Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

Wing Patterns in the Mist

Arnaud Martin is with University of California Irvine, Durrell D. Kapan is with University of Hawaii at Manoa, Lawrence E. Gilbert is with UT Austin.The aesthetic appeal of butterfly wing patterns has been costly to their status as a tool of fundamental scientific inquiry. Thus, while mimetic convergence in wing patterns between edible “Batesian” mimics and distasteful models, or between different distasteful “Müllerian” mimics (species that cooperate to educate predators) has long been the subject of genetic analysis [1] and field experiments [2], most biology text books confine mimicry to sections on striking adaptations without applying these examples to broader topics of evolution. Meanwhile, the study of color patterns in animals, often tucked into the same sections of texts, is undergoing a revolution in this age of evo-devo and genomics [3]. Among insect models for studying color pattern, the genus Heliconius is gaining the attention of an ever-widening audience.Biological Sciences, School o

Post-diagnosis serum insulin-like growth factors in relation to dietary and lifestyle changes in the Prostate testing for cancer and Treatment (ProtecT) trial.

PURPOSE: The insulin-like growth factor (IGF) system is modifiable by diet and lifestyle, and has been linked to prostate cancer development and progression. METHODS: We conducted a prospective cohort study of 621 men diagnosed with localized prostate cancer to investigate the associations of dietary and lifestyle changes with post-diagnosis circulating levels of IGF-I and IGFBP-3. We used analysis of covariance to estimate the associations, controlling for baseline IGF-I or IGFBP-3, respectively. RESULTS: Mean IGF-I levels were 6.5% (95% CI -12.8, -0.3%, p = 0.04) lower in men who decreased their protein intake after diagnosis compared to men who did not change. Men who changed their fruit and vegetable intake had lower IGF-I levels compared to non-changers [Decreased intake: -10.1%, 95% CI -18.4, -1.8%, p = 0.02; Increased intake: -12.0%, 95% CI -18.4, -1.8%, p = 0.002]. IGFBP-3 was 14.6% (95% CI -24.5, -4.8%, p = 0.004) lower in men who achieved a healthy body mass index after diagnosis. Men who became inactive had 9.5% higher average IGF-I levels (95% CI 0.1, 18.9%, p = 0.05). CONCLUSIONS: Decreased protein intake and body mass index, and increased physical activity and fruit and vegetable intake, following a prostate cancer diagnosis were associated with reduced post-diagnosis serum IGF-I and IGFBP-3. Counterintuitively, reduced fruit and vegetable intake was also associated with reduced IGF-I, but with weak statistical support, possibly implicating chance. If confirmed in other studies, our findings may inform potential lifestyle interventions in prostate cancer. ProtecT was registered at International Standard Randomised Controlled Trial Registry, http://isrctn.org as ISRCTN20141297

The air quality impacts of road closures associated with the 2004 Democratic National Convention in Boston

BACKGROUND: The Democratic National Convention (DNC) in Boston, Massachusetts in 2004 provided an opportunity to evaluate the impacts of a localized and short-term but potentially significant change in traffic patterns on air quality, and to determine the optimal monitoring approach to address events of this nature. It was anticipated that the road closures associated with the DNC would both influence the overall air pollution level and the distribution of concentrations across the city, through shifts in traffic patterns. METHODS: To capture these effects, we placed passive nitrogen dioxide badges at 40 sites around metropolitan Boston before, during, and after the DNC, with the goal of capturing the array of hypothesized impacts. In addition, we continuously measured elemental carbon at three sites, and gathered continuous air pollution data from US EPA fixed-site monitors and traffic count data from the Massachusetts Highway Department. RESULTS: There were significant reductions in traffic volume on the highway with closures north of Boston, with relatively little change along other highways, indicating a more isolated traffic reduction rather than an across-the-board decrease. For our nitrogen dioxide samples, while there was a relatively small change in mean concentrations, there was significant heterogeneity across sites, which corresponded with our a priori classifications of road segments. The median ratio of nitrogen dioxide concentrations during the DNC relative to non-DNC sampling periods was 0.58 at sites with hypothesized traffic reductions, versus 0.88 for sites with no changes hypothesized and 1.15 for sites with hypothesized traffic increases. Continuous monitors measured slightly lower concentrations of elemental carbon and nitrogen dioxide during road closure periods at monitors proximate to closed highway segments, but not for PM(2.5 )or further from major highways. CONCLUSION: We conclude that there was a small but measurable influence of DNC-related road closures on air quality patterns in the Boston area, and that a low-cost monitoring study combining passive badges for spatial heterogeneity and continuous monitors for temporal heterogeneity can provide useful insight for community air quality assessments

Long-term Exposure to Traffic-related Air Pollution and Type 2 Diabetes Prevalence in a Cross-sectional Screening-study in the Netherlands

<p>Abstract</p> <p>Background</p> <p>Air pollution may promote type 2 diabetes by increasing adipose inflammation and insulin resistance. This study examined the relation between long-term exposure to traffic-related air pollution and type 2 diabetes prevalence among 50- to 75-year-old subjects living in Westfriesland, the Netherlands.</p> <p>Methods</p> <p>Participants were recruited in a cross-sectional diabetes screening-study conducted between 1998 and 2000. Exposure to traffic-related air pollution was characterized at the participants' home-address. Indicators of exposure were land use regression modeled nitrogen dioxide (NO₂) concentration, distance to the nearest main road, traffic flow at the nearest main road and traffic in a 250 m circular buffer. Crude and age-, gender- and neighborhood income adjusted associations were examined by logistic regression.</p> <p>Results</p> <p>8,018 participants were included, of whom 619 (8%) subjects had type 2 diabetes. Smoothed plots of exposure versus type 2 diabetes supported some association with traffic in a 250 m buffer (the highest three quartiles compared to the lowest also showed increased prevalence, though non-significant and not increasing with increasing quartile), but not with the other exposure metrics. Modeled NO₂-concentration, distance to the nearest main road and traffic flow at the nearest main road were not associated with diabetes. Exposure-response relations seemed somewhat more pronounced for women than for men (non-significant).</p> <p>Conclusions</p> <p>We did not find consistent associations between type 2 diabetes prevalence and exposure to traffic-related air pollution, though there were some indications for a relation with traffic in a 250 m buffer.</p