Inverse Polynomial Model Research Articles

Characterization of Lactation Curve Patterns using Non-linear Models in Crossbred Dairy Cattle

Background: Lactation curve patterns are currently integrated in dairy cow’s management software. Lactation curve modeling is useful for monitoring individual yields for diet planning, determining optimum strategies for insemination and genetic evaluation. It also helps for predicting expected missing values on field records and gives concise summary of biological efficiency and persistency of dairy cows.Methods: The study was aimed to characterize the lactation curve pattern for crossbred dairy cattle using different non-linear models. During the period 1991 to 2018, daily milk yield (DMY) consisted of 281698 records of 750 crossbred dairy cows maintained at Livestock Farms. GADVASU, Ludhiana, were collected for the study. Different non-linear models viz. exponential decline function (EDF), parabolic exponential model (PEM), inverse polynomial model (IPM), gamma-type function (GTF), mixed log function (MLF) and Ali and Schaeffer model (ASF) were used for the analysis. The model(s) that best fit and describe the curve characteristics was selected on the basis of coefficient of determination (R2), coefficient of variation (CV), Akaike information criterion (AIC) and mean square error (MSE).Result: The study clearly revealed that the PRM gave highest fit to DMY data with R2, MSE, AIC and CV values of 98.10%, 0.087, -743.31 and 2.37%, respectively. The IPM had also best fitted the observed DMY data with highest R2 (98.05%), lower MSE (0.089), low AIC (-735.8972) and lower CV (2.40%) values. The fitting of observed DMY data with predicted DMY were also found to be higher in the MLF (R2= 96.46%, MSE= 0.159, AIC= -558.16 and CV= 3.21%) and GTF (R2= 95.85%, MSE= 0.190, AIC= -505.24 and CV= 3.50%), whilst the EDF and PEM Models depicted relatively low fit to the DMY data when compared with the other non-linear models. However, IPM and GTF models can be used for accurate prediction of daily milk yield in the crossbred cattle population because they were typical standard lactation curves.

Modern Semi-Active Control Schemes for a Suspension with MR Actuator for Vibration Attenuation

This article describes semi-active modern control schemes for a quarter-vehicle suspension with a magnetorheological damper (MRD) to attenuate vibrations and simultaneously improve the passenger comfort and the vehicle road-holding. The first solution is a multiple positive position feedback (MPPF) control scheme to attenuate the vibration amplitude at the two modal frequencies. The second solution is based on elementary passivity considerations on the exact regulation error dynamics passive output. The passive output feedback is used to improve the control aims. Finally, the third solution deals with a disturbance rejection control (DRC) based on an extended state observer. The three proposed control schemes consider an inverse polynomial model of a commercial MRD for numerical implementation and are evaluated by comfort and road-holding performance indexes proposed in the literature. Furthermore, the effects of variation in the sprung mass (emulating different number of passengers) on the controllers’ performance is analysed. The numerical results show in both scenarios (constant and variable sprung mass) that passivity based control (PBC) and DRC improve the performance indexes compared with the classical sky-hook control and the open-loop systems with a different constant current input for the MRD. Obtained results for damping force and power consumption are within the operation range of the considered commercial MRD showing the viability for experimental implementation of the proposed control schemes.

Optical Method to Determine Gait Parameters Using Position Sensitive Detector

This study suggests an optical method to measure cardinal of gait (step width, step length, and stride length) with position sensitive detector (PSD). The effect of reflector’s shape (flat and cylinder) on the PSD output voltage was examined for the application of the suggested system to real situations with a curved shape reflector (e.g. shoes). Various mathematical models were evaluated to find the optimal equation for the distance measurement. Considering the effect of shape on detected signal, the inverse polynomial model was developed. The suggested method is simple to operate, low in cost, small in size, and can evaluate gait parameters in real time. This method is expected to be useful in the field of rehabilitation and sport science

