Large deviations of the empirical volume fraction for stationary Poisson grain models

We study the existence of the (thermodynamic) limit of the scaled cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap W_n|} of the empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the d-dimensional Lebesgue measure. Here \Xi=\bigcup_{i\ge1}(\Xi_i+X_i) denotes a d-dimensional Poisson grain model (also known as a Boolean model) defined by a stationary Poisson process \Pi_{\lambda}=\sum_{i\ge1}\delta_{X_i} with intensity \lambda >0 and a sequence of independent copies \Xi_1,\Xi_2,... of a random compact set \Xi_0. For an increasing family of compact convex sets {W_n, n\ge1} which expand unboundedly in all directions, we prove the existence and analyticity of the limit lim_{n\to\infty}L_n(z) on some disk in the complex plane whenever E\exp{a|\Xi_0|}0. Moreover, closely connected with this result, we obtain exponential inequalities and the exact asymptotics for the large deviation probabilities of the empirical volume fraction in the sense of Cram\'er and Chernoff.Comment: Published at http://dx.doi.org/10.1214/105051604000001007 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^2$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ523 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). arXiv admin note: substantial text overlap with arXiv:1205.504

Central limit theorems for Poisson hyperplane tessellations

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640--656] for intersection points of motion-invariant Poisson line processes in $\mathbb{R}^2$. Our proof is based on Hoeffding's decomposition of $U$-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the ``method of moments'' used in [Adv. in Appl. Probab. 30 (1998) 640--656] to treat the case $d=2$. Moreover, we extend our central limit theorem in several directions. First we consider $k$-flat processes induced by Poisson hyperplane processes in $\mathbb{R}^d$ for $0\le k\le d-1$. Second we derive (asymptotic) confidence intervals for the intensities of these $k$-flat processes and, third, we prove multivariate central limit theorems for the $d$-dimensional joint vectors of numbers of $k$-flats and their $k$-volumes, respectively, in an increasing spherical region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit theorems for functionals on the facets of stationary random tessellations

We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which are induced on the $k$-facets of $X$ ($1\le k\le d-1$) by their intersections with the $(d-1)$-facets of independent and identically distributed motion-invariant tessellations $X_n$ generated within each cell $\Xi_n$ of $X$. The cases of $X$ being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in $W$ are approximately normally distributed when $W$ is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Praxisbaustein: Das Schulparlament (Integrierte Gesamtschule Ernst Bloch, Ludwigshafen, Rheinland-Pfalz)

An der Integrierten Gesamtschule (IGS) Ernst Bloch wurde auf Antrag des Schulelternbeirats in der Gesamtkonferenz vom 16.11.2004 die Einführung eines Schulparlaments für die Dauer von zwei Jahren beschlossen. Im April und Mai des Jahres 2005 wurde auf der Ebene der Jahrgangsstufen in allen Klassen, aus den Gruppen der Klassenelternsprecher und aus den Jahrgangsteams der Lehrkräfte jeweils ein Vertreter für dieses Gremium gewählt. Diese Abgeordneten bilden in Drittelparität zusammen mit den Mitgliedern des Schulausschusses das Plenum des Schulparlaments. Aus diesem Kreis wurde wiederum ein Präsidium gewählt, in dem je zwei Vertreter der Schüler, Eltern und Lehrkräfte arbeiten, d. h. die Sitzungen vorbereiten, protokollieren und leiten. Mit dem Schulparlament wurde eine neue Institution geschaffen, die alle pädagogischen Belange der Schule thematisieren und diskutieren soll und deren Mehrheitsentscheidungen für die Gesamtkonferenz Ratgeber und Stimmungsbarometer sein sollen. Das Material ist eine Veröffentlichung aus der Reihe der „Praxisbausteine“ des BLK-Programms „Demokratie lernen & leben“

Variance asymptotics for the area of planar cylinder processes generated by Brillinger-mixing point processes

We introduce cylinder processes in the plane defined as union sets of dilated straight lines (appearing as mutually overlapping infinitely long strips) generated by a stationary independently marked point process on the real line, where the marks describe the width and orientation of the individual cylinders. We study the behavior of the total area of the union of strips contained in a space-filling window ϱK as ϱ → ∞. In the case the unmarked point process is Brillinger mixing, we prove themean-square convergence of the area fraction of the cylinder process in ϱK. Under stronger versions of Brillinger mixing, we obtain the exact variance asymptotics of the area of the cylinder process in ϱK as ϱ → ∞. Due to the long-range dependence of the cylinder process, this variance increases asymptotically proportionally to ϱ3

Contributions of chemistry and material sciences to the translational research: examples of the current research

Translational research involves basic research, patient-oriented clinical research and population related research targeting to improve sustainably the public-health. New approaches to materials, preventions of disease, diagnostics and therapies access clinical trials in order to enhance steadily the therapeutic success for the affected patients. Essential requirements are the efficient partnership ofphysicians, researches in natural, biomedical and material sciences, and the medical device and pharmaceutical industry as well. Briefly outlined examples of the collaboration between the natural sciences in Tomsk and Muenster (Germany) and an orthopedic clinic and a radiation therapeutic/oncologic department (Muenster, Germany) demonstrate the contribution of chemistry and material sciences to the translational research

Lower and upper bounds for chord power integrals of ellipsoids

Dedicated to Professor Marius Stoka on the occasion of his 80th birthday Copyright c © 2014 Lothar Heinrich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. First we discuss different representations of chord power integrals Ip(K) of any order p ≥ 0 for convex bodies K ⊂ Rd with inner points. Second we derive closed-term expressions of Ip(E(a)) for an ellipsoid E(a) with semi-axes a = (a1,..., ad) in terms of the support function of E(a) and prove upper and lower bounds expressed by the volume and the mean breadth of E(a), respectively. A further inequality conjectured in Davy (1984) is proved for ellipsoids. Some remarks on chord power integrals of superellipsoids and simplices round off the topic

Complete high-quality genome sequence of Clostridium limosum (Hathewaya limosa) isolate 14S0207, recovered from a cow with suspected blackleg in Germany

Clostridium limosum can be found in soil and the intestinal tract of animals. In 2014, C. limosum was isolated from a suspected blackleg outbreak in cattle in Schleswig-Holstein, Germany. We present a complete genome sequence of a C. limosum strain represented by a circular chromosome and three plasmids