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Neural network toolbox

Manufactured by MathWorks
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The Neural Network Toolbox is a software tool developed by MathWorks for the design, implementation, and visualization of neural network models. It provides a comprehensive set of algorithms and tools for training, validating, and deploying neural networks. The toolbox supports a wide range of neural network architectures, including feedforward, recurrent, and convolutional networks. It also includes functions for preprocessing data, optimizing network parameters, and analyzing network performance.

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9 protocols using neural network toolbox

1

Backstroke Start Modeling using ANN

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Multilayer perceptron, an ANN model, designed using Matlab’s Neural Network Toolbox (v. 4.0.3, The MathWorks, Incorporated, USA), was adopted to model the backstroke start nonlinear behaviour. Eleven kinematic and 15 kinetic variables from 35 valid start trials were inputted to the development of a feed-forward ANN with four neurons in a single hidden layer for modelling and predicting the 5 m backstroke start time (output variable). The model complexity was arbitrarily chosen until a reasonable performance had been achieved and the Levenberg-Marquardt optimisation algorithm (Allen et al., 2015 (link); Maszczyk et al., 2012 (link); Novatchkov and Baca, 2013 (link)) was used for training procedures and measure performance regarding the precision of training and the validation phase outputs (50 models randomly sorted, with 90 and 10% of data, respectively). Results were analysed based on each model output accuracy by mean absolute percentage error calculation (MAPE; Tsai et al., 2013 (link)). ANN results were compared with LM, which is a linear combination of the same inputs used in ANN, being the least squares problem solved by means of QR factorization to estimate the LM variables.
The coefficient of variation (CV) of the four backstroke start trials for each swimmer and for each variant was calculated for kinematic and kinetic variables.
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2

Predicting Biochemical Recurrence in Prostate Cancer

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Artificial neural network and LR models were computed using the MATLAB-software and the Neural Network Toolbox (Mathworks, Natick, MA, USA). Each ANN (feed forward network with error back propagation) had three layers: input layer with four neurons, hidden layer with two neurons and output layer with one neuron representing the nonBCR probability. Follow-up data after LRP were collected every 6 months and respectively added into the separate models. Every 6 months separate models (ANN and LR) were calculated with those patients still not having a BCR at this time-point (those with a BCR earlier were excluded) and those who were not censored. For all models, internal validation was performed with the leave one out method.
Statistical analysis was performed using SPSS 19.0 (IBM, Chicago, IL, USA) and MedCalc 12.4.0 (MedCalc Software, Mariakerke, Belgium) to compare all variables using receiver operating characteristic (ROC) analyses regarding sensitivity, specificity and areas under ROC curve (AUC). The comparison of ROC curves were performed with the method of Delong and the comparison of prediction results were conducted using Mann–Whitney U test for continuous variables and Fisher's exact test for ordinal variables. Differences were considered statistically significant if P < 0.05.
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3

Dual-beam UV-Vis Spectrophotometry Analysis

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The UV- Visible spectrophotometer JASCO dual beam (Tokyo, Japan) model V-630 was utilized with the included programmer spectra II manager. The spectral slit had a width of 2 nm, and the scanning rate was 1000 nm/min. All chemometric techniques were applied using MATLAB®8.3.0.532 (R2014a), PLS Toolbox (version 2.1), MCR-ALS Toolbox, and Neural Network Toolbox (Math Works, United States).
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4

Predicting Rubber Curing Characteristics with ANN

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The implementation of the ANN model for predicting the curing characteristics of RBs with different contents of CB filler at various cure temperatures was performed in the MATLAB® software package, Version 9.0.0.341360 R2016a 64-bit, equipped with a Neural Network Toolbox (Math Works, Natic, MA, USA), that provides a number of built-in tools for sufficiently powerful and user-friendly work with ANNs of a wide range of types and architectures. The GRNN was used to solve the given function approximation problem, in particular for its extremely high learning rate and rapid convergence to optimal regression levels, even in the case of a small amount of training data [31 ].
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5

