Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.     

Gaussian Quadrature Rules with Simple Node-Weight Relations

In this paper, we consider the symmetric Gaussian and L-Gaussian quadrature rules associated with twin periodic recurrence relations with possible variations in the initial coefficient. We show that the weights of the associated Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 4. We also show that the weights of the associated L-Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 5. Special cases of these quadrature rules are given. Finally, an easy to implement procedure for the evaluation of the nodes is described.     

GlueVaR risk measures in capital allocation applications

GlueVaR risk measures defined by Belles-Sampera et al. (2014) generalize the traditional quantile-based approach to risk measurement, while a subfamily of these risk measures has been shown to satisfy the tail-subadditivity property. In this paper we show how GlueVaR risk measures can be implemented to solve problems of proportional capital allocation. In addition, the classical capital allocation framework suggested by Dhaene et al. (2012) is generalized to allow the application of the Value-at-Risk (VaR) measure in combination with a stand-alone proportional allocation criterion (i.e., to accommodate the Haircut allocation principle). Two new proportional capital allocation principles based on GlueVaR risk measures are defined. An example based on insurance claims data is presented, in which allocation solutions with tail-subadditive risk measures are discussed.     

A generalized partially linear framework for variance functions

When model the heteroscedasticity in a broad class of partially linear models, we allow the variance function to be a partial linear model as well and the parameters in the variance function to be different from those in the mean function. We develop a two-step estimation procedure, where in the first step some initial estimates of the parameters in both the mean and variance functions are obtained and then in the second step the estimates are updated using the weights calculated based on the initial estimates. The resulting weighted estimators of the linear coefficients in both the mean and variance functions are shown to be asymptotically normal, more efficient than the initial un-weighted estimators, and most efficient in the sense of semiparametric efficiency for some special cases. Simulation experiments are conducted to examine the numerical performance of the proposed procedure, which is also applied to data from an air pollution study in Mexico City.     

Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements

Linear consecutively connected systems (LCCSs) are systems containing a linear sequence of ordered nodes. Connection elements (CE) characterized by diverse connection ranges, time-to-failure and time-to-repair distributions are allocated to different nodes to provide the system connectivity, i.e., a connection between the source and sink nodes of the LCCS. Examples of LCCSs abound in practical applications such as flow transmission systems and radio communication systems. Considerable research efforts have been expended in modeling and optimizing LCCSs. However, most of the existing works have assumed that CEs either are non-repairable or undergo a restrictive minimal repair policy with constant repair time. This paper makes new technical contributions by modeling and optimizing LCCSs with CEs under corrective maintenance with random repair time and different repair policies (minimal, perfect, and imperfect). The characteristics of CEs can depend on their location because the distance between adjacent nodes and conditions of CE operation and maintenance at different nodes can be different, which further complicates the problem. We first propose a discrete numerical algorithm to evaluate the instantaneous availability of each CE. A universal generating function based method is then implemented for assessing instantaneous and expected system connectivity for a specific CE allocation. As the CE allocation can have significant impacts on the system connectivity, we further define and solve the optimal CE allocation problem, whose objective is to find the CE allocation among LCCS nodes maximizing the expected system connectivity over a given mission time. Effects of different parameters including repair efficiency, mission time and repair time are investigated. As illustrated through examples, optimization results can facilitate optimal decisions on robust design and effective operation and maintenance managements of LCCSs.     

超网络中心性度量的υ-Position值方法

利用合作博弈理论的分配规则如Shapley值、Banzhaf值等来度量政治、经济和社会网络中节点的中心性或者重要性是识别网络中关键节点的一类重要方法。考虑到在超网络中代表各类组织的超边在网络中发挥的作用不同,本文研究了超网络博弈上一类广义Position值的分配规则,被称为υ-position值。它可以作为网络中度值测度的一类推广,以此来度量网络中参与者的中心性和相对重要性。其次,证明了超网络结构上类Shapley-position值可由分支超边指数和局部平衡超边贡献两个性质所唯一刻画。最后, 举例分析了υ-position值在超网络中心性测度中的应用。     

On Dual Based Lower Bounds for the Sequential Ordering Problem with Precedences and Due Dates

The Sequential Ordering Problem (herewith, SOP) with precedence relationships was introduced in Escudero (1988), and extended to cover release and due dates in Escudero and Sciomachen (1993). It has a broad range of applications, mainly in production planning for manufacturing systems. The problem consists of finding a minimum weight Hamiltonian path on a directed graph with weights on the nodes and the arcs, satisfying precedence relationships among the nodes and given lower and upper bounds on the weights of the Hamiltonian subpaths. In this paper we present a model for the constrained minimum weight Hamiltonian path problem with precedences and due dates forcing constraints, and introduce related valid cuts that can be used in a separation framework for the dual (Lagrangian based) relaxation of the problem. We also provide an heuristic separation procedure to obtain those cuts, so-called the Lagrangian Relax-and-Cut (LRC) scheme. Computational experience is given for variations of some SOP cases already reported in the literature.     

Approximation of Dense-n/2-Subgraph and the Complement of Min-Bisection

We consider the DENSE-n/2-SUBGRAPH problem, i.e., determine a block of half number nodes from a weighted graph such that the sum of the edge weights, within the subgraph induced by the block, is maximized. We prove that a strengthened semidefinite relaxation with a mixed rounding technique yields a 0.586 approximations of the problem. The previous best-known results for approximating this problem are 0.25 using a simple coin-toss randomization, 0.48 using a semidefinite relaxation, 0.5 using a linear programming relaxation or another semidefinite relaxation. In fact, an un-strengthened SDP relaxation provably yields no more than 0.5 approximation. We also consider the complement of the graph MIN-BISECTION problem, i.e., partitioning the nodes into two blocks of equal cardinality so as to maximize the weights of non-crossing edges. We present a 0.602 approximation of the complement of MIN-BISECTION.     

