Search results for: Ensemble methods
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4051

Search results for: Ensemble methods

3991 Temperature Effect on the Mechanical Properties of Pd3Rh and PdRh3 Ordered Alloys

Authors: J. Davoodi , J. Moradi

Abstract:

The aim of this research was to calculate the mechanical properties of Pd3Rh and PdRh3 ordered alloys. The molecular dynamics (MD) simulation technique was used to obtain temperature dependence of the energy, the Yong modulus, the shear modulus, the bulk modulus, Poisson-s ratio and the elastic stiffness constants at the isobaric-isothermal (NPT) ensemble in the range of 100-325 K. The interatomic potential energy and force on atoms were calculated by Quantum Sutton-Chen (Q-SC) many body potential. Our MD simulation results show the effect of temperature on the cohesive energy and mechanical properties of Pd3Rh as well as PdRh3 alloys. Our computed results show good agreement with the experimental results where they have been available.

Keywords: Pd-Rh alloy; Mechanical properties; Moleculardynamics simulation

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3990 Predictive Semi-Empirical NOx Model for Diesel Engine

Authors: Saurabh Sharma, Yong Sun, Bruce Vernham

Abstract:

Accurate prediction of NOx emission is a continuous challenge in the field of diesel engine-out emission modeling. Performing experiments for each conditions and scenario cost significant amount of money and man hours, therefore model-based development strategy has been implemented in order to solve that issue. NOx formation is highly dependent on the burn gas temperature and the O2 concentration inside the cylinder. The current empirical models are developed by calibrating the parameters representing the engine operating conditions with respect to the measured NOx. This makes the prediction of purely empirical models limited to the region where it has been calibrated. An alternative solution to that is presented in this paper, which focus on the utilization of in-cylinder combustion parameters to form a predictive semi-empirical NOx model. The result of this work is shown by developing a fast and predictive NOx model by using the physical parameters and empirical correlation. The model is developed based on the steady state data collected at entire operating region of the engine and the predictive combustion model, which is developed in Gamma Technology (GT)-Power by using Direct Injected (DI)-Pulse combustion object. In this approach, temperature in both burned and unburnt zone is considered during the combustion period i.e. from Intake Valve Closing (IVC) to Exhaust Valve Opening (EVO). Also, the oxygen concentration consumed in burnt zone and trapped fuel mass is also considered while developing the reported model.  Several statistical methods are used to construct the model, including individual machine learning methods and ensemble machine learning methods. A detailed validation of the model on multiple diesel engines is reported in this work. Substantial numbers of cases are tested for different engine configurations over a large span of speed and load points. Different sweeps of operating conditions such as Exhaust Gas Recirculation (EGR), injection timing and Variable Valve Timing (VVT) are also considered for the validation. Model shows a very good predictability and robustness at both sea level and altitude condition with different ambient conditions. The various advantages such as high accuracy and robustness at different operating conditions, low computational time and lower number of data points requires for the calibration establishes the platform where the model-based approach can be used for the engine calibration and development process. Moreover, the focus of this work is towards establishing a framework for the future model development for other various targets such as soot, Combustion Noise Level (CNL), NO2/NOx ratio etc.

Keywords: Diesel engine, machine learning, NOx emission, semi-empirical.

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3989 Cirrhosis Mortality Prediction as Classification Using Frequent Subgraph Mining

Authors: Abdolghani Ebrahimi, Diego Klabjan, Chenxi Ge, Daniela Ladner, Parker Stride

Abstract:

In this work, we use machine learning and data analysis techniques to predict the one-year mortality of cirrhotic patients. Data from 2,322 patients with liver cirrhosis are collected at a single medical center. Different machine learning models are applied to predict one-year mortality. A comprehensive feature space including demographic information, comorbidity, clinical procedure and laboratory tests is being analyzed. A temporal pattern mining technic called Frequent Subgraph Mining (FSM) is being used. Model for End-stage liver disease (MELD) prediction of mortality is used as a comparator. All of our models statistically significantly outperform the MELD-score model and show an average 10% improvement of the area under the curve (AUC). The FSM technic itself does not improve the model significantly, but FSM, together with a machine learning technique called an ensemble, further improves the model performance. With the abundance of data available in healthcare through electronic health records (EHR), existing predictive models can be refined to identify and treat patients at risk for higher mortality. However, due to the sparsity of the temporal information needed by FSM, the FSM model does not yield significant improvements. Our work applies modern machine learning algorithms and data analysis methods on predicting one-year mortality of cirrhotic patients and builds a model that predicts one-year mortality significantly more accurate than the MELD score. We have also tested the potential of FSM and provided a new perspective of the importance of clinical features.

