scholarly journals Real entropy rigidity under quasi-conformal deformations

2021 ◽  
Vol 25 (1) ◽  
pp. 1-33
Author(s):  
Khashayar Filom
Keyword(s):  
Complete Classification ◽  
Rational Maps ◽  
Rigidity Result ◽  
Content Type ◽  
The Real ◽  
Real Analytic ◽  
Set Up ◽  
Conformal Deformations ◽  
Classification Of Maps

We set up a real entropy function h R h_\Bbb {R} on the space M d ′ \mathcal {M}’_d of Möbius conjugacy classes of real rational maps of degree d d by assigning to each class the real entropy of a representative f ∈ R ( z ) f\in \Bbb {R}(z) ; namely, the topological entropy of its restriction f ↾ R ^ f\restriction _{\hat {\Bbb {R}}} to the real circle. We prove a rigidity result stating that h R h_\Bbb {R} is locally constant on the subspace determined by real maps quasi-conformally conjugate to f f . As examples of this result, we analyze real analytic stable families of hyperbolic and flexible Lattès maps with real coefficients along with numerous families of degree d d real maps of real entropy log ⁡ ( d ) \log (d) . The latter discussion moreover entails a complete classification of maps of maximal real entropy.

Using transfer learning for diabetic retinopathy stage classification

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Enas M.F. El Houby
Keyword(s):  
Diabetic Retinopathy ◽  
Transfer Learning ◽  
Grade Level ◽  
Design Methodology ◽  
Content Type ◽  
Stage Classification ◽  
Set Up ◽  
Retinal Fundus ◽  
Automated Methods

PurposeDiabetic retinopathy (DR) is one of the dangerous complications of diabetes. Its grade level must be tracked to manage its progress and to start the appropriate decision for treatment in time. Effective automated methods for the detection of DR and the classification of its severity stage are necessary to reduce the burden on ophthalmologists and diagnostic contradictions among manual readers.Design/methodology/approachIn this research, convolutional neural network (CNN) was used based on colored retinal fundus images for the detection of DR and classification of its stages. CNN can recognize sophisticated features on the retina and provides an automatic diagnosis. The pre-trained VGG-16 CNN model was applied using a transfer learning (TL) approach to utilize the already learned parameters in the detection.FindingsBy conducting different experiments set up with different severity groupings, the achieved results are promising. The best-achieved accuracies for 2-class, 3-class, 4-class and 5-class classifications are 86.5, 80.5, 63.5 and 73.7, respectively.Originality/valueIn this research, VGG-16 was used to detect and classify DR stages using the TL approach. Different combinations of classes were used in the classification of DR severity stages to illustrate the ability of the model to differentiate between the classes and verify the effect of these changes on the performance of the model.

Empirical investigation of wireless sensor network performance in noisy environments

2014 ◽  
Vol 12 (1) ◽  
pp. 29-38
Author(s):  
Silvanus Teneng Kiyang ◽  
Robert Van Zyl
Keyword(s):  
Ambient Noise ◽  
Network Performance ◽  
Signal To Noise Ratio ◽  
Real Life ◽  
Wireless Sensor ◽  
Mathematical Tool ◽  
Content Type ◽  
The Real ◽  
Test Platform ◽  
Set Up

Purpose – The purpose of this work is to assess the influence of ambient noise on the performance of wireless sensor networks (WSNs) empirically and, based on these findings, develop a mathematical tool to assist technicians to determine the maximum inter-node separation before deploying a new WSN. Design/methodology/approach – A WSN test platform is set up in an electromagnetically shielded environment (RF chamber) to accurately control and quantify the ambient noise level. The test platform is subsequently placed in an operational laboratory to record network performance in typical unshielded spaces. Results from the RF chamber and the real-life environments are analysed. Findings – A minimum signal-to-noise ratio (SNR) at which the network still functions was found to be of the order 30 dB. In the real-life scenarios (machines, telecommunications and computer laboratories), the measured SNR exceeded this minimum value by more than 20 dB. This is due to the low ambient industrial noise levels observed in the 2.4 GHz ISM band for typical environments found at academic institutions. It, therefore, suggests that WSNs are less prone to industrial interferences than anticipated. Originality/value – A predictive mathematical tool is developed that can be used by technicians to determine the maximum inter-node separation before the WSN is deployed. The tool yields reliable results and promises to save installation time.

CLASSIFICATION OF REAL ALGEBRAIC VECTOR BUNDLES OVER THE REAL ANISOTROPIC CONIC

2005 ◽  
Vol 16 (10) ◽  
pp. 1207-1220 ◽  
Author(s):  
INDRANIL BISWAS ◽  
D. S. NAGARAJ
Keyword(s):  
Vector Bundles ◽  
Complete Classification ◽  
Real Numbers ◽  
The Real ◽  
Isomorphism Classes ◽  
Algebraic Vector

We give a complete classification of isomorphism classes of real algebraic vector bundles over the scheme defined by a nondegenerate anisotropic conic defined over the field of real numbers.

scholarly journals Maximally inflected real trigonal curves on Hirzebruch surfaces

2021 ◽  
pp. 331-345
Author(s):  
V. Zvonilov
Keyword(s):  
Complete Classification ◽  
Type I ◽  
Type Ii ◽  
Simple Graphs ◽  
Content Type ◽  
Hirzebruch Surfaces ◽  
Trigonal Curves ◽  
Arbitrary Genus

In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base B B of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for B = P 1 B=\mathbb {P}^1 obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over B = P 1 B=\mathbb {P}^1 .

