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This paper introduces an innovative approach to address the distribution network reconfiguration (DNR) challenge, aiming to reduce power loss through an advanced hyperbolic tangent particle swarm optimization (HT-PSO) method. This approach is distinguished by the adoption of a novel hyperbolic tangent function, which effectively limits the rate of change values, offering a significant improvement over traditional sigmoid function-based methods. A key feature of this new approach is the integration of a tunable parameter, δ , into the HT-PSO, enhancing the curve's adaptability. The careful optimization of δ ensures superior control over the rate of change across the entire operational range. This enhanced control mechanism substantially improves the efficiency of the search and convergence processes in DNR. Comparative simulations conducted on 33- and 94-bus systems show an improvement in convergence, demonstrating a more exhaustive exploration of the search space than existing methods documented in the literature based on PSO and variations where functions are proposed for the rate of change of values. [ABSTRACT FROM AUTHOR]

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle's Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance. [ABSTRACT FROM AUTHOR]

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet, successfully simplified post-processing and integrated post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent (HTBNet). First of all, we propose the Binarization of Hyperbolic Tangent (HTB), optimized along with which the segmentation network can expedite the initial convergent speed by reducing the number of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention (MSCA). Meanwhile, considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial (FMCS), which can fuse the multi-scale feature maps from channel and spatial dimensions. Finally, we adopt cross-entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet, compared with lightweight models, has achieved competitive performance and speed on Total-Text (F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30). [ABSTRACT FROM AUTHOR]

In this study, the advancing and receding contact angles of three types of pure liquid on four different surfaces have been measured. The contact angles of the droplet have been measured by analysing the captured photo by tilted plate method. Droplet behaviour has been modelled by two experimental equations. Additionally, the data has been modelled by an artificial neural network using genetic algorithm and a hyperbolic tangent activation function. The input parameters are density, molecular weight of pure liquid and solid, viscosity and surface tension of pure liquid, roughness of the solid surface and the two outputs are advancing and receding contact angles of the droplet. Number of 81 data points were used for training, 27 data for validation and 28 data for testing. The topography of {7,7,2} for artificial neural network has been proposed. The resulting RMS errors were 8%, 8% and 7% for training, validation and testing, respectively. [ABSTRACT FROM AUTHOR]

The use of ultrasonic waves to change the structure of the gums leads to the modification and improvement of their functional characteristics and rheological properties. In this research, the effects of ultrasonic intensity and treatment time on apparent viscosity, consistency coefficient, and flow behavior index of different concentrations of xanthan gum were investigated and modeled. Genetic algorithm-artificial neural network method with three inputs (ultrasonic power, treatment time and gum concentration) and three outputs (viscosity, consistency coefficient, and flow behavior index) was used to model the process. The apparent viscosities of the xanthan gum control sample (untreated) at concentrations of 0.1, 0.15, and 0.2% were 21.0, 39.9, and 66.5 mPa.s, respectively. The results of this research showed that gum viscosity decreased with increasing intensity and duration of ultrasound application. Ultrasonic treatment for 20 min significantly reduced the apparent viscosity of xanthan gum from 39.9 to 23.2 mPa.s (p< 0.05). The genetic algorithm-artificial neural network modeling results showed that the network with 3-5-3 structure in a hidden layer and using the hyperbolic tangent activation function can predict the rheological parameters of xanthan gum with high correlation coefficient and low error value. Values of mean squared error (MSE), normalized mean squared error (NMSE), mean absolute error (MAE), and correlation coefficient (r) to predict the apparent viscosity of xanthan gum were 73.17, 0.20, 6.48, and 0.90, respectively. Based on the results of the sensitivity analysis test, ultrasonic treatment intensity was the most effective factor in changing the apparent viscosity, consistency coefficient, and flow behavior index of xanthan gum. [ABSTRACT FROM AUTHOR]

Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors' shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors. The autonomous version of this system was studied previously. Inspired by the former work and applying a forcing term to this system, its dynamics are studied. All forcing term parameters' impacts are investigated alongside the initial condition-dependent behaviors to confirm the system's megastability. The dynamical analysis utilizes one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, Kaplan–Yorke dimension, and attraction basin. Because of this system's megastability, the one-dimensional bifurcation diagrams and Kaplan–Yorke dimension are plotted with three distinct initial conditions. Its analog circuit is simulated in the OrCAD environment to confirm the numerical simulations' correctness. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative approach to address the distribution network reconfiguration (DNR) challenge, aiming to reduce power loss through an advanced hyperbolic tangent particle swarm optimization (HT-PSO) method. This approach is distinguished by the adoption of a novel hyperbolic tangent function, which effectively limits the rate of change values, offering a significant improvement over traditional sigmoid function-based methods. A key feature of this new approach is the integration of a tunable parameter, δ, into the HT-PSO, enhancing the curve’s adaptability. The careful optimization of δ ensures superior control over the rate of change across the entire operational range. This enhanced control mechanism substantially improves the efficiency of the search and convergence processes in DNR. Comparative simulations conducted on 33- and 94-bus systems show an improvement in convergence, demonstrating a more exhaustive exploration of the search space than existing methods documented in the literature based on PSO and variations where functions are proposed for the rate of change of values.

Aim: Describe the utility of an inverse reinforcement learning pathway to develop a novel model to predict and manage the spread of COVID-19. Materials & methods: Convolutional neural network (CNN) with multilayer perceptron (MLP) modeling functions utilized inverse reinforcement learning to predict COVID-19 outcomes based on a comprehensive array of factors. Results: Our model demonstrates a sensitivity of 0.67 in the receiver operating characteristic curve and can correctly identify approximately 67% of the positive cases. Conclusion: We demonstrate the ability to augment clinical decision-making with a novel artificial intelligence (AI) solution that accurately predicted the susceptibility of transplant patients to COVID-19. This enables physicians to administer treatment and take appropriate preventative measures based on patients' risk factors. Artificial intelligence (AI) is about creating intelligent machines that can replicate human cognitive functions like learning and problem-solving. These AI systems can help to predict and address problems, and their power lies in learning from large datasets. AI can help to understand and respond to COVID-19 risks, particularly for certain groups of patients, like heart transplant patients. Figuring out how COVID-19 affects heart transplant patients is tough because we don't have much information about it. Combining medical knowledge with AI seems to be an effective way to solve problems during the pandemic. However, using AI in medicine is challenging as the use and adoption of AI in clinical practice remains limited, with many AI algorithms at the design and development stage. Considerable progress has been made, but continued research is needed for better monitoring and diagnosis. [ABSTRACT FROM AUTHOR]

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle’s Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet, successfully simplified post-processing and integrated post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent (HTBNet). First of all, we propose the Binarization of Hyperbolic Tangent (HTB), optimized along with which the segmentation network can expedite the initial convergent speed by reducing the number of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention (MSCA). Meanwhile, considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial (FMCS), which can fuse the multi-scale feature maps from channel and spatial dimensions. Finally, we adopt cross-entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet, compared with lightweight models, has achieved competitive performance and speed on Total-Text (F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

