Simon two stage optimal design
two-stage stochastic programming
two-stage stochastic programmingTwo-stage stochastic programming is a mathematical optimization approach used to solve decision-making problems under uncertainty. It is commonly applied in various fields such as operations research, finance, energy planning, and supply chain management. In this approach, decisions are made in two stages: the first stage involves decisions made before uncertainty is realized, and the second stage involves decisions made after observing the uncertain events.In two-stage stochastic programming, the decision-maker aims to optimize their decisions by considering both the expected value and the risk associated with different outcomes. The problem is typically formulated as a mathematical program with constraints and objective functions that capture the decision variables, uncertain parameters, and their probabilistic distributions.The first stage decisions are typically made with theknowledge of the uncertain parameters, but without knowing their actual realization. These decisions are usually strategic and long-term in nature, such as investment decisions, capacity planning, or resource allocation. The objective in the first stage is to minimize the expected cost or maximize the expected profit.The second stage decisions are made after observing the actual realization of the uncertain events. These decisions are typically tactical or operational in nature, such as production planning, inventory management, or scheduling. The objective in the second stage is to minimize the cost or maximize the profit given the realized values of the uncertain parameters.To solve two-stage stochastic programming problems, various solution methods can be employed. One common approach is to use scenario-based methods, where a set of scenarios representing different realizations of the uncertain events is generated. Each scenario is associated with a probability weight, and the problem is then transformed into a deterministic equivalent problem byreplacing the uncertain parameters with their corresponding scenario values. The deterministic problem can be solved using traditional optimization techniques such as linear programming or mixed-integer programming.Another approach is to use sample average approximation, where the expected value in the objective function is approximated by averaging the objective function valuesover a large number of randomly generated scenarios. This method can be computationally efficient but may introduce some approximation errors.Furthermore, there are also robust optimization techniques that aim to find solutions that are robust against the uncertainty, regardless of the actualrealization of the uncertain events. These methods focus on minimizing the worst-case cost or maximizing the worst-case profit.In summary, two-stage stochastic programming is a powerful approach for decision-making under uncertainty. It allows decision-makers to consider both the expected valueand the risk associated with uncertain events. By formulating the problem as a mathematical program and employing various solution methods, optimal or near-optimal solutions can be obtained to guide decision-making in a wide range of applications.。
Multidisciplinary Design Optimization
Multidisciplinary Design Optimization Multidisciplinary Design Optimization (MDO) is a complex and challenging process that involves integrating various engineering disciplines to achieve the best possible design solution. It requires a holistic approach that takes into account the interactions and trade-offs between different design parameters, such as structural, thermal, aerodynamic, and control systems. MDO is crucial in modern engineering as it allows for the development of more efficient and cost-effective designs, ultimately leading to better products and systems. One of the key challenges in MDO is the need to balance conflicting design requirements. For example, in the design of an aircraft, engineers must consider the trade-offs between weight, aerodynamics, and structural integrity. Optimizing one aspect of the design may have a negative impact on another, so it is essential to find the right balance that meets all requirements. This requires close collaboration between engineers from different disciplines, as well as the use of advanced modeling and simulation tools to evaluate the design space and identify the best solutions. Another challenge in MDO is the complexity of the design space. With multiple interacting disciplines and a large number of design variables, the search for the optimal solution can be extremely challenging. Traditional design optimization methods often struggle to handle this complexity, leading to suboptimal solutions. MDO requires the use of advanced optimization algorithms and techniques, such as genetic algorithms, neural networks, and multi-objective optimization, to efficiently explore the design space and identify the best solutions. Furthermore, MDO also requires a significant amount of computational resources. The integration of multiple disciplines and the use of advanced optimization techniques often result in computationally intensive processes that require large-scale computing resources. This can be a barrier for small engineering teams or organizations with limited resources, as it may be challenging to access the necessary computational infrastructure to support MDO activities. However, with the advancement of cloud computing and high-performance computing technologies, these barriers are gradually being overcome, making MDO more accessible to a wider range of engineering teams. Despite these challenges, the benefits of MDO are significant. By considering multiple disciplinessimultaneously, MDO can lead to designs that are more efficient, reliable, and cost-effective. It can also help to identify innovative design solutions that may not be apparent when considering each discipline in isolation. Ultimately, MDO has the potential to revolutionize the way engineering design is conducted, leading to the development of better products and systems across a wide range of industries. In conclusion, Multidisciplinary Design Optimization is a complex and challenging process that requires a holistic approach to balance conflicting design requirements, handle the complexity of the design space, and access significant computational resources. Despite these challenges, the benefits of MDO are significant, leading to more efficient, reliable, and cost-effective designs. As technology continues to advance, MDO is expected to play an increasingly important role in modern engineering, ultimately leading to the development of better products and systems across a wide range of industries.。
two-stage least squares analysis
two-stage least squares analysis [twostage least squares analysis]Introduction to Two-stage Least Squares Analysis:Two-stage least squares (2SLS) analysis is a statistical technique that is often used in econometrics and social science research to deal with endogeneity issues. Endogeneity occurs when there is a two-way causal relationship between the independent and dependent variables, leading to biased and inconsistent estimates. 2SLS analysis provides a solution to this problem by using instrumental variables to estimate the causal relationship between the variables of interest.Step 1: Identification of Endogeneity Problem:The first step in conducting a two-stage least squares analysis is to identify the potential endogeneity problem. This can be done by examining the theoretical underpinnings of the relationship between the variables and looking for sources of omitted variable bias or reverse causality. For example, in a study investigating the effect of education on income, endogeneity may arise if individuals with higher initial income levels are more likely to invest in education.Step 2: Selection of Instrumental Variables:Once the endogeneity problem is identified, the next step is to select appropriate instrumental variables. Instrumental variables are variables that are correlated with the endogenous variable but are not directly related to the dependent variable. The instrumental variables should satisfy the conditions of relevance and exogeneity. Relevance means that the instrumental variables have a significant impact on the endogenous variable, while exogeneity implies that the instrumental variables are not affected by the outcome variable.Step 3: Estimation of First Stage Regressions:In the first stage of two-stage least squares analysis, the instrumental variables are used to estimate the relationship between the endogenous variable and the instrumental variables. This estimation is done through a regression analysis, where the endogenous variable is regressed on the instrumental variables. The estimated coefficients from this regression represent the predicted values of the endogenous variable, which are then used in the second stage of the analysis.Step 4: Check for Strong Instruments:After estimating the first stage regressions, it is important to evaluate the strength of the instrumental variables. Weak instruments can lead to biased estimates and reduced precision. Several statistical tests, such as the F-statistic and the Kleibergen-Paap Wald rk F statistic, can be used to assess the strength of the instruments. If the instruments are weak, alternative identification strategies or different instrumental variables should be considered.Step 5: Estimation of Second Stage Regressions:In the second stage of two-stage least squares analysis, the predicted values of the endogenous variable obtained from the first stage regression are used as an instrumental variable in the regression of the dependent variable on the endogenous variable and other control variables. This two-stage regression effectively eliminates the endogeneity problem and provides consistent and unbiased estimates of the causal relationship of interest.Step 6: Interpretation of Results:After conducting the two-stage least squares analysis, the estimated coefficients from the second stage regression can beinterpreted as the causal effects of the independent variables on the dependent variable, accounting for the endogeneity problem. These estimates should be evaluated in conjunction with their statistical significance and the goodness of fit of the regression model.Conclusion:Two-stage least squares analysis is a valuable technique for addressing endogeneity issues in econometric and social science research. By using instrumental variables and conductingtwo-stage regressions, this method provides unbiased and consistent estimates of causal relationships. However, it is important to carefully select appropriate instruments and assess their strength to ensure the validity of the analysis.。
刺激-反应联结学习在项目特异性比例一致效应中的作用
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效应。研究者认为，可能存在局部的、项目特异 性的认知控制机制，可以根据单个项目的比例偏 置情况选择性地进行注意资源分配从而影响不同 项目的反应（Jacoby et al., 2003）。
然而，注意调节理论近来受到了其他研究的 挑战（Schmidt & Besner, 2008; Schmidt & Lemercier, 2019）。Schmidt 和 Besner 认为，ISPC 效应中比例 一致性与刺激–反应的可能性混合在一起，可以 用更经济的可能性学习来解释这一效应。该研究 提出了可能性学习假说（contingency learning hypothesis）， 表 示 认 知 控 制 不 是 必 要 的 ， 被 试 完 全可以通过学习发现刺激无关维度与正确反应的 可能性关系，并基于此预测正确的反应。在冲突 任务中，一致试次占多数时，刺激常常伴随着一 致的任务无关的刺激属性，这一属性有很大可能 性可以去预测正确的反应，而多数试次为不一致 时，被试可能根据伴随的不一致的任务无关刺激 属性去预测反应（Schmidt & Lemercier, 2019）。这 一策略可以加快一致或不一致试次的反应，从而 产生 ISPC 效应。可能性学习假说基于刺激–反应 （stimulus-response, S-R）之间的联结解释了 ISPC 效应，是 S-R 联结学习的一种方式（Schmidt, 2013）。
心理与行为研究 2021，19(3)：326~333 Studies of Psychology and Behavior
刺激–反应联结学习在项目特异性 比例一致效应中的作用 *
夏天生1 谭 玲2
(1 广东工业大学艺术与设计学院，广州 510090) (2 广东工业大学管理学院，广州 510520)
Solving two-stage robust optimization problems using a column-and-constraint generation method
Solving two-stage robust optimization problems using a column-and-constraint generation method
Bo Zeng ∗ , Long Zhao
Department of Industrial and Management Systems Engineering, University of South Florida, United States
∗
Corresponding author. Tel.: +1 813 974 5588. E-mail addresses: bzeng@ (B. Zeng), longzhao@ (L. Zhao).
0167-6377/$ – see front matter © 2013 Elsevier B.V. All rights reserved. /10.1016/j.orl.2013.05.003
Article history: Received 27 August 2012 Received in revised form 5 April 2013 Accepted 11 May 2013 Available online 3 June 2013 Keywords: Two-stage robust optimization Cutting plane algorithm Location-and-transportation
OperatiБайду номын сангаасns Research Letters 41 (2013) 457–461
Contents lists available at ScienceDirect
Optimal Designs for Mixed-Effects Models with Random Nested Factors
Optimal Designs for Mixed-Effects Models with Random Nested FactorsB RUCE E. A NKENMAN, ankenman@Phone: (847) 491-5674; Fax: (847) 491-8005A NA I VELISSE A VILES, ivelisse@Northwestern UniversityDepartment of Industrial Engineering and Management Sciences2145 Sheridan Rd. MEAS C210, Evanston, IL 60208J OSE C. P INHEIRO, jcp@Bell Laboratories, Lucent Technologies600 Mountain Ave. Room 2C-258, Murray Hill, NJ 07974ABSTRACTThe problem of experimental design for the purpose of estimating the fixed effects and the variance components corresponding to random nested factors is a widely applicable problem in industry. Random nested factors arise from quantity designations such as lot or batch and from sampling and measurement procedures. We introduce a new class of designs, called assembled designs, where all the nested factors are nested under the treatment combinations of the crossed factors. We provide parameters and notation for describing and enumerating assembled designs. Using maximum likelihood estimation and the D-optimality criterion, we show that, for most practical situations, designs that are as balanced as possible are optimal for estimating both fixed effects and variance components in a mixed-effects model.KEYWORDS: Assembled Designs, Crossed and Nested Factors, D-Optimality, Experimental Design, Fixed and Random Effects, Hierarchical Nested Design, Maximum Likelihood, Nested Factorials, Variance Components.1. IntroductionIn many experimental settings, different types of factors affect the measured response. The factors of primary interest can usually be set independently of each other and thus are called crossed factors. For example, crossed factors are factors like temperature and pressure where each level of temperature can be applied independently of the level of pressure. These effects are often modeled as fixed effects. Nested factors cannot be set independently because the level of one factor takes on a different meaning when other factors are changed. Random nested factors arise from quantity designations such as lot or batch and from sampling and measurement procedures that are often inherent in the experimentation. The variances of the random effects associated with nested factors are called variance components since they are components of the random variation of the response. Batch-to-batch variation and sample-to-sample variation are examples of variance components.The nested or hierarchical nested design (HND), which is used in many sampling and testing situations, is a design where the levels of each factor are nested within the levels of another factor. Balanced HNDs for estimating variance components have an equal number of observations for each branch at a given level of nesting. Not only do these designs tend to require a large number of observations, but they also tend to produce precise estimates of certain variance components and poor estimates of others. Some articles that address these issues are Bainbridge (1965) and, more recently, Smith and Beverly (1981) and Naik and Khattree (1998). These articles use unbalanced HNDs, called staggered nested designs, to spread the information in the experiment more equally among the variance components. A staggered nested design only branches once at eachlevel of nesting and, thus, there is only one degree of freedom for estimating each variance component. Of course, if a staggered nested design is replicated n times then each variance component will have n degrees of freedom for estimation. Goldsmith and Gaylor (1970) address the optimality of unbalanced HNDs. Delgado and Iyer (1999) extend this work to obtain nearly optimal HNDs for the estimation of variance components using a limit argument combined with numerical optimization.When the fixed effects of crossed factors and variance components from nested random factors appear in the same model, there are many analysis techniques available for estimation and inference (see Searle, Casella, and McCulloch, 1992; Khuri, Matthew, and Sinha, 1998; or Pinheiro and Bates, 2000). However, only limited work has been done to determine what experimental designs should be used when both crossed factors and variance components occur in a single experiment. Smith and Beverly (1981) introduced the idea of a nested factorial, which is an experimental design where some factors appear in factorial relationships and others in nested relationships. They propose placing staggered nested designs at each treatment combination of a crossed factorial design and called the resulting designs staggered nested factorials.Ankenman, Liu, Karr, and Picka (1998) introduced what they call split factorials, which split a fractional factorial design into subexperiments. A different nested design is used for each subexperiment, but within a subexperiment all design points have the same nested design. The nested designs in a split factorial only branch at a single level and thus, the effect is to study a different variance component in each subexperiment.The general problem of experimental design for the purpose of estimating both crossed factor effects and variance components is a quite broad and widely applicable problem in industry. Some examples could be:1)Chemical or pharmaceutical production where certain reactor settings or catalysts are the crossed factors and raw material lot-to-lot variation, reactor batch-to-batch variation, and sample-to-sample variation are the variance components. In this case, knowing the size of the variance components may help to determine the most economical size for a batch.2)A molding process where machine settings such as mold zone temperatures or mold timings are the crossed factors and shift-to-shift variation, part-to-part variation, and measurement-to-measurement variation are the variance components. Knowing which variation source is largest could help to focus quality improvement efforts.3)Concrete mixing where recipe factors such as the size of the aggregate used in the concrete and the ratio of water to cement powder are crossed factors and batch-to-batch variation and sample-to-sample variation are the variance components. Knowing about the variance components can help engineers to understand how variation in the properties of the concrete will change throughout large concrete structures.The purpose of this paper is to provide experimental design procedures for the estimation of the fixed effects of crossed factors as well as variance components associated with nested factors that arise from sampling and measurement procedures. We introduce a special class of nested factorials, called assembled designs, where all the nested factors are random and nested under the treatment combinations of the crossed factors. The class of assembled designs includes both the split factorials and thestaggered nested factorial designs. In Section 2, we provide parameters and notation for describing and enumerating assembled designs. In Section 3, we describe a linear mixed-effects model, which can be used to analyze assembled designs. The fixed effects and the variance components are estimated using maximum likelihood (ML). We present expressions for the information matrix for the fixed effects and the variance components in assembled designs with two variance components in Section 4. In Section 5, we provide theorems which show that under most practical situations, the design which is the most balanced (i.e., spreading the observations as uniformly as possible between the branches in the nested designs) is