scholarly journals Estimation of the mean normal measure from flat sections

2008 ◽  
Vol 40 (01) ◽  
pp. 31-48
Author(s):  
Markus Kiderlen

We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝ d by taking measurements at the intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z if k ≥ 3 or if k = 2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊d / k⌋ + 1. This even holds for almost all m-tuples of k-dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

2008 ◽  
Vol 40 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Markus Kiderlen

We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝd by taking measurements at the intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z if k ≥ 3 or if k = 2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊d / k⌋ + 1. This even holds for almost all m-tuples of k-dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.


2002 ◽  
Vol 34 (3) ◽  
pp. 505-519 ◽  
Author(s):  
Markus Kiderlen

Let be the mean normal measure of a stationary random set Z in the extended convex ring in ℝd. For k ∈ {1,…,d-1}, connections are shown between and the mean of . Here, the mean is understood to be with respect to the random isotropic k-dimensional linear subspace ξk and the mean normal measure of the intersection is computed in ξk. This mean to be well defined, a suitable spherical lifting must be applied to before averaging. A large class of liftings and their resulting means are discussed. In particular, a geometrically motivated lifting is presented, for which the mean of liftings of determines uniquely for any fixed k ∈ {2,…,d-1}.


2002 ◽  
Vol 34 (03) ◽  
pp. 505-519 ◽  
Author(s):  
Markus Kiderlen

Let be the mean normal measure of a stationary random set Z in the extended convex ring in ℝ d . For k ∈ {1,…,d-1}, connections are shown between and the mean of . Here, the mean is understood to be with respect to the random isotropic k-dimensional linear subspace ξ k and the mean normal measure of the intersection is computed in ξ k . This mean to be well defined, a suitable spherical lifting must be applied to before averaging. A large class of liftings and their resulting means are discussed. In particular, a geometrically motivated lifting is presented, for which the mean of liftings of determines uniquely for any fixed k ∈ {2,…,d-1}.


1994 ◽  
Vol 40 (9) ◽  
pp. 1686-1691 ◽  
Author(s):  
M Maes ◽  
S Scharpé ◽  
I De Meester ◽  
P Goossens ◽  
A Wauters ◽  
...  

Abstract We investigated the components of biological variation in plasma prolyl endopeptidase (PEP; EC 3.4.21.26) and dipeptidyl-peptidase IV (DPP IV; EC 3.4..14.5) activity in healthy individuals. We took monthly blood samples from 26 healthy volunteers for determination of plasma PEP and DPP IV activity during one calendar year. The estimated CVs for PEP activity were: total (CVt) = 25.0%, interindividual (CVg) = 13.9%, and intraindividual (CVi) = 16.8%. There was a statistically significant (P < 0.0001) seasonal pattern in plasma PEP activity, with significantly higher values in the fall than in the other seasons. The peak-trough difference in the yearly variation in PEP activity, expressed as a percentage of the mean, was as high as 56.8%. The estimated CVs for DPP IV activity were: CVt = 17.1%, CVg = 14.5%, and CVi = 8.2%. DPP IV activity was significantly (P < 0.0001) higher in summer than in the other seasons but the amplitude of the yearly variation was small.


VLSI Design ◽  
1999 ◽  
Vol 9 (3) ◽  
pp. 237-251 ◽  
Author(s):  
Raghunandan Rajan ◽  
Radharamanan Radhakrishnan ◽  
Philip A. Wilsey

The performance of Time Warp parallel discrete event simulators can be affected by the cancellation strategy used to send anti-messages. Under aggressive cancellation, antimessage generation occurs immediately after a straggler message is detected. In contrast, lazy cancellation delays the sending of anti-messages until forward processing from a straggler message confirms that the premature computation did indeed generate an incorrect message. Previous studies have shown that neither approach is clearly superior to the other in all cases (even within the same application domain). Furthermore, no strategy exists to make a priori determination of the more favorable cancellation strategy. Most existing Time Warp systems merely provide a switch for the user to select the cancellation strategy employed. This paper explores the use of simulation time decision procedures to select cancellation strategies. The approach is termed Dynamic Cancellation and it assigns the capability for selecting cancellation strategies to the Logical Processes (LPs) in a Time Warp simulation. Thus, within a single parallel simulation both strategies may be employed by distinct LPs and even across the simulation lifetime of an LP. Empirical analysis using several control strategies show that dynamic cancellation always performs with the best static strategy and, in some cases, dynamic cancellation provides some nominal (5–10%) performance gain over the best static strategy.


1972 ◽  
Vol 50 (2) ◽  
pp. 217-225 ◽  
Author(s):  
A. M. Bize ◽  
J. Soussen-Jacob ◽  
J. Vincent-Geisse ◽  
D. Legay ◽  
J. P. Perchard

The band width and profile of v3 mode of carbonyl sulfide (OCS) dissolved in about 30 solvents have been examined. The study of temperature broadening permits the separation of the vibrational and rotational effects and the determination of the potential barrier to rotation. Correlation functions have been plotted from the experimental results; the mean squared torques acting on carbonyl sulfide in various solvents have been calculated from the second and the fourth moments. The obtained results bear evidence of a dominant rotational effect for solutions in saturated hydrocarbons while, for the other solvents, vibrational broadening proves important.