The Echo State Network (ESN) is one of the most used machine learning methods for predicting chaotic time series. The topology of an ESN comprises three layers, namely: input, hidden, and output layer. In this work, different ESN topologies are analyzed by modifying the structure and number of internal connections in the hidden layer, which neurons are connected randomly. The ESN topologies are analyzed to have 2%, 6%, 20%, 40 % , ... , and up to 100% of internal connections. The prediction error is associated to the Mean Squared Error (MSE), which results have similar values for all ESN topologies, as long as the Echo state property is guaranteed. It is highlighted that the prediction horizon obtained with 2% of internal connections, is more significant than that obtained with 100%, providing a prediction of 80 and 60 steps-ahead, respectively. The prediction results significantly impact the implementation in a field-programmable gate array (FPGA), so that an enhanced hardware realization is introduced herein by reducing the use of multipliers by more than 90% compared with a fully connected topology, without significantly affecting the measure of the prediction horizon and MSE. Another contribution is the FPGA implementation of the activation function that is an hyperbolic tangent function for which different alternatives are shown to minimize the error of the approximated function without significantly increasing the implementation cost or latency. • FPGA implementation of the hyperbolic tangent function with reduced error. • Analysis of ESN topologies to verify chaotic time series prediction of large horizons. • Hardware reduction of the ESN reflected in about 90% of less multipliers. [ABSTRACT FROM AUTHOR]

The conversion of solar radiation to thermal energy has recently attracted a lot of interest as the requirement for renewable heat and power grows. Due to their enhanced ability to promote heat transmission, nanofluids can significantly contribute to enhancing the efficiency of solar-thermal systems. This article focus solar energy aspect on the effects of the thermal radiation in the flow of a hyperbolic tangent nanofluid containing magnesium oxide (MgO) and silver (Ag) are the nanoparticle with the base fluid as kerosene through a wedge and stagnation. The system of hybrid nanofluid transport equations are transformed into ordinary differential systems using the appropriate self-similarity transformations. These systems are then determined by using the Runge-Kutta 4th order with shooting technique in the MATLAB solver. Graphs and tables illustrate the effects of significant factors on the fluid transport qualities. The velocity is growths but it is declarations in temperature by increasing values in the power law index parameter. Weissenberg numbers with higher values improve the temperature and velocity in thewedge and stagnation, respectively. The thermal radiation and Eckert number both parameters intensification the rate of heat transfer forwedge and stagnation, respectively. The heat transfer rate in fluid flowover a stagnation point is found to be 14.0346% higher compared to flowover awedge. Moreover, incorporating hybrid nanoparticles into the base fluid enhances the heat transfer rate by 8.92% for the wedge case and 13.26% for the stagnation point case. [ABSTRACT FROM AUTHOR]

Toughness and the transition from ductile to brittle behavior are long-standing concerns for applications of ferritic steel such as line-pipe. Three algorithms have been developed to fit a hyperbolic tangent curve to any Charpy V-notch dataset and estimate the uncertainty for (1) the 85% shear appearance area transition temperature and (2) the upper shelf absorbed energy. To fit the hyperbolic tangent curve to the data the (I) first algorithm relied on iterative estimation of four-parameters; (II) the second algorithm on two parameters (after simplification based on physical assumptions); and (III) the third algorithm on only one parameter (after further simplification). The algorithms were written using the open-source programing language, R. The minimum input requirements for the algorithm are experimental data for shear appearance area and absorbed energy from at least four temperatures for the four-parameter algorithm, two temperatures for the two-parameter algorithm, and one temperature for the one-parameter algorithm. The test temperatures and quantity of tests at each temperature can vary. The algorithms are described in detail and demonstrated using a data set of 12 Charpy test results (shear area and absorbed energy) from one API-5L grade X52 pipe with 4.5 mm thick Charpy bars. A future paper will test and compare the algorithms using a wide variety of Charpy V-notch data sets to clarify their applicability and possible limitations. [ABSTRACT FROM AUTHOR]

The Grey Wolf Optimization Algorithm (GWO) replicates the leadership and foraging mechanisms of the natural grey wolf and excels in solving problems in a variety of domains. However, the algorithm tends to converge to a local optimal and has a slow convergence rate. This paper proposes an enhanced Grey Wolf optimization algorithm (HTGWO) based on hyperbolic tangent inertia weights to solve this problem. HTGWO employs inertia weights based on hyperbolic tangent functions to balance GWO’s global and local search capabilities of the GWO. HTGWO has a faster convergence rate and more accurate solutions than GWO. Five classical test functions were used to construct comparative experiments between the HWGWO and five classical intelligent optimization algorithms. The comparison results indicate that HWGWO has superior convergence speed, solution precision, and stability compared with the other five classical intelligent optimization algorithms. Moreover, experimental evidence suggests that the HWGWO is more effective at solving multimodal functions than unimodal functions. In addition, HTGWO can balance exploration and exploitation by adjusting the parameters according to the characteristics of different problems.

