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.

Implementation study of a clinical prediction score to rule out cardiogenic chest pain in community: Cluster randomized trial

1.1 Fundamentals Chest pain is a common complaint in primary care patients (1 to 3% of all consultations) (1) and its aetiology can be miscellaneous, from harmless to potentially life threatening conditions. In primary care practice, the most prevalent aetiologies are: chest wall syndrome (43%), coronary heart disease (12%) and anxiety (7%) (2). In up to 20% of cases, potentially serious conditions as cardiac, respiratory or neoplasic diseases underlie chest pain. In this context, a large number of laboratory tests are run (42%) and over 16% of patients are referred to a specialist or hospitalized (2).¦A cardiovascular origin to chest pain can threaten patient's life and investigations run to exclude a serious condition can be expensive and involve a large number of exams or referral to specialist -­‐ often without real clinical need. In emergency settings, up to 80% of chest pains in patients are due to cardiovascular events (3) and scoring methods have been developed to identify conditions such as coronary heart disease (HD) quickly and efficiently (4-­‐6). In primary care, a cardiovascular origin is present in only about 12% of patients with chest pain (2) and general practitioners (GPs) need to exclude as safely as possible a potential serious condition underlying chest pain. A simple clinical prediction rule (CPR) like those available in emergency settings may therefore help GPs and spare time and extra investigations in ruling out CHD in primary care patients. Such a tool may also help GPs reassure patients with more common origin to chest pain.

Caution, children crossing: Heterogeneity of victim's cost of care and negligence rule

The paper deals with a bilateral accident situation in which victims haveheterogeneous costs of care. With perfect information,efficient care bythe injurer raises with the victim's cost. When the injurer cannot observeat all the victim's type, and this fact can be verified by Courts, first-bestcannot be implemented with the use of a negligence rule based on thefirst-best levels of care. Second-best leads the injurer to intermediate care,and the two types of victims to choose the best response to it. This second-bestsolution can be easily implemented by a negligence rule with second-best as duecare. We explore imperfect observation of the victim's type, characterizing theoptimal solution and examining the different legal alternatives when Courts cannotverify the injurers' statements. Counterintuitively, we show that there is nodifference at all between the use by Courts of a rule of complete trust and arule of complete distrust towards the injurers' statements. We then relate thefindings of the model to existing rules and doctrines in Common Law and Civil Lawlegal systems.

Consumer Advisory Bulletin, Price-Gouging Rule in Effect in Storm- and Flood-damaged Counties, August 2007

The Attorney General’s Consumer Protection Division receives hundreds of calls and consumer complaints every year. Follow these tips to avoid unexpected expense and disappointments. This record is about: Price-Gouging Rule in Effect in Storm- and Flood-damaged Counties

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Sources and propagation of international cycles: Common shocks or transmission?

This paper studies the generation and transmission of international cycles in a multi-country model with production and consumption interdependencies. Two sources of disturbance are considered and three channels of propagation are compared. In the short run the contemporaneous correlation of disturbances determines the main features of the transmission. In the medium run production interdependencies account for the transmission of technology shocks and consumption interdependencies account for the transmission of government shocks. Technology disturbances, which are mildly correlated across countries, are more successful than government expenditure disturbances in reproducing actual data. The model also accounts for the low cross country consumption correlations observed in the data.

Optimal negligence rule under limited liability

We study the standard economic model of unilateral accidents, in its simplest form, assumingthat the injurers have limited assets.We identify a second-best optimal rule that selects as duecare the minimum of first-best care, and a level of care that takes into account the wealth ofthe injurer. We show that such a rule in fact maximizes the precautionary effort by a potentialinjurer. The idea is counterintuitive: Being softer on an injurer, in terms of the required level ofcare, actually improves the incentives to take care when he is potentially insolvent. We extendthe basic result to an entire population of potentially insolvent injurers, and find that the optimalgeneral standards of care do depend on wealth, and distribution of income. We also show theconditions for the result that higher income levels in a given society call for higher levels of carefor accidents.

Promoting rule compliance in daily-life: Evidence from a randomized field experiment in the public libraries of Barcelona

We study how to promote compliance with rules in everyday situations. Having access to unique data on the universe of users of all public libraries inBarcelona, we test the effect of sending email messages with dierent contents.We find that users return their items earlier if asked to do so in a simple email.Emails reminding users of the penalties associated with late returns are more effective than emails with only a generic reminder. We find differential treatmenteffects by user types. The characteristics we analyze are previous compliance,gender, age, and nationality.

A simple access pricing rule to achieve the Ramsey outcome for interconnected networks

This paper considers a general and informationally efficient approach to determine the optimal access pricing rule for interconnected networks. It shows that there exists a simple rule that achieves the Ramsey outcome as the unique equilibrium when networks compete in linear prices without network-based price discrimination. The approach is informationally efficient in the sense that the regulator is required to know only the marginal cost structure, i.e. the marginal cost of making and terminating a call. The approach is general in that access prices can depend not only on the marginal costs but also on the retail prices, which can be observed by consumers and therefore by the regulator as well. In particular, I consider the set of linear access pricing rules which includes any fixed access price, the Efficient Component Pricing Rule (ECPR) and the Modified ECPR as special cases. I show that in this set, there is a unique rule that implements the Ramsey outcome as the unique equilibrium independently of the underlying demand conditions.