Keywords: machine learning, liver cirrhosis, subgraph mining, supervised learning

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3988 Unit Commitment Solution Methods

Authors: Sayeed Salam

Abstract:

An effort to develop a unit commitment approach capable of handling large power systems consisting of both thermal and hydro generating units offers a large profitable return. In order to be feasible, the method to be developed must be flexible, efficient and reliable. In this paper, various proposed methods have been described along with their strengths and weaknesses. As all of these methods have some sort of weaknesses, a comprehensive algorithm that combines the strengths of different methods and overcomes each other-s weaknesses would be a suitable approach for solving industry-grade unit commitment problem.

Keywords: Unit commitment, Solution methods, and Comprehensive algorithm.

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3987 Integration of Support Vector Machine and Bayesian Neural Network for Data Mining and Classification

Authors: Essam Al-Daoud

Abstract:

Several combinations of the preprocessing algorithms, feature selection techniques and classifiers can be applied to the data classification tasks. This study introduces a new accurate classifier, the proposed classifier consist from four components: Signal-to- Noise as a feature selection technique, support vector machine, Bayesian neural network and AdaBoost as an ensemble algorithm. To verify the effectiveness of the proposed classifier, seven well known classifiers are applied to four datasets. The experiments show that using the suggested classifier enhances the classification rates for all datasets.

Keywords: AdaBoost, Bayesian neural network, Signal-to-Noise, support vector machine, MCMC.

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3986 Molecular Dynamics Simulation of Thermal Properties of Au3Ni Nanowire

Authors: J. Davoodi, F. Katouzi

Abstract:

The aim of this research was to calculate the thermal properties of Au3Ni Nanowire. The molecular dynamics (MD) simulation technique was used to obtain the effect of radius size on the energy, the melting temperature and the latent heat of fusion at the isobaric-isothermal (NPT) ensemble. The Quantum Sutton-Chen (Q-SC) many body interatomic potentials energy have been used for Gold (Au) and Nickel (Ni) elements and a mixing rule has been devised to obtain the parameters of these potentials for nanowire stats. Our MD simulation results show the melting temperature and latent heat of fusion increase upon increasing diameter of nanowire. Moreover, the cohesive energy decreased with increasing diameter of nanowire.

Keywords: Au3Ni Nanowire, Thermal properties, Molecular dynamics simulation

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3985 Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation

Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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3984 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems

Authors: Shengfeng Li, Rujing Wang

Abstract:

In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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3983 Coding Considerations for Standalone Molecular Dynamics Simulations of Atomistic Structures

Authors: R. O. Ocaya, J. J. Terblans

Abstract:

The laws of Newtonian mechanics allow ab-initio molecular dynamics to model and simulate particle trajectories in material science by defining a differentiable potential function. This paper discusses some considerations for the coding of ab-initio programs for simulation on a standalone computer and illustrates the approach by C language codes in the context of embedded metallic atoms in the face-centred cubic structure. The algorithms use velocity-time integration to determine particle parameter evolution for up to several thousands of particles in a thermodynamical ensemble. Such functions are reusable and can be placed in a redistributable header library file. While there are both commercial and free packages available, their heuristic nature prevents dissection. In addition, developing own codes has the obvious advantage of teaching techniques applicable to new problems.

Keywords: C-language, molecular dynamics, simulation, embedded atom method.

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3982 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

Authors: Jalil Rashidinia, Reza Jalilian

Abstract:

In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.

Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.

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3981 Interpolation of Geofield Parameters

Authors: A. Pashayev, C. Ardil, R. Sadiqov

Abstract:

Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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3980 Effective Class of Discreet Programing Problems

Authors: Kaziyev G. Z., Nabiyeva G. S., Kalizhanova A.U.

Abstract:

We consider herein a concise view of discreet programming models and methods. There has been conducted the models and methods analysis. On the basis of discreet programming models there has been elaborated and offered a new class of problems, i.e. block-symmetry models and methods of applied tasks statements and solutions.

Keywords: Discreet programming, block-symmetry, analysis methods, information systems development.

