Improving the cost-effectiveness of Chlamydia screening with targeted screening strategies

Chlamydia is the most common sexually transmitted infection in the UK and constitutes a major public health problem. The UK Department of Health is phasing in a National Chlamydia Screening Programme (NCSP) but there is concern that blanket screening of the entire at risk population will simply add extra burden to the already overstretched health economy. This paper demonstrates that certain high-risk sub-groups within the general population are critical in the infection dynamics. Improved targeting of these high-risk populations achieves greater cost-effectiveness. Statistical risk-group clustering techniques have been used to identify indicators that are strong predictors in determining high-risk status while geomapping techniques visually display prevalence geographically across the region, thus identifying high prevalence postcode clusters and informing public health planners where to target intervention and screening strategies. A System Dynamics simulation model has been used to capture the infection dynamics and measure the cost-effectiveness of the intervention strategies. The model incorporates risk-group behaviour as identified by the above geomapping and statistical analysis components of the research. The combined use of computer simulation, statistical analysis and geomapping methodologies has provided a unique holistic view of the problem.     

Ups and Downs of First Order Sentences on Random Graphs

whenever is a fixed positive irrational. This raises the question what zero-one valued functions on the positive irrationals arise as the limit probability of a first order sentence on these graphs. Here we prove two necessary conditions on these functions, a number-theoretic and a complexity condition. We hope to prove in a subsequent paper that these conditions together with two simpler and previously proved conditions are also sufficient and thus they constitute a characterization. Received October 2, 1998     

Evaluation of different strategies for building and displaying models to describe bacterial growth in foods

This paper compares the different methods for acquiring datadescribing microorganism growth, the types of model that canbe built from such data, and the different ways in which suchmodels can be presented for use.     

The Ups and Downs of Percent (and Some Interesting Connections)

Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.     

Some strategies for mastermind

Summary The aim of this paper is to present some methods of construction for strategies for the game Mastermind.Some of these methods were already published before by other authors, but in this paper an approach unifying most of these methods is used. Numerical results for expectation and maximum number of questions needed to finish the game are presented for different versions of the game. By combining some of these methods a strategy slightly better than all strategies published by other authors is constructed for the most popular version of the game.

---

Zusammenfassung Der vorliegende Artikel will mehrere Konstruktionsmethoden für Strategien für das Spiel Mastermind darstellen und miteinander vergleichen.Einige dieser Methoden wurden bereits von anderen Autoren publiziert, der vorliegende Artikel beschreibt allerdings ein übergeordnetes Konzept, in das alle diese Methoden eingeordnet werden können. Numerische Ergebnisse für den Erwartungswert und die maximal notwendige Anzahl von Fragen bis zum Spielende werden für verschiedene Strategien und verschiedene Versionen dieses Spiels präsentiert. Durch Kombination mehrerer Methoden ist es sogar möglich, für die bekannteste Version dieses Spiels eine — wenn auch nur geringfügig — bessere Strategie als alle bisher publizierten anzugeben.

     

Optimal sampling strategies for quicksort

A well-known improvement on the basic Quicksort algorithm is to sample from the subarray at each recursive stage and to use the sample median as the partition element. General sampling strategies, which allow sample size to vary as a function of subarray size, are analyzed here in terms of the total cost of comparisons required for sorting plus those required for median selection. Both this generalization and this cost measure are new to the analysis of Quicksort. A square-root strategy, which takes a sample of size Φ(√n) for a subarray of size n, is shown to be optimal over a large class of strategies. The square-root strategy has O(n^1,5) worst-case cost. The exact optimal strategy for a standard implementation of Quicksort is found computationally for n below 3000. © 1995 John Wiley & Sons, Inc.     

Optimal intervention strategies for tuberculosis

This paper deals with the problem of optimal control of a deterministic model of tuberculosis (abbreviated as TB for tubercle bacillus). We first present and analyze an uncontrolled tuberculosis model which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated basic reproduction number is less than the unity. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control problem, indicating how control terms on the chemoprophylaxis and detection should be introduced in the population to reduce the number of individuals with active TB. Results provide a framework for designing the cost-effective strategies for TB with two intervention methods.     

