Quantile based entropy function in past lifetime

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach

The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Evaluation of the cumulative evidence for freedom from BSE in birth cohorts

Substantial resources are used for surveillance of bovine spongiform encephalopathy (BSE) despite an extremely low detection rate, especially in healthy slaughtered cattle. We have developed a method based on the geometric waiting time distribution to establish and update the statistical evidence for BSE-freedom for defined birth cohorts using continued surveillance data. The results suggest that currently (data included till September 2004) a birth cohort of Danish cattle born after March 1999 is free from BSE with probability (power) of 0.8746 or 0.8509, depending on the choice of a model for the diagnostic sensitivity. These results apply to an assumed design prevalence of 1 in 10,000 and account for prevalence heterogeneity. The age-dependent, diagnostic sensitivity for the detection of BSE has been identified as major determinant of the power. The incorporation of heterogeneity was deemed adequate on scientific grounds and led to improved power values. We propose our model as a decision tool for possible future modification of the BSE surveillance and discuss public health and international trade implications.

Use of 16S rRNA-targeted oligonucleotide probes to investigate function and phylogeny of sulphate-reducing bacteria and methanogenic archaea in a UK estuary

Sulphate-reducing bacteria (SRB) and methanogenic archaea (MA) are important anaerobic terminal oxidisers of organic matter. However, we have little knowledge about the distribution and types of SRB and MA in the environment or the functional role they play in situ. Here we have utilised sediment slurry microcosms amended with ecologically significant substrates, including acetate and hydrogen, and specific functional inhibitors, to identify the important SRB and MA groups in two contrasting sites on a UK estuary. Substrate and inhibitor additions had significant effects on methane production and on acetate and sulphate consumption in the slurries. By using specific 16S-targeted oligonucleotide probes we were able to link specific SRB and MA groups to the use of the added substrates. Acetate consumption in the freshwater-dominated sediments was mediated by Methanosarcinales under low-sulphate conditions and Desulfobacter under the high-sulphate conditions that simulated a tidal incursion. In the marine-dominated sediments, acetate consumption was linked to Desulfobacter. Addition of trimethylamine, a non-competitive substrate for methanogenesis, led to a large increase in Methanosarcinales signal in marine slurries. Desulfobulbus was linked to non-sulphate-dependent H-2 consumption in the freshwater sediments. The addition of sulphate to freshwater sediments inhibited methane production and reduced signal from probes targeted to Methanosarcinales and Methanomicrobiales, while the addition of molybdate to marine sediments inhibited Desulfobulbus and Desulfobacterium. These data complement our understanding of the ecophysiology of the organisms detected and make a firm connection between the capabilities of species, as observed in the laboratory, to their roles in the environment. (C) 2003 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.

The full-spectrum correlated-k method for longwave atmospheric radiative transfer using an effective Planck function

The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

Variation in the FFAR1 gene modifies BMI, body composition and plasma lipids but not plasma insulin or Beta-cell function in overweight subjects

Background FFAR1 receptor is a long chain fatty acid G-protein coupled receptor which is expressed widely, but found in high density in the pancreas and central nervous system. It has been suggested that FFAR1 may play a role in insulin sensitivity, lipotoxicity and is associated with type 2 diabetes. Here we investigate the effect of three common SNPs of FFAR1 (rs2301151; rs16970264; rs1573611) on pancreatic function, BMI, body composition and plasma lipids. Methodology/Principal Findings For this enquiry we used the baseline RISCK data, which provides a cohort of overweight subjects at increased cardiometabolic risk with detailed phenotyping. The key findings were SNPs of the FFAR1 gene region were associated with differences in body composition and lipids, and the effects of the 3 SNPs combined were cumulative on BMI, body composition and total cholesterol. The effects on BMI and body fat were predominantly mediated by rs1573611 (1.06 kg/m2 higher (P = 0.009) BMI and 1.53% higher (P = 0.002) body fat per C allele). Differences in plasma lipids were also associated with the BMI-increasing allele of rs2301151 including higher total cholesterol (0.2 mmol/L per G allele, P = 0.01) and with the variant A allele of rs16970264 associated with lower total (0.3 mmol/L, P = 0.02) and LDL (0.2 mmol/L, P<0.05) cholesterol, but also with lower HDL-cholesterol (0.09 mmol/L, P<0.05) although the difference was not apparent when controlling for multiple testing. There were no statistically significant effects of the three SNPs on insulin sensitivity or beta cell function. However accumulated risk allele showed a lower beta cell function on increasing plasma fatty acids with a carbon chain greater than six. Conclusions/Significance Differences in body composition and lipids associated with common SNPs in the FFAR1 gene were apparently not mediated by changes in insulin sensitivity or beta-cell function.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Does high-frequency repetitive transcranial magnetic stimulation produce residual and/or cumulative effects within an experimental session?

