COVID-19 Data Prediction and Visualization in Mainland China

Contemporarily, COVID-19 shows a sign of recurrence in Mainland China. To better understand the situation, this paper investigates the growth pattern of COVID-19 based on the research of past data through regression models. The proposed work collects the data on COVID-19 in Mainland China from January 21st, 2020, to April 30th, 2020, including confirmed, recovered, and death cases. Based on polynomial regression and support vector machine regressor, it predicts the further trend of COVID-19. The paper uses root mean squared error to evaluate the performance of both models and concludes that there is no best model due to the high frequency of daily changes. According to the analysis, support vector machine regressors fit the growth of COVID-19 confirmed case better than polynomial regression does. The best solution is to utilize different types of models to generate a range of prediction result. These results shed light on guiding further exploration of the growth of COVID-19. © 2023 SPIE.

Novel Degree-Based Topological Descriptors of Fenofibrate Using M-Polynomial

Chemical graph theory is currently expanding the use of topological indices to numerically encode chemical structure. The prediction of the characteristics provided by the chemical structure of the molecule is a key feature of these topological indices. The concepts from graph theory are presented in a brief discussion of one of its many applications to chemistry, namely, the use of topological indices in quantitative structure-activity relationship (QSAR) studies and quantitative structure-property relationship (QSPR) studies. This study uses the M-polynomial approach, a newly discovered technique, to determine the topological indices of the medication fenofibrate. With the use of degree-based topological indices, we additionally construct a few novel degree based topological descriptors of fenofibrate structure using M-polynomial. When using M-polynomials in place of degree-based indices, the computation of the topological indices can be completed relatively quickly. The topological indices are also plotted. Using M-polynomial, we compute novel formulas for the modified first Zagreb index, modified second Zagreb index, first and second hyper Zagreb indices, SK index, SK1 index, SK2 index, modified Albertson index, redefined first Zagreb index, and degree-based topological indices.

Wild Bootstrap-Based Bias Correction for Spatial Quantile Panel Data Models with Varying Coefficients

This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for approximating varying coefficients, including B-spline and local polynomial approximation. A fixed-effects quantile regression (FEQR) estimator is typically biased in the presence of the spatial lag variable. The wild bootstrap method is employed to attenuate the estimation bias. Simulations are conducted to study the performance of the proposed method and show that the proposed methods are stable and efficient. Further, the estimators based on the B-spline method perform much better than those of the local polynomial approximation method, especially for location-varying coefficients. Real data about economic development in China are also analyzed to illustrate application of the proposed procedure.

Estimating Moisture Content of Sausages with Different Types of Casings via Hyperspectral Imaging in Tandem with Multivariate

The moisture levels in sausages that were stored for 16 days and added with different concentrations of orange extracts to a modification solution were assessed using response surface methodology (RSM). Among the 32 treatment matrixes, treatment 10 presented a higher moisture content than that of treatment 19. Spectral pre-treatments were employed to enhance the model's robustness. The raw and pre-processed spectral data, as well as moisture content, were fitted to a regression model. The RSM outcomes showed that the interactive effects of [soy lecithin concentration] × [soy oil concentration] and [soy oil concentration] × [orange extract addition] on moisture were significant (p < 0.05), resulting in an R2 value of 78.28% derived from a second-order polynomial model. Hesperidin was identified as the primary component of the orange extracts using high-performance liquid chromatography (HPLC). The PLSR model developed from reflectance data after normalization and 1st derivation pre-treatment showed a higher coefficient of determination in the calibration set (0.7157) than the untreated data (0.2602). Furthermore, the selection of nine key wavelengths (405, 445, 425, 455, 585, 630, 1000, 1075, and 1095 nm) could render the model simpler and allow for easy industrial applications.

A novel COVID-19 predictor model inspired by Flower Pollination Algorithm

The COVID-19 outbreak turned the world upside down by infecting hundred million people, killing more than five million and disrupting everyday life across the planet. The Wuhan virus shattered the global economy and brought daily life to a grinding halt in much of the world. The second largest populated country India had no escape as well. Since the very beginning of 20th century, machine learning based methodologies have been largely applied in epidemiological data analysis in order to control diseases and other health issues. In this regard, researchers have come up with various predictor models to forecast the future impact of the Wuhan virus, so that further spreading of virus can be controlled by implementing precautionary measures. The purpose behind this work is to investigate the prediction capability of Legendre Polynomial Neural Network (LEPNN) trained using the very popular bio-inspired Flower Pollination Algorithm on the real data set of three categories of COVID cases in India as well as Odisha. The three types are the confirmed, deceased and recovery cases of daily basis. The prediction performance of the LEPNN-FPA model has been assessed with respect to the performance of two other models. © 2022 IEEE.

