Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

Understanding organizational context and heart failure management in long term care homes in Ontario, Canada

This study examined the prevalence of Control Intervention (CI) use in adult in-patient psychiatric units/hospitals in Ontario and developed a profile of those patients who had CI use during their admission between April 2006 and March 2010. Control intervention types included mechanical/physical, chair prevents rising, acute control medications, and seclusion. The profiles of patients with control intervention use included an examination of sociodemographic, mental health service use, and mental health clinical characteristics.Supported by an unrestricted grant-in-aid from the Heart and Stroke Foundation of Ontari

Interim modelling analysis to validate reported increases in condom use and assess HIV infections averted among female sex workers and clients in southern India following a targeted HIV prevention programme.

OBJECTIVES: This study assesses whether the observed declines in HIV prevalence since the beginning of the 'Avahan' India HIV/AIDS prevention initiative are consistent with self-reported increases in condom use by female sex workers (FSWs) in two districts of southern India, and provides estimates of the fraction of new infections averted among FSWs and clients due to increases in condom use in commercial sex after 2004. METHODS: A deterministic compartmental model of HIV/sexually transmitted infection (STI) transmission incorporating heterogeneous sexual behaviour was developed, parameterised and fitted using data from two districts in Karnataka, India. Three hypotheses of condom use among FSWs were tested: (H(0)), that condom use increased in line with reported FSW survey data prior to the Avahan initiative but remained constant afterwards; (H(1)) that condom use increased following the Avahan initiative, in accordance with survey data; (H(2)) that condom use increased according to estimates derived from condom distribution data. The proportion of fits to HIV/STI prevalence data was examined to determine which hypothesis was most consistent. RESULTS: For Mysore 0/36/82.7 fits were identified per million parameter sets explored under hypothesis H(0)/H(1)/H(2), respectively, while for Belgaum 9.7/8.3/0 fits were identified. The HIV epidemics in Belgaum and Mysore are both declining. In Mysore, increases in condom use during commercial sex between 2004 and 2009 may have averted 31.2% to 47.4% of new HIV infections in FSWs, while in Belgaum it may have averted 24.8% to 43.2%, if there was an increase in condom use. DISCUSSION: Increased condom use following the Avahan intervention is likely to have played a role in curbing the HIV epidemic in Mysore. In Belgaum, given the limitations in available data, this method cannot be used alone to decide if there has been an increase in condom use

HST observations of the Local Group dwarf galaxy Leo I

We present deep HST F555W (V) and F814W (I) observations of a central field in the Local Group dwarf spheroidal (dSph) galaxy Leo I. The resulting color-magnitude diagram (CMD) reaches I \simeq 26 and reveals the oldest ~10-15 Gyr old turnoffs. Nevertheless, a horizontal branch is not obvious in the CMD. Given the low metallicity of the galaxy, this likely indicates that the first substantial star formation in the galaxy may have been somehow delayed in Leo I in comparison with the other dSph satellites of the Milky Way. The subgiant region is well and uniformly populated from the oldest turnoffs up to the 1 Gyr old turnoff, indicating that star formation has proceeded in a continuous way, with possible variations in intensity but no big gaps between successive bursts, over the galaxy's lifetime. The structure of the red-clump of core He-burning stars is consistent with the large amount of intermediate-age population inferred from the main sequence and the subgiant region. In spite of the lack of gas in Leo I, the CMD clearly shows star formation continuing until 1 Gyr ago and possibly until a few hundred Myrs ago in the central part of the galaxy.Comment: 26 pages with 8 figures (fig 2 not available electronically). To be published in ApJ, April 1 1999 (vol.514, #2

Entropy, Lyapunov Exponents and Escape Rates in Open Systems

We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapunov exponents. Central to the discussion is the formulation of a class of invariant measures supported on the survivor set over which we take the supremum to measure the pressure. Upper bounds for escape rates are proved for general diffeomorphisms of manifolds, possibly with singularities, for arbitrary holes and natural initial distributions including Lebesgue and SRB measures. Lower bounds do not hold in such generality, but for systems admitting Markov tower extensions with spectral gaps, we prove the equality of the escape rate with the absolute value of the pressure and the existence of an invariant measure realizing the escape rate, i.e. we prove a full variational principle. As an application of our results, we prove a variational principle for the billiard map associated with a planar Lorentz gas of finite horizon with holes.Comment: 34 pages, 1 figure; This research is partially supported by NSF grant DMS-080113

Nonmalignant respiratory disease mortality among woodworkers participating in the American Cancer Society Cancer Prevention Study-II (CPS-II)

Nonmalignant respiratory disease (NMRD) mortality was examined among woodworkers participating in the American Cancer Society’s CPS-II cohort study. During the 6-year prospective follow-up, there were 97 NMRD deaths among 11,541 men reporting employment in wood-related occupations and 1,338 NMRD deaths among 317,424 men reporting no exposure to wood dust or wood-related jobs. Relative risks, adjusted for age and smoking, were calculated using Poisson regression. A small excess of NMRD was observed among woodworkers. However, the relative risk was higher among woodworkers who did not report exposure to wood dust (RR = 1.52, 95% CI = 1.18–1.97) than those who did (RR = 1.27, 95% CI = 0.91–1.77), and no clear trend with duration of exposure was observed. An excess of NMRD was observed among woodworkers reporting exposure to asbestos (RR = 1.59, 95% CI = 0.85–2.96), as well as the small number of woodworkers reporting exposure to formaldehyde (RR = 1.95, 95% CI = 0.63–6.06), but men not reporting exposure to these substances also had an excess risk. Although limited by a short follow-up period and crude indicators of exposure, the strengths of this analysis were the ability to compare woodworkers to a similar, healthy population and to adjust for the effects of smoking. Cohort studies with better exposure information are needed to examine the role of occupational exposures among woodworkers in the etiology of respiratory disease

Cancer mortality and wood dust exposure among participants in the American Cancer Society Cancer Prevention Study-II (CPS-II).

