Stochastic models which separate fractal dimension and Hurst effect

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure

The effect of exogenous glucose infusion on early embryonic development in lactating dairy cows

peer-reviewedThe objective of this study was to examine the effect of intravenous infusion of glucose on early embryonic development in lactating dairy cows. Nonpregnant, lactating dairy cows (n = 12) were enrolled in the study (276 ± 17 d in milk). On d 7 after a synchronized estrus, cows were randomly assigned to receive an intravenous infusion of either 750 g/d of exogenous glucose (GLUC; 78 mL/h of 40% glucose wt/vol) or saline (CTRL; 78 mL/h of 0.9% saline solution). The infusion period lasted 7 d and cows were confined to metabolism stalls for the duration of the study. Coincident with the commencement of the infusion on d 7 after estrus, 15 in vitro-produced grade 1 blastocysts were transferred into the uterine horn ipsilateral to the corpus luteum. All animals were slaughtered on d 14 to recover conceptuses, uterine fluid, and endometrial tissue. Glucose infusion increased circulating glucose concentrations (4.70 ± 0.12 vs. 4.15 ± 0.12 mmol/L) but did not affect milk production or dry matter intake. Circulating β-hydroxybutyrate concentrations were decreased (0.51 ± 0.01 vs. 0.70 ± 0.01 mmol/L for GLUC vs. CTRL, respectively) but plasma fatty acids, progesterone, and insulin concentrations were unaffected by treatment. Treatment did not affect either uterine lumen fluid glucose concentration or the mRNA abundance of specific glucose transporters in the endometrium. Mean conceptus length, width, and area on d 14 were reduced in the GLUC treatment compared with the CTRL treatment. A greater proportion of embryos in the CTRL group had elongated to all length cut-off measurements between 11 and 20 mm (measured in 1-mm increments) compared with the GLUC treatment. In conclusion, infusion of glucose into lactating dairy cows from d 7 to d 14 post-estrus during the critical period of conceptus elongation had an adverse impact on early embryonic development

Superflares on Ordinary Solar-Type Stars

Short duration flares are well known to occur on cool main-sequence stars as well as on many types of `exotic' stars. Ordinary main-sequence stars are usually pictured as being static on time scales of millions or billions of years. Our sun has occasional flares involving up to $\sim 10^{31}$ ergs which produce optical brightenings too small in amplitude to be detected in disk-integrated brightness. However, we identify nine cases of superflares involving $10^{33}$ to $10^{38}$ ergs on normal solar-type stars. That is, these stars are on or near the main-sequence, are of spectral class from F8 to G8, are single (or in very wide binaries), are not rapid rotators, and are not exceedingly young in age. This class of stars includes many those recently discovered to have planets as well as our own Sun, and the consequences for any life on surrounding planets could be profound. For the case of the Sun, historical records suggest that no superflares have occurred in the last two millennia.Comment: 16 pages, accepted for publication in Ap

Lithium in a Short-Period Tidally Locked Binary of M67: Implications for Stellar Evolution, Galactic Lithium Evolution, and Cosmology

In open clusters, late-F stars exhibit a Li maximum (the Li \u27peak\u27 region) at lower abundance with age, which could be due either to stellar depletion or Galactic Li enrichment (or some other cause). We have observed a short-period tidally locked binary (SPTLB) on the Li peak region in the old cluster M67 to distinguish between alternatives. SPTLBs which synchronized in the early pre-main sequence would avoid the rotational mixing which, according to Yale models, may be responsible for depleting Li with age in open cluster dwarfs. We find that both components of the M67 SPTLB have a Li abundance lying about a factor of 2 or more above any other M67 single star and about a factor of 3 or more above the mean Li peak region abundance in M67. Our results suggest that the initial Li abundance in M67 is at least as high as approximately 3.0 = 12 + log (NLi/NH). Our high M67 SPTLB Li abundance and those in other clusters support the combination of Zahn\u27s tidal circularization and the Yale rotational mixing theories and may indicate that the halo Li plateau (analogous to the cluster Li peak region) abundance has been depleted from a higher primordial value. Implications are discussed

Total anomalous pulmonary venous connection: Results of surgical repair of 100 patients at a single institution

