More than 15,000 prescriptions and over the counter drugs are available according to the US Food and Drug Administration website. Moreover, several herbal medicines and dietary supplements are readily available to add to the list of possible drugs, which can potentially cause adverse drug interactions. These are a pressing concern for all as they can interfere with many dental procedures. Additionally, the number of geriatric patients seen in routine dental practice has increased over time. This implies that there are more patients with multiple diseases and health conditions like hypertension, diabetes, problems associated with the cardiovascular, renal and gastrointestinal systems, arthritis, osteoporosis, etc. All these require patients to be on certain medications. Furthermore, advancement in the dental field has led to more complex dental procedures (implants, grafts) being carried out in a general dental practice. These advanced and slightly more invasive treatments require the use of certain drugs before, during and after the treatment like local anesthetics, vasoconstrictors, anxiolytics, analgesics and antibiotics. All of these can possibly interact with medications a patient is already taking and can also interfere with the current dental treatment and create complications. This article aims to provide necessary information about commonly encountered systemic diseases and associated treating medications, their mechanism of action, possible complications and their management. The classes of drugs discussed include anti-platelet agents, vitamin K antagonists, novel oral anticoagulants, bisphosphonates, disease-modifying anti-rheumatic drugs and oral contraceptives.

Background: A significant proportion of SARS-CoV-2-infected patients develops respiratory failure. Thromboembolism is also prevalent in coronavirus disease 2019 (Covid-19). Vitamin K plays a role in coagulation and possibly also in lung diseases. We therefore hypothesized that vitamin K is implicated in Covid-19 pathogenesis. Methods: 134 Covid-19 patients and 184 controls were included. Inactive vitamin K-dependent matrix Gla protein (i.e.dp-ucMGP) and prothrombin (i.e. PIVKA-II) were measured, which are inversely related to respectively extrahepatic and hepatic vitamin K status. Desmosine was measured to quantify elastic fiber degradation. Lung involvement and arterial calcifications severity were assessed by computed tomography. Results Dp-ucMGP was elevated in Covid-19 patients compared to controls (P=0.001). Higher dp-ucMGP was found in Covid-19 patients with poor compared to better outcomes (P=0.002). PIVKA-II was normal in 81.8%, mildly elevated in 14.0% and moderately elevated in 4.1% of Covid-19 patients not using vitamin K antagonists. Dp-ucMGP in Covid-19 patients was correlated with desmosine (P<0.001), thoracic aortic calcification (P<0.001) but not with pneumonia severity. Conclusions: Extrahepatic vitamin K status was severely reduced in Covid-19 patients, as reflected by elevated inactive MGP, and related to poor outcome. Procoagulant prothrombin activity remained preserved in the majority of Covid-19 patients, which is compatible with the increased thrombogenicity that is frequently observed in severe Covid-19. Impaired MGP activation was linked to accelerated elastic fiber degradation and premorbid vascular calcifications. A trial should assess whether increasing MGP and protein S activity by vitamin K administration improves Covid-19 outcomes.

Following legalization, cannabis has quickly become an important horticultural crop in Canada and increasingly so in other parts of the world. However, due to previous legal restrictions on cannabis research there are limited scientific data on the relationship between nitrogen (N), phosphorus (P), and potassium (K) supply (collectively: NPK) and the crop yield and quality. This study examined the response of a high delta-9-tetrahydrocannabinol (THC) Cannabis sativa cultivar grown in deep-water culture with different nutrient solution treatments varying in their concentrations (mg L^-1) of N (70, 120, 180, 250, 290), P (20, 40, 60, 80, 100) and K (60, 120, 200, 280, 340) according to a central composite design. Results demonstrated that inflorescence yield responded quadratically to N and P, with the optimal concentrations predicted to be 194 and 59 mg L^-1, respectively. Inflorescence yield did not respond to K in the tested range. These results can provide guidance to cultivators when formulating nutrient solutions for soilless cannabis production and demonstrates the utility of surface response design for efficient multi-nutrient optimization.

Predicting the outcome of a future game between two National Basketball Association (NBA) teams poses a challenging problem of interest to statistical scientists as well as the general public. In this article, we formalize the problem of predicting the game results as a classification problem and apply the principle of maximum entropy to construct NBA maximum entropy (NBAME) model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs by the NBAME model. The best NBAME model is able to correctly predict the winning team 74.4 percent of the time as compared to some other machine learning algorithms which is correct 69.3 percent of the time.

