Sheaves and Duality in the Two-Vertex Graph Riemann-Roch Theorem

For each graph on two vertices, and each divisor on the graph in the sense of Baker-Norine, we describe a sheaf of vector spaces on a finite category whose zeroth Betti number is the Baker-Norine "Graph Riemann-Roch" rank of the divisor plus one. We prove duality theorems that generalize the Baker-Norine "Graph Riemann-Roch" Theorem

Euler Characteristics and Duality in Riemann Functions and the Graph Riemann-Roch Rank

By a {\em Riemann function} we mean a function $f\colon{\mathbb Z}^n\to{\mathbb Z}$ such that $f({\bf d})=f(d_1,\ldots,d_n)$ is equals $0$ for ${\rm deg}({\bf d})=d_1+\cdots+d_n$ sufficiently small, and equals $d_1+\cdots+d_n+C$ for a constant, $C$ -- the {\em offset of $f$} -- for ${\rm deg}({\bf d})$ sufficiently large. By adding $1$ to the Baker-Norine rank function of a graph, one gets an equivalent Riemann function, and similarly for related rank functions. For such an $f$, for any ${\bf K}\in{\mathbb Z}^n$ there is a unique Riemann function $f^\wedge_{\bf K}$ such that for all ${\bf d}\in{\mathbb Z}^n$ we have $$f({\bf d}) - f^\wedge_{\bf K}({\bf K}-{\bf d}) = {\rm deg}({\bf d})+C$$ which we call a {\em generalized Riemann-Roch formula}. We show that any such equation can be viewed as an Euler charactersitic equation of sheaves of a particular simple type that we call {\em diagrams}. This article does not assume any prior knowledge of sheaf theory. To certain Riemann functions $f\colon{\mathbb Z}^2\to{\mathbb Z}$ there is a simple family of diagrams $\{{\mathcal{M}}_{W,{\bf d}}\}_{{\bf d}\in{\mathbb Z}^2}$ such that $f({\bf d})=b^0({\mathcal{M}}_{W,{\bf d}})$ and $f^\wedge_{{\bf K}}({\bf K}-{\bf d})=b^1({\mathcal{M}}_{W,{\bf d}})$. Furthermore we give a canonical isomorphism $$H^1({\mathcal{M}}_{W,{\bf d}})^* \to H^0({\mathcal{M}}_{W',{\bf K}-{\bf d}})$$ where $W'$ is the weight of $f^\wedge_{\bf K}$. General Riemann functions $f\colon{\mathbb Z}^2\to{\mathbb Z}$ are similarly modeled with formal differences of diagrams. Riemann functions ${\mathbb Z}^n\to{\mathbb Z}$ are modeled using their restrictions to two of their variables. These constructions involve some ad hoc choices, although the equivalence class of virtual diagram obtained is independent of the ad hoc choices

ENTRAINMENT DURING BICYCLE ERGOMETRY IN ELITE CYCLISTS

While it is widely accepted that ventilation increases abruptly at the onset of muscular exercise (D'Angelo and Torelli, 1971; Jensen, Vejby-Christensen and Petersen, 1972; Krogh and Lin~~ard, 1913) the control of the respiratory pattern, i.e., the relationship between ventilation (V', Vi', Ve'), tidal volume (Vt), and respiratory frequency (fR) or respiratory cycle times (Tt, Ti, Te) is not clearly understood (Wasserman, 1978). There are a number of factors, which may be classified as humoral, neurogenic, or neurohumoral, involved in respiratory regulation (Dejours, 1960), but the importance of any single factor is difficult to determine because of the associated problems of controlling for the other variables involved in the total response. One such factor is the coordination of the respiratory pattern to the movement pattern referred to as entrainment. The purpose of the present study was to examine the relationship between the variables that control the respiratory pattern and to test the hypothesis that entrainment would be more prevalent in athletes who were highly trained for a particular mode of exercise, based on a work minimization theory (Priban and Fincham, 1965; Yamashiro and Grodins, 1973; Cherniack, 1980), than in non-athletes unaccustomed to the exercise

Heat flow over the equatorial mid-Atlantic ridge.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Geology and Geophysics, 1969.Bibliography: leaves 19-20.M.S

The gravity field and plate boundaries in Venezuela

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1972Free-air and simple Bouguer anomaly maps of the Venezuelan continental margin (from 60°W to 72°W and from 7°N to 13°N) are presented. The major features of the free-air map are: the large lows associated with the deep sedimentary basins, -200 mgal in the Eastern Venezuela basin and -164 mgal in the Maracaibo basin; the high of greater than 300 mgal over the Venezuelan Andes; and a belt of highs associated with the offshore islands extending from Blanquilla to Curacao and then over the Guajira peninsula, where they terminate. The Bouguer anomaly map shows a large low (-196 mgal) over the Eastern Venezuela basin and relative minimums over the coastal mountains. A minimum associated with the Venezuelan Andes is shifted to the northwest of the topographic axis and lies over the flank of the Andes and part of the Maracaibo basin. Using the gravity data, structural sections were constructed for a series of profiles across the Venezuelan Andes and Caribbean mountains. They show that there is no light crustal root under the Andes, the relative mass excess is as much as 600 kg/cm2, and that there is an excess of low density material under the Maracaibo basin. This appears to be caused by a combination of a southeastward dipping shear zone in the lithosphere under the basin-mountain boundary and a component of compressive stress perpendicular to this zone, both of which have resulted in the uplift of the crust under the Andes, and downwarp under the basin. The apparent flexural rigidity of the lithosphere under the Maracaibo basin is 0.6 x 1023 newton-m, a normal value for lithosphere deformations of Miocene age. The Caribbean mountains have a light crustal root which has been formed by the sliding of blocks of crustal material from the north over the rocks to the south, and perhaps by the underthrusting of oceanic crust under the continental crust. This underthrusting may have been a result of the formation of a downgoing slab of lithosphere along the Venezuelan continental margin during the late Cretaceous. The downgoing slab may have existed until mid-Eocene time. The gravity minimum over the Eastern Venezuela basin is due to the downwarping of lighter crustal material into the higher density mantle. This may be a result of compression from the north along a north-south direction causing plastic downbuckling of the lithosphere. The present deformation along the northern boundary appears to be due to differences in relative motion between the North and South American plates. Because the Caribbean mountains are partially isostatically compensated, while the Venezuelan Andes are above isostatic equilibrium, this suggests that the relative motion of the Caribbean plate with respect to the South American plate is eastward. The compressive stress across the boundary in the region of the Venezuelan Andes is probably greater than the compressive stress across the Caribbean mountains.This investigation was supported by a grant from the National Science Foundation GA-12204, and by contract N00014-66-C-024l with the Office of Naval Research