This research investigates two-dimensional MHD incompressible boundary layer Hyperbolic Tangent nanofluid flow across a non-linear stretching plate. Similarity transformations are employed to convert the governing non-linear partial differential equations (PDEs) into coupled non-linear ordinary differential equations (ODEs). The MATLAB built-in routine bvp4c has been used for finding the numerical solutions of the dimensionless velocity, temperature, and concentration profiles. The current findings are validated with already published results. The influence of some important parameters on the velocity, temperature, and concentration profiles are displayed through graphs and tables. It is observed that for increasing values of magnetic parameter M and hyperbolic Tangent parameter We, the boundary layer thickness of the velocity profile decreases while it increases for the temperature profile.

Abstract. In this paper, we give a new proof of Iv´ady double inequality: for x > 0, we have √1 − exp − x²/ (1 + x²) 1/2 < tanh x < ³√ 1 − exp − x³/ (1 + x³) 1/2. [ABSTRACT FROM AUTHOR]

In machine learning, the input data is often given in different dimensions. As a result of the scientific papers review, it is shown that the initial data described in different types of scales and units of measurement should be converted into a single representation by normalization or standardization. The difference between these operations is shown. The paper systematizes the basic operations presented in these scales, as well as the main variants of the function normalization. A new scale of parts is suggested and examples of the data normalization for correct analysis are given. Analysis of publications has shown that there is no universal method of data normalization, but normalization of the initial data makes it possible to increase the accuracy of their classification. It is better to perform data clustering by methods using distance functions after converting all features into a single scale. The results of classification and clustering by different methods can be compared with different scoring functions, which often have different ranges of values. To select the most accurate function, it is reasonable to normalize several functions and to compare their estimates on a single scale. The rules for separating features of tree-like classifiers are invariant to scales of quantitative features. Only comparison operation is used. Perhaps due to this property, the random forest classifier, as a result of numerous experiments, is recognized as one of the best classifiers in the analysis of data of different nature.

Toughness and the transition from ductile to brittle behavior are long-standing concerns for applications of ferritic steel such as line-pipe. Three algorithms have been developed to fit a hyperbolic tangent curve to any Charpy V-notch dataset and estimate the uncertainty for (1) the 85% shear appearance area transition temperature and (2) the upper shelf absorbed energy. To fit the hyperbolic tangent curve to the data the (I) first algorithm relied on iterative estimation of four-parameters; (II) the second algorithm on two parameters (after simplification based on physical assumptions); and (III) the third algorithm on only one parameter (after further simplification). The algorithms were written using the open-source programing language, R. The minimum input requirements for the algorithm are experimental data for shear appearance area and absorbed energy from at least four temperatures for the four-parameter algorithm, two temperatures for the two-parameter algorithm, and one temperature for the one-parameter algorithm. The test temperatures and quantity of tests at each temperature can vary. The algorithms are described in detail and demonstrated using a data set of 12 Charpy test results (shear area and absorbed energy) from one API-5L grade X52 pipe with 4.5 mm thick Charpy bars. A future paper will test and compare the algorithms using a wide variety of Charpy V-notch data sets to clarify their applicability and possible limitations.