This paper presents the results of an experimental investigation about target detecting with passive sonar in Persian Gulf. Detecting propagated sounds in the water is one of the basic challenges of the researchers in sonar field. This challenge will be complex in shallow water (like Persian Gulf) and noise less vessels. Generally, in passive sonar the targets are detected by sonar equation (with constant threshold) which increase the detection error in shallow water. Purpose of this study is proposed a new method for detecting targets in passive sonars using adaptive threshold. In this method, target signal (sound) is processed in time and frequency domain. For classifying, Bayesian classification is used and prior distribution is estimated by Maximum Likelihood algorithm. Finally, target was detected by combining the detection points in both domains using LMS adaptive filter. Results of this paper has showed that proposed method has improved true detection rate about 27% compare other the best detection method.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

Exact solutions to conformable time fractional (3+1)- dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo-Miwa, the Zakharov-Kuznetsov and the modified Zakharov-Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

Based on K-ε Standard Wall turbulence model (2-Equation) and Navier-Stokes (N-S) equations defined for incompressible fluids, fluid flow behaviour around hyperloop pods in an evacuated tube was simulated using ANSYS fluent solver assuming steady state and two dimensional conditions. In this research, to develop the case studies, using combination of different head and tail shape profile, four kind of hyperloop pods were developed with the aid of SolidWorks. These four pods have been investigated for their aerodynamic behaviour as four different case scenarios. The results of simulation depicts that an atmospheric pressure of 100 Pa with blockage ratio of 0.36 in tube provides the best possible aerodynamic behaviour for the designed hyperloop pod models. This research finds that overall aerodynamic behaviour of hyperloop pods can be varied by changing the head and tail shape profile of pods and a particular combination of head and tail shape profile can provide optimally best aerodynamic capabilities. Thus, this research paper provides a novel method of obtaining best aerodynamic capabilities in hyperloop pods by designing head profile optimally in combination with tail profile. This outcome will provide major contribution towards the development of hyperloop pods in future with better aerodynamic behaviour resulting in lesser electrical energy required to propel the hyperloop pods in evacuated tube.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

The three dimensional conformable time fractional Kadomtsev-Petviashvili and the conformable time fractional modified Kawahara equations are solved by implementing the Kudryashov's procedure. The corresponding wave transformation reduces both equations to some ODEs. Balancing the nonlinear and the highest order derivative terms gives the structure of the solutions in the finite series form. The useful symbolic tools are used to solve the resultant algebraic systems. The solutions are expressed in explicit forms.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Molecularly imprinted polymers (MIPs) were synthesized and applied for the selective extraction of oblongifolin C (OC) from fruit extracts of Garcinia yunnanensis Hu. A series of experiments and computational approaches were employed to improve the efficiency of screening for optimal MIP systems in the study. The molar ratio (1:4) was chosen at last based on the comparison of the binding energy of the complexes between the template (OC) and functional monomers using density functional theory (DFT) at the RI-PBE-D3-gCP/def2-TZVP level of theory. The binding characterization and the molecular recognition mechanism of MIPs were further explained using the molecular modeling method and NMR and IR spectra data. The reusability of this approach was demonstrated in over 20 batch rebinding experiments. 140.5 mg of OC (>95% purity) was obtained from the 5 g extracts with 2 g of MIPs with the best binding properties through gradient elution program from 35% to 70% methanol-water solution. At the same time, another structural analog, 46.5 mg of guttiferone K (GK) (>88% purity), was also obtained by the gradient elution procedure. Our results showed that the structural analogs could be separated from the crude extracts by the molecularly imprinted solid-phase extraction (MISPE) using a gradient elution procedure for the first time.

The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations.

The k-means is one of the most popular and widely used clustering algorithm, however, it is limited to only numeric data. The k-prototypes algorithm is one of the famous algorithms for dealing with both numeric and categorical data. However, there have been no studies to accelerate k-prototypes algorithm. In this paper, we propose a new fast k-prototypes algorithm that gives the same answer as original k-prototypes. The proposed algorithm avoids distance computations using partial distance computation. Our k-prototypes algorithm finds minimum distance without distance computations of all attributes between an object and a cluster center, which allows it to reduce time complexity. A partial distance computation uses a fact that a value of the maximum difference between two categorical attributes is 1 during distance computations. If data objects have m categorical attributes, maximum difference of categorical attributes between an object and a cluster center is m. Our algorithm first computes distance with only numeric attributes. If a difference of the minimum distance and the second smallest with numeric attributes is higher than m, we can find minimum distance between an object and a cluster center without distance computations of categorical attributes. The experimental shows proposed k-prototypes algorithm improves computational performance than original k-prototypes algorithm in our dataset.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Feature selection is a crucial step to overcome the curse of dimensionality problem in data mining. This work proposes Recursive k-means Silhouette Elimination (RkSE) as a new unsupervised feature selection algorithm to reduce dimensionality in univariate and multivariate time-series datasets. Where k-means clustering is applied recursively to select the cluster representative features, following a unique application of silhouette measure for each cluster and a user-defined threshold as the feature selection or elimination criteria. The proposed method is evaluated on a hydraulic test rig, multi sensor readings in two different fashions: (1) Reduce the dimensionality in a multivariate classification problem using various classifiers of different functionalities. (2) Classification of univariate data in a sliding window scenario, where RkSE is used as a window compression method, to reduce the window dimensionality by selecting the best time points in a sliding window. Moreover, the results are validated using 10-fold cross validation technique. As well as, compared to the results when the classification is pulled directly with no feature selection applied. Additionally, a new taxonomy for k-means based feature selection methods is proposed. The experimental results and observations in the two comprehensive experiments demonstrated in this work reveal the capabilities and accuracy of the proposed method.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

