Efficient Computation of Probabilities of Events Described by Order Statistics and Applications to Queue Inference

This paper derives recursive algorithms for efficiently computing event probabilities related to order statistics and applies the results in a queue inferencing setting. Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. Both a forward and a backward recursive O(N3 ) algorithm are developed for computing the probability that the order statistics vector lies in a given N-rectangle. The new algorithms have applicability in inferring the statistical behavior of Poisson arrival queues, given only the start and stop times of service of all N customers served in a period of continuous congestion. The queue inference results extend the theory of the "Queue Inference Engine" (QIE), originally developed by Larson in 1990 [8]. The methodology is extended to a third O(N 3 ) algorithm, employing both forward and backward recursion, that computes the conditional probability that a random customer of the N served waited in queue less than r minutes, given the observed customer departure times and assuming first come, first served service. To our knowledge, this result is the first O(N3 ) exact algorithm for computing points on the in-queue waiting time distribution function,conditioned on the start and stop time data. The paper concludes with an extension to the computation of certain correlations of in-queue waiting times. Illustrative computational results are included throughout

Efficient Computation of Probabilities of Events Described by Order Statistics and Application to a Problem of Queues

Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. In this note an O(N3) algorithm is developed for computing the probability that the order statistics vector lies in a given rectangle. The new algorithm is then applied to a problem of statistical inference in queues. Illustrative computational results are included

The Semantics of the Plural Pronoun Construction

No abstract

Effect of eicosapentaenoic and docosahexaenoic acid on resting and exercise-induced inflammatory and oxidative stress biomarkers: a randomized, placebo controlled, cross-over study

<p>Abstract</p> <p>Background</p> <p>The purpose of the present investigation was to determine the effects of EPA/DHA supplementation on resting and exercise-induced inflammation and oxidative stress in exercise-trained men. Fourteen men supplemented with 2224 mg EPA+2208 mg DHA and a placebo for 6 weeks in a random order, double blind cross-over design (with an 8 week washout) prior to performing a 60 minute treadmill climb using a weighted pack. Blood was collected pre and post exercise and analyzed for a variety of oxidative stress and inflammatory biomarkers. Blood lactate, muscle soreness, and creatine kinase activity were also measured.</p> <p>Results</p> <p>Treatment with EPA/DHA resulted in a significant increase in blood levels of both EPA (18 ± 2 μmol·L^-1vs. 143 ± 23 μmol·L^-1; p < 0.0001) and DHA (67 ± 4 μmol·L^-1vs. 157 ± 13 μmol·L^-1; p < 0.0001), while no differences were noted for placebo. Resting levels of CRP and TNF-α were lower with EPA/DHA compared to placebo (p < 0.05). Resting oxidative stress markers were not different (p > 0.05). There was a mild increase in oxidative stress in response to exercise (XO and H₂O₂) (p < 0.05). No interaction effects were noted. However, a condition effect was noted for CRP and TNF-α, with lower values with the EPA/DHA condition.</p> <p>Conclusion</p> <p>EPA/DHA supplementation increases blood levels of these fatty acids and results in decreased resting levels of inflammatory biomarkers in exercise-trained men, but does not appear necessary for exercise-induced attenuation in either inflammation or oxidative stress. This may be due to the finding that trained men exhibit a minimal increase in both inflammation and oxidative stress in response to moderate duration (60 minute) aerobic exercise.</p

Laboratory Focus on Improving the Culture of Biosafety: Statewide Risk Assessment of Clinical Laboratories That Process Specimens for Microbiologic Analysis