In this paper, we prove the following inequality with hyperbolic tangent: for x > 0, we have ... where the constants α = 1/2 and β = 1/6 are the best possible. [ABSTRACT FROM AUTHOR]

This article extends the previous research on the notion of a standardized call function and how to obtain an approximate model of the Black-Scholes formula via the hyperbolic tangent. Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options. This is particularly important for traders because it represents the risk of the underlying, and is the main factor in the option price. The approximation error of the suggested solution was estimated and the results compared with the most common methods available in the literature. A new formula was provided to correct some cases of underestimation of implied volatility. Graphic evidence, stress tests and Monte Carlo analysis confirm the quality of the results obtained. Finally, further literature is provided as to why implied volatility is used in decision making. [ABSTRACT FROM AUTHOR]

Transcendental nonlinear function design in deep neural accelerators principally concerns performance parameters such as area, power, delay, and throughput. Neural hardware demands resource-intensive blocks such as adders, multipliers, and nonlinear activation functions. This work addresses the issues related to the implementation of the activation function for deep neural accelerators. The proposed design implements an activation function unit with the help of stochastic computing along with clock gating techniques to reduce the active power dissipation in the hardware. But a complete deep neural network uses various activation functions in the hidden layers. To overcome the problem of implementing individual hardware design corresponding to each activation function, we have designed the streamlined composite activation function unit for neural accelerators (SCAN), which implements hyperbolic tangent and ReLU activation functions. The proposed method using stochastic computing along with clock gating is compared with other states of the art. The area is reduced by approximately 74.14 % as compared to that of CORDIC-based design. While implementing a single neuron, both area and power are reduced by manifold, enhancing the performance of deep neural accelerators. Testing accuracy and inference time are calculated using the benchmark dataset (MNIST) on AlexNet architecture. Testing accuracy in the proposed implementation is increased by 1.08 % , and loss is reduced by 40.66 % . [ABSTRACT FROM AUTHOR]

This study presents an artificial neural network approach in combination with numerical methods to calculate the heat transfer area assuming a nonlinear variation of the global heat transfer coefficient as a consequence of the thermophysical properties of the fluids, the geometry of the surfaces, and other factors. The development of the article is presented in two applications. The first application takes up the database described by Allan P. Colburn, four possibilities are proposed using functions from the field of artificial neural networks to create several approaches. The second application is presented to verify the goodness of the proposed methodology, the artificial neural network model is applied in an experimental data set of double‐pipe vertical heat exchangers, the comparison between the calculated and experimental heat transfer area shows a relative percentage error smaller than 2.8%. The results in the applications are evidence of the competitiveness of the artificial neural network for the prediction of the heat transfer area considering a variable overall heat transfer coefficient. [ABSTRACT FROM AUTHOR]

We present smooth approximations to the absolute value function |x| using sigmoid functions. In particular, x erf(x/μ) is proved to be a better smooth approximation for |x| than x tanh(x/μ) and x2+μ\sqrt {{x^2} + \mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.

Recently, enormous datasets have made power dissipation and area usage lie at the heart of designs for artificial neural networks (ANNs). Considering the significant role of activation functions in neurons and the growth of hardware-based neural networks like memristive neural networks, this work proposes a novel design for a hyperbolic tangent activation function (Tanh) to be used in memristive-based neuromorphic architectures. The purpose of implementing a CMOS-based design for Tanh is to decrease power dissipation and area usage. This design also increases the overall speed of computation in ANNs, while keeping the accuracy in an acceptable range. The proposed design is one of the first analog designs for the hyperbolic tangent and its performance is analyzed by using two well-known datsets, including the Modified National Institute of Standards and Technology (MNIST) and Fashion-MNIST. The direct implementation of the proposed design for Tanh is proposed and investigated via software and hardware modeling. [ABSTRACT FROM AUTHOR]

