Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

Density and distribution of nests of Mycetophylax simplex (Emery) (Hymenoptera, Formicidae) in areas with mobile dunes on the northern coast of Rio Grande do Sul, Brazil

Studies on lower attines are scarce, especially on nesting and foraging ecology and behavior. This study aimed to contribute to the knowledge of an Attini in dunes ecosystems through the description of density and spatial distribution of Mycetophylax simplex (Emery, 1887) nests in a strip of mobile dunes in the Praia Grande beach, Torres, northern coast of Rio Grande do Sul, Brazil. The density and spatial distribution of nests were estimated in four plots of 2,500 m² each, in which were found 20, 209, 284 and 324 nests, with average densities of 0.01 nests/m², 0.09, 0.11 and 0.13 nests/m², respectively. The nests were found near to the vegetation and showed clumped distribution. The density and distribution pattern of the nests seem to be related to the availability of nesting places and foraging resources.

Trabecular bone score is associated with volumetric bone density and microarchitecture as assessed by central QCT and HRpQCT in Chinese American and white women.

Although high-resolution peripheral quantitative computed tomography (HRpQCT) and central quantitative computed tomography (QCT) studies have shown bone structural differences between Chinese American (CH) and white (WH) women, these techniques are not readily available in the clinical setting. The trabecular bone score (TBS) estimates trabecular microarchitecture from dual-energy X-ray absorptiometry spine images. We assessed TBS in CH and WH women and investigated whether TBS is associated with QCT and HRpQCT indices. Areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry, lumbar spine (LS) TBS, QCT of the LS and hip, and HRpQCT of the radius and tibia were performed in 71 pre- (37 WH and 34 CH) and 44 postmenopausal (21 WH and 23 CH) women. TBS did not differ by race in either pre- or postmenopausal women. In the entire cohort, TBS positively correlated with LS trabecular volumetric bone mineral density (vBMD) (r = 0.664), femoral neck integral (r = 0.651), trabecular (r = 0.641) and cortical vBMD (r = 0.346), and cortical thickness (C/I; r = 0.540) by QCT (p < 0.001 for all). TBS also correlated with integral (r = 0.643), trabecular (r = 0.574) and cortical vBMD (r = 0.491), and C/I (r = 0.541) at the total hip (p < 0.001 for all). The combination of TBS and LS aBMD predicted more of the variance in QCT measures than aBMD alone. TBS was associated with all HRpQCT indices (r = 0.20-0.52) except radial cortical thickness and tibial trabecular thickness. Significant associations between TBS and measures of HRpQCT and QCT in WH and CH pre- and postmenopausal women demonstrated here suggest that TBS may be a useful adjunct to aBMD for assessing bone quality.

Malliavin calculus in finance

This article is an introduction to Malliavin Calculus for practitioners.We treat one specific application to the calculation of greeks in Finance.We consider also the kernel density method to compute greeks and anextension of the Vega index called the local vega index.

Testing for convergence clubs in income per-capita: A predictive density approach

The paper proposes a technique to jointly test for groupings of unknown size in the cross sectional dimension of a panel and estimates the parameters of each group, and applies it to identifying convergence clubs in income per-capita. The approach uses the predictive density of the data, conditional on the parameters of the model. The steady state distribution of European regional data clusters around four poles of attraction with different economic features. The distribution of incomeper-capita of OECD countries has two poles of attraction and each grouphas clearly identifiable economic characteristics.

Dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus (Diptera, Culicidae) by Bacillus thuringiensis var israelensis, related with temperature, density and concentration of insecticide

The dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus, (Diptera, Culicidae) by Bacillus thuringiensis var israelensis has been related with the temperature, density and concentration of the insecticide. A mathematical model for biological control of Aedes aegypti with Bacillus thuringiensis var israelensis (Bti) was constructed by using data from the literature regarding the biology of the vector. The life cycle was described by differential equations. Lethal concentrations (LC50 and LC95) of Bti were determined in the laboratory under different experimental conditions. Temperature, colony, larvae density and bioinsecticide concentration presented marked differences in the analysis of the whole set of variables; although when analyzed individually, only the temperature and concentration showed changes. The simulations indicated an inverse relationship between temperature and mosquito population, nonetheless, faster growth of populations is reached at higher temperatures. As conclusion, the model suggests the use of integrated control strategies for immature and adult mosquitoes in order to achieve a reduction of Aedes aegypti.

Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped.

Combining multivariate density forecasts using predictive criteria

This paper combines multivariate density forecasts of output growth, inflationand interest rates from a suite of models. An out-of-sample weighting scheme based onthe predictive likelihood as proposed by Eklund and Karlsson (2005) and Andersson andKarlsson (2007) is used to combine the models. Three classes of models are considered: aBayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR)and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australiandata, we find that, at short forecast horizons, the Bayesian VAR model is assignedthe most weight, while at intermediate and longer horizons the factor model is preferred.The DSGE model is assigned little weight at all horizons, a result that can be attributedto the DSGE model producing density forecasts that are very wide when compared withthe actual distribution of observations. While a density forecast evaluation exercise revealslittle formal evidence that the optimally combined densities are superior to those from thebest-performing individual model, or a simple equal-weighting scheme, this may be a resultof the short sample available.