Development and validation of a clinical decision rule for the diagnosis of influenza.

INTRODUCTION: A clinical decision rule to improve the accuracy of a diagnosis of influenza could help clinicians avoid unnecessary use of diagnostic tests and treatments. Our objective was to develop and validate a simple clinical decision rule for diagnosis of influenza. METHODS: We combined data from 2 studies of influenza diagnosis in adult outpatients with suspected influenza: one set in California and one in Switzerland. Patients in both studies underwent a structured history and physical examination and had a reference standard test for influenza (polymerase chain reaction or culture). We randomly divided the dataset into derivation and validation groups and then evaluated simple heuristics and decision rules from previous studies and 3 rules based on our own multivariate analysis. Cutpoints for stratification of risk groups in each model were determined using the derivation group before evaluating them in the validation group. For each decision rule, the positive predictive value and likelihood ratio for influenza in low-, moderate-, and high-risk groups, and the percentage of patients allocated to each risk group, were reported. RESULTS: The simple heuristics (fever and cough; fever, cough, and acute onset) were helpful when positive but not when negative. The most useful and accurate clinical rule assigned 2 points for fever plus cough, 2 points for myalgias, and 1 point each for duration <48 hours and chills or sweats. The risk of influenza was 8% for 0 to 2 points, 30% for 3 points, and 59% for 4 to 6 points; the rule performed similarly in derivation and validation groups. Approximately two-thirds of patients fell into the low- or high-risk group and would not require further diagnostic testing. CONCLUSION: A simple, valid clinical rule can be used to guide point-of-care testing and empiric therapy for patients with suspected influenza.

The Effects of Headcut and Knickpoint Propagation on Bridges in Iowa, October 2008

Headcuts (known also as primary knickpoints) and knickpoints (known also as secondary knickpoints) have been found to contribute to the accelerated riverbed degradation problem in the midwestern United States. Step-changes that occur at the head of channel networks are referred to as headcuts, and those that occur within the confines of channel banks are referred to as knickpoints. The formation of headcuts and knickpoints and their upstream migration have been linked to the over-steepening of stream reaches when the flow plunges to the bed and creates a plunge pool. Secondary flow currents and seepage are believed to be some other parameters contributing to the formation and evolution of headcuts and knickpoints. Ongoing research suggests that headcuts and knickpoints, where they form and migrate, may account for 60% (or more) of the bed erosion in the streams. Based on preliminary observations, there is a strong indication that headcuts and knickpoints can also have a greater influence on flow thalweg alignment (line of deepest flow) for small rivers. A shift in thalweg toward a riverbank or embankment is usually a prime factor contributing to riverbank erosion and scour.

Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Statistical analysis and modelling of weather radar beam propagation conditions in the Po Valley (Italy)

Ground clutter caused by anomalous propagation (anaprop) can affect seriously radar rain rate estimates, particularly in fully automatic radar processing systems, and, if not filtered, can produce frequent false alarms. A statistical study of anomalous propagation detected from two operational C-band radars in the northern Italian region of Emilia Romagna is discussed, paying particular attention to its diurnal and seasonal variability. The analysis shows a high incidence of anaprop in summer, mainly in the morning and evening, due to the humid and hot summer climate of the Po Valley, particularly in the coastal zone. Thereafter, a comparison between different techniques and datasets to retrieve the vertical profile of the refractive index gradient in the boundary layer is also presented. In particular, their capability to detect anomalous propagation conditions is compared. Furthermore, beam path trajectories are simulated using a multilayer ray-tracing model and the influence of the propagation conditions on the beam trajectory and shape is examined. High resolution radiosounding data are identified as the best available dataset to reproduce accurately the local propagation conditions, while lower resolution standard TEMP data suffers from interpolation degradation and Numerical Weather Prediction model data (Lokal Model) are able to retrieve a tendency to superrefraction but not to detect ducting conditions. Observing the ray tracing of the centre, lower and upper limits of the radar antenna 3-dB half-power main beam lobe it is concluded that ducting layers produce a change in the measured volume and in the power distribution that can lead to an additional error in the reflectivity estimate and, subsequently, in the estimated rainfall rate.

Modelling of weather radar echoes from anomalous propagation using a hybrid parabolic equation method and NWP model data

Contamination of weather radar echoes by anomalous propagation (anaprop) mechanisms remains a serious issue in quality control of radar precipitation estimates. Although significant progress has been made identifying clutter due to anaprop there is no unique method that solves the question of data reliability without removing genuine data. The work described here relates to the development of a software application that uses a numerical weather prediction (NWP) model to obtain the temperature, humidity and pressure fields to calculate the three dimensional structure of the atmospheric refractive index structure, from which a physically based prediction of the incidence of clutter can be made. This technique can be used in conjunction with existing methods for clutter removal by modifying parameters of detectors or filters according to the physical evidence for anomalous propagation conditions. The parabolic equation method (PEM) is a well established technique for solving the equations for beam propagation in a non-uniformly stratified atmosphere, but although intrinsically very efficient, is not sufficiently fast to be practicable for near real-time modelling of clutter over the entire area observed by a typical weather radar. We demonstrate a fast hybrid PEM technique that is capable of providing acceptable results in conjunction with a high-resolution terrain elevation model, using a standard desktop personal computer. We discuss the performance of the method and approaches for the improvement of the model profiles in the lowest levels of the troposphere.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.