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.

Tricube Weighted Linear Regression and Interquartile for Cloud Infrastructural Resource Optimization

Cloud infrastructural resource optimization is the process of precisely selecting the allocating the correct resources either to a workload or application.When workload execution,accuracy,and cost are accurately stabilized in opposition to the best possible framework in real-time,efficiency is attained.In addition,every workload or application required for the framework is characteristic and these essentials change over time.But,the existing method was failed to ensure the high Quality of Service(QoS).In order to address this issue,a Tricube Weighted Linear Regression-based Inter Quartile(TWLR-IQ)for Cloud Infrastructural Resource Optimization is introduced.A Tricube Weighted Linear Regression is presented in the proposed method to estimate the resources(i.e.,CPU,RAM,and network bandwidth utilization)based on the usage history in each cloud server.Then,Inter Quartile Range is applied to efficiently predict the overload hosts for ensuring a smooth migration.Experimental results show that our proposed method is better than the approach in Cloudsim under various performance metrics.The results clearly showed that the proposed method can reduce the energy consumption and provide a high level of commitment with ensuring the minimum number of Virtual Machine(VM)Migrations as compared to the state-of-the-art methods.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local reconstructions.Unlike the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals one.Further,a very simple smoothness indicator for the global stencil is proposed.The new scheme can achieve sixth-order accuracy in smooth regions.Numerical tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

Landslides susceptibility mapping in Guizhou province based on fuzzy theory

The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity to drainage and annual precipitation were taken as independent, causal factors in this study.A landslide hazard evaluation factor system was established by classifying these factors into more subclasses according to some rules.Secondly, a trapezoidal fuzzy number weighting(TFNW) approach was used to assess the importance of six causal factors to landslides in an ArcGIS environment.Thirdly, a landslide susceptibility map was created based on a weighted linear combination model.According to this susceptibility map, the study area was classified into four categories of landslide susceptibility:low, moderate, high and very high.Finally, in order to verify the results obtained, the susceptibility map and the landslide inventory map were combined in the GIS.In addition, the weighting procedure showed that TFNW is an efficient method for weighting causal landslide factors.

Prediction of flyrock induced by mine blasting using a novel kernel-based extreme learning machine

Blasting is a common method of breaking rock in surface mines.Although the fragmentation with proper size is the main purpose,other undesirable effects such as flyrock are inevitable.This study is carried out to evaluate the capability of a novel kernel-based extreme learning machine algorithm,called kernel extreme learning machine(KELM),by which the flyrock distance(FRD) is predicted.Furthermore,the other three data-driven models including local weighted linear regression(LWLR),response surface methodology(RSM) and boosted regression tree(BRT) are also developed to validate the main model.A database gathered from three quarry sites in Malaysia is employed to construct the proposed models using 73 sets of spacing,burden,stemming length and powder factor data as inputs and FRD as target.Afterwards,the validity of the models is evaluated by comparing the corresponding values of some statistical metrics and validation tools.Finally,the results verify that the proposed KELM model on account of highest correlation coefficient(R) and lowest root mean square error(RMSE) is more computationally efficient,leading to better predictive capability compared to LWLR,RSM and BRT models for all data sets.

Land use suitability analysis for town development planning in Nanjing hilly areas: A case study of Tangshan new town, China

Land use suitability analysis plays an important role in sustainable land use and solving environmental problems caused by rapid urban development.A land use suitability mapping approach for town development planning in hilly areas was constructed based on two multi-criteria evaluation methods:Weighted Linear Combination(WLC)and Ordered Weighted Averaging(OWA),to comparatively evaluate and map land use suitability of Tangshan new town in Nanjing,China.Fourteen evaluation factors related to topographic,environmental,socio-economics and historical sites data were used as suitability criteria.The analytic hierarchy process(AHP)method and GIS techniques were integrated into the evaluation models to create the land use suitability map for town development planning.The results of WLC approach showed that 11.4%of the total area is highly suitable while the 48.6%is unsuitable.The results of WLC and OWA approach showed the distribution of degree of land use suitability is almost the same.The areas located at the southern and eastern flat regions are highly suitable for land use,whereas the areas close to the mountain forests,steep slopes,waters,and hot springs,have lower suitability for land use.Sensitivity analysis indicated that the suitability results of the two proposed methods are robust.Indirect validation was achieved by mutual comparison of suitability maps derived from the WLC and OWA methods.It demonstrated that the overall agreement is 90.81%and kappa coefficient is 0.81,indicating that both methods provide very similar spatial suitability distributions.By overlaying the resultant map with the previous master plan map of Tangshan new town,the overlay map once again indicated a satisfactory ecological fit between the two maps.At last,several recommendations are proposed aiming at improving the long-term town development plan for Tangshan new town.