Many packaging cushion materials follow the hyperbolic tangent type of constitutive relation, so a hyperbolic tangent stiffness non‐linearity was derived to describe the stiffness property of the package. Transport package was modelled as the single degree of freedom (SDOF) of hyperbolic tangent spring–mass–damping (SMD) system. The displacement and velocity responses of the system were obtained by Fokker–Planck–Kolmogorov (FPK) equation. Based on the kinematic equation and integral transforming, the approximate analytic solution of the acceleration response power spectral density (PSD) of the hyperbolic tangent package was established for the first time, and the influences of system non‐linearities on the acceleration response PSD were investigated. Validation experiment with a complete packaged computer was carried out to verify the proposed approach. Non‐linearity of the stiffness influenced the acceleration response PSD through the effect of parameter γ and statistical moment mi0. The frequency corresponding to acceleration response peak was determined by the damping correlation coefficient α and parameter γ, which was determined by system characteristic parameter β, frequency parameter ω0 and statistical moment mi0. The proposed approach can be used to predict the acceleration response PSD of transport package, and the analysis has important value for packaging optimization design. [ABSTRACT FROM AUTHOR]

We propose the approximation of tanh (i.e. the hyperbolic tangent) by specific formation of cubic splines. Thus, we save many multiplications and a division required for the standard double precision evaluation of this function. The cost we have to pay is to admit at most 2–4 decimal digits of accuracy in the final approximation. As a result, a speeding in neural networks performance is experienced after implementing this new approximant as transfer function. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm to find a non-zero real root of the transcendental equations using hyperbolic tangent function. Indeed, the new proposed algorithm is based on the combination of hyperbolic tangent series and Newton Raphson method, which produces better approximate root than Newton Raphson method. The implementation of the proposed algorithm is programmed in MATLAB and Maple. Certain numerical examples are presented to validate the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. Differently from other solutions proposed in the literature, this formula is invertible; hence, it is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option's price. That is what trading desks focus on. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in the literature, we discuss the challenges of this approach. [ABSTRACT FROM AUTHOR]

A process of creating a static neural network intended for diagnosing bypass gas turbine aircraft engines by a method of categorizing the technical state of the engine flow path was considered. Diagnostics depth was "to the structural assembly". A variant of diagnosing single faults of the flow path was considered. The following tasks were set: ‒ select the best neuron activation functions in the network layers; ‒ determine the number of layers; ‒ determine the optimal number of neurons in layers; ‒ determine the optimal size of the training set. The problem was solved taking into account the influence of parameter measurement errors. The method of structure optimization implies training the network of the selected configuration using a training data set. The training was periodically interrupted to analyze the results of the network operation according to the criterion characterizing the quality of classification of the engine technical state. The assessment was performed with training and control sets. The network that provides the best value of the classification quality parameter assessed by the test set was selected as the final network. The PS-90A turbojet engine was selected as the object of diagnostics. Diagnostics was carried out on takeoff mode and during the initial climb. Primary optimization was carried out according to the data with no measurement errors. It was shown that a two-layer network with the use of neurons having a hyperbolic tangent function in both layers is sufficient to solve the problem. The size of the first network layer was finally optimized according to the data containing measurement errors. A two-layer network with eight neurons in the first layer was obtained. The share of erroneous diagnoses measured 14.5 [ABSTRACT FROM AUTHOR]

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or $\alpha$ -stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise. [ABSTRACT FROM AUTHOR]

Forage cactus presents high phytomass production in semiarid regions, due to its high energy value, high non-fibrous carbohydrate contents, high acceptability, high water reserves and easy propagation. The aim of this study was to define the best relation between plant height and cladode number of Nopalea cochenillifera with and without "pornunça". The design was performed in randomized blocks, with single cacti and "pornunça" consortium, with three repetitions. The experimental unit was composed of three rows of cactus, with spacing between rows of 1.60m and between plants of 0.20m, which is equivalent to a population density of 31,250 plants ha-1. The plant height and cladode number were related through regression models, which were evaluated by four criteria of selection. There was no difference between plant height and cladode number of cactus with and without consortium. The Nopalea cochenillifera consortium with "pornunça" is promising, and it presents agronomic viability and advantages. The adoption of the hyperbolic tangent model H=80.78*tanh(0.059*DAP0.67CN-0.052) allows the explanation of the height of Nopalea cochenillifera, with high precision and low cost, depending on the age of the plant and total number of cladode per plant. [ABSTRACT FROM AUTHOR]