Mauritius as an offshore financial centre and laws relating to tax avoidance and evasion

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ambareen Beebeejaun
Keyword(s):  
Tax Evasion ◽  
Critical Analysis ◽  
Academic Research ◽  
Tax Avoidance ◽  
World Health ◽  
Content Type ◽  
Financial Centre ◽  
Tax Practitioners ◽  
Set Up

Purpose While Mauritius is ranked as the fastest growing financial centre in Africa and the second-fastest-growing offshore financial centre (OFC) in the word by the New World Health in 2019, the country is facing severe allegations that it is progressing at the expense of other developing countries. In this respect, this paper aims to assess the contribution of the Mauritius OFC, the robustness of tax avoidance and evasion laws, the endeavours undertaken by the Mauritius Government to promote Mauritius OFC and the alleged classification of Mauritius as a tax haven. Design/methodology/approach To achieve the above research objectives, this paper will adopt the black letter approach. That is, the relevant legislation and case laws will be scrutinised. Also, books, journal articles, newspaper articles, reports from international bodies amongst others will be used. The research methodology also comprising a critical analysis which implies that existing studies conducted on the subject matter of this research will be assessed and the extent to which the researcher agrees with the existing work will be weighed. Findings Based on the critical analysis, this paper recommends that the Mauritius Income Tax Act be amended to provide for punitive and corrective actions for those engaged in impermissible tax avoidance. Additionally, for transparency and clarity, it is suggested that the Mauritius Revenue Authority (MRA) clarifies in a practice note the factors that it considers when determining the tax liability that should have been payable or when detecting tax avoidance cases. Similarly, to discourage tax evasion, the fines and penalties for tax-evading offences should be more strict and a regulatory framework for tax practitioners need to be set up. Originality/value To the author’s knowledge, this paper is amongst the first academic research that emphasises the position of Mauritius as an OFC and critically analysed the related laws relating to the financial world.

Rational maps of ℙn with prescribed fixed points and the smooth conic case

2014 ◽  
Vol 13 (08) ◽  
pp. 1450066 ◽  
Author(s):  
J. A. Vargas ◽  
A. S. Argáez
Keyword(s):  
Fixed Point ◽  
Complete Classification ◽  
Rational Maps ◽  
Plane Curves ◽  
Canonical Forms ◽  
Fixed Point Set ◽  
Constant Degree ◽  
Point Set ◽  
Quadratic Hypersurfaces

We construct rational maps of ℙn which have a prescribed variety as a component of their fixed point set. The resulting maps fix a pencil of lines for the case of hypersurfaces; thus including the cases of plane curves. We also determine the Cremona maps among the constructed ones for quadratic hypersurfaces. Our methods are based on associated matrices of forms of constant degree and the "triple action" of G = PGL n+1 on them. We include a complete classification of these maps and matrices for the case of the smooth conic curve in ℙ2. We obtain invariants and canonical forms for the orbits of our matrices under the triple action of G, modulo syzygies of a row vector. We obtain invariants and canonical forms for the orbits of the constructed rational maps under conjugation by G.

scholarly journals Analytic classification of germs of parabolic antiholomorphic diffeomorphisms of codimension k

2021 ◽  
pp. 1-37
Author(s):  
JONATHAN GODIN ◽  
CHRISTIANE ROUSSEAU
Keyword(s):  
Fixed Point ◽  
Modulus Space ◽  
Normal Form ◽  
Complete Classification ◽  
Invariant Curves ◽  
Analytic Classification ◽  
Real Analytic ◽  
Analytic Invariant ◽  
Parabolic Fixed Point

Abstract We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic fixed point under analytic conjugacy. We then study some geometric applications: existence of real analytic invariant curves, existence of holomorphic and antiholomorphic roots of holomorphic and antiholomorphic parabolic germs, and commuting holomorphic and antiholomorphic parabolic germs.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Implementation of a deep learning model for automated classification of Aedes aegypti (Linnaeus) and Aedes albopictus (Skuse) in real time

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Song-Quan Ong ◽  
Hamdan Ahmad ◽  
Gomesh Nair ◽  
Pradeep Isawasan ◽  
Abdul Hafiz Ab Majid
Keyword(s):  
Deep Learning ◽  
Aedes Aegypti ◽  
Real Time ◽  
Aedes Albopictus ◽  
Automated Classification ◽  
Expert Performance ◽  
Deep Convolutional Neural Networks ◽  
Significant Difference ◽  
Set Up

AbstractClassification of Aedes aegypti (Linnaeus) and Aedes albopictus (Skuse) by humans remains challenging. We proposed a highly accessible method to develop a deep learning (DL) model and implement the model for mosquito image classification by using hardware that could regulate the development process. In particular, we constructed a dataset with 4120 images of Aedes mosquitoes that were older than 12 days old and had common morphological features that disappeared, and we illustrated how to set up supervised deep convolutional neural networks (DCNNs) with hyperparameter adjustment. The model application was first conducted by deploying the model externally in real time on three different generations of mosquitoes, and the accuracy was compared with human expert performance. Our results showed that both the learning rate and epochs significantly affected the accuracy, and the best-performing hyperparameters achieved an accuracy of more than 98% at classifying mosquitoes, which showed no significant difference from human-level performance. We demonstrated the feasibility of the method to construct a model with the DCNN when deployed externally on mosquitoes in real time.

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