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3979 A Comparison of Deterministic and Probabilistic Methods for Determining the Required Amount of Spinning Reserve

Authors: A. Ehsani, A. Karimizadeh, H. Fallahi, A. Jalali

Abstract:

In an electric power system, spinning reserve requirements can be determined by using deterministic and/or probabilistic measures. Although deterministic methods are usual in many systems, application of probabilistic methods becomes increasingly important in the new environment of the electric power utility industry. This is because of the increased uncertainty associated with competition. In this paper 1) a new probabilistic method is presented which considers the reliability of transmission system in a simplified manner and 2) deterministic and probabilistic methods are compared. The studied methods are applied to the Roy Billinton Test System (RBTS).

Keywords: Reliability, Spinning Reserve, Risk, Transmission, Unit Commitment.

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3978 Event Related Potentials in Terms of Visual and Auditory Stimuli

Authors: Seokbeen Lim, KyeongSeok Sim, DaKyeong Shin, Gilwon Yoon

Abstract:

Event-related potential (ERP) is one of the useful tools for investigating cognitive reactions. In this study, the potential of ERP components detected after auditory and visual stimuli was examined. Subjects were asked to respond upon stimuli that were of three categories; Target, Non-Target and Standard stimuli. The ERP after stimulus was measured. In the experiment of visual evoked potentials (VEPs), the subjects were asked to gaze at a center point on the monitor screen where the stimuli were provided by the reversal pattern of the checkerboard. In consequence of the VEP experiments, we observed consistent reactions. Each peak voltage could be measured when the ensemble average was applied. Visual stimuli had smaller amplitude and a longer latency compared to that of auditory stimuli. The amplitude was the highest with Target and the smallest with Standard in both stimuli.

Keywords: Auditory stimulus, EEG, event related potential, oddball task, visual stimulus.

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3977 Comparison of Full Graph Methods of Switched Circuits Solution

Authors: Zdeňka Dostálová, David Matoušek, Bohumil Brtnik

Abstract:

As there are also graph methods of circuit analysis in addition to algebraic methods, it is, in theory, clearly possible to carry out an analysis of a whole switched circuit in two-phase switching exclusively by the graph method as well. This article deals with two methods of full-graph solving of switched circuits: by transformation graphs and by two-graphs. It deals with the circuit switched capacitors and the switched current, too. All methods are presented in an equally detailed steps to be able to compare.

Keywords: Switched capacitors of two phases, switched currents of two phases, transformation graph, two-graph, Mason's formula, voltage transfer, summary graph.

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3976 An Overview of Islanding Detection Methods in Photovoltaic Systems

Authors: Wei Yee Teoh, Chee Wei Tan

Abstract:

The issue of unintentional islanding in PV grid interconnection still remains as a challenge in grid-connected photovoltaic (PV) systems. This paper discusses the overview of popularly used anti-islanding detection methods, practically applied in PV grid-connected systems. Anti-islanding methods generally can be classified into four major groups, which include passive methods, active methods, hybrid methods and communication base methods. Active methods have been the preferred detection technique over the years due to very small non-detected zone (NDZ) in small scale distribution generation. Passive method is comparatively simpler than active method in terms of circuitry and operations. However, it suffers from large NDZ that significantly reduces its performance. Communication base methods inherit the advantages of active and passive methods with reduced drawbacks. Hybrid method which evolved from the combination of both active and passive methods has been proven to achieve accurate anti-islanding detection by many researchers. For each of the studied anti-islanding methods, the operation analysis is described while the advantages and disadvantages are compared and discussed. It is difficult to pinpoint a generic method for a specific application, because most of the methods discussed are governed by the nature of application and system dependent elements. This study concludes that the setup and operation cost is the vital factor for anti-islanding method selection in order to achieve minimal compromising between cost and system quality.

Keywords: Active method, hybrid method, islanding detection, passive method, photovoltaic (PV), utility method

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3975 A Comparison of Inflow Generation Methods for Large-Eddy Simulation

Authors: Francois T. Pronk, Steven J. Hulshoff

Abstract:

A study of various turbulent inflow generation methods was performed to compare their relative effectiveness for LES computations of turbulent boundary layers. This study confirmed the quality of the turbulent information produced by the family of recycling and rescaling methods which take information from within the computational domain. Furthermore, more general inflow methods also proved applicable to such simulations, with a precursor-like inflow and a random inflow augmented with forcing planes showing promising results.