Curva de crescimento de diferentes linhagens de frango de corte caipira

Objetivou-se identificar o modelo de regressão não linear mais adequado para descrever a curva de crescimento de quatro linhagens de frangos caipira e compará-las entre as linhagens. Foram utilizadas 100 aves, sendo 13 machos e 12 fêmeas de cada uma das linhagens. Foram testados 13 modelos de regressão não linear e, após a seleção do melhor modelo, foi verificada a igualdade de parâmetros e identidade de modelos não lineares. O peso médio aos 77 dias de idade foi de 3.017, 2.781, 2.724 e 2.587kg para a Pesadão, Mista, Carijó e Pescoço Pelado, respectivamente. O modelo Quadrático Logarítmico apresentou melhor ajuste dos dados para as linhagens Pesadão, Carijó e Mista, segundo o quadrado médio do resíduo e desvio médio absoluto. Para a linhagem Pescoço Pelado, os critérios estatísticos apontaram como mais adequado o modelo Polinomial Inverso, seguido do Quadrático Logarítmico. As curvas de crescimento entre machos e entre fêmeas das linhagens foram diferentes, assim, como as curvas de crescimento de machos e fêmeas dentro de linhagens. A divergência entre as classes avaliadas foi atribuída à taxa de decréscimo de peso, parâmetro c do modelo Quadrático Logarítmico. O modelo Quadrático Logarítmico pode ser utilizado para descrever a curva de crescimento das quatro linhagens. A linhagem Pesadão tem o crescimento mais acelerado e a linhagem Pescoço Pelado tem o crescimento mais lento. A partir do 35o dia de idade, sugere-se o ajuste do manejo nutricional para alterar a curva de crescimento e atender a legislação vigente e o mercado consumidor.

광섬유 종단각도 효과를 이용한 관절각 측정

The measurement of joint angle is important to evaluate the patient’s disability. The modified fiber tip and light propagation of the developed fiber sensor were investigated to increase the range of angle detection. Different shapes of fiber tips were manufactured with a polishing machine to deliver light signal in various patterns. Output signals were analyzed to obtain joint angle change with inverse polynomial models. The measured joint angles were displayed with LabVIEW program and the reliability was tested by comparing with a commercial angle sensor. This method can be used in rehabilitation field to determine patient’s progress.

Development of an Optical Fiber Sensor for Angular Displacement Measurements

For diagnostic and therapeutic purposes, the joint angle measurement of a patient after an accident or a surgical operation is significant for monitoring and evaluating the recovering process. This paper proposed an optical fiber sensor for the measurement of angular displacement. The effect of beveled fiber angle on the detected light signal was investigated to find an appropriate mathematical model. Beveled fiber tips redirected the light over a range of angles away from the fiber axis. Inverse polynomial models were applied to directly obtain and display the joint angle change in real time with the Lab-VIEW program. The actual joint angle correlated well with the calculated LabVIEW output angle over the test range. The proposed optical sensor is simple, cost effective, small in size, and can evaluate the joint angle in real time. This method is expected to be useful in the field of rehabilitation and sport science.

Relative risk regression models with inverse polynomials

The proportional hazards model assumes that the log hazard ratio is a linear function of parameters. In the current paper, we model the log relative risk as an inverse polynomial, which is particularly suitable for modeling bounded and asymmetric functions. The parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal. The advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation. The utility of the method is further supported by analyzing two real data sets, addressing the specific question of the location of the minimum risk threshold.

Spectral Efficiency in Single-Hop Ad-Hoc Wireless Networks with Interference Using Adaptive Antenna Arrays

Receivers with N antennas in single-hop, ad-hoc wireless networks with nodes randomly distributed on an infinite plane with uniform area density are studied. Transmitting nodes have single antennas and transmit simultaneously in the same frequency band with power P that decays with distance via the commonly-used inverse-polynomial model with path-loss- exponent (PLE) greater than 2. This model applies to shared spectrum systems where multiple links share the same frequency band. In the interference-limited regime, the average spectral efficiency of a representative link E[C] (b/s/Hz/link) is found to grow as log(N) and linearly with PLE, and its variance decays as 1/N. The average signal-to-interference-plus-noise-ratio (SINR) on a representative link is found to grow faster than linearly with N. With multiple-input-multiple-output (MIMO) links where transmit nodes have multiple antennas without Channel- State-Information, it is found that E[C] in the network can be improved if nodes transmit using the optimum number of antennas compared to the optimum selfish strategy of transmitting equal-power streams from every antenna. The results are extended to random code-division-multiple-access systems where the optimum spreading factor for a given link length is found. These results are developed as asymptotic expressions using infinite random matrix theory and are validated by Monte-Carlo simulations.