Many clinical research datasets have a large percentage of missing values that directly impacts their usefulness in yielding high accuracy classifiers when used for training in supervised machine learning. While missing value imputation methods have been shown to work well with smaller percentages of missing values, their ability to impute sparse clinical research data can be problem specific. We previously attempted to learn quantitative guidelines for ordering cardiac magnetic resonance imaging during the evaluation for pediatric cardiomyopathy, but missing data significantly reduced our usable sample size. In this work, we sought to determine if increasing the usable sample size through imputation would allow us to learn better guidelines. We first review several machine learning methods for estimating missing data. Then, we apply four popular methods (mean imputation, decision tree, k-nearest neighbors, and self-organizing maps) to a clinical research dataset of pediatric patients undergoing evaluation for cardiomyopathy. Using Bayesian Rule Learning (BRL) to learn ruleset models, we compared the performance of imputation-augmented models versus unaugmented models. We found that all four imputation-augmented models performed similarly to unaugmented models. While imputation did not improve performance, it did provide evidence for the robustness of our learned models.

This paper presents an effective heart disease prediction model through detecting the anomalies, also known as outliers, in healthcare data using the unsupervised K-means clustering algorithm. Most existing approaches for detecting anomalies are based on constructing profiles of normal instances. However, such techniques require an adequate number of normal profiles to justify those models. Our proposed model first evaluates an \textit{optimal} value of K using Silhouette method. Next, it intends to locate anomalies that are far from a certain threshold distance with respect to their clusters. Finally, the five most popular classification techniques such as K-Nearest Neighbor (KNN), Random Forest (RF), Support Vector Machines (SVM), Naive Bayes (NB), and Logistic Regression (LR) are applied to build the resultant prediction model. The effectiveness of the proposed methodology is justified using a benchmark dataset of heart disease.

In this paper, we study the fractional pseudo-parabolic equations u_t + (−△)^s u + (−△)^s u_t = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)^s and the fractional Sobolev space H^s and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u₀) < d, the solution is global in time with I(u₀) > 0 or ∥u₀∥X_0(Ω) = 0 and blows up +∞ with I(u₀) < 0; for the critical initial energy J(u₀) = d, the solution is global in time with I(u₀) ≥ 0 and blows up at +∞ with I(u₀) < 0. The decay estimate of the energy functional for the global solution is also given.

Various type of soils have been identified based on their electrical and magnetic properties, especially with regards to peat soils. Peat soils are commonly considered as partly decomposed vegetation. In this study, electrical and magnetic properties have been used in K-means clustering to identify layers of peat soils. K-means clustering is a partitioning method that treats observations in the data. Data cores were obtained at every centimeter and examined for their electrical conductivity (σ) and magnetic susceptibility (χ_m) properties. A 291 cm core was obtained at Tegal Arum Village in South Kalimantan, Indonesia. The K-means clustering results indicate two different layers at 148 cm, and this is supported by loss on ignition (LOI) measurements. In the first layers, a 87.65% LOI was found associated with peat soils (above 248 cm). Whereas, in the second layers, there was a 26.11% LOI associated with mineral soils (below 248 cm). The results of this study using K-means clustering can be used to delineate soil layers.

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze the time-fractional nonlinear predator-prey population model. The population model is coupled fractional order nonlinear partial differential equations often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with great freedom and flexibility by choosing appropriate parameters. The convergence of results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

While lidar-based forest inventory methods have been widely demonstrated, prediction of tree diameters with lidar is not well understood. The performance metrics typically used in studies for prediction of diameters can be difficult to interpret and may not support comparative inferences between sampling designs or study areas. We evaluate a variety of lidar and k nearest neighbor (k-NN) strategies for prediction of tree diameter distributions using two indices which are easier to interpret and compare. The indices are based on the coefficient of determination (R²), and root mean square deviation (RMSD). These indices facilitate comparisons with alternative (non-lidar) inventory strategies, and with other project areas. We evaluate k nearest neighbors (k-NN) dbh density (relative frequency by dbh class) prediction strategies with lidar for 190 training plots distribute across the 800 km² Savannah River Site in South Carolina, USA. We evaluate the performance of k-NN with respect to distance metrics, number of neighbors, predictor sets, and response sets. Amongst the examined strategies we found Mahalanobis distance with k = 3 neighbors performed best according to a number of criteria.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

Permanent magnet synchronous motor (PMSM) AC servo system shows the characteristics of uncertainty, time-varying and non-linearity, which makes it difficult for traditional PID control to achieve ideal control effect. Fuzzy control has strong adaptability to the problems of parameter variation, non-linearity and model inaccuracy of the controlled object. Vector control strategy is used to study its control principle and the realization of SVPWM. Because the motor object has certain fractional order characteristics, the fuzzy parameter self-tuning PIλ control is chosen as the position regulator of servo motor. It combines the accuracy of fractional order PI control and the adaptability of fuzzy control. A simulation model of PMSM three-closed-loop system is built in MATLAB/Simulink environment. The results show that the control method is effective and can satisfy the trajectory tracking of servo control.