Keywords: Boundary layer, Flat plate, Inflow modeling, LES

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3974 Numerical Methods versus Bjerksund and Stensland Approximations for American Options Pricing

Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

Abstract:

Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, Computational analysis, Finance, Options pricing, Numerical methods.

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3973 Orchestra Course Outcomes in Terms of Values Education

Authors: Z. Kurtaslan, H. Hakan Okay, E. Can Dönmez, I. Kuçukdoğan

Abstract:

Music education aims to bring up individuals most appropriately and to advanced levels as a balanced whole physically, cognitively, affectively, and kinesthetically while making a major contribution to the physical and spiritual development of the individual. The most crucial aim of music education, an influential education medium per se, is to make music be loved; yet, among its educational aims are concepts such as affinity, friendship, goodness, philanthropy, responsibility, and respect all extremely crucial bringing up individuals as a balanced whole. One of the most essential assets of the music education is the training of making music together, solidifying musical knowledge and enabling the acquisition of cooperation. This habit requires internalization of values like responsibility, patience, cooperativeness, respect, self-control, friendship, and fairness. If musicians lack these values, the ensemble will become after some certain time a cacophony. In this qualitative research, the attitudes of music teacher candidates in orchestra/chamber music classes will be examined in terms of values.

Keywords: Education, music, orchestra/chamber music, values.

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3972 Parallel Multisplitting Methods for Singular Linear Systems

Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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3971 Internet: a New Medium to Promote Traditional Dances in Indonesia

Authors: Maria Satya Rani, Fandy Tjiptono, Suyoto

Abstract:

As a multicultural country, Indonesia has many subcultures with unique performing arts. Some of them are well-known to international tourists, such as music ensemble (known as gamelan) in Bali and Java, shadow puppet play (wayang) in Java, and martial arts (known as pencak silat) in Sumatra. Some examples of famous traditional dances in Indonesia are Srimpi from Yogyakarta and Solo, Legong from Bali, and Gong dance from Kalimantan. Performing arts show the identity of a nation. However, they are a complex subject, especially when they are addressed to children. The performing arts, e.g. music, dance theatre, and opera are experiential, experimental, and emotionally charged. Therefore, the right strategy and promotion need to be developed to engage children to appreciate and preserve traditional dances. This study aims to explore and identify possibilities of internet usage as a medium to promote traditional dances, especially to children in Indonesia.

Keywords: children education, culture preservation in Indonesia, national identity, online promotion

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3970 Generation of Artificial Earthquake Accelerogram Compatible with Spectrum using the Wavelet Packet Transform and Nero-Fuzzy Networks

Authors: Peyman Shadman Heidari, Mohammad Khorasani

Abstract:

The principal purpose of this article is to present a new method based on Adaptive Neural Network Fuzzy Inference System (ANFIS) to generate additional artificial earthquake accelerograms from presented data, which are compatible with specified response spectra. The proposed method uses the learning abilities of ANFIS to develop the knowledge of the inverse mapping from response spectrum to earthquake records. In addition, wavelet packet transform is used to decompose specified earthquake records and then ANFISs are trained to relate the response spectrum of records to their wavelet packet coefficients. Finally, an interpretive example is presented which uses an ensemble of recorded accelerograms to demonstrate the effectiveness of the proposed method.

Keywords: Adaptive Neural Network Fuzzy Inference System, Wavelet Packet Transform, Response Spectrum.

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3969 Iterative Methods for An Inverse Problem

Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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3968 Concurrent Testing of ADC for Embedded System

Authors: Y.B.Gandole

Abstract:

Compaction testing methods allow at-speed detecting of errors while possessing low cost of implementation. Owing to this distinctive feature, compaction methods have been widely used for built-in testing, as well as external testing. In the latter case, the bandwidth requirements to the automated test equipment employed are relaxed which reduces the overall cost of testing. Concurrent compaction testing methods use operational signals to detect misbehavior of the device under test and do not require input test stimuli. These methods have been employed for digital systems only. In the present work, we extend the use of compaction methods for concurrent testing of analog-to-digital converters. We estimate tolerance bounds for the result of compaction and evaluate the aliasing rate.

