General construction of symmetric parabolic structures

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained in this way. Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors. Finally, we explicitly construct all non-trivial contact geometries with non-complex simple groups of symmetries. We also indicate geometric interpretations of some of them.     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

SiOx precipitate composition in Si,revisited: Discussion closed?

The composition SiO_x of oxide precipitates in Si has been discussed for the past thirty years with experimentally estimated x ‐values ranging between 1 and 2. It is shown that this spread of x ‐values can be explained by calculating the average composition taking into account temperature and anneal time dependent size and shape of the precipitates and the limitations and probing volumes of the various characterization techniques. Hereby it is assumed that the oxygen‐rich (SiO₂?) core of the precipitates is surrounded by a 2 nm thin SiO layer as revealed by recent electron energy loss spectroscopy analyses. For plate‐like precipitates thinner than and for octahedral precipitates smaller than 6 nm, x ≈ 1. For larger precipitates, the central part of the precipitate consists of SiO_x with x close to 2 and the precipitate has an average x between 1 and 1.3 for plate‐like and up to 1.9 for octahedral precipitates. The predicted x ‐values for different precipitate sizes and morphologies, are compared with published experimental data. SiO_x precipitate nucleation and initial growth should be simulated assuming x = 1 and Fourier transform infrared spectra of precipitates assuming a mixture of SiO₂ and amorphous Si. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Bounding the distance among longest paths in a connected graph

It is easy to see that in a connected graph any $2$ longest paths have a vertex in common. For $k\ge 7$, Skupień in 1966 obtained a connected graph in which some $k$ longest paths have no common vertex, but every $k?1$ longest paths have a common vertex. It is not known whether every $3$ longest paths in a connected graph have a common vertex and similarly for 4, 5, and $6$ longest path. Fujita et al. in 2015 give an upper bound on distance among $3$ longest paths in a connected graph. In this paper we give a similar upper bound on distance between $4$ longest paths and also for $k$ longest paths, in general.     

Noisy scale-free networks

The impact of observational noise on the analysis of scale-free networks is studied. Various noise sources are modeled as random link removal, random link exchange and random link addition. Emphasis is on the resulting modifications for the node-degree distribution and for a functional ranking based on betweenness centrality. The implications for estimated gene-expressed networks for childhood acute lymphoblastic leukemia are discussed.     

Ends,tangles and critical vertex sets

We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph is critical if its deletion leaves some infinitely many components each with neighbourhood precisely equal to X. We further provide a concrete separation system whose ?₀‐tangles are precisely the ends plus critical vertex sets. Our tangle compactification is a quotient of Diestel's (denoted by ), and both use tangles to compactify a graph in much the same way as the ends of a locally finite and connected graph compactify it in its Freudenthal compactification. Finally, generalising both Diestel's construction of and our construction of , we show that G can be compactified by every inverse limit of compactifications of the sets of components obtained by deleting a finite set of vertices. Diestel's is the finest such compactification, and our is the coarsest one. Both coincide if and only if all tangles are ends. This answers two questions of Diestel.     

SU(4) Fermi liquid state and spin filtering in a double quantum dot system

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.     

Long alternating paths in bicolored point sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length . We disprove a conjecture of Erd?s by constructing an example without any such path of length greater than .