A QRD-RLS-Based Predistortion Scheme for High-Power Amplifier Linearization

A digital baseband predistortion (PD) scheme for high-power amplifier (HPA) linearization is proposed and analyzed in this brief. The proposed approach utilizes the QR-decomposition-based recursive least squares (QRD-RLS) algorithm to estimate the memoryless complex polynomial coefficients that characterize the HPA. The inverse polynomial model coefficients corresponding to the PD are similarly extracted using QRD-RLS. The performance of the proposed PD scheme is analyzed via simulations and compared with previously published techniques. Results show that the QRD-RLS-based solution offers improved performance over its comparatives

Application of different models to the lactation curves of unimproved Awassi ewes in Turkey

The objective of this study was to investigate the use of four different mathematical functions (Wood, Inverse Polynomial, Quadratic and Cubic models) for describing the lactation curve of unimproved Awassi ewes. Data were collected from 136 ewes from the same flock raised on the State Farm of Gözlü in the Konya Province of Turkey. The differences in estimated total milk yields between the models were not statistically significant. All models were adequate in describing total milk yield, though total milk yield estimated using the Cubic model was very close to total milk yield calculated by the Fleischmann method. Age effects on model parameters were not significant. The Inverse Polynomial model overestimated the peak yield significantly. Estimated peak yields of the Wood and Cubic model were similar while that obtained from the Quadratic model was significantly lower than that of the other models. Day of peak yield estimated by the models varied between 10.2 and 56.4 days. The differences between days of peak yield estimated using the different models were significant. R2 values of the models ranged from 0.724 to 0.977. The Cubic model gave the best R2 value. The lowest mean square prediction error was found using the Cubic model. Correlation coefficients between total milk yield calculated by the Fleischmann method and estimated total milk yield from the other models ranged from 0.933 to 0.998. The highest correlation coefficient was found for the Cubic model. As a result, the Cubic model showed the best fit to the data collected from unimproved Awassi ewes and allowed a suitable description of the shape of the lactation curve. South African Journal of Animal Science Vol. 35(4) 2005: 238-243

Development of Methods to Classify Mass Transfer Behaviour of Plant Tissues During Osmotic Dehydration

The purpose of this study was to develop a method to classify the mass transfer behavior of different plant materials during osmotic dehydration. The method of classification is based on the description of the material behavior according to easily measurable parameters. These parameters are water loss and solids gain. By fitting an inverse polynomial model to the kinetics data, rates and mass fluxes were calculated. Two methods of classification were developed based on both the rates and fluxes. The method based on fluxes accommodates the different geometries of the samples. Subsequently a single parameter, ϕ, the ratio of the bulk flow transport to diffusion transport at the interface of the solution at zero time, was used. Based on this parameter, the seven materials were analysed and ranked. This method of classification has provided an insight into the behavior of various plant tissues during osmotic dehydration.

Mass Transfer Behavior of Plant Tissues During Osmotic Dehydration

Biological structures and behavior of biomaterials are difficult to describe in quantitative terms. In a process such as osmotic dehydration of plant tissues, these complex structures pose a challenging factor in the optimization process and design of equipment. The structure and properties of the tissues affect the mass transfer phenomena occurring in plant tissues during osmotic dehydration. The purpose of this study was to develop a method to classify the mass transfer behavior of different plant materials during osmotic dehydration. The method of classification was based on the description of the material behavior according to easily measurable parameters. These parameters were water loss and solids gain. By fitting an inverse polynomial model to the kinetics data, rates and fluxes of mass transfer were calculated. Two methods of classification were developed based on the rates and fluxes of mass transfer. The method based on fluxes accommodated for the different geometries of the samples. The two methods were combined to calculate the value of, which is the ratio of the bulk flow transport to diffusion transport at the interface of the solution at time 0. The seven kinds of fresh fruit materials that were analyzed were divided into three classes. Their mass transfer behaviors were then described in quantitative terms as either “fast”, “average” or “slow”. These methods of classification have provided description of the behavior of various plant tissues during osmotic dehydration.

Technical note: The ability of mathematical models to describe the shape of lactation curves.

Seven of the best-known mathematical models based on least squares linear regression were fitted to data following the peaking (standard) lactation curve, termed type I, and a continuously decreasing lactation curve, termed type II. The Wood (1967) gamma function, the Cobby and Le du (1978) weighed least squares gamma function, quadratic and the Sikka (1950) model fitted to both types of curve. In contrast, the Jenkins and Ferrell (1984) and the inverse polynomial model always produced curves of type I, whereas the Brody et al. (1923) model always produced curves of type II. Data should be carefully examined to prevent the use of models unable to render the appropriate curve type described by yield data.

