Fourth Hankel Determinant for a Subclass of Starlike Functions Based on Modified Sigmoid

In our present investigation, we obtain the improved third-order Hankel determinant for a class of starlike functions connected with modified sigmoid functions. Further, we investigate the fourth-order Hankel determinant, Zalcman conjecture, and also evaluate the fourth-order Hankel determinants for 2-fold, 3-fold, and 4-fold symmetric starlike functions.

Hankel determinants for starlike and convex functions associated with sigmoid functions

This paper is concerned with Hankel determinants for starlike and convex functions related to modified sigmoid functions. Sharp bounds are given for second and third Hankel determinants.

Broad Autoencoder Features Learning for Classification Problem

Activation functions such as Tanh and Sigmoid functions are widely used in Deep Neural Networks (DNNs) and pattern classification problems. To take advantages of different activation functions, the Broad Autoencoder Features (BAF) is proposed in this work. The BAF consists of four parallel-connected Stacked Autoencoders (SAEs) and each of them uses a different activation function, including Sigmoid, Tanh, ReLU, and Softplus. The final learned features can merge such features by various nonlinear mappings from original input features with such a broad setting. This helps to excavate more information from the original input features. Experimental results show that the BAF yields better-learned features and classification performances.

Broad Autoencoder Features Learning for Classification Problem

Activation functions such as Tanh and Sigmoid functions are widely used in Deep Neural Networks (DNNs) and pattern classification problems. To take advantages of different activation functions, the Broad Autoencoder Features (BAF) is proposed in this work. The BAF consists of four parallel-connected Stacked Autoencoders (SAEs) and each of them uses a different activation function, including Sigmoid, Tanh, ReLU, and Softplus. The final learned features can merge such features by various nonlinear mappings from original input features with such a broad setting. This helps to excavate more information from the original input features. Experimental results show that the BAF yields better-learned features and classification performances.

A Study of $\tau^-$ and $\mu^-$ in the Field of Nuclei Using Neural Network Techniques

The rate of a heavy lepton (muon or tau) capture by nuclei as well as the heavy lepton to electron conversion rate can be calculated when the heavy lepton wavefunction is known. Analytical calculation of the wavefunction of any of these leptons around any nucleus is not feasible owning to their small Bohr radii, on the one hand, and to the finite nuclear extend on the other. A new numerical calculation algorithm is proposed hereby, which makes use of the concept of neural networks. The main advantage of this new technique is that the wave function is produced analytically as a sum of sigmoid functions.

A novel method for in-cylinder pressure prediction using the engine instantaneous crankshaft torque

Current practices of condition assessment in large marine engines are largely based on the measurement of cylinder pressure using external kits, which poses challenges due to sensors synchronisation and durability issues, as well as the inability to perform continuous monitoring. For addressing these challenges, this study aims at developing a novel method to solve the inverse problem of predicting the pressure variations in all engine cylinders, by using the Instantaneous Crankshaft Torque (ICT) measurement for large internal combustion engines. This method is developed by considering the Initial Value Problem (IVP) technique along with the integration of a direct crankshaft dynamics model incorporating the sensitivity parameters and stability criteria calculation based on the Lyapunov Exponent (LE) as well as a state-of-the-art Nonmonotone Self-Adaptive Levenberg-Marquardt (NSALMN) optimisation algorithm. The method is tested for a number of case studies using different combustion models based on the Weibe and sigmoid functions, as well as for healthy, degraded and faulty engine conditions. The derived results demonstrate adequate accuracy exhibiting a maximum error of 0.3% in the prediction of the mean peak in-cylinder pressure. The analysis of the calculated sensitivity parameters resulted in the identification of the parameters that significantly impact the solution, thus providing improved insights for selecting the developed method settings. The developed method renders the continuous and non-intrusive in-cylinder pressures monitoring feasible, by using a permanently installed shaft power metre sensor with higher sample rates.

Global consistency in response of terrestrial ecosystem respiration to temperature

<p>Many studies have been carried out to quantify the trend of terrestrial ecosystem respiration (Re) in a warming world, but a conclusive answer has not yet been confirmed because the temperature sensitivity of Re was found inconsistent under different scales or regarding different types of respiratory flux.  Aiming at clarifying the relationship between temperature and Re across different scales, we proposed a method to counteract the confounding effect and applied nine empirical models to a 1,387 site-years FLUXNET dataset.  Regarding the temperature sensitivity of half-hourly Re records, we found a surprisingly consistent result that the sigmoid functions outcompeted other statistical models in almost all datasets (account for 82%), and on average, achieved a staggering R<sup>2</sup> value of 0.92, indicating the positive correlation between Re and temperature on fine time scale (within one site-year dataset).  Even though Re of all biomes followed sigmoid functions, the parameters of the S-curve varied strongly across sites.  This explains why measured Q<sub>10</sub> value (an index denote temperature sensitivity) largely depends on observation season and site.  Furthermore, on the interannual variation of Re, we did not find any relationship between mean annual temperature (MAT) and mean annual Re within any site, which implies that the small year-to-year variation of the sigmoid pattern is large enough to counteract the warming effect on Re.  This study thereby put forward a conceptual model to integrate the relationship between temperature and Re under different scales. It also provided evidences to support the argument that the relationship between MAT and mean annual Re (i.e., respiration under global warming) should not be inferred from studies on other temporal or spatial scales.</p>

Sigmoid functions for the smooth approximation to the absolute value function

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 \sqrt {{x^2} + \mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.

Fuzzy-Neuro Network in a CO-OFDM system: Various Membership Functions Comparison

Fuzzy-Neuro Network based nonlinear equalizer (FNN-NLE) has been used for the extenuation of nonlinearities in optical communication systems. Until now, many membership functions with resilient backpropagation activation function was used for making FNN-NLE in a coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. Despite this, no research is reflecting the comparison of different membership functions (MFs). In this paper, various membership functions such as gaussian MF, gaussian combination MF, triangular MF, difference between two sigmoidal functions MF, pi shaped MF, generalized bell shaped MF, trapezoidal MF and product of two sigmoid functions MF has been compared. From this study, the maximum performance in terms of BER is achieved with gaussian membership function has been concluded.

Applications of Modified Sigmoid Functions to a Class of Starlike Functions

The main focus of this investigation is the applications of modified sigmoid functions. Due to its various uses in physics, engineering, and computer science, we discuss several geometric properties like necessary and sufficient conditions in the form of convolutions for functions to be in the special class S S G ∗ earlier introduced by Goel and Kumar and obtaining third-order Hankel determinant for this class using modified sigmoid functions. Also, the third-order Hankel determinant for 2- and 3-fold symmetric functions of this class is evaluated.