Degree Polynomial Regression Model Research Articles

Design admissibility and de la Garza phenomenon in multifactor experiments

The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular, several authors have developed sufficient conditions for the existence of minimally supported designs in univariate models, where the number of support points of the optimal design equals the number of parameters. These results generalize the celebrated de la Garza phenomenon (Ann. Math. Statistics 25 (1954) 123–130), which states that for a polynomial regression model of degree k−1 any optimal design can be based on k points. This paper provides—for the first time—extensions of these results for models with a multivariate predictor. In particular, we study a geometric characterization of the support points of an optimal design to provide sufficient conditions for the occurrence of the de la Garza phenomenon in models with multivariate predictors and characterize properties of admissible designs in terms of admissibility of designs in conditional univariate regression models.

Metasurface-based solar absorber with absorption prediction using machine learning

We propose a metasurface-based solar absorber design using machine learning. The absorption analysis for two complementary metasurface-based designs is presented. The complementary circular array metasurface design and circular array metasurface design are investigated for visible, infrared, and ultraviolet regions with a wavelength range of 0.2 μm–0.8 μm. The highest average absorption is observed for complementary circular array metasurface design. This design is further investigated for different parameter variations like resonator thickness, SiO2 height, SiO2 width, and graphene chemical potential. All these parameter variations and their absorption results are also predicted with machine learning algorithms. Experiments are performed using different degrees of polynomial regression models for predicting the absorption values for missing/intermediate wavelengths. Two test cases R-30 and R-50 are designed to test the regressor models and R2 Score metric is used to test the prediction efficiency of the regressor model. It is observed from the experimental results that, prediction efficiency of more than 0.99 (R2) can be achieved using higher degree polynomial regression models. The proposed metasurface-based solar absorber design can be used for solar energy harvesting applications.

Investigation and Analysis of ICT development index (IDI) for measuring ICT resources in Georgia

Abstract. Information and communication technologies (ICT) are a set of equipment (devices, systems, etc.) and techniques with associated software (software systems and software tools) that have been developed and used for more efficient communication, creation, distribution, storage and management of information. The IDI (ICT Development Index) index is most often used to measure ICT resources, which is defined as a composite index that combines 11 indicators (classified into 3 sub-indices: Access, Use and Skills). Data on values of IDI index has been retrieved from Measuring the Information Society Report (MISR), which since 2008 has been publishing by International Telecommunications Union (ITU). The IDI index for 2017 was determined for 176 countries of the world, with the first on the ranking list was Iceland with IDI2017=8.98 and the last Eritrea with IDI2017=0.96. The mean value of IDI index for 2017 was Avg=5.11, standard deviation was StD=2.22 and coefficient of variation was CoV=43.52. In this paper is given of analysis of IDI (ICT development index) for measuring ICT resources in Georgia. The data were approximated using a 3rd degree polynomial regression model (PRM3) with a correlation coefficient R=0.9964, determination coefficient R2=0.9928 and adjustment coefficient of determination is AdjR2=0.9885.

Ameliorative Effects of Dietary Ocimum gratissimum Leafmeal on African Catfish, Clarias gariepinus Subjected to Pathogenic and Transportation-Induced Stress

The primary aim of this project is the use of functional feed supplements to ameliorate or reduce the effects of stressors rather than using chemicals that could be harmful and expensive. Specifically, assessment of the ameliorative effect of locally available phytogenic product, Ocimum gratissimum on the negative effects of stress in African catfish production was carried out in a study that lasted for 70 days. Five experimental diets were formulated, at different inclusion levels of O. gratissimum , as 0.00 g (control), 0.05 g, 0.10 g, 0.15 g, 0.20 g per 100 g of diet denoted as T1 (control), T2, T3, T4, and T5 respectively. At the end of the feeding trial, stress-induced treatments of experimental fish were done using pathogenic and transportation stressors. Zootechnical parameters in terms of growth and nutrient utilization were evaluated. Physiological stress assessment (Aspartate transaminase, AST and Alanine transaminase, ALT) and stress biomarkers (cortisol and glucose) were carried out using liver and blood samples from experimental fish. Results showed that zootechnical parameters were significantly (P < 0.05) enhanced with increasing supplementation levels of O. gratissimum. There were better performances in the growth and nutrient utilization indices like weight gain, specific growth rate, protein efficiency and feed conversion ratio as the level of O. gratissimum was increased to 0.15 mg/g in the diets. Curvilinear trends were recorded with a second degree polynomial regression model depicting a strong relationship between SGR and O. gratissimum supplementation in fish diet followed by adverse responses when increased to 0.20 mg/g in the diet. There were significant reduction in stress parameters with increasing supplementation levels of O. gratissimum leaf extract in the diets. The best supplementation level of O. gratissimum was 0.15 mg/g in T4. From the above deductions, this study confirmed the positive ameliorating effects of O. gratissimum on the African catfish during stressful episodes.

