Sums Of Rates Research Articles

Probabilistic Combinatorial Model of the Epidemic for a University

The aim of the research was to identify the main causes of infection of teachers and students in a university. Two probabilistic combinatorial problems are considered analytically to determine the probabilities and rates of infection of teachers and students in a university as a result of the appearance of infected persons among the contingent of students. The mathematical apparatus of probability theory and combinatorics is used to solve the problems. For the factorials of combinations arising in the structure, the asymptotic Stirling’s formula is used. Convergent series arise in the final formulas, reflecting the multiplicity of scenarios of the probabilistic approach. Analytical formulas for the sums of series, probabilities and rates of infection of teachers and students are obtained. It is shown that the infection of teachers and students occurs through «dangerous» spatially close contacts, when a teacher and a student talk at a distance of less than 0.5 meter. It is impossible to exclude such contacts in the students’ environment during full-time study. Among teachers, there is also a less probable classroom mechanism of infection through the volume of air infected with viruses.

Variations of significant contribution regions of NOx and PN emissions for passenger cars in the real-world driving

Nitrogen oxides (NOx) and particulate number (PN) emissions are the main concerns of the passenger cars in the real-world driving. NOx and PN emissions are greatly dependent on the driving behaviors which differ significantly between standard driving cycles and real-world driving. However, the significant contribution regions (short durations corresponding to high proportions of total emissions) of NOx and PN emissions regarding different driving behaviors (e.g. vehicle speed and acceleration) are still uncovered. NOx20% and NOx50% refer to instantaneous NOx emission rates when NOx emission rates are ranked from high to low level where the sums of NOx emission rates being higher than NOx20% and NOx50% correspond to 20% and 50% of total NOx emissions, respectively. t20% and t50% are corresponding durations where NOx emission rates are higher than NOx20% and NOx50%. In this paper, three Euro-6 compliant direct injection gasoline passenger cars and a diesel passenger car are tested in a real-world driving trial in which nineteen drivers are involved. Novel key performance indicators with reference to the regimes of specific NOx and PN contributions to total emissions are defined. Instantaneous NOx and PN emissions are monitored using a portable emission measurement system (PEMS) in the test. The results indicate that the maximum and minimum average speed over the four cars being approximately 32.3 km/h s and 42.6 km/h, respectively. Average PN emission factor of the diesel car is the lowest among the four given cars. Average t20% and t50% corresponding to NOx20% and NOx50% are lower than 3% and 12%, respectively, for all the passenger cars; additionally, these two parameters show the same pattern. The corresponding t20% and t50% variations of the Euro-6a gasoline car and the diesel car are much lower than the other two. Average acceleration corresponding to 20% and 50% of total NOx emissions for the given diesel car is approximately 1.25 m/s2 and 0.6 m/s2, respectively, being much higher than that of the other three gasoline cars (lower than 1 m/s2 and 0.4 m/s2 respectively) over the specific driving route and drivers. The average PN20% and PN50% of the given diesel car are approximately 7 × 107#/s and 3 × 107#/s respectively, being much lower than the three given gasoline cars (higher than 8 ×109#/s and 2 ×109#/s respectively) under the given test conditions; the corresponding t20% and t50% are lower than 4% and 17% respectively for all the three gasoline cars.

Abstract 1190: Comparison of cumulative incidence rates of colorectal cancer among Asians and Pacific Islanders (API) populations in Guam, Hawai'i, and the United States