Landfill Siting Using GIS and AHP （Analytical Hierarchy Process）： A Case Study AI-Qasim Qadhaa, Babylon, Iraq

The selection of a landfill site is considered as a complicated task because this process is based on many factors and restrictions. For Al-Qasim Qadhaa, which is situated in the southern part of the Babylon Governorate, Iraq, there is no landfill site in that area that conforms to the scientific criteria for selecting sites for landfill. For this reason, 15 criteria were adopted in this study （groundwater depth, rivers, soil types, agriculture lands use, land use, elevation, slope, gas pipelines, oil pipelines, power lines, roads, railways, urban centers, villages and archaeological sites） using GIS （geographic information system）, which has a large ability to manage input data. In addition, the AHP （analytical hierarchy process） method was used to derive the relative weightings for each criterion using pair-wise comparison. To obtain the suitability index for candidate landfill sites, a weighted linear combination method was used. After combining these methods, two suitable candidate landfill sites, with areas of 2.766 km2 and 2.055 km2, respectively, were found to satisfy the scientific and environmental requirements. The area of these sites can accommodate solid waste from 2020 until 2030 based on the required area, which was 0.702 km2.

Very Short-Term Probabilistic Prediction Method for Wind Speed Based on ALASSO-Nonlinear Quantile Regression and Integrated Criterion

To enhance the performance of the prediction intervals (PIs), a novel very short-term probabilistic prediction method for wind speed via nonlinear quantile regression (NQR) based on adaptive least absolute shrinkage and selection operator (ALASSO) and integrated criterion (IC) is proposed. The ALASSO method is studied for shrinkage of output weights and selection of variables. Furthermore, for the better performance of PIs, composite weighted linear programming (CWLP) is proposed to modify the conventional linear programming cost function of quantile regression (QR), by combining it with Bayesian information criterion (BIC) as an IC to optimize the coefficients of PIs. Then, the multiple fold cross model (MFCM) is utilized to improve the PIs performance. Multistep probabilistic prediction of 15-minute wind speed is performed based on the real wind farm data from the northeast of China. The effectiveness of the proposed approach is validated through the performances' comparisons with conventional methods.

Random Weighting T-Statistics in Linear Regression Models

In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n-1/2). Thus, we have provided a more practical distribution approximating method.

Analysis of Shoreline Changes in Ikoli River in Niger Delta Region Yenagoa,Bayelsa State Using Digital Shoreline Analysis System(DSAS)

The use of Digital Shoreline Analysis System was used to determine shoreline changes in Ikoli River,Yenagoa,Bayelsa State.Shoreline data were extracted from satellite imagery over thirty years(1991-2021).The basis of this study is to use Digital Shoreline Analysis System to determine erosion and accretion areas.The result reveals that the average erosion rate in the study area is 1.16 m/year and the accretion rate is 1.62 m/year along the Ikoli River in Ogbogoro Community in Yenagoa,Bayelsa State.The mean shoreline length is 5.24 km with a baseline length of 5.2 km and the area is classified into four zones to delineate properly area of erosion and accretion based on the five class of Linear regression rate,endpoint rate and weighted linear rate of which zone Ⅰ contain very high erosion and high erosion with an area of landmass 255449.93 m^(2) of 38%,zone Ⅱ contain moderate accretion,very high accretion and high accretion with a land area of 1666816.46 m^(2) with 24%,zone Ⅲ has very high erosion and high erosion with an area of landmass 241610.85 m^(2) of 34% and zone Ⅳ contain moderate accretion and high accretion with land area 30888.08 m^(2) with 4%.Out of the four zones,zone Ⅰ and Ⅱ were found to be eroding with 72% and zone Ⅱ and Ⅳ contain accretion with 28%.The result shows that 44% of the area have been eroded.Therefore,coastal engineers,planners,and shoreline zone management authorities can use DSAS to create more appropriate management plans and regulations for coastal zones and other coastal parts of the state with similar geographic features.