Banks are normally offered two kinds of deposit accounts. It consists of deposits like current/saving account and term deposits like fixed or recurring deposits. For enhancing the maximized profit from bank as well as customer perspective, term deposit can accelerate uplifting of finance fields. This paper focuses on likelihood of term deposit subscription taken by the customers. Bank campaign efforts and customer detail analysis can influence term deposit subscription chances. An automated system is approached in this paper that works towards prediction of term deposit investment possibilities in advance. This paper proposes deep learning based hybrid model that stacks Convolutional layers and Recurrent Neural Network (RNN) layers as predictive model. For RNN, Gated Recurrent Unit (GRU) is employed. The proposed predictive model is later compared with other benchmark classifiers such as k-Nearest Neighbor (k-NN), Decision tree classifier (DT), and Multi-layer perceptron classifier (MLP). Experimental study concludes that proposed model attains an accuracy of 89.59% and MSE of 0.1041 which outperform well other baseline models.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Nowadays, the research and development of on-chip LiDAR sensors for vehicle collision avoidance is growing very fast. Therefore, the assessment of the reliability in obstacle detection using the information provided by LiDAR sensors has become a key issue to be explored by the scientific community. This paper presents the design and implementation of a self-tuning method in order to maximize the reliability of an Internet-of-Things sensors network and to minimize the number of sensors to localize with the required accuracy obstacles by a detection threshold. In order to achieve this goal, models that predict accuracy (i.e., prediction error) for object localization using data collected by LIDAR sensors are designed and implemented in Webots Automobile 3D simulation tool. The approach is based on combining different techniques. Firstly, point-cloud clustering technique and an error prediction model library composed by a multilayer perceptron neural network with backpropagation, k-nearest neighbors and linear regression are explored. Secondly the above-mentioned techniques for modeling are also combined with a supervised and reinforcement machine learning technique, Q-learning in order to minimize the detection threshold. In addition, a IoT driving assistance simulated scenario with a LiDAR sensor network is designed in order to validate the prediction model and the optimal configuration of the sensor network to guarantee reliability in obstacle localization. The results demonstrate that the self-tuning method is appropriate to increase the reliability of the sensor network whereas minimizing the detection threshold

The contamination on the insulators may increase its surface conductivity and, as a consequence, electrical discharges occur more frequently, which can lead to interruptions in the power supply. To maintain reliability in the electrical distribution power system, components that have lost their insulating properties must be replaced. Identifying the components that need maintenance, is a difficult task as there are several levels of contamination that are hardly noticed during inspections. To improve the quality of inspections, this paper proposes to use the k-nearest neighbours (k-NN) to classify the levels of insulator contamination, based on the image of insulators at various levels of contamination simulated in the laboratory. Using computer vision features such as mean, variance, asymmetry, kurtosis, energy, and entropy are used for training the k-NN. To assess the robustness of the proposed approach, statistical analysis and a comparative assessment with well-consolidated algorithms such as decision tree, ensemble subspace, and support vector machine models are presented. The k-NN showed results of up to 85.17 % accuracy using the k-fold cross-validation method, with an average accuracy higher than 82 % for multi-classification of the contamination of the insulators, being superior to the compared models.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

A quantum hybrid (QH) intelligent approach that blends the adaptive search capability of the quantum-behaved particle swarm optimisation (QPSO) method with the intuitionistic rationality of traditional fuzzy k-nearest neighbours (Fuzzy k-NN) algorithm (known simply as the Q-Fuzzy approach) is proposed for efficient feature selection and classification of cells in cervical smeared (CS) images. From an initial multitude of seventeen (17) features describing the geometry, colour, and texture of the CS images, the QPSO stage of our proposed technique is used to select the best subset features (i.e. global best particles) that represent a pruned down collection of seven (7) features. Using a dataset of almost 1000 images, performance evaluation of our proposed Q-Fuzzy approach assesses the impact of our feature selection on classification accuracy by way of three experimental scenarios that are compared alongside two other approaches: The All-features (i.e. classification without prior feature selection) and another hybrid technique combining the standard PSO algorithm with the Fuzzy k-NN technique (P-Fuzzy approach). In the first and second scenarios, we further divided the assessment criteria in terms of classification accuracy based on the choice of best features and those in terms of the different categories of the cervical cells. In the third scenario, we introduced new QH hybrid techniques, i.e. QPSO combined with other supervised learning methods, and compared the classification accuracy alongside our proposed Q-Fuzzy approach. Furthermore, we employed statistical approaches to establish qualitative agreement with regards to the feature selection in scenarios 1 and 3. The synergy between the QPSO and Fuzzy k-NN in the proposed Q-Fuzzy approach marginally improves classification accuracy as manifest in the reduction in number cell features, which is crucial for effective cervical cancer detection and diagnosis.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