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach's accuracy and utility, and it is presented in symmetric forms.

Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach

We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. The objective of this research was to halt the global spread of a disease. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.

Collaborative Filtering Model of Graph Neural Network Based on Random Walk

This paper proposes a novel graph neural network recommendation method to alleviate the user cold-start problem caused by too few relevant items in personalized recommendation collaborative filtering. A deep feedforward neural network is constructed to transform the bipartite graph of user–item interactions into the spectral domain, using a random wandering method to discover potential correlation information between users and items. Then, a finite-order polynomial is used to optimize the convolution process and accelerate the convergence of the convolutional network, so that deep connections between users and items in the spectral domain can be discovered quickly. We conducted experiments on the classic dataset MovieLens-1M. The recall and precision were improved, and the results show that the method can improve the accuracy of recommendation results, tap the association information between users and items more effectively, and significantly alleviate the user cold-start problem.

Numerical analysis of fractional coronavirus model with Atangana-Baleanu derivative in Liouville-Caputo sense.

The novel coronavirus which emerged at the end of the year 2019 has made a huge impact on the population in all parts of the world. The causes of the outbreak of this deadliest virus in human beings are not yet known to the full extent. In this paper, an investigation is carried out for a new convergent solution of the time-fractional coronavirus model and a reliable homotopy perturbation transform method (HPTM) is used to explore the possible solution. In the presented model, the Atangana-Baleanu derivative in the Liouville-Caputo sense is used. The variations of the susceptible, the exposed, the infected, the quarantined susceptible (isolated and exposed), the hospitalized and the recovered population with time are presented through figures and are further discussed. The effects of selected parameters on the population with the time are also shown through figures. The convergence of solution by the HPTM is shown through tables. The results reveal that the HPTM is efficient, systematic, very effective, and easy to use in getting a solution to this new time-fractional mathematical model of coronavirus disease.

Optimization of ultrasonication-assisted extraction conditions using RSM-I-Optimal experimental design to recover vitamin D2 and K1 from selected green leafy vegetable samples

This study employed the response surface methodology to optimize the extraction conditions for recovering vitamins D2 and K1 from green leafy vegetables using ultrasonication-assisted extraction. The vitamin content was determined using an Accucore C18 column and a UPLC-Q-ToF/MS method. An RSM-I-Optimal design was used for designing the experiment to find the best combination of solvent level (mL), sonication time (min), sonication frequency (kHz), and temperature (°C). The experimental data from a 25-sample set were fitted to a second-order polynomial equation using multiple regression analysis. The extraction models had R2 values of 0.895 and 0.896, respectively, and the probability values (p < 0.0001) indicated that the regression model was highly significant. The optimal extraction conditions were: solvent level of 65 mL, sonication time of 45 min, sonication frequency of 70 kHz, and temperature of 45 °C. Under these conditions, the predicted recovery (%) values for vitamins D2 and K1 were 90.7% and 90.4%, respectively. This study has the potential to use the reported extraction method for routine quantification of vitamins D2 and K1 in the laboratory using UPLC-Q-ToF/MS.

Energy Optimal Trajectory Algorithm for a Robotic Manipulator

In the context of the decrease in the number of industrial workers and the increase in labor costs, industrial robots have developed rapidly due to their many advantages. Especially after the COVID-19 epidemics, enterprises have accelerated the upgrade of robots intellectually. The quantity of china's industrial robots grew by 20% in 2020. The 2021 year's growth will reach 21%. At the same time, in the face of the global energy crisis, power rationing, energy conservation & emission reduction, the energy savings of robots are also inevitable. Under the same starting point and ending point, the energy consumption of different motion trajectory planning is very different. Based on the current mainstream industrial robot trajectory planning methods, this paper gives the trajectory algorithm formulas and optimizes them, and then combines the Lagrangian-Euler dynamics formula to derive the energy consumption formula. By simulating mainstream 6DOF manipulator robots, set the same starting point and ending point in the MatLab environment, testing different trajectories of various methods, planning and computing time-consuming, and energy consumption of the entire trajectory. The experimental results demonstrate that the energy consumption of the shortest path method is 1.4 times that of the quartic polynomial method, and the planning time is more than 800 times that of the quartic polynomial method. The energy consumption of the cubic Bezier curve method is 8.08 times that of the quartic polynomial method, and the planning time is 781 times that of the quartic polynomial method. The energy consumption of the seventh-degree polynomial method is 1.6 times that of the fourth-degree polynomial method, and the planning time is 1.28 times that of the quartic polynomial method. The time and energy consumption of the quartic polynomial and quantic polynomial methods are almost the same. Relatively speaking, the quartic polynomial interpolation method is better than the quintic polynomial. © 2022 IEEE.