Rainstorm Analysis and Rainfall Erosivity of a Seasonal Tropical Region with a Strong Cyclonic Influence on the Pacific Coast of Mexico

Abstract The objective of this paper is to analyse the rainstorm pattern and rainfall erosivity of a seasonal tropical region in Mexico. Depth, duration, and intensity values of precipitation were obtained for all individual storms from continuous chart records during the period of 1983–90 near Chamela on the Pacific coast of Mexico. The rainstorm pattern was analyzed by fitting the total series to a gamma probability distribution. Intensity–duration and intensity–depth relationships were fit with an inverse polynomial model. The rainfall pattern of Chamela has two types of storms: convective and tropical cyclone. The first has low depth and high-occurrence frequency. As a consequence, distribution data of depth, duration, and intensity were skewed to the lower values. However, cyclonic storms strongly influenced rainfall pattern, annual precipitation, and runoff production. Rainfall intensity correlated significantly with depth by cyclone influence. The mean annual erosivity was 6525.2 MJ mm ha−1 h−1, an...

Predictability of software-reliability models

A two-component predictability measure that characterizes the long-term predictive capability of a model is presented. One component, average error, measures how well a model predicts throughout the testing phase. The other component, average bias, measures the general tendency to overestimate or underestimate the number of faults. Data sets for both large and small projects from diverse sources with various initial fault density ranges have been analyzed. The results show that: (i) the logarithmic model seems to predict well in most data sets, (ii) the inverse polynomial model can be used as the next alternative, and (iii) the delayed S-shaped model, which in some data sets fit well generally performed poorly. The statistical analysis shows that these models have appreciably different predictive capabilities. >

Influence of Constant Temperature on Development, Survival and Fecundity of Sugarcane Mealybug, Saccharicoccus-Sacchari (Cockerell) (Hemiptera, Pseudococcidae)

Generation time of S. sacchari females reared on potted cane ranged from 107 days at 20-degrees-C to 25 days at 30-degrees-C. Three models were fitted to developmental data. The linear model indicated a minimum threshold temperature of 17-degrees-C and the inverse polynomial model a maximum development rate at 30.4-degrees-C. Developmental response to temperature varied from that previously reported in Egypt and the Philippines. The largest and most fecund females were produced at 30-degrees-C. Net reproductive rate varied from 82.0 and 79.7 at 20 and 33-degrees-C respectively to 205.5 at 30-degrees-C. The intrinsic rate of natural increase (r(m) increased from 0.038 at 20-degrees-C to 0.186 at 30-degrees-C. The value of the common shape parameter of the Weibull distribution used to describe adult survivorship curves was 3.5, indicating type I survivorship curves. The ovipositional threshold (V0) was estimated as 16.5-degrees-C. The rate of development of individuals had a major influence on fecundity, both directly and indirectly, through adult female size and the duration of the oviposition period. The ability of S. sacchari to produce large individuals with high fecundities when corresponding rates of development were highest give this tropical species a capacity for rapid population growth at high temperature.

Calibration of an electronic measuring system for ultrasonic analysis of solutions

The problem of calibrating a system that measures the concentration of methanol in water is described. The limitations of polynomial and inverse-polynomial models used for this purpose are demonstrated. The cubic-spline interpolation is chosen and examined as a flexible means of calibration. A method for experimental validation of the results of calibration is proposed. It is concluded that spline-based calibration is much more flexible than the procedures dedicated to the fixed-polynomial or inverse-polynomial models. It allows the utilization of a much greater amount of calibration data, thus improving the accuracy of calibration, and requires much less a priori information on the relationships between quantities involved in the measurement process. >

Relationships Among Some Biological and Empirical Fertilizer Response Models and Use of the Power Family of Transformations to Identify an Appropriate Model

AbstractA systematic procedure is often needed to select the best model for representing response to fertilizer input. Several traditional fertilizer response models are shown to belong to a series consisting of the Power Family of transformations of (A‐y) where y is the yield and A is the maximum yield. Transformations of both A‐y and x, the level of added nutrient, also belong to the series. Tukey’s method of plotting the data and trying different transformations of (A‐y) (and perhaps x) to linearize the data is recommended for finding a model which best approximates the relationship. There is a great deal of flexibility in the system so the best model may turn out to be one of the traditional fertilizer response models or it may be a less common member of the series of transformations of (A‐y) in the Power series. Of the traditional models the quadratic model represents the weakest transformation that will linearize the A‐y vs. x plot; Balmukand’s and Nelder’s inverse polynomial models are among the strongest. Mitscherlich’s model represents an intermediate transformation between the quadratic and Nelder’s model.