Hyperspectral image (HSI) classification is a mechanism of analyzing differentiated land cover in remotely sensed hyperspectral images. In the last two decades, a number of different types of classification algorithms have been proposed for classifying hyperspectral data. These algorithms include supervised as well as unsupervised methods. Each of these algorithms has its own limitations. In this research, three different types of unsupervised classification methods are used to classify different datasets i-e Pavia Center, Pavia University, Cuprite, Moffett Field. The main objective is to assess the performance of all three classifiers K-Means, Spectral Matching, and Abundance Mapping, and observing their applicability on different datasets. This research also includes spectral feature extraction for hyperspectral datasets.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

New exact solutions to conformable time fractional EW and modified EW equations are constructed by using Sine-Gordon expansion approach. The fractional traveling wave transform and homogeneous balance have significant roles in the solution procedure. The predicted solution is of the form of some finite series of multiplication of powers of cos and sin functions. The relation among trigonometric and hyperbolic functions in sense of Sine-Gordon expansion gives opportunity to construct the solutions in terms of hyperbolic functions.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

This paper considers the detection of fluctuating target in heavy-tailed clutter through the use of dynamic programming based on track-before-detect (DP-TBD) in radar systems. The clutter is modeled in terms of K-distribution, which can be widely used to describe non-Gaussian clutter received from high-resolution radars and radars working at small grazing angle. Swerling type 1 is considered to describe the target fluctuation between scans. Conventional TBD techniques suffer from significant performance loss in heavy-tailed environments due to the more frequent occurrences of target-like outliers. In this paper, we resort to DP-TBD algorithm based on prior information, which can enhance the detection performance by using the environment and target fluctuating information during the integration process of TBD. Under non-Gaussian background, the expressions of the likelihood ratio merit function for Swerling type 1 target are derived first. However, the closed analytical form of the merit function is difficult to be obtained. In order to reduce the complexity of evaluating the merit function and the computational load, an efficient approximation method as well as a two-stage detection approach is proposed and used in the integration process. Finally, several numerical simulations of the new strategy and the comparisons are presented to verify that the proposed algorithm can improve the detection performance, especially for fluctuating target in heavy-tailed clutter.

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

Speckle noise corrupt the major part of ultrasound image, because of which the quality deteriorate and loss of valuable information leads to false diagnosis. A large community of images like synthetic aperture radar (SAR) image, Synthetic image, and simulated ultrasound image, require despeckling at pre-processing stage for better processing. Cleaning the speckle from image and preserving the edge details is a vital task. Nowadays not only despeckling is considered as an important process but also preserving information at boundary and edges of image is also important. As most of the algorithms able to remove speckle noise but fails to preserve the details of edges. This paper covers several recent methods for removal of speckle noise along with various metrics opted for comparisons. The distinctive part of this paper is, a mathematical and parametric review has been done. Also a table is also included which summarizes the entire paper.

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

This paper explores the dynamic interplay of K-12 education, the Fourth Industrial Revolution (IR 4.0), and internationalization in the Philippines. Through qualitative content analysis, key themes emerged, shedding light on the impact of K-12 education on global competitiveness, challenges in embracing IR 4.0 technologies, and opportunities arising from internationalization efforts. The findings underscore the significance of curriculum alignment with international standards, comprehensive digital literacy training, and fostering a global mindset to prepare students for the digitally-driven, interconnected world. Understanding the implications of these themes is crucial for the Philippines' education system, as it navigates towards a transformative and globally competitive future. Further, this research offers evidence-based recommendations and addresses research gaps, contributing to a broader understanding of how the convergence of these forces shapes the future of Philippine education. Future research avenues may explore long-term impacts on workforce preparedness, innovative IR 4.0 integration, and the effectiveness of internationalization efforts on educational outcomes. Eventually, this study inspires an education system that nurtures learners equipped to thrive in an ever-evolving global landscape.