D-optimal for estimating both fixed effects and two variance components. In Section 6, we show with examples how to obtain the D-optimal design for the requirements of an experiment. Conclusions and discussion are then presented in Section 7.2. Assembled DesignsAn assembled design is a crossed factor design that has an HND placed at each design point of the crossed factor design. If the assembled design has the same number of observations at each design point, it can be described by the following parameters: r , the number of design points in the crossed factor design; n , the number of observations at each design point; q , the number of variance components; and s , the number of different HNDs used. For the special case of only two variance components (q =2), we will use the terms batch and sample to refer to the higher and lower level of random effects,respectively. Also for this case, we define B T as the total number of batches; B j as the number of batches in the j th HND; and r j as the number of design points that contain the j th HND. Thus, T sj j j B B r =∑=1We will use a simplified version of the concrete experiment in Jaiswal, Picka, Igusa,Karr, Shah, Ankenman, and Styer (2000) to illustrate the concepts of and introduce the notation for assembled designs. The objective of the concrete experiment is to determine the effects of certain crossed factors on the permeability of concrete and the variability of the permeability from batch-to-batch and from sample-to-sample. The design has three two-level factors (Aggregate Grade, Water to Cement (W/C) Ratio, and Max Size of Aggregate) and two variance components (q=2), Batch and Sample. The design (Figure1) has a total of 20 batches (B T =20).In Figure 1, each vertex of the cube represents one of the eight possible concrete recipes or design points (r=8) that can be made using the two levels of Grade, W/C Ratio,and Max Size. Thus, the front upper left-hand vertex represents a concrete recipe with the low level of Grade, the low level of W/C Ratio, and the high level of Max Size. The branching structure coming from each vertex represents batches and test samples to be made from that recipe. There are four samples per recipe (n=4).In the context of an assembled design, HNDs that are attached to the crossed factor design points will be referred to as structures . In the concrete experiment, there are twoFigure 1: An Assembled Design (B T = 20, r = 8, q = 2, n = 4, s = 2).Grade W/C RatioMax SizeLevel 2Level 2Level 2Level 1Level 1Level 1Guide to StructuresStructure 1Structure 2different structures (s=2). Structure 1 consists of three batches (B 1=3) where two samples are cast from one of the batches and one sample is cast from each of the other two batches. Structure 1 appears at four of the design points, so r 1=4. Structure 2appears at the other four design points (r 2=4) and consists of two batches (B 2=2) and two samples cast from each batch.In order to compare all possible assembled designs with the same parameter values,we will begin by discussing what structures are available for building the assembled designs. Let N represent the number of structures available for a given n and let k be the number of batches. The number of structures available for given n and k , with two variance components (q =2) is∑∑∑∑∑ −−++−=++−= = −−= −−−=−−−−−−=)3()(2)(11231322121111221231k k i i n i i i i n i i k n i k i n i i k i i n i i k k k k k k k N ,where x called floor[x ], gives the greatest integer less than or equal to x . The total number of structures is then, ∑==nk k N N 1. Figure 2 shows the number of possible structures that are available for use in assembled designs for various values of n and q =2and provides some examples.In a structure, the total number of degrees of freedom is equal to the number of observations and each degree of freedom can be thought of as a piece of information with a cost equal to that of a single observation. For a single structure, the degrees of freedom available for estimating the first variance component equals its number of branches minus one. More generally, the degrees of freedom associated with the i th nested random factor equals the number of branches at the i th level of nesting minus the number of branches at the (i -1)st level of nesting. Figure 3 shows an example of calculations for degrees offreedom for an HND with q =4. (Note that an HND can also be thought of as an assembled design with one structure and one design point.)The notation for a single q -level structure consists of q –1 different sets of parentheses/brackets. The i th nested random factor in a q-stage hierarchical design (i =1,…,q -1) is represented by a specific set of parentheses including as many elements as the number of i th nested random factor branches. For the q th variance component, the number of observations at the last level of nesting is specified. For uniqueness of equivalent nested designs, the elements at the last level of nesting as well as the number of elements at the i th level of nesting, i =1,…,q -1, are specified in descending order,starting from the q th level of nesting and ending with the first level of nesting.Notation can be understood easier by examples. Figure 4 shows the notation for the two structures in the concrete experiment. Structure 1 has three batches and thus has notation (2,1,1), where each element refers to the number of samples cast from eachFigure 3: Degrees of Freedom for an HND (q =4).22334557611n# of Structures Structures 715All available structures Some examplesFigure 2: The Number of Possible Structures (HNDs) for n =[2,7] and q =2. EUDQFKHV/ / / /batch. Structure 2 consists of two batches and two samples cast from each batch and thus has notation (2,2). Note that for q=2, there is just one set of parenthesis. Figure 5 shows an example of notation for a structure with four variance components.Figure 2 shows that as n increases, there are more available structures and it follows that, for a given number of design points, r , there are more potential assembled designs which have the same number of observations at each design point (n ).Building on the notation used for individual structures, the notation for an assembled design is ,} structure with points @{design structure 1∑=sj j j where the design points need to be ordered in some way. For assembled designs, we order the design points so that all rows with the same structure are in adjacent rows. This order is called design order .Recall that r j is the number of design points with structure j . The notation in design order would be ∑=−−++s j j j j R ,R R j 111},,21{@ structure , where ∑==jh h j r R 1 and .00=R Figure 6 shows that structures in the concrete experiment were assigned to the design points using the interaction ABC and it also shows the comparison of design order and standard order (see Myers and Montgomery 1995, p. 84) for a two-level factorial. TheseFigure 5: Notation for HND (q = 4).Figure 4: Concrete Experiment; Notation for HND (q =2).Notation for this Structure:{[(2,2,1),(3),(1)],[(3,2,2),(2,1)]}n =19lot batch samplemeasurement q =4(2,2)(2,1,1)batch ; sampleStructure 1Structure 2orderings are for convenience in describing the experiment and in manipulating the expressions of the model and analysis. When conducting the experiment, the order of observations should be randomly determined whenever possible.In an assembled design, the number of degrees of freedom is equal to the total number of observations. Thus, an assembled design with nr observations has a total of nr degrees of freedom. There are r degrees of freedom for estimating the fixed effects including the constant. There are nr -r degrees of freedom left for estimating variance components. We will designate the number of degrees of freedom for estimating the i th variance component as d i . When q=2, ()r B r B r B r d T sj j s j j j s j j j −=−=−=∑∑∑===11111 and d 2=nr-d 1-r=nr-B T .3. Analysis of Assembled Designs3.1. Model and Variance StructureThe linear mixed-effects model used to represent the response in an assembled design with nr observations and q variance components is,∑=+=q i i i 1u Z X y ,(1)Figure 6: Concrete Experiment (A=Grade, B=W/C Ratio, and C=Max Size);Comparison of Standard Order and Design Order.D esignO rder S ta ndard O rderA B C A B C S tructure11----24++--36+-+-47-++-52+--+63-+-+75--++88++++,5,8}(2,2)@{2,3,4,6,7}(2,1,1)@{1 :Order Standard in Notation ,7,8}(2,2)@{5,6,2,3,4}(2,1,1)@{1 :Order Design in Notation ++where y is a vector of nr observations, X is the fixed-effects design matrix, is a vector of r unknown coefficients including the constant term, Z i is an indicator matrix associated with the i th variance component, u i is a vector of normally distributed independent random effects associated with the i th variance component such that ()I 0u 2 i i N a . Let V be the nr ×nr variance-covariance matrix of the observations.Assume that the variance components do not depend on the crossed factor levels. Then,∑=′==qi i i i Var 12 Z Z y V .(2)Let X D be the full rank r r × design matrix (including the constant column) for a single replicate of a crossed factor design, where rows are ordered in design order. Also let the observations in X be ordered such that X =X D §1n , where 1n is an n -length vector of ones and § represents the Kronecker product. This ordering in X gives rise to Z-matrices that have the form ,1it rt i Z Z ⊕== where ⊕ refers to the Kronecker sum and Z it isthe indicator matrix related to the observations associated with variance component i for the treatment combination t . For the fixed effects, X t is the portion of the X matrix associated with the t th treatment combination. X t is a n ×r matrix where all n rows are identical. Let t D X ′ represent the row of X D corresponding to the t th treatment combination, then X t = t D X ′§1n . Let V t be the n ×n variance-covariance matrix associated with the treatment combination t , then , 12∑=′=qi it it i t Z Z V which relates to (2). Thus, Vcan be written as: .1t rt V V ⊕==Consider the case of two variance components (q =2) and denote by 21σ the batchvariance and by 22σ the sample variance. Z 2, the sample indicator matrix, is the identity matrix of order nr . Z 1t has n rows and as many columns as the number of batches used with treatment combination t . Z 1, the batch indicator matrix for an assembled design, has as many rows as total number of samples (nr ) and as many columns as total number of batches (B T ). As an example, recall that in the concrete experiment (introduced in Section 2) there are eight design points (r =8), two structures (s =2), and four observations at each design point (n =4). Recall that Structure 1 is (2,1,1) and Structure 2 is (2,2).Thus, based on treatment combinations: Z 2=I 32, Z 2t =I 4, t =1,2, (8). and ,10100101,100010001001181716151413121111817161514131211=========Z 00Z 00000000Z 00000000Z 0000000Z 0000000Z 00000000Z 00000000Z Z Z Z Z Z Z Z Z Z 3.2. Analysis TechniquesDifferent estimation methods have been proposed for the analysis of linear mixed-effects models. Currently, the two most commonly used methods are maximum likelihood (ML) and restricted maximum likelihood (REML). The method of maximum likelihood prescribes the maximization of the likelihood function over the parameter space, conditional on the observed data. Such optimization involves iterative numerical methods, which only became widely applicable with recent advances in computer technology. REML estimation is effectively ML estimation based on the likelihood of the ordinary least-squares residuals of the response vector y regressed on the X matrix ofthe fixed effects. Because it takes into account the loss of degrees of freedom due to the estimation of the fixed effects, REML estimates of variance components tend to be less biased than the corresponding ML estimates. In this paper, we will use ML estimation for the fixed effects and variance components, because of the greater simplicity of the associated asymptotic variance-covariance matrices (which are used to determine the D-optimal designs). Since ML and REML estimators are asymptotically equivalent, we expect that the D-optimal designs for ML will be at least close to optimal for REML.Conditional on the variance components, the estimation of the fixed effects is a generalized least squares (GLS) problem, with solution ()y V X X V X111ˆ−−−′′= (see Thiel, 1971, p. 238 for further details). In general, the variance components need to be estimated from the data, in which case the GLS methodology becomes equivalent to ML.It follows from the model assumptions that, conditional on the variance components,the variance-covariance matrix of the fixed-effects estimators is ().11−−′X V X In practice,the unknown variance components are replaced by their ML estimates. In this case,under the assumption of normality, the variance-covariance matrix ofˆ is the inverse of the information matrix corresponding to (see Searle, Casella, and McCulloch, 1992, p.252-254). Because of the independence of the observations at different treatmentcombinations, ,)()(11∑=−=′=rt t Inf Inf X V X where t t t t Inf X V X 1)(−′=. It thenfollows that ()()()()∑∑=−=−′⊗′=⊗′⊗′⊗=rt n t n t t rt n ttn t Inf 11111)(1V 1X X 1X V 1X D D D D .Since n t n 1V 11−′ is a scalar,.)(11∑=−′′=rt t t n t n Inf D D X X 1V 1 (3)There are only asymptotic results available for the variance-covariance matrix of the variance component estimators. Denoting the vector of ML estimators by 2ˆσ, the asymptotic variance-covariance matrix of q variance-components estimators for an assembled design is (see Searle, Casella, and McCulloch, 1992, p. 253):()()()()()111111111111111112222122ˆˆˆˆ−−−−−−−−−′′′′′′′′≈=qq q q q q q q q tr tr tr tr Var Var Z Z V Z Z V Z Z V Z Z V Z Z V Z Z V Z Z V Z Z Vσσσ,where tr () indicates the trace function of a matrix. The information matrix of the variance components for treatment combination t is()()()()′′′′′′′′=−−−−−−−−qt qt t qt qt t t t t qt qt t qt qt t t t t t t t t t t t tr tr tr tr Inf Z Z V Z Z V Z Z V Z Z V Z Z V Z Z V Z Z V Z Z V 1111111111111111221)( .The information matrix of variance-components estimators is ∑==rt t Inf Inf 122)()( .4. Information Matrix for Two Variance ComponentsAssembled designs are a very large class of designs, many of which are too complicated for practical use. Since the most likely assembled designs to be used in practice are the most simple, we will study assembled designs for two variance components (q =2) in detail. Detailed study of assembled designs with more than two variance components is left for future research.The simplest assembled design with r =1 design point and s =1 structure is equivalent to an HND. Hence, it is fundamental to study a single HND or the j th structure. For notational simplification, we will use B instead of j B to represent the number of batches in a structure for the case of q =2, r =1, and s =1. Using the notation established in Section3 for HNDs, any structure with B batches and q =2 levels of nesting can be represented by()B B m m m m ,,,,121− , where i m is the number of samples in batch i and 1+≥i im m .To develop the information matrix for fixed effects at a single design point, the expressions in terms of m i ’s for a treatment combination t are:[]i i m m Bi nt t t t t t t I J I Z Z Z Z Z Z V 2221122112122221121+=+′=′+′=⊕=,where J n is an n ×n square matrix with all elements equal to one. Note that for q =2,n t t I Z Z =′22. Also,++−=⊕=−i i m m i Bi tm I J V 2221222221111) ( and from (3), it can be shown that the information for fixed-effects estimator (in this case just the mean) of a structure at a design point given n , B , and q =2 is∑∑==−−+=++−=′′=′=B i i i Bi i i i tt n t n t t t t m mm m m Inf 1212212221222222111. ) ( ) (D D X X 1V 1X V X (4)Note that for a single design point (r =1), X D t =1, thus and ) (t Inf are scalars.The asymptotic results for the variance-covariance matrix of the variance-components estimators for ML (q =2) are:()()()()()()()()1211121112121112)(2ˆ−−−−−′′′≈tt t t t t tt tt t tr tr tr tr Var V Z Z V Z Z V Z Z V σand()()()()()()()()()+−+−++++=′′′=∑∑∑∑====−−−−Bi i i i i B i i i Bi iiB i i i t t t t t t t t t t t m m m m m m m m m m tr tr tr tr Inf 1222121212242211121112121112)1()1())1(1()1()1()1(21)(21ττττττσV Z Z V Z Z V Z Z V σ(5)where τ is defined as the variance ratio 2221σσ. Expressions in terms of the i m ’s in (5)are derived in Appendix 1.The information matrix for []′2 is block diagonal (see Searle, Casella, andMcCulloch, 1992, p. 239) and, therefore, the estimators for the fixed effects and the variance components are asymptotically uncorrelated.5. Optimal Assembled DesignsAs n increases, there become a large number of assembled designs that are essentially equivalent according to their parameters. In Section 4, expressions were provided for the asymptotic variance-covariance matrices of the estimates from assembled designs. In this section, designs are compared in terms of their ability to accurately estimate the fixed effects and the variance components. There are many criteria that have been used to compare experimental designs. These optimality criteria are based on minimizing in some sense the variance of the estimates of the fixed effects and variance components.The D-optimality criterion is possibly the best known and most widely accepted (see Myers and Montgomery, 1995, p. 364 and Pukelsheim, 1993, p. 136). A design is D-optimal if it minimizes the determinant of the variance-covariance matrix of the estimates, often called the generalized variance of the estimates. Because no closed form expressions are available for the variance-covariance matrix of the maximum likelihood estimates in a linear mixed-effects model, we rely on the asymptotic results of Section 4and investigate (approximate) D-optimal assembled designs using the asymptotic variance-covariance matrices. Equivalently, we will then seek the assembled design that maximizes the determinant of the information matrix of the fixed effects and the variance components. Because the information matrix is block diagonal, its determinant is theproduct of the determinant of the fixed-effects information matrix and the determinant of the variance-components information matrix. It follows that if the same design that maximizes the determinant of fixed-effects information matrix also maximizes the determinant of the variance-components information matrix, then that design is D-optimal.Recall that for q =2, any HND with B batches can be represented by ()B B m m m m ,,,,121−= m , where i m is the number of samples in batch i, i=1,2,…,B and 1+≥i i m m . Define M B as the set of all feasible and non-trivial HNDs,{}1;,,2,1;,,,,M 1121B −<=≥∈=++−n B B i m m m m m m m i i i B B ),(6)where )+ denotes the set of positive integers (i.e., at least a sample is taken per produced batch). Note that, by definition, n m Bi i =∑=1. We consider the HNDs where n B = or1−=n B to be trivial, since there is only one HND for each of these cases and thus theymust be optimal.5.1. Fixed-Effects OptimalityFor a single HND, the D-optimality criterion for the fixed effects is the determinant of the matrix defined in (4). Since (4) is a scalar, it is the D-optimality criterion. The D-optimal HND for fixed effects can be found for any choice of n and B by solving Problem I : n m m m Bi i Bi i i=+∑∑==∈112122M subject to max Bσσm .Problem I is non-linear and has implicit integer constraints. A solution to Problem I is found by comparing any given HND with another that subtracts one observation from 1m and adds one observation to B m . By the definition of M B in (6), 1+≥i i m m , 1m and B m are respectively the maximum and minimum number of samples per batch in m . Theorem。
4TpyesofPersonalities
Phlegmatic (SI)
Choleric (NE)
Sanguine (SE)
Two dimensions of personality
Introversion Extraversion
• Simple Descriptive Basis
– Self reports
3rd Qtr
4th Qtr
Morningness/Eveningness and BT
(Baehr, Revelle and Eastman, 2000)
Temperature (¡C)
100 3 7.5
80
3 7.0
60
40 3 6.5
M -types
E-types
20
3 6.0
0
1 6 : 00
•Keep in the background.
