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

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figure

Escape Rates and Physically Relevant Measures for Billiards with Small Holes

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure

Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I

We explore how well crowded field point-source photometry can be accomplished with SDSS data: We present a photometric pipeline based on DoPhot, and tuned for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations we show that the completeness of source extraction is above 80% to i < 21 (AB) and a stellar surface density of about 200 sq.amin. Hence, a specialized data pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS images, where the standard SDSS photometric package Photo, when applied in normal survey mode, gives poor results. We apply our pipeline to an area of about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and construct a high S/N star-count map of Leo I via an optimized filter in color-magnitude space (g,r,i). Although the radial surface-density profile of the dwarf deviates from the best fit empirical King model towards outer radii, we find no evidence for tidal debris out to a stellar surface-density of 4*10^(-3) of the central value. We determine the total luminosity of Leo I, and model its mass using the spherical and isotropic Jeans equation. Assuming that 'mass follows light' we constrain a lower limit of the total mass of the dSph to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a constant density dark-matter (DM) halo, then the mass within the central 12' is (2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and possibly >75 if the DM halo dominates the mass and extends further out than 12'. In summary, our results show that Leo I is a symmetric, relaxed and bound system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A

Проблема коррупции в современном обществе

Abstract Background Agricultural workers may be exposed to potential carcinogens including pesticides, sensitizing agents and solar radiation. Previous studies indicate increased risks of hematopoietic cancers and decreased risks at other sites, possibly due to differences in lifestyle or risk behaviours. We present findings from CanCHEC (Canadian Census Health and Environment Cohort), the largest national population-based cohort of agricultural workers. Methods Statistics Canada created the cohort using deterministic and probabilistic linkage of the 1991 Canadian Long Form Census to National Cancer Registry records for 1992–2010. Self-reported occupations were coded using the Standard Occupational Classification (1991) system. Analyses were restricted to employed persons aged 25–74 years at baseline (N = 2,051,315), with follow-up until December 31, 2010. Hazard ratios (HR) and 95% confidence intervals (CI) were modeled using Cox proportional hazards for all workers in agricultural occupations (n = 70,570; 70.8% male), stratified by sex, and adjusted for age at cohort entry, province of residence, and highest level of education. Results A total of 9515 incident cancer cases (7295 in males) occurred in agricultural workers. Among men, increased risks were observed for non-Hodgkin lymphoma (HR = 1.10, 95% CI = 1.00–1.21), prostate (HR = 1.11, 95% CI = 1.06–1.16), melanoma (HR = 1.15, 95% CI = 1.02–1.31), and lip cancer (HR = 2.14, 95% CI = 1.70–2.70). Decreased risks in males were observed for lung, larynx, and liver cancers. Among female agricultural workers there was an increased risk of pancreatic cancer (HR = 1.36, 95% CI = 1.07–1.72). Increased risks of melanoma (HR = 1.79, 95% CI = 1.17–2.73), leukemia (HR = 2.01, 95% CI = 1.24–3.25) and multiple myeloma (HR = 2.25, 95% CI = 1.16–4.37) were observed in a subset of female crop farmers. Conclusions Exposure to pesticides may have contributed to increased risks of hematopoietic cancers, while increased risks of lip cancer and melanoma may be attributed to sun exposure. The array of decreased risks suggests reduced smoking and alcohol consumption in this occupational group compared to the general population

Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography

We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel Au-Ag micro patterned template stripped surface. DNA arrays have been investigated by atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) showing that the patterned template stripped substrate enables easy retrieval of the DPN-functionalized zone with a standard optical microscope permitting a multi-instrument and multi-technique local detection and analysis. Moreover the smooth surface of the Au squares (abput 5-10 angstrom roughness) allows to be sensitive to the hybridization of the oligonucleotide array with label-free target DNA. Our Au-Ag substrates, combining the retrieving capabilities of the patterned surface with the smoothness of the template stripped technique, are candidates for the investigation of DPN nanostructures and for the development of label free detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted

The distance to the Leo I dwarf spheroidal galaxy from the Red Giant Branch Tip

We present V and I photometry of a 9.4 arcmin X 9.4 arcmin field centered on the dwarf spheroidal galaxy Leo I. The I magnitude of the tip of the Red Giant Branch is robustly estimated from two different datasets (I^{TRGB}=17.97 +0.05/-0.03). From this estimate, adopting [M/H]=-1.2 from the comparison of RGB stars with Galactic templates, we obtain a distance modulus (m-M)_0=22.02 +/- 0.13, corresponding to a distance D=254 +16/-19 Kpc.Comment: 6 pages, 5 figures, Fig. 1 and 2 provided in low resolution version. Latex. Accepted for publication by MNRA