Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Numerical simulation of inlet placement on sewage characteristics in the rounded square aquaculture tank with single inlet

To improve the self-cleaning ability of aquaculture tank and the efficiency of circulating water,physical and numerical experiments were conducted on the influence of inlet structure on sewage discharge in a rounded square aquaculture tank with a single inlet.Based on the physical model of the tank,analysis of how inlet structure adjustment affects sewage discharge efficiency and flow field characteristics was conducted to provide suitable flow field conditions for sinkable solid particle discharge.In addition,an internal flow field simulation was conducted using the RNG k-εturbulence model in hydraulic drive mode.Then a solid-fluid multiphase model was created to investigate how the inlet structure affects sewage collection in the rounded square aquaculture tank with single inlet and outlet.The finding revealed that the impact of inlet structure is considerably affecting sewage collection.The conditions of C/B=0.07-0.11(the ratio of horizontal distance between the center of the inlet pipe and the tank wall(C)to length of the tank(B))andα=25°(αis the angle between the direction of the jet and the tangential direction of the arc angle)resulted in optimal sewage collection,which is similar to the flow field experiment in the rounded square aquaculture tank with single inlet and outlet.An excellent correlation was revealed between sewage collection and fluid circulation stability in the aquaculture tank.The present study provided a reference for design and optimization of circulating aquaculture tanks in aquaculture industry.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Least Squares One-Class Support Tensor Machine

One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

PSR-SQUARES:基于程序空间约简器的SQL逆向合成系统

针对SQUARES程序空间增长过快,导致程序合成效率偏低的问题,在SQUARES的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的<被查询表,查询结果>示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向量。约简器根据神经网络的输出结果,采用末N位淘汰策略,删除与目标SQL语句相关性弱的合成规则,以减少候选SQL语句的生成和验证,提升系统合成效率。对约简器中深度神经网络的结构设计、训练样本集的生成方法和网络训练过程进行了详细描述。同时将PSR-SQUARES与当前有代表性SQL逆向合成系统进行实验对比,实验结果表明,PSR-SQUARES的综合性能不同程度地优于其他合成系统,平均合成时间由SQUARES的251 s降低至130 s,目标程序合成成功率由80%提升至89%。

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.

Factor-square-full半模

作为factor-square-full模的真推广,引入了factor-square-full半模的概念.设S是半环,M是左S-半模.称M的真subtractive子半模X是d-square,若存在正规满同态f:M→(M/X)2;称M的真subtractive子半模X是quasi-d-square,若存在M的d-square子半模Y使得X≤Y;称M是factor-square-full,若M的任意真subtractive子半模是quasi-d-square.讨论了这些子半模类及factor-square-full半模的性质.

EFFECTIVE DOUBLE LOOP CONTROL FOR A SQUARE WAVE BRUSHLESS DC MOTOR

A new type of brushless DC motor has been developed by using a square wave rare earth permanent magnet synchronous motor with its double loop control circuit. The double loop control scheme of the drive system yields a combination of desired characteristics including simplified control structure, small ripple torque, high speed accuracy, wide operating speed range, and fast dynamic response. Experimental results confirm excellent characteristics of the motor.

Experimental Study of Submergence Ratio on Local Scour Around a Square Pile in Steady Flow

Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in non-uniform sand were tested in the approaching flow velocity to critical velocity(larger than which the sediment particle is motivated)ratios of 0.56 and 1.03,respectively.The influences of flow depth were investigated on the basis of analysis of the three-dimensional topography,temporal maximum scour depth,bed profile development,and equilibrium scour depth.Results showed that the maximum scour depth was at the upstream corners of the pile other than at the stagnation point.The evolutions of the maximum scour depth data in non-uniform sand were well fitted with a recent exponential function,which characterized the initial,developing,and equilibrium stages of scour depth.The scour hole slopes upstream of the pile were found to be parallel to each other in the process of each test and were mainly governed by the sediment repose underwater.The equilibrium scour depth varied slightly with flow depth when the submergence ratio was larger than 1 in uniform sand while it was 2 in non-uniform sand.The armoring effects of coarse sediment particles markedly reduced the sediment transport in non-uniform sand despite the 0.34 increment in non-uniformity.