•Find it difficult to approach others.
•Would describe my experiences as somewhat dull.
4
•Keep others at a distance.
Obvious behavioral correlates
(Levy and Eysenck, 1972)
I-E and conditioning
• Newman’s work on psychopaths and conditioning – ability to stop
• Gray’s model of anxiety, impulsivity and conditioning (reinforcement sensitivity)
复合材料双悬臂梁试验Ⅰ型分层扩展的三维近场动力学模拟
复合材料双悬臂梁试验Ⅰ型分层扩展的三维近场动力学模拟姜晓伟; 汪海【期刊名称】《《科学技术与工程》》【年(卷),期】2019(019)021【总页数】6页(P35-40)【关键词】复合材料; 近场动力学; Ⅰ型分层扩展; 双悬臂梁试验【作者】姜晓伟; 汪海【作者单位】上海交通大学航空航天学院上海200240【正文语种】中文【中图分类】O351.2纤维增强复合材料在航空结构中已经得到广泛的应用，主要源于其比刚度、比强度很高、热膨胀系数很低以及优良的抗疲劳特性。
在复合材料结构设计中，由于复合材料的昂贵，设计人员往往需要采用一定的分析手段来取代试验。
这其中，涉及到复合材料损伤扩展的分析，传统解析方法所能提供的结果比较有限，公开资料中，数值分析方法已经成为主流的分析方法。
分层损伤作为复合材料结构的主要损伤模式之一，是纤维增强复合材料结构设计与分析中需要着重考量的关键因素[1—4]。
目前复合材料分层损伤的分析主要采用有限元法，具体技术包括粘接元(cohesive zone method, CZM)和虚拟裂纹闭合技术(virtual crack closure technique, VCCT)。
尽管这些分析手段已经能够解决很多分层损伤的问题[5—7]，通常情况下，这些技术需要预先设置分层的扩展路径，这对很多实际的工程问题来说是很困难的。
此外，正如这些研究工作[8—10]中指出的，构建于连续介质力学基础上的有限元方法，理论上与复材分层扩展带来的空间不连续性相冲突，这种冲突常常会引起分层前缘的收敛性问题。
近年来，Silling 教授等[11—13]提出的近场动力学理论(peridynamics，PD)作为计算力学领域的前沿性理论，在复合材料损伤扩展分析中体现出了一定的优势。
近场动力学已经被成功地应用于复合材料的损伤分析，并能够捕捉分层损伤。
Askari 等[8,14]给出了复合材料层板低速冲击下的层间分层损伤。
Optimal2-StageDesigns
INTRODUCTION A phase II study of a cancer treatment is ari uncontrolled trial for obtaining an initial estimate of the degree of antitumor effect of the treatment. Phase I trials provide information about the maximum tolerated dose(s) of the treatment, which is important because most cancer treatments must be delivered at maximum dose for maximum effect. Phase I trials generally treat only three to six patients per dose level, however, and the patients are diverse with regard to their cancer diagnosis [1]. Consequently such trials provide little or no information about antitumor activity. The proportion of patients whose tumors shrink by at least 50% is the primary endpoint of most phase II trials although the durability of such responses is also of interest. Such trials are not controlled and do not determine the "effectiveness" of the treatment or the role of the drug in the treatment of the disease. The purpose of a phase II trial of a new anticancer drug is to determine whether the drug has sufficient activity against a specified type of tumor to warrant its further development. Further development may mean combining the drug with other drugs, evaluation in patients with less advanced disease, or initiation of phase III studies in which survival results are compared to those for a standard treatment. Phase II trials of combination regimens are also conducted to determine whether
山东省宁津县第一中学2024-2025学年高三上学期创新学部9月考试英语试题
山东省宁津县第一中学2024-2025学年高三上学期创新学部9月考试英语试题一、阅读理解As summer holiday’s arriving, the seniors access the glimmer of getting rid of “cage”. During the vacation, if you have been fed up with playing games while lying on the sofa, why not step with me to enjoy some anime so as to fill the hole in your heart? Let’s give it a shot at these following marvelous!Sword Art OnlineThe film tells a death game called “Sword Art Online” made by Heathcliff that sixty thousand players enrolled reluctantly in an era when the VRMMO was received. With romance, fight and fantasy, it’s a splendid harem work. Although there’re some comments like “No Sword Art Online after SAO”. The Editor thought it’s also a must-to-red about the continuation.86-Eighty SixFame for “the love on Internet to be true”, it features mechanical battle and love. 86 teens had to sacrifice their lives due to the racial discrimination, but as a result they fell into the dilemma, which was that they decided to fight for their nonexistent pride. “Trace” misery (苦难) , so it’s accessible to you. By the way, the end of the anime could be only a start of their way to future!The Eminence in ShadowWhat will it spark when the elements like Dragon Proud Sky and Reincarnation (人物名称) are merged into one position? Have it a try! As an addict to anime, the main character Reincarnation through the truck after he saved his classmate without intention and pretended to be a pass-by and restart his life in the other world. But to my dissatisfaction, it’s too short!1．What is NOT TRUE about Sword Art Online?A．It’s a VRMMO work.B．Players are willing to continue.C．There are many female characters.D．It’s an ordinary work but with some unrecognized comments.2．What is the reason on fighting of the 86 teens?A．To devote themselves.B．Racial discrimination.C．To open their way.D．Fighting for their nonexistent pride.3．What person is the main character probably?A．Modest.B．Normal.C．Responsible.D．Anti-realistic.Hypixel is a popular Minecraft server, which is one of the best-selling video games all over the world. It contains a variety of games, ranging from Survival-themed mini-games like UHC (极限生存冠军) to PvP mini-games like Skywars. Starting its history in 2013, the game server had the most daily online players and became the top Minecraft server. Due to the intention of serving players around the world, it can reach up to 70,000 players sometimes.In the game, you can fight against enemies around the world and cooperate with your teammates in team mode, but cross-team (跨队联合) are still not allowed in that game mode. “We aim to create some unique and interesting games to attract more players and help other players understand the game better,” said Simon on YouTube, one of the owners of the server. In practice, the popularity of Skyblock, a game mode, has caused the number of players to increase dramatically once again, since the last surge in the number of players was during the testing of Bedwars.Cheating is one of the most complex problems in all games, including Hypixel. The development team has implemented some anti-cheat measures to combat cheaters, such as the use of a plugin called Watchdog, which bans cheaters for their illegal actions. However, as these anti-cheat methods are used, it also causes some unavoidable issues for legitimate players. Eventually, with the help of staff checks, the number of cheating players is kept at a lower level.In recent years, the number of players has decreased a lot. The existing game modes couldn’t attract new players, while some old players couldn’t be enticed to play the same content. Some staff even quit their jobs at Hypixel for unknown reasons. “I wish more new game updates were released, or it’s too hard to reach the original peak number of players,” said YZ Ljc , a playerwho still plays on the server.4．How does the author introduce Hypixel according to Paragraph 1?A．By comparing with other games.B．By introducing the feeling of his playing experience.C．By introducing the general game mode.D．By listing the game’s problems.5．Which of the following sentences can be used to describe Hypixel?A．Popular but meeting challenges.B．A few games with lots of cheaters.C．They didn’t have an innovative developing team.D．It’s an illegal game server.6．What can be learned from the passage?A．Hypixel doesn’t have any cheaters now.B．A staff called Watchdog participated in managing Hypixel.C．You can cooperate with your enemies in the team mode.D．Bedwars is popular since it was published.7．What is the most needed according to YZLjc’s words to save Hypixel?A．Let staffs play games with players.B．Design a dedicated Store website.C．Create creative games and prevent cheaters wisely.D．Recruit more cheaters to manage Hypixel.Qi Xia woke up at a large round table, with the other nine people waking up. He saw a strange man wearing a sheep mask, “Everyone, please start our game.” Everyone realized they couldn’t move, so they had no choice but to play that. “It’s a game of honesty, whose goal is to find the only liar. “But Qi Xia quickly understood the essence of the game when others were suspicious of each other. Then he said to others, “My name is Qi Xia, and I will start to tell a lie!”All above is the beginning of the novel The End of the Final Ten Days (《十日终焉》). This book is about a strange place called “The End”(终焉之地) and a special man, the protagonist of the story, Qi Xia, who try to find the truth of the world and himself.What attracts readers most is its distinctive feature, which focuses on the gambling of intelligence quotient. IQ is something that a strong man in this place must have. It just so happens that Qi Xia is a wise man who has enough power to support him forward. For example, when faced with a very difficult question, he remained calm and gave an answer. The question is: You are free to assign fifty black chess pieces and fifty white chess pieces to two jars, and then you have to be blindfolded to pick the jars that are out of order. Then you have to pick a piece in this jar while blindfolded, and if you get a black one, you will win the game. But Qi Xia only gave the answer after a short thought. He put one piece into one jar and the other ninety-nine into the other, and got the highest probability. Then he won the game with a little psychological skill.Another attractive feature is the magical power, the echo (回响), which is about the faith and can provide an auxiliary effect. The power is different from person to person. The “scapegoat” (替罪) can allows owner to die in the place of someone else. The “imputation” (嫁祸) can transfer the pain to someone else. The “crazy man (癫人) ” can copy the power of others’ echo. And Qi Xia got the most special echo in “The End”, which shocked almost everyone.Qi Xia met another smart man, Chu Tianqiu, who always remained mysterious. When Qi wanted to meet him for the first time, Chu knew Qi is very smart and then sent a message from his men to tell Qi, “The king does not want to show himself to another king”. Later, Qi found Chu has an extremely crazy plan that shocks him. This will lead to exciting confrontations between the two. Qi Xia has some very strange questions of his own. He always has a girl called “Y u Nianan” in his mind, but he can’t be sure if she was real. He has lost a lot of memories and has some secrets that even he doesn’t know.If you like to enjoy brainstorming and exciting wits fights, please read it in person, and you’re sure to be immersed in it.8．What is the author’s purpose in writing the paragraph 1?A．To show the magic of this place.B．To tell the reader the truth of the story.C．To attract the reader’s interest.D．To introduce the main character.9．What color should this individual piece be, and what is the highest probability?A．white, 50%.B．black, about 75%.C．white, about 80%.D．black, almost 100%.10．What the real meaning of the underlined sentence might be?A．He doesn't think Qi has enough IQ to be qualified.B．He admits that Qi is powerful, but he doesn’t want to show himself up now.C．He thinks Qi should be a crazy king like himself.D．He will offer to meet Qi next time.11．What is the most important thing in “The End”?A．Powerful echo.B．Enough ambition and courage.C．Teamwork and trust.D．Intelligence quotient and faith.A new study published on May 20, 2024, found that when teenagers played a game named Arknights (明日方舟), it motivated their brain activity, leading to increased intelligence. This study was conducted by Han, an expert from Ning Jin Yi Zhong, and it made a significant impact on the common perspective of games. Han invited 500 students from Ning Jin Yi Zhong to participate in the study. He divided these students into ten groups and asked them to play different kinds of games. Eventually, he used a device capable of testing brain motivation to assess the students, discovering that those who played Arknights exhibited the highest motivation and performed the best in class.Professor Wang, who collaborated with Han, stated, “It’s surprising to discover the positive effects of this game. The improvement it brought to students was remarkable. I recommend that all students should play Arknights.”Arknights is a game that requires players to strategically place characters to defend against enemies, each with various abilities to threaten the player’s base. This necessitates players to utilize their intelligence and skills to place characters in optimal positions. Consequently, players’ brains receive sufficient stimulation, enhancing their motivation and cognitive abilities. Moreover, the game’s attractive characters and scenes captivate players, igniting their passion for playing and amplifying its positive impact on their intelligence.A participant named Zhang Kangbo remarked, “When you start playing this game, you’ll notice that it sharpens your problem-solving abilities and improves sociability. Let’s invite your friends to play Arknights together quickly.”With the publication of this study, an increasing number of students began to try playing Arknights. Ying Jiao Company, the developer behind the game, was astonished by the growing number of players. An engineer witnessing this phenomenon expressed, “It’s gratifying to see so many people eager to play our game. I hope every player enjoys their time, and we will continue to enhance the quality and provide more welfare to every player.”12．Which is the impact of Arknights on students?A．Make them feel positive.B．Sharpen students’ intelligence.C．Boost students’ motivation of brain.D．Sharpen students’ game skill.13．How does Dr. Han conduct this study?A．Compared students’ performance after playing different games.B．Analyze the former studies’ data.C．Play different games in person.D．Ask professor Wang’s to play Arknights.14．What is professor Wang’s attitude to the study according to Paragraph 2?A．Favorable.B．Cautious.C．Doubted.D．Surprised.15．What can we learn from the last paragraph?A．Many people don’t like playing other games except Arknights.B．Ying Jiao Company will improve the quality of Arknights.C．More welfare will be given to the participants.D．Ying Jiao Company have the best engineers in the world.How to deal with your homework? As a senior student, you might face the cruel fact that homework is so much that you could not finish them on time. It’s usually unnecessary to do homework because those that you have done might be only papers which are thrown away into a trash bin to add money to class. If you are a student with principles, you must struggle with the way to finish it. 16Uncover the potential of time.Time is like water in sponges, if you want to press it, you might find that Lu Xun was cheating you. Zhang Jianyu, a famous educator, suggested that you could spare time when teachers are in class. 17 You could put your homework under the book that the teacher is using to make you finish homework in the classroom safely.18To finish your homework, you could turn to the Internet for help. Some software might help you a lot. 19 Because the answers on these apps are always standard.Help each other.The best friend is the people who want to help you do your homework positively. So you could ask your friends for help. And remember that you still need to help them sparing no effort.Think about the price.If you couldn’t finish the homework, 20 Once thinking this, you might want to finish them. And if not, just enjoy your holiday and make your day.All these are my suggestions, which you should consider carefully before putting those into practice. Last but not least, hope you can have a nice holiday!A．To finish homework quickly, just copy it.B．But remember don’t copy it completely.C．Follow those tips may be helpful to deal the different situation.D．Obtain help from Internet.E．you might felt depressed when you think the sense of duty as a student.F．Because using the time to do homework is better than thinking other meaningless things. G．you might be punished by your teacher like cleaning your class.二、完形填空Flutter is regarded as a crazy man because what he said always made the others confused. One day a rainstorm stepped into his village. He was 21 with a music playing. Suddenly, a lightning hit his car. It was that time when the surroundings and the car turned into a large light shinny circle which was too bright for Flutter to see 22 . So he just ran into a tree.Cleaning his eyes, he realized that he had become a(an) 23 with a tall body and a bignose which looked like a pipe. He was 24 and wanted to scream, but the only voice he heard was a piercing voice made by a beast (野兽). He turned around, suddenly, he was hit by a large 25 . Scaredly, he found that a dinosaur stood on the ground, looking at him who 26 on the ground due to the unexpectedly crashing. The giant aggressor roared with contempt (蔑视) shown, “Your territory has been taken over by us, go out!” He rose to his feet with his 27 difficultly because his legs (肢体) couldn’t move just now. He escaped not fluently.He kept running till he came across a group of elephants. Seeing him, they said angrily, “We were so excited to spot you again, my leader. It was the dinosaur that let us 28 . Please voice for us bravely! Thinking the fact that the dinosaur looked 29 him, he had recognized how seriously the situation it was. Instead of being afraid, he accepted his fate, leading his family to get back their home. Flutter said loudly and inspiringly. “I will try my best to help us back to our habitat. For the first thing, let’s collect some woods and stones, for which I had planned to drive out those wicked opponents.” He decided to use his wisdom as a(an) 30 to get tools and achieve their final goal. With Flutter’s leading, they finally produced dozens of hatchets that were made up of 31 materials. “It must be a successful war for us!” Flutter picked up his weapons (武器), walking in the front of their army to 32 for their territory. They transformed their team into a 33 to trap the dinosaur into it. Countless hatchets flew to them and they finally escaped from the lands with 34 .Flutter and his family stepped into their land excitedly, congratulating by bathing in the river. Suddenly, Flutter was drawn into water. When he opened his eyes, he just found himself sitting in his car like before. He jumped out and told his experience to the surrounding people. “Are you OK”, they asked. Flutter can’t help shouting like an elephant “How 35 human you are!”21．A．dancing B．driving C．singing D．running 22．A．something B．everything C．anything D．nothing 23．A．bird B．elephant C．dinosaur D．tiger 24．A．happy B．excited C．depressed D．frightened 25．A．figure B．thing C．voice D．lightning 26．A．sat B．lay C．stood D．slept27．A．tail B．ears C．legs D．nose28．A．released B．angry C．homeless D．hungry 29．A．down on B．over C．after D．at 30．A．human B．elephant C．bird D．dinosaur 31．A．rough B．natural C．delicate D．raw 32．A．agree B．play C．fight D．reason 33．A．hatchet B．fire C．round D．circle 34．A．anger B．blood C．wounds D．tears 35．A．foolish B．wise C．kind D．imaginative三、语法填空阅读下面材料，在题后空白处填入1个适当的单词或括号内单词的正确形式。
