Taylor Series Approach Research Articles

Estimasi Nonlinear Least Trimmed Squares (NLTS) pada Model Regresi Nonlinier yang Dikenai Outlier

Constant Elasticity of Substitution (CES) production function is the intrinsic nonlinear regression models that are often used to estimate the data in an industry. Intrinsic nonlinear regression model is a kindof nonlinear regression that can not be linearized, so as to estimate the beta parameters nonlinear statistical model used was Nonlinear Least Squares (NLS) using a first order taylor series approach used in the GaussNewton iteration. One of the problems often encountered in the analysis of data is an outlier, the presence of outliers in the data analysis greatly influence the results of the analysis so it becomes less valid and the estimationbecome biased. One method that is resistant to outliers regression is a method of Nonlinear Least Trimmed Squares. This research aims to determine the characteristics of parameter CES production function whichcontains outlier. The result shows that parameter of the production function CES which contains outliers are bias, inconsistent. So the CES production function which does not contain outliers better than the are containsoutliers.

Development of computational algorithm for multiserver queue with renewal input and synchronous vacation

In this paper, we develop a new computational algorithm for calculating the Markov chain stationary distribution based on a Taylor series approach, where the Taylor series coefficients are expressed in closed-form in terms of the fundamental matrix of the underlying Markov chain. Additionally, we provide an approximate expression for the remainder term of the Taylor series that can be computed in an efficient manner. Specifically, we demonstrate the application of the proposed framework in analyzing a multi-server queueing system with synchronous vacation. The only required assumption of the proposed framework is that the entries of the transition matrix are differentiable functions with respect to a control parameter. Numerical examples are sketched out to illustrate the accuracy of the proposed method.

Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems

In this paper, we integrate goal programming (GP), Tay- lor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complemen- tary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.

Taylor Series Approach for Solving Multi-level Large Scale Fractional Programming Problem with Stochastic Parameters in Constraints

This paper presents a solution algorithm to solve a multi-level large scale fractional programming problem with individual chance constraints (CH-MLLSFP). We assume that there is randomness in the right-hand side of the constraints only and that the random variables are normally distributed. The basic idea in treating (CH-MLLSFP) is to convert the probabilistic nature of this problem into a deterministic multi-level large scale fractional programming problem (MLLSFPP). A solution of multi-level large scale fractional programming problem is presented using aTaylor series to avoid the complexity of fractional nature. An illustrative example is discussed to demonstrate the correctness of the proposed solution method.

A Taylor series approach to pricing and implied volatility for local–stochastic volatility models

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local–stochastic volatility setting. Our price approximations require only a normal cumulative distribution function and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, approximate prices can be computed as efficiently as Black– Scholes prices, and approximate implied volatilities can be computed nearly instantaneously.

Protein-protein interactions in dilute to concentrated solutions: α-chymotrypsinogen in acidic conditions.

Protein–protein interactions were investigated for α-chymotrypsinogen by static and dynamic light scattering (SLS and DLS, respectively), as well as small-angle neutron scattering (SANS), as a function of protein and salt concentration at acidic conditions. Net protein–protein interactions were probed via the Kirkwood–Buff integral G22 and the static structure factor S(q) from SLS and SANS data. G22 was obtained by regressing the Rayleigh ratio versus protein concentration with a local Taylor series approach, which does not require one to assume the underlying form or nature of intermolecular interactions. In addition, G22 and S(q) were further analyzed by traditional methods involving fits to effective interaction potentials. Although the fitted model parameters were not always physically realistic, the numerical values for G22 and S(q → 0) were in good agreement from SLS and SANS as a function of protein concentration. In the dilute regime, fitted G22 values agreed with those obtained via the osmotic second virial coefficient B22 and showed that electrostatic interactions are the dominant contribution for colloidal interactions in α-chymotrypsinogen solutions. However, as protein concentration increases, the strength of protein–protein interactions decreases, with a more pronounced decrease at low salt concentrations. The results are consistent with an effective “crowding” or excluded volume contribution to G22 due to the long-ranged electrostatic repulsions that are prominent even at the moderate range of protein concentrations used here (<40 g/L). These apparent crowding effects were confirmed and quantified by assessing the hydrodynamic factor H(q → 0), which is obtained by combining measurements of the collective diffusion coefficient from DLS data with measurements of S(q → 0). H(q → 0) was significantly less than that for a corresponding hard-sphere system and showed that hydrodynamic nonidealities can lead to qualitatively incorrect conclusions regarding B22, G22, and static protein–protein interactions if one uses only DLS to assess protein interactions.

