Fundamentals of the analytic network process — Dependence and feedback in decision-making with a single network

The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics...all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and governments.     

Synthesis of CaCO3 crystals using hydroxypropylmethyl cellulose hydrogel as template

Calcium carbonate crystallization was performed in hydrogel of hydroxypropylmethyl cellulose (HPMC). Results showed that the polyhydroxy functionalities in HPMC gel network facilitated the nucleation of aragonite which was not found in experiment without HPMC hydrogel and in experiment using methylcellulose (MC) hydrogel as template. On the other hand, due to the unique assembly of the macromolecules in HPMC hydrogel network, which was different from other hydrogels used in some previous reports, particular crystal morphology, corncob-like CaCO_3, was obtained for the first time.     

Gene product expression of cyclin D<Subscript>2</Subscript> and p16 during the transition from cardiac myocyte hyperplasia to hypertrophy

The current study was to investigate mRNA expression of cyclin D₂ and p16 during the transition from cardiac myocyte hyperplasia to hypertrophy. Cultured cardiac myocytes (CM) and fibroblasts (FC) obtained from 1-day-old Sparague-Dawley rats were used in this study. We have determined (1) hyperplasia by cell growth curve and fluorescence activated cell sorting (FACS); and (2) ultrastructure by electron microscope observation; and (3) expresions of cyclin D₂ mRNA and p16 mRNA by using in situ hybridization and image analysis. The results were shown (1) Results of cell growth curve and FACS analysis showed CM could proliferate in the first 3 cultured days (4 days in postnatal development). But the ability decreased quickly, concomitant with the differentiation. (2) The ultrastructure of CM showed the large amount of myofilaments and mitochondrion and FC showed moderate amount of rough endoplasmic reticulum. (3) The expression of cyclin D₂ mRNA in 3−, 4−, 5−day CM group was 0.89 times (p<0.05), 0.80 times (p<0.05) and 0.56 times (p<0.01) of that in 1-day group respectively. P16 mRNA in 2−, 3−, 4−, 5−day CM group were 1.63 times (p<0.01), 1.72 times (p<0.01), 1.99 times (p<0.01) and 2.84 times (p<0.01) of that in 1−day group respectively. It can be concluded that cultured neonatal rat cardiac myocytes could proliferate during the first 3 cultured days, but the ability of proliferation decreased, from the fourth day, concomitant with differentiation. Cyclin D₂ and p16 have the key roles during the transition from myocyte hyperplasia to hypertrophy. Biography: Zhang Yu-xia (1974-), female, Master, research direction: cardiovascular pathology.     

FINITE TIME TRACKING CONTROL FOR RIGID ROBOTIC MANIPULATORS WITH FRICTION AND EXTERNAL DISTURBANCES

1.Introduction Variable structure control is well known for its robustness to system uncertainties and external disturbances and has been successfully applied to the rigid robotic manipulator systems(Utkin(1992),Zinober(1990)).Generally,a linear sliding mode is firstly designed to describe the desired system error dynamics,a robust controller drives the switching plane variables to reach the sliding mode,and the error dynamics will asymptotically converge to zero on the linear sliding mode.Si…     

Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q-process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q-processes in random environments.     

网络最大流的割集矩阵算法

利用网络单位流量及网络可行流的流量平衡关系,得出流量关系矩阵,由流量关系矩阵,得出网络割矩阵,从而求出网络图的割集,最后根据网络最大流等于最小割容量,求得网络最大流,此方法使得计算网络最大流变得简便,且具有很强的实用性.     

EC,ASMC and Macrophage Oxidize Human Low Density Lipoprotein

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COMPARISON OF MAX—MIN APPROACH AND NN METHOD FOR RELIABILITY OPTIMIZATION OF SERIES—PARALLEL SYSTEM

Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are consideredfor the redundancy allocation problem with series-parallel structure. The max-min approach canformulate the problem as an integer linear programming problem instead of an integer nonlinearproblem. This paper presents a comparison between those methods from the standpoint of solutionquality and computational complexity. The experimental results show that the max-min approach issuperior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems,but analysis of computational complexity shows that the max-min approach is inferior to other greedyheuristics.     

环形磁头输出再生波形的模拟分析

引用互易定律对环形磁头输出再生波形进行模拟分析，所得结果与实验一致。