Data analysis of COVID-2019 epidemic using machine learning methods: a case study of India.

At this time, COVID-2019 is spreading its foot in the form of a huge epidemic for the world. This epidemic is spreading its foot very fast in India too. One of the World Health Organization states that COVID-2019 is a serious disease that spreads from one person to another at very fast speed through contact routes and respiratory drops. On this day, India and the world should rise to an effective step to analyze this disease and eliminate the effects of this epidemic. In this paper presented, the growing database of COVID-2019 has been analyzed from March 1, 2020, to April 11, 2020, and the next one is predicted for the number of patients suffering from the rising COVID-2019. Different regression analysis models have been utilized for data analysis of COVID-2019 of India based on data stored by Kaggle in between 1 March 2020 to 11 April 2020. In this study, we have been utilized six regression analysis based models namely quadratic, third degree, fourth degree, fifth degree, sixth degree, and exponential polynomial respectively for the COVID-2019 dataset. We have calculated the root mean square of these six regression analysis models. In these six models, the root mean square error of sixth degree polynomial is very less in compared other like quadratic, third degree, fourth degree, fifth degree, and exponential polynomial. Therefore the sixth degree polynomial regression model is very good models for forecasting the next 6 days for COVID-2019 data analysis in India. In this study, we have found that the sixth degree polynomial regression models will help Indian doctors and the Government in preparing their plans in the next 7 days. Based on further regression analysis study, this model can be tuned for forecasting over long term intervals.

Long Term Interferometric Temporal Coherence and DInSAR Phase in Northern Peatlands

Peatlands of northern temperate and cold climates are significant pools of stored carbon. Understanding seasonal dynamics of peatland surface height and volume, often referred to as mire breathing or oscillation, is the key to improve spatial models of material flow and gas exchange. The monitoring of this type of dynamics over large areas is only feasible by remote sensing instruments. The objective of this study is to examine the applicability of Sentinel-1 synthetic aperture radar interferometry (InSAR) to characterize seasonal dynamics of peatland surface height and water table (WT) over open raised bog areas in Endla mire complex in central Estonia, characteristic for northern temperate bogs. Our results show that InSAR temporal coherence, sufficient for differential InSAR (DInSAR), is preserved in the open bog over more than six months of temporal baseline. Moreover, the coherence which is lost in a dry summer, make a recovery in autumn correlate with WT dynamics. The relationship between the coherence from a single master image and the corresponding WT difference is described by the second degree polynomial regression model (Root Mean Squared Error RMSE = 0.041 for coherence magnitude). It is also demonstrated that DInSAR phase is connected to bog surface dynamics and reveals differences between bogs and for ecotopes within a bog. These findings suggest that InSAR long term temporal coherence could be used to describe seasonal bog WT dynamics and differentiate between mire types and ecotopes within a bog. Moreover, DInSAR analysis has the potential to characterize seasonal mire surface oscillation which may be important for assessing the capacity of water storage or restoration success in northern temperate bogs.

A Few Methods for Estimating Life Expectancy

In this paper, firstly, an extensive empirical investigation is done by fitting linear regressions exhaustively to observe the pattern and nature of linear relationships of life expectancies of each age-group with that of all other age-groups in fifty-four Sample Registration System (SRS) life tables of Assam state of India. Secondly, two second degree polynomial regression models have been proposed for estimating life expectancies at birth (e0). Both the models have been empirically illustrated in fifty-four SRS life tables of India and fifty-four SRS life tables of each of 16 major Indian states. The estimated values of e0 are examined in relation to estimated values of the same by some other methods and e0 values available in SRS tables of the years 2001-05 and 2011-15. Moreover, e0 values for all districts of Assam are estimated by using one of the proposed polynomial regressions together with some indirect techniques of estimation.