Design of optimal solvent for extraction of bio-active
Biochemical Engineering Journal37(2007)271–278Design of optimal solvent for extraction of bio-activeingredients from mulberry leavesJong-Min Kim a,Sang-Mok Chang a,In-Ho Kim b,Young-Eun Kim c,Ji-Hwan Hwang c,Kyo-Seon Kim d,Woo-Sik Kim c,∗a Department of Chemical Engineering,Dong-A University,Saha-ku,Hadan2-dong840,Busan604-714,Republic of Koreab Department of Chemical Engineering,Choongnam University,Yusung-ku Kung-dong,Daejeon305-764,Republic of Koreac Department of Chemical Engineering,Kyunghee University,Yongin Kiheung Seochun1,Kyungki-Do449-701,Republic of Koread Department of Chemical Engineering,Kangwon National University,Chuncheon Hyoja2-Dong,Kangwon-Do200-701,Republic of KoreaReceived3October2006;received in revised form8April2007;accepted13May2007AbstractA method of designing solvents for the optimal extraction of bio-active ingredients from natural resources was developed using an alcohol–water binary solvent.The target bio-active ingredient of polyphenols,anti-oxidation and anti-tyrosinase ingredients exhibited different dependency of extraction efficiency on the alcohol species(methanol,ethanol,n-propanol and i-propanol)and composition of binary ing the solubility parameter,the extraction efficiency of the bio-active ingredients was correlated with the solvent polarity.As a result,the optimal solvent polarities for the extraction of polyphenols,anti-oxidation and anti-tyrosinase ingredients were predicted as38.5,37.33,and33.0[MPa1/2],respectively.These predictions also agreed well with the optimal solvent conditions of the water–alcohol mixtures depending on the alcohol species and composition. Plus,the correlation was confirmed with model solvents designed using other solvent species,including acetone and ethylene glycol.©2007Elsevier B.V.All rights reserved.Keywords:Extraction;Alcohol–water binary solvent;Bio-active ingredients;Solvent polarity1.IntroductionRecent studies on exploiting natural compounds for medicine and cosmetics have drawn much attention to the effective extrac-tion of the desired bio-active ingredients from natural products. Typically,various solvents of water,alcohols,acetone and ether, etc.are used to extract bio-active substances from natural prod-ucts due to their broad solubility propensity on solvents,where water is generally applied to extract high polar ingredients,such as carbohydrates,glycosides,and amino acids,while ether is used to extract low polar ingredients,such as aromatic com-pounds.Thereby,alcohol–water mixtures are used to extract out various ingredients having broad range of solubility propensity for the investigation of the specific functionality of the molecular compounds from extracted ingredients.For example,Doi et ed hexane and butanol to extract ingredients having low polarity from mulberry roots∗Corresponding author.Fax:+82312021946.E-mail address:wskim@khu.ac.kr(W.-S.Kim).[1],then investigated the specific functional compounds of prenyflavas,glycoside,iso-quercetine,and astragalin from extracted solution.Methanol is frequently used to extract spe-cific bio-active ingredients from various natural resources.As such,anti-inflammatory ingredients have been found in the methanol extraction from Culcasia scadens P.Beauv[2],anti-microbial compounds from Ceanothus americanus[3],and anti-histaminic compounds from Mentha spicata[4].Plus, ethylacetate and n-hexane have also been applied to extract bio-active ingredients.Thus,from the above previous studies, the solvent polarity would appear to be important for extract-ing specific functional ingredients from a natural resource. Thus,a variety of solvents,pure and mixtures,have been applied to extract bio-active ingredients with various polarities[5].A few studies have already examined the optimal extraction conditions for bio-active ingredients.For example,ethanol for the extraction of anti-oxidants from Spirulina platenis has been suggested as the best solvent among hexane,petroleum ether, and water,while the extraction temperature and time had a min-imal influence on the extraction of the anti-oxidants[6].Mean-1369-703X/$–see front matter©2007Elsevier B.V.All rights reserved. doi:10.1016/j.bej.2007.05.006272J.-M.Kim et al./Biochemical Engineering Journal37(2007)271–278while,Chandrika and Fereidoon attempted tofind the optimal solvent conditions for extracting polyphenolic compounds from wheat using mixture of methanol,ethanol and acetone with vary-ing the solvent composition,extraction temperature,and time [7].Although such previous studies have shown that the optimal solvent conditions for extraction can be found based on trials with various species of solvent and compositions,no system-atic method has yet been suggested for determining the optimal extraction solvent for natural resources.Accordingly,the present study is focused to develop a method for determining the optimal solvent conditions and designing a solvent for the optimal extraction of bio-active ingredients from mulberry leaf known to contain the active ingredients for anti-oxidation and anti-hyperpigmentation.Since the extrac-tion of specific ingredients from natural resources depends on the polarity of the solvent,as implied in previous studies,the extraction efficiency of the solvent for bio-active ingredients is investigated,along with the variation in the polarity of the solvent according to the species and composition of a binary alcohol–water solvent.Here,methanol,ethanol,n-propanol,and iso-propanol are used as the alcohol species for the binary mixture.Plus,ethylene glycol and acetone are used to design model solvents to confirm the relationship between the extrac-tion of bio-active ingredients and the solvent polarity.Based on the extraction of mulberry leaf,activities of ingredients spe-cific to anti-oxidation and anti-hyperpigmentation are used as references to evaluate the extraction efficiency of the solvent [8,9].2.Experimental2.1.ExtractionMulberry(Morus alba L.)leaf,purchased from a herbal market in Korea,was completely dried in a convection oven at60–80◦C for a couple of days,thenfinely pulverized using a milling machine.Next,the leaf powder was meshed with an aperture size of200m and kept in a desiccator. To extract the bio-active ingredients,2g of the leaf powder were added to10ml of a solvent made of a binary mix-ture of alcohol and water for1h in a hot bath at80◦C. The extracted solution was then separated from the solid leaf using a centrifuge(Hanil Science Industrial Co.Ltd.,HA-500, Korea)and the contents of the bio-active ingredients examined, including the polyphenolic compounds,anti-oxidants,and anti-tyrosinase.The solvent conditions for extracting the bio-active ingre-dients were varied by adjusting the alcohol composition and species in the alcohol–water binary mixture.Methanol,ethanol, n-propanol and iso-propanol were used for the binary mixture and their compositions were changed from0to100%.Plus,ethy-lene glycol and acetone were also applied to formulate a binary mixture solvent to evaluate the optimal extraction conditions for the solvent.For the present experiment,all chemicals were pur-chased from Sigma–Aldrich Chemical Co.(U.S.A.)and ACS grade.2.2.Assay of phenolic compoundsBased on the method of Goldstein and Swain[10],the total content of polyphenolic compounds in the extraction was eval-uated.First,the extraction was dilutedfifty times with distilled water(1/50,v/v),then100l of the diluted sample was com-pletely mixed with1250l of the Folin-Denis reagent(ACS grade,Fluka,Switzerland)that had been diluted ten times with distilled water(1/10,v/v).Thereafter,the mixture solution was incubated at25◦C for20min after adding250l of satu-rated sodium ing a UV spectrophotometer with a 760nm wavelength(JASCO,Model V-570,Japan),the content of polyphenolic compounds was estimated by comparing with a standard concentration curve for tannic acid that has an equiv-alent absorbance to the UV wavelength.The standard curve for tannic acid was prepared using the same procedure used to mea-sure the UV absorbance of the extracted sample.Thus,100l of a tannic acid solution was mixed with1250l of the same Folin-Denis reagent and250l of saturated sodium carbonate, then incubated at25◦C for20min.The UV absorbance of the tannic acid solution relative to the concentration resulted in the following standard curve:C P=A T−0.01980.00472(1)where C P is the tanic acid concentration[g ml−1]and A T is the UV absorbance.Eq.(1)was then used to estimate the polyphenol concentration equivalent to the tannic acid concentration.2.3.Anti-oxidation activityThe anti-oxidation activity of the extraction was evaluated based on the degree of scavenging1,1-diphenyl-2-picryhydrazyl (DPPH)free radicals[11].First,a free radical solution was pre-pared with0.15mM DPPH in2000l of ethanol and100l of a0.5%(v/v)Tween-20solution.The pH of the radical solu-tion was then adjusted to7.4using1800l of a0.1M Tris–HCl buffer.After adding10l of the extraction sample to the radical solution,the mixture was allowed to react for30min at room temperature,then the UV absorbance was measured at a wave-length of517nm.The blank solvent containing no extraction was used as a base reference for the anti-oxidation activity.The activity of the extraction(C AO)was expressed on a relative scale as:C AO(%)=A AO−A ROA RO×100(2)where A AO and A RO are the UV absorbances of the extraction sample and blank solvent,respectively.2.4.Anti-tyrosinase activityBased on the method suggested by Lee et al.[9],the mush-room tyrosinase inhibition of the ingredients was measured as indicative activity of anti-hyperpigmentation.The extraction sample was diluted50%(v/v)with methanol,then320l of the diluted sample was mixed with960l of0.83mM l-dopaJ.-M.Kim et al./Biochemical Engineering Journal37(2007)271–278273 and320l of a tyrosinase solution,containing125units ml−1and buffered with0.1M phosphate at pH6.8.The mixture wasquickly cooled to0◦C right after being incubated at37◦C for10min,then the UV absorbance of the solution at490nm wasmeasured.The blank mixture without tyrosinase was used as abase reference for the anti-tyrosinase activity.The activity of theextraction(C AT)was then expressed on a relative scale as:C AT(%)=A AT−A RTRT×100(3)where A AT and A RT are the UV absorbances of the extraction sample and blank mixture,respectively.3.Results and discussion3.1.Extraction of bio-active ingredientsIt is already known that most of the natural plant bio-active ingredients that are polyphenolic compounds,such as mulber-roside F,quercetine,catechin,and rutin,etc.in mulberry leaves, have broad solubility propensities due to their molecular polar-ities.Thus,solvents composed of a broad range of alcohol species and compositions were used for effective extraction of the bio-active ingredients from mulberry leaves.The extrac-tion efficiency of the solvents was evaluated based on three criteria:the total polyphenolic content,anti-oxidation activity (DPPH radical scavenging),and anti-tyrosinase activity(mush-room tyrosinase inhibition)of the extracted solution.As shown in Fig.1,the total content of polyphenols extracted from the mulberry leaves varied with the composition and species of alcohol in the binary mixture solvent.The extrac-tion efficiency of a propanol binary mixture(n-propanol–water and iso-propanol–water mixtures)was slightly maximized with an alcohol composition of about20%,then dramatically reduced when increasing the propanol composition.Meanwhile,with an ethanol–water mixture,the optimum condition for extraction appeared with an alcohol composition of about40%.In the case of a methanol–water mixture,the optimum condition for extrac-tion shifted further to an alcohol composition of60%although the extraction efficiency somewhatfluctuated with the alcohol composition,and the dependency of the extraction efficiency on the methanol composition was significantly diminished when compared to that with a propanol–watermixture.Fig.1.Extraction of polyphenol content by alcohol–water binary mixtures.The extraction of organic ingredients from plant leaves is directly related to the compatibility of the ingredients to the sol-vent;thus,when the ingredients are well matched in polarity with the solvent they will be easily extracted,otherwise,it will be hard to extract them.Therefore,based on the current experi-mental results,it was supposed that an optimal solvent condition of polarity could maximize the total content of polyphenol compounds extracted from mulberry leaves.Also,when using different species for a binary mixture,the solvent composition for optimal polarity was varied due to the distinct polarity of each solvent species.As a result,the optimal alcohol–water mixture appeared at a low composition with propanols and shifted to a high composition with methanol,as the methanol was more polar than the propanols,as displayed in Table1.Since the polar-ity range for the methanol–water mixture was smaller than that for the propanol–water mixture,the extraction efficiency of the methanol–water mixture was found to be much less sensitive to the composition than with any of the other alcohol–water mixtures.The anti-oxidation activity,equivalent capability of scav-enging DPPH free radicals,of the extracted solution was also evaluated under various solvent conditions,as shown in Fig.2. When methanol was used for the binary mixture,the maximum anti-oxidation activity of the extracted solution was obtained at about60%of methanol composition,yet this shifted to a lower alcohol fraction when using ethanol and propanols.It was inter-esting to note that the anti-oxidation activity of the extractedTable1Cohesive energies and solubility parameter of solventsSolvent Molecular weight(g mol−1)Molecular volume(cm3mol−1)δ(MPa1/2)δdδpδhδ(25◦C)δ(80◦C) Water18.0218.112.222.840.448.044.1 Methanol32.040.711.613.024.029.727.3 Ethanol46.158.712.611.220.026.124.0n-Propanol60.175.214.110.517.724.922.9iso-Propanol60.176.814.09.816.023.421.5 Ethylene glycol62.155.910.115.129.834.932.1 Acetone58.174.013.09.811.019.718.1274J.-M.Kim et al./Biochemical Engineering Journal 37(2007)271–278Fig.2.Extraction of bio-active ingredients for anti-oxidation by alcohol–waterbinary mixture.solution was more sensitive to the solvent conditions (species and composition of alcohol)than the polyphenol extraction effi-ciency.In particular,when using methanol for the binary water mixture,the anti-oxidation activity of the solution extracted with a high alcohol composition (above 80%)was dramati-cally reduced,while the extraction efficiency of polyphenolic compounds remained almost the same with only a slight drop from the maximum extraction efficiency.Consequently,it would appear that among the polyphenolic compounds in the extracted solution,the effective ingredients related to anti-oxidation activ-ity were quite polar and their solubility was very sensitive to the solvent polarity.However,the anti-tyrosinase activity of the extracted solution behaved quite differently when varying the alcohol species and composition of the solvent.As shown in Fig.3,when using methanol in the solvent,the activity of the solution continued to be enhanced when increasing the methanol fraction,up to an alcohol composition of around 80%,after which it slightly dropped,whereas in the cases of ethanol and propanols,theFig.3.Extraction of bio-active ingredients for anti-tyrosinase by alcohol–waterbinary mixture.optimal solvent condition was found at an alcohol composition of around 60%.This means that the bio-active ingredients related to anti-tyrosinase activity were more favorably extracted by a solvent with a lower polarity than the polyphenols and anti-oxidation ingredients.3.2.Design of solvents for extraction of bio-active ingredientsAs shown in the above experiment,the extraction efficiency of the bio-active ingredients was directly related to the polarity of the binary solvent,which was varied based on the alcohol fraction and species.Thus,an optimal solvent for the extraction of specific active ingredients could be designed if the relation-ship between the solvent polarity and the extraction efficiency were available.Hence,the solubility parameter [12]is intro-duced as a simple way of representing the polarity of a solvent and correlating the extraction efficiency of the polyphenol con-tent,anti-oxidation ingredients,and anti-tyrosinase ingredients with the polarity of the solvent.Actually,this parameter has already been frequently used to predict the miscibility and solu-bility of materials with a particular solvent [13,14].According to Hildebrand [12],the solubility parameter is directly dictated by the cohesive energy (E coh,i )composed of a linear combination of contributions from the dispersion interaction (E d,i ),polar inter-action (E p,i ),and hydrogen bonding interaction (E h ,i ),defined as:δi =E coh ,ii = E d,i +E p,i +E h,i i (4)Since the cohesion parameters are related to the correspondinginteraction energies as:E d,i +E p,i +E h,i =δ2d,i +δ2p,i +δ2h,i(5)the solubility parameter can be rearranged as:δi =δ2d,i +δ2p,i +δ2h,i(6)where δi is the solubility parameter [MPa 1/2]for species i andV i is the mole volume for species i .For pure solvents of current study,the values of the cohesion parameters,as summarized in Table 1,were then used to calculate the solubility parameters for the water and alcohol species,and the solubility parameters for the alcohol–water mixtures estimated based on a simple mixing rule as follows:δm = ix i δi (7)where δm is the solubility parameter for the alcohol–water mix-ture and x i is the volume fraction of species i in the mixture.In addition,the temperature adjustment for the solubility parameter is considered by Barton [12]: δ1δ2 2=T 2T 1(8)where T i indicates the extraction temperature [K].J.