Based on the insight gained from single jet analysis performed earlier [1], CFD analysis on turbulent jets impinging on one another at an angle was performed. Multiple impingement angles were considered for this study to gain better understanding of the parameters affecting resultant jet growth and velocity distribution. From the study of single jet, it was concluded that the SST k-ω turbulence model was the ideal turbulence model capable of accurately predicting the flow physics of the jets exiting a fully developed pipe at low Reynolds number. Hence, for the study of impinging jets, SST k-ω turbulence model was used to study the velocity and jet growth characteristics. It became evident that the mesh alignment with the velocity vector at exit of the pipe domain plays a crucial role in the accuracy of the results. The parameter used to evaluate this condition was identified as False Diffusion and was observed to affect the TKE parameter significantly. Methods to reduce false diffusion are also discussed in this article. Based on the mesh obtained from the grid sensitivity study, jets impinging at 30, 45 and 60 degrees at Reynolds number of 7500 were numerically analyzed. It was observed that the profile of the resultant jet closely matched with the prediction of elliptical profile predicted by past researchers, [2] and [3]. Also, it was seen that higher jet growth was predicted in case of jets impinging at a higher impingement angle.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

Suitable measures of grazing impacts on ground cover, that enable separation of the effects of climatic variations, are needed to inform land managers and policy makers across the arid rangelands of the Northern Territory of Australia. This work developed and tested a time-series, change-point detection method for application to time series of vegetation fractional cover derived from Landsat data to identify irregular and episodic ground-cover growth cycles. These cycles were classified to distinguish grazing impacts from that of climate variability. A measure of grazing impact was developed using a multivariate technique to quantify the rate and degree of ground cover change. The method was successful in detecting both long term (> 3 years) and short term (< 3 years) growth cycles. Growth cycle detection was assessed against rainfall surplus measures indicating a relationship with high rainfall periods. Ground cover change associated with grazing impacts was also assessed against field measurements of ground cover indicating a relationship between both field and remotely sensed ground cover. Cause and effects between grazing practices and ground cover resilience can now be explored in isolation to climatic drivers. This is important to the long term balance between ground cover utilisation and overall landscape function and resilience.

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. It has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7. Any polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7, we give an explicit construction of a Pogorelov and a non-Pogorelov polytopes. Any Pogorelov polytope different from Löbel polytopes can be constructed from the 5- or the 6-barrel by cuttings off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes there is a stronger result. Any fullerene different from the 5-barrel and the (5, 0)-nanotubes can be constructed by only cuttings off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result can not be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cuttings off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons.

The visualization of hyperspectral images in display devices, having RGB colour composition channels is quite difficult due to the high dimensionality of these images. Thus, principal component analysis has been used as a dimensionality reduction algorithm to reduce information loss, by creating uncorrelated features. To classify regions in the hyperspectral images, K-means clustering has been used to form clusters/regions. These two algorithms have been implemented on the three datasets imaged by AVIRIS and ROSIS sensors.

A non-Newtonian fluid model is used to investigate the two-dimensional pulsatile blood flow through a tapered artery with a stenosis. The mixed convection effects of heat and mass transfer are also taken into account. By applying non-dimensionalization and radial coordinate transformation, we simplify the system in a tube. Under the finite difference scheme, numerical solutions are calculated for velocity, temperature concentration, resistance, impedance, wall shear stress and shearing stress at the stenosis throat. Finally, Quantitative analysis is carried out.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

With a data revolution underway for some time, there is an increasing demand for formal privacy protection mechanisms that are not so destructive. Hereof microaggregation is a popular high-utility approach designed to satisfy the popular k-anonymity criteria while applying low distortion to data. However, standard performance metrics are commonly based on mean square error, which will hardly capture the utility degradation related to a specific application domain of data. In this work, we evaluate the performance of k-anonymous microaggregation in terms of the loss in classification accuracy of the machine learned models built from perturbed data. Systematic experimentation is carried out on four microaggregation algorithms that are tested over four data sets. The empirical utility of the resulting microaggregated data is assessed using the learning algorithm that obtains the highest accuracy from original data. Validation tests are performed on a test set of non perturbed data. The results confirm k-anonymous microaggregation as a high-utility privacy mechanism in this context and distortion based on mean squared error as a poor predictor of practical utility. Finally, we corroborate the beneficial effects for empirical utility of exploiting the statistical properties of data when constructing privacy preserving algorithms.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

This paper deals with the analysis of trends in road accidents on major highways in Brazil. Using updated time series techniques, our results indicate that a low degree of long memory was detected in the series with shocks having transitory effects over time. We further find that the number of accidents taking place in Brazil has been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we use the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determine variation in the different residuals. Also, we use non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduce WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we show 5-fold cross validation to verify our model.