How should we determine normal echocardiographic right ventricle function reference values in pediatrics?

Several models have been used to establish pediatric Z-scores for echocardiographic right ventricle (RV) variables. This study aimed to determine the most appropriate mathematical model for RV function reference values in pediatrics. Prospective cross-sectional study among 314 healthy children ages 2days to 18years (46% female, 88 infants, 26 neonates, 226 children). RV parameters (S', E', A' waves, TEI index, TAPSE) were modelized with four explanatory variables: age, height, weight and body surface area. Four mathematical models were applied: a linear model, a polynomial model of degree 2, a linear regression model by spline with free knot, and a polynomial regression model of degree 2 by spline with a free knot. The choice of the best method used the adjusted coefficient of determination (aR2). The modelization of RV variables did not follow a linear model. A single explanatory variable could not determine all Z-scores, as specific and independent variables were required for each parameter. The quadratic spline model best adjusted the modelization of RV variables. The S' wave was best modelized by the spline model with the weight (knot at 6.86kg). The E' wave was best modelized by the spline model with the age (knot at 0.29years). The A' wave was best modelized by the model with the height (knot at 81cm). The TAPSE was best modelized by the spline model with the weight (knot at 9.04kg). The spline regression models best applies to echocardiographic RV reference values in pediatrics.

Echocardiographic right ventricular function reference values in pediatrics: Which is the best mathematical model to define Z-scores?

Echocardiographic assessment of right ventricle (RV) function has become essential in pediatric cardiology. The aim of our study was to determine the most appropriate mathematical model for RV function reference values in children. Normal children aged 0 to 18 years referred to the pediatric cardiology consultation were screened in this prospective cross-sectional study. Each RV parameters (S’, E’, A’ waves, TEI index, TAPSE) was modeled with four explanatory variables: age, size, weight and body surface area. Four different mathematical models were applied: a linear model, a polynomial model of degree 2, a linear regression model by spline with free knot, and a polynomial regression model of degree 2 by spline with a free knot. The choice of the best explanatory variable and modelization method was made on the basis of the model's coefficient of determination ( R 2 ). We included 314 normal children aged 2 days to 18 years (46% female, 88 infants, 26 neonates, 226 children). The modelization of the RV variables over all ages did not follow a linear model, with the lowest coefficients of determination in the four explanatory variables. The quadratic spline model best adjusted the modelization of all RV variables. No model accurately explained the TEI index in any of the four explanatory variables. The S’ wave was best modelized by the quadratic spline model with the weight. The knot at 6.86 kg corresponded to the curves’ break. The E’ wave was best modelized by the quadratic spline model with the age. The knot at 0.29 years corresponded to the curve's break. The A’ wave was best modelized by the quadratic model with the size. The knot at 81 cm corresponded to the break of the curve. The TAPSE was best modelized by the quadratic spline model with the weight. The knot at 9.04 kg corresponded to the curve's break. The quadratic spline model best applies to echocardiographic RV reference values in pediatrics.

Relation between hypericin content and morphometric leaf parameters in Hypericum spp.: A case of cubic degree polynomial function

Higher plants often accumulate secondary metabolites in multicellular structures or in secretory reservoirs. Biotechnological production of such compounds by cell cultures lacking proper morphological structures is difficult, therefore possibilities for an efficient increase of their formation by organ cultures are being searched. The genus Hypericum comprises many species that store photoactive and phototoxic naphthodianthrones in the dark nodules on their above-ground parts. To date, the relation between the content of hypericins and their proto-forms accumulated in the nodules, and morphological characters of the plant parts containing these structures has not been sufficiently explained. The content of hypericins and leaf morphology characters were measured in 12 selected diploid seed-derived Hypericum species cultured in vitro. The leaf volume and the volume of the nodules per leaf were calculated. Based on these data, a cubic degree polynomial regression model with high reliability was constructed. The model enables an estimate of the biosynthetic capacity of the cultures, and may be useful in designing the experiments aimed at elicitation of these unique secondary metabolites in shoot cultures of Hypericum spp. An analogous model may be developed for interpretation of experimental results for other plant species which accumulate metabolites in specialized morphological structures.

