Novel Low Complexity BP Decoding Algorithms for Polar Codes: Simplifying on Non-Linear Operations

The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introduces high-complexity non-linear operations in the iterative messages update process, this paper proposes to simplify these operations and develops two novel low complexity BP decoding algorithms, namely, exponential BP (Exp-BP) decoding algorithm and quantization function BP (QF-BP) decoding algorithm. The proposed algorithms simplify the compound hyperbolic tangent function by using probability distribution fitting techniques. Specifically, the Exp-BP algorithm simplifies two types of non-linear operations into single non-linear operation using the piece-wise exponential model function, which can approximate the hyperbolic tangent function in the updating formula. The QF-BP algorithm eliminates non-linear operations using the non-uniform quantization in the updating formula, which is effective in reducing computational complexity. According to the simulation results, the proposed algorithms can reduce the computational complexity up to 50% in each iteration with a loss of less than 0.1 dB compared with the BP decoding algorithm, which can facilitate the hardware implementation.

Wavelets as activation functions in Neural Networks

Traditionally, a few activation functions have been considered in neural networks, including bounded functions such as threshold, sigmoidal and hyperbolic-tangent, as well as unbounded ReLU, GELU, and Soft-plus, among other functions for deep learning, but the search for new activation functions still being an open research area. In this paper, wavelets are reconsidered as activation functions in neural networks and the performance of Gaussian family wavelets (first, second and third derivatives) are studied together with other functions available in Keras-Tensorflow. Experimental results show how the combination of these activation functions can improve the performance and supports the idea of extending the list of activation functions to wavelets which can be available in high performance platforms.

A study of sharp coefficient bounds for a new subfamily of starlike functions

In this article, by employing the hyperbolic tangent function tanhz, a subfamily $\mathcal{S}_{\tanh }^{\ast }$ S tanh ∗ of starlike functions in the open unit disk $\mathbb{D}\subset \mathbb{C}$ D ⊂ C : $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$ D = { z : z ∈ C and | z | < 1 } is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class $\mathcal{S}_{\tanh }^{\ast } $ S tanh ∗ of starlike functions in $\mathbb{D}$ D . In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here.

Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials

Nanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the rotation effect. The thermal energy expression is derived by the contribution of Joule heat and viscous dissipation. Flow equations were modeled by using the concept of boundary layer theory, which occurs in the form of a coupled system of partial differential equations (PDEs). To reduce the complexity, the derived PDEs (partial differential equations) were transformed into a set of ordinary differential equations (ODEs) by engaging in similarity transformations. Afterwards, the converted ODEs were handled via a finite element procedure. The utilization and effectiveness of the methodology are demonstrated by listing the mesh-free survey and comparative analysis. Several important graphs were prepared to show the contribution of emerging parameters on fluid velocity and temperature profile. The findings show that the finite element method is a powerful tool for handling the complex coupled ordinary differential equation system, arising in fluid mechanics and other related dissipation applications in applied science. Furthermore, enhancements in the Forchheimer parameter and the Weissenberg number are necessary to control the fluid velocity.

Novel Modeling of Parameters Related to Intra-Firm Diffusion Innovation

In this paper, we present a novel intra-firm diffusion model to predict the variation of Penetration Level (PL) with the Intensity of Use (IU) and Speed of Adoption (SA) with respect to information and communication technologies (I.C.T) within Tunisian Small Medium Enterprises (SMEs). The study was motivated by the work of Youssef et al., (2014), and its inspired data scope/range. The method of modeling focuses on optimization and non-linear regression. The first model has the capacity to compute the variation of PL with IU. However, this first model was modified to a second model through transformation in order to derive physical meaning to the parameters. The modified second model shows a quasi-vertical curvature which approximates the reciprocal of hyperbolic tangent. The Variation of PL with the SA was computed using the second model which estimated the parameters with the variables explaining about 62% variation in PL with SA &chi;2=0.0655, R2=0.61651 . We further formulated a third model to predict correlation of SA with PL, while imposing boundary assumptions to avoid problems of divergence; with the final model having a PL as the only adjustable parameter. The model exhibited a plateau effect at points (0.9933,0.4373) and (0,0) between two steeply vertical asymptotes at -0.06105 and 1.0013, respectively. The developed model can be useful for eliciting information when data from different countries (or surveys) are compared for same or different span time through examining the behavior of the parameters, especially after Covid-19 era.

An adiabatic method to train binarized artificial neural networks

An artificial neural network consists of neurons and synapses. Neuron gives output based on its input according to non-linear activation functions such as the Sigmoid, Hyperbolic Tangent (Tanh), or Rectified Linear Unit (ReLU) functions, etc.. Synapses connect the neuron outputs to their inputs with tunable real-valued weights. The most resource-demanding operations in realizing such neural networks are the multiplication and accumulate (MAC) operations that compute the dot product between real-valued outputs from neurons and the synapses weights. The efficiency of neural networks can be drastically enhanced if the neuron outputs and/or the weights can be trained to take binary values $$\pm 1$$ ± 1 only, for which the MAC can be replaced by the simple XNOR operations. In this paper, we demonstrate an adiabatic training method that can binarize the fully-connected neural networks and the convolutional neural networks without modifying the network structure and size. This adiabatic training method only requires very minimal changes in training algorithms, and is tested in the following four tasks: the recognition of hand-writing numbers using a usual fully-connected network, the cat-dog recognition and the audio recognition using convolutional neural networks, the image recognition with 10 classes (CIFAR-10) using ResNet-20 and VGG-Small networks. In all tasks, the performance of the binary neural networks trained by the adiabatic method are almost identical to the networks trained using the conventional ReLU or Sigmoid activations with real-valued activations and weights. This adiabatic method can be easily applied to binarize different types of networks, and will increase the computational efficiency considerably and greatly simplify the deployment of neural networks.

Inclusion of hybrid nanoparticles in hyperbolic tangent material to explore thermal transportation via finite element approach engaging Cattaneo-Christov heat flux

This report is prepared to examine the heat transport in stagnation point mixed convective hyperbolic tangent material flow past over a linear heated stretching sheet in the presence of magnetic dipole. Phenomenon of thermal transmission plays a vital role in several industrial manufacturing processes. Heat generation is along with thermal relaxation due to Cattaneo-Christov flux is engaged while modeling the energy equation. In order to improve the thermal performance, inclusion of hybrid nanoparticles is mixed in hyperbolic tangent liquid. The conservation laws are modeled in Cartesian coordinate system and simplified via boundary layer approximation. The modeled partial differential equations (PDEs) system are converted into ordinary differential equations (ODEs) system by engaging the scaling group transformation. The converted system of modeled equations has been tackled via finite element procedure (FEP). The efficiency of used scheme has been presented by establishing the grid independent survey. Moreover, accurateness of results is shown with the help of comparative study. It is worth mentioning that the inclusion of hybrid nanoparticles has significant higher impact on heat conduction as compared with nanoparticle. Moreover, hybrid nanoparticles are more efficient to conduct maximum production of heat energy as compared with the production of heat energy of nanoparticles. Hence, hybrid nanoparticles (MoS2/Ag) are observed more significant to conduct more heat energy rather than nanoparticle (Ag).