The Wisconsin State Laboratory of Hygiene challenged Wisconsin laboratories to examine their biosafety practices and improve their culture of biosafety. One hundred three clinical and public health laboratories completed a questionnaire-based, microbiology-focused biosafety risk assessment. Greater than 96% of the respondents performed activities related to specimen processing, direct microscopic examination, and rapid nonmolecular testing, while approximately 60% performed culture interpretation. Although they are important to the assessment of risk, data specific to patient occupation, symptoms, and travel history were often unavailable to the laboratory and, therefore, less contributory to a microbiology-focused biosafety risk assessment than information on the specimen source and test requisition. Over 88% of the respondents complied with more than three-quarters of the mitigation control measures listed in the survey. Facility assessment revealed that subsets of laboratories that claim biosafety level 1, 2, or 3 status did not possess all of the biosafety elements considered minimally standard for their respective classifications. Many laboratories reported being able to quickly correct the minor deficiencies identified. Task assessment identified deficiencies that trended higher within the general (not microbiology-specific) laboratory for core activities, such as packaging and shipping, direct microscopic examination, and culture modalities solely involving screens for organism growth. For traditional microbiology departments, opportunities for improvement in the cultivation and management of highly infectious agents, such as acid-fast bacilli and systemic fungi, were revealed. These results derived from a survey of a large cohort of small- and large-scale laboratories suggest the necessity for continued microbiology-based understanding of biosafety practices, vigilance toward biosafety, and enforcement of biosafety practices throughout the laboratory setting

The Role of Column Density in the Formation of Stars and Black Holes

The stellar mass in disk galaxies scales approximately with the fourth power of the rotation velocity, and the masses of the central black holes in galactic nuclei scale approximately with the fourth power of the bulge velocity dispersion. It is shown here that these relations can be accounted for if, in a forming galaxy with an isothermal mass distribution, gas with a column density above about 8 Msun/pc^2 goes into stars while gas with a column density above about 2 g/cm^2 (10^4 Msun/pc^2) goes into a central black hole. The lower critical value is close to the column density of about 10 Msun/pc^2 at which atomic gas becomes molecular, and the upper value agrees approximately with the column density of about 1 g/cm^2 at which the gas becomes optically thick to its cooling radiation. These results are plausible because molecule formation is evidently necessary for star formation, and because the onset of a high optical depth in a galactic nucleus may suppress continuing star formation and favour the growth of a central black hole.Comment: Accepted by Nature Physic

Outliers from the Mass--Metallicity Relation II: A Sample of Massive Metal-Poor Galaxies from SDSS

We present a sample of 42 high-mass low-metallicity outliers from the mass--metallicity relation of star-forming galaxies. These galaxies have stellar masses that span log(M_*/M_sun) ~9.4 to 11.1 and are offset from the mass--metallicity relation by -0.3 to -0.85 dex in 12+log(O/H). In general, they are extremely blue, have high star formation rates for their masses, and are morphologically disturbed. Tidal interactions are expected to induce large-scale gas inflow to the galaxies' central regions, and we find that these galaxies' gas-phase oxygen abundances are consistent with large quantities of low-metallicity gas from large galactocentric radii diluting the central metal-rich gas. We conclude with implications for deducing gas-phase metallicities of individual galaxies based solely on their luminosities, specifically in the case of long gamma-ray burst host galaxies.Comment: Accepted for publication in ApJ; 11 pages, 11 figure

Angular Momentum and the Formation of Stars and Black Holes

The formation of compact objects like stars and black holes is strongly constrained by the requirement that nearly all of the initial angular momentum of the diffuse material from which they form must be removed or redistributed during the formation process. The mechanisms that may be involved and their implications are discussed for (1) low-mass stars, most of which probably form in binary or multiple systems; (2) massive stars, which typically form in clusters; and (3) supermassive black holes that form in galactic nuclei. It is suggested that in all cases, gravitational interactions with other stars or mass concentrations in a forming system play an important role in redistributing angular momentum and thereby enabling the formation of a compact object. If this is true, the formation of stars and black holes must be a more complex, dynamic, and chaotic process than in standard models. The gravitational interactions that redistribute angular momentum tend to couple the mass of a forming object to the mass of the system, and this may have important implications for mass ratios in binaries, the upper stellar IMF in clusters, and the masses of supermassive black holes in galaxies.Comment: Accepted by Reports on Progress in Physic