Estimating COVID-19 Cases Using Machine Learning Regression Algorithms

Background: Coronavirus refers to a large group of RNA viruses that infects the respira-tory tract in humans and also causes diseases in birds and mammals. SARS-CoV-2 gives rise to the infectious disease “COVID-19”. In March 2020, coronavirus was declared a pandemic by the WHO. The transmission rate of COVID-19 has been increasing rapidly;thus, it becomes indispensable to estimate the number of confirmed infected cases in the future. Objective: The study aims to forecast coronavirus cases using three ML algorithms, viz., support vector regression (SVR), polynomial regression (PR), and Bayesian ridge regression (BRR). Methods: There are several ML algorithms like decision tree, K-nearest neighbor algorithm, Ran-dom forest, neural networks, and Naïve Bayes, but we have chosen PR, SVR, and BRR as they have many advantages in comparison to other algorithms. SVM is a widely used supervised ML algorithm developed by Vapnik and Cortes in 1990. It is used for both classification and regression. PR is known as a particular case of Multiple Linear Regression in Machine Learning. It models the rela-tionship between an independent and dependent variable as nth degree polynomial. Results: In this study, we have predicted the number of infected confirmed cases using three ML algorithms, viz. SVR, PR, and BRR. We have assumed that there are no precautionary measures in place. Conclusion: In this paper, predictions are made for the upcoming number of infected confirmed cases by analyzing datasets containing information about the day-wise past confirmed cases using ML models (SVR, PR and BRR). According to this paper, as compared to SVR and PR, BRR performed far better in the future forecasting of the infected confirmed cases owing to coronavirus. © 2022 Bentham Science Publishers.

Polynomial Interpolation and Cubic Spline to Determine Approximate Function of COVID-19 Tweet Dataset

As we know theoretically if we are going to construct a polynomial interpolation function through a mapped base, we create an approximation function. In this study, we try to build an approximation function using all sample data available. The approximation function obtained represents the data whose graph goes through a given set of data points. We determine the value of a function at different points and specific intervals using the interpolation model. The first derivative of the function is obtained to find the growth rate of tweet data. The experimental data is a crawling tweet with the keyword COVID-19. Then we get the amount of data per time duration representing a value of the function at a node. The interpolation includes such as Lagrange, Newton's divided difference, and cubic spline. In this study, we compared polynomial interpolation with cubic splines to obtain optimal results. With the functional approach obtained, a pattern of tweets related to COVID-19 can be seen from its graph that passes through the given data points. The graph and the estimated values obtained show that the cubic spline is the optimal interpolation as an approximation function.

A stochastic algorithm for solving the posterior inference problem in topic models

Latent Dirichlet allocation (LDA) is an important probabilistic generative model and has usually used in many domains such as text mining, retrieving information, or natural language processing domains. The posterior inference is the important problem in deciding the quality of the LDA model, but it is usually non-deterministic polynomial (NP)-hard and often intractable, especially in the worst case. For individual texts, some proposed methods such as variational Bayesian (VB), collapsed variational Bayesian (CVB), collapsed Gibb's sampling (CGS), and online maximum a posteriori estimation (OPE) to avoid solving this problem directly, but they usually do not have any guarantee of convergence rate or quality of learned models excepting variants of OPE. Based on OPE and using the Bernoulli distribution combined, we design an algorithm namely general online maximum a posteriori estimation using two stochastic bounds (GOPE2) for solving the posterior inference problem in LDA model. It also is the NP-hard non-convex optimization problem. Via proof of theory and experimental results on the large datasets, we realize that GOPE2 is performed to develop the efficient method for learning topic models from big text collections especially massive/streaming texts, and more efficient than previous methods.