Keywords: Analog-to Digital Converter, Embedded system, Concurrent Testing

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3967 Influences of Juice Extraction and Drying Methods on the Chemical Analysis of Lemon Peels

Authors: Azza A. Abou-Arab, Marwa H. Mahmoud, Ferial M. Abu-Salem

Abstract:

This study aimed to determine the influence of some different juice extraction methods (screw type hand operated juice extractor and pressed squeeze juice extractor) as well as drying methods (microwave, solar and oven drying) on the chemical properties of lemon peels. It could be concluded that extraction of juice by screw type and drying of peel using the microwave drying method were the best preparative processing steps methods for lemon peel utilization as food additives.

Keywords: Lemon peel, extraction of juice methods, chemical analysis.

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3966 A Survey of Business Component Identification Methods and Related Techniques

Authors: Zhongjie Wang, Xiaofei Xu, Dechen Zhan

Abstract:

With deep development of software reuse, componentrelated technologies have been widely applied in the development of large-scale complex applications. Component identification (CI) is one of the primary research problems in software reuse, by analyzing domain business models to get a set of business components with high reuse value and good reuse performance to support effective reuse. Based on the concept and classification of CI, its technical stack is briefly discussed from four views, i.e., form of input business models, identification goals, identification strategies, and identification process. Then various CI methods presented in literatures are classified into four types, i.e., domain analysis based methods, cohesion-coupling based clustering methods, CRUD matrix based methods, and other methods, with the comparisons between these methods for their advantages and disadvantages. Additionally, some insufficiencies of study on CI are discussed, and the causes are explained subsequently. Finally, it is concluded with some significantly promising tendency about research on this problem.

Keywords: Business component, component granularity, component identification, reuse performance.

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3965 A Comparison of First and Second Order Training Algorithms for Artificial Neural Networks

Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

Abstract:

Minimization methods for training feed-forward networks with Backpropagation are compared. Feedforward network training is a special case of functional minimization, where no explicit model of the data is assumed. Therefore due to the high dimensionality of the data, linearization of the training problem through use of orthogonal basis functions is not desirable. The focus is functional minimization on any basis. A number of methods based on local gradient and Hessian matrices are discussed. Modifications of many methods of first and second order training methods are considered. Using share rates data, experimentally it is proved that Conjugate gradient and Quasi Newton?s methods outperformed the Gradient Descent methods. In case of the Levenberg-Marquardt algorithm is of special interest in financial forecasting.

Keywords: Backpropagation algorithm, conjugacy condition, line search, matrix perturbation

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3964 Breast Cancer Prediction Using Score-Level Fusion of Machine Learning and Deep Learning Models

Authors: [email protected]

Abstract:

Breast cancer is one of the most common types in women. Early prediction of breast cancer helps physicians detect cancer in its early stages. Big cancer data need a very powerful tool to analyze and extract predictions. Machine learning and deep learning are two of the most efficient tools for predicting cancer based on textual data. In this study, we developed a fusion model of two machine learning and deep learning models. To obtain the final prediction, Long-Short Term Memory (LSTM), ensemble learning with hyper parameters optimization, and score-level fusion is used. Experiments are done on the Breast Cancer Surveillance Consortium (BCSC) dataset after balancing and grouping the class categories. Five different training scenarios are used, and the tests show that the designed fusion model improved the performance by 3.3% compared to the individual models.

Keywords: Machine learning, Deep learning, cancer prediction, breast cancer, LSTM, Score-Level Fusion.

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3963 Theoretical Analysis of the Effect of Accounting for Special Methods in Similarity-Based Cohesion Measurement

Authors: Jehad Al Dallal

Abstract:

Class cohesion is an important object-oriented software quality attributes, and it refers to the degree of relatedness of class attributes and methods. Several class cohesion measures are proposed in the literature, and the impact of considering the special methods (i.e., constructors, destructors, and access and delegation methods) in cohesion calculation is not thoroughly theoretically studied for most of them. In this paper, we address this issue for three popular similarity-based class cohesion measures. For each of the considered measures we theoretically study the impact of including or excluding special methods on the values that are obtained by applying the measure. This study is based on analyzing the definitions and formulas that are proposed for the measures. The results show that including/excluding special methods has a considerable effect on the obtained cohesion values and that this effect varies from one measure to another. The study shows the importance of considering the types of methods that have to be accounted for when proposing a similarity-based cohesion measure.

Keywords: Object-oriented class, software quality, class cohesion measure, class cohesion, special methods.

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3962 Localized Meshfree Methods for Solving 3D-Helmholtz Equation

Authors: Reza Mollapourasl, Majid Haghi

Abstract:

In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: Radial basis functions, Hermite finite difference, Helmholtz equation, stability.

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