The tame-wild principle for discriminant relations for number fields

Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.Comment: 31 pages, 11 figures. Version 2 fixes a normalization error: |G| is corrected to n in Section 7.5. Version 3 fixes an off-by-one error in Section 6.

Role of a plausible nuisance contributor in the declining obesity-mortality risks over time.

CONTEXT: Recent analyses of epidemiological data including the National Health and Nutrition Examination Survey (NHANES) have suggested that the harmful effects of obesity may have decreased over calendar time. The shifting BMI distribution over time coupled with the application of fixed broad BMI categories in these analyses could be a plausible nuisance contributor to this observed change in the obesity-associated mortality over calendar time. OBJECTIVE: To evaluate the extent to which observed temporal changes in the obesity-mortality association may be due to a shifting population distribution for body mass index (BMI), coupled with analyses based on static, broad BMI categories. DESIGN, SETTING, AND PARTICIPANTS: Simulations were conducted using data from NHANES I and III linked with mortality data. Data from NHANES I were used to fit a true model treating BMI as a continuous variable. Coefficients estimated from this model were used to simulate mortality for participants in NHANES III. Hence, the population-level association between BMI and mortality in NHANES III was fixed to be identical to the association estimated in NHANES I. Hazard ratios (HRs) for obesity categories based on BMI for NHANES III with simulated mortality data were compared to the corresponding estimated HRs from NHANES I. MAIN OUTCOME MEASURES: Change in hazard ratios for simulated data in NHANES III compared to observed estimates from NHANES I. RESULTS: On average, hazard ratios for NHANES III based on simulated mortality data were 29.3% lower than the estimates from NHANES I using observed mortality follow-up. This reduction accounted for roughly three-fourths of the apparent decrease in the obesity-mortality association observed in a previous analysis of these data. CONCLUSIONS: Some of the apparent diminution of the association between obesity and mortality may be an artifact of treating BMI as a categorical variable

Full-Field, Carrier-Less, Polarization-Diversity, Direct Detection Receiver based on Phase Retrieval

We realize dual-polarization full-field recovery using intensity only measurements and phase retrieval techniques based on dispersive elements. 30-Gbaud QPSK waveforms are transmitted over 520-km standard single-mode fiber and equalized from the receiver outputs using 2X2 MIMO

Automated visual tracking for studying the ontogeny of zebrafish swimming

The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fish's body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s–1. Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing) fish

Mistrust and Ambivalence between Residents and the Police: Evidence from Four Chicago Neighborhoods

This brief examines the fractured relationship between residents in high-crime Chicago neighborhoods and the police that serve those communities. Based on surveys of people living in and police officers serving in four Chicago police districts on the city's south and west sides collected as part of the evaluation of the Chicago Violence Reduction Strategy, these data demonstrate ambivalence between the police and residents. Community members do not generally perceive the police as acting in a procedurally fair manner and do not support their work; this perception is particularly high among people with recent arrest histories in co-offending networks. Police officers do not believe the community trusts them, and officers express little confidence or trust in those living in the districts they police. However, residents are generally willing to cooperate with the police on crime control efforts

Overweight, obesity, and colorectal cancer screening: Disparity between men and women

BACKGROUND: To estimate the association between body-mass index (BMI: kg/m(2)) and colorectal cancer (CRC) screening among US adults aged ≥ 50 years. METHODS: Population-based data from the 2001 Behavioral Risk Factor Surveillance Survey. Adults (N = 84,284) aged ≥ 50 years were classified by BMI as normal weight (18.5–<25), overweight (25–<30), obesity class I (30–<35), obesity class II (35–<40), and obesity class III (≥ 40). Interval since most recent screening fecal occult blood test (FOBT): (0 = >1 year since last screening vs. 1 = screened within the past year), and screening sigmoidoscopy (SIG): (0 = > 5 years since last screening vs. 1 = within the past 5 years) were the outcomes. RESULTS: Results differed between men and women. After adjusting for age, health insurance, race, and smoking, we found that, compared to normal weight men, men in the overweight (odds ratio [OR] 1.25, 95% CI = 1.05–1.51) and obesity class I (OR = 1.21, 95% CI = 1.03–1.75) categories were more likely to have obtained a screening SIG within the previous 5 years, while women in the obesity class I (OR = 0.86, 95%CI = 0.78–0.94) and II (OR = 0.88, 95%CI = 0.79–0.99) categories were less likely to have obtained a screening SIG compared to normal weight women. BMI was not associated with FOBT. CONCLUSION: Weight may be a correlate of CRC screening behavior but in a different way between men and women

Rhizosphere control of soil nitrogen cycling: a key component of plant economic strategies

Understanding how plant species influence soil nutrient cycling is a major theme in terrestrial ecosystem ecology. However, the prevailing paradigm has mostly focused on litter decomposition, while rhizosphere effects on soil organic matter (SOM) decomposition have attracted little attention. Using a dual(13)C/N-15 labeling approach in a 'common garden' glasshouse experiment, we investigated how the economic strategies of 12 grassland plant species (graminoids, forbs and legumes) drive soil nitrogen (N) cycling via rhizosphere processes, and how this in turn affects plant N acquisition and growth. Acquisitive species with higher photosynthesis, carbon rhizodeposition and N uptake than conservative species induced a stronger acceleration of soil N cycling through rhizosphere priming of SOM decomposition. This allowed them to take up larger amounts of N and allocate it above ground to promote photosynthesis, thereby sustaining their faster growth. The N-2-fixation ability of legumes enhanced rhizosphere priming by promoting photosynthesis and rhizodeposition. Our study demonstrates that the economic strategies of plant species regulate a plant-soil carbon-nitrogen feedback operating through the rhizosphere. These findings provide novel mechanistic insights into how plant species with contrasting economic strategies sustain their nutrition and growth through regulating the cycling of nutrients by soil microbes in their rhizosphere