LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Fitting method of pseudo-polynomial for solving nonlinear parametric adjustment

The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [

NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS

The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.

A SPARSITY AND COMPRESSION RATIO JOINT ADJUSTMENT METHOD FOR COLLABORATIVE SPECTRUM SENSING

Spectrum sensing is the fundamental task for Cognitive Radio (CR). To overcome the challenge of high sampling rate in traditional spectral estimation methods, Compressed Sensing (CS) theory is developed. A sparsity and compression ratio joint adjustment algorithm for compressed spectrum sensing in CR network is investigated, with the hypothesis that the sparsity level is unknown as priori knowledge at CR terminals. As perfect spectrum reconstruction is not necessarily required during spectrum detection process, the proposed algorithm only performs a rough estimate of sparsity level. Meanwhile, in order to further reduce the sensing measurement, different compression ratios for CR terminals with varying Signal-to-Noise Ratio (SNR) are considered. The proposed algorithm, which optimizes the compression ratio as well as the estimated sparsity level, can greatly reduce the sensing measurement without degrading the detection performance. It also requires less steps of iteration for convergence. Corroborating simulation results are presented to testify the effectiveness of the proposed algorithm for collaborative spectrum sensing.

An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems

A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

Research on the adjustment model of ventilation characteristic parameters based on integrated method of circuit and path

Ventilation characteristic parameters are the base of ventilation network solution; however, they are apt to be affected by operating errors, reading errors, airflow stability, and other factors, and it is difficult to obtain accurate results. In order to check the ventilation characteristic parameters of mines more accurately, the integrated method of circuit and path is adopted to overcome the drawbacks caused by the traditional path method or circuit method in the digital debugging process of ventilation system, which can improve the large local error or the inconsistency between the airflow direction and the actual situation caused by inaccuracy of the ventilation characteristic parameters or checking in the ventilation network solution. The results show that this method can effectively reduce the local error and prevent the pseudo-airflow reversal phenomenon; in addition, the solution results are consistent with the actual situation of mines, and the effect is obvious.

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.

Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis

Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.

PTSD Outcome,Adjustment Disorder and Methods of Treatment

This research is pointed up on“Adjustment disorder and adaptation with anxiety,stress and depression following the catastrophic life events”.We explained the results of psychopathological and psychosocial effects of post-traumatic stress disorder(PTSD),especially depression and anxiety caused by catastrophic stressful life events or other factors(war,terrorist acts,etc.),and then discussed and presented different methods and forms of treatments.Our theoretical studies,in the fields of PTSD-Psychogeriatry and Psychiatry in one side and different Seminars in Paris etc.in other side,have completed this research;the studies at the University of Illinois,as full time Prof.are developed in this working research.Anxiety disorders,depression and stresses are not a new phenomenon in the field of psychiatry,they have existed several years B.C.,but their aetiology and physiopathology were not clear.Moreover,the treatments were on the basis of some medical plants or traditional and local methods which existed yet,more or less in some African or Asiatic countries,the hospitals for mental disorders had been limited;in plus,environmental factors,also heredity,quality of life and the degree of the vulnerability of individuals and the capacity of the patients to cope with the pain.etc were neglected.In our time,because of multifactorial reasons,anxiety disorders and depression,which are often accompanied by obsessive-compulsive disorders,are the most prevalent pathology in Psychiatry that we discussed in this paper(Figure 1).Actually,because of the global COVID-19 pandemic,the frequency of depression and anxiety disorders,according to the global news and audio-visual information,are significantly increased.Our teaching experiences,also clinical researches and observations in the Mental Health Centres showed clearly that in extreme cases when major depression and anxiety are accumulating and occur to coexist together,they can exert serious pathological effects not only on the cardiovascular system and endocrine glands but also on the cognitive system more particularly on flexibility,memory,creativity and attention(Figure 2);moreover,the coexistence of anxiety and a psychiatric condition can produce not only cognitive disorder,but in some cases-ex.inability to cope with pain or inadaptability to stress,may hasten and intensify ageing process.In many cases as shown,the anxious subjects,when confronted to psychosocial crisis,feel fear and expect to be facing to adverse events or catastrophic situations and believe to live negative future events;in plus,exhibit emotional distress,repetitive dreams and severe insomnia.In these cases,according to our experiences,in parallel to pharmacotherapy,the relaxation and complete massages in one side,physical education,meditation,positive emotion and muscular release etc.in other side,are useful to help these patients for a best control of emotional distress and relatively reduce anxiety and depression.We add that the syndrome of stress,depression and anxiety has been recognized not only in the different victims of war,but also in the non-war(cf.other factors noted in this paper:fig.1)traumatized population.

