A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm.

In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.

Establishing the Durability and Reliability of a Dental Bur Based on the Wear.

This paper analyzes the phenomenon that conditions the durability and reliability of a type of dental bur based on the wear of the active part and with effect on its quality. For the experimental study, a conical-cylindrical dental bur and a sample dental material in cobalt-chromium alloy, cylindrical shape, tested on a specially made experimental installation were used. In this paper, the most significant parameter was considered (loss of mass, mw, through the wear of the active part of a tested dental bur), which highlights the studied wear phenomenon. This is useful for the establishment of the durability and reliability of the dental bur by the extension of the lifetime or even optimization of its operation. The wear phenomenon of the active part of dental bur is studied based on the results and experimental data obtained in the work process that was validated by interpolation and led to polynomial functions which approximate very well the dependent parameter, mw, considered in the experimental program. The results of the interpolation showed that in the first 11 h of work, the dental bur works with high efficiency (allow optimizing operation or offering new ideas for constructive solutions), after which it can be easily decommissioned; i.e., it should be replaced with a new one (establishing some possible criteria for replacing the used dental bur).

A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation.

This study formulates a Monkeypox model with protected travelers. The fixed point theorem is used to obtain the existence and uniqueness of the solution with Ulam-Hyers stability for the analysis of the solution to the model. The Newton polynomial interpolation scheme is employed to solve an approximate solution of the fractional Monkeypox model. The numerical simulations and the graphical representations suggest that the fractional order affects the dynamics of the Monkeypox. The fractional order shows other underlining transmission trends of the Monkeypox disease. We conclude that the result obtained for each compartment conforms to reality as the fractional order approaches unity.

COVID-19 epidemic curve in Brazil: a sum of multiple epidemics, whose inequality and population density in the states are correlated with growth rate and daily acceleration. An ecological study

ABSTRACT Background: The epidemic curve has been obtained based on the 7-day moving average of the events. Although it facilitates the visualization of discrete variables, it does not allow the calculation of the absolute variation rate. Recently, we demonstrated that the polynomial interpolation method can be used to accurately calculate the daily acceleration of cases and deaths due to COVID-19. This study aimed to measure the diversity of epidemic curves and understand the importance of socioeconomic variables in the acceleration, peak cases, and deaths due to COVID-19 in Brazilian states. Methods: Epidemiological data for COVID-19 from federative units in Brazil were obtained from the Ministry of Health's website from February 25 to July 11, 2020. Socioeconomic data were obtained from the Instituto Brasileiro de Geografia e Estatística (https://www.ibge.gov.br/). Using the polynomial interpolation methods, daily cases, deaths and acceleration were calculated. Moreover, the correlation coefficient between the epidemic curve data and socioeconomic data was determined. Results: The combination of daily data and case acceleration determined that Brazilian states were in different stages of the epidemic. Maximum case acceleration, peak of cases, maximum death acceleration, and peak of deaths were associated with the Gini index of the gross domestic product of Brazilian states and population density but did not correlate with the per capita gross domestic product of Brazilian states. Conclusions: Brazilian states showed heterogeneous data curves. Population density and socioeconomic inequality were correlated with a more rapid exponential growth in new cases and deaths.

Some new mathematical models of the fractional-order system of human immune against IAV infection.

Fractional derivative operators of non-integer order can be utilized as a powerful tool to model nonlinear fractional differential equations. In this paper, we propose numerical solutions for simulating fractional-order derivative operators with the power-law and exponential-law kernels. We construct the numerical schemes with the help the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. These schemes are applied to simulate the dynamical fractional-order model of the immune response (FMIR) to the uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Numerical results are then presented to show the applicability and efficiency on the FMIR.

Covid-19 growth rate analysis: application of a low-complexity tool for understanding and comparing epidemic curves

Abstract INTRODUCTION: The acceleration of new cases is important for the characterization and comparison of epidemic curves. The objective of this study was to quantify the acceleration of daily confirmed cases and death curves using the polynomial interpolation method. METHODS: Covid-19 epidemic curves from Brazil, Germany, the United States, and Russia were obtained. We calculated the instantaneous acceleration of the curve using the first derivative of the representative polynomial. RESULTS: The acceleration for all curves was obtained. CONCLUSIONS: Incorporating acceleration into an analysis of the Covid-19 time series may enable a better understanding of the epidemiological situation.

Aggregated Throughput Prediction for Collated Massive Machine-Type Communications in 5G Wireless Networks.