Ozone and PM(2.5) Exposure and Acute Pulmonary Health Effects: A Study of Hikers in the Great Smoky Mountains National Park

To address the lack of research on the pulmonary health effects of ozone and fine particulate matter (≤ 2.5 μm in aerodynamic diameter; PM(2.5)) on individuals who recreate in the Great Smoky Mountains National Park (USA) and to replicate a study performed at Mt. Washington, New Hampshire (USA), we conducted an observational study of adult (18–82 years of age) day hikers of the Charlies Bunion trail during 71 days of fall 2002 and summer 2003. Volunteer hikers performed pre- and posthike pulmonary function tests (spirometry), and we continuously monitored ambient O(3), PM(2.5), temperature, and relative humidity at the trailhead. Of the 817 hikers who participated, 354 (43%) met inclusion criteria (nonsmokers and no use of bronchodilators within 48 hr) and gave acceptable and reproducible spirometry. For these 354 hikers, we calculated the posthike percentage change in forced vital capacity (FVC), forced expiratory volume in 1 sec (FEV(1)), FVC/FEV(1), peak expiratory flow, and mean flow rate between 25 and 75% of the FVC and regressed each separately against pollutant (O(3) or PM(2.5)) concentration, adjusting for age, sex, hours hiked, smoking status (former vs. never), history of asthma or wheeze symptoms, hike load, reaching the summit, and mean daily temperature. O(3) and PM(2.5) concentrations measured during the study were below the current federal standards, and we found no significant associations of acute changes in pulmonary function with either pollutant. These findings are contrasted with those in the Mt. Washington study to examine the hypothesis that pulmonary health effects are associated with exposure to O(3) and PM(2.5) in healthy adults engaged in moderate exercise

Acute Pulmonary Function Response to Ozone in Young Adults As a Function of Body Mass Index

Recent studies have shown enhanced responsiveness to ozone in obese mice. Adiposity has not been examined as a possible modulator of ozone response in humans. We therefore examined the relationship between body mass index and the acute spirometric response to ozone (O3) exposure among 197 non-asthmatic young adults (aged 18-35) studied in our human exposure facility from 1992-1998. Each subject had been exposed to 0.42 ppm O3 for 1.5 h with intermittent exercise designed to produce a minute ventilation of 20 l/min / m2 body surface area (BSA). Spirometry (pulmonary function) was measured pre- and immediately post- exposure to determine acute ozone-induced changes. The decrement in forced expiratory volume in 1s (Δ FEV1) in % of baseline was significantly correlated with BMI, r = −0.16, p = 0.03 with a slightly stronger correlation in women (n=75), r = −0.22, p = 0.05, and no significant correlation in men. BMI had a greater range in women than in men in our study. In women greater ozone-induced decrements were seen in overweight (BMI > 25 kg/m2) than in normal weight (BMI 18.5 to 25 kg/m2), and in normal weight than in underweight (BMI < 18.5 kg/m2) for all spirometric variables considered (P trend ≤ 0.022). Although our population studied was predominantly normal weight, we found that higher body mass index may be a modest risk factor for adverse pulmonary effects associated with ozone exposure, especially for women

Is there adaptation in the ozone mortality relationship: A multi-city case-crossover analysis

<p>Abstract</p> <p>Background</p> <p>Ozone has been associated with daily mortality, mainly in the summer period. Despite the ample literature on adaptation of inflammatory and pulmonary responses to ozone, and the link, in cohort studies, between lung function and mortality risk there has been little done to date to examine the question of adaptation in the acute mortality risk associated with ambient ozone.</p> <p>Methods</p> <p>We applied a case-crossover design in 48 US cities to examine the ozone effect by season, by month and by age groups, particularly focusing on whether there was an adaptation effect.</p> <p>Results</p> <p>We found that the same day ozone effect was highest in summer with a 0.5% (95% CI: 0.38, 0.62) increase in total mortality for 10 ppb increase in 8-hr ozone, whilst the effect decrease to null in autumn and winter. We found higher effects in the months May- July with a 0.46% (95% CI: 0.24, 0.68) increase in total mortality for 10 ppb increase in ozone in June, and a 0.65% (95% CI: 0.47, 0.82) increase in mortality during July. The effect decreased in August and became null in September. We found similar effects from the age group 51–60 up to age 80 and a lower effect in 80 years and older.</p> <p>Conclusion</p> <p>The mortality effects of ozone appear diminished later in the ozone season, reaching the null effect previously reported in winter by September. More work should address this issue and examine the biological mechanism of adaptation.</p