Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

L2−estimates for the DG IIPG-0 scheme

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions.

Inter-informant agreement and prevalence estimates for mood syndromes: Direct interview vs. family history method.

BACKGROUND: The use of the family history method is recommended in family studies as a type of proxy interview of non-participating relatives. However, using different sources of information can result in bias as direct interviews may provide a higher likelihood of assigning diagnoses than family history reports. The aims of the present study were to: 1) compare diagnoses for threshold and subthreshold mood syndromes from interviews to those relying on information from relatives; 2) test the appropriateness of lowering the diagnostic threshold and combining multiple reports from the family history method to obtain comparable prevalence estimates to the interviews; 3) identify factors that influence the likelihood of agreement and reporting of disorders by informants. METHODS: Within a family study, 1621 informant-index subject pairs were identified. DSM-5 diagnoses from direct interviews of index subjects were compared to those derived from family history information provided by their first-degree relatives. RESULTS: 1) Inter-informant agreement was acceptable for Mania, but low for all other mood syndromes. 2) Except for Mania and subthreshold depression, the family history method provided significantly lower prevalence estimates. The gap improved for all other syndromes after lowering the threshold of the family history method. 3) Individuals who had a history of depression themselves were more likely to report depression in their relatives. LIMITATIONS: Low proportion of affected individuals for manic syndromes and lack of independence of data. CONCLUSIONS: The higher likelihood of reporting disorders by affected informants entails the risk of overestimation of the size of familial aggregation of depression.

Equidistribution estimates for Fekete points on complex manifolds

We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.

Optimal robust estimates using the Hellinger distance

Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance.We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too.We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates.

Linking temperature estimates and microstructures in deformed polymineralic mantle rocks

To constrain deformation temperatures of mantle shear zones, we studied a strike-slip shear zone (Hilti massif, Semail ophiolite, Oman) and focused on the interaction between microstructural mechanisms and chemical equilibration processes. Quantitative microfabric analysis on harzburgites with different deformation intensity (porphyroclastic tectonite, mylonite, and ultramylonite) was combined with orthopyroxene geothermometry. The average grain size of all phases decreases with decreasing shear zone thickness. Dynamic recrystallization of porphyroclasts in combination with dissolution-precipitation and nucleation result in small-sized, chemically equilibrated pyroxenes. The composition of orthopyroxene was used to calculate deformation temperatures. In the case of the porphyroclastic tectonites, the chemical composition of orthopyroxene has been reset by diffusion yielding temperature estimates of 880-900 degrees C. The mylonites were deformed by dislocation creep of olivine and show a broad range of calculated temperatures, which result from a combination of grain size reduction and inheritance of equilibrium compositions from earlier high-temperature events and diffusion. In mylonites, diffusion profiles combined with geothermometry and grain size analysis indicate a mylonitic deformation temperature of 800-900 degrees C possibly followed by diffusion. In ultramylonites, the smallest grains (<30 mu m) reveal equilibration at temperatures of similar to 700 degrees C during the last stages of ductile deformation, which was dominated by diffusion creep of olivine. Our results provide a crucial link between temperature and evolution of microstructures from dislocation creep to diffusion creep in mantle shear zones.

Estimates of electronic coupling for excess electron transfer in DNA

Electronic coupling Vda is one of the key parameters that determine the rate of charge transfer through DNA. While there have been several computational studies of Vda for hole transfer, estimates of electronic couplings for excess electron transfer (ET) in DNA remain unavailable. In the paper, an efficient strategy is established for calculating the ET matrix elements between base pairs in a π stack. Two approaches are considered. First, we employ the diabatic-state (DS) method in which donor and acceptor are represented with radical anions of the canonical base pairs adenine-thymine (AT) and guanine-cytosine (GC). In this approach, similar values of Vda are obtained with the standard 6-31 G* and extended 6-31++ G* basis sets. Second, the electronic couplings are derived from lowest unoccupied molecular orbitals (LUMOs) of neutral systems by using the generalized Mulliken-Hush or fragment charge methods. Because the radical-anion states of AT and GC are well reproduced by LUMOs of the neutral base pairs calculated without diffuse functions, the estimated values of Vda are in good agreement with the couplings obtained for radical-anion states using the DS method. However, when the calculation of a neutral stack is carried out with diffuse functions, LUMOs of the system exhibit the dipole-bound character and cannot be used for estimating electronic couplings. Our calculations suggest that the ET matrix elements Vda for models containing intrastrand thymine and cytosine bases are essentially larger than the couplings in complexes with interstrand pyrimidine bases. The matrix elements for excess electron transfer are found to be considerably smaller than the corresponding values for hole transfer and to be very responsive to structural changes in a DNA stack

Determining the best population-level alcohol consumption model and its impact on estimates of alcohol-attributable harms.