1869 ◽  
Vol 17 ◽  
pp. 426-427

The observations made by the author were of the three usual elements —the Dip, Declination, and Intensity of the Horizontal Component of the Force. They were taken with instruments supplied to the Colaba Observatory in the year 1867 through the Kew Committee of the British Association, after having been tested at the Kew Observatory. The dip-circle was made by Barrow of London, and is furnished with two needles; the other instrument, the unifilar magnetometer, which serves both for observations of declination and horizontal force, was made by Elliott Brothers of London. The results of the observations for dip only have as yet been received from the author. A complete observation consists of thirty-two readings, each end of the needle being read twice in each different position of the needle and circle; and the mean of the thirty-two is taken as the result of the observation. The observations were 178 in number, commencing on the 29th of April 1867, and extending to the 29th of December 1868. They were generally taken, with the two needles alternately, on particular days of the week. Up to August 17, 1867, the observations commenced with either end (A or B) of the needle dipping, and without remagnetizing the needle; i. e . the magnetization for the latter half of one observation was made to serve for the first half of the next observation with the same needle, the two needles having been kept during the interval with contrary poles adjacent in a zinc box; but after August 17, 1867, the needle was always remagnetized, so as to make the end A dip during the first half of the observation. The effect of this change of practice was to produce a marked increase in the accordance of successive observations. Tables are given containing every complete observation made up to the end of 1868, and showing, as well as the mean dip, the partial results in each position of the circle, and with each end of the needle dipping, and also the mean weekly and mean monthly values. The mean dip obtained for the months April to December 1867 was 19° 2'.00, and for the year 1868 was 19° 3'.87. The period embraced by the observations is too limited to allow of an exact determination of the rate of secular change; nevertheless the observations show distinctly that the dip is increasing. The author takes + l'.3 as the rate of annual change.


2002 ◽  
Vol 85 (3) ◽  
pp. 744-750 ◽  
Author(s):  
Mauricio Boscolo ◽  
Luiz G Andrade-Sobrinho ◽  
Benedito S Lima-Neto ◽  
Douglas W Franco ◽  
Marcia Miguel Castro Ferreira

Abstract A new methodology was developed for determination of caramel in spirits aged in oak casks. The method is based on differences between the electronic spectra of oak aqueous alcoholic extracts and caramel solutions in the same solvent. The data were treated by 2 different approaches: the simplest one was based on the plot of caramel concentration versus the ratio of absorbance at 210 and 282 nm; the other was based on a partial least squares (PLS) calibration model using the first derivative of the spectral data. Both methodologies were applied to analysis of 159 aged spirit samples. The mean caramel content of several Brazilian sugar cane spirits (cachaça) and all United States whiskies was smaller than that of Scottish whiskies and other brandies from several countries. Correlation was good between caramel concentrations for the same sample calculated by the 2 methods. The uncertainties following PLS and the absorbance ratio method were 0.01 and 0.03 g/L, respectively, for a sample containing 0.45 g/L caramel. Treatment of UV-VIS spectra by pattern recognition using hierarchical clustering analysis and principal components analysis allowed discrimination of the samples as a function of their caramel content. It was possible to distinguish U.S. whiskies from other whiskies, but a clear differentiation among Brazilian cachaças as a function of their geographic origin was not feasible. Small caramel quantities as low as 0.08 g/L were clearly detected by these methodologies.


1977 ◽  
Vol 9 (1-2) ◽  
pp. 84-104 ◽  
Author(s):  
Maria Amélia Cabral ◽  
Jorge Afonso Garcia

The study and analysis of the various factors influencing insurance risks constitutes an intricate and usually quite extensive problem. We have to consider on the one hand the nature and heterogeneity of the elements we have been able to measure, and on the other the problem of deciding—without knowing exactly what results to expect—on the types of analysis to carry out and the form in which to present the results.These difficulties, essentially stemming from the fact that we cannot easily define “a priori” a measure of influence, can be overcome only by using highly sophisticated mathematical models. The researcher must define his objectives clearly if he is to avoid spending too much of his time in exploring such models.Either for these reasons or for lack of our experience in this field we were led to the study of three models, presenting entirely different characteristics though based on the analysis and behaviour of mean value fluctuations, measured by their variances or by the least-squares method.Our first model, described in II. 1, associates the notion of influence with the notion of variance. It analyses in detail the alteration of the mean values variance, when what we refer to as a “margination” is executed in the parameter space, taking each of the parameters in turn. We start off by having n distinct parameters, reducing them by one with each step.


2011 ◽  
Vol 25 (3) ◽  
pp. 129
Author(s):  
Thordis Linda Thorarinsdottir

In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.


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