GRNN ANN Modeling on Windows 10

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The GRNN model was implemented in the MATLAB® software package, Version R2016a 64-bit (win64), with the inclusion of the Neural Network Toolbox and Parallel Computing Toolbox (MathWorks, Natick, MA, USA). These toolboxes offer all the necessary resources for efficient work with ANNs and parallel computing. The MATLAB® software package was installed on a personal computer running Windows 10; Intel® CoreTM i5-12450H, CPU@ 2.4 GHz, 16 GB RAM, 64-bit; SSD 250 GB; GPU: NVIDIA GeForce GTX 1650, 6 GB.
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6

Optimization and Statistical Analysis of Experiments

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The Optimization Toolbox™ (for implementing second-order polynomial central composite design of RSM), Neural Network Toolbox™ (Feed-forward ANN comprising MLP with BP algorithm implementation) of MATLAB R2015b software (The Mathworks, Inc., Ver. 8.6.0.347, MA, USA), and Microsoft Excel 2013 (15.0.44) (Microsoft Corporation, Redmond, WA, USA) were used for carrying out the one-way analysis of variance (ANOVA) and differences between the means were calculated using a Duncan multiple range test at significance level of p < 0.05.
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7

Wavelet-Based Data Compression for Voltammetric Modeling

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In order to reduce the large amount of information generated for each sample (2 sensors x 390 current values at different potential) a preprocessing stage was necessary to compress the original data. The objective of this step is to reduce the complexity of the input data while preserving the relevant information; also the compression of the data allows to reduce the training time, avoid redundancy in input data and to obtain a model with better generalization ability.
The chosen method was the Discrete Wavelet Transform (DWT) [27] , each voltammogram was normalized and then compressed using Daubechies 4 wavelet mother function and a fourth decomposition level. In this manner, the original data was reduced to 60 coefficients without any loss of relevant information; additionally Causal Index [28] was employed to further refine the model by eliminating the inputs that make relatively small contributions to the model. With this double compression-pruning approach, the 780 inputs per sample were reduced down to 21 coefficients, achieving a compression ratio up to 97.31%. Chemometric processing of data was performed by specific routines written by the authors using MATLAB 7.1 (MathWorks, Natick, MA) and its Neural Network Toolbox (v.4.0.6).
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8

Predicting Stool Biomarkers using ANN

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Sample sizes were calculated for correlation coefficients of 0.5, Type I error at 0.05 and Type II error at 0.20. The calculations required 30 samples. Categorical data were analysed for frequency (per cent), and continuous data for mean and range (unless stated otherwise). Data calculations were performed using the statistical programme Stata 14 (StataCorp, Texas, USA). The artificial neural network (ANN) was created using the MATLAB 2012a program and it's Neural Network Toolbox, Feed-Forward network with back propagation leaning algorithm, log sigmoid function for hidden layer and linear function for output (MathWorks, Inc.). The ANN training used wave levels and stool colour card grade as inputs and STB as the outcome.
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9

Artificial Neural Network Modeling of Enzymatic Hydrolysis

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Two artificial neural network (ANN) models were developed in this work (i.e. subtilisin and trypsin), where DH was related to the reaction temperature (T), the enzyme-substrate ratio (ES) and the time of reaction (t) as input variables. Both ANN models were constructed by means of the Neural Network Toolbox, implemented in Matlab 7.0 (Mathworks, USA).
Both artificial neural networks comprised an input layer, a single hidden layer and an output layer.
The input layer comprised three neurons, corresponding to the 3 input variables (T, ES, t). This layer is connected to the hidden layer, whose number of neurons was varied from 1 to 10 neurons.
Each neuron k of the hidden layer received a weighted signal from the input layer sk, expressed as follows:
where wik were the weight factors and bk was the bias for the neuron k. Each neuron of the hidden layer processes the signal sk by means of a transfer function. The sigmoid function (implemented in Matlab as logsig) was selected as transfer function in the hidden layer, which returns a value ranging between 0 and 1 according to Eq. 3:
The k responses exiting the hidden layer are combined into a single weighted signal t, which is
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