Association of different lipid measures for atherogenic lipid fractions and risk of coronary events in patients receiving combination antiretroviral therapy: the Swiss HIV Cohort Study

Background: Evidence for a better performance of different highly atherogenic versus traditional lipid parameters for coronary heart disease (CHD) risk prediction is conflicting. We investigated the association of the ratios of sma11 dense low density lipoprotein(LDL)/apoplipoprotein A, aolipoprotein B/apolipoprotein A-I and total cholesterol! HDL-cholesterol and CHD events in patients on combination antiretroviral therapy (cART).Methods: Case control study nested into the Swiss HIV Cohort Study: for each cART-treated patient with a first coronary event between April 1, 2000 and July 31, 2008 (case) we selected four control patients (1) that were without coronary events until the date of the event of the index case, (2) had a plasma sample within ±30 days of the sample date of the respective case, (3) received cART and (4) were then matched for age, gender and smoking status. Lipoproteins were measured by ultracentrifugation. Conditional logistic regression models were used to estimate the independent effects of different lipid ratios and the occurrence of coronary events.Results: In total, 98 cases (19 fatal myocardial infarctions [MI] and 79 non-fatal coronary events [53 definite MIs, 15 possible MIs and 11 coronary angioplasties or bypassesJ) were matched with 392 controls. Cases were more often injecting drug users, less likely to be virologically suppressed and more often on abacavir-containing regimens. In separa te multivariable models of total cholesterol, triglycerides, HDL-cholesterol, systolic blood pressure, abdominal obesity, diabetes and family history of CHD, small dense-LDL and apolipoprotein B were each statistically significantly associated with CHD events (for 1 mg/dl increase: odds ratio [OR] 1.05, 95% CI 1.00-1.11 and 1.15, 95% CI 1.01-1.31, respectively), but the ratiosof small dense-LDLlapolipoprotein A-I (OR 1.26, 95% CI 0.95-1.67), apolipoprotein B/apolipoprotein A-I (OR 1.02, 95% CI 0.97-1.07) and HDL-cholesterol! total cholesterol (OR 0.99 95% CI 0.98-1.00) were not. Following adjustment for HIV related and cART variables these associations were weakened in each model: apolipoprotein B (OR 1.27, 95% CI 1.00-1.30), sd-LDL (OR 1.04, 95% CI 0.99-1.20), small dense-LDLlapolipoprotein A-I (OR 1.17, 95% CI 0.87-1.58), apolipoprotein B/apolipoprotein A-I (OR 1.02, 95% CI 0.97-1.07) and total cholesterolJHDL- cholesterol (OR 0.99, 95% CI 0.99-1.00).Conclusions: In patients receiving cART, small dense-LDL and apolipoprotein B showed the strongest associations with CHD events in models controlling for traditional CHD risk factors including total cholesterol and triglycerides. Adding small dense LDLlapoplipoprotein A-l, apolipoprotein B/apolipoprotein A-I and total cholesterol! HDL-cholesterol ratios did not further improve models of lipid parameters and associations of increased risk for CHD events.

A house price index defined in the potential outcomes framework

Current methods for constructing house price indices are based on comparisons of sale prices of residential properties sold two or more times and on regression of the sale prices on the attributes of the properties and of their locations. The two methods have well recognised deficiencies, selection bias and model assumptions, respectively. We introduce a new method based on propensity score matching. The average house prices for two periods are compared by selecting pairs of properties, one sold in each period, that are as similar on a set of available attributes (covariates) as is feasible to arrange. The uncertainty associated with such matching is addressed by multiple imputation, framing the problem as involving missing values. The method is applied to aregister of transactions ofresidential properties in New Zealand and compared with the established alternatives.

Measuring the stability of histogram appearance when the anchor position is changed

Although the histogram is the most widely used density estimator, itis well--known that the appearance of a constructed histogram for a given binwidth can change markedly for different choices of anchor position. In thispaper we construct a stability index $G$ that assesses the potential changesin the appearance of histograms for a given data set and bin width as theanchor position changes. If a particular bin width choice leads to an unstableappearance, the arbitrary choice of any one anchor position is dangerous, anda different bin width should be considered. The index is based on the statisticalroughness of the histogram estimate. We show via Monte Carlo simulation thatdensities with more structure are more likely to lead to histograms withunstable appearance. In addition, ignoring the precision to which the datavalues are provided when choosing the bin width leads to instability. We provideseveral real data examples to illustrate the properties of $G$. Applicationsto other binned density estimators are also discussed.

Iowa Leading Indicators Index Report, July 2006

The Iowa Leading Indicators Index (ILII) is a tool for monitoring the future direction of the Iowa economy and State revenues. Its eight components include an agricultural futures price index, an Iowa stock market index, average weekly manufacturing hours in Iowa, initial unemployment claims in Iowa, an Iowa new orders index, diesel fuel consumption in Iowa, residential building permits in Iowa, and the national yield spread.