First-order Polynomial Research Articles

Self-similarity of higher-order moving averages

In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).

A Novel Decimal Logarithmic Converter Based on First-Order Polynomial Approximation

This paper presents a decimal logarithmic converter based on the decimal first-order polynomial (linear) approximation algorithm. The proposed approach is mainly based on a look-up table, followed a decimal linear approximation step. Compared with a binary-based decimal linear approximation algorithm (Algorithm 1), the proposed algorithm (Algorithm 2) is error-free in the conversion between the decimal and the binary formats. The proposed architecture is implemented by the combinational logic in the binary coded decimal (BCD) encoding on Virtex5 XC5VLX110T FPGA. The results of the comparison show that the hardware performance of Algorithm 2 can run 2.15 times faster than Algorithm 1, with the expense of 1.14 times more area.

Estimation of Grasping Force from Features of Intramuscular EMG Signals with Mirrored Bilateral Training

This study investigates the use of features extracted from intramuscular electromyography (EMG) for estimating grasping force in the ipsilateral and contralateral (mirrored) hand, during bilateral grasping tasks. This is relevant since force estimation using mirror tasks is a potentially useful pathway for the clinical training of unilateral amputees. Bilateral grasping force and intramuscular EMG (wire electrodes) of the right forearm were measured in 10 able-bodied subjects. The features extracted from the EMG signal were the root mean square, the global discharge rate, the standard sample entropy, and the constraint sample entropy (CSE). The association between the EMG features and force was modeled using a first-order polynomial model, a second-order exponential model, and an artificial neural network (ANN). The accuracies of estimation of ipsilateral and mirrored grasping force were not significantly different (e.g., R(2) = 0.89 ± 0.02 for ipsilateral and 0.88 ± 0.017 for mirrored, when using CSE and the ANN). It was concluded that it is possible to use just one channel of intramuscular EMG for force estimation. This result suggests that intramuscular EMG signals may be suitable for proportional myoelectric control and that training of the association between intramuscular EMG features and force can be performed using mirror tasks, which is a needed condition for applications in unilateral amputees.

Dose-response relationship between alcohol consumption before and during pregnancy and the risks of low birthweight, preterm birth and small for gestational age (SGA)-a systematic review and meta-analyses.

Descriptions of the effects of moderate alcohol consumption during pregnancy on adverse pregnancy outcomes have been inconsistent. To review systematically and perform meta-analyses on the effect of maternal alcohol exposure on the risk of low birthweight, preterm birth and small for gestational age (SGA). Using Medical Subject Headings, a literature search of MEDLINE, EMBASE, CINAHL, CABS, WHOlist, SIGLE, ETOH, and Web of Science between 1 January 1980 and 1 August 2009 was performed followed by manual searches. Case-control or cohort studies were assessed for quality (STROBE), 36 available studies were included. Two reviewers independently extracted the information on low birthweight, preterm birth and SGA using a standardised protocol. Meta-analyses on dose-response relationships were performed using linear as well as first-order and second-order fractional polynomial regressions to estimate best fitting curves to the data. Compared with abstainers, the overall dose-response relationships for low birthweight and SGA showed no effect up to 10 g pure alcohol/day (an average of about 1 drink/day) and preterm birth showed no effect up to 18 g pure alcohol/day (an average of 1.5 drinks/day); thereafter, the relationship showed a monotonically increasing risk for increasing maternal alcohol consumption. Moderate consumption during pre-pregnancy was associated with reduced risks for all outcomes. Dose-response relationship indicates that heavy alcohol consumption during pregnancy increases the risks of all three outcomes whereas light to moderate alcohol consumption shows no effect. Preventive measures during antenatal consultations should be initiated.

Dynamics of incoherent elastic layers

Abstract A transversely isotropic plate is said incoherent when the transverse isotropy material axis is at an angle with the geometrical axis orthogonal to the plate cross section. In this paper two plate theories for the free-vibration of such plates are formulated. These theories are based on two different representations for the displacement field, both consisting in first-order polynomials in an axial coordinate along, respectively, the material axis and the geometrical axis. The effects of incoherence on free-wave propagation are investigated in a three-dimensional layer, and the results are used as a benchmark to test the accuracy of the two plate theories.