-M.Kim et al./Biochemical Engineering Journal37(2007)271–278275Fig.4.Correlations of extraction of bio-active ingredients form mulberry leaves with polarity of solvent:(a)content of polyphenols,(b)anti-oxidation ingredients and(c)anti-tyrosinase ingredients.As shown in Fig.4,the extraction efficiencies of the solvents for the bio-active ingredients in mulberry leaves,obtained using various alcohol species and compositions,correlated well with the single parameter of the solvent polarity.The optimal extrac-tion for polyphenolic compounds was achieved with a solvent polarity of38.5[MPa1/2](Fig.4(a)),corresponding to a36.9% methanol fraction,30.9%ethanol fraction,29.3%n-propanol fractions,and27.5%iso-propanol fraction in the binary mixture. Meanwhile,the optimal extraction for anti-oxidation ingredients was achieved with a solvent polarity of37.3[MPa1/2](Fig.4(b)), representing a slight increase in the alcohol fraction in the binary mixture(42%methanol,35.1%ethanol,33.3%n-propanol,and 31.2%iso-propanol fraction in the binary mixture).As such, these correlation results on the optimal solvent polarity for extraction would seem to explain why the optimal alcohol com-position varied with the alcohol species in Figs.1and2,and agreed well with the extraction efficiency profiles relative to the alcohol composition.However,the optimal solvent polarity for the anti-tyrosinase ingredients was about33.0[MPa1/2],which was lower than that for the polyphenols and anti-oxidation ingredients,as shown in Fig.4(c).From those experiment results,it would be inferred that the anti-tyrosinase ingredients were less polar and then optimally extracted out with the lower polarity of the solvent than anti-oxidation ingredients.As a result,this low polar condition for the optimum solvent meant a high alcohol fraction was required, such as a70.3%methanol,58.7%ethanol,55.7%n-propanol, and52.3%iso-propanol fraction in the binary mixture,to extract the anti-tyrosinase ingredients.The correlations of the extraction efficiency for bio-active ingredients with the solvent polarity were evaluated using model solvents with a broad polarity range.As summarized in Table2, ethylene glycol,acetone,methanol,and water were used to make the model solvents with polarities ranging from24.8to41.0 [MPa1/2],and applied to extract the bio-active ingredients,as shown in Fig.5.Despite the different species and composi-tions of the model solvents,their extraction efficiencies for the polyphenol content,anti-oxidation and anti-tyrosinase ingredi-ents were well matched with the correlations obtained using the alcohol–water binary mixtures.Furthermore,the polarities of quercetine and mulberroside F were estimated to confirm the above correlation using a func-276J.-M.Kim et al./Biochemical Engineering Journal 37(2007)271–278Table 2Solubility parameters of model solvents (at 80◦C)Solventδ(MPa 1/2)Symbols (for Fig.5)PolyphenolsAnti-oxidant Anti-tyrosinase25%ethylene glycol in water 41.10᭹42%ethylene glycol in water 39.0558%ethylene glycol in water 37.1247%acetone in water 31.8857%acetone in water 29.28♦27%acetone inmethanol24.81parison of extraction of bio-active ingredients by model solvents with correlation of extraction along with solvent polarity.tional group contribution theory [12,15],as these compounds,molecular structures shown in Fig.6,were the most active anti-oxidation and anti-tyrosinase compoundsfrom the mulberry leaves,respectively.Due to the unavailability of cohesive energyFig.6.Molecular structures of (a)quercetine and (b)mulberroside F that are most active ingredients for anti-oxidation and anti-tyrosinase,respectively,in mulberry leaves.data,the solubility parameter for quercetine and mulberroside F was predicted from the molar vaporization energy (g U i )and molar volume (g V i )of the functional group in each compound using the following equation [12]:δi = g U igV i1/2(8)As summarized in Table 3,when using the functional group data on the molar vaporization energy and molar volume with Eq.(8),the polarity of quercetine and mulberroside F was pre-dicted as 36.1and 34.5[MPa 1/2],respectively.Consequently,these polarity values for the compounds,which were consistent with the optimal solvent polarities for the extractions,provide a possible explanation why the optimal solvent conditions for the anti-tyrosinase extraction occurred at a lower solvent polarity than the anti-oxidation extraction in the correlations.The correlation of the extraction efficiency with the solvent polarity was also examined by comparing the contents of a target ingredient extracted under different solvent conditions.As shown in Fig.7,when extracted at three different solvent polarities (21.5,32.0,and 44.1[MPa 1/2]),the thin layer chro-matography spectra clearly revealed that the extraction with a solvent polarity of 32.0[MPa 1/2]contained a higher concen-tration of mulberroside F than any of the other extractions,as expected from the above correlation with the anti-tyrosinase ingredients.Table 3The molar vaporation energy and molar volume of functional groups for predic-tion of solubility parameters of quercetine and mulberroside F [9](at 25◦C)Groupg U(kJ mol −1)g V (cm 3mol −1)CH 3 4.7133.5CH 2 4.9416.1>CH 3.43−1.0CH 4.3113.5>C4.31−5.5Ring closure,five or more atoms1.0516Conjugation in ring,for each double bond1.67−2.2OH (disubstituted or on adjacent C atoms)21.913.0OH 29.810.0O 3.35 3.8CO17.410.8J.-M.Kim et al./Biochemical Engineering Journal37(2007)271–278277parison of concentration of mulberroside F extacted at three different solvent conditions.4.ConclusionsAn effective solvent for extracting bio-active ingredients, such as anti-oxidants and anti-tyrosinases,from mulberry leaves was identified by varying the solvent species and composi-tions.For the effective extraction of target ingredients with a specific activity from among many ingredients,the solvent con-dition was determined based on the polar propensity of the target ingredients.As such,the active anti-oxidation ingredi-ents and polyphenols with a high polar propensity required an alcohol–water binary solvent with a methanol fraction of about 60%for optimal extraction,whereas the anti-tyrosinase ingre-dients were most favorably drawn out by a binary solvent with an80%methanol fraction.In addition,due to the lower polar propensity of ethanol and propanols than methanol,their frac-tions of the binary mixture for the optimal extraction of the active ingredients were lower than the methanol fraction.This dependency of the optimal extraction on the solvent species and composition can be simply described by the sol-vent polarity represented by the solubility parameter.Based on correlating the extraction efficiency of the anti-oxidation and anti-tyrosinase ingredients with the solvent polarity,the opti-mal conditions for the solvent were predicted as a solubility parameter above38.0and33.0[MPa1/2],respectively.These predictions for the optimal solvent conditions for the extraction of the anti-oxidation and anti-tyrosinase ingredients were also consistent with model solvent conditions designed using acetone and ethylene glycol,and confirmed by the extracted contents of quercetine and mulberroside F,the most active anti-oxidation and anti-tyrosinase compounds in mulberry leaves,respectively.Accordingly,the correlations between the extracted contents of bio-active ingredients and the solvent polarity would appear to provide useful information on the optimal solvent conditions for the extraction of target ingredients with specific activity,which may prove to be helpful in the design of industrial processes and solvents.AcknowledgementThe authors are grateful for grants from the Korean Ministry of Health and 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Optimal
Optimal spaced seeds for faster approximate stringmatchingMartin Farach-Colton∗Gad ndau†S.Cenk Sahinalp‡Dekel Tsur§AbstractFiltering is a standard technique for fast approximate string matching in practice.Infiltering,a quickfirst step is used to rule out almost all positions of a text as possiblestarting positions for a pattern.Typically this step consists offinding the exact matchesof small parts of the pattern.In the followup step,a slow method is used to verify oreliminate each remaining position.The running time of such a method depends largelyon the quality of thefiltering step,as measured by its false positives rate.The qualityof such a method depends on the number of true matches that it misses,that is,on itsfalse negative rate.A spaced seed is a recently introduced type offilter pattern that allows gaps(i.e.don’t cares)in the small sub-pattern to be searched for.Spaced seeds promise toyield a much lower false positives rate,and thus have been extensively studied,thoughheretofore only heuristically or statistically.In this paper,we show how to design almost optimal spaced seeds that yield no false negatives.Keywords pattern matching,Hamming distance,seeds designAMS subject classifications68Q25,68R151IntroductionGiven a pattern string P of length m,a text string T of length ,and an integer k,the approximate pattern matching problem is tofind all substrings of T whose edit distance or Hamming distance to P is at most k.The basic idea employed in many approximate pattern matching algorithms[7,14]andcommonly used software tools such as BLAST[1]isfiltering based on the use of the pigeon-hole principle:Let P and S be two strings with edit distance or Hamming distance at most k.Then P and S must have identical substrings(contiguous blocks)whose sizes are at least(m−k)/(k+1) .This simple observation can be used to perform efficient approximate pattern matching through the following approach.(i)Anchorfinding:Choose some b≤ (m−k)/(k+1) .Consider each substring of P ofsize b,andfind all of its exact occurrences in T.(ii)Anchor verification:Verify whether each initial exact match extends to a complete ap-proximate match,through the use of(a localized)dynamic program or any other appropriatemethod.When the text string T is available off-line,the anchorfinding step above can be imple-mented very efficiently:(i)build a compact trie of all substrings in T of size b;(ii)search each substring in P of size b on the compact trie.By the use of suffix links,the compact trie can be built in O( )time and the anchorfinding step can be completed in O(m)time,both independent of the size of b.The running time of the anchor verification step depends on the specific method for extending an initial exact match and the value of b.As b increases,the number of false positives is expected to decrease,but if b> (m−k)/(k+1) some actual occurrences of the pattern may be missed,yielding false negatives.In the remainder of this paper we will focus onfiltering processes that yield to no falsenegatives,except as noted.Under this constraint,much of the literature on pattern matchingviafiltering focuses on improving the specific method for verifying anchors.The fastest approximate pattern matching algorithms based onfiltering have a running time of O( (1+ poly k·polylogk log k)[2].1.1The performance of thefiltering approachAlthough thefiltering approach does not always speed up pattern matching,it is usually quite efficient on high-entropy texts,such as those in which each character is drawn uniformly at random from the input alphabet(of sizeσ).Given a pattern P,suppose that the text string T is a concatenation of(1)actual matches of P:substrings of size m whose Hamming distance to P is at most k;(2)high entropy text:long stretches of characters,determined uniform i.i.d.from the input alphabet.On this T and P we can estimate the performance of the anchor verification step and thus thefiltering approach in general as follows.Let the number of actual matches be#occ. Each such match(i.e.true positive)will be identified as an anchor due to the pigeonhole principle.There will be other anchors yielding false positives.It is the expected number of false positives which will determine the performance of the anchor verification step and thus2the overall algorithm.The false positives,i.e.substrings from the high entropy text thatwill be identified as anchors,can be calculated as follows.The probability that a substringT[i:i+m−1]is identified as an anchor,i.e.has a block of size b which exactly matches its corresponding block in P,is≤mσ−b.The expected number of anchors from the highentropy text is thus≤ mσ−b.This implies that the running time of thefiltering approach is proportional to#occ+ mσ−b as well as the time required to verify a given anchor.The above estimate of the performance of thefiltering approach is determined mostlyby problem specific parameters,#occ, ,m or the time for verifying a given anchor,none of which can be changed.There is only one variable,b,that can be determined by thefilterdesigner.Unfortunately,in order to avoid false negatives b must be at most (m−k)/(k+1) .It is possible to relax the above constraint on b by performingfiltering through the use of non-contiguous blocks,namely substrings with a number of gaps(i.e.don’t care symbols).Tounderstand why searching with blocks having don’t care symbols can help,consider the case when k=1,that is,we allow one mismatch.When contiguous blocks are used,the maximumvalue of b is (m−1)/2 .Now consider using a block of size b+1with one don’t care symbolin the center position.How large can b be while guaranteeing that each substring of T with a single mismatching character with P will be found?No matter where the mismatch occurs,we are guaranteed that such a substring can be found even when b=2 m/3 −1.This is a substantial improvement over ungapped search,where b≤ (m−1)/2 ,reducing the timespent on false positives by a factor of≈σm/6.1.2Previous workThe idea of using gappedfilters(which are called spaced seeds)was introduced in[6],and the problem of designing the best possible seed wasfirst posed in[5].The design of spaced seedshas been extensively studied for the case when thefilter is allowed to have false negatives (lossyfilter),e.g.