Abstract Background: Colorectal cancer is one of 4 most common cancers on Guam, Hawai'i (HI) and the US. However, incidence rates vary between ethnic groups and location. Objective: The objective of the study was to compare cumulative incidence rates (CIRs) among ethnic groups in Guam, HI, and the US; specifically, Chamorros in Guam, Filipinos in Guam, HI and the US, and Native Hawaiians in HI and the US. CIRs are weighted sums of age-specific incidence rates therefore they can be used for comparisons between populations. They are relatively stable and thus provide a good estimate of cumulative risk of cancer. Methods: This study included all colorectal cancer cases (n=562) reported to the Guam Cancer Registry and all colorectal cancer cases (n=253,782) reported to the Surveillance, Epidemiology, and End Results (SEER) 9-Registry from 2000 to 2014. Cumulative incidence rates were calculated for three time periods: 2000-2004, 2005-2009, and 2010-2014 and compared by age, ethnicity and location. Results: Differences were seen in CIRs by time-period, age, ethnicity, and location. For all three time periods: 2000-2004, 2005-2009, 2010-2014, the lifetime cumulative incidence rates (age 0-79) were highest for Hawai'i (5.7%, 5.4%, and 5.3% respectively), followed by the US (5.2%, 4.5%, and 3.7%) and Guam (4.3%, 3.3%, and 3.6%). Interestingly, there were large differences in lifetime CIRs between Filipinos in HI, Filipinos in the US and Filipinos on Guam (i.e. 6.5%, 3.7%, and 2.4% respectively in 2005-2009). The Chamorros on Guam had the rate at least 1.5 times higher than Filipinos on Guam (4.3 % vs 3.3%) and close to the rate of Native Hawaiians in HI (4.9%). Overall, there was downward trend for the lifetime CIRs over time. Only for the Filipinos in HI, the rates went up. However, early onset CIRs (age 0-49) went up across all locations and ethnic groups. Conclusions: Disparities in colorectal cancer incidence were identified. Further study is needed to examine how exposure to risk factors and screening changes with immigration and how this variation contributes to the incidence disparities. Citation Format: Grazyna Badowski. Comparison of cumulative incidence rates of colorectal cancer among Asians and Pacific Islanders (API) populations in Guam, Hawai'i, and the United States [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 1190.

Sum rules in multiphoton coincidence rates

We show that sums of carefully chosen coincidence rates in a multiphoton interferometry experiment can be simplified by replacing the original unitary scattering matrix with a coset matrix containing 0s. The number and placement of these 0s reduces the complexity of each term in the sum without affecting the original sum of rates. In particular, the evaluation of sums of modulus squared of permanents is shown to turn in some cases into a sum of modulus squared of determinants. The sums of rates are shown to be equivalent to the removal of some optical elements in the interferometer.

Usefulness of continuous probability distributions of rates for modelling radionuclide biokinetics in humans and animals

Modelling the biokinetics of radionuclide excretion or retention is important in nuclear medicine and following accidental/malicious radioactivity releases. Sums of discrete exponential decay rates are often used, but we hypothesized that continuous probability distributions (CPD) of decay rates can describe the data more parsimoniously and robustly. We tested this hypothesis on diverse human and animal data sets involving various radionuclides (including plutonium, strontium, caesium) measured in the laboratory and in regions contaminated by the Fukushima and Chernobyl nuclear accidents. We used four models on each data set: mono-exponential (ME) with one discrete decay rate, bi-exponential (BE) with two rates, gamma-exponential (GE) with a Gamma distribution of stretched-exponential rates, and power-decay (PD) with a Gamma distribution of power-decay rates. Information-theoretic model selection suggested that radionuclide biokinetics, e.g. for plutonium in humans, are often better described by CPD models like GE and PD, than by discrete rates (ME and BE). Extrapolation of models fitted to data at short times to longer times was frequently more robust for CPD formalisms. We suggest that using a set of several CPD and discrete-rate models, and comparing them by information-theoretic methods, is a promising strategy to enhance the analysis of radionuclide excretion and retention kinetics.

Prediction of drug-induced liver injury using keratinocytes.

Drug-induced liver injury (DILI) is one of the most common adverse drug reactions. DILI is often accompanied by skin reactions, including rash and pruritus. However, it is still unknown whether DILI-associated genes such as S100 calcium-binding protein A and interleukin (IL)-1β are involved in drug-induced skin toxicity. In the present study, most of the tested hepatotoxic drugs such as pioglitazone and diclofenac induced DILI-associated genes in human and mouse keratinocytes. Keratinocytes of mice at higher risk for DILI exhibited an increased IL-1β basal expression. They also showed a higher inducibility of IL-1β when treated by pioglitazone. Mice at higher risk for DILI showed even higher sums of DILI-associated gene basal expression levels and induction rates in keratinocytes. Our data suggest that DILI-associated genes might be involved in the onset and progression of drug-induced skin toxicity. Furthermore, we might be able to identify individuals at higher risk of developing DILI less invasively by examining gene expression patterns in keratinocytes. Copyright © 2017 John Wiley & Sons, Ltd.