Testing strategies for model specification

A crucial element in the development of econometric methodology during the past decade has been the concern with testing as opposed to estimating econometric models. In this paper we discuss—especially for the econometric analysis of time series—the main types of test procedures, and we also investigate the opportunities to uphold the Neyman-Pearson theory in the context of thorough model specification testing. In applied work it is quite usual to carry out several tests on the same set of sample data. We consider an extension of the Neyman-Pearson framework to the case of such repeated testing, and examine situations where the various hypotheses under test have a particular nesting structure. For the case where a sequence of superposed alternatives is tested by so-called marginal tests, we prove that the various test statistics are asymptotically independent under a common null hypothesis if the statistics are based on either the likelihood-ratio, or the Wald, or the Lagrange-multiplier approach. Testing a particular null hypothesis against a series of juxtaposed alternatives appears to lead to independent test statistics only in specific circumstances. It is shown how independence of test statistics enables the control over the overall Type I error probability, which is an essential element in the Neyman-Pearson theory. Using the notions of constructive hypotheses and auxiliary hypotheses, we can draw a clear distinction between specification tests and misspecification tests. Next an overview is given of approaches to and examples of specification and misspecification testing. With respect to the former, attention is paid to the problem determining the order of dynamics and discriminating between system dynamics and error dynamics. The misspecification testing is reviewed for specification error, nonconstancy of coefficients, heteroscedasticity, serial dependence, and nonnormality of disturbances. Also the problem of testing for several misspecifications jointly or sequentially is considered. Finally we discuss the options and associated difficulties in implementing the various tests in an overall testing strategy.     

Drilling strategies for frontier areas

A procedure for selecting oil and gas drilling sites in a frontier area is developed. The effect of information gained from drilling on future decisions is directly incorporated. Multiple and potentially conflicting objectives of the drilling organization are reflected in the procedure, which identifies efficient sets of drilling prospects. Data from a variety of sources may be integrated in the analysis through assessments by earth scientists and exploration professionals. Application of the procedure to other stages of the exploration process are discussed, as well as alternative objectives and constraints. An example using Alaskan North Slope data is provided.     

Factorization strategies for third-order tensors

Operations with tensors, or multiway arrays, have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer products using either the CANDECOMP/PARAFAC (CP) or the Tucker models, or some variation thereof. Such decompositions are motivated by specific applications where the goal is to find an approximate such representation for a given multiway array. The specifics of the approximate representation (such as how many terms to use in the sum, orthogonality constraints, etc.) depend on the application.In this paper, we explore an alternate representation of tensors which shows promise with respect to the tensor approximation problem. Reminiscent of matrix factorizations, we present a new factorization of a tensor as a product of tensors. To derive the new factorization, we define a closed multiplication operation between tensors. A major motivation for considering this new type of tensor multiplication is to devise new types of factorizations for tensors which can then be used in applications.Specifically, this new multiplication allows us to introduce concepts such as tensor transpose, inverse, and identity, which lead to the notion of an orthogonal tensor. The multiplication also gives rise to a linear operator, and the null space of the resulting operator is identified. We extend the concept of outer products of vectors to outer products of matrices. All derivations are presented for third-order tensors. However, they can be easily extended to the order-p(p>3) case. We conclude with an application in image deblurring.     

Semi-cooperative strategies for differential games

The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative semi-cooperative pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.Revised: May 2004     

Optimal strategies for the uninformed player

This paper provides a counterpart of the well-known recursive formula for finitely repeated zero-sum games with lack of information on one side from the point of view of the uninformed player. Applying the results to a specific game that has already been discussed by Mertens and Zamir, for the first time a nontrivial sequence of values and optimal strategies is explicitly computed. This allows to recover their startling result on the appearance of the normal law in such models by entirely different arguments.     

Randomized strategies for the plurality problem

We consider a game played by two players, Paul and Carol. At the beginning of the game, Carol fixes a coloring of n balls. At each turn, Paul chooses a pair of the balls and asks Carol whether the balls have the same color. Carol truthfully answers his question. Paul’s goal is to determine the most frequent (plurality) color in the coloring by asking as few questions as possible. The game is studied in the probabilistic setting when Paul is allowed to choose his next question randomly.We give asymptotically tight bounds both for the case of two colors and many colors. For the balls colored by k colors, we prove a lower bound Ω(kn) on the expected number of questions; this is asymptotically optimal. For the balls colored by two colors, we provide a strategy for Paul to determine the plurality color with the expected number of questions; this almost matches the lower bound .     