[3,4,9,13].In this scenario,the goal is tofind a seed that minimizes thefalse negatives rate,or in other words,a seed that maximizes the hit probability.In theabove papers,the seed design problem is solved using computational methods,namely,an optimal seed is found by enumerating all possible seeds and computing the hit probabilityof each seed.More recent work study the design of multiple spaced seeds,and also use computational methods[12,15,16].Unlike the case of one seed,going over all possible setsof seeds is impractical.Therefore,heuristic methods are used tofind a set of seeds whichmay be far from optimal.For some applications,it is desirable to construct seeds that are lossless,i.e.,seeds thatfind all matches of any pattern P of length m under Hamming distance k.Alternatively,one can want tofind all matches of any pattern P of length m ≥m within error rate k/m. The lossless seed design problem was studied in[5],and was solved using computationalmethods.Burkhardt and K¨a rkk¨a inen posed the question how tofind optimal seeds more directly.This combinatorial seed design problem has remained open both in the lossless and the lossycase.31.3Our contributionsIn this paper we study the combinatorial seed design problem in the lossless case.We give explicit design of seeds that are(almost)optimal for high entropy texts.Our specific results are as follows.The combinatorial seed design problem has four parameters:minimum pattern length m,the number of“solid”symbols in the seed b,the number of“don’t care”symbols in the seed g,and the maximum number of allowed errors between the pattern and its match k.We denote by n the seed length,namely n=g+b. One can optimize any one of the parameters,given the values of the other three parameters. In this paper we focus on two variants of this optimization problem:1.We study the following problem:Given m,n,and g,what is the spaced seed(of lengthn and with g don’t cares)that maximizes the number of allowed errors k?i.e.we want tofind a seed which guarantees that all matches of a pattern of length m within Hamming distance k are found,for the largest possible value of k.Our result for this problem is explicit construction of seeds(for various values of m,n,and g)which we prove to be almost optimal.2.More interestingly,given the number of errors k and minimum pattern length m,weare interested in the seed with largest possible b such that b+g=n≤m,which guarantees no false negatives for matches with at most k errors.Clearly this seed minimizes the time spent on false positives and thus maximizes the performance of the filtering approach for any given pattern of size m with k errors.Again,we give explicit construction of seeds that are almost optimal.Ourfinal result is on the design of multiple seeds:For anyfixed pattern length m and number of errors k(alternatively minimum pattern length m≤m and error rate k/m),we show that by the use of s≥m1/k seeds one can guarantee to improve on the maximum size of b achievable by a single seed.We note that the problem of maximizing b for the case when k is constant was solved in[10].Moreover,[10]considers the problem of maximizing n forfixed k,m,and g,and solves it for the case g=1.This problem is analogous to the problem of maximizing k.Our results are more general:We study the problem of maximizing k for wider range of g,and the problem of maximizing b for wider range of k.2PreliminariesFor the remainder of the paper,the letters A and B will be used to denote strings over the alphabet{0,1}.For a string A and an integer l,A l denotes the concatenation of A l times. Let Zeros(A)be the number zeros in the string A.A[i:j]denotes the substring of A that starts at the i-th character of A and ends at the j-th character.For two strings A and B of equal lengths,we write A≤B if A[i]≤B[i]for all i= 1,...,|A|.Note that this differs from lexicographic ordering.We say that a string A covers a string B if there is a substring B of B of length|A|such that A≤B .In words,A covers4B if we can align A against B such that every zero in the aligned region of B,is aligned against a zero in A.We will say that such an alignment covers B.The connection between the above definitions and the seed design problem is as follows: a seed of length n will be represented by a string A of length n such that A[i]=0if the i-th symbol of the seed is a don’t care,and A[i]=1otherwise.Given a pattern string P and a substring T of some text T of length m,let B be a string of length m,such that B[i]=0 if P[i]=T [i],and B[i]=1otherwise.Then,thefiltering algorithm using seed A willfind a match between P and T if and only if A covers B.We define k(n,g,m)to be the maximum k such that there is a string A of length n containing g zeros that covers every string B of length m with at most k zeros.In other words,for a seed length of n with g don’t cares,k(n,g,m)is the maximum possible number of errors between any P and any substring T of length m that is guaranteed to be detected by the best possible seed.Also,b(k,m)is the maximum b such that there is a string A with b ones that covers every string B of length m with at most k zeros.In other words,given the maximum number of errors k,b(k,m)is the maximum number of solid symbols one can have in a seed so that a match between any P and T with k errors could be detected by the best possible seed.In the next sections we will give upper and lower bounds on k(n,g,m)and b(k,m)for various values of parameters,effectively solving the combinatorial seed design problem.Our lower bounds on k(n,g,m)and are proved by giving explicit constructions of a seeds with desired value of k.The lower bounds on b(k,m)are proved using explicit constructions and probabilistic arguments.The respective upper bounds on k(n,g,m)and b(k,m)show that the seeds we construct are almost to optimal.3Spaced seeds that maximize kWefirst present our results on how to design a seed that maximizes the number of errors k when the other parameters n,g and m arefixed.In other words,we describe a seed with length n and g don’t care symbols that guarantees tofind all substrings T of size m whose Hamming distance to pattern P is as high as possible.Our results also extend to the problem of maximizing the error rate k /m for any pattern P of length m ≥m withfixed n and g.3.1Maximizing k for constant gTheorem1.For everyfixed g,k(n,g,m)=(2−1n±O(max(1,m2g+1,2·n2g+1,and ones elsewhere.5A1010111111 B 101111111111(a)A1010111111B 110111111111(b)A1010111111B 111110111111(c)Figure1:An example for the proof of the lower bound in Theorem1.Suppose that n=10 and g=2.Then,A=1010111111.If B is a string of length m with at least mg+1)·m2−1/(g+1).Lemma2.Let B be a string of length at least n with at most(2−1n−3zeros.Then, either there is a substring of B of length n containing no zeros,or there is a substring Bof B of length2L containing exactly one zero,and the zero appears in thefirst L characters of B .Proof.We prove the lemma using induction on|B|.The base of the induction is when |B|≤n+2L.In this case we have that B contains no zeros(since(2−1n−3<1). Now,suppose that B is a string of length greater than n+2L.W.l.o.g.B contains at least two zeros,and let x1and x2be the indices of the rightmost zero and second rightmost zero in B,respectively.If|B|−x1+1≤L,then the prefix of B of length x1−1contains at most (2−1n−4≤(2−1n−3ones,and by the induction hypothesis we have that B satisfies the statement of the lemma.If|B|−x2+1≤2L,then the prefix of B of length x2−1contains at most(2−1n−5≤(2−1n−3ones,and again we use the induction hypothesis.If neither of these two cases above occurs,we take B to be the suffix of B of length2L.Now we can complete the proof for the lower bound.Let B be a string of length m with at most(2−1n−3zeros.If B contains a substring of length n with no zeros,then clearly A≤B.Otherwise,let B be a substring of B of length2L that contains exactly onezero,and this zero appears in thefirst L characters of B .There are2L−n+1ways to alignA againstB ,and at least one of these alignments cover B (see Figure1for an example).More precisely,let j be the index such that B [j]=0,and let s be the integer for whichs2g+1n.Note that s≤g since j≤L.For s=0,the alignment of A and Bin which A[1]is aligned with B [j+1]covers B .For s≥1,the alignment of A and B in which the s-th zero in A is aligned against B [j]covers B6For every n which is not divisible by2g+1,let A be the string constructed above for the length n =(2g+1) n/(2g+1) ,and let A be the prefix of length n of A (if A contains less than g zeros,arbitrarily change some ones into zeros).A covers every string that is covered by A .Therefore,the seed A described above covers any string B of length m with k= 2−1n −3zeros or less.Thus we get the following bound for the maximum value of k that is achievable by any seed:k(n,g,m)≥ 2−1n −3≥ 2−1n+2g−3= 2−1n−(2−1n(n+2g)−3.Upper bound.We now give an upper bound on k(n,g,m),demonstrating that no seed can achieve a much higher value for k than the seed we described above.Let A be any seed of length n with g zeros.We will construct strings B0,...,B g that are not covered by A,+O(max(1,msuch that at least one of these strings has at most(2−1nn,then d0≥g+12g+1n−g22g+1(a)(b)Figure 2:An example for the proof of the upper bound in Theorem 1.Figure (a)shows a string A with two zeros,and the values of z 1and z 2.Figure (b)shows the corresponding strings B 0,B 1,and B 2.so B 0is defined andZeros (B 0)=m g +12=2g +1n +O (m 2g +1n ,so there is an index i ≥1such that z i +1−z i >12>12,so for large n ,d i >0(and also d i >0).Moreover,d i +d i ≥n −1+z i +1−z i −2|Y |≥n +1d i +d i +1≤2m 2g +1n −g 2+1=2g +1n +O (max(1,m n)Hamming errors.In this section we consider the case whereg ,the number of don’t care symbols,is not constant but g ≤n 1−1/r for some r ≥2.We show how to construct an (almost)optimal seed for this case,which turns out to be capable of capturing all matches of any pattern P within ≈r m l −r +2)·mn 1+1/r )).8Proof.Recall that in the construction of Theorem1,we were able tofind an alignment of A and B such that the aligned region of B contained the character0at most once,and this character was aligned against one of the zeros in A.Here,we willfind an alignment that contains at most r zeros in the aligned region of B,which will be aligned against zeros in A.Wefirst prove the theorem for the case r=2.Suppose that√n is divisible by3l−2.A is then constructed as follows.The seed A consists of√n.The blocks numbered2i n for i= 1,...,l−1contain only zeros.The other blocks contain√l )·m n3−2/l(n n)−5.Let B such a string,and define L=nn)that contains at most two zeros,and these zeros appears in thefirst2(L+√3l−2n+2√3l−2n+2√3l−2n+2√3l−2n+2√3l−2n].Notethat A[2s3l−2√3l−2n−j the position in A which is aligned against B [j ].Let d be the distancefrom position i to the nearest occurrence of a zero in A to the left of i,and d=i if there is no such occurrence.Since d<√n is not integer,or when√n is an integer divisible by3l−2,and we take A to be the prefix of length n of A .We now deal with the case of r>2.If n1/r is an integer divisible by(r+1)(l−r+1)+1, then we build the string A as follows:We begin by taking A=1n.We then partition A into blocks of different levels.Level i(i=0,...,r−1)consists of n1−i/r blocks of size n i/r each. For every i=0,...,r−2,and every j which is divisible by n1/r,we change block number j in level i to consists of all zeros.Furthermore,for j=1,...,l−r+1,we change block number j·l−r+2l−r+2 ·m n1+1/r)),9we have that either there is a substring of B of length n without zeros,or there is a substring B of B of length(r+1)/(r+1−rl−r+2)+O(n1−1/r)characters of B .Assume thatthe second case occurs.Suppose w.l.o.g.that B contains exactly r zeros.We create an alignment of A and B that covers B as follows:First,we align the rightmost zero in B withthe rightmost character of the appropriate zeros block of level r−1.Then,for i=2,...,r, we move A to the right,until the i-th zero from the right in B is either aligned against the rightmost character of some zeros block of level r−i,or it is outside the aligned region.Byour construction,the movement of A is no more than n1−(i−1)/r−1positions.Moreover, during the movements of A the following invariant is kept:For every j≤i−1,after the i-thmovement,the j-th zero from the right in B is aligned against a character of some zeros block of level j ,where r−i−1≤j ≤r−j.In particular,at the end,all the zeros in B are aligned against zeros in A,and therefore A covers B.The case when n1/r is not an integer,or when n1/r is not divisible by(r+1)(l−r+1)+1, is handled the same as before.The following theorem gives an upper bound that matches the lower bound in Theorem3,demonstrating that the seed it describes is(almost)optimal.Theorem4.For every integer r≥2,if g≤n1−1/r then k(n,g,m)≤r·mn+r.4Maximizing bWe now show how to maximize b,the number of solid symbols in a seed,given the numberof errors k and the pattern length m.As the number of false positives depends heavily on b,the resulting seed simply optimizes the performance of thefiltering method.Our result also provides the maximum b for the problem offinding all matches of any pattern P of size m ≥m within error rate k /m =k/m.10Theorem5.For every k<1.311Upper bound.Denote M= 1M.Since the number of k-tuples that satisfy(1)above is at least m−2M k /M,we have that there is a k-tuple(j,i1,...,i k−1)that satisfies(1)but does not satisfy(2).We now construct a string B of length m that contains zeros in positions jM,jM−i1,...,jM−i k−1and ones elsewhere.If A covers B,then consider some alignment of A and B that covers B,and suppose that A[1]is aligned with B[y].Since the length of A is at least b≥m−M+1,we have that y≤M.Therefore,B[jM]is aligned with A[x]for some x∈I j.It follows that (j,i1,...,i k−1)∈Y,a contradiction.Therefore,A does not cover B,and the upper bound follows.Theorem6.For every k≥1k log mklog m).Proof.The lower bound is trivial if k=Ω(m),so assume that k<m8·m k that contains b=Θ(n)ones and covers every string of length8n with at most log n zeros.If B is a string of length m with at most k zeros,then by the pigeon-hole principle,there is a substring B of B of length8n that has at most k·8nk≤log n zeros,and therefore A covers B .Thus,A covers B.Upper bound.Suppose that A is a string of length n with b≥mlog1b·log m≤k,and the upper bound follows.124.1Multiple seedsTo model multiple seeds,we define that a set of strings{A1,...,A s}covers a string B if at least one string A i from the set covers B.Let b(k,m,s)be the maximum b such that there is a set of strings{A1,...,A s}that covers every string B of length m with at most k zeros,and each string A i contains at least b ones.The following theorem shows that using multiple seeds can give better results than one seed,namely,b(k,m,m1/k)is slightly larger than b(k,m)(see Theorem5).Theorem7.For every k<log log m,b(k,m,m1/k)≥m−O(km1−1/k). Proof.We take s= m1/k ,and build a string A of length n=m− k−1l=0s l,that has k−1 levels of blocks as in the proof of Theorem5.Then,we build strings A1,...,A s−1,where A i is obtained by taking the string A and adding zeros at positions js−i for j≥s.It is easy to verify that{A1,...,A s−1}covers every string of length m with at most k zeros.References[1]S.Altschul,W.Gisch,ler,E.Myers,and D.Lipman.Basic local alignmentsearch tool.J.of Molecular Biology,215(3):403–410,1990.[2]A.Amir,M.Lewenstein,and E.Porat.Faster algorithms for string matching with kmismatches.J.of Algorithms,50(2):257–275,2004.[3]B.Brejov´a,D.G.Brown,and T.Vinar.Vector seeds:An extension to spaced seeds.J.Comput.Syst.Sci.,70(3):364–380,2005.[4]J.Buhler,U.Keich,and Y.Sun.Designing seeds for similarity search in genomic DNA.put.Syst.Sci.,70(3):342–363,2005.[5]S.Burkhardt and J.K¨a rkk¨a inen.Betterfiltering with gapped q-grams.Fundam.In-form.,56(1–2):51–70,2003.[6]A.Califano and I.Rigoutsos.FLASH:A fast look-up algorithm for string homology.InProc.1st International Conference on Intelligent Systems for Molecular Biology(ISMB), pages56–64,1993.[7]R.Cole and R.Hariharan.Approximate string matching:A simpler faster algorithm.SIAM put.,31(6):1761–1782,2002.[8]M.Karpinski and A.Zelikovsky.Approximating dense cases of covering problems.Electronic Colloquium on Computational Complexity(ECCC),4(4),1997.[9]U.Keich,M.Li,B.Ma,and J.Tromp.On spaced seeds for similarity search.DiscreteApplied Mathematics,138(3):253–263,2004.13[10]G.Kucherov,L.No´e,and M.A.Roytberg.Multiseed losslessfiltration.IEEE/ACMput.Biology Bioinform.,2(1):51–61,2005.[11]ndau and U.Vishkin.Fast parallel and serial approximate string matching.J.of Algorithms,10(2):157–169,1989.[12]M.Li,B.Ma,D.Kisman,and J.Tromp.Patternhunter II:Highly sensitive and fasthomology search.J.Bioinformatics and Computational Biology,2(3):417–440,2004.[13]B.Ma,J.Tromp,and M.Li.Patternhunter:faster and more sensitive homology search.Bioinformatics,18(3):440–445,2002.[14]S.C.Sahinalp and U.Vishkin.Efficient approximate and dynamic matching of patternsusing a labeling paradigm.In Proc.37th Symposium on Foundation of Computer Science (FOCS),pages320–328,1996.[15]Y.Sun and J.Buhler.Designing multiple simultaneous seeds for dna similarity search.J.of Computational Biology,12(6):847–861,2005.[16]J.Xu,D.G.Brown,M.Li,and B.Ma.Optimizing multiple spaced seeds for homologysearch.In Proc.14th Annual Symposium on Combinatorial Pattern Matching(CPM), pages47–58,2004.14。
Incomplete Contracts and the Product Cycle