Quantitative energy-dispersive X-ray fluorescence analysis for unknown samples using full-spectrum least-squares regression

The full-spectrum least-squares(FSLS) method is introduced to perform quantitative energy-dispersive X-ray fluorescence analysis for unknown solid samples.Based on the conventional least-squares principle, this spectrum evaluation method is able to obtain the background-corrected and interference-free net peaks, which is significant for quantization analyses. A variety of analytical parameters and functions to describe the features of the fluorescence spectra of pure elements are used and established, such as the mass absorption coefficient, the Gi factor, and fundamental fluorescence formulas. The FSLS iterative program was compiled in the C language. The content of each component should reach the convergence criterion at the end of the calculations. After a basic theory analysis and experimental preparation, 13 national standard soil samples were detected using a spectrometer to test the feasibility of using the algorithm. The results show that the calculated contents of Ti, Fe, Ni, Cu, and Zn have the same changing tendency as the corresponding standard content in the 13 reference samples. Accuracies of 0.35% and 14.03% are obtained, respectively, for Fe and Ti, whose standard concentrations are 8.82% and 0.578%, respectively. However, the calculated results of trace elements (only tens of lg/g) deviate from the standard values. This may be because of measurement accuracy and mutual effects between the elements.

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

A global interpolating meshless shape function based on the generalized moving least-square （GMLS） is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS （IGMLS） shape function, an improved element-free Galerkin （EFG） method is proposed for the structural dynamic analysis. Compared with the conven- tional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasi- bility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

Big-M based MILP method for SCUC considering allowable wind power output interval and its adjustable conservativeness

In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable conservativeness.The wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power integration.Therefore,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is presented.Furthermore,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust solutions.This can establish a trade-off between economy and security.To develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable conservativeness.Simulation studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.

Adaptive algorithm for solving different types and different precisions and nonlinear surveying and mapping parameters adjustment

Approximate linear methods and nonlinear methods were adopted usually for solving models of nonlinear surveying and mapping parameters adjustment. But, these iterative algorithms need to compare harsh initial value. A kind of new algorithm-adaptive algorithm based on analyzing the general methods was put forward. The new algorithm has quick rate of convergence and low dependence for initial value, so it can avoid calculating complex second derivative of the target function. The results indicate that its performance is better than those of the others.

Solution model of nonlinear integral adjustment including different kinds of observing data with different precisions

In order to process different kinds of observing data with different precisions, a new solution model of nonlinear dynamic integral least squares adjustment was put forward, which is not dependent on their derivatives. The partial derivative of each component in the target function is not computed while iteratively solving the problem. Especially when the nonlinear target function is more complex and very difficult to solve the problem, the method can greatly reduce the computing load.

THE CHARACTERISTICS OF THUNDERSTORM FREQUENCY VARIATION AND THEIR POSSIBLE RELATION WITH THE ADJUSTMENT OF CROP DISTRIBUTION IN THE LEIZHOU PENINSULA

In order to research possible influences of the adjustment of plant distribution on the development frequency of thunderstorms over the Leizhou Peninsula, mathematic statistic methods, including correlation analyses, 11 kinds of fitting models and all-variable regression methods, were used for analyses and research. The results show that the average trend of the number of annual thunderstorm days is descending obviously, and there are thunderstorms in all seasons, in which warm post-midday thunderstorms have taken up the most part, and high frequency is found from May to September, and the starting and ending dates of thunderstorms have a great annual discrepancy. The vegetation structure has been improved along with the reduction of rice fields and the area increment of sugarcane and fruits planting, which results in the decrease of the number of thunderstorm days; the change in the characteristics of winter spare fields, which is caused by the planting of vegetables, limits the formation of thunderstorms in early winter and late spring. Meanwhile, the area adjustment of peanut planting has little influence on the variation of thunderstorm days. The adjustment of principal crop distribution, such as rice, sugarcane, fruits and vegetables, may have obvious influence on the formation of thunderstorms, and sugarcane has the largest effect, followed in turn by rice, vegetables and fruits, and the adjustment of crop distribution has little influence on the starting and ending dates of thunderstorms.