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.

Comparison of gadoteric acid and gadobutrol for detection as well as morphologic and dynamic characterization of lesions on breast dynamic contrast-enhanced magnetic resonance imaging

OBJECTIVE In contrast to conventional breast imaging techniques, one major diagnostic benefit of breast magnetic resonance imaging (MRI) is the simultaneous acquisition of morphologic and dynamic enhancement characteristics, which are based on angiogenesis and therefore provide insights into tumor pathophysiology. The aim of this investigation was to intraindividually compare 2 macrocyclic MRI contrast agents, with low risk for nephrogenic systemic fibrosis, in the morphologic and dynamic characterization of histologically verified mass breast lesions, analyzed by blinded human evaluation and a fully automatic computer-assisted diagnosis (CAD) technique. MATERIALS AND METHODS Institutional review board approval and patient informed consent were obtained. In this prospective, single-center study, 45 women with 51 histopathologically verified (41 malignant, 10 benign) mass lesions underwent 2 identical examinations at 1.5 T (mean time interval, 2.1 days) with 0.1-mmol kg doses of gadoteric acid and gadobutrol. All magnetic resonance images were visually evaluated by 2 experienced, blinded breast radiologists in consensus and by an automatic CAD system, whereas the morphologic and dynamic characterization as well as the final human classification of lesions were performed based on the categories of the Breast imaging reporting and data system MRI atlas. Lesions were also classified by defining their probability of malignancy (morpho-dynamic index; 0%-100%) by the CAD system. Imaging results were correlated with histopathology as gold standard. RESULTS The CAD system coded 49 of 51 lesions with gadoteric acid and gadobutrol (detection rate, 96.1%); initial signal increase was significantly higher for gadobutrol than for gadoteric acid for all and the malignant coded lesions (P < 0.05). Gadoteric acid resulted in more postinitial washout curves and fewer continuous increases of all and the malignant lesions compared with gadobutrol (CAD hot spot regions, P < 0.05). Morphologically, the margins of the malignancies were different between the 2 agents, whereas gadobutrol demonstrated more spiculated and fewer smooth margins (P < 0.05). Lesion classifications by the human observers and by the morpho-dynamic index compared with the histopathologic results did not significantly differ between gadoteric acid and gadobutrol. CONCLUSIONS Macrocyclic contrast media can be reliably used for breast dynamic contrast-enhanced MRI. However, gadoteric acid and gadobutrol differed in some dynamic and morphologic characterization of histologically verified breast lesions in an intraindividual, comparison. Besides the standardization of technical parameters and imaging evaluation of breast MRI, the standardization of the applied contrast medium seems to be important to receive best comparable MRI interpretation.

Stopping rules in Bayesian adaptive threshold estimation

Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

Versão brasileira do Dynamic Gait Index

O Dynamic Gait Index (DGI) é um teste que avalia o equilíbrio e marcha do corpo humano. OBJETIVOS: Os objetivos deste estudo foram adaptar culturalmente o DGI para o português e avaliar a sua confiabilidade. MATERIAL E MÉTODO: Seguiu-se o método de Guillemin et al. (1993) para a adaptação cultural do instrumento. Trata-se de estudo prospectivo em que 46 pacientes foram avaliados na fase de adaptação cultural e os itens que apresentaram 20% ou mais de incompreensão foram reformulados e reaplicados. A versão final do DGI em português foi aplicada em 35 idosos para examinar a confiabilidade intra e inter-observadores. O coeficiente de Spearman foi utilizado para correlacionar os escores inter e intra-observador e o teste de Wilcoxon para comparar as pontuações. A consistência interna foi analisada pelo coeficiente alfa de Cronbach. RESULTADOS: Houve correlações estatisticamente significantes entre os escores obtidos às avaliações inter e intra-observadores para todos os itens (p<0,001), classificadas como boa a muito forte (com de variação de r=0,655 a r=0,951). O DGI mostrou alta consistência interna entre seus itens nas avaliações inter e intra-observadores (variação de µ ou = 0,820 a a=0,894). CONCLUSÃO: O DGI foi adaptado culturalmente para o português brasileiro, mostrando-se um instrumento confiável.

Use of a dynamic foot pressure index to monitor the effects of treatment for equinus gait in children with cerebral palsy.