Formulating spread of species with habitat dependent growth and dispersal in heterogeneous landscapes

Habitat heterogeneity can have profound effects on the spreading dynamics of invasive species. Using integro-difference equations, we investigate the spreading dynamics in a one-dimensional heterogeneous landscape comprising alternating favourable and unfavourable habitat patches or randomly generated habitat patches with given spatial autocorrelation. We assume that population growth and dispersal (including emigration probability and dispersal distance) are dependent on habitat quality. We derived an approximation of the rate of spread in such heterogeneous landscapes, suggesting the sensitivity of spread to the periodic length of the alternating favourable and unfavourable patches, as well as their spatial autocorrelation. A dispersal-limited population tends to spread faster in landscapes with shorter periodic length. The spreading dynamics in a heterogeneous landscape was found to be not only dependent on the availability of favourable habitats, but also the dispersal strategy. Estimates of time lag before detection and the condition for boom-and-bust spreading dynamics were explained. Furthermore, rates of spread in heterogeneous landscapes and corresponding homogeneous landscapes were compared, using weighted sums of vital rates.

Simple Learned Weighted Sums of Inferior Temporal Neuronal Firing Rates Accurately Predict Human Core Object Recognition Performance.

To go beyond qualitative models of the biological substrate of object recognition, we ask: can a single ventral stream neuronal linking hypothesis quantitatively account for core object recognition performance over a broad range of tasks? We measured human performance in 64 object recognition tests using thousands of challenging images that explore shape similarity and identity preserving object variation. We then used multielectrode arrays to measure neuronal population responses to those same images in visual areas V4 and inferior temporal (IT) cortex of monkeys and simulated V1 population responses. We tested leading candidate linking hypotheses and control hypotheses, each postulating how ventral stream neuronal responses underlie object recognition behavior. Specifically, for each hypothesis, we computed the predicted performance on the 64 tests and compared it with the measured pattern of human performance. All tested hypotheses based on low- and mid-level visually evoked activity (pixels, V1, and V4) were very poor predictors of the human behavioral pattern. However, simple learned weighted sums of distributed average IT firing rates exactly predicted the behavioral pattern. More elaborate linking hypotheses relying on IT trial-by-trial correlational structure, finer IT temporal codes, or ones that strictly respect the known spatial substructures of IT ("face patches") did not improve predictive power. Although these results do not reject those more elaborate hypotheses, they suggest a simple, sufficient quantitative model: each object recognition task is learned from the spatially distributed mean firing rates (100 ms) of ∼60,000 IT neurons and is executed as a simple weighted sum of those firing rates. Significance statement: We sought to go beyond qualitative models of visual object recognition and determine whether a single neuronal linking hypothesis can quantitatively account for core object recognition behavior. To achieve this, we designed a database of images for evaluating object recognition performance. We used multielectrode arrays to characterize hundreds of neurons in the visual ventral stream of nonhuman primates and measured the object recognition performance of >100 human observers. Remarkably, we found that simple learned weighted sums of firing rates of neurons in monkey inferior temporal (IT) cortex accurately predicted human performance. Although previous work led us to expect that IT would outperform V4, we were surprised by the quantitative precision with which simple IT-based linking hypotheses accounted for human behavior.

New Approaches for Modeling Radiopharmaceutical Pharmacokinetics Using Continuous Distributions of Rates.

