The shape of incomplete preferences

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.Comment: Published at http://dx.doi.org/10.1214/009053606000000740 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A behaviorally-based approach to measuring inequality

The measurement of inequality is often made using observed population-based distributions, such as the distribution of income or the distribution of members of different groups across neighborhoods. Unfortunately, such distributions confound the behavior of a given year with earlier events that influence the composition of the population. Here, we advocate measuring inequality using current behavioral measures and their compositional implications, and show how such measures may be obtained from frequently available data. The approach is then applied to trends in inequality between men and women in the distribution of ages at death. Observed death distributions indicate that, since 1970, mortality in 4 Western countries experienced increases in inequality that recently leveled off. In contrast, life table death distributions, which solely reflect the implications of a given year’s mortality rates, reveal a peak in inequality followed (in 3 of the 4 countries) by appreciable declines. The results are insensitive to whether inequality is measured by entropy, the Gini Index, or the Index of Dissimilarity. However, the type of distribution analyzed---whether observed or behaviorally derived---can make a significant difference in the results obtained. Because behaviorally derived distributions reflect the inequality implications of actual behavior, they are recommended for greater use in analyses of inequality.behaviorally-based, entropy, Gini Index, index of dissimilarity, inequality, measurement

ANALYSIS OF CONDUCTOR VIBRATION

Considerable attention has been given to conductor vibration of suspended transmission lines during the past 25 years. Even so, the engineers of the public utilities feel that they have only started to get a solution to the vibration problems. Extensive research programs are being conducted at the present time by manufacturers of conductor cable and ground wires and by numerous public utilities themselves. Aeolian vibrations are the chief concern because they occur whenever a steady wind, of from one mile per hour to hurricane velocity, blows across the suspended line. Thus, millions of flexures, however small or large in amplitude, may be produced in a relatively short period of time. Each flexure will contribute to fatigue, especially if its affects are concentrated at a suspension point. Stockbridge dampers and armor rods are two popular means of combating aeolian vibrations. Heretofore most analysists have considered these means of reducing conductor vibrations as being energy absorbers or dissipaters. By introducing the electrical analog it is easily shown that Stockbridge dampers, armor rods and similar dampers do not function as energy absorbers. They are mechanical impedance matching devices, which introduce reflected waves of the proper amplitude to cancel the unwanted waves. Dampers of the Stockbridge type are tuned mechanical impedance matching devices, and armor rods and festoons are untuned impedance matching devices. Proper design and installation of these dampers (impedance matching devices) can make them much more effective. Ten public utilities and manufacturers of cable recently reported vibration data and experiences. Each of the reports contributes considerable to the analysis of conductor vibration, although only two of them have been given publication as technical papers. The valuable data and experiences of these ten reports are reviewed and correlated in this paper, Analysis of Conductor Vibration. The limitations for stressing overhead high-strength shield or grounding cable should be lowered to 15% of ultimate strength at 600F. as compared with the present National Electrical Safety Code of 25% of ultimate at 60°F. Flexible suspension clamps should be used. The conductors of high voltage transmission lines should be sagged to carry a tension of not to exceed 20% of ultimate strength at 60°F. Stockbridge or similar dampers should best be installed at all supports. It has been found desirable in many cases to also install armor rods at each flexible suspension support and dead end. It is known that armor rods effectively suppress vibration and give added protection. However, the collected data indicated that properly installed dampers of the Stockbridge type, and others, should sufficiently reduce aeolian vibrations

Discrete Fourier multipliers and cylindrical boundary value problems

We consider operator-valued boundary value problems in $(0,2\pi)^n$ with periodic or, more generally, $\nu$-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the unique solvability of the boundary value problem. As an application, we study vector-valued parabolic initial boundary value problems in cylindrical domains $(0,2\pi)^n\times V$ with $\nu$-periodic boundary conditions in the cylindrical directions. We show that under suitable assumptions on the coefficients, we obtain maximal $L^q$-regularity for such problems.Comment: Konstanzer Schriften in Mathematik 279 (2011

Polymer mechanochemistry-enabled pericyclic reactions

Over the past decades, it became clear that next to heat and light, pericyclic reactions can be induced mechanochemically when the reacting motifs are embedded as latent force-responsive groups (mechanophores) into polymer architectures. Not only does this enable a variety of functions and applications on a material level, but moreover grants access to symmetry-forbidden reaction products with respect to the Woodward-Hoffmann rules. The latter indicates that polymer mechanochemistry follows its own set of rules that, however, regarding underlying mechanisms and design rationales is far from being holistically understood. Here we review the existing body of literature and identify common structural features and substitution prerequisites to the polymer framework shining light on the differences between polymer mechanochemical pericyclic reactions and their traditional counterparts. By this, we believe to contribute to the major challenge of not only retrospectively describing force-induced reactivity but eventually finding a common molecular design guideline. © The Royal Society of Chemistry 2020