ObjectiveSurgical repair of total anomalous pulmonary venous connection is associated with significant mortality and morbidity, especially in patients with single-ventricle physiology. This study analyzes total anomalous pulmonary venous connection surgical repair results at one institution to identify trends and indicators of positive outcome.MethodsOur cardiac surgery database identified 100 patients undergoing surgical repair of total anomalous pulmonary venous connection (1990–2008): supracardiac (52), cardiac (15), infracardiac (23), and mixed (10). The median age at repair was 14.6 days (range, 0–4 years), and the median weight was 3.5 kg (range, 1.3–15 kg). Patients were divided into 2 groups: biventricular (n = 83) or single-ventricle (n = 17) physiology. All but 1 of the patients with single-ventricle physiology had heterotaxy syndrome (94%), and 13 of 17 patients had supracardiac anatomy.ResultsThere were 12 operative deaths (4 in the biventricular group [5%] and 8 in the single-ventricle group [47%], P < .01) and 9 late deaths (6 in the biventricular group [7%] and 3 in the single-ventricle group [18%], P < .05). Death by total anomalous pulmonary venous connection type was supracardiac (12/52; 23.1%), cardiac (1/15; 6.7%), infracardiac (3/23; 13.0%), and mixed (5/10; 50%). Pulmonary venous obstruction was present in 22 patients in the biventricular group (27%) and in 7 patients in the single-ventricle group (41%; P = .25). Mortality was 9 of 29 (31%) in those with pulmonary venous obstruction and 12 of 71 (17%) in those with nonpulmonary venous obstruction (P = .23). Deep hypothermic circulatory arrest was used in 38 patients (27 in the biventricular group, 32.5%; 11 in the single-ventricle group, 64.7%). Mean deep hypothermic circulatory arrest time was 31.4 ± 10.7 minutes (P = not significant between groups). Median postoperative length of stay was 11 days (range, 0–281 days). Nineteen patients required reoperation for pulmonary venous stenosis (14 in the biventricular group and 5 in the single-ventricle group. P = .045); the median time to reoperation was 104 days (range, 4–753 days).ConclusionPatients with total anomalous pulmonary venous connection with biventricular anatomy have good outcomes. Patients with single-ventricle anatomy have higher mortality and increased risk for pulmonary vein stenosis requiring reoperation. Mortality is highest in patients with mixed-type total anomalous pulmonary venous connection

Length functions on currents and applications to dynamics and counting

The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of projective geodesic currents with uniform north-south dynamics.Comment: 35pp, 2 figures, comments welcome! Second version: minor corrections. To appear as a chapter in the forthcoming book "In the tradition of Thurston" edited by V. Alberge, K. Ohshika and A. Papadopoulo

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Collective and independent-particle motion in two-electron artificial atoms

Investigations of the exactly solvable excitation spectra of two-electron quantum dots with a parabolic confinement, for different values of the parameter R_W expressing the relative magnitudes of the interelectron repulsion and the zero-point kinetic energy of the confined electrons, reveal for large R_W a remarkably well-developed ro-vibrational spectrum associated with formation of a linear trimeric rigid molecule composed of the two electrons and the infinitely heavy confining dot. This spectrum transforms to one characteristic of a "floppy" molecule for smaller values of R_W. The conditional probability distribution calculated for the exact two-electron wave functions allows for the identification of the ro-vibrational excitations as rotations and stretching/bending vibrations, and provides direct evidence pertaining to the formation of such molecules.Comment: Published version. Latex/Revtex, 5 pages with 2 postscript figures embedded in the text. For related papers, see http://www.prism.gatech.edu/~ph274c

Smoking status in relation to serum folate and dietary vitamin intake

Objective Cigarette smoke itself is an abundant source of free radicals and a major cause of oxidative stress, to which plasma antioxidants function as a vital protective and counterbalancing mechanism. The objective of this study was to investigate into the relationship between smoking status and serum and dietary micronutrient concentrations. Design Cross-sectional study Subjects ' Setting 502 farmers from the Valley of Messara in Crete were randomly selected and examined. Complete three-day and 24-hr recall questionnaires were collected along with anthropometrical, physical activity and clinical data from all participating subjects. Results After adjusting for age, gender and number of fasting days adhered to per year, current smokers were found to have a lower dietary intake of vitamin C (112.1 mg vs. 136.4 mg, p = 0.03), fibre (16.6 g vs. 19.1 g, p = 0.006) and fruits and vegetables (339 g vs. 412 g, p = 0.014), while dietary vitamin B1 intake was found to be higher (1.7 mg vs. 1.4 mg, p = 0.02) in comparison to non/ex smokers. Dietary intake of meat, folate and vitami A, E, B2, B6 and B12 did not differ between the groups. Controlling age, gender, fasting days and dietary micronutrient intake, serum folate levels were found to be lower among smokers (geometric mean 15.3 nmol/L vs. 17.7 nmol/L, p = 0.023), while serum iron and vitamin B12 levels were not affected by smoking status. Conclusion Current smoking status affects dietary nutrient intake as well as plasma folate levels. The above coherence between antioxidant depletion and reduced antioxidant intake may predispose smokers to the premature development of tobacco related mortality and morbidity