Radiopharmaceutical pharmacokinetics are usually approximated by sums of discrete first-order rates, using 3 or more parameters. We hypothesized that pharmacokinetic processes can be modeled even better by continuous probability distributions (CPD) of rates, using only 1-2 parameters. To test this hypothesis, we used biodistribution data for 188Re-labeled melanin-specific antibody in blood, kidneys, liver, bone marrow, and lungs of melanoma xenograft-bearing mice. We used 3 discrete-rate models (monoexponential, monoexponential with constant, and biexponential) and 4 CPD models (stretched-exponential, modified stretched-exponential, simplified versions of stretched-exponential, and modified stretched-exponential). They were compared by sample-size-corrected Akaike information criterion. Total time integrals of radioactivity were computed for each model and averaged across all models. The ratio of weights of evidence for CPD versus discrete-rate models was high for blood (12.2) and lungs (2.7), almost unity (0.99) for bone marrow, and slightly lower for kidneys (0.81) and liver (0.73). In all organs or tissues except lungs, model-averaged time integrals were 12.7%-54.0% higher than biexponential model estimates. Simple CPD models often outperform more complex discrete-rate models on pharmacokinetic data. Radioactivity time integrals are more robustly estimated by multimodel inference than using any single model.

Chlortetracycline degradation by photocatalytic ozonation in the aqueous phase: mineralization and the effects on biodegradability

Chlortetracycline (CTC) is a hazardous material in aquatic environments. This study was focused on optimization of photocatalytic ozonation processes for removal of CTC from wastewater at pH 2.2 and 7.0. In this study, the tested processes for CTC removal were arranged from the least efficient to the most efficient as: UV, UV/TiO2, O3, O3/UV and O3/UV/TiO2. Ozonation efficiency was due to ozone affinity for electron-rich sites on the CTC molecule. In the O3/UV and O3/UV/TiO2 processes, efficiency was increased by the photolysis of CTC and generation of •OH. At pH 7.0, all the processes were more efficient for CTC degradation than at pH 2.2 due to CTC speciation, ozone decay to •OH and the attractions between ionized CTC and TiO2 particles. UV/O3 at pH 7.0 showed an additive effect while other combination processes showed a synergistic effect that resulted in higher rates of reactions than the sums of individual reaction rates. The TOC removal ranged from 8% to 41% after one hour of reaction, with the above-mentioned order of efficiency. The biodegradability increased rapidly during the early minutes of the reaction. A reaction time of 10–15 min was sufficient for near maximum biodegradability, making these processes good pretreatments for the biological processes.

Estimating the germination dynamics of Plasmopara viticola oospores using hydro‐thermal time

The effects of environmental conditions on the variability in germination dynamics of Plasmopara viticola oospores were studied from 1999 to 2003. The germination course was determined indirectly as the relative infection incidence (RII) occurring on grape leaf discs kept in contact with oospores sampled from a vineyard between March and July. The time elapsed between 1 January and the infection occurrence was expressed as physiological time, using four methods: (i) sums of daily temperatures > 8°C; (ii) hourly temperatures > 10°C; (iii) sums of hourly rates from a temperature‐dependent function; or (iv) sums of these rates in hours with a rain or vapour pressure deficit ≤ 4·5 hPa (hydro‐thermal time, HT). An equation of Gompertz in the form RII = exp[−a · exp(−b · HT)] produced an accurate fit for both separate years (R2 = 0·97 to 0·99) and pooled data (R2 = 0·89), as well as a good accuracy in cross‐estimating new data (r between observed and cross‐estimated data were between 0·93 and 0·99, P < 0·0001). It also accounted for a great part of the variability in oospore germination between years and both between and within sampling periods. Therefore, the equation of Gompertz (with a = 15·9 ± 2·63 and b = 0·653 ± 0·034) calculated over hydro‐thermal time, a physiological time accounting for the effects of both temperature and moisture, produced a consistent modelling of the general relationships between the germination dynamics of a population of P. viticola oospores and weather conditions. It represents the relative density of the seasonal oospores that should have produced sporangia when they have experienced favourable conditions for germination.

Calculation of Stagnation-Point Heating Rates Associated with Stardust Vehicle

Stagnation-point heating rate is calculated for the Stardust entry vehicle and for its heat-shieldmodels tested in an arcjetwind tunnel. The calculations aremade for the convective component for both the laminar and turbulent cases, the radiative component produced by the gas flow, and the radiative component produced by solid particles. A onedimensional viscous shock layer method is used with an up-to-date thermochemical, gas–surface interaction, radiation, turbulence, and particulate models. For the flight cases, radiation absorption in the boundary layer is found to increase the convective heating rate by a factor of up to two. The calculated sums of all heating rates for the flight cases are nearly the same as those obtained by Olynick et al., and are substantially larger than those by Gupta. The calculated sums of all heating rates for the arcjet test cases are smaller than those calculated by the formula of Fay and Riddell, and are nearly the same as those experimentally determined using copper calorimeters.