On smoothing of data using Sobolev polynomials

Data smoothing is a method that involves finding a sequence of values that exhibits the trend of a given set of data. This technique has useful applications in dealing with time series data with underlying fluctuations or seasonality and is commonly carried out by solving a minimization problem with a discrete solution that takes into account data fidelity and smoothness. In this paper, we propose a method to obtain the smooth approximation of data by solving a minimization problem in a function space. The existence of the unique minimizer is shown. Using polynomial basis functions, the problem is projected to a finite dimension. Unlike the standard discrete approach, the complexity of our method does not depend on the number of data points. Since the calculated smooth data is represented by a polynomial, additional information about the behavior of the data, such as rate of change, extreme values, concavity, etc., can be drawn. Furthermore, interpolation and extrapolation are straightforward. We demonstrate our proposed method in obtaining smooth mortality rates for the Philippines, analyzing the underlying trend in COVID-19 datasets, and handling incomplete and high-frequency data. © 2022 the Author(s), licensee AIMS Press.

Introduction to the special issue on Data Science for COVID-19

An introduction to this Special Issue on Data Science for COVID-19 is included in this paper. It contains a general overview about methods and applications of nonparametric inference and other flexible data science methods for the COVID-19 pandemic. Specifically, some methods existing before the COVID-19 outbreak are surveyed, followed by an account of survival analysis methods for COVID-related times. Then, several nonparametric tools for the estimation of certain COVID rates are revised, along with the forecasting of most relevant series counts, and some other related problems. Within this setup, the papers published in this special issue are briefly commented in this introductory article. [ FROM AUTHOR] Copyright of Journal of Nonparametric Statistics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.

Suitable model prediction based on COVID 19 Phase I data

This paper integrates multiple standard regression models for prediction of COVID-19 infected data. We have taken Linear Regression, Polynomial Regression and Logistic Regression for our modelling and prediction purposes. These models are created, trialled and tested in MATLAB software with available data for Covid 19 infected cases. These models evolves as we get more and more data to show better predictions. Explanations of these models are valuable. The models’ forecasts are credible to epidemiologists and provide confidence in end-users such as policy makers and healthcare institutions as an output of this study. These models can be applied at different geographic resolutions, and in this paper, it is demonstrated for states in India. The model supplies more exact forecasts, in metrics averaged across the entire India. Lastly, we analyse the performance of our models for various datapoints and regression parameters to recommend optimized regression model.

A Hybrid Interpolation Method for Fractional PDEs and Its Applications to Fractional Diffusion and Buckmaster Equations

This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. In this method, we apply the Newton interpolation numerical scheme in Laplace space, and then, the solution is returned to real space through the inverse Laplace transform. The Newton polynomial provides good results as compared to the Lagrangian polynomial, which is used to construct the Adams–Bashforth method. This procedure is used to solve fractional Buckmaster and diffusion equations. Finally, a few numerical simulations are presented, ensuring that this strategy is highly stable and quickly converges to an exact solution.

Gravity data processing of field camp geophysics in Karangsambung (2005-2019)

Gravity data was collected from a previous survey in Karangsambung 2005-2019 (before the restriction of field camp activities due to the Covid-19 pandemic). Luk-Ulo Mélange Complex in the Karangsambung area has been the subject of local and regional studies for geoscience students due to the interesting exposure of outcrops that have been interpreted as product of subduction (the Indo-Australian plate under the Eurasian plate in the Late Cretaceous to Early Paleocene time). The data for this gravimetric study based on 2592 observations over an area of inside (9.1 × 9.1) square kilometers. The gravity data were observed by students in the field camps for several years and then we compile. In this work we present simple data processing and simple calculation for modeling. The Bouguer anomaly map was processed using a density estimate of 2.31 g/cc for slab-Bouguer and terrain correction/reduction. The residual anomaly map was obtained by simple calculation of trend surface analysis (second order polynomial order). The inverse model was calculated using a simple algorithm for 2.5D and the program was built by accomodate topographic variations in the study area. Slice sections (SW-NE) of residual anomalies with a length of more than 8 km were inverted to obtain the contrast density distribution as a subsurface model. The subsurface images can then be analyzed and correlated with geological surface maps in the study area. The work in this paper is mainly presented as an ilustration of simple data processing and inverse modeling, so that the outcomes of this work are: (1) Bouguer anomaly map, (2) residual anomaly map, and (3) contrast density distribution as SW-NE section in the Karangsambung area. The value of the Bouguer anomaly map from this study is in the range of 88 to 112 mGal, and the value of the residual anomaly map is in the range of -12 to 10 mGal. The contrast density distribution from the inverse model in this study is in the range of -0.3 to 0.6 g/cc.