Investigation of Some Estimators Via Taylor Series Approach and an Application

In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.

Equivalent Sources: Rapid Calculation in the Frequency Domain and Application to Leveling Correction

The equivalent source is usually calculated by an iterative method, designed to converge on the observed potential field, magnetic or gravitational. Each iteration involves two Fourier transforms, one forward and one inverse. As the number of grid point increases the time penalty may become prohibitive. However, the number of transforms can be dramatically reduced by the a priori transformation of the observed potential field to the frequency domain. We describe this method which reduces the number of Fourier transforms from n to two, and demonstrate its use on a simple magnetic anomaly. An extension of this equivalent source technique is also given for the case of a draped magnetic survey that requires leveling correction. The observed data is separated into layers according to the height changes, and the equivalent source is iteratively calculated via comparisons of the upward continued data. Whilst this process is computationally intensive, it is designed to scale with the complexity, and hence the discretisation, of the topographical changes. This gives the method a speed advantage compared with similar Taylor series approaches. A synthetic example containing multiple dipole sources is used to test the method, and to illustrate the advantages and differences of draped surveys and the need to reduce the data to a common datum.

A New Approach for Filtering and Derivative Estimation of Noisy Signals

Filtering and estimation of derivatives in a single step from noisy signals is an important and challenging task in signal processing. The aim of this paper is to propose a new tracking differentiator based on only one parameter; this differentiator is able to synchronously filter noise and estimate the derivative of the input signal. The new tracking differentiator design is based on an inverse Taylor series approach. Both error and stability analyses of the tracking differentiator design are provided. Theoretical analysis and computer simulation results show that this tracking differentiator cannot only obtain better filtering results than previous approaches but can also estimate the derivatives with high accuracy.

A Taylor Series Approach to Pricing and Implied Vol for LSV Models

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such approximate prices can be computed as efficiently as Black-Scholes prices, and approximate implied volatilities can be computed nearly instantaneously.

The inpatient economic and mortality impact of hepatocellular carcinoma from 2005 to 2009: analysis of the US nationwide inpatient sample

Hepatocellular carcinoma (HCC) is an important complication of cirrhosis. Our aim was to assess the inpatient economic and mortality of HCC in the USA METHODS: Five cycles of Nationwide Inpatient Sample (NIS) conducted from 2005 to 2009 were used. Demographics, inpatient mortality, severity of illness, payer type, length of stay (LoS) and charges were available. Changes and associated factors related to inpatient HCC were assessed using simple linear regression. Odds ratios and 95% CIs for hospital mortality were analysed using log-linked regression model. To estimate the sampling variances for complex survey data, we used Taylor series approach. SAS(®) v.9.3 was used for statistical analysis. From 2005 to 2009, 32,697,993 inpatient cases were reported to NIS. During these 5 years, primary diagnosis of HCC increased from 4401 (2005), 4170 (2006), 5065 (2007), 6540 (2008) to 6364 (2009). HCC as any diagnosis increased from 68 per 100,000 discharges (2005) to 99 per 100,000 (2009). However, inpatient mortality associated with HCC decreased from 12% (2005) to 10% (2009) (P < 0.046) and LoS remained stable. However, median inflation-adjusted charges at the time of discharge increased from $29,466 per case (2005) to $31,656 per case (2009). Total national HCC charges rose from $1.0 billion (2005) to $2.0 billion (2009). In multivariate analysis, hospital characteristic was independently associated with decreasing in-hospital mortality (all P < 0.05). Liver transplantation for HCC was the main contributor to high inpatient charges. Longer LoS and other procedures also contributed to higher inpatient charges. There is an increase in the number of inpatient cases of HCC. Although inpatient mortality is decreasing and the LoS is stable, the inpatient charges associated with HCC continue to increase.