In 1994, the International Agency for Research on Cancer (IARC) classified wood dust as a human carcinogen, based on very strong evidence of a carcinogenic risk of sino-nasal cancer. Excesses of other cancers, including lung and stomach, have been reported among persons employed in wood industries or occupationally exposed to wood dust, but not as consistently. We investigated such possible associations using the mortality experience of 362,823 men enrolled in the American Cancer Society’s Cancer Prevention Study—II in 1982 and followed up for 6 years. Within this group, 45,399 men (12.5%) reported either employment in a wood-related occupation or exposure to wood dust or both. Among woodworkers, a small but significant excess risk was found for all causes of death (RR 1.17 (95% CI 1.11–1.24)) and for total malignancies (RR 1.17 (1.05–1.30)). Among men who reported exposure to wood dust, there was an elevated risk of total mortality (RR 1.07 (1.03–1.11)), total malignancies (RR 1.08 (1.01—1.15)), and lung cancer (RR 1.17 (1.04–1.31)). Among woodworkers, a significant trend (P = 0.02) of increasing risk of lung cancer with increasing duration of exposure was observed. An unexpected, significantly increased mortality from prostate cancer was observed in both wood-employed and wood-exposed, and a twofold increased risk of fatal brain cancer was seen among the former. Lung cancer mortality was especially high among woodworkers who also reported exposure to asbestos or formaldehyde, and it appears that exposure to these known carcinogens may partly explain the observed increased risks. Excess sino-nasal cancer was not observed, but the number of cases was small

Patchwork Gridshells::Using Modularity to Facilitate Prefabrication and Simplify Construction

Modern architectural design has seen a shift towards iconic doubly-curved envelopes enclosing large column-free spaces. Gridshells have long been considered an efficient solution to such designs, but their actual use in practice has not spread worldwide. For elastic gridshells, their advantages in terms of substantial material savings can often be overshadowed by the significant challenges associated with their construction. Similarly, for rigid gridshells, the manufacture of a large number of different members and nodal connections is often a barrier to their implementation. This paper proposes an effective way of designing, fabricating and erecting gridshells. The “Patchwork Gridshell” consists of a number of efficient elastic gridshell patches assembled using rigid gridshell frames. It can easily generate a number of different configurations, use a wide range of materials, and allows more architectural expression of practical long-span forms. The benefits of combining the ingenuously simple efficiency of elastic lattices and the power of digital fabrication are demonstrated by digitally rebuilding four alternative configurations of the Japan Pavilion of the Hanover Expo 2000 as a case study. The result is a flexible digital workflow which creates large column-free spaces that are capable of being constructed efficiently by nonspecialist contractors.</p

Patchwork Gridshells::Using Modularity to Facilitate Prefabrication and Simplify Construction

Modern architectural design has seen a shift towards iconic doubly-curved envelopes enclosing large column-free spaces. Gridshells have long been considered an efficient solution to such designs, but their actual use in practice has not spread worldwide. For elastic gridshells, their advantages in terms of substantial material savings can often be overshadowed by the significant challenges associated with their construction. Similarly, for rigid gridshells, the manufacture of a large number of different members and nodal connections is often a barrier to their implementation. This paper proposes an effective way of designing, fabricating and erecting gridshells. The “Patchwork Gridshell” consists of a number of efficient elastic gridshell patches assembled using rigid gridshell frames. It can easily generate a number of different configurations, use a wide range of materials, and allows more architectural expression of practical long-span forms. The benefits of combining the ingenuously simple efficiency of elastic lattices and the power of digital fabrication are demonstrated by digitally rebuilding four alternative configurations of the Japan Pavilion of the Hanover Expo 2000 as a case study. The result is a flexible digital workflow which creates large column-free spaces that are capable of being constructed efficiently by nonspecialist contractors.</p

Exposure-Response Analyses of Asbestos and Lung Cancer Subtypes in a Pooled Analysis of Case-Control Studies

BackgroundEvidence is limited regarding risk and the shape of the exposure-response curve at low asbestos exposure levels. We estimated the exposure-response for occupational asbestos exposure and assessed the joint effect of asbestos exposure and smoking by sex and lung cancer subtype in general population studies.MethodsWe pooled 14 case-control studies conducted in 1985-2010 in Europe and Canada, including 17,705 lung cancer cases and 21,813 controls with detailed information on tobacco habits and lifetime occupations. We developed a quantitative job-exposure-matrix to estimate job-, time period-, and region-specific exposure levels. Fiber-years (ff/ml-years) were calculated for each subject by linking the matrix with individual occupational histories. We fit unconditional logistic regression models to estimate odds ratios (ORs), 95% confidence intervals (CIs), and trends.ResultsThe fully adjusted OR for ever-exposure to asbestos was 1.24 (95% CI, 1.18, 1.31) in men and 1.12 (95% CI, 0.95, 1.31) in women. In men, increasing lung cancer risk was observed with increasing exposure in all smoking categories and for all three major lung cancer subtypes. In women, lung cancer risk for all subtypes was increased in current smokers (ORs ~two-fold). The joint effect of asbestos exposure and smoking did not deviate from multiplicativity among men, and was more than additive among women.ConclusionsOur results in men showed an excess risk of lung cancer and its subtypes at low cumulative exposure levels, with a steeper exposure-response slope in this exposure range than at higher, previously studied levels. (See video abstract at, http://links.lww.com/EDE/B161.)