The purpose of this study is to introduce and describe a newly developed index using foot pressure analysis to quantify the degree of equinus gait in children with cerebral palsy before and after injection with botulinum toxin. Data were captured preinjection and 12 weeks postinjection. Ten children aged 2(1/2) to 6(1/2) years took part (5 boys and 5 girls). Three of them had a diagnosis of spastic diplegia and 7 of congenital hemiplegia. In total, 13 limbs were analyzed. After orientation and segmentation of raw pedobarographic data, we determined a dynamic foot pressure index graded 0 to 100 that quantified the relative degree of heel and forefoot contact during stance. These data were correlated (Pearson correlation) with clinical measurements of dorsiflexion at the ankle (on a slow and fast stretch) and video observation (using the Observational Gait Scale). Pedobarograph data were strongly correlated with both the Observational Gait Scale scores (R = 0.79, P < 0.005) and clinical measurements of dorsiflexion on a fast stretch, which is reflective of spasticity (R = 0.70, P < 0.005). We demonstrated the index's sensitivity in detecting changes in spasticity and good correlation with video observations seems to indicate this technique's potential validity. When manipulated and segmented appropriately, and with the development of a simple ordinal index, we found that foot pressure data provided a useful tool in tracking changes in patients with spastic equinus.

Self-rule Index for Local Authorities (Release 1.0)

Local autonomy is a highly valued feature of good governance. The continuous attempts of many European countries to strengthen the autonomy of local government show the importance given to decentralisation and far-reaching competences at the lowest units of a state. Measuring and comparing local autonomy, however, has proven to be a difficult task. Not only are there diverging ideas about the core elements of local autonomy, there are also considerable difficulties to apply specific concepts to different countries. This project suggests a comprehensive methodology to measure local autonomy. It analyses 39 European countries and reports changes between 1990 and 2014. A network of experts on local government assessed the autonomy of local government of their respective countries on the basis of a common code book. The eleven variables measured are located on seven imensions and can be combined to a "Local Autonomy Index" (LAI). The data show an increase of local autonomy between 1990 and 2005, especially in the new Central and Eastern European countries. Countries with a particularly high degree of local autonomy are Switzerland, the Nordic countries, Germany and Poland.

A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

Linear readout of dynamic phase modulation index in an optical voltage sensor using the new J(1) ... J(3) spectral method

The J(1)...J(3) is a recent optical method for linear readout of dynamic phase modulation index in homodyne interferometers. In this work, the J(1)... J(3) method is applied to measure voltage in an optical voltage sensor. Based on the classical J(1)...J(4) method, the J(1)... J(3) technique shows to be more stable to phase drift and simpler for implementation than the original one. The sensor dynamic range is enhanced. The agreement between theoretical and experimental results, based on 1/f noise, is demonstrated.

Spatial Disparity and Dynamic Trajectory of Convergence in China: Construction and Application of a Composite Index of Regional Development

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

Proposal of a dynamic performance index to analyze driving pattern effect on car emissions

The contributions of driver behaviour as well as surrounding infrastructure are decisive on pollutant emissions from vehicles in real traffic situations. This article deals with the preliminary study of the interaction between the dynamic variables recorded in a vehicle (driving pattern) and pollutant emissions produced over a given urban route. It has been established a “dynamic performance index”-DPI, which is calculated from some driving pattern parameters, which in turn depends on traffic congestion level and route characteristics, in order to determine whether the driving has been aggressive, normal or calm. Two passenger cars instrumented with a portable activity measurement system -to record dynamic variables- and on-board emission measurement equipment have been used. This study has shown that smooth driving patterns can reduce up to 80% NOX emissions and up to 20% of fuel in the same route

Assessment of expected damage on buildings subjected to Lorca earthquake through an energy-based seismic index method and nonlinear dynamic response analyses

The city of Lorca (Spain) was hit on May 11th, 2011, by two consecutive earth-quakes of magnitudes 4.6 and 5.2 Mw, causing casualties and important damage in buildings. Many of the damaged structures were reinforced concrete frames with wide beams. This study quantifies the expected level of damage on this structural type in the case of the Lorca earth-quake by means of a seismic index Iv that compares the energy input by the earthquake with the energy absorption/dissipation capacity of the structure. The prototype frames investigated represent structures designed in two time periods (1994–2002 and 2003–2008), in which the applicable codes were different. The influence of the masonry infill walls and the proneness of the frames to concentrate damage in a given story were further investigated through nonlinear dynamic response analyses. It is found that (1) the seismic index method predicts levels of damage that range from moderate/severe to complete collapse; this prediction is consistent with the observed damage; (2) the presence of masonry infill walls makes the structure very prone to damage concentration and reduces the overall seismic capacity of the building; and (3) a proper hierarchy of strength between beams and columns that guarantees the formation of a strong column-weak beam mechanism (as prescribed by seismic codes), as well as the adoption of counter-measures to avoid the negative interaction between non-structural infill walls and the main frame, would have reduced the level of damage from Iv=1 (collapse) to about Iv=0.5 (moderate/severe damage)

English parsing: comprising the rules of syntax, exemplified by appropriate lessons under each rule, with an index, containing all the parts of speech in the different lessons unparsed, for the use of schools, private teachers, and elder students.

Mode of access: Internet.