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

The effects of high temperature level on square Bt protein concen-tration of Bt cotton

Higher boll worm survival rates were detected after high temperature presented during square period in Bt cotton. The objective of this study was to investigate the effects of high temperature level on the Bt efficacy of two different types of Bt cotton cultivars at squaring stage. During the 2011 to 2013 cotton growth seasons, high temperature treatments ranged from 34 to 44°C in climate chambers, and field experiments under high temperature weather with various temperature levels were conducted to investigate the effects of the high temperature level on square Bt protein concentration and nitrogen metabolism. The climate chamber experiments showed that the square insecticidal protein contents reduced after 24 h elevated temperature treatments for both cultivars, whereas significant declines of the square insecticidal protein contents were detected at temperature 〉38°C, and only slightly numerical reductions were observed when temperature below 38°C. Similar high temperature responses were also observed at the two field experimental sites in 2013. Correspondingly, high temperature below 38°C seems have little effect on the square amino acid concentrations, soluble protein contents, glutamic-pyruvic transaminase（GPT） and glutamic-oxalacetic transaminase（GOT） activities as well as protease and peptidase activities; however, when the temperature was above 38°C, reduced soluble protein contents, enhanced amino acid concentrations, decreased GPT and GOT activities, bolstered protease and peptidase activities in square were detected. In general, the higher the temperature is（〉38°C）, the larger the changes for the above compound contents and key enzymes activities of the square protein cycle. The findings indicated that the unstable insect resistance of the square was related to high temperature level during square stage.

240 nm AlGaN-based deep ultraviolet micro-LEDs:size effect versus edge effect

240 nm AlGaN-based micro-LEDs with different sizes are designed and fabricated.Then,the external quantum efficiency(EQE)and light extraction efficiency(LEE)are systematically investigated by comparing size and edge effects.Here,it is revealed that the peak optical output power increases by 81.83%with the size shrinking from 50.0 to 25.0μm.Thereinto,the LEE increases by 26.21%and the LEE enhancement mainly comes from the sidewall light extraction.Most notably,transversemagnetic(TM)mode light intensifies faster as the size shrinks due to the tilted mesa side-wall and Al reflector design.However,when it turns to 12.5μm sized micro-LEDs,the output power is lower than 25.0μm sized ones.The underlying mechanism is that even though protected by SiO2 passivation,the edge effect which leads to current leakage and Shockley-Read-Hall(SRH)recombination deteriorates rapidly with the size further shrinking.Moreover,the ratio of the p-contact area to mesa area is much lower,which deteriorates the p-type current spreading at the mesa edge.These findings show a role of thumb for the design of high efficiency micro-LEDs with wavelength below 250 nm,which will pave the way for wide applications of deep ultraviolet(DUV)micro-LEDs.

Effects of square micro-pillar array porosity on the liquid motion of near surface layer

The influence rules of square micro-pillar array porosity on the liquid motion characteristics of the near-surface layer are investigated by quartz crystal microbalance(QCM).QCM is a powerful and promising technique in studying the interfacial behavior,which exhibits great advantages in investigating the effects of surface microstructure,roughness,and array.In our experiments,three different arrays with the same height of about 280 nm and center distance of 200μm,but different diameters of about 78μm,139μm,and 179μm are investigated.The results indicate that when the surface array has a large porosity,its influence on the liquid motion of the near surface layer is slight,thus resulting in a small increase of half-bandwidth variation due to the additional friction energy dissipation.When the surface array has a small porosity,the array tends to make the liquid film trapped in the array oscillating with the substrate,then there may be a layer of liquid film behaving like rigid film,and it also will make the liquid motion near the array layer more complicated.Thus for the#3 surface with a small porosity,both the absolute values of frequency shift|Δf3|and half-bandwidth variationΔΓ3 increase obviously.The experimental results show good consistence with the theoretical model of Daikhin and Urbakh.This study sheds light on understanding the influence mechanism of surface array porosity on the liquid motion of near-surface layer.