Reordering strategies for a newsboy-type product

This paper considers the very common situation in which a single-period ‘newsboy’ type product may be ordered or produced twice during a season/period. We show that the explicit consideration of this reorder opportunity makes the newsboy problem very much richer. The specific version considered in this paper allows a reorder during mid-season after the early-season demand has been observed, and this reorder arrives after a given lead time. The demand distributions during the various portions of the season may have very general distribution forms; also, the late-season and early-season demands may be dependent. Solution procedures are developed to find the best way to exploit this reorder opportunity, and our numerical solutions indicate that this reorder opportunity can improve profits considerably as long as the product's profit margin is not very high. Other real-world variations of this two-order newsboy problem are briefly discussed.     

Priority dispatching strategies for EMS systems

Emergency medical service (EMS) systems provide urgent medical care and transport. In this study we implement dispatching policies for EMS systems that incorporate the severity of the call in order to increase the survival probability of patients. A simulation model is developed to evaluate the performance of EMS systems. Performance is measured in terms of patients’ survival probability, since survival probability more directly mirrors patient outcomes. Different response strategies are evaluated utilizing several examples to study the nature of the optimal dispatching policy. The results show that dispatching the closest vehicle is not always optimal and dispatching vehicles considering priority of the call leads to an increase in the average survival probability of patients. A heuristic algorithm, that is easy to implement, is developed to dispatch ambulances for large-scale EMS systems. Computational examples show that the dispatching algorithm is valuable in increasing the patients’ survival probability.     

Repair-replace strategies for two-dimensional warranty policies

For repairable items sold with free replacement warranty, the actions available to the manufacturer to rectify failures under warranty are to

1. (1) repair the failed item or

2. (2) replace it with a new one.

A proper repair-replace strategy can reduce the expected cost of servicing the warranty. In this paper, we study repair-replace strategies for items sold with a two-dimensional free replacement warranty.     

Optimal strategies for equal-sum dice games

In this paper, we consider a non-cooperative two-person zero-sum matrix game, called dice game. In an (n,σ) dice game, two players can independently choose a dice from a collection of hypothetical dice having n faces and with a total of σ eyes distributed over these faces. They independently roll their dice and the player showing the highest number of eyes wins (in case of a tie, none of the players wins). The problem at hand in this paper is the characterization of all optimal strategies for these games. More precisely, we determine the (n,σ) dice games for which optimal strategies exist and derive for these games the number of optimal strategies as well as their explicit form.     

Neuroevolution strategies for episodic reinforcement learning

Because of their convincing performance, there is a growing interest in using evolutionary algorithms for reinforcement learning. We propose learning of neural network policies by the covariance matrix adaptation evolution strategy (CMA-ES), a randomized variable-metric search algorithm for continuous optimization. We argue that this approach, which we refer to as CMA Neuroevolution Strategy (CMA-NeuroES), is ideally suited for reinforcement learning, in particular because it is based on ranking policies (and therefore robust against noise), efficiently detects correlations between parameters, and infers a search direction from scalar reinforcement signals. We evaluate the CMA-NeuroES on five different (Markovian and non-Markovian) variants of the common pole balancing problem. The results are compared to those described in a recent study covering several RL algorithms, and the CMA-NeuroES shows the overall best performance.     

Robust strategies for natural gas procurement

In order to serve their customers, natural gas local distribution companies (LDCs) can select from a variety of financial and non-financial contracts. The present paper is concerned with the choice of an appropriate portfolio of natural gas purchases that would allow a LDC to satisfy its demand with a minimum tradeoff between cost and risk, while taking into account risk associated with modeling error. We propose two types of strategies for natural gas procurement. Dynamic strategies model the procurement problem as a mean-risk stochastic program with various risk measures. Naive strategies hedge a fixed fraction of winter demand. The hedge is allocated equally between storage, futures and options. We propose a simulation framework to evaluate the proposed strategies and show that: (i) when the appropriate model for spot prices and its derivatives is used, dynamic strategies provide cheaper gas with low risk compared to naive strategies. (ii) In the presence of a modeling error, dynamic strategies are unable to control the variance of the procurement cost though they provide cheaper cost on average. Based on these results, we define robust strategies as convex combinations of dynamic and naive strategies. The weight of each strategy represents the fraction of demand to be satisfied following this strategy. A mean–variance problem is then solved to obtain optimal weights and construct an efficient frontier of robust strategies that take advantage of the diversification effect.