8,667 research outputs found
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 -optimal design in the class of efficient lack of
fit designs for polynomial regression of degree .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 , we consider a game where two players, and ,
alternatingly color edges of in red and in blue respectively. Let be
the maximum number of moves in which is able to keep the red and the blue
subgraphs isomorphic, if plays optimally to destroy the isomorphism. This
value is a lower bound for the duration of any avoidance game on under the
assumption that plays optimally. We prove that if is a path or a cycle
of odd length , then . The lower
bound is based on relations with Ehrenfeucht games from model theory. We also
consider complete graphs and prove that .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 TiO
Oxygen-deficient TiO in the rutile structure as well as the TiO
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) 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-Ti coordination as well as
entangled states, become localized due to site-dependent
electronic correlations. Charge localization and strong orbital polarization
occur in the V-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-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
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