Group Comparisons on Cognitive Attributes Using the Least Squares Distance Model of Cognitive Diagnosis

2010 Mathematics Subject Classification: 62P15.

A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method.

Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. The simulation method is explained in detail. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

High-Throughput Prediction of Acacia and Eucalypt Lignin Syringyl/Guaiacyl Content Using FT-Raman Spectroscopy and Partial Least Squares Modeling

High-throughput techniques are necessary to efficiently screen potential lignocellulosic feedstocks for the production of renewable fuels, chemicals, and bio-based materials, thereby reducing experimental time and expense while supplanting tedious, destructive methods. The ratio of lignin syringyl (S) to guaiacyl (G) monomers has been routinely quantified as a way to probe biomass recalcitrance. Mid-infrared and Raman spectroscopy have been demonstrated to produce robust partial least squares models for the prediction of lignin S/G ratios in a diverse group of Acacia and eucalypt trees. The most accurate Raman model has now been used to predict the S/G ratio from 269 unknown Acacia and eucalypt feedstocks. This study demonstrates the application of a partial least squares model composed of Raman spectral data and lignin S/G ratios measured using pyrolysis/molecular beam mass spectrometry (pyMBMS) for the prediction of S/G ratios in an unknown data set. The predicted S/G ratios calculated by the model were averaged according to plant species, and the means were not found to differ from the pyMBMS ratios when evaluating the mean values of each method within the 95 % confidence interval. Pairwise comparisons within each data set were employed to assess statistical differences between each biomass species. While some pairwise appraisals failed to differentiate between species, Acacias, in both data sets, clearly display significant differences in their S/G composition which distinguish them from eucalypts. This research shows the power of using Raman spectroscopy to supplant tedious, destructive methods for the evaluation of the lignin S/G ratio of diverse plant biomass materials. © 2015, The Author(s).

Efecto determinante de la motivación de viaje sobre la imagen de destino en turistas de ocio a un destino urbano: El caso de Monterrey, México. Una aproximación por medio de mínimos cuadrados parciales (PLS) = Determinant effect of travel motivation on the destination image of leisure tourist in an urban destination: the case of Monterrey, México. An approach through partial least squares (PLS)

Los turistas urbanos se caracterizan por ser uno de los segmentos de mayor crecimiento en los mercados turísticos actuales. Monterrey (México), uno de los principales destinos urbanos del país, ha apostado en la actualidad por mejorar su competitividad. Esta investigación se propuso encontrar evidencia acerca de la relación causal de la motivación de viaje sobre la imagen percibida del destino, dos variables importantes por su influencia en la satisfacción de los visitantes. Una revisión de la literatura permitió proponer constructos teóricos integrados en un instrumento para la recogida de datos vía encuesta a una muestra representativa. Por medio del método de regresión y ecuaciones estructurales por mínimos cuadrados parciales (PLS), se identificaron los componentes principales de ambas variables y se obtuvo un modelo explicativo de la imagen percibida del destino en función de la motivación de viaje. Finalmente, se emiten recomendaciones para la gestión del destino urbano en función de los resultados obtenidos. ABSTRACT: Abstract Urban tourists are recognized as one of the fastest growing segments in today’s tourism markets. Monterrey, Mexico, one of the main urban destinations in the country aims at improving its competitiveness. This research work had the purpose of finding evidence on the causal relationship between travel motivation and destination image, two important variables because of their influence on visitors’ satisfaction. A literature review enabled the proposal of a research instrument with theoretically based constructs to gather data through survey from a representative sample. Using regression and structural equations modelling by partial least squares (pls) a set of main components of both variables were identified thus enabling the obtention of a explanatory model of destination image in terms of travel motivations. Finally based on the results some recommendations of tourism management are given.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.

A Comparative Analysis Between Genetic Algorithms and Complex Nonlinear Least Squares on Electrical Impedance Characterization

This paper compares the performance of the complex nonlinear least squares algorithm implemented in the LEVM/LEVMW software with the performance of a genetic algorithm in the characterization of an electrical impedance of known topology. The effect of the number of measured frequency points and of measurement uncertainty on the estimation of circuit parameters is presented. The analysis is performed on the equivalent circuit impedance of a humidity sensor.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.