Echocardiographic right ventricular function reference values in pediatrics: Which is the best mathematical model to define Z-Scores?

The aim of our study was to determine the most appropriate mathematical model for right ventricular (RV) function normal values in children. Normal children aged 0 to 18 years referred to the pediatric cardiology consultation were screened in this prospective cross-sectional study. Each RV parameters (S’, E’, A’ waves, TEI index, TAPSE) was modeled with four explanatory variables: age, size, weight and body surface area. Four different mathematical models were successively applied: a linear model, a polynomial model of degree 2, a linear regression model by spline with free knot, and a polynomial regression model of degree 2 by spline with a free knot. The choice of the best explanatory variable and the best modelization method was made on the basis of the model's coefficient of determination (R 2 ). We included 314 normal children aged 2 days to 18 years (46% female, 88 infants, 26 neonates, 226 children). The modelization of the RV variables over all ages did not follow a linear model, with the lowest coefficients of determination in the four explanatory variables. The quadratic spline model best adjusted the modelization of all RV variables. No model accurately explained the TEI index in any of the four explanatory variables. The S’ wave was best modelized by the quadratic spline model with the weight. The knot at 6.86 kg corresponded to the curves’ break. The E’ wave was best modelized by the quadratic spline model with the age. The knot at 0.29 years corresponded to the curve's break. The A’ wave was best modelized by the quadratic model with the size. The knot at 81 cm corresponded to the break of the curve. The TAPSE was best modelized by the quadratic spline model with the weight ( Fig. 1 ). The knot at 9.04 kg corresponded to the curve's break ( Fig. 1 ). The quadratic spline model best applies to echocardiographic RV reference values in pediatrics.

Comparative analysis of extracted heights from topographic maps and measured reduced levels in Kumasi, Ghana

No other mapping product has had widespread applications in developmental planning than the topographic map. Topographic maps represent the three-dimensional landscape by providing relief information in the form of contours in addition to plan information on which natural and man-made landmarks are quite accurately represented. Height information, extractible from topographic maps, comes in handy for most land use planning. However, generalizations during contouring and the need to interpolate between successive contours for specific grid nodes introduce errors in extracted heights. There is therefore, the necessity to use some mathematical modeling to remove discrepancies in the interpolation process to improve elevation data extracted from topographic maps. In this study, the accuracy of spot heights derived from interpolated and extracted heights from topographical maps is assessed. Two different mathematical models - a third degree polynomial regression model and the Thompson’s Multiple Variable Polynomial regression models, were respectively used to model the relationship between extracted heights and ground reduced levels. Results from the two models indicate that, the latter presents better refinements to converting extracted heights into reduced levels with a coefficient of determination value of 95.9%, although further research is recommended to investigate numerical techniques that could improve the solution to the Thompson’s polynomial. The Thompson’s model was implemented as a crude height refiner program that receives extracted heights to return corrected heights. The implication of these results for the mapping community is that, it is possible to model a correction function that can help obtain reasonably accurate heights from topographic maps. This will reduce the necessity of always going back to the field for field surveys in spite of the fact that topographic maps covering an area already exists.Keywords: Topographic maps, Interpolation, Thompson’s polynomial, Levelling, Terrain models

Allelopathic potential of Inga laurina leaf extract on lettuce seed germination

The aim of this study was to evaluate the allelopathic potential of Inga laurina leaves on the germination and growth of Lactuca sativa L. seedlings. The extract was obtained by blending 50 g of leaves in 500 ml of distilled water. Extracts were obtained by diluting the leaf homogenate in water to concentrations of 0 (control), 25, 50, 75 and 100%. The bioassay was conducted in a completely randomized design with five treatments and four repetitions of 50 seeds of L. sativa . The characteristics observed were germination and abnormal seedlings, germination rate, shoot length and root length, dry weight of seedlings and allelopathy index. There was no difference between extracts for germination ranging from 98%to 100%. The speed of germination rate and seedling root length decreased with increasing concentration and could be explained by second degree polynomial regression models with R 2 above 98%. The fresh mass increased with higher concentrations of the extract. The allelopathic index was negative, indicating inhibition, and increased with increasing extract concentration. The leaf extract of Inga laurina at different concentrations did not affect lettuce seed germination. Allelopathic potential was seen in the developmental characteristics of lettuce seedlings.