The demand for extensive data rates in dense-traffic wireless networks has expanded and needs proper controlling schemes. The fifth generation of mobile communications (5G) will accommodate these massive communications, such as massive Machine Type Communications (mMTC), which is considered to be one of its top services. To achieve optimal throughput, which is considered a mandatory quality of service (QoS) metric, the carrier sense multiple access (CSMA) transmission attempt rate needs optimization. As the gradient descent algorithms consume a long time to converge, an approximation technique that distributes a dense global network into local neighborhoods that are less complex than the global ones is presented in this paper. Newton's method of optimization was used to achieve fast convergence rates, thus, obtaining optimal throughput. The convergence rate depended only on the size of the local networks instead of global dense ones. Additionally, polynomial interpolation was used to estimate the average throughput of the network as a function of the number of nodes and target service rates. Three-dimensional planes of the average throughput were presented to give a profound description to network's performance. The fast convergence time of the proposed model and its lower complexity are more practical than the previous gradient descent algorithm.

Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains.

The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented. These schemes are based on the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. We introduce a simple modification of the step size in the two-step Lagrange polynomial interpolation to obtain stability in a larger region. Moreover, necessary and sufficient conditions for the control problem are considered. Some numerical simulations are given to validate the theoretical results.

Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra.

When using spectroscopic instrumentation for quantitative analysis of mixture, spectral intensity non-linearity and peak shift make it challenging for building calibration model. In this study, we investigated the performance of a nonlinear model, namely nonlinear least squares with local polynomial interpolation (NLSLPI). In NLSLPI, the parameters to be optimized are the concentrations of the components. Levenberg-Marquardt (L-M) method is used to solve the nonlinear-least-squares optimization problem and local polynomial interpolation is used to generate the nonlinear function for each component. We tested the robustness of NLSLPI on a computer-simulation dataset. We also compared NLSLPI, in terms of RMSEP, to partial least squares (PLS), classical least squares (CLS) and piecewise classical least squares (PCLS) on a real-world dataset. Experimental results demonstrate the effectiveness of the proposed method.

Quantum algorithm for multivariate polynomial interpolation.

How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyse quantum algorithms for this multivariate polynomial interpolation problem over the fields [Formula: see text], [Formula: see text] and [Formula: see text]. We show that [Formula: see text] and [Formula: see text] queries suffice to achieve probability 1 for [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] except for d=2 and four other special cases. For [Formula: see text], we show that ⌈(d/(n+d))(n+dd) ⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is (n+dd) , so our result provides a speed-up by a factor of n+1, (n+1)/2 and (n+d)/d for [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Thus, we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of [Formula: see text], we conjecture that [Formula: see text] queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.

Critical low temperature for the survival of Aedes aegypti in Taiwan.

BACKGROUND: Taiwan is geographically located in a region that spans both tropical and subtropical climates (22-25°N and 120-122°E). The Taiwan Centers for Disease Control have found that the ecological habitat of Aedes aegypti appears only south of 23.5°N. Low temperatures may contribute to this particular habitat distribution of Ae. aegypti under the influence of the East Asian winter monsoon. However, the threshold condition related to critically low temperatures remains unclear because of the lack of large-scale spatial studies. This topic warrants further study, particularly through national entomological surveillance and satellite-derived land surface temperature (LST) data. METHODS: We hypothesized that the distribution of Ae. aegypti is highly correlated with the threshold nighttime LST and that a critical low LST limits the survival of Ae. aegypti. A mosquito dataset collected from the Taiwan Centers for Disease Control was utilized in conjunction with image data obtained from the moderate resolution imaging spectroradiometer (MODIS) during 2009-2011. Spatial interpolation and phi coefficient methods were used to analyze the correlation between the distributions of immature forms of Ae. aegypti and threshold LST, which was predicted from MODIS calculations for 348 townships in Taiwan. RESULTS: According to the evaluation of the correlation between estimated nighttime temperatures and the occurrence of Ae. aegypti, winter had the highest peak phi coefficient, and the corresponding estimated threshold temperatures ranged from 13.7 to 14 °C in the ordinary kriging model, which was the optimal interpolation model in terms of the root mean square error. The mean threshold temperature was determined to be 13.8 °C, which is a critical temperature to limit the occurrence of Ae. aegypti. CONCLUSIONS: An LST of 13.8 °C was found to be the critical temperature for Ae. aegypti larvae, which results in the near disappearance of Ae. aegypti during winter in the subtropical regions of Taiwan under the influence of the prevailing East Asian winter monsoon.

Application of Interpolation Technology in Comparing CT and MRI Images / 医疗卫生装备

Objective To improve the quality of medical image and make diagnoses more convenient. Methods By using the image processing function and programming tomography to give interpolation to the CT and MRI images of same liver cyst case and compare the images of interpolation. Results The quality of images has been improved after giving interpolation to the source CT and MRI images. Conclusion The MATLAB interpolation functions can simplify the program work and improve the quality of image well.