A common procedure for studying the effects on cognition of repetitive transcranial magnetic stimulation (rTMS) is to deliver rTMS concurrent with task performance, and to compare task performance on these trials versus on trials without rTMS. Recent evidence that TMS can have effects on neural activity that persist longer than the experimental session itself, however, raise questions about the assumption of the transient nature of rTMS that underlies many concurrent (or "online") rTMS designs. To our knowledge, there have been no studies in the cognitive domain examining whether the application of brief trains of rTMS during specific epochs of a complex task may have effects that spill over into subsequent task epochs, and perhaps into subsequent trials. We looked for possible immediate spill-over and longer-term cumulative effects of rTMS in data from two studies of visual short-term delayed recognition. In 54 subjects, 10-Hz rTMS trains were applied to five different brain regions during the 3-s delay period of a spatial task, and in a second group of 15 subjects, electroencephalography (EEG) was recorded while 10-Hz rTMS was applied to two brain areas during the 3-s delay period of both spatial and object tasks. No evidence for immediate effects was found in the comparison of the memory probe-evoked response on trials that were vs. were not preceded by delay-period rTMS. No evidence for cumulative effects was found in analyses of behavioral performance, and of EEG signal, as a function of task block. The implications of these findings, and their relation to the broader literature on acute vs. long-lasting effects of rTMS, are considered.

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

The importance of moisture distribution for the growth and energetics of mid-latitude systems

A primitive equation model is used to study the sensitivity of baroclinic wave life cycles to the initial latitude-height distribution of humidity. Diabatic heating is parametrized only as a consequence of condensation in regions of large-scale ascent. Experiments are performed in which the initial relative humidity is a simple function of model level, and in some cases latitude bands are specified which are initially relatively dry. It is found that the presence of moisture can either increase or decrease the peak eddy kinetic energy of the developing wave, depending on the initial moisture distribution. A relative abundance of moisture at mid-latitudes tends to weaken the wave, while a relative abundance at low latitudes tends to strengthen it. This sensitivity exists because competing processes are at work. These processes are described in terms of energy box diagnostics. The most realistic case lies on the cusp of this sensitivity. Further physical parametrizations are then added, including surface fluxes and upright moist convection. These have the effect of increasing wave amplitude, but the sensitivity to initial conditions of relative humidity remains. Finally, 'control' and 'doubled CO2' life cycles are performed, with initial conditions taken from the time-mean zonal-mean output of equilibrium GCM experiments. The attenuation of the wave resulting from reduced baroclinicity is more pronounced than any effect due to changes in initial moisture.

A radial basis function network classifier to maximise leave-one-out mutual information

tWe develop an orthogonal forward selection (OFS) approach to construct radial basis function (RBF)network classifiers for two-class problems. Our approach integrates several concepts in probabilisticmodelling, including cross validation, mutual information and Bayesian hyperparameter fitting. At eachstage of the OFS procedure, one model term is selected by maximising the leave-one-out mutual infor-mation (LOOMI) between the classifier’s predicted class labels and the true class labels. We derive theformula of LOOMI within the OFS framework so that the LOOMI can be evaluated efficiently for modelterm selection. Furthermore, a Bayesian procedure of hyperparameter fitting is also integrated into theeach stage of the OFS to infer the l2-norm based local regularisation parameter from the data. Since eachforward stage is effectively fitting of a one-variable model, this task is very fast. The classifier construc-tion procedure is automatically terminated without the need of using additional stopping criterion toyield very sparse RBF classifiers with excellent classification generalisation performance, which is par-ticular useful for the noisy data sets with highly overlapping class distribution. A number of benchmarkexamples are employed to demonstrate the effectiveness of our proposed approach.

A novel interaction between FlnA and Syk regulates platelet ITAM-mediated receptor signaling and function

Filamin A (FlnA) cross-links actin filaments and connects the Von Willebrand factor receptor GPIb-IX-V to the underlying cytoskeleton in platelets. Because FlnA deficiency is embryonic lethal, mice lacking FlnA in platelets were generated by breeding FlnA(loxP/loxP) females with GATA1-Cre males. FlnA(loxP/y) GATA1-Cre males have a macrothrombocytopenia and increased tail bleeding times. FlnA-null platelets have decreased expression and altered surface distribution of GPIbalpha because they lack the normal cytoskeletal linkage of GPIbalpha to underlying actin filaments. This results in approximately 70% less platelet coverage on collagen-coated surfaces at shear rates of 1,500/s, compared with wild-type platelets. Unexpectedly, however, immunoreceptor tyrosine-based activation motif (ITAM)- and ITAM-like-mediated signals are severely compromised in FlnA-null platelets. FlnA-null platelets fail to spread and have decreased alpha-granule secretion, integrin alphaIIbbeta3 activation, and protein tyrosine phosphorylation, particularly that of the protein tyrosine kinase Syk and phospholipase C-gamma2, in response to stimulation through the collagen receptor GPVI and the C-type lectin-like receptor 2. This signaling defect was traced to the loss of a novel FlnA-Syk interaction, as Syk binds to FlnA at immunoglobulin-like repeat 5. Our findings reveal that the interaction between FlnA and Syk regulates ITAM- and ITAM-like-containing receptor signaling and platelet function.