BACKGROUND: The goals of our study are to determine the most appropriate model for alcohol consumption as an exposure for burden of disease, to analyze the effect of the chosen alcohol consumption distribution on the estimation of the alcohol Population- Attributable Fractions (PAFs), and to characterize the chosen alcohol consumption distribution by exploring if there is a global relationship within the distribution. METHODS: To identify the best model, the Log-Normal, Gamma, and Weibull prevalence distributions were examined using data from 41 surveys from Gender, Alcohol and Culture: An International Study (GENACIS) and from the European Comparative Alcohol Study. To assess the effect of these distributions on the estimated alcohol PAFs, we calculated the alcohol PAF for diabetes, breast cancer, and pancreatitis using the three above-named distributions and using the more traditional approach based on categories. The relationship between the mean and the standard deviation from the Gamma distribution was estimated using data from 851 datasets for 66 countries from GENACIS and from the STEPwise approach to Surveillance from the World Health Organization. RESULTS: The Log-Normal distribution provided a poor fit for the survey data, with Gamma and Weibull distributions providing better fits. Additionally, our analyses showed that there were no marked differences for the alcohol PAF estimates based on the Gamma or Weibull distributions compared to PAFs based on categorical alcohol consumption estimates. The standard deviation of the alcohol distribution was highly dependent on the mean, with a unit increase in alcohol consumption associated with a unit increase in the mean of 1.258 (95% CI: 1.223 to 1.293) (R2 = 0.9207) for women and 1.171 (95% CI: 1.144 to 1.197) (R2 = 0. 9474) for men. CONCLUSIONS: Although the Gamma distribution and the Weibull distribution provided similar results, the Gamma distribution is recommended to model alcohol consumption from population surveys due to its fit, flexibility, and the ease with which it can be modified. The results showed that a large degree of variance of the standard deviation of the alcohol consumption Gamma distribution was explained by the mean alcohol consumption, allowing for alcohol consumption to be modeled through a Gamma distribution using only average consumption.

Global alcohol exposure estimates by country, territory and region for 2005--a contribution to the Comparative Risk Assessment for the 2010 Global Burden of Disease Study.

AIMS: This study aimed to estimate the prevalence of life-time abstainers, former drinkers and current drinkers, adult per-capita consumption of alcohol and pattern of drinking scores, by country and Global Burden of Disease region for 2005, and to forecast these indicators for 2010. DESIGN: Statistical modelling based on survey data and routine statistics. SETTING AND PARTICIPANTS: A total of 241 countries and territories. MEASUREMENTS: Per-capita consumption data were obtained with the help of the World Health Organization's Global Information System on Alcohol and Health. Drinking status data were obtained from Gender, Alcohol and Culture: An International Study, the STEPwise approach to Surveillance study, the World Health Survey/Multi-Country Study and other surveys. Consumption and drinking status data were triangulated to estimate alcohol consumption across multiple categories. FINDINGS: In 2005 adult per-capita annual consumption of alcohol was 6.1 litres, with 1.7 litres stemming from unrecorded consumption; 17.1 litres of alcohol were consumed per drinker, 45.8% of all adults were life-time abstainers, 13.6% were former drinkers and 40.6% were current drinkers. Life-time abstention was most prevalent in North Africa/Middle East and South Asia. Eastern Europe and Southern sub-Saharan Africa had the most detrimental pattern of drinking scores, while drinkers in Europe (Eastern and Central) and sub-Saharan Africa (Southern and West) consumed the most alcohol. CONCLUSIONS: Just over 40% of the world's adult population consumes alcohol and the average consumption per drinker is 17.1 litres per year. However, the prevalence of abstention, level of alcohol consumption and patterns of drinking vary widely across regions of the world.

Low estimates of dietary acid load are positively associated with bone ultrasound in women older than 75 years of age with a lifetime fracture

Dietary acid load from Western diets may be a risk factor for osteoporosis. It can be estimated by net endogenous acid production (NEAP). No data currently exists for NEAP estimates and bone indices in the very elderly (i.e. > or = 75 y). The aim of this study was to determine the association between NEAP estimates by using the potential renal acid load (PRAL) equation and quantitative bone ultrasound (QUS) measurements at the heel [broadband ultrasound attenuation (BUA)] in Caucasian women. We assessed NEAP and QUS in 401 very elderly Swiss ambulatory women. We evaluated dietary intake and NEAP estimates with a validated FFQ. QUS was measured using Achilles (Lunar). We identified 2 subgroups: 256 women (80.6 y +/- 3; BUA, 96.8 dB/MHz) with a fracture history and the remaining 145 (79.9 y SD 2.9; BUA, 101.7 dB/MHz) without. Women who reported having suffered a fracture had lower BUA (P < 0.001) than nonfractured women but did not differ in nutrient intakes and NEAP. Lower NEAP (P = 0.023) and higher potassium intake (P = 0.033) were correlated with higher BUA, which remained significant even after adjustment for age, BMI, and osteoporosis treatment. BUA was positively correlated with calcium (P = 0.016) and BMI (P < 0.001). Women who reported no fractures had no significant correlations between nutrient intake, NEAP, and BUA. Low nutritional acid load was correlated with higher BUA in very elderly women with a fracture history. Although relatively weak compared with age and BMI, this association was significant and may be an important additional risk factor that might be particularly relevant in frail patients with an already high fracture risk.