A note on ‘Taylor series approach to fuzzy multiple objective linear fractional programming’

Toksari, in his paper ‘Taylor series approach to fuzzy multiobjective linear fractional programming’, published in Information Sciences 178 (2008), proposed a new method to solve multiple objective linear fractional programming problems and declared that it is more effective when compare to previous methods. He constructed fuzzy goals and then used first order Taylor-polynomials to approximate the corresponding linear fractional membership functions by linear functions. Aggregating the linear functions Toksari obtained a crisp linear programming problem and claimed that it is ‘equal’ to the fuzzy fractional one. In this paper, we indicate the fallacy that arises by using Taylor approximation and propose an improved method that guarantees the efficiency of the solution it provides. Both practical applications from Toksari’s paper are recalled to show that the improvements we suggest are effective.

PCV16 Associations Between Patient Demographics, Pharmacotherapy Use, and Cost, Resource Utilization, and Quality-of-Life Burden in Adult Cardiac Arrhythmia Patients

To examine a cohort of patients with all forms of cardiac arrhythmia (CA) and identify factors associated with cost of care, health care resource utilization, antiarrhythmic agent use, and quality of life. This retrospective database analysis utilized the household component data from 2004 to 2009 Agency for Healthcare Research and Quality Medical Panel Expenditure Survey. Patients aged ≥ 18 and had any form of CA (identified via ICD-9-CM codes 427.0-427.2, 427.31-427.32, 427.60-427.61, 427.69, 427.81, 427.89, 427.9, 785.0-785.1) were included. Primary independent variables of interest included age, gender, race/ethnicity, and pharmacotherapy use. Total annual health care expenditure, total annual prescribed medicine expenditure, physical and mental component summary scores (PCS and MCS) of the Short-Form 12 version 2 (SF-12), EuroQoL-5D (EQ-5D) utility scores (US version), proportion of patients using antiarrhythmic medications, number of prescribed medications associated with their cardiac arrhythmia, and proportion of patients with inpatient, outpatient, or emergency room visits were the primary outcomes of interest. Multivariate ordinary least squares (OLS) and generalized linear models (GLM) were used to analyze factors related to the aforementioned outcomes. To provide national estimates, all results were weighted and used standard errors (SE) calculated via Taylor-series approaches. Annually, 5,750,440 non-institutionalized US persons were estimated to suffer from cardiac arrhythmia between 2004 and 2009. Higher health care expenditure and utilization appeared in non-Hispanic whites and patients aged ≥ 65 (p<0.05). As compared to male patients, females had significantly higher prescribed medication expenditure, lower proportion of inpatient and emergency department visits related to arrhythmia, and lower PCS score (p<0.05). Patients on antiarrhythmics had significantly higher health care expenditures, lower proportion of emergency department visits related to arrhythmia, and higher MCS score (p<0.05) compared with their counterparts. Potential health disparities exist across age, gender, race, and antiarrhythmic use among CA patients.

Fuzzy linear fractional bi-level multi-objective programming problems

The Kuhn-Tuker condition has become nowadays an important tool in the hands of investigation for checking the optimality in optimization literature. In the present paper with use of a Taylor series and Kuhn-Tucker conditions approach, we solve a fuzzy linear fractional bilevel multi-objective programming (FLFBL-MOP) problem. The Taylor series is an expansion of a series that represents a function. In the proposed approach, membership functions associated with each level(s) of the objective(s) of FLFBL-MOP problems are transformed and unied by using a Taylor series approach. By using the Kuhn-Tucker conditions, the problem is reduced to a single objective and nally, numericalexample is given to illustrates the efficiency and superiority of the proposed approach.