Hispanic-White Differences in Lifespan Variability in the United States

This study is the first to investigate whether and, if so, why Hispanics and non-Hispanic whites in the United States differ in the variability of their lifespans. Although Hispanics enjoy higher life expectancy than whites, very little is known about how lifespan variability—and thus uncertainty about length of life—differs by race/ethnicity. We use 2010 U.S. National Vital Statistics System data to calculate lifespan variance at ages 10 and older for Hispanics and whites, and then decompose the Hispanic-white variance difference into cause-specific spread, allocation, and timing effects. In addition to their higher life expectancy relative to whites, Hispanics also exhibit 7 % lower lifespan variability, with a larger gap among women than men. Differences in cause-specific incidence (allocation effects) explain nearly two-thirds of Hispanics’ lower lifespan variability, mainly because of the higher mortality from suicide, accidental poisoning, and lung cancer among whites. Most of the remaining Hispanic-white variance difference is due to greater age dispersion (spread effects) in mortality from heart disease and residual causes among whites than Hispanics. Thus, the Hispanic paradox—that a socioeconomically disadvantaged population (Hispanics) enjoys a mortality advantage over a socioeconomically advantaged population (whites)—pertains to lifespan variability as well as to life expectancy. Efforts to reduce U.S. lifespan variability and simultaneously increase life expectancy, especially for whites, should target premature, young adult causes of death—in particular, suicide, accidental poisoning, and homicide. We conclude by discussing how the analysis of Hispanic-white differences in lifespan variability contributes to our understanding of the Hispanic paradox

Limits on the HI content of the dwarf galaxy Hydra II

Sensitive 21cm HI observations have been made with the Green Bank Telescope toward the newly-discovered Local Group dwarf galaxy Hydra II, which may lie within the leading arm of the Magellanic Stream. No neutral hydrogen was detected. Our 5-sigma limit of MHI < 210 solar masses for a 15 km/s linewidth gives a gas-to-luminosity ratio MHI/L_V < 2.6 x 10^{-2} Mo / Lo. The limits on HI mass and MHI/L_V are typical of dwarf galaxies found within a few hundred kpc of the Milky Way. Whatever the origin of Hydra II, its neutral gas properties are not unusual.Comment: Accepted for publication in Astronomy & Astrophysic

Associations of physical inactivity and COVID-19 outcomes among subgroups

Introduction Physical activity before COVID-19 infection is associated with less severe outcomes. The study determined whether a dose‒response association was observed and whether the associations were consistent across demographic subgroups and chronic conditions. Methods A retrospective cohort study of Kaiser Permanente Southern California adult patients who had a positive COVID-19 diagnosis between January 1, 2020 and May 31, 2021 was created. The exposure was the median of at least 3 physical activity self-reports before diagnosis. Patients were categorized as follows: always inactive, all assessments at 10 minutes/week or less; mostly inactive, median of 0–60 minutes per week; some activity, median of 60–150 minutes per week; consistently active, median>150 minutes per week; and always active, all assessments>150 minutes per week. Outcomes were hospitalization, deterioration event, or death 90 days after a COVID-19 diagnosis. Data were analyzed in 2022. Results Of 194,191 adults with COVID-19 infection, 6.3% were hospitalized, 3.1% experienced a deterioration event, and 2.8% died within 90 days. Dose‒response effects were strong; for example, patients in the some activity category had higher odds of hospitalization (OR=1.43; 95% CI=1.26, 1.63), deterioration (OR=1.83; 95% CI=1.49, 2.25), and death (OR=1.92; 95% CI=1.48, 2.49) than those in the always active category. Results were generally consistent across sex, race and ethnicity, age, and BMI categories and for patients with cardiovascular disease or hypertension. Conclusions There were protective associations of physical activity for adverse COVID-19 outcomes across demographic and clinical characteristics. Public health leaders should add physical activity to pandemic control strategies

The Design and Methodology of the Ohio COVID-19 Survey

Background: Governments worldwide are balancing contrasting needs to curtail the toll that coronavirus disease 2019 (COVID-19) takes on lives and health care systems and to preserve their economies. To support decisions, data that simultaneously measure the health status of the population and the economic impact of COVID-19 mitigation strategies are needed. In the United States, prior to the onset of COVID-19, surveys or tracking systems usually focused on public health or economic indicators, but not both. However, tracking public health and economic measures together allow policy makers and epidemiologists to understand how policy and program decisions are associated. The Ohio COVID-19 Survey (OCS) attempts to track both measures in Ohio as one of the first statewide population surveys on COVID-19. To achieve this there are several methodological challenges which need to be overcome. Methods: The OCS utilizes a representative panel offering both cross-sectional and longitudinal analyses. It targets 700 to 1000 respondents per week for a total of 12 600 to 18 000 respondents over an 18-week period. Leveraging a sample of 24 000 adult Ohioans developed from a statewide population health survey conducted in fall 2019, the OCS produces weekly economic and health measures that can be compared to baseline measures obtained before the COVID-19 pandemic began. Results: The OCS was able to quickly launch and achieve high participation (45.2%) and retention across waves. Conclusion: The OCS demonstrates how it is possible to leverage an existing health-based survey in Ohio to generate a panel which can be used to quickly track fast-breaking health issues like COVID-19