Median inverse problem and approximating the number of kk-median inverses of a permutation

We introduce the "Median Inverse Problem" for metric spaces. In particular, having a permutation $\pi$ in the symmetric group $S_n$ (endowed with the breakpoint distance), we study the set of all $k$-subsets $\{x_1,...,x_k\}\subset S_n$ for which $\pi$ is a breakpoint median. The set of all $k$-tuples $(x_1,...,x_k)$ with this property is called the $k$-median inverse of $\pi$. Finding an upper bound for the cardinality of this set, we provide an asymptotic upper bound for the probability that $\pi$ is a breakpoint median of $k$ permutations $\xi_1^{(n)},...,\xi_k^{(n)}$ chosen uniformly and independently at random from $S_n$

Genome reorganization in different cancer types: detection of cancer specific breakpoint regions

Background: Tumorigenesis is a multi-step process which is accompanied by substantial changes in genome organization. The development of these changes is not only a random process, but rather comprise specific DNA regions that are prone to the reorganization process. Results: We have analyzed previously published SNP arrays from three different cancer types (pancreatic adenocarcinoma, breast cancer and metastatic melanoma) and from non-malignant control samples. We calculated segmental copy number variations as well as breakpoint regions. Some of these regions were not randomly involved in genome reorganization since we detected fifteen of them in at least 20% of all tumor samples and one region on chromosome 9 where 43% of tumors have a breakpoint. Further, the top-15 breakpoint regions show an association to known fragile sites. The relevance of these common breakpoint regions was further confirmed by analyzing SNP arrays from 917 cancer cell lines. Conclusion: Our analyses suggest that genome reorganization is common in tumorigenesis and that some breakpoint regions can be found across all cancer types, while others exclusively occur in specific entities

Thermal stability of some aircraft turbine fuels derived from oil shale and coal

Thermal stability breakpoint temperatures are shown for 32 jet fuels prepared from oil shale and coal syncrudes by various degrees of hydrogenation. Low severity hydrotreated shale oils, with nitrogen contents of 0.1 to 0.24 weight percent, had breakpoint temperatures in the 477 to 505 K (400 to 450 F) range. Higher severity treatment, lowering nitrogen levels to 0.008 to 0.017 weight percent, resulted in breakpoint temperatures in the 505 to 533 K (450 to 500 F) range. Coal derived fuels showed generally increasing breakpoint temperatures with increasing weight percent hydrogen, fuels below 13 weight percent hydrogen having breakpoints below 533 K (500 F). Comparisons are shown with similar literature data

Structure of the breakpoint region in CVC of the intrinsic Josephson junctions

A fine structure of the breakpoint region in the current-voltage characteristics of the coupled intrinsic Josephson junctions in the layered superconductors is found. We establish a correspondence between the features in the current-voltage characteristics and the character of the charge oscillations in superconducting layers in the stack and explain the origin of the breakpoint region structure.Comment: 5 pages, 5 figures. Accepted for Phys.Rev.

Experimental observation of the longitudinal plasma excitation in intrinsic Josephson junctions

We have investigated the current-voltage characteristics (IVCs) of intrinsic Josephson junctions (IJJs). Recently, it is predicted that the longitudinal plasma wave can be excited by the parametric resonance in IJJs. Such an excitation induces a singularity called as breakpoint region around switch back region in the IVC. We have succeeded in the observation of the breakpoint region in the IVC of the mesa with 5 IJJs at 4.2 K. Furthermore, it is found that the temperature dependence of the breakpoint current