Increased nutrient withdrawal by rapidly expanding intensive cropping systems, in combination with imbalanced fertilization, is leading to potassium (K) depletion from agricultural soils in Asia. There is an urgent need to better understand the soil K-supplying capacity and K-use efficiency of crops to address this issue. Maize is increasingly being grown in rice-based systems in South Asia, particularly in Bangladesh and North East India. The high nutrient extraction, especially K, however, causes concerns for the sustainability of maize production systems in the region. The present study was designed to estimate, through a plant-based method, the magnitude, and variation in K-supplying capacity of a range of soils from the maize-growing areas and the K-use efficiency of maize in Bangladesh. Eighteen diverse soils were collected from several upazillas (or sub-districts) under 11 agro-ecological zones to examine their K-supplying capacity from the soil reserves and from K fertilization (@ 100 mg K kg-1 soil) for successive seven maize crops grown up to V10-V12 in pots inside a net house. A validation field experiment was conducted with five levels of K (0, 40, 80, 120 and 160 kg ha-1) and two fertilizer recommendations based on “Nutrient Expert for Maize-NEM” and “Maize Crop Manager-MCM” decision support tools (DSSs) in 12 farmers’ fields in Rangpur, Rajshahi and Comilla districts in Bangladesh. Grain yield and yield attributes of maize responded significantly (P < 0.001) to K fertilizer, with grain yield increase from 18 to 79% over control in all locations. Total K uptake by plants not receiving K fertilizer, considered as potential K-supplying capacity of the soil in the pot experiment, followed the order: Modhukhali >Mithapukur >Rangpur Sadar >Dinajpur Sadar >Jhinaidah Sadar >Gangachara >Binerpota >Tarash >Gopalpur >Daudkandi >Paba >Modhupur >Nawabganj Sadar >Shibganj >Birganj >Godagari >Barura >Durgapur. Likewise in the validation field experiment, the K-supplying capacity of soils was 83.5, 60.5 and 57.2 kg ha-1 in Rangpur, Rajshahi, and Comilla, respectively. Further, the order of K-supplying capacity for three sites was similar to the results from pot study confirming the applicability of results to other soils and maize-growing areas in Bangladesh and similar soils and areas across South Asia. Based on the results from pot and field experiments, we conclude that the site-specific K management using the fertilizer DSSs can be the better and more efficient K management strategy for maize.

Data mining plays a critical role in the sustainable decision making. The k-prototypes algorithm is one of the best-known algorithm for clustering both numeric and categorical data. Despite this, however, clustering a large number of spatial object with mixed numeric and categorical attributes is still inefficient due to its high time complexity. In this paper, we propose an efficient grid-based k-prototypes algorithms, GK-prototypes, which achieves high performance for clustering spatial objects. The first proposed algorithm utilizes both maximum and minimum distance between cluster centers and a cell, which can remove unnecessary distance calculation. The second proposed algorithm as extensions of the first proposed algorithm utilizes spatial dependence that spatial data tend to be more similar as objects are closer. Each cell has a bitmap index which stores categorical values of all objects in the same cell for each attribute. This bitmap index can improve the performance in case that a categorical data is skewed. Our evaluation experiments showed that proposed algorithms can achieve better performance than the existing pruning technique in the k-prototypes algorithm.

Animal behavior analysis is a crucial tasks for the industrial farming. In an indoor farm setting, extracting Key joints of animal is essential for tracking the animal for longer period of time. In this paper, we proposed a deep network that exploit transfer learning to trained the network for the pig skeleton extraction in an end to end fashion. The backbone of the architecture is based on hourglass stacked dense-net. In order to train the network, key frames are selected from the test data using K-mean sampler. In total, 9 Keypoints are annotated that gives a brief detailed behavior analysis in the farm setting. Extensive experiments are conducted and the quantitative results show that the network has the potential of increasing the tracking performance by a substantial margin.

This paper uses the $\exp(-\Phi(\xi))$-Expansion method to investigate solitons to the M-fractional nonlinear Schrödingers equation with cubic nonlinearity. The results obtained are dark solitons, trigonometric function solutions, hyperbolic solutions and rational solutions. Thus, the constraint relations between the model coefficients and the traveling wave frequency coefficient for the existence of solitons solutions are also derived.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

General characteristics of K changes together with their fine structure associated with ground flashes in Sri Lanka in the tropics are presented. It is found that on average there are about 2 K changes associated with each return stroke. Analysis of the fine structure of the K changes shows that the K change is a chaotic pulse burst. Some of these chaotic pulse bursts start and the others end as a regular pulse bursts. Sometimes the chaotic part occurs in between two regular pulse bursts. This is in agreement with the recent published results that claim that chaotic pulse bursts are a random superposition of regular pulse bursts. The results show that the small step fields identified in the literature as K changes are the static fields associated with these pulse bursts.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of creep-damage process in salt rock. A computer-controlled creep setup is employed to carry out a creep test of salt rock lasted as long as 359 days under a constant uniaxial stress. The AE space-time evolution and energy releasing characteristics during creep test are studied in the meantime. A new creep-damage model is proposed on the basis of fractional derivative by combining the AE statistical regularity. It indicates that the AE data in non-decay creep process of salt rock can be divided into three stages. Furthermore, the parameters of new creep-damage model are determined by Quasi-Newton method. The fitting analysis suggests that the creep-damage model based on fractional derivative in this paper provides a precise description of full creep regions in salt rock.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

