How to distribute antidote to control epidemics

We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Learning to represent,representing to learn

This study explores how students learn to create, discuss, and reason with representations to solve problems. A summer school algebra class for seventh and eighth graders provided opportunities for students to create and use representations as problem-solving tools. This case study follows the learning trajectories of three boys. Two of the three boys had been low-achievers in their previous math classes, and one was a high achiever. Analysis of all three boys’ written work reveals how their representations became more sophisticated over time. Their small group interactions while problem-solving also show changes in how they communicated and reasoned with representations. For these boys, representation functioned as a learning practice. Through constructing and reasoning with representations, the boys were able to engage in generalizing and justifying claims, discuss quadratic growth, and collaborate and persist in problem-solving. Negotiating different student-constructed representations of a problem also gave them opportunities to act with agency, as they made choices and judgments about the validity of the different perspectives. These findings have implications for the importance of giving all students access to mathematics through representations, with representational thinking serving as a central disciplinary practice and as a learning practice that supports further mathematics learning.     

When to rebuild or when to adjust scorecards

Data-based scorecards, such as those used in credit scoring, age with time and need to be rebuilt or readjusted. Unlike the huge literature on modelling the replacement and maintenance of equipment there have been hardly any models that deal with this problem for scorecards. This paper identifies an effective way of describing the predictive ability of the scorecard and from this describes a simple model for how its predictive ability will develop. Using a dynamic programming approach one is then able to find when it is optimal to rebuild and when to readjust a scorecard. Failing to readjust or rebuild a scorecard when they aged was one of the defects in credit scoring identified in the investigations into the sub-prime mortgage crisis.     

Options to expand and to contract in combination

This work presents a real options approach to the valuation of multiple investment projects, focusing on the case of option to expand and/or to contract. Proper valuation formulas are obtained by solving Black–Scholes PDE and the impact of strategic interaction among multiple options is studied.     

Boolean approaches to graph embeddings related to VLSI

This paper discusses the development of Boolean methods in some topics on graph embeddings which are related to VLSI. They are mainly the general theory of graph embeddability, the orientabilities of a graph and the rectilinear layout of an electronic circuit.     

Categorical approach to modelling and to coupling of models

Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic model, one has to think carefully about the modelling process. Particularly in the case of coupled problems when several models are coupled together to represent a given physical phenomenon. This paper presents an approach based on the category theory that allows to describe this modelling process on a more abstract level. Using the advantages of abstract level, one can describe the coupling process in a concise way and introduce certain criteria to check consistency of a coupled model. The main idea of the proposed approach is to introduce a structure in the modelling process, which allows to see how different models interact without a precise look into them. Copyright © 2016 John Wiley & Sons, Ltd.     

A Portfolio Approach to Capital Budgeting: An Application to the Expansion to Additional Product Lines

The importance of the covariance of returns between capital assets is one of the basic principles of modern portfolio theory. An investor should seek capital assets which have negative covariance of returns, or if such capital assets are not available, capital assets with low covariance should be sought for a portfolio. From the variance-covariance structure of returns of the capital assets and the expected returns for each capital asset, a risk-reward trade-off or efficient frontier can be generated. The trade-off represents the minimum risk, as measured by portfolio variance, that could be incurred to realize a desired rate of return for the portfolio. This concept applies to a portfolio of capital budgeting projects as well as to a portfolio of securities. This paper demonstrates how this concept of portfolio diversification can be applied to a capital budgeting problem. The problem involves an actual problem faced by a U.S. distributor who must decide whether to expand sales into one of two industries. Quadratic programming is used to generate the risk-reward relationships and it is shown that the entry into one industry clearly provides a superior risk-reward relationship than entry into the other industry and compared to the company's present sales policy.     

Sampling to provide or to bound: With applications to fully dynamic graph algorithms

In dynamic graph algorithms the following provide-or-bound problem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements from S testing for membership in R, either (i) provide an element of R, or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dynamic graph algorithms by a factor of O(log n). For example, it improves the time per update for fully dynamic connectivity from O(log³n) to O(log²n). © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 369–379 (1997)     

