ◽  
pp. 197-203
Author(s):  
Shalom Feigelstock
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Actual Number ◽  
Nilpotent Ring ◽  
Ring Structures ◽  
Free Case ◽  
Torsion Free

AbstractThe abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.

ON AN INVERSE PROBLEM TO FROBENIUS' THEOREM II

2012 ◽  
Vol 11 (05) ◽  
pp. 1250092 ◽  
Author(s):  
WEI MENG ◽  
JIANGTAO SHI ◽  
KELIN CHEN
Keyword(s):  
Inverse Problem ◽  
Finite Group ◽  
Positive Integer ◽  
Upper Bound ◽  
Complete Classification ◽  
Frobenius Theorem ◽  
A Finite Group

Let G be a finite group and e a positive integer dividing |G|, the order of G. Denoting Le(G) = {x ∈ G|xe = 1}. Frobenius proved that |Le(G)| = ke for some positive integer k ≥ 1. Let k(G) be the upper bound of the set {k||Le(G)| = ke, ∀ e ||G|}. In this paper, a complete classification of the finite group G with k(G) = 3 is obtained.

scholarly journals An improvement of a transcendence measure of Galochkin and Mahler's S-numbers

1992 ◽  
Vol 52 (1) ◽  
pp. 130-140 ◽  
Author(s):  
Masaaki Amou
Keyword(s):  
Upper Bound ◽  
Functional Equations ◽  
Special Values ◽  
Transcendental Numbers ◽  
Transcendence Measure

AbstractWe give a transcendence measure of special values of functions satisfying certain functional equations. This improves an earlier result of Galochkin, and gives a better upper bound of the type for such a number as an S-number in the classification of transcendental numbers by Mahler.

scholarly journals Automatic Classification of A-Lines in Intravascular OCT Images Using Deep Learning and Estimation of Attenuation Coefficients

2021 ◽  
Vol 11 (16) ◽  
pp. 7412
Author(s):  
Grigorios-Aris Cheimariotis ◽  
Maria Riga ◽  
Kostas Haris ◽  
Konstantinos Toutouzas ◽  
Aggelos K. Katsaggelos ◽  
...  
Keyword(s):  
Deep Learning ◽  
Positive Contribution ◽  
Imaging Data ◽  
Attenuation Coefficients ◽  
Mean Values ◽  
Processing Step ◽  
Automatic Methods ◽  
Intravascular Optical Coherence Tomography

Intravascular Optical Coherence Tomography (IVOCT) images provide important insight into every aspect of atherosclerosis. Specifically, the extent of plaque and its type, which are indicative of the patient’s condition, are better assessed by OCT images in comparison to other in vivo modalities. A large amount of imaging data per patient require automatic methods for rapid results. An effective step towards automatic plaque detection and plaque characterization is axial lines (A-lines) based classification into normal and various plaque types. In this work, a novel automatic method for A-line classification is proposed. The method employed convolutional neural networks (CNNs) for classification in its core and comprised the following pre-processing steps: arterial wall segmentation and an OCT-specific (depth-resolved) transformation and a post-processing step based on the majority of classifications. The important step was the OCT-specific transformation, which was based on the estimation of the attenuation coefficient in every pixel of the OCT image. The dataset used for training and testing consisted of 183 images from 33 patients. In these images, four different plaque types were delineated. The method was evaluated by cross-validation. The mean values of accuracy, sensitivity and specificity were 74.73%, 87.78%, and 61.45%, respectively, when classifying into plaque and normal A-lines. When plaque A-lines were classified into fibrolipidic and fibrocalcific, the overall accuracy was 83.47% for A-lines of OCT-specific transformed images and 74.94% for A-lines of original images. This large improvement in accuracy indicates the advantage of using attenuation coefficients when characterizing plaque types. The proposed automatic deep-learning pipeline constitutes a positive contribution to the accurate classification of A-lines in intravascular OCT images.

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