Stability of Barbiturates in Fixed Tissues and Formalin Solutions

This study reports the results of the retention and quantitation of barbiturates in fresh tissue, in liver tissue fixed in formalin, and in the formalin solutions in which the same tissues were fixed for six months. Biological materials came from four cases of death due to phenobarbital and two due to butalbital. Results showed the presence of barbiturates in all studied materials. Mean recovery rates of phenobarbital in fixed liver were 57.11% and 30.84% in formalin from liver; and those of butalbital in fixed liver were 21.66% and 66.56% in formalin from liver. Total sums of recovery rates in formalin solutions and fixed tissues for phenobarbital (87.95%) and butalbital (88.22%) were comparable with those of the extraction efficiency of the method (90.2%) and indicate that these barbiturates have good stability even in biological specimens subjected to chemical fixation. This fact may be useful in qualitative evaluation of cases.

A frontier analysis approach for benchmarking hospital performance in the treatment of acute myocardial infarction.

This paper uses a non-parametric frontier model and adaptations of the concepts of cross-efficiency and peer-appraisal to develop a formal methodology for benchmarking provider performance in the treatment of Acute Myocardial Infarction (AMI). Parameters used in the benchmarking process are the rates of proper recognition of indications of six standard treatment processes for AMI; the decision making units (DMUs) to be compared are the Medicare eligible hospitals of a particular state; the analysis produces an ordinal ranking of individual hospital performance scores. The cross-efficiency/peer-appraisal calculation process is constructed to accommodate DMUs that experience no patients in some of the treatment categories. While continuing to rate highly the performances of DMUs which are efficient in the Pareto-optimal sense, our model produces individual DMU performance scores that correlate significantly with good overall performance, as determined by a comparison of the sums of the individual DMU recognition rates for the six standard treatment processes. The methodology is applied to data collected from 107 state Medicare hospitals.

Modeling of rates over a hierarchical health administrative structure

AbstractIdentifying the distribution of the incidence rate of a disease over a region is a prediction problem where area‐specific random effects are to be estimated. The authors consider the inclusion of such effects at different levels of a hierarchical health administrative structure. They develop inference procedures for this type of multi‐level model and show that the predicted rates are approximately weighted sums of the crude rates obtained by pooling data on each level of the hierarchy. Their techniques are illustrated using infant mortality data from British Columbia.

Méthode de Monte-Carlo par échanges pour le calcul des bilans radiatifs au sein d'une cavité 2D remplie de gaz

A formulation is presented based on the reciprocity principle in which radiative budgets are expressed as sums of Net Exchange Rates between all volume and surface elements. On this basis, a Monte-Carlo Method has been developed that proves to be numerically very efficient compared to standard Analogue Monte-Carlo Methods. It was used for computation of radiative budgets inside a two-dimensional cavity field with a participating gas. Strongly irregular grids and a wide range of optical thicknesses can be studied with this method.

Artificial surfactant for therapy in hydrocarbon-induced lung injury in sheep.