Evaluation of the intracellular lipid-lowering effect of polyphenols extract from highland barley in HepG2 cells

Active ingredients from highland barley have received considerable attention as natural products for developing treatments and dietary supplements against obesity.In practical application,the research of food combinations is more significant than a specific food component.This study investigated the lipid-lowering effect of highland barley polyphenols via lipase assay in vitro and HepG2 cells induced by oleic acid(OA).Five indexes,triglyceride(TG),total cholesterol(T-CHO),low density lipoprotein-cholesterol(LDL-C),aspartate aminotransferase(AST),and alanine aminotransferase(ALT),were used to evaluate the lipidlowering effect of highland barley extract.We also preliminary studied the lipid-lowering mechanism by Realtime fluorescent quantitative polymerase chain reaction(q PCR).The results indicated that highland barley extract contains many components with lipid-lowering effects,such as hyperoside and scoparone.In vitro,the lipase assay showed an 18.4%lipase inhibition rate when the additive contents of highland barley extract were 100μg/m L.The intracellular lipid-lowering effect of highland barley extract was examined using 0.25 mmol/L OA-induced HepG2 cells.The results showed that intracellular TG,LDL-C,and T-CHO content decreased by 34.4%,51.2%,and 18.4%,respectively.ALT and AST decreased by 51.6%and 20.7%compared with the untreated hyperlipidemic HepG2 cells.q PCR results showed that highland barley polyphenols could up-regulation the expression of lipid metabolism-related genes such as PPARγand Fabp4.

Engineering Strategies for Suppressing the Shuttle Effect in Lithium–Sulfur Batteries

Lithium–sulfur(Li–S)batteries are supposed to be one of the most potential next-generation batteries owing to their high theoretical capacity and low cost.Nevertheless,the shuttle effect of firm multi-step two-electron reaction between sulfur and lithium in liquid electrolyte makes the capacity much smaller than the theoretical value.Many methods were proposed for inhibiting the shuttle effect of polysulfide,improving corresponding redox kinetics and enhancing the integral performance of Li–S batteries.Here,we will comprehensively and systematically summarize the strategies for inhibiting the shuttle effect from all components of Li–S batteries.First,the electrochemical principles/mechanism and origin of the shuttle effect are described in detail.Moreover,the efficient strategies,including boosting the sulfur conversion rate of sulfur,confining sulfur or lithium polysulfides(LPS)within cathode host,confining LPS in the shield layer,and preventing LPS from contacting the anode,will be discussed to suppress the shuttle effect.Then,recent advances in inhibition of shuttle effect in cathode,electrolyte,separator,and anode with the aforementioned strategies have been summarized to direct the further design of efficient materials for Li–S batteries.Finally,we present prospects for inhibition of the LPS shuttle and potential development directions in Li–S batteries.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Experimental study on the effect of water absorption level on rockburst occurrence of sandstone

To investigate the mechanism of rockburst prevention by spraying water onto the surrounding rocks,15 experiments are performed considering different water absorption levels on a single face.High-speed photography and acoustic emission(AE)system are used to monitor the rockburst process.The effect of water on sandstone rockburst and the prevention mechanism of water on sandstone rockburst are analyzed from the perspective of energy and failure mode.The results show that the higher the ab-sorption degree,the lower the intensity of the rockburst after absorbing water on single side of sand-stone.This is reflected in the fact that with the increase in the water absorption level,the ejection velocity of rockburst fragments is smaller,the depth of the rockburst pit is shallower,and the AE energy is smaller.Under the water absorption level of 100%,the magnitude of rockburst intensity changes from medium to slight.The prevention mechanism of water on sandstone rockburst is that water reduces the capacity of sandstone to store strain energy and accelerates the expansion of shear cracks,which is not conducive to the occurrence of plate cracking before rockburst,and destroys the conditions for rockburst incubation.