Non-compensatory composite indicators for the evaluation of urban planning policy: The Land-Use Policy Efficiency Index (LUPEI)

In this research paper, we define and test an ELECTRE III-based approach to the construction of non-compensatory composite indicators; these indicators are used for the evaluation of environmental and social performances of urban and regional planning policies. We tested the methodology for the construction of the Land-Use Policy Efficiency Index (LUPEI) on the municipal scale applied to a sample of municipalities in the Apulia Region (Southern Italy). Based on the literature review concerning composite indicators, we found that linear aggregation rules are the most widely applied aggregation procedures for composite indicators. However, their applicability depends on a set of strong theoretical and operational conditions. If these conditions do not hold, then other aggregation and weighting procedures must be applied to construct the composite indicators. We tested the ELECTRE III via a fruitful interaction with three experts who were participating in a focus group. We found that composite indicators are powerful tools when it comes to the assessment of multidimensional planning issues. Since each sub-indicator provides different information and responds to different goals, rankings and assessment based on mono-indicator frameworks can lead to incomplete or even biased results that do not consider an integrated approach to land-use policy efficiency. Moreover, both experts and decision-makers appreciated the role of composite indicators in increasing knowledge and providing deeper insights into complex phenomena in the domains of urban and regional planning.     

On conditions of coincidence of curvatures of the first and second types on distribution of planes

We consider distributions of planes in a multidimensional projective space and construct curvatures of the first and second types of group connections induced by composite equipments of the distributions. Conditions of coincidence of these curvatures are found. An internal composite equipment of a distribution of planes is performed. We prove that this equipment induces internal curvatures of the first and second types in the principal fiber bundle.     

PROPERTIES ON MEROMORPHIC SOLUTIONS OF COMPOSITE FUNCTIONAL-DIFFERENTIAL EQUATIONS

With the aid of Nevanlinna value distribution theory, differential equation theory and difference equation theory, we estimate the non-integrated counting function of meromorphic solutions on composite functional-differential equations under proper conditions.We also get the form of meromorphic solutions on a type of system of composite functional equations.Examples are constructed to show that our results are accurate.     

On the Poincaré inequality for periodic composite structures

We consider periodic composite structures characterized by a periodic Borel measure equal to the sum of at least two periodic measures. For such a composite structure, verifying the Poincaré inequality may be a difficult problem. Thus, we are interested in finding conditions under which it suffices to verify the Poincaré inequality separately for each of the simpler structure components instead of verifying it for the composite structure.     

Differentiation of Multivariable Composite Functions and Bell Polynomials

We generalize the Bell polynomials in order to derive an operational tool for the differentiation of composite functions in several variables. In particular we show a formula that relates the Bell polynomials for multivariable composite functions to the classical ones. Some applications are suggested.     

The Finite Difference Based Fast Adaptive Composite Grid Method

The fast adaptive composite grid (FAC) method is an iterative method for solving discrete boundary value problems on composite grids. McCormick introduced the method in [8] and considered the convergence behaviour for discrete problems resulting from finite volume element discretization on composite grids. In this paper we consider discrete problems resulting from finite difference discretization on composite grids. We distinguish between two obvious discretization approaches at the grid points on the interfaces between fine and coarse subgrids. The FAC method for solving such discrete problems is described. In the FAC method several intergrid transfer operators appear. We study how the convergence behaviour depends on these intergrid transfer operators. Based on theoretical insights, (quasi-)optimal intergrid transfer operators are derived. Numerical results illustrate the fast convergence of the FAC method using these intergrid transfer operators.     

An effective method to reduce the computational complexity of composite quantile regression

In this article, we aim to reduce the computational complexity of the recently proposed composite quantile regression (CQR). We propose a new regression method called infinitely composite quantile regression (ICQR) to avoid the determination of the number of uniform quantile positions. Unlike the composite quantile regression, our proposed ICQR method allows combining continuous and infinite quantile positions. We show that the proposed ICQR criterion can be readily transformed into a linear programming problem. Furthermore, the computing time of the ICQR estimate is far less than that of the CQR, though it is slightly larger than that of the quantile regression. The oracle properties of the penalized ICQR are also provided. The simulations are conducted to compare different estimators. A real data analysis is used to illustrate the performance.     

The composite Milstein methods for the numerical solution of Ito stochastic differential equations

In this paper, we present the composite Milstein methods for the strong solution of Ito stochastic differential equations. These methods are a combination of semi-implicit and implicit Milstein methods. We give a criterion for choosing either the implicit or the semi-implicit scheme at each step of our numerical solution. The stability and convergence properties are investigated and discussed for the linear test equation. The convergence properties for the nonlinear case are shown numerically to be the same as the linear case. The stability properties of the composite Milstein methods are found to be more superior compared to those of the Milstein, the Euler and even better than the composite Euler method. This superiority in stability makes the methods a better candidate for the solution of stiff SDEs.     

