OFDM blind channel estimation based on polynomial models

A two-dimensional （2-D） polynomial regression model is set up to approximate the time-frequency response of slowly time-varying orthogonal frequency-division multiplexing （OFDM） systems. With this model the estimation of the OFDM time-frequency response is turned into the optimization of some time-invariant model parameters. A new algorithm based on the expectation-maximization （EM） method is proposed to obtain the maximum-likelihood （ML） estimation of the polynomial model parameters over the 2-D observed data. At the same time, in order to reduce the complexity and avoid the computation instability, a novel recursive approach （RPEMTO） is given to calculate the values of the parameters. It is further shown that this 2-D polynomial EM-based algorithm for time-varying OFDM （PEMTO） can be simplified mathematically to handle the one-dimensional sequential estimation. Simulations illustrate that the proposed algorithms achieve a lower bit error rate （BER） than other blind algorithms.

POLYNOMIAL MODEL BASED FAST FRACTIONAL PIXEL SEARCH ALGORITHM FOR H.264/AVC

This paper proposed a novel fast fractional pixel search algorithm based on polynomial model. With the analysis of distribution characteristics of motion compensation error surface inside tractional pixel searching window, the matching error is fitted with parabola along horizontal and vertical direction respectively. The proposcd searching strategy needs to check only 6 points rather than 16 or 24 points, which are used in the l lierarchical Fractional Pel Search algorithm （HFPS） for 1/4-pel and 1/8-pel Motion Estimation （ME）. The experimental results show that the proposed algorithm shows very good capability in keeping the rate distortion performance while reduces computation load to a large extent compared with HFPS algorithm.

The Polynomial Function Model in Born-Infeld Theory

Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation,we investigate the polynomial function model in Born-Infeld theory in this paper with the form of-([10α(φ′)^(2)]φ′)′=λf(φ(x)),whereλ>0 is a real parameter,f∈C 2(0,+∞)is a nonlinear function.We are interested in the exact number of positive solutions of the above nonlinear equation.We specifically develop for the problem combined with a careful analysis of a time-map method.

Application of Polynomial Mathematical Models for the Extraction of Bioactive Compounds from Plant Sources

This article focuses on the mathematical modelling of the extraction process of bioactive compounds from grape marc and berries (Aronia, rosehip, rowan, and hawthorn). The composition of the extraction medium (the concentration of the ethyl alcohol) served as a factor of influence. Furthermore, 8 experimental measured parameters were used as variables. The experimental results were processed using Hermite polynomials. In order to adapt the degree of the polynomial, the following conditions were imposed: high precision of the mathematical model by appealing to models on interval;obtaining a nominal model and two uncertain models (upper and lower);deduction of two predictive models, one superior and one inferior. It was found that the mathematical models based on Hermite polynomials do not provide explicit analytical expressions, although they allow the establishment of parameter values for any concentration of the extraction medium. In some cases, only high-grade polynomial models ensure the modelling error below 2%. Uncertain models (upper and lower 95%) include all experimental data. Predictive mathematical models (upper and lower) were established for a high prediction. The analytical expressions of the mathematical models on intervals are non-gaps, the coefficients having non-zero values. Dependencies between the measured parameters and the composition of the extraction solvent were analyzed, the results being presented through the calculation of a surface, with all the experimental values and their average values. Thus, it was found that polynomial mathematical models provide complete information for modelling the extraction processes of bioactive compounds of plant origin.

An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target

A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.

Computation and analysis Computation and analysis of the geomagnetic field model in China and its adjacent area for 2003

Based on the geomagnetic data at 135 stations and 35 observatories in China in 2003, the Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area for 2003 were established. In the model calculation, the truncation order of the model and the influences of the boundary restriction on the model calculation were carefully analyzed. The results show that the geomagnetic data used are precise and reliable, and the selection of the truncation order is reasonable. The Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area established in this paper are consistent very well.

A two-step rectification algorithm for airborne linear images with POS data

Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.

A Hybrid Particle Swarm Optimization to Forecast Implied Volatility Risk

The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective.The complex characteristics of implied volatility risk index such as non-linearity structure,time-varying and nonstationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters.We use the Hybrid Particle Swarm Optimization(HPSO)tool to identify the model parameters of nonlinear polynomial Hammerstein model.Findings indicate that,following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input(ARX)behaviour,the fear index in US financial market is significantly affected by COVID-19-infected cases in the US,COVID-19-infected cases in the world and COVID-19-infected cases in China,respectively.Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China(MAPE(2.1013%);R2(91.78%)and RMSE(0.6363 percentage points)).The proposed approaches have also shown good convergence characteristics and accurate fits of the data.

Protein acetylation sites with complex-valued polynomial model

Protein acetylation refers to a process of adding acetyl groups(CH3CO-)to lysine residues on protein chains.As one of the most commonly used protein post-translational modifications,lysine acetylation plays an important role in different organisms.In our study,we developed a humanspecific method which uses a cascade classifier of complexvalued polynomial model(CVPM),combined with sequence and structural feature descriptors to solve the problem of imbalance between positive and negative samples.Complexvalued gene expression programming and differential evolution are utilized to search the optimal CVPM model.We also made a systematic and comprehensive analysis of the acetylation data and the prediction results.The performances of our proposed method are 79.15%in Sp,78.17%in Sn,78.66%in ACC 78.76%in F1,and 0.5733 in MCC,which performs better than other state-of-the-art methods.

