An algorithm for generating color scales for both categorical and ordinal coding

Previous research has shown multihue scales to be well‐suited to code categorical features and shown lightness scales to be well‐suited to code ordinal quantities. We introduce an algorithm, Motley, that produces color scales varying in both hue and lightness, intended to be effective for both categorical and ordinal coding, allowing users to determine both absolute and relative quantities efficiently and accurately. The algorithm first determines the lightnesses of scale colors to maximize perceived lightness differences and establish the lightness ordering, generating separate search spaces for each scale position. It then selects hues by heuristic search to maximize the discriminability of the scale. It produces scales that are ordered with respect to lightness but unordered with respect to hue and thus more discriminable than typical multihue lightness scales. In an experimental evaluation on human subjects, Motley's scales enabled accurate judgments of relative quantity, with response times superior to unordered multihue scales and comparable to ordered lightness scales, and enabled accuracy and speed of judgments of absolute quantity superior to lightness scales and comparable to multihue scales. Published 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.     

Spectral element solutions for the PN neutron transport equations

This paper discusses the application of the Legendre spectral element method to the steady one-velocity P_N equations describing neutron transport in a one-dimensional heterogeneous slab. Emphasis is put on the implementation of the method. Some key elements related to its efficiency are analyzed to prepare further developments in higher dimensions to evaluate benchmark solutions to the simplified P_N equations.     

两类距离图的分式色数和点色数

分式色数和点色数是图的两个重要参数。本文在文献 [1]的基础上给出了两类距离图G(Z ,Dm ,k,k + 1)与G(Z ,Dm ,k ,k + 1,k + 2 )的分式色数和点色数。     

The Limiting Density of Unit Root Test Statistics: A Unifying Technique

In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively.
AMS 1991 subject classification. Primary 62M10; secondary 62E20.     

Nash and integrated solutions in a just-in-time seller–buyer supply chain with buyer's ordering cost reductions

The seller frequently offers the buyer trade credit to settle the purchase amount. From the seller's prospective, granting trade credit increases not only the opportunity cost (i.e., the interest loss on the buyer's purchase amount during the credit period) but also the default risk (i.e., the rate that the buyer will be unable to pay off his/her debt obligations). On the other hand, granting trade credit increases sales volume and revenue. Consequently, trade credit is an important strategy to increase seller's profitability. In this paper, we assume that the seller uses trade credit and number of shipments in a production run as decision variables to maximise his/her profit, while the buyer determines his/her replenishment cycle time and capital investment as decision variables to reduce his/her ordering cost and achieve his/her maximum profit. We then derive non-cooperative Nash solution and cooperative integrated solution in a just-in-time inventory system, in which granting trade credit increases not only the demand but also the opportunity cost and default risk, and the relationship between the capital investment and the ordering cost reduction is logarithmic. Then, we use a software to solve and compare these two distinct solutions. Finally, we use sensitivity analysis to obtain some managerial insights.     

An inequality for the empirical D.F. in the non–I.I.D. case

A generalization to the non-i.i.d. case of an inequality for the empirical df. due to Mason (1981) is proved     

Multi‐agent rotating consensus without relative velocity measurements in three‐dimensional space

In this paper, we study distributed rotating consensus in networks of second‐order agents using only local position information in three‐dimensional space. We propose a protocol to make the multi‐agent system finally move together around a common point and present corresponding conditions for rotating consensus of the system. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive stabilization of a class of high‐order uncertain nonholonomic systems with unknown control coefficients

This paper is concerned with the globally stabilizing control design for a class of high‐order nonholonomic systems. Compared with the existing literature, the high‐order nonholonomic systems under investigations have more uncertainties and unknowns, such as neither lower nor upper bound is known for each control coefficient of the systems. This renders the existing control methods highly difficult to the control problems of the systems or even inapplicable. In this paper, by defining two new unknown parameters whose dynamic updating laws are properly chosen and also by using the discontinuous coordinates transformation and the method of adding a power integrator, a new design approach is given to the adaptive stabilizing controllers for the systems. A numerical simulation is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Microscopic order parameter of two nematogenic compounds using X-rays

X-ray Laue type diffraction patterns were recorded using the image plate system at different temperatures in the nematic phase for two nematogenic compounds. Micro-orientational order parameters have been computed using different methods. These are compared with the microscopic orientational order parameters obtained from refractive index data. Higher order parameters have also been computed and compared. Distribution function at various temperatures for the two nematogenic compounds from Deutsch method has been reported.     

Statistical analysis of large on-chip power grid networks by variational reduction scheme

One of the most critical challenges in today's CMOS VLSI design is the lack of predictability in chip performance at design stage. One of the process variabilities comes from the voltage drop variations in on-chip power distribution networks. In this paper, we present a novel analysis approach for computing voltage drops of large power grid networks under process variations. The new algorithm is very efficient and scalable for huge networks with a large number of variational variables. This approach, called variational extended truncated balanced realization (varETBR), is based on model order reduction techniques to reduce the circuit matrices before the variational simulation. It performs the parameterized reduction on the original system using variation-bearing subspaces. After the reduction, Monte Carlo based statistical simulation is performed on the reduced system and the statistical responses of the original system are obtained thereafter. varETBR calculates variational response Grammians by Monte Carlo based numerical integration considering both system and input source variations in generating the projection subspace. varETBR is very scalable for the number of variables and flexible for different variational distributions and ranges as demonstrated in experimental results. Experimental results, on a number of IBM benchmark circuits up to 1.6 million nodes, show that the varETBR can be 1900X faster than the Monte Carlo method and is much more scalable than one of the recently proposed approaches.