In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

The logistic sigmoid function curve provides an accurate description of the baroreflex input-output relationship and is the most commonly used equation for this purpose. The threshold (Thr) and saturation (Sat) values for the baroreflex are commonly defined as the values of mean arterial pressure (MAP) at which the reflexly controlled variable (e.g., heart rate or sympathetic nerve activity) is...

-The sigmoid fimction & very widely used as a neuron activation fimction in artificial neural networks. which makes its attributes a matter o f some interest. This paper presents some general results on the derivatives o f the sigmoid. These results relate the coefficients o f various derivatives to standard number sequences from combinatorial theory, and thus provide a standard efficient way o...

As our colleague so aptly demonstrated ( http://www.win-vector.com/blog/2011/09/the-simplerderivation-of-logistic-regression/ (link) ) there is one derivation of Logistic Regression that is particularly beautiful. It is not as general as that found in Agresti[Agresti, 1990] (which deals with generalized linear models in their full generality), but gets to the important balance equations very qu...

This paper discusses the representability of discrete logit-type models including multinomial logit and nested logit model from a mathematical approach. It is shown that the logit-type models can be reconstructed from mathematical approximation theory with sigmoidal functions widely used in Neural Network modeling without the basic assumptions such as IIA and iid, and the distribution (or densi...

The softmax link is used in many probabilistic model dealing with both discrete and continuous data. However, efficient Bayesian inference for this type of model is still an open problem due to the lack of efficient upper bound for the sum of exponentials. We propose three different bounds for this function and study their approximation properties. We give a direct application to the Bayesian t...

Short-term Load Forecast (STLF) is a load forecasting that very important to study because it determines the operating pattern of electrical system. Forecasting errors, both positive and negative, result in considerable losses costs increase ultimately lead waste. STLF research Indonesia, especially State Electricity Company (PLN Sulselrabar), has yet be widely used. Methods mainly used are man...

In this article we present the multivariate approximation of time splitting random functions defined on a box or RN,N∈N, by neural network operators quasi-interpolation type. We achieve these approximations obtaining quantitative-type Jackson inequalities engaging modulus continuity related function its partial high-order derivatives. use density to define our operators. These derive from logis...

Neural network is one of the new soft computing methods commonly used for prediction of the thermodynamic properties of pure fluids and mixtures. In this study, we have used this soft computing method to predict the coefficients of the Antoine vapor pressure equation. Three transfer functions of tan-sigmoid (tansig), log-sigmoid (logsig), and linear were used to evaluate the performance of diff...

Special attention must be paid to an efficient approximation of the sigmoid function in implementing FPGA-based reprogrammable hardware-based artificial neural networks. Four previously published piecewise linear and one piecewise second-order approximation of the sigmoid function are compared with SIG-sigmoid, a purely combinational approximation. The approximations are compared in terms of sp...