Different forces play a key-role in the stability of food colloid dispersions. Focus is here on those controlling attraction and/or repulsion, which concur to stabilization, phase separation, coagulation, and are quite evident in water-based systems. Combination of attractive and repulsive forces favors, or hinders, the association of colloid entities; such processes are often met in food technology. The above processes depend on the forces at work, and on colloid concentration in the medium (i.e. on inter-particle distance). Worked examples deals with milk manipulation procedures, ending in cheese formation. The whole milk-working sequence is controlled by the combination of forces leading to aggregation and phase separation of casein and other milk components. Thereafter, one gets either fresh, for prompt consumption, or aged cheeses. The combination of attractive (van der Waals, vdW, and depletion) with repulsive (double layer, DL, but also with steric) forces results in the dominance of aggregation versus dispersion modes in all steps of milk transformation, which depend on the distance among colloid particles, on the amplitude of the mentioned forces, and on their decay length. The combined role of double layer and van der Waals (vdW) forces is at the basis of the DLVO theory on colloid stability, which is properly modified when these forces overlap with steric stabilization and, eventually, with depletion. Steric effects are dispersive, depletion ones favor colloid nucleation in a single phase. The milk manipulation chain is a worked example of the intriguing association features controlled by the mentioned forces (and of ancillary ones, as well), and indicates which forces favor the formation of products such as Parmesan or Mozzarella cheese, but are not alien to the preparation of many other dairy products.

Although the signaling function of Na/K ATPase is been studied for decades, the chasm between the pumping function and the signaling function of Na/K – ATPase is still an open issue. This article explores the relationship between ion pumping and signaling with attention to the amplification of oxidants through this signaling function. Starting with some experimental observations published by our laboratories and others, we develop some predictions regarding cellular oxidant stress.

In this study we used a non-autonomous Chua’s Circuit, and the fractional Lorenz chaos system together with a detection method from Extension theory to analyze the voltage signals. The measured bearing signals by acceleration sensor were introduced into the master and slave systems through a Chua’s Circuit. In a chaotic system minor differences can cause significant changes that generate dynamic errors, and extension matter-element models can be used to judge the bearing conditions. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from Discrete Fourier Transform analysis, Wavelet analysis and an integer order chaos system. The diagnostic ratio showed the fractional order master and slave chaos system calculations. The results show that the method presented in this paper is very suitable for monitoring the operational state of ball bearing system to be superior to the other methods. The diagnosis ratio was better and there were other significant advantages such as low cost and few.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Mints emit diverse scents that exert specific biological functions and are relevance for applications. The current work strives to develop electronic noses that can electronically discriminate the scents emitted by different species of Mint as alternative to conventional profiling by gas chromatography. Here, 12 different sensing materials including 4 different metal oxide nanoparticle dispersions (AZO, ZnO, SnO2, ITO), one Metal-Organic Frame as Cu(BPDC), and 7 different polymer films including PVA, PEDOT: PSS, PFO, SB, SW, SG, PB were used for functionalizing of QCM sensors. The purpose was to discriminate six economically relevant Mint species (Mentha x piperita, Mentha spicata, Mentha spicata ssp. crispa, Mentha longifolia, Agastache rugosa, and Nepeta cataria). The adsorption and desorption datasets obtained from each modified QCM sensor were processed by three different classification models including Principal Component Analy-sis (PCA), Linear Discriminant Analysis (LDA), and k-Nearest Neighbor Analysis (k-NN). This allowed discriminating the different Mints with classification accuracies of 97.2% (PCA), 100% (LDA), and 99.9% (k-NN), respectively. Prediction accuracies with a repeating test measurement reached up to 90.6% for LDA, and 85.6% for k-NN. These data demonstrate that this electronic nose can discriminate different Mint scents in a reliable and efficient manner.

Hyperspectral imaging provides vital information about the objects and elements present inside the image. That’s why they are very useful in satellite imagery as well as image forensics. Hyperspectral document analysis (HSDI) can be used for document authentication using ink analysis which can provide sufficient information about the composition and type of ink. In this project, we have implemented HSDI based ink classification technique using Principle Component Analysis for dimensionality reduction and K-means clustering for ink classification. This is unsupervised learning approach and it is very simple and efficient in order to classify limited number of bands. We have used this technique to classify 33 different bands of ink.

Hyper spectral imaging (HSI) is a technique that is used to obtain the spectrum for each pixel in the image. It helps in finding objects and identifying materials etc. Such an identification is very difficult using other imaging techniques. It allows the researchers to investigate the documents without any physical contact. Nowadays detection of unequal Ink mismatch based on HSI has shown vast improvement in distinguishing the inks. Detection of unequal Ink mismatch is an unbalanced clustering problem. This paper used K-means Clustering for ink mismatch detection. K-means Clustering find same subgroups in the data based on Euclidean distance. This paper demonstrates performance in unequal Ink mismatch based on HSI.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.