Incomplete Contracts and the Product CycleBy P OL A NTRA`S*I present a model in which the incomplete nature of contracts governing interna-tional transactions limits the extent to which the production process can be frag-mented across borders.Because of contractual frictions,goods are initially manufactured in the same country where product development takes place.Only when the good becomes sufficiently standardized is the manufacturing stage of production shifted to a low-wage foreign location.Solving for the optimal organi-zational structure,I develop a new version of the product cycle hypothesis in which manufacturing is shifted abroadfirst withinfirm boundaries,and only at a later stage to independent foreignfirms.(JEL D23,F12,F14,F21,F23,L22,L33)In an enormously influential article,Ray-mond Vernon(1966)described a natural life cycle for the typical commodity.Most new goods,he argued,are initially manufactured in the country where they arefirst developed,with the bulk of innovations occurring in the indus-trialized North.Only when the appropriate de-signs have been worked out,and the production techniques have been standardized,is the locus of production shifted to the less developed South,where wages are lower.Vernon empha-sized the role of multinationalfirms in the in-ternational transfer of technology.In his formulation of a product’s life cycle,the shift of production to the South is a profit-maximizing decision from the point of view of the innovat-ingfirm.The“product cycle hypothesis”soon gave rise to an extensive empirical literature that searched for evidence of the patterns suggested by Vernon.1The picture emerging from this literature turned out to be much richer than Vernon originally envisioned.The evidence in-deed supports the existence of product cycles, but it has become clear that foreign direct in-vestment by multinationalfirms is not the only vehicle of production transfer to the South.The literature has identified several instances in which technologies have been transferred to the South through licensing,subcontracting,and other similar arm’s length arrangements.More interestingly,several studies have pointed out that the choice between intrafirm and market transactions is significantly affected by both the degree of standardization of the technology and by the resources devoted to product develop-ment by the transferor.2In particular,overseas assembly of relatively new and unstandardized products tends to be undertaken withinfirm boundaries,while innovators seem more willing to resort to licensing and subcontracting in stan-dardized goods with few product development requirements.The product cycle hypothesis has also at-tracted considerable attention among interna-tional trade theorists eager to explore the*Department of Economics,Harvard University,Lit-tauer230,Cambridge,MA02138,National Bureau of Eco-nomic Research,and Centre for Economic Policy Research (e-mail:pantras@).I am grateful to Daron Acemoglu,Marios Angeletos,Gene Grossman,and Jaume Ventura for invaluable guidance,and to Richard Baldwin, Lucia Breierova,Francesco Franco,Gordon Hanson,El-hanan Helpman,Simon Johnson,Giovanni Maggi,Marc Melitz,and Roberto Rigobon for their helpful commentsand suggestions.The paper was substantially improved by the thoughtful comments of the editor and two anonymous referees.I have also benefited from suggestions by seminar participants at various institutions.Thefirst draft of this paper was written while visiting the International Econom-ics Section at Princeton University,whose hospitality is gratefully acknowledged.I have also benefited fromfinan-cial support from the Bank of Spain.All remaining errors are my own.1See William Gruber et al.(1967),Seev Hirsch(1967), Louis T.Wells,Jr.(1969),and Thomas G.Parry(1975)for early tests of the theory.2See,for instance,Robert W.Wilson(1977),Edwin Mansfield et al.(1979),Mansfield and Anthony A.Romeo (1980),and William H.Davidson and Donald G.McFetridge(1984,1985).These studies will be discussed in more detail in Section III.1054macroeconomic and trade implications of Ver-non’s insights.Paul Krugman(1979)developed a simple model of trade in which new goods are produced in the industrialized North and ex-changed for old goods produced in the South. In order to concentrate on the effects of product cycles on tradeflows and relative wages,Krugman(1979)specified a very simple form of technological transfer,with new goods becoming old goods at an exogenous rate.This “imitation lag,”as he called it,was later endo-genized by Gene M.Grossman and Elhanan Helpman(1991a,b)using the machinery devel-oped by the endogenous growth literature.In particular,Grossman and Helpman(1991a,b) developed models in which purposeful innova-tion and imitation gave rise to endogenous prod-uct cycles,with the timing of production transfer being a function of the imitation effort exerted byfirms in the South.3As the empirical literature on the product cycle suggests,how-ever,the bulk of technology transfer is driven by voluntary decisions of Northernfirms,which choose to undertake offshore production within firm boundaries or transact with independent subcontractors or licensees.4In this paper,I provide a theory of the prod-uct cycle that is much more akin to Vernon’s (1966)original formulation and that delivers implications that are very much in line with the findings of the empirical literature discussed above.In the model,goods are produced com-bining a high-tech input,which I associate with product development,and a low-tech input, which is meant to capture the simple assembly or manufacturing of the good.As in Grossman and Helpman(1991a,b),the North is assumed to have a high enough comparative advantage in product development so as to ensure that this activity is always undertaken there.My speci-fication of technology differs,however,from that in Grossman and Helpman(1991a,b)in that I treat product development as a continu-ously active sector along the life cycle of a good.The concept of product development used here is therefore quite broad and is meant to include,among other things,the development of ideas for improving existing products,as well as the marketing and advertising of these prod-ucts.Following Vernon(1966),this specifica-tion of technology enables me to capture the standardization process of a good along its life cycle.More specifically,I assume that the con-tribution of product development to output(as measured by the output elasticity of the high-tech input)is inversely related to the age or maturity of the good.Intuitively,the initial phases of a product’s life cycle entail substantial testing and retesting of prototypes,as well as considerable marketing efforts to make con-sumers aware of the existence of the good.As the good matures and production techniques become standardized,the mere assembly of the product becomes a much more significant input in production.Following Vernon(1966)and contrary to Grossman and Helpman(1991a,b),I allow Northernfirms to split the production process internationally and transact with manufacturing plants in the South.5With no frictions to the international fragmentation of the production process,I show that the model fails to deliver a product cycle.Intuitively,provided that labor is paid a lower wage in the South than in the North,manufacturing will be shifted to the South even for the most unstandardized, product development–intensive goods.Vernon (1966)was well aware that his theory required some type of friction that delayed offshore assem-bly.In fact,he argued that in the initial phase of a product’s life cycle,overseas production would be discouraged by a low price elasticity3See Richard A.Jensen and Marie C.Thursby(1987), and Paul S.Segerstrom et al.(1990)for related theories of endogenous product cycles.See also Edwin i (1998)for an interesting extension of the Grossman andHelpman(1991a)model that incorporates foreign direct investment.4Grossman and Helpman(1991b)claimed that purpose-ful imitation was an important driving force in the transfer of production of microprocessors from the United States and Japan to Taiwan and Korea.Based on recent studies,I argue below that even in the case of the electronics industry, the spectacular increase in the market share of Korean producers might be better explained by technology transfer from foreign-basedfirms than by simple imitation by do-mesticfirms in Korea.5There is a recent literature in international trade docu-menting an increasing international disintegration of the production process(cf.,Robert C.Feenstra,1998;Kei-Mu Yi,2003).A variety of terms has been used to refer to this phenomenon:“international outsourcing,”“slicing of the value chain,”“vertical specialization,”“global production sharing,”and many others.Feenstra(1998)discusses the widely cited example of Nike,which subcontracts most parts of its production process to independent manufactur-ing plants in Asia.1055VOL.95NO.4ANTRA`S:INCOMPLETE CONTRACTS AND THE PRODUCT CYCLEof demand,the need for a thick market for inputs,and the need for swift and effective com-munication between producers and suppliers. This paper,instead,supports the view that what limits the international fragmentation of the production process is the incomplete nature of contracts governing international transac-tions.Building on the seminal work of Oliver E. Williamson(1985)and Sanford J.Grossman and Oliver D.Hart(1986),I show that the presence of incomplete contracts creates hold-up problems,which in turn give rise to suboptimal relationship-specific investments by the parties involved in an international transac-tion.The product development manager of a Northernfirm can alleviate this type of distor-tions by keeping the manufacturing process in the North,where contracts can be better en-forced.In choosing between domestic and over-seas manufacturing,the product development manager therefore faces a trade-off between the lower costs of Southern manufacturing and the higher incomplete-contracting distortions asso-ciated with it.This trade-off is shown to lead naturally to the emergence of product cycles: when the good is new and unstandardized, Southern production is very unattractive be-cause it bears the full cost of incomplete con-tracting(which affects both the manufacturing and the product development stages of produc-tion)with little benefit from the lower wage in the South.Conversely,when the good is mature and requires very little product development, the benefits from lower wages in the South fare much better against the distortions from incom-plete contracting,and if the Southern wage is low enough,the good is manufactured in the South.Following the property-rights approach to the theory of thefirm(Grossman and Hart,1986; Hart and John H.Moore,1990),the same force that creates product cycles in the model,i.e., incomplete contracts,opens the door to a par-allel analysis of the determinants of ownership structure,which I carry out in Section II.As in Grossman and Hart(1986),I associate owner-ship with the entitlement of some residual rights of control.When parties undertake noncontract-ible,relationship-specific investments,the allo-cation of these residual rights has a critical effect on each party’s ex post outside option, which in turn determines each party’s ex ante incentives to invest.Ex ante efficiency(i.e.,transaction-cost minimization)is shown to dic-tate that residual rights be controlled by the party whose investment contributes most to the value of the relationship.In terms of the model, the attractiveness of integrating the transfer of production to the South for a Northern product development manager is shown to be increasing in the output elasticity of product development, and thus decreasing in the maturity of the good at the time of the transfer.As a result,a new version of the product cycle emerges.If the maturity at which manu-facturing is shifted to the South is low enough, production will be transferred internally to a wholly owned foreign affiliate in the South,and the Northernfirm will become a multinational firm.In such case,only at a later stage in the product’s life cycle will the product develop-ment managerfind it optimal to give away the residual rights of control and assign assembly to an independent subcontractor in the South,an arrangement that is analogous to the Northern firm licensing its technology(high-tech input). For a higher maturity of the good at the time of the transfer,the model predicts that the transfer to the South will occur directly at arm’s length and multinationals will not arise.In Section III, I discuss several cross-sectional and time-series implications of the model and relate them to the empirical literature on the product cycle.For instance,the model is shown to be useful for understanding the evolution of the Korean elec-tronics industry after the Korean War.The paper is structured as follows.Section I develops a simple dynamic model that shows how the presence of incomplete contracts gives rise to product cycles.In Section II,I allow for intrafirm production transfers and describe the richer product life cycle that emerges from it. Section III reviews thefindings of the empirical literature on the product cycle and relates them to the predictions of the model.Section IV offers some concluding comments.I.Incomplete Contracts and the Life Cycle of aProductThis section develops a simple model in which a product development manager decides how to organize production of a particular good, taking the behavior of other producers and wages as given.I willfirst analyze the static1056THE AMERICAN ECONOMIC REVIEW SEPTEMBER2005problem and then show how a product cycle emerges in a simple dynamic extension in which the good gets standardized over time.A.SetupConsider a world with two countries,the North and the South,and a single good y pro-duced only with labor.I denote the wage rate in the North by w N and the wage rate in the South by w S.Consumer preferences are such that the unique producer of good y faces the following isoelastic demand function:(1)yϭpϪ1/͑1Ϫ␣͒,0Ͻ␣Ͻ1 where p is the price of the good andis a parameter that the producer takes as given.6 Production of good y requires the develop-ment of a special and distinct high-tech input, x h,as well as the production of a special and distinct low-tech input,x l.As discussed in the introduction,the high-tech input is meant to comprise research and product development, marketing,and other similar skill-demanding tasks.The low-tech input is,instead,meant to capture the mere manufacturing or assembly of the good.Specialized inputs can be of good or bad quality.If either of the two inputs is of bad quality,the output of thefinal good is zero.If both inputs are of good quality,production of thefinal good requires no additional inputs and output is given by(2)yϭz x h1Ϫz x l z,0ՅzՅ1 wherezϭzϪz(1Ϫz)Ϫ(1Ϫz).The unit cost function for producing the high-tech input varies by country.In the North,pro-duction of one unit of a good-quality high-tech input requires the employment of one unit of Northern labor.The South is much less efficient at producing the high-tech input.For simplicity, the productivity advantage of the North is as-sumed large enough to ensure that x h is pro-duced only in the North.Meanwhile,production of one unit of good-quality low-tech input also requires labor,but the unit input requirement is assumed to be equal to1in both countries. Production of any type of bad-quality input can be undertaken at a positive but negligible cost. All types of inputs are assumed to be freely tradable.There are two types of producers:a research center and a manufacturing plant.A research center is defined as the producer of the high-tech input and will thus always locate in the North.I assume for now that the research center needs to contract with an independent manufac-turing plant for the provision of the low-tech input.In the next section,I will let the research center obtain the low-tech input from an inte-grated plant.As discussed at the beginning of this paper,I allow for an international fragmentation of the production process.Before any investment is made,a research center decides whether to pro-duce a high-tech input and,if so,whether to obtain the low-tech input from an independent manufacturing plant in the North or from one in the South.Upon entry,the manufacturer makes a lump-sum transfer T to the research center. Because,ex ante,there is a large number of identical,potential manufacturers of the good, competition among them will make T adjust so as to make the chosen manufacturer break even.7The research center chooses the location of manufacturing to maximize its ex ante prof-its,which include the transfer.Investments are assumed to be relationship specific.The research center tailors the high-tech input specifically to the manufacturing plant,while the low-tech input is customized according to the specific needs of the research center.In sum,the investments in labor needed to produce x h and x l are incurred upon entry and are useless outside the relationship.The setting is one of incomplete contracts in situations of international production sharing.In particular,it is assumed that only when both inputs are produced in the same country can an outside party distinguish between a good-quality and a6This demand function is derived from preferences in the general-equilibrium version of the model presented in the Appendix.7When y is produced by the manufacturing plant,the transfer T can be interpreted as a lump-sum licensing fee for the use of the high-tech input.The presence of this transfer simplifies the general-equilibrium model outlined in the Appendix.For the results in the present section,it would suffice to assume that nofirm is cash constrained,so that the equilibrium location of manufacturing maximizes the joint value of the relationship.1057VOL.95NO.4ANTRA`S:INCOMPLETE CONTRACTS AND THE PRODUCT CYCLEbad-quality intermediate input.8Hence,the man-ager of the research center and that of a Southern manufacturing plant cannot sign an enforceable contract specifying the purchase of a certain type of intermediate input for a certain price.If they did,the party receiving a positive payment would have an incentive to produce the bad-quality input at the negligible cost.It is equally assumed that no outside party can verify the amount of ex ante investments in labor.If these were verifiable,the managers could contract on them,and the cost-reducing benefit of producing a bad-quality input would disappear.For the same reason,it is as-sumed that the parties cannot write contracts con-tingent on the volume of sale revenues obtained when the final good is sold.The only contractible ex ante is the transfer T between the parties.9When the research center chooses to transact with a manufacturing plant in the North,the fact that labor investments are not contractible is irrelevant because the parties can always appeal to an outside party to enforce quality-contingent contracts.In contrast,when the low-tech input is produced by a plant in the South,no enforce-able contract will be signed ex ante and the two parties will bargain over the surplus of the re-lationship after the inputs have been produced.At this point,the quality of the inputs is observ-able to both parties and thus the costless bar-gaining will yield an ex post efficient outcome.I model this ex post bargaining as a Symmetric Nash Bargaining game in which the parties share equally the ex post gains from trade.10Because the inputs are tailored specifically to the other party in the transaction,if the two parties fail to agree on a division of the surplus,both are left with nothing.This completes the description of the model.The timing of events is summarized in Figure 1.B.Firm BehaviorAs discussed above,the North has a suffi-ciently high productivity advantage in produc-ing the high-tech input to ensure that x h is produced there.The decision of where to pro-duce the low-tech input,however,is nontrivial.In his choice,the manager of the research center compares the ex ante profits associated with two options,which I analyze in turn.