Basic Research on Structural Optimum Design of G/T 250ton Class Double-ended Car-Ferry Ship

In this paper, It was performed to optimize for the deck's structural design of a double ended car ferry ship respect to Goal-Driven Optimization (GDO). It was examined for the strength and deformation of the deck and determined to save economic cost the optimal point. The deck thickness based on the Design of Experiments (DOE) and response surface method was increased to 110%. and can improve the deck's strength and stiffness. By performing the regression analysis respect to the result, we propose the optimal regression model formula as a third degree polynomial regression models. The coefficient of determination was about 0.98 and reliability could be obtained.

Time Series Analysis of New Cars Sale in Bosnia and Herzegovina

The paper provides analysis of new car sales in Bosnia and Herzegovina for the period 2007-2014. For the examined period new car sales in B&H was reduced by 53.67%, from 12449 in 2007 to 6682 in 2014. The trend can be approximated using 3rd degree polynomial regression model with coefficient of determination R2=0,845. Most new cars sold were by Skoda and least was sold by Porsche. Total number of sold vehicles for this period was 73152. We also present annual growth, chain growth and cumulative growth index for the given period.

Relationship between 28-year food consumption trends and the 10-year global risk of death due to cardiovascular diseases in the adult Warsaw population.

Diet plays an important role in the aetiology of cardiovascular (CV) disease. SCORE risk charts are popular and simple tools for the assessment of the global risk of CV death. To evaluate food consumption trends in the adult Warsaw population in 1984-2012 and to establish their relationship to the 10-year global risk of death due to CV diseases. Nutrient intake and CV risk factors were assessed in independent representative samples of the Warsaw population in the Pol-MONICA projects (in 1984, 1988, 1993, and 2001) and the WAW-KARD project (in 2012). Overall, these surveys included 3404 men and 3446 women aged 35-64 years. The global CV risk was calculated using the SCORE risk chart for high-risk European regions. On the basis of the collected data, trends of dietary intakes and the SCORE risk values in the years 1984-2012 were estimated by linear and nonlinear regressions and correlations. Over the period of 28 years (1984-2012), a significant decrease in the SCORE risk (by 20% in men and by 35% in women) was seen, accompanied by significant changes in the dietary habits of the Warsaw population. Declining trends (an exponential model) were noted for total energy, total fat, cholesterol, and added animal fat intake. Intake of saturated fatty acids decreased until 2001 and increased thereafter (a second degree polynomial regression model). These changes in the dietary habits of the Warsaw population correlated with the SCORE risk values. Significant correlations were noted for total energy, total fat, and dietary cholesterol intake in both sexes, and animal fat and saturated fatty acid intake in men, with the correlation coefficients ranging from 0.85 to 0.98. A significant reduction in the SCORE risk was seen in the Warsaw population in 1984-2012, which was associated with positive dietary changes. However, an unexpected decrease and reversal of the favourable trends in the structure of fat consumption occurred in the last decade.

Factors influencing the diameter of human anterior and posterior intercostal arteries.

At present, there have not been any detailed studies examining the size relationships of the intercostal arteries. This study was carried out to investigate the relationship between the vessel lumenal diameter of ipsilateral, paired anterior and posterior IC arteries, as well as with the length of the IC space supplied by each artery. Samples were collected from the second-sixth anterior and posterior IC arteries near their site of origin, and the lengths of the corresponding IC spaces were measured in 42 cadavers. Lumenal diameters of both the anterior and posterior IC arteries at consecutive IC space closely followed second degree polynomial regression models (R(2) = 0.9655, and R(2) = 0.9741, respectively), and reached maximum size at the fifth IC space, which was found to be the longest of the IC spaces. No direct relationship was observed between diameters of the paired anterior and posterior IC arteries, although there was a trend for the larger anterior IC arteries to be paired with the larger posterior IC arteries. The calculated rate of blood flow at each IC artery was approximately two-fold greater in males than in females. These results suggest that the length of the IC space, and hence the extent of the thoracic wall supplied, is a major factor in determining the diameter of both anterior and posterior IC arteries. Since COPD is such a prevalent disease, this study also examined its influence on the IC arteries, and found that the posterior IC arteries are significantly larger among afflicted subjects.