To document the effect of administering artificial surfactant into the trachea, either by instillation or aerosolization, on acute lung injury experimentally induced with kerosene in sheep. Randomized, prospective, controlled study. Research laboratory. Sheep (n = 24), weighing 8.5 to 25.2 kg (average 16.6). In anesthetized, tracheally intubated sheep with pulmonary and femoral artery catheters inserted, lung injury was induced by instilling kerosene (0.3 mL/kg) into the trachea. After 15 mins of spontaneous breathing, mechanical ventilation was instituted with a uniform F10(2) and a tidal volume of 10 mL/kg. Sheep were then assigned randomly to one of four regimens as follows: exogenous surfactant or saline (5 mL/kg each) was administered as a bolus intratracheally or by aerosolization for 6 hrs. Arterial and mixed venous blood gases, pH, airway pressure, and static respiratory system compliance were measured and compared between aerosol saline and aerosol surfactant and between bolus saline and bolus surfactant. For all variables except static respiratory system compliance, the hourly rate of change from 15 mins, 1 hr, and 6 hrs after kerosene instillation was determined for each animal, and group rank sums of hourly rates of change were compared. For static respiratory system compliance, the slope of the pressure-volume curve with volumes of 100, 200, 300, 400, and 500 mL was computed for each animal at baseline and at 3 and 6 hrs after kerosene instillation. Group rank sums for static respiratory system compliance at 3 and 6 hrs were compared. Also, the 3- and 6-hr static respiratory system compliance values at each of the volumes were compared. With saline, six of eight sheep died; with surfactant, no sheep died (p = .001). When compared with saline at 15 mins, 1 hr, and 6 hrs after kerosene instillation, surfactant, regardless of whether administered by aerosol or bolus, significantly increased rate of change of arterial oxygen saturation, mixed venous oxygen saturation, and PO2. In the present animal study, artificial surfactant was an effective treatment for hydrocarbon aspiration. Aerosolized surfactant achieved results similar to instilled surfactant but at a lower total dose.

Simulation of the effect of drought stress on the rate of photosynthesis in cotton

The purpose of this study was to use field experimental data to evaluate the quantitative effects of drought stress on the rate of photosynthesis of cotton plants. Measurements were made on plants growing at various distances from a single line source. Relationships between daily sums of photosynthetic rates and noon values of leaf water potential (LWP), and between LWP and a drought stress factor computed in the model have been evaluated. The derived equation for the effect of drought stress on the rate of photosynthesis was used in a modified model, and it significantly improved the simulation results. The modified model was tested with data from four treatments of a drip irrigation experiment, which represent extreme soil moisture conditions during two irrigation periods. The simulation results also agreed closely with the experimental data.

Optimum simple step-stress accelerated life-tests with competing causes of failure

Optimum simple step-stress accelerated life tests (ALTs) for products with competing causes of failure are presented. The life distribution of each failure cause, which is independent of the others, is assumed to be exponential with a mean that is a log-linear function of the stress, and a cumulative exposure model is assumed. Optimum plans for time-step and failure-step ALTs are obtained which minimize the sum over all failure causes of asymptotic variances of the maximum likelihood estimators of the log mean lives at design stress. The competing causes of failure affect the optimum test plan only through the product of two ratios-the ratio of the sums of the mean lives and the ratio of the sums of the failure rates over all failure causes at low and high stress levels. The effect of this product (of two ratios) is studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modelling Marital Fertility by Age and Duration: An Empirical Appraisal of the Page Model

Demographers studied data from 38 completed World Fertility Surveys by using the Page model of marital fertility by both age and duration of 1st marriage. Researchers measured goodness of fit of the Page model with generalized linear models (GLIM) and found a significant lack of fit at the 1% level in 11 countries and at the 5% level in 2 countries. All of these countries lie in Africa or Asia. On the other hand the Page model fits the data very well for Latin American and Caribbean countries. Haiti was found to have the worst fit. The model tends to overestimate fertility in the 1st year of marriage and to underestimate it the following year however. Researchers also judged its ability to replicate observed total marital fertility. When including all durations up to 36-37 years the fitted sums of marital fertility rates were close to observed rates (average absolute percentage error = 1.46% over 38 countries; maximum = 7.62% Nigeria). The highest natural fertility level was in Jordan at 12.6% < the maximum. The lowest level was in Haiti at 48.6% < the maximum. Additionally natural fertility increases by 1 percentage point for every additional month of breastfeeding and also by 1 point for every increase of 2% in use of contraception for spacing. Nepal had the lowest degree of control of marital fertility with an index of 1% which means that after 10 years of marriage the fertility of women is on 1% < the natural fertility which corresponds to their age at the time. Portugal had a value of 69.8. A clear monotonic relationship exists between the marital fertility index and contraceptive use (linear regression coefficient = .856). This index may be considered roughly equivalent to the contraceptive prevalence rate.