Assessment of cartographic potential of EgyptSat-1 satellite image (case study in flat areas)

Egypt has launched its first Earth remote sensing satellite EgyptSat-1 in 2007. A series of evaluations of the usefulness and limitations of EgyptSat-1 images for different applications are required. This research is concerned with the investigation of the geometric and cartographic potential of EgyptSat-1 image in order to know to what scale EgyptSat-1 image is suitable for map production and map updating. The geometrical accuracy of rectification of EgyptSat-1 based on non-parametric rectification (polynomial approach and rubber sheeting) has been evaluated. Four methods of rectification have been compared: different orders of 2D polynomials (first-order polynomial, second-order polynomial, third-order polynomial) and rubber sheeting method. Different sets of ground control points (observed with differential global positioning system) have been tested. Several experiments were performed to rectify EgyptSat-1 image using the four rectification methods. For each method, different numbers of ground control points (GCPs) were used starting at 15 points, and then the number was reduced each time till the minimum number of GCPs for each method is reached and with three different GCP distributions. Various issues such as the solutions, feasibility, accuracy, and requirements for control information are addressed. The results show that rubber sheeting followed by third-order polynomial then second-order polynomial then first-order polynomial gives the best root mean square error. Actually, a serious mapping should be based on a satisfying by the theory justified mathematical model so that rubber sheeting should not be used for a serious mapping even it shows smaller discrepancies, but for the flat test area, an approximate 2D transformation can be accepted. Also although third-order polynomial is accurate in the proximity of GCPs and shows smaller discrepancies compared to the first- and the second-order polynomials, they can lead to significant errors for regions outside the GCP range and should not be used for a serious mapping. One can be considered the best resulted rectified image that obtained from second-order polynomial followed by the first-order polynomial. It was found in our study area that the minimum number of control points for each method gives accuracy better than a pixel. The first-order polynomial and rubber sheeting are good from the economical cost that they use minimum number of control points (three). It was found that the planimetric accuracy of rectified EgyptSat image met the 1:25,000 mapping standard (National Map Accuracy Standards). Also from the assessment of the information content of the EgyptSat image, it was found that it is consistent with the map scale of 1:25,000. In conclusion by analysis of the results, it is obvious that EgyptSat images are able to produce and update map of scale 1:25,000.

Development of hydroxyapatite-ciprofloxacin bone-implants using »Quality by design«

The present study deals with the development of hydroxyapatite (HAp)-ciprofloxacin bone-implants using the »Quality by design« approach. The effect of various synthesis parameters like drug amount added in the process, stirring speed and addition rate of orthophosphoric acid in the synthesis on drug concentration in the HAp-ciprofloxacin system synthesized by the precipitation technique using 23 factorial design was analyzed. Optimization methodology utillizing the first-order polynomial equation was used to search for optimal drug concentration in the HAp-ciprofloxacin implant system. The observed responses coincided well with the predicted values from the optimization technique. New implants were manufactured using various HAp-ciprofloxacin composites and 1.5 % (m/V) guar gum as a binder. Characterization of the delivery system was done by XRPD, FTIR spectroscopy and SEM. Even at highest drug concentration (76.6 ± 0.5 %, m/m), ciprofloxacin was present in noncrystalline state. The in vitro ciprofloxacin release from various bone-implants was sustained for several weeks and the drug release pattern correlated well with the Korsmeyer- Peppas model.

Methodology for Determining the Acceptability of Given Designs in Uncertain Environments

Managers wish to verify that a particular engineering design meets their requirements. This design's future environment will differ from the environment assumed during the design. Therefore it is crucial to determine which variations in the environment may make this design unacceptable. The proposed methodology estimates which uncertain environmental parameters are important (so managers can become pro-active) and which parameter combinations (scenarios) make the design unacceptable. The methodology combines simulation, bootstrapping, and metamodeling. The methodology is illustrated through a simulated manufacturing system, including fourteen uncertain parameters of the input distributions for the various arrival and service times. These parameters are investigated through sixteen scenarios, selected through a two-level fractional-factorial design. The resulting simulation Input/Output (I/O) data are analyzed through a first-order polynomial metamodel and bootstrapping. A second experiment gives some outputs that are indeed unacceptable. Polynomials fitted to the I/O data estimate the border line (frontier) between acceptable and unacceptable environments.

