Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more precise performance of the model, fractional-order derivatives have been used to solve the disease model numerically. The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts (OC) and bone formation or osteoblasts (OB). The connections of OC and OB are represented by a nonlinear differential system based on the cellular components, which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD. Untreated myeloma causes by increasing the OC and reducing the osteoblasts, resulting in net bone waste the tumor growth. The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation (LVMBP) neural networks (NN), i.e., LVMBPNN. The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN. The static structural performances are 82% for investigation and 9% for both learning and certification. The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism. To accomplish the capability, steadiness, accuracy, and ability of the LVMBPNN, the performances of the error histograms (EHs), mean square error (MSE), recurrence, and state transitions (STs) will be provided.     

Effect of pre-steaming on production of partially-parboiled rice using hot-air fluidization technique

Fluidization technique was widely used to dry agriculture products because of its effectiveness in drying. To produce partial-parboiled rice using hot-air fluidization technique has been received increasing attention due to simplicity of operation. Thus, the purpose of this work was to investigate the effects of pre-steaming time and drying temperatures on qualities of partial-parboiled rice. The results revealed that head rice yield, pasting temperature and degree of gelatinization increased with an increase in pre-steaming time whereas white belly decreased. The percentage of water uptake of pre-steamed rice decreased with an increase in drying temperature while the percentage of solid loss and stickiness were not affected. The hardness of pre-steamed rice was higher than that of reference rice and it increased with an increase in drying temperature. To obtain the suitable conditions for producing partially-parboiled rice using hot-air fluidization technique, paddy was soaked at temperature of 80 °C for 5 h and then it was blown with saturated steam temperature of 102 °C for 70 s (pre-steaming). After that it was dried using fluidization technique at hot-air temperature of 140 °C for 2 min and then it was tempered for 30 min; furthermore, it was ventilated at ambient air temperature until the final moisture content was approximately 14–16% d.b.     

An Intelligence Computational Approach for the Fractional 4D Chaotic Financial Model

The main purpose of the study is to present a numerical approach to investigate the numerical performances of the fractional 4-D chaotic financial system using a stochastic procedure. The stochastic procedures mainly depend on the combination of the artificial neural network (ANNs) along with the Levenberg-Marquardt Backpropagation (LMB) i.e., ANNs-LMB technique. The fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional order α. The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and 1. The data proportion is applied as 73%, 15%, and 12% for training, testing, and certification to solve the chaotic fractional system. The acquired results are verified through the comparison of the reference solution, which indicates the proposed technique is efficient and robust. The 4-D chaotic model is numerically solved by using the ANNs-LMB technique to reduce the mean square error (MSE). To authenticate the exactness, and consistency of the technique, the obtained performances are plotted in the figures of correlation measures, error histograms, and regressions. From these figures, it can be witnessed that the provided technique is effective for solving such models to give some new insight into the physical behavior of the model.     

Swarming Computational Techniques for the Influenza Disease System

The current study relates to designing a swarming computational paradigm to solve the influenza disease system (IDS). The nonlinear system’s mathematical form depends upon four classes: susceptible individuals, infected people, recovered individuals and cross-immune people. The solutions of the IDS are provided by using the artificial neural networks (ANNs) together with the swarming computational paradigm-based particle swarm optimization (PSO) and interior-point scheme (IPA) that are the global and local search approaches. The ANNs-PSO-IPA has never been applied to solve the IDS. Instead a merit function in the sense of mean square error is constructed using the differential form of each class of the IDS and then optimized by the PSOIPA. The correctness and accuracy of the scheme are observed to perform the comparative analysis of the obtained IDS results with the Adams solutions (reference solutions). An absolute error in suitable measures shows the precision of the proposed ANNs procedures and the optimization efficiency of the PSOIPA. Furthermore, the reliability and competence of the proposed computing method are enhanced through the statistical performances.     

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

The purpose of this paper is to present a numerical approach based on the artificial neural networks (ANNs) for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system. The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation (LMB), named the ANNs-LMB. This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution. Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model. The selection of the data to solve the fractional-order chaotic financial model are selected as 75% for training, 10% for testing, and 15% for certification. The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise. The obtained results are testified to reduce the mean square error (MSE) for solving the fractional model and verified through the various measures including correlation, MSE, regression histogram of the errors, and state transition (ST).     

Enzymatic preparation of enantiomerically pure sn-2,3-diacylglycerols: A stereoselective ethanolysis approach

Stereoselective ethanolysis of monoacid TAG by immobilized Rhizomucor miehei lipase (RML) was studied for preparation of optically pure sn-2,3-DAG. Trioctanoylglycerol (TO) was used as a model substrate. The enantiomeric purity of the product, sn-2,3-dioctanoylglycerol (sn-2,3-DO), was very high (percent enantiomeric excess >99%) when an excess of ethanol was used. The result indicated that RML was highly stereoselective toward the sn-1 position of TO under conditions of excess ethanol. The stereoselectivity of RML depended on the amount of ethanol. The larger the amount of ethanol was, the higher the stereoselectivity became. After optimizing the parameters such as reactant molar ratio, water content, and temperature, (ethanol/TO molar ratio =31∶1 and water content =7.5 wt% of the reactants at 25°C), optically pure sn-2,3-DO was obtained at 61.1 mol% in the glyceride fraction in 20 min. The above conditions were further applied for ethanolysis of monoacid TAG with different acyl groups such as tridecanoylglycerol (C10∶0), tridodecanoylglycerol (C12∶0), tritetradecanoylglycerol (C14∶0) and trioctadecenoylglycerol [triolein, (C18∶1)]. The yields and enantiomeric purities of 1,2(2,3)-DAG were dramatically reduced when TAG with FA longer than decanoic acid were used.     

Novel Computing for the Delay Differential Two-Prey and One-Predator System

The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system. The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system. Therefore, a stochastic numerical paradigm based artificial neural network (ANN) along with the Levenberg-Marquardt backpropagation (L-MB) neural networks (NNs), i.e., L-MBNNs is proposed to solve the dynamical two-prey and one-predator model. Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs. The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13% for testing, 12% for authorization and 75% for training. The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and one-predator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10⁻⁰⁵ to 10⁻⁰⁷. To check the validation, constancy, validity, exactness, competence of the L-MBNNs, the obtained state transitions (STs), regression actions, correlation presentations, MSE and error histograms (EHs) are also provided.     

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans , infected humans , recovered humans , infected vectors , and susceptible vector based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.