A systematic framework of constructing surrogate model for slider track peeling strength prediction

Peeling strength can comprehensively reflect slider track safety and is crucial in car seat safety assessments.Current methods for determining slider peeling strength are primarily physical testing and numerical simulation.However,these methods encounter the potential challenges of high costs and overlong time consumption which have not been adequately addressed.Therefore,the efficient and low-cost surrogate model emerges as a promising solution.Nevertheless,currently used surrogate models suffer from inefficiencies and complexity in data sampling,lack of robustness in local model predictions,and isolation between data sampling and model prediction.To overcome these challenges,this paper aims to set up a systematic framework for slider track peeling strength prediction,including sensitivity analysis,dataset sampling,and model prediction.Specifically,the interpretable linear regression is performed to identify the sensitivity of various geometric variables to peeling strength.Based on the variable sensitivity,a distance metric is constructed to measure the disparity of different variable groups.Then,the sparsity-targeted sampling(STS)is proposed to formulate a representative dataset.Finally,the sequentially selected local weighted linear regression(SLWLR)is designed to achieve accurate track peeling strength prediction.Additionally,a quantitative cost assessment of the supplementary dataset is proposed by utilizing the minimum adjacent sample distance as a mediator.Experimental results validate the efficacy of sequential selection and the weighting mechanism in enhancing localization robustness.Furthermore,the proposed SLWLR method surpasses similar approaches and other common surrogate methods in terms of prediction performance and data quantity requirements,achieving an average absolute error of 3.3 kN in the simulated test dataset.

Piecewise Linear Weighted Iterative Algorithm for Beam Alignment in Scanning Beam Interference Lithography

To obtain a good interference fringe contrast and high fidelity,an automated beam iterative alignment is achieved in scanning beam interference lithography(SBIL).To solve the problem of alignment failure caused by a large beam angle(or position)overshoot exceeding the detector range while also speeding up the convergence,a weighted iterative algorithm using a weight parameter that is changed linearly piecewise is proposed.The changes in the beam angle and position deviation during the alignment process based on different iterative algorithms are compared by experiment and simulation.The results show that the proposed iterative algorithm can be used to suppress the beam angle(or position)overshoot,avoiding alignment failure caused by over-ranging.In addition,the convergence speed can be effectively increased.The algorithm proposed can optimize the beam alignment process in SBIL.

Projection-based Consistent Test for Linear Regression Model with Missing Response and Covariates

In recent years,there has been a large amount of literature on missing data.Most of them focus on situations where there is only missingness in response or covariate.In this paper,we consider the adequacy check for the linear regression model with the response and covariates missing simultaneously.We apply model adjustment and inverse probability weighting methods to deal with the missingness of response and covariate,respectively.In order to avoid the curse of dimension,we propose an empirical process test with the linear indicator weighting function.The asymptotic properties of the proposed test under the null,local and global alternative hypothe tical models are rigorously investigated.A consisten t wild boot strap method is developed to approximate the critical value.Finally,simulation studies and real data analysis are performed to show that the proposed method performed well.

The Determination on Weight Hierarchies of q-Ary Linear Codes of Dimension 5 in Class IV

The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.

A Research into the Evaluation Target System and Comprehensive Evaluation Method About the Science and Technology Development of Provinces

Based on the systematic theory and the system analytic method, this thesis expounds manifestly the evaluation target system and comprehensive evaluation method about the science and technology development of provinces (cities and districts). By putting it into practice of provinces (cities and districts) science and technology development, this set of target system and method may fully reflect the impact on the social development. The acceleration of transferring the extensive economy to the intensive one in province (cities and districts) and the relation of coordinated growth of science and technology, economy, society are of momentous current significance.

The Inductive Blockwise Alperin Weight Condition for PSL（3, q）

The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B. Recently, the inductive blockwise Alperin weight condition has been introduced such that the blockwise Alperin weight conjecture holds if all non-abelian simple groups satisfy these conditions. We will verify the inductive blockwise Alperin weight condition for the finite simple groups PSL（3, q） in this paper.

Effects of inventory classifications on CONWIP system: a case study

This paper studies the effects of integrating four inventory classification methods into constant work-in-process(CONWIP)systems in a multistage batch production.The inventory classification methods are multiple closed-loop CONWIP(MCC),parallel CONWIP(PC),analytical hierarchy procedure,and weighted linear optimization(WLO).Discrete-event simulation models were built.A full-factorial experimental design was employed.Response surface methodology generated suitable regression models for performance comparison of different ABC analysis methods.In the second stage of experiment,the ABC analysis methods from the first stage were fine-tuned and compared.PC and WLO are the most preferred methods because of higher total outputs,lower work-in-process levels,and shorter flow times compared with the other two methods.However,the revenue accrued through WLO is higher than that accrued via PC.This study complements existing literature on price setting in manufacturing organizations by delineating classification of finished goods based on both exogenous and production factors.