Methodology for determining the acceptability of system designs in uncertain environments

In practice, managers often wish to ascertain that a particular engineering design of a production system meets their requirements. The future environment of this design is likely to differ from the environment assumed during the design. Therefore it is crucial to find out which variations in that environment may make this design unacceptable (unfeasible). This article proposes a methodology for estimating which uncertain environmental parameters are important (so managers can become pro-active) and which combinations of parameter values (scenarios) make the design unacceptable. The proposed methodology combines simulation, bootstrapping, design of experiments, and linear regression metamodeling. This methodology is illustrated through a simulated manufacturing system, including fourteen uncertain parameters of the input distributions for the various arrival and service times. These parameters are investigated through the simulation of sixteen scenarios, selected through a two-level fractional–factorial statistical design. The resulting simulation Input/Output (I/O) data are analyzed through a first-order polynomial metamodel and bootstrapping. A second experiment with other scenarios gives some outputs that turn out to be unacceptable. In general, polynomials fitted to the simulation’s I/O data can estimate the border line (frontier) between acceptable and unacceptable environments.

A viscosity model for the (NaF + AlF 3 + CaF 2 + Al 2O 3) electrolyte

A model has been developed for the viscosity of multicomponent inorganic molten salts or liquid alloys. Over the past several years, through critical evaluation of all available thermodynamic and phase equilibrium data, we have developed a quantitative thermodynamic description of multicomponent molten salt systems and liquid alloys using the Modified Quasichemical Model in the Quadruplet (or Pair) Approximation for short-range ordering. The viscosity is modelled using an Eyring equation with molar activation energy for viscous flow expanded as a first-order polynomial in the quadruplet (or pair) mole fractions. The quadruplets (or pairs) may be regarded as structural units and can be calculated from the thermodynamic model. In the present article, the viscosity model is applied to the (NaF + AlF 3 + CaF 2 + Al 2O 3) electrolyte. All available viscosity data were collected and critically evaluated, and optimized model parameters have been found. This new model can be used with Gibbs free energy minimization software, to calculate the viscosity of cryolite-based melts used for the electro-reduction of alumina in Hall–Héroult cells. The viscosity model described in the present paper has not yet been tested on molten salts whose viscosity can increase by more than one order of magnitude.

Change with Age in Regression Construction of Fat Percentage for BMI in School-Age Children

In this study, curvilinear regression was applied to the relationship between BMI and body fat percentage, and an analysis was done to see whether there are characteristic changes in that curvilinear regression from elementary to middle school. Then, by simultaneously investigating the changes with age in BMI and body fat percentage, the essential differences in BMI and body fat percentage were demonstrated. The subjects were 789 boys and girls (469 boys, 320 girls) aged 7.5 to 14.5 years from all parts of Japan who participated in regular sports activities. Body weight, total body water (TBW), soft lean mass (SLM), body fat percentage, and fat mass were measured with a body composition analyzer (Tanita BC-521 Inner Scan), using segmental bioelectrical impedance analysis & multi-frequency bioelectrical impedance analysis. Height was measured with a digital height measurer. Body mass index (BMI) was calculated as body weight (km) divided by the square of height (m). The results for the validity of regression polynomials of body fat percentage against BMI showed that, for both boys and girls, first-order polynomials were valid in all school years. With regard to changes with age in BMI and body fat percentage, the results showed a temporary drop at 9 years in the aging distance curve in boys, followed by an increasing trend. Peaks were seen in the velocity curve at 9.7 and 11.9 years, but the MPV was presumed to be at 11.9 years. Among girls, a decreasing trend was seen in the aging distance curve, which was opposite to the changes in the aging distance curve for body fat percentage.

Fast First-Order Polynomials Convolution Interpolation for Real-Time Digital Image Reconstruction

This letter presents a high-performance architecture of a novel first-order polynomial convolution interpolation for digital image scaling. A better quality of interpolation is achieved by using higher order model that requires complex computations. The kernel of the proposed method is built up of first-order polynomials and approximates the ideal sinc-function in the interval [-2, 2]. The proposed architecture reduces the computational complexity of generating weighting coefficients and provides a simple hardware architecture design and low computation cost, and easily meets real-time requirements. The architecture is implemented on the Virtex-II FPGA, and the high-performance very-large-scale integration architecture has been successfully designed and implemented with the TSMC 0.13 μm standard cell library. The simulation results indicate that the interpolation quality of the proposed architecture is mostly better than cubic convolution interpolations, and is able to process varying-ratio image scaling for high-definition television in real-time.

Quantification of Rubber and Chain-Based Resistance Modes

Rubber-based resistance (RBR) bands and standard link steel (SLS) chains are 2 forms of variable resistance used throughout the strength and conditioning and rehabilitation communities. The purpose of this study was to quantify the tension of RBR bands and the mass of SLS chains as a function of displacement (increasing in 10-cm increments). Five sets of RBR bands (14-, 22-, 30-, 48-, and 67-mm widths) and 5 sets of SLS chains (6-, 8-, 10-, 13-, 16-mm diameters) were measured using a load cell and a force plate. The RBR bands exhibited curvilinear tension-deformation relationships and were best represented (R >or= 0.99) by second-order polynomial functions, whereas the SLS chains exhibited linear mass-displacement relationships and were best represented (R = 1) by first-order polynomial functions. There were no significant differences (p > 0.05) in force outputs between the load cell and the force plate testing, although the strain gauge is a relatively cheap and viable method of quantifying the variable resistance of chains and bands. The strength and conditioning practitioner when purchasing bands needs to be aware of resting length differences (3.5-5.2%), which resulted in mean tension imbalances of 8-19% in the same color band. This study provides the strength and conditioning coach and clinician with a methodology to quantify variable resistance, which may be useful in the prescription of specific loading intensities.

A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance

<i>Context. <i/>Weak gravitational lensing is one of the most promising tools to investigate the equation-of-state of dark energy. In order to obtain reliable parameter estimations for current and future experiments, a good theoretical understanding of dark matter clustering is essential. Of particular interest is the statistical precision to which weak lensing observables, such as cosmic shear correlation functions, can be determined.<i>Aims. <i/>We construct a fitting formula for the non-Gaussian part of the covariance of the lensing power spectrum. The Gaussian contribution to the covariance, which is proportional to the lensing power spectrum squared, and optionally shape noise can be included easily by adding their contributions.<i>Methods. <i/>Starting from a canonical estimator for the dimensionless lensing power spectrum, we model first the covariance in the halo model approach including all four halo terms for one fiducial cosmology and then fit two polynomials to the expression found. On large scales, we use a first-order polynomial in the wave-numbers and dimensionless power spectra that goes asymptotically towards 1.1 for 0, i.e., the result for the non-Gaussian part of the covariance using tree-level perturbation theory. On the other hand, for small scales we employ a second-order polynomial in the dimensionless power spectra for the fit.<i>Results. <i/>We obtain a fitting formula for the non-Gaussian contribution of the convergence power spectrum covariance that is accurate to 10% for the off-diagonal elements, and to 5% for the diagonal elements, in the range 50 5000 nd can be used for single source redshifts <i>z<i/><sub>s<sub/> <i>∈<i/> [0.5,2.0] in WMAP5-like cosmologies.

ISAR Imaging of Maneuvering Targets Based on the Range Centroid Doppler Technique

A new inverse synthetic aperture radar (ISAR) imaging approach is presented for application in situations where the maneuverability of noncooperative target is not too severe and the Doppler variation of subechoes from scatterers can be approximated as a first-order polynomial. The proposed algorithm is referred to as the range centroid Doppler (RCD) ISAR imaging technique and is based on the stretch Keystone-Wigner transform (SKWT). The SKWT introduces a stretch weight factor containing a range of chirp rate into the autocorrelation function of each cross-range profile and uses a 1-D interpolation of the phase history which we call stretch keystone formatting. The processing simultaneously eliminates the effects of linear frequency migration for all signal components regardless of their unknown chirp rate in time-frequency plane, but not for the noise or for the cross terms. By utilizing this novel technique, clear ISAR imaging can be achieved for maneuvering targets without an exhaustive search procedure for the motion parameters. Performance comparison is carried out to evaluate the improvement of the RCD technique versus other methods such as the conventional range Doppler (RD) technique, the range instantaneous Doppler (RID) technique, and adaptive joint time-frequency (AJTF) technique. Examples provided demonstrate the effectiveness of the RCD technique with both simulated and experimental ISAR data.

Onboard Estimation and Classification of a Railroad Curvature

When performing tests on a rail vehicle, it is often necessary to categorize the target data according to the characteristics of the railroad plane geometry. In this paper, a method to classify and identify the railroad plane geometry is considered, employing railroad curvature readings formed by onboard sensor data. The aim is to extract the characteristics of the railroad track to identify and categorize different segments of the track. The railroad curvature is modeled as a first-order piecewise linear polynomial representing sections of straight tracks, transition curves, and circular curves along the railroad. The sensor data are preprocessed in a Global Positioning System-aided dead reckoning navigation system to debias the curvature readings. Subsequently, the noise in the curvature readings is suppressed by nonlinear filtering techniques. Furthermore, the observed curvatures are processed with a linear filter by minimizing a discounted least-squares criterion, yielding the final estimate of the railroad curvature and its rate of change, which further on are utilized to form a detector where the position of a trend change in curvature measurements is located. The result from the presented method has been compared against database values on plane geometry from Banverkets Information System-a system belonging to the Swedish Rail Administration office. The reported accuracy of detecting a change in the railroad curvature has varied in the range of ±7 m in difference between the position entries in the curvature database and the positions found with the developed method.

Sensitivity analysis of simulation models: an overview

This Invited Lecture covers classic and modern designs, and their metamodels. Classic resolution-III designs including fractional-factorial two-level designs assume first-order polynomial metamodels. Resolution-IV and resolution-V designs assume such polynomials augmented with two-factor interactions. Central Composite Designs (CCDs) assume second-degree polynomials. Simulations with many factors require modern factor-screening designs; e.g., sequential bifurcation and Morris's designs. Globally fitted Kriging metamodels require space-filling designs; e.g., Latin Hypercube Sampling (LHS). Sensitivity analysis also serves optimization of the simulated system. Classic Response Surface Methodology (RSM) is popular. Novel methods select one of the multiple simulation outputs as goal variable, and satisfy given constraints on the other outputs and the inputs. Taguchian robust optimization allows for uncertainties in some (environmental) inputs.

Determination of d-saccharic acid-1,4-lactone from brewed kombucha broth by high-performance capillary electrophoresis

Kombucha is a health tonic. D-saccharic acid-1,4-lactone (DSL), a component of kombucha, inhibits the activity of glucuronidase, an enzyme indirectly related with cancers. To date, there is no efficient method to determine the content of DSL in kombucha samples. In this paper, we report a rapid and simple method for the separation and determination of DSL in kombucha samples, using the high-performance capillary electrophoresis (HPCE) method with diode array detection (DAD). With optimized conditions, DSL can be separated in a 50 cm length capillary at a separation voltage of 20 kV in 40 mmol/L borax buffer (pH 6.5) containing 30 mmol/L SDS and 15% methanol (v/v). Quantitative evaluation of DSL was determined by ultraviolet absorption at lambda=190 nm. The relationship between the peak areas and the DSL concentrations, in a specified working range with linear response, was determined by first-order polynomial regression over the range 50-1500 microg/mL with a detection limit of 17.5 microg/mL. Our method demonstrated excellent reproducibility and accuracy with relative standard deviations (RSD) of less than 5% DSL content (n=5). This is the first report to determine DSL by HPCE. We have successfully applied this method to determine DSL in kombucha samples in various fermented conditions.

Integrable and superintegrable systems with spin in three-dimensional Euclidean space

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spins 0 and is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one nontrivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound-state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.

Explicit Runge–Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems

We analyze explicit Runge-Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs type. For the time discretization, we consider explicit second- and third-order Runge-Kutta schemes. We identify a general set of properties on the space stabilization, encompassing continuous and discontinuous finite elements, under which we prove stability estimates using energy arguments. Then we establish $L^2$-norm error estimates with quasi-optimal convergence rates for smooth solutions in space and time. These results hold under the usual CFL condition for third-order Runge-Kutta schemes and any polynomial degree in space and for second-order Runge-Kutta schemes and first-order polynomials in space. For second-order Runge-Kutta schemes and higher polynomial degrees in space, a tightened 4/3-CFL condition is required. Numerical results are presented for smooth and rough solutions. The case of finite volumes is briefly discussed.