Optimal designs which are efficient for lack of fit tests

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the linear model can be checked are accepted in practice. For important linear regression models such as polynomial regression, optimal designs do not have this property. To get practically attractive designs, we suggest the following strategy. One part of the design points is used to allow one to carry out a lack of fit test with good power for practically interesting alternatives. The rest of the design points are determined in such a way that the whole design is optimal for inference on the unknown parameter in case the lack of fit test does not reject the linear regression model. To solve this problem, we introduce efficient lack of fit designs. Then we explicitly determine the $\mathbf{e}_k$-optimal design in the class of efficient lack of fit designs for polynomial regression of degree $k-1$.Comment: Published at http://dx.doi.org/10.1214/009053606000000597 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Lengths of Symmetry Breaking-Preserving Games on Graphs

Given a graph $G$, we consider a game where two players, $A$ and $B$, alternatingly color edges of $G$ in red and in blue respectively. Let $l(G)$ be the maximum number of moves in which $B$ is able to keep the red and the blue subgraphs isomorphic, if $A$ plays optimally to destroy the isomorphism. This value is a lower bound for the duration of any avoidance game on $G$ under the assumption that $B$ plays optimally. We prove that if $G$ is a path or a cycle of odd length $n$, then $\Omega(\log n)\le l(G)\le O(\log^2 n)$. The lower bound is based on relations with Ehrenfeucht games from model theory. We also consider complete graphs and prove that $l(K_n)=O(1)$.Comment: 20 page

ROSAT HRI catalogue of X-ray sources in the LMC region

All 543 pointed observations of the ROSAT High Resolution Imager (HRI) with exposure times higher than 50 sec in a field of 10 deg x 10 deg covering the Large Magellanic Cloud (LMC) were analyzed. A catalogue was produced containing 397 X-ray sources with their properties measured by the HRI. The list was cross-correlated with the ROSAT Position Sensitive Propotional Counter (PSPC) source catalogue presented by Haberl & Pietsch (1999), the SIMBAD data base, and the TYCHO catalogue. 138 HRI sources are contained in the PSPC catalogue. The spatial resolution of the HRI was higher than that of the PSPC and the source position could be determined with errors mostly smaller than 15 arcsec which are dominated by systematic attitude errors. 94 HRI sources were identified with known objects based on their positional coincidence and X-ray properties. The catalogue contains 39 foreground stars, 24 supernova remnants (SNRs), five supersoft sources (SSSs), nine X-ray binaries (XBs), and nine AGN well known from literature. Another eight sources were identified with known candidates for these source classes. Additional 21 HRI sources are suggested in the present work as candidates for SNR, X-ray binary in the LMC, or background AGN because of their extent, hardness ratios, X-ray to optical flux ratio, or flux variability.Comment: 22 pages, 8 figures, 4 table

Phosphorus Nitride P3N5

Pure, stoichiometric, hydrogen-free, and crystalline phosphorus nitride P3N5 has been obtained for the first time by reaction of (PNCl2)3 and NH4Cl between 770 and 1050 K. The compound has been characterized by elemental analyses, 31P and 15N MAS NMR, EXAFS, IR spectroscopy, X-ray powder diffraction, and electron microscopy. In the solid a three-dimensional cross-linked network structure of corner sharing PN4 tetrahedra has been identified with 2/5 of the nitrogen atoms bonded to three P atoms and 3/5 of the nitrogen atoms bonded to two P atoms. By electron diffraction (ED) and high-resolution transmission electron microscopy (HRTEM) two distinguishable modifications α-P3N5 and β-P3N5 have been identified which differentiate only by the stacking order of identical sheets similar to the polytypes of SiC

Role of RNA Interference (RNAi) in the Moss Physcomitrella patens

RNA interference (RNAi) is a mechanism that regulates genes by either transcriptional (TGS) or posttranscriptional gene silencing (PTGS), required for genome maintenance and proper development of an organism. Small non-coding RNAs are the key players in RNAi and have been intensively studied in eukaryotes. In plants, several classes of small RNAs with specific sizes and dedicated functions have evolved. The major classes of small RNAs include microRNAs (miRNAs) and small interfering RNAs (siRNAs), which differ in their biogenesis. miRNAs are synthesized from a short hairpin structure while siRNAs are derived from long double-stranded RNAs (dsRNA). Both miRNA and siRNAs control the expression of cognate target RNAs by binding to reverse complementary sequences mediating cleavage or translational inhibition of the target RNA. They also act on the DNA and cause epigenetic changes such as DNA methylation and histone modifications. In the last years, the analysis of plant RNAi pathways was extended to the bryophyte Physcomitrella patens, a non-flowering, non-vascular ancient land plant that diverged from the lineage of seed plants approximately 450 million years ago. Based on a number of characteristic features and its phylogenetic key position in land plant evolution P. patens emerged as a plant model species to address basic as well as applied topics in plant biology. Here we summarize the current knowledge on the role of RNAi in P. patens that shows functional overlap with RNAi pathways from seed plants, and also unique features specific to this species

Kolmogorov complexity and the Recursion Theorem

Several classes of DNR functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wtt-compute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of the initial segments of A. Furthermore, A can Turing compute a DNR function iff there is a nontrivial A-recursive lower bound on the Kolmogorov complexity of the initial segements of A. A is PA-complete, that is, A can compute a {0,1}-valued DNR function, iff A can compute a function F such that F(n) is a string of length n and maximal C-complexity among the strings of length n. A solves the halting problem iff A can compute a function F such that F(n) is a string of length n and maximal H-complexity among the strings of length n. Further characterizations for these classes are given. The existence of a DNR function in a Turing degree is equivalent to the failure of the Recursion Theorem for this degree; thus the provided results characterize those Turing degrees in terms of Kolmogorov complexity which do no longer permit the usage of the Recursion Theorem.Comment: Full version of paper presented at STACS 2006, Lecture Notes in Computer Science 3884 (2006), 149--16

Oxygen-vacancy driven electron localization and itinerancy in rutile-based TiO2_2

Oxygen-deficient TiO$_2$ in the rutile structure as well as the Ti$_3$O$_5$ Magn{\'e}li phase is investigated within the charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT). It is shown that an isolated oxygen vacancy (V$_{\rm O}$) in titanium dioxide is not sufficient to metallize the system at low temperatures. In a semiconducting phase, an in-gap state is identified at \varepsilon_{\rm IG}^{\hfill}\sim -0.75\,eV\, in excellent agreement with experimental data. Band-like impurity levels, resulting from a threefold V$_{\rm O}$-Ti coordination as well as entangled $(t_{2g},e_g)$ states, become localized due to site-dependent electronic correlations. Charge localization and strong orbital polarization occur in the V$_{\rm O}$-near Ti ions, which details can be modified by a variation of the correlated subspace. At higher oxygen vacancy concentration, a correlated metal is stabilized in the Magn{\'e}li phase. A V$_{\rm O}$-defect rutile structure of identical stoichiometry shows key differences in the orbital-resolved character and the spectral properties. Charge disproportionation is vital in the oxygen-deficient compounds, but obvious metal-insulator transitions driven or sustained by charge order are not identified.Comment: 11 pages, 11 figure