In this review paper, we present a pellucid proof of how x tanh(x=y) approximates jxj and is better than ... when we are concerned with accuracy. [ABSTRACT FROM AUTHOR]

—This paper describes the architecture of a neural network for edge detection. Different filters for first-layer neurons are compared. Neural network learning based on a cosine measure algorithm shows much worse results than an error backpropagation algorithm. Optimal parameters for the first-layer neuron operation are given. The proposed architecture fulfills the stated tasks on edge selection. [ABSTRACT FROM AUTHOR]

Mechanical micro-machining of Ti6Al4V is finding great demand because of its wide range of application in various fields such as communication, optics and biomedical devices. Increasing demands on functioning and performance requires components to be free from burrs after the machining process. Presence of burrs on micro-mechanical parts or features significantly affects quality and proper assembly of the parts. Also in micro-machining, the size of burr is comparable to that of micro-features. Since the formation of burr is inevitable in any machining process, generally the deburring operation is performed to remove burrs. Burr thickness is one of the important parameters which describe the time and method necessary for the deburring operation. Burrs on micro-parts are generally characterized using scanning electron microscope, which is a time-consuming, costly and non-value-added activity. However, a proper mathematical model will help predict burr thickness easily. In this article, a mathematical model to predict burr thickness during micro-end milling of Ti6Al4V is presented. The proposed model was developed based on the principle of continuity of work at the transition from chip formation to burr formation. Ti6Al4V titanium alloy is one of the materials which generates segmented (saw-tooth) chips at low cutting speeds. Hence, initially an appropriate material constitutive model was selected based on better prediction of burr thickness. Then, to reduce the prediction error, machining temperature was evaluated for all experimental conditions and included in the model. From the initial study, it was found that Hyperbolic TANgent material model gives a better prediction compared to Johnson--Cook material model. Later, after including machining temperature into the model it was observed that the prediction error was reduced. The proposed model was validated with the experimental results. [ABSTRACT FROM AUTHOR]

This work establishes a 2D numerical model to simulate the cutting process of workpieces made of Ti–6Al–4V, by applying an improved Smoothed Particle Hydrodynamics algorithm together with a modified constitutive model based on the Johnson–Cook model known as Hyperbolic Tangent (TANH). The location information of the surface particles obtained by the SPH cutting model are used to evaluate the variation trend of surface roughness with different parameters. Parameters that affect the surface roughness are investigated in detail by using the Taguchi method and the SPH cutting model. The present work provides an efficient and cost-effective approach to determine the optimal parameters for cutting processes for Ti–6AL–4V workpieces, through computer simulations in virtual environments, instead of expensive and time-consuming cutting experiments using actual workpieces. [ABSTRACT FROM AUTHOR]

The challenge for computational rheologists is to develop efficient and stable numerical schemes in order to obtain accurate numerical solutions for the governing equations at values of practical interest of the Weissenberg number. This study presents a new approach to preserve the symmetric positive definiteness of the conformation tensor and to bound the magnitude of its eigenvalues. The idea behind this transformation lies with the matrix logarithm formulation. Under the logarithmic transformation, the eigenvalue spectrum of the new conformation tensor varies from infinite positive to infinite negative. However reconstructing the classical formulation from unbounded eigenvalues does not achieve meaningful results. This enhanced formulation, expressed in terms of the hyperbolic tangent, overcomes the failure of alternative formulations by bounding the magnitude of eigenvalues in a manner that positive definite is always satisfied. In order to evaluate the capability of the hyperbolic tangent formulation, we performed a numerical simulation of FENE-P fluid in a rectangular channel in the context of the finite element method. Under this new transformation, the maximum attainable Weissenberg number increases by 21.4% and 112.5% compared to the standard log-conformation and classical constitutive equation, respectively. [ABSTRACT FROM AUTHOR]