The Relationship Between Cup-to-Disc Ratio and Estimated Number of Retinal Ganglion Cells

To investigate the relationship between cup-to-disc ratio (CDR) and estimates of retinal ganglion cell (RGC) number. This cross-sectional study included 156 healthy eyes, 53 glaucoma suspects, and 127 eyes with glaucoma. All eyes had standard automated perimetry (SAP), Cirrus SD-OCT, and stereoscopic optic disc photography within 6 months. CDR was determined from stereoscopic photographs by two or more masked graders. The number of RGCs in each eye was estimated using a published model that combines estimates of RGC number from SAP sensitivity thresholds and SD-OCT retinal nerve fiber layer measurements. The mean estimated RGC count was 1,063,809 in healthy eyes; 828,522 in eyes with suspected glaucoma; and 774,200 in early, 468,568 in moderate, and 218,471 in advanced glaucoma. Healthy eyes had a mean vertical CDR of 0.45 ± 0.15 vs. 0.80 ± 0.16 in glaucomatous eyes. There was good correlation between stereophotographic vertical CDR and SD-OCT vertical CDR (R(2) = 0.825; P < 0.001). The relationship between estimated RGCs and vertical CDR was best represented using a third degree polynomial regression model, including age and optic disc area, which accounted for 83.3% of the variation in estimated RGC counts. The nonlinear relationship between RGC estimates and CDRs indicated that eyes with a large CDR would require loss of large RGC numbers for a small increase in CDR. The relationship between estimated RGC counts and CDR suggests that assessment of change in CDR is an insensitive method for evaluation of progressive neural losses in glaucoma. Even relatively small changes in CDR may be associated with large losses of RGCs, especially in eyes with large CDRs. (ClinicalTrials.gov numbers, NCT00221923, NCT00221897.).

Mathematical modeling of the native Mexican turkey’s growth

Little is known about the productive performance of Mexican turkey, so the objective of the present study was to characterize growth performance curves of backyard turkey under a confined system. Forty fertile eggs were artificially incubated and turkey weight was recorded at hatch. During growth performance weekly weight was measured until 385 days of age. Turkey commercial feed and water were offered ad libitum. To characterize growth curves, a fourth degree polynomial model regression and a Richards biological model were used, which were compared by determination coefficient (r2), to reach the best fit model. The best fit model was the fourth degree polynomial regression model from a mathematical standpoint of view. It was found that maximum tom growth was reached at 15.7 weeks with a weight gain of 259.3 g/week and in hens at 12.4 weeks with a weight gain of 112.0 g/week. Body weight reached by toms at 40 weeks was 6 kg and hens at 35 weeks with 3.6 kg.

Modeling the recovery patterns from solid phase extraction purification of secoisolariciresinol diglucoside, p-coumaric acid glucoside, and ferulic acid glucoside from microwave-assisted flaxseed extracts

Flaxseed extracts obtained by microwave-assisted extraction (MAE) were cleaned of leftover salts from hydrolysis by solid phase extraction (SPE). The SPE set up was affordable, non-automated and vacuum-driven. The recovery patterns of secoisolariciresinol diglucoside (SDG), p-coumaric acid glucoside (PCouAG), and ferulic acid glucoside (FerAG) were modeled in two stages using regression procedures (p<0.05). At stage one, the recovery patterns were predicted as a function of SPE eluent concentration in ethanol (10–50%). At stage two, the accuracy of the predictions was increased by enlarging the SPE eluent regressor's range (0–100% ethanol in water) and arranging the solvent system into three practical elution groups. The groups 1, 2 and 3 reflected the major loss, the major recovery and the minor loss of SDG, respectively. Second degree polynomial regression models were fitted for accurately predicting the recoveries of compounds. Microwave-assisted extracts obtained from 0.6 and 1.5g defatted flaxseed meal were purified; the total SDG recoveries from the SPE funnel were 97.8 and 99.8%; and the SDG amounts obtained were 8.54 and 20mg, respectively. The HPLC analysis of eluates pooled into practical groups allows for significant reductions in HPLC analysis time and solvent consumption which could have a positive impact on future purification studies. The results of this study allow for designing simplified, efficient and economical pilot scale studies for the purification of SDG from flaxseed extracts.