Anstee的两个定理的订正

本文的目的有二个,其一是给出反例说明Anstee的两个定理是欠妥的,其二是订正这二个定理。为方便起见,我们沿用[2]中的有关记号和定义。 设R和S分别为m维和n维非负整数向量,P=(P_(ij))_(m×n)为每列至多有一个1的(0,1)-矩阵。令_p(R,S)是一切以R为行和向量、S为列和向量且覆盖(cover)P的(0,1)-矩阵组成的集合。一个列向量a若是_p(R,S)中某个矩阵的第k列,则称a为_p(R,S)的     

三人博弈问题的模型和一种解法的修正

简要叙述了三个擂台赛博弈问题,指出解法[1]的错误所在,其一是将无限延伸的博弈树以有限的形式看待,其二是概率计算过程与结果错误,提出一种新的解法,并比较了结果的大小。     

Approximation to measurable functions and its relation to probabilistic computation

A theory of approximation to measurable sets and measurable functions based on the concepts of recursion theory and discrete complexity theory is developed. The approximation method uses a model of oracle Turing machines, and so the computational complexity may be defined in a natural way. This complexity measure may be viewed as a formulation of the average-case complexity of real functions—in contrast to the more restrictive worst-case complexity. The relationship between these two complexity measures is further studied and compared with the notion of the distribution-free probabilistic computation. The computational complexity of the Lebesgue integral of polynomial-time approximable functions is studied and related to the question “FP = ♯P?”.     

A numerical approach to variational problems subject to convexity constraint

Summary. We describe an algorithm to approximate the minimizer of an elliptic functional in the form on the set of convex functions u in an appropriate functional space X. Such problems arise for instance in mathematical economics [4]. A special case gives the convex envelope of a given function . Let be any quasiuniform sequence of meshes whose diameter goes to zero, and the corresponding affine interpolation operators. We prove that the minimizer over is the limit of the sequence , where minimizes the functional over . We give an implementable characterization of . Then the finite dimensional problem turns out to be a minimization problem with linear constraints. Received November 24, 1999 / Published online October 16, 2000     

How to talk to strangers: ways to leverage connectivity between R, Java and Objective C

R has certain limitations either introduced by design or historically that are not easy to resolve directly. Among those are lack of support for multi-threading or graphical user interfaces. Often we can find a solution in another system or environment. In this paper we show several possibilities of talking between R and other environments and languages that allow the developer to leverage technologies that are not directly accessible from within R. Most prominently the Java and Objective C interfaces in R have been simplified recently such that their use is much easier and ready for wide deployment. We will give a short introduction to their use, focus on package development and discuss some implementation issues.     

Using video to teach future teachers to learn from teaching

Video is commonly used in teacher preparation programs. Teacher educators use video for various purposes. In this study, we describe the Learning to Learn from Mathematics Teaching project. In this project, video is used to develop pre-service teachers’ (PSTs) orientations, knowledge and skills for analyzing and reflecting on mathematics teaching in ways that generate knowledge for improvement. We discuss the ways we have used video in a course aimed at developing elementary PSTs’ abilities to learn from teaching. In addition, we report on a study that investigated PSTs’ changes in lesson analysis abilities as a result of participating in the course.     

Conditions for Gaussian homogeneous fields to belong to classes

This paper is the continuation of [1], [2]. In it questions of approximation of functions are discussed, when a realization of the homogeneous Gaussian field belongs to the class H _p ^r (G)₀.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 126–143, 1990.     

The location of public facilities intermediate to the journey to work

Location—allocation models typically locate facilities with respect to points to be served, for example to the homes of potential patrons. Certain types of facility, however, are employed by persons who travel to the facility from their homes and continue their journey to another location. Child care facilities are an example of this pattern of patronage, with parents dropping children off at a centre en route to work. The paper presents a discrete-space location—allocation model minimizing the diversion of patrons' journeys to work. The problem reduces to the structure and combinatorial dimensions of the simple P-median problem. The model is applied to the transit worktrip patterns of single parents in Edmonton, Canada. The facilities generated by the model tend to central locations in the city where workplaces are concentrated and transit connections are efficient. The model provides a compromise between ones minimizing home-facility travel times and facility-workplace travel times.     

升值之言该如何听

自今年6月中国暗示将松动人民币汇率以来,人民币升值幅度仅为0．4％,这大大低于华盛顿的期待,因此,中美两国的关系日益紧张起来。随着失业率的膨胀,以及选举年即将到来,美国国会再一次将人民币汇率摆上了议事日程：9月6日,华盛顿两位高官为缓和中美关系前往北京,就人民币及其他重要问题进行高峰会晤,以期达成共识。     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.