A functional approximation for the M/G/1/N queue

This paper presents a new approach to the functional approximation of the M/G/1/N built on a Taylor series approach. Specifically, we establish an approximative expression for the remainder term of the Taylor series that can be computed in an efficient manner. As we will illustrate with numerical examples, the resulting Taylor series approximation turns out to be of practical value.

Towards a High Speed Flight Attitude Updating Device Based on FPGA

High speed attitude reference system is essential for large maneuverable flight, however, current flight attitude updating system is difficult to update attitude with both high speed and high precision performance. A high speed attitude updating algorithm (HSAU) with third-order computational accuracy is presented to increase computational efficiency firstly. And then the algorithm is simplified with the linear interpolation and Taylor series approaches. Finally, the algorithm is implemented on the FPGA with the Finite state machine and local parallel structure. Theoretic experiment shows that the presented simplified algorithm is more accurate than the fourth-order Runge-Kutta method in the high speed attitude updating process, and semi-physical simulation status shows that the new device is appropriate to supply timely and accurate attitude for large maneuverable flight.

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi–Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinement of the polynomial Lyapunov function so as to make it share the fuzzy structure of the model proves advantageous. Conditions thus obtained are tested via available SOS software.

A Taylor matrix method for the solution of a two-dimensional linear hyperbolic equation

A Taylor matrix method is proposed for the numerical solution of the two-space-dimensional linear hyperbolic equation. This method transforms the equation into a matrix equation and the unknown of this equation is a Taylor coefficients matrix. Solutions are easily acquired by using this matrix equation, which corresponds to a system of linear algebraic equations. As a result, the finite Taylor series approach with three variables is obtained. The accuracy of the proposed method is demonstrated with one example.

Análise dos métodos de diferenças finitas e expansão rápida na migração reversa no tempo

Neste trabalho mostramos atraves da solucao analitica da equacao da onda no tempo e do metodo de expansao rapida (REM) que e possivel obter a solucao da equacao da onda que utiliza esquemas de diferencas-finitas de qualquer ordem no tempo. Alem disso, demonstramos que a grande vantagem do REM e que o metodo permite usar qualquer intervalo de amostragem temporal para realizar a extrapolacao do campo de ondas, enquanto que o metodo de diferencas finitas impoe limites ao intervalo usado, devido a condicao de estabilidade e a dispersao numerica. Fizemos tambem uma analise das aproximacoes em series de Taylor e em polinomios de Chebyshev para a funcao cosseno que aparece na solucao analitica da equacao da onda no tempo. E finalizamos este trabalho mostrando o desempenho dos metodos numericos na migracao reversa no tempo pos e pre-empilhamento e demonstramos que o REM, combinado com o metodo espectral para calcular as derivadas espaciais, pode ser usado para obter resultados numericamente estaveis e com menor custo computacional do que um metodo de extrapolacao do campo de ondas no tempo com um esquema de diferencas-finitas, dentro do mesmo nivel de precisao.

Two-dimensional Blasius viscous flow of a power-law fluid over a semi-infinite flat plane

Analytic results are obtained for the similarity equation governing the two-dimensional Blasius viscous flow of a power-law fluid over a semi-infinite flat plane via Taylor series for small values of the independent similarity variable. Then, an analytic perturbative procedure is used to determine an approximate solution that exhibits the correct asymptotic behavior. This perturbation method allows for the computation of the shear stress at the wall, something which is impossible with a Taylor series approach. It is found that the perturbation solutions converge sufficiently rapidly; indeed, a first order approximation gives qualitatively accurate results. Furthermore, we employ the perturbation method to deduce the influence of the power-law index, n, on the obtained similarity solutions.