(a)Manufacturing by an Independent Plant in the North.—Consider first the case of a re-search center that decides to deal with an inde-pendent manufacturing plant in the North.In that case,the two parties can write an ex ante quality-contingent contract that will not be re-negotiated ex post.The initial contract stipu-lates production of good-quality inputs in an amount that maximizes the research center’s ex ante profits,which from equations (1)and (2),and taking account of the transfer T ,are givenby N ϭ1Ϫ␣z ␣x h ␣(1Ϫz )x l ␣zϪw N x h Ϫw N x l .It is straightforward to check that this program yields the following optimal price for the final good:8This can be interpreted as a physical constraint im-posed on the outside party,which might not be able to verify the quality of both inputs when these are produced in distant locations.More generally,the assumption is meant to cap-ture broader contractual difficulties in international transac-tions,such as ambiguous jurisdiction,language conflicts,or,more simply,weak protection of property rights in low-wage countries.9I take the fact that contracts are incomplete as given.Philippe Aghion et al.(1994),Georg No ¨ldeke and Klaus M.Schmidt (1995),and others have shown that allowing for specific performance contracts may lead to efficient ex ante relationship-specific investments.Nevertheless,Yeon-Koo Che and Donald B.Hausch (1999)have identified condi-tions under which specific performance contracts do not lead to first-best investment levels,and may actually have no value.10In Antra `s (2004),I extend the analysis to the case of Generalized NashBargaining.F IGURE 1.T IMINGOFE VENTS1058THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005p N͑z͒ϭw N ␣.Because the research center faces a constant elasticity of demand,the optimal price is equal to a constant markup over marginal cost.Ex ante profits for the research center are in turn equal to(3)N͑z͒ϭ͑1Ϫ␣͒ͩw N␣ͪϪ␣/͑1Ϫ␣͒.(b)Manufacturing by an Independent Plant in the South.—Consider next the problem faced by a research center that decides to transact with a plant in the South.As discussed above,in this case the initial contract stipulates only the trans-fer T.The game played by the manager of the research center and that of the manufacturing plant is solved by backward induction.If both producers make good-quality intermediate in-puts and thefirms agree in the bargaining,the potential revenues from the sale of thefinal good are Rϭ1Ϫ␣z␣x h␣(1Ϫz)x l␣z.In contrast,if the parties fail to agree in the bargaining,both are left with nothing.The quasi-rents of the relationship are therefore equal to sale revenues, i.e.,R.The Nash bargaining leaves each man-ager with one-half of these quasi-rents.Rolling back in time,the research center manager sets x h to maximize1⁄2RϪw N x h,while the manu-facturing plant simultaneously chooses x l to maximize1⁄2RϪw S x l.11Combining thefirst-order conditions of these two programs yields the following optimal price for thefinal good:p S͑z͒ϭ2͑w N͒1Ϫz͑w S͒z␣.If parties could write complete contracts in in-ternational transactions,the research center would instead set a price equal to (w N)1Ϫz(w S)z/␣.The overinflated price reflects the distortions arising from incomplete con-tracting.Intuitively,the parties will tend to un-derinvest in x h and x l because in the ex post bargaining they fail to capture the full marginal return to their investments.As a result,output will tend to be suboptimal and the move along the demand function will also be reflected in an inefficiently high price.Setting T so as to make the manufacturing plant break even leads to the following expres-sion for the research center’s ex ante profits: (4)S͑z͒ϭͩ1Ϫ1␣ͪͩ2(w N)1Ϫz(w S)z␣ͪϪ␣/͑1Ϫ␣͒.C.The Equilibrium ChoiceFrom comparison of equations(3)and(4),it follows that the low-tech input will be produced in the South only if A(z)Յϵw N/w S,where(5)A͑z͒ϵͩ1Ϫ␣͑1Ϫ12␣͒͑12͒␣/͑1Ϫ␣͒ͪ͑1Ϫ␣͒/␣z.It is straightforward to show that A(z)is nonin-creasing in z for zʦ[0,1],with lim z30A(z)ϭϩϱand A(1)Ͼ1.12This implies that(a)for high enough product development intensities of thefinal good,manufacturing is necessarily as-signed to a manufacturing plant in the North; and(b)unless the wage in the North is higher than that in the South,manufacturing by an independent plant in the South will never be chosen.Intuitively,the benefits of Southern as-sembly are able to offset the distortions created by incomplete contracting only when the man-ufacturing stage is sufficiently important in pro-duction or when the wage in the South is sufficiently lower than that in the North.To make matters interesting,I assume that:ASSUMPTION1:ϾA(1)Ͼ1.In Antra`s(2004),I show that this condition necessarily holds in a simple general-equilibrium extension of the model,in which the relative wageis endogenously pinned down.Intuitively,in the general equilibrium the relative wage in the North necessarily adjusts to11It is easily checked that in equilibrium both partiesreceive a strictly positive ex post payoff from producing a good-quality input.It follows that bad-quality inputs are never produced.12This follows from the fact that(1Ϫ␣x)x␣/(1Ϫ␣)is increasing in x for␣ʦ(0,1)and xʦ(0,1).1059VOL.95NO.4ANTRA`S:INCOMPLETE CONTRACTS AND THE PRODUCT CYCLEensure positive labor demand in the South.This extension is briefly outlined in the Appendix.A salient feature of the analysis is that as long as contracts governing international transactions are incomplete,the equilibrium wage in the North necessarily exceeds that in the South.13Assumption 1ensures that N (z )ϽS (z )for sufficiently high z ʦ[0,1].Figure 2depicts the profit-maximizing choice of location as a func-tion of z .It is apparent that:LEMMA 1:Under Assumption 1,there exists a unique threshold z ʦ(0,1)such that the low-tech input is produced in the North if z Ͻz ϵA Ϫ1(),while it is produced in the South if z Ͼz ϵA Ϫ1(),where A (z )is given by equation (5)and is the relative wage in the North.From direct inspection of Figure 2,it is clear that an increase in the relative wage in the North reduces the threshold z .Intuitively,an increase in makes Southern manufacturing relatively more profitable and leads to a reduction in the measure of product development intensities for which the whole production process stays in the North.D.Dynamics:The Product Cycle As discussed earlier,one of the premises of Vernon’s (1966)original product cycle hypoth-esis is that as a good matures throughout its life cycle it becomes more and more standardized.14Vernon believed that the unstandardized nature of new goods was crucial to understanding that they would first be produced in a high-wage country.To capture this standardization process in a simple way,consider the following simple dy-namic extension of the static model developed above.Time is continuous,indexed by t ,with t ʦ[0,ϱ).Consumers are infinitely lived and,at any t ʦ[0,ϱ),their preferences for good y are captured by the demand function (1).The rela-tive wage is assumed to be time-invariant.15The output elasticity of the low-tech input is instead assumed to increase through time.In particular,this elasticity is given byz ͑t ͒ϭh ͑t ͒,with h Ј͑t ͒Ͼ0,h ͑0͒ϭ0,and lim t 3ϱh ͑t ͒ϭ1.I,therefore,assume that the product develop-ment intensity of the good is inversely related to its maturity.Following the discussion at the beginning of this paper,this is meant to capture the idea that most goods require a lot of R&D and product development in the early stages of their life cycle,while the assembling or manu-facturing becomes a much more significant in-put in production as the good matures.I will take these dynamics as given,but it can be shown that,under Assumption 1,profits for the Northern research center are weakly increasing in z .It follows that the smooth process of stan-dardization specified here could,in principle,be derived endogenously in a richer framework that incorporated some costs of standardiza-13Another appealing characteristic of the general-equilibrium analysis is that the cross-sectional picture that emerges from the model is very similar to that in the classical Ricardian model with a continuum of goods of Rudiger Dornbusch et al.(1977).14In discussing previous empirical studies on the loca-tion of industry,Vernon wrote,“In the early stages of introduction of a new good,producers were usually con-fronted with a number of critical,albeit transitory,condi-tions.For one thing,the product itself may be quite unstandardized for a time;its inputs,its processing,and its final specifications may cover a wide range.Contrast the great variety of automobiles produced and marketed before 1910with the thoroughly standardized product of the 1930s,or the variegated radio designs of the 1920s with the uni-form models of the 1930s”(Vernon,1966,p.197).15The latter assumption is relaxed in the general equi-librium version of the model developed in Antra `s (2004)and sketched in theAppendix.F IGURE 2.T HE C HOICEOFL OCATION1060THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005。
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4.统计学分析 本文中使用的统计学软件为SPSS 22.0,应用项 目分析、信度分析、效度分析检验量表的适用性。
结果
(2) 结构效度分析
KMO检验的抽样适度测定值为0.901( &检验结果为P < 0. 01 (卡方值为
355. 69)。经主成分分析法提取到3个公因子，累计方
差贡献率为75.91 %。各题项的因子载荷量>0.5,共
同度均>0.4。
3. 信度分析
总量表的Chronbach's a系数为0. 917。各项目
综上所述，2 型糖尿病患者饮食行为依从性量表在 评估2型糖尿病患者饮食依从性方面具有较高的信效 度，适用性较高，能够较为客观地评价2型糖尿病患者 的饮食依从性,为了解影响患者饮食依从行为的影响因 素以及开展饮食干预和健康指导提供了客观依据。
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中国卫生统计2021年6月第38卷第3期
中国卫生统计2021年6月第38卷第3期
・409・
2型糖尿病患者饮食行为依从性量表的编制及信效度研究
周丹1高岩2包乌仁2王程敏1
【提 要】目的 探讨2型糖尿病患者饮食行为依从性量表的信效度。方法 选取本院2017年9月至2018年10
月收治的180例2型糖尿病患者进行研究,向其发放自行编制的2型糖尿病患者饮食行为依从性量表，回收有效量表166
参考文献
[1 ]陈峰，夏结来主编.药物临床试验设计与实施丛书：临床试验统计 学.2018版.北京:人民卫生出版社,2018,404-406.
Markets and Hierarchies
TRANSACTION COST FRAMEWORK
Copyright © 2018, 2013, 2009 Pearson Education, Inc All Rights Reserved
corruption of the strategic decision-making process – tops managers of departments further their own goals rather than the overall goals of the organisations
INFORMATION AND ORGANISATIONAL DESIGN
LUBS5002
Markets and Hierarchies
OBJECTIVES
Apply the concepts of transaction cost economics to the understanding of efficient organisational structure.
• Effects on internal/external TC’s are industry specific but most dramatic for ‘information goods’ (books, films, music).
DIGITIZATION AND TRANSACTION COSTS
control – location decision-making rights within hierarchy
(Besanko et al, 1996)
中华人民共和国城市规划法中英对照
中华人民共和国城市规划法中英对照中华人民共和国城市规划法City Planning Law of the People's Republic of China第一条为了确定城市的规模和发展方向，实现城市的经济和社会发展目标，合理地制定城市规划和进行城市建设，适应社会主义现代化建设的需要，制定本法。
Article 1. This Law is formulated to determine the size of a city, define the orientation of its development, realize the goals of its economic and social development, and map out its plan and carry out its construction on a rational basis in order to meet the needs in socialist modernization.第二条制定和实施城市规划，在城市规划区内进行建设，必须遵守本法。
Article 2. This Law shall be observed when the plan for a city is being formulated or implemented, or when construction is being carried out within a planned urban area.第三条本法所称城市，是指国家按行政建制设立的直辖市、市、镇。
Article 3. The term " city " used in this Law applies to a municipality directly under the Central Government, a city or a town established as one of the administrative divisions of the state.本法所称城市规划区、是指城市市区、近郊区以及城市行政区域内因城市建设和发展需要实行规划控制的区域。
上海柔性推迟退休年龄问题研究-开题报告
一、论文名称：上海柔性推迟退休年龄问题研究
二、本课题的研究目的与意义
随着上海人口老龄化进程的不断加快、人口预期寿命延长以及经济增长速度的放慢，养老和就业问题面临更加严峻的形势。
在权衡养老和就业问题之间，调整退休年龄的话题成为社会各界争论的焦点。
由此想到上海出台柔性推迟退休年龄必然会面临阻力和困难，本课题通过研究上海老龄化问题，论证该政策的重要性和可行性，分析柔性推迟退休年龄的正效应，阐述实行柔性退休年龄政策是解决上海当前养老金空帐等问题的重要措施。
根据本课题的研究，提出柔性推迟退休年龄的具体建议和措施，让人们认识到上海柔性推迟退休年龄政策是应对老化挑战的有效举措。
经皮给药系统研究进展
经皮给药系统研究进展李传俊;李绵瑱;蒋玉仁【摘要】经皮给药系统把皮肤作为可行的给药路径,使药物经过皮肤进入体内起治疗作用,具有使用方便、降低个体给药差异、延长药物作用时间、降低给药次数、血药浓度稳定和降低药物毒副作用等优点.经皮给药可代替传统的口服给药和注射给药,具有广阔的发展空间.【期刊名称】《广州化工》【年(卷),期】2013(041)013【总页数】3页(P30-32)【关键词】经皮给药;压敏胶;化学促渗;物理促渗;微装置【作者】李传俊;李绵瑱;蒋玉仁【作者单位】中南大学化学化工学院,湖南长沙410083;中南大学化学化工学院,湖南长沙410083;中南大学化学化工学院,湖南长沙410083【正文语种】中文【中图分类】R94通过皮肤给药分为皮肤的局部作用 (皮肤表层给药)和通过皮肤渗透的全身作用 (透皮吸收给药，经皮给药)。
经皮给药是一种能够维持体内有效药物水平、非损伤性的给药途径，可以实现预期作用时间和长期作用时间的药物控制释放。
经皮给药系统是设计用来控制药物从给药装置中传递治疗成分至皮肤或穿透皮肤进入体循环的装置。
与传统的口服给药或注射给药方式相比，经皮给药可避免胃肠道代谢和肝脏代谢中的首过效应，减少副作用，降低给药频率和改善血药浓度，具有更广泛的应用前景［1］。
压敏胶和药物的渗透性是经皮给药系统中的两个研究热点，新型经皮给药微装置的研究，对经皮给药系统的发展也有重要的影响。
本文对经皮给药系统中热点问题的研究现状进行了总结。
1 压敏胶压敏胶提供与皮肤黏合的作用，在含药压敏胶系统中压敏胶还是包容药物和其他辅料的处方基质。
在经皮给药系统中，压敏胶对经皮给药系统的安全、疗效和质量是至关重要的［2］。
除了粘性要求外，用于经皮给药系统的压敏胶必须和皮肤有很好的生物相容性、和药物剂型的各种成分有很好的化学相容性，提供始终如一的有效的药物释放。
经皮给药系统中三种最常用的压敏胶是聚异丁烯、聚丙烯酸酯和聚二甲基硅氧烷［3］。
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Contents lists available at SciVerse ScienceDirect
Contemporary Clinical Trials
journal homepage: /locate/conclintrial
A new adaptive design based on Simon's two-stage optimal design for phase II clinical trials
Hua Jin ⁎, Zhen Wei
School of Mathematical Sciences, South China Normal University, 510631, PR China
1256
H. Jin, Z. Wei / Contemporary Clinical Trials 33 (2012) 1255–1260
decision-theoretic construct and the random search simulated annealing algorithm, they derived an optimal adaptive two-stage design. For details refer to Appendix A and [9]. Their optimal designs always gave better results than those from Simon's designs in the sense that the expected sample sizes were smaller, although the gains were modest with a 3–5% decrease in the expected sample size under the null hypothesis. However, as pointed out by themselves, the major disadvantage of their design is its counter-intuitive feature: as the response in the first stage increases, the second-stage sample size increases till a certain point and then abruptly becomes zero. So, in this paper, we propose a new adaptive design in order to get more reasonable results. In Section 2, we briefly review Simon's optimal two-stage design. We formulate our adaptive design in Section 3 and give the results (including comparison to Banerjee and Tsiatis' approach) in Section 4. Discussion is presented in Section 5.
abstract
Phase II clinical trials are conducted to determine whether a new agent or drug regimen has sufficient promise in treating cancer to merit further testing in larger groups of patients. Both ethical and practical considerations often require early termination of phase II trials if early results clearly indicate that the new regimen is not active or worthy of further investigation. Simon's two-stage designs (1989) are common methods for conducting phase II studies investigating new cancer therapies. Banerjee and Tsiatis (2006) proposed an adaptive two-stage design which allows the sample size at the second stage to depend on the results at the first stage. Their design is more flexible than Simon's, but it is somewhat counter-intuitive: as the response in the first stage increases, the second-stage sample size increases till a certain point and then abruptly becomes zero. In this paper, based on Simon's two-stage optimal design, we propose a new adaptive one which depends on the first stage results using the restrict conditions the conditional type I error and the conditional power. Comparisons are made between Banerjee and Tsiatis' results and our new adaptive designs.
1551-7144/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/t.2012.07.003
However, a disadvantage of these “classical” sequential designs is that, based on certain assumptions at the beginning of the trial, the number of interim analyses as well as the numbers of patients per stage have to be fixed. Once the design has been fixed and the trial has been started, it has to be conducted according to the pre-specified decision rules. That is, trial design modifications based on the information collected up to an interim analysis are not possible. In this context, adaptive designs, which allow for some types of prospectively planned mid-study change, develop.
© 2012 Elsevier Inc. All rights reserved.
1. Introduction
Phase II clinical trials are conducted to determine whether a new agent or drug regimen has sufficient promise in treating cancer to merit further testing in larger groups of patients. The primary goal is not to provide definitive evidence of drug efficacy, but to propose a promising drug for further investigations. Both ethical and practical considerations often require early termination of phase II trials if early results clearly indicate that the new regimen is not active or worthy of further investigation.
⁎ Corresponding author at: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China. Tel.: +86 13570103286.
E-mail address: jinh1@ (H. Jin).
article info
Article history: Received 25 January 2012 Revised 6 June 2012 Accepted 2 July 2012 Available online 6 July als Simon's two-stage optimal design Adaptive design Conditional type I error Conditional power