A solution for the local plane strain problems using elliptic integrals of Cauchy type

We consider a parallel fiber‐reinforced periodic elastic composite that present an imperfect contact of spring type between the fiber and the matrix. We use the elliptic integral of Cauchy type for solving the plane strain local problems that arise from the asymptotic homogenization method. Several general conditions are assumed, which include that the fibers are disposed of arbitrary manner in the local cell, that all fibers present contact perfect with different constants of imperfection, and that their cross section is a smooth closed arbitrary curve. We find that there are infinity solutions for these problems, and we find relations between these solutions and effective coefficients of the composite. Finally, we obtain analytic formulae for the circular fiber case and show some numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling loss data using composite models

We develop several new composite models based on the Weibull distribution for heavy tailed insurance loss data. The composite model assumes different weighted distributions for the head and tail of the distribution and several such models have been introduced in the literature for modeling insurance loss data. For each model proposed in this paper, we specify two parameters as a function of the remaining parameters. These models are fitted to two real insurance loss data sets and their goodness-of-fit is tested. We also present an application to risk measurements and compare the suitability of the models to empirical results.     

Composite generalized Laguerre–Legendre pseudospectral method for Fokker–Planck equation in an infinite channel

In this paper, we propose a composite generalized Laguerre–Legendre pseudospectral method for the Fokker–Planck equation in an infinite channel, which behaves like a parabolic equation in one direction, and behaves like a hyperbolic equation in other direction. We establish some approximation results on the composite generalized Laguerre–Legendre–Gauss–Radau interpolation, with which the convergence of proposed composite scheme follows. An efficient implementation is provided. Numerical results show the spectral accuracy in space of this approach and coincide well with theoretical analysis. The approximation results and techniques developed in this paper are also very appropriate for many other problems on multiple-dimensional unbounded domains, which are not of standard types.     

Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium

In this paper a one-dimensional space fractional diffusion equation in a composite medium consisting of two layers in contact is studied both analytically and numerically. Since domain decomposition is the only approach available to solve this problem, we at first investigate analytical and numerical strategies for a composite medium with the same fractal dimension in each layer to ascertain which domain decomposition approach is the most accurate and consistent with a global solution methodology, which is available in this case. We utilise a matrix representation of the fractional-in-space operator to generate a system of linear ODEs with the matrix raised to the same fractional exponent. We show that the global and domain decomposition numerical strategies for this problem produce simulation results that are in good agreement with their analytic counterparts and conclude that the domain decomposition that imposes the Neumann condition at the interface produces the most consistent results. Finally, we carry this finding to study the composite problem with different fractal dimensions, where we again favourably compare analytic and numerical solutions. The resulting method can be naturally extended to space fractional diffusion in a composite medium consisting of more than two layers.     

A tensor product matrix approximation problem in quantum physics

We consider a matrix approximation problem arising in the study of entanglement in quantum physics. This notion represents a certain type of correlations between subsystems in a composite quantum system. The states of a system are described by a density matrix, which is a positive semidefinite matrix with trace one. The goal is to approximate such a given density matrix by a so-called separable density matrix, and the distance between these matrices gives information about the degree of entanglement in the system. Separability here is expressed in terms of tensor products. We discuss this approximation problem for a composite system with two subsystems and show that it can be written as a convex optimization problem with special structure. We investigate related convex sets, and suggest an algorithm for this approximation problem which exploits the tensor product structure in certain subproblems. Finally some computational results and experiences are presented.     

Efficient estimation and variable selection for infinite variance autoregressive models

In this paper, a self-weighted composite quantile regression estimation procedure is developed to estimate unknown parameter in an infinite variance autoregressive (IVAR) model. The proposed estimator is asymptotically normal and more efficient than a single quantile regression estimator. At the same time, the adaptive least absolute shrinkage and selection operator (LASSO) for variable selection are also suggested. We show that the adaptive LASSO based on the self-weighted composite quantile regression enjoys the oracle properties. Simulation studies and a real data example are conducted to examine the performance of the proposed approaches.     

Traveling wave solutions of the Camassa-Holm equation

All weak traveling wave solutions of the Camassa-Holm equation are classified. We show that, in addition to smooth solutions, there are a multitude of traveling waves with singularities: peakons, cuspons, stumpons, and composite waves.     

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.     

一种循环修正的组合评价方法

提出了一种循环修正的组合评价方法.首先,对所研究的问题选取几种综合评价方法进行综合评价.其次,用Sperm an等级相关系数法检验几种综合评价法的一致性.进一步重复采用平均值法、Boarda法、C om peland法和模糊Board法对上述综合评价结果进行组合评价,直到标准差均收敛于0为止,得到最优的组合评价结果.最后以辽宁省2001年实际统计资料为例,对各地区的经济实力进行了综合评价和排序.     

Consistent learning by composite proximal thresholding

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consistent in a statistical sense, and we design an error-tolerant composite proximal thresholding algorithm for computing such estimators. New results on the asymptotic behavior of the proximal forward–backward splitting method are derived and exploited to establish the convergence properties of the proposed algorithm. In particular, our method features a o(1 / m) convergence rate in objective values.