A species delimitation approach in the Trochulus sericeus/hispidus complex reveals two cryptic species within a sharp contact zone.

BACKGROUND: Mitochondrial DNA sequencing increasingly results in the recognition of genetically divergent, but morphologically cryptic lineages. Species delimitation approaches that rely on multiple lines of evidence in areas of co-occurrence are particularly powerful to infer their specific status. We investigated the species boundaries of two cryptic lineages of the land snail genus Trochulus in a contact zone, using mitochondrial and nuclear DNA marker as well as shell morphometrics. RESULTS: Both mitochondrial lineages have a distinct geographical distribution with a small zone of co-occurrence. In the same area, we detected two nuclear genotype clusters, each being highly significantly associated to one mitochondrial lineage. This association however had exceptions: a small number of individuals in the contact zone showed intermediate genotypes (4%) or cytonuclear disequilibrium (12%). Both mitochondrial lineage and nuclear cluster were statistically significant predictors for the shell shape indicating morphological divergence. Nevertheless, the lineage morphospaces largely overlapped (low posterior classification success rate of 69% and 78%, respectively): the two lineages are truly cryptic. CONCLUSION: The integrative approach using multiple lines of evidence supported the hypothesis that the investigated Trochulus lineages are reproductively isolated species. In the small contact area, however, the lineages hybridise to a limited extent. This detection of a hybrid zone adds an instance to the rare reported cases of hybridisation in land snails.

Velocity estimates for signal propagation leading to systemic jasmonic acid accumulation in wounded Arabidopsis.

The wound response prohormone jasmonic acid (JA) accumulates rapidly in tissues both proximal and distal to injury sites in plants. Using quantitative liquid chromatography-mass spectrometry after flash freezing of tissues, we found that JA accumulated within 30 s of injury in wounded Arabidopsis leaves (p = 3.5 e(-7)). JA augmentation distal to wounds was strongest in unwounded leaves with direct vascular connections to wounded leaves wherein JA levels increased significantly within 120 s of wounding (p = 0.00027). This gave conservative and statistically robust temporal boundaries for the average velocity of the long distance signal leading to distal JA accumulation in unwounded leaves of 3.4-4.5 cm min(-1). Like JA, transcripts of the JA synthesis gene LIPOXYGENASE2 (LOX2) and the jasmonate response gene JAZ10.3 also accumulated to higher levels in directly interconnected leaves than in indirectly connected leaves. JA accumulation in a lox2-1 mutant plant was initiated rapidly after wounding then slowed progressively compared with the wild type (WT). Despite this, JAZ10.3 expression in the two genotypes was similar. Free cyclopentenone jasmonate levels were similar in both resting WT and lox2-1. In contrast, bound cyclopentenone jasmonates (arabidopsides) were far lower in lox2-1 than in the WT. The major roles of LOX2 are to generate arabidopsides and the large levels of JA that accumulate proximal to the wound. LOX2 is not essential for some of the most rapid events elicited by wounding.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

Nutritional ecology of blowflies (Diptera, Calliphoridae): estimates of critical larval weight for pupation on two different

Under natural environmental conditions, blowflies utilize discrete and ephemeral feeding resources such as decaying carcasses. Competition for food on such feeding substrates is usually very severe, and only the individuals that are capable of attaining the critical larval weight for pupation will be able to survive. This critical weight is hitherto unknown for several blowfly species; therefore, the current work is aimed at obtaining such a critical value for four blowfly species of the genera Chrysomya and Lucilia, deploying two types of feeding substrate, namely, artificial diet and macerated bovine meat. On the whole, the critical weights ranged from 30 to 35 mg. The lowest larval weight which permitted pupation was 30.0 mg for Chrysomya megacephala reared on macerated bovine meat. This species was also the best adapted to pupation at low larval weights in relation to the maximum larval weight for males. Regarding the pupation of females, the best-adapted individual was a C. albiceps specimen exhibiting a critical weight that was equal to 39.20 % of the maximum value obtained. Concerning all the species and diet types, the female individuals exhibited the lowest critical weights that produced viable pupae, probably representing an evolutionary strategy that favoured the survival of females, responsible for the egg formation, contributing to the establishment of future generations. Regarding the loss (in percentage) of adult biomass in relation to the third instar larvae, the females of C. megacephala lost less weight than males in both feeding substrates. On the other hand, such a loss of weight occurred in males of C. albiceps and L. cuprina.