Iterative Corrections and a Posteriori Error Estimate for Integral Equations

Starting from a well known operator identity we obtain a recurrence formula, i.e., an iterative correction scheme, for the integral equations with computable kernel. From this we can increase the order of convergence step by step, say, from 4th to 8th to 12th. What is more interesting in this scheme, besides its fast acceleration, is its weak requirement on the integral kernel: the regularity of the kernel will not be strengthened during the correction procedure.     

Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been successful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler.     

Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification

Kohonen's self-organizing map (SOM) network is one of the most important network architectures developed during the 1980s. The main function of SOM networks is to map the input data from an n-dimensional space to a lower-dimensional (usually one or two dimensional) plot while maintaining the original topological relations. A well known limitation of the Kohonen network is the ‘boundary effect’ of nodes on or near the edge of the network. The boundary effect is responsible for the undue influence of the initial random weights assigned to the nodes of the network, which can lead to incorrect topological representations. To overcome this limitation, we use a modified, ‘circular’, weight adjustment algorithm. Our procedure is most effective with the class of problems where the actual coordinates of the output map do not need to correspond to the original input topology. This class of problems includes applications requiring clustering or classification of input data. We tested our method with a well known example problem from the domain of Group Technology, which is typical of this class of problems. Test results show that the circular weight adjustment procedure has better convergence properties, and that the clusters formed using the circular approach are at least as good as, and in many cases superior to, the basic SOM method for these types of problems.     

Semi-radial technical efficiency measurement

Semi-radial efficiency measurement combines technical efficiency, as captured by the classical Farrell measure, with an economically meaningful mix efficiency component. The semi-radial evaluation we propose proceeds in two steps. First, we build on the price interpretation of the generally accepted Koopmans efficiency notion to characterize appropriate benchmarks. Next, we present both a quantity-based distance measure and its dual (price-based) equivalent to evaluate the mix efficiency factor. The type of measures we propose may, e.g., be used to provide a price rationale for the Zieschang technical efficiency evaluation procedure.     

A hybrid Outer-Approximation/Benders Decomposition algorithm for the single allocation hub location problem under congestion

An efficient procedure that concurrently generates Outer-Approximation and Benders cuts is devised to tackle the single allocation hub location problem under congestion, an MINLP. The proposed method is able to optimally solve large instances (up to 200 nodes) in reasonable time. The combination of both cuts is an algorithmic novelty.     

Portfolio symmetry and momentum

This paper presents a novel theoretical framework to model the evolution of a dynamic portfolio (i.e., a portfolio whose weights vary over time), considering a given investment policy. The framework is based on graph theory and the quantum probability. Embedding the dynamics of a portfolio into a graph, each node of the graph representing a plausible portfolio, we provide the probabilities for a dynamic portfolio to lie on different nodes of the graph, characterizing its optimality in terms of returns. The framework embeds cross-sectional phenomena, such as the momentum effect, in stochastic processes, using portfolios instead of individual stocks. We apply our methodology to an investment policy similar to the momentum strategy of Jegadeesh and Titman (1993). We find that the strategy symmetry is a source of momentum.     

基于统一价格拍卖的初始排污权分配方法

针对初始排污权总量分配的实际问题,基于统一价格拍卖的思想提出了一种具有激励性的可变总量的分配方法,分别给出了排污企业对称和排污企业非对称两种情形下的线性均衡报价策略,并证明了该方法的可行性和有效性,从而为建设排污权分配和交易制度提供了理论依据和方法参考.     

A heuristic to generate rank-1 GMI cuts

Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use previously generated GMI cuts. We demonstrate that for problems in MIPLIB 3.0 and MIPLIB 2003, the cuts we generate form an important subclass of all rank-1 mixed-integer rounding cuts. Further, we use our heuristic to generate globally valid rank-1 GMI cuts at nodes of a branch-and-cut tree and use these cuts to solve a difficult problem from MIPLIB 2003, namely timtab2, without using problem-specific cuts.     

Efficient estimation of functional-coefficient regression models with different smoothing variables

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.     

Beyond the Chu-construction

Starting from symmetric monoidal closed (= autonomous) categories, Po-Hsiang Chu showed how to construct new *-autonomous categories, i.e., autonomous categories that are self-dual by virtue of having a dualizing object. Recently, Michael Barr extended this to the nonsymmetric, but closed, case, utilizing monads and modules between them. Since these notions are well-understood for bicategories, we introduce a notion of cyclic *-autonomy for these that implies closedness and, moreover, is inherited when forming bicategories of monads and of interpolads. Since the initial step of Barr's construction also carries over to the bicategorical setting, we recover his main result as an easy corollary. Furthermore, the Chu-construction at this level may be viewed as a procedure for turning the endo-1-cells of a closed bicategory into the objects of a new closed bicategory, and hence conceptually is similar to constructing bicategories of monads and of interpolads.     

A .699-approximation algorithm for Max-Bisection

We present a .699-approximation algorithm for Max-Bisection, i.e., partitioning the nodes of a weighted graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. This is an improved result from the .651-approximation algorithm of Frieze and Jerrum and the semidefinite programming relaxation of Goemans and Williamson. Received: October 1999 / Accepted: July 2000?Published online January 17, 2001     

Sequencing games without initial order

In this note we study uncertainty sequencing situations, i.e., one-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (Eur J Oper Res 40:344–351, 1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times.