scholarly journals Extensions of the Shannon Entropy and the Chaos Game Algorithm to Hyperbolic Numbers Plane

Fractals ◽  
2020 ◽  
Author(s):  
G. Y. Tellez-Sanchez ◽  
J. Bory-Reyes
Keyword(s):  
Shannon Entropy ◽  
Hyperbolic Numbers ◽  
Chaos Game

scholarly journals MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS
Keyword(s):  
Information Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Shannon Entropy ◽  
Three Dimensional ◽  
Spin Network ◽  
Spin Foam Models ◽  
Foam Model ◽  
Spin Foam Model ◽  
Spin Foam

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.

scholarly journals Developing a Fuzzy TOPSIS Model Combining MACBETH and Fuzzy Shannon Entropy to Select a Gamification App

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1034
Author(s):  
María Carmen Carnero
Keyword(s):  
Shannon Entropy ◽  
Fuzzy Topsis ◽  
Preference Ranking ◽  
Promethee Ii ◽  
Ciudad Real ◽  
Industrial Manufacturing ◽  
Model Combining ◽  
La Mancha ◽  
University Course ◽  
The University

Due to the important advantages it offers, gamification is one of the fastest-growing industries in the world, and interest from the market and from users continues to grow. This has led to the development of more and more applications aimed at different fields, and in particular the education sector. Choosing the most suitable application is increasingly difficult, and so to solve this problem, our study designed a model which is an innovative combination of fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with the Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) and Shannon entropy theory, to choose the most suitable gamification application for the Industrial Manufacturing and Organisation Systems course in the degree programmes for Electrical Engineering and Industrial and Automatic Electronics at the Higher Technical School of Industrial Engineering of Ciudad Real, part of the University of Castilla-La Mancha. There is no precedent in the literature that combines MACBETH and fuzzy Shannon entropy to simultaneously consider the subjective and objective weights of criteria to achieve a more accurate model. The objective weights computed from fuzzy Shannon entropy were compared with those calculated from De Luca and Termini entropy and exponential entropy. The validity of the proposed method is tested through the Preference Ranking Organisation METHod for Enrichment of Evaluations (PROMETHEE) II, ELimination and Choice Expressing REality (ELECTRE) III, and fuzzy VIKOR method (VIsekriterijumska optimizacija i KOmpromisno Resenje). The results show that Quizizz is the best option for this course, and it was used in two academic years. There are no precedents in the literature using fuzzy multicriteria decision analysis techniques to select the most suitable gamification application for a degree-level university course.

scholarly journals Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Neural Network ◽  
Maximum Likelihood ◽  
Image Reconstruction ◽  
Image Recognition ◽  
Shannon Entropy ◽  
Reconstruction Error ◽  
Likelihood Method ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
D Wave

AbstractRestricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter ($$\beta $$ β ) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

scholarly journals Proton Exchange Membrane Fuel Cells Modeling Using Chaos Game Optimization Technique

2021 ◽  
Vol 13 (14) ◽  
pp. 7911
Author(s):  
Ibrahim Alsaidan ◽  
Mohamed A. M. Shaheen ◽  
Hany M. Hasanien ◽  
Muhannad Alaraj ◽  
Abrar S. Alnafisah
Keyword(s):  
Fuel Cell ◽  
Objective Function ◽  
Proton Exchange Membrane ◽  
Optimization Technique ◽  
Proton Exchange ◽  
Simulation Performance ◽  
Terminal Voltage ◽  
Chaos Game ◽  
Simulation Results ◽  
Exchange Membrane

For the precise simulation performance, the accuracy of fuel cell modeling is important. Therefore, this paper presents a developed optimization method called Chaos Game Optimization Algorithm (CGO). The developed method provides the ability to accurately model the proton exchange membrane fuel cell (PEMFC). The accuracy of the model is tested by comparing the simulation results with the practical measurements of several standard PEMFCs such as Ballard Mark V, AVISTA SR-12.5 kW, and 6 kW of the Nedstack PS6 stacks. The complexity of the studied problem stems from the nonlinearity of the PEMFC polarization curve that leads to a nonlinear optimization problem, which must be solved to determine the seven PEMFC design variables. The objective function is formulated mathematically as the total error squared between the laboratory measured terminal voltage of PEMFC and the estimated terminal voltage yields from the simulation results using the developed model. The CGO is used to find the best way to fulfill the preset requirements of the objective function. The results of the simulation are tested under different temperature and pressure conditions. Moreover, the results of the proposed CGO simulations are compared with alternative optimization methods showing higher accuracy.

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