Long-Term Trends and Its Best Functional Form Estimation of Yearly Maximum and Minimum Temperatures at Cotonou City by Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Method

The understanding of the long-term trend in climatic variables is necessary for the climate change impacts studies and for modeling several processes in environmental engineering. However, for climatic variables, long-term trend is usually unknown whether there is a trend component and, if so, the functional form of this trend is also unknown. In this context, a conventional strategy consists to assume randomly the shape of the local trends in the time series. For example, the polynomial forms with random order are arbitrarily chosen as the shape of the trend without any previous justification. This study aims to 1) estimate the real long-term nonlinear trend and the changing rate of the yearly high temperature among the daily minimum (YHTaDMinT) and maximum temperatures (YHTaDMaxT) observed at Cotonou city, 2) find out for these real trend and trend increment, the best polynomial trend model among four trend models (linear, quadratic, third-order and fourth-order polynomial function). For both time series, the results show that YHTaDMinT and YHTaDMaxT time series are characterized by nonlinear and monotonically increasing trend. The trend increments present different phases in their nonmonotone variations. Among the four trend estimations models, the trend obtained by third-order and fourth-order polynomial functions exhibits a close pattern with the real long-term nonlinear trend given by the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). But, the fourth-order polynomial function is optimal, therefore, it can be used as the functional form of trend. In the trend increment case, for the YHTaDMaxT time series, the fourth-order fit is systematically the best among the four proposed trend models. Whereas for the YHTaDMinT time series, the third-order and fourth-order polynomial functions present the same performance. They can both be used as the functional form of trend increments. Overall, the fourth-order polynomial function presents a good performance in terms of trend and trend increments estimation.

Estimation in the polynomial errors-in-variables model

Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.

Detecting Change Points in Polynomial Regression Models with an Application to Cable Data Sets

In this paper, the Schwarz Information Criterion (SIC) is used to detect the change points in polynomial regression models. Switching quadratic regression models with same amount of model deviation and switching polynomial regression models with different amount of model deviation for different segments of regression are considered. The number of separate regimes and their corresponding regression orders are assume to be known. The method is then applied to cable data sets and the change points are successfully detected.

A polynomial hybrid reflection model and measurement of its parameters based on images of sample

Reflectance model is a basic concept in computer vision. Some existing models combining the classical diffuse reflectance model and those for surfaces containing specular components can approximately describe real reflectance. But the ratio of diffuse and specular reflection decided manually has no clear meaning. We propose a new polynomial hybrid reflectance model. The reflectance map equation with a known shape （for example cylinder） as a sample is used to estimate parameters of the proposed reflectance model by least square regression algorithm. Then the reflectance parameters for surfaces of the same class of materials can be determined. Experiments are performed for a metal surface. The synthesis images produced by the proposed method and existing ones are compared with the real acquired image, and the results show that the proposed reflectance model is suitable for describing real reflectance.

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.

Polynomial network autoregressive models with divergent orders

We propose a novel polynomial network autoregressive model by incorporating higher-order connected relationships to simultaneously model the effects of both direct and indirect connections. A quasimaximum likelihood estimation method is proposed to estimate the unknown influence parameters, and we demonstrate its consistency and asymptotic normality without imposing any distribution assumption. Moreover,an extended Bayesian information criterion is set for order selection with a divergent upper order. The application of the proposed polynomial network autoregressive model is demonstrated through both the simulation and the real data analysis.

A two-stage parametric subspace model for efficient contrast-preserving decolorization

The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete searching solver has a great potential in its c6nversion ability. In this paper, we present a two-step strategy to efficiently extend the parameter searching solver to a two-order multivariance polynomial model, as a sum of three subspaces. We show that the first subspace in the two-order model is the most important and the second one can be seen as a refinement. In the first stage of our model, the gradient correlation similarity （Gcs） measure is used on the first subspace to obtain an immediate grayed image. Then, Gcs is applied again to select the optimal result from the immettiate grayed image plus the second subspace-induced candidate images. Experimental results show the advantages of the proposed approach in terms of quantitative evaluation, qualitative evaluation, and algorithm complexity.

A survey on the local refinable splines

This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis.

Over-Smoothing Algorithm and Its Application to GCN Semi-supervised Classification

The feature information of the local graph structure and the nodes may be over-smoothing due to the large number of encodings,which causes the node characterization to converge to one or several values.In other words,nodes from different clusters become difficult to distinguish,as two different classes of nodes with closer topological distance are more likely to belong to the same class and vice versa.To alleviate this problem,an over-smoothing algorithm is proposed,and a method of reweighted mechanism is applied to make the tradeoff of the information representation of nodes and neighborhoods more reasonable.By improving several propagation models,including Chebyshev polynomial kernel model and Laplace linear 1st Chebyshev kernel model,a new model named RWGCN based on different propagation kernels was proposed logically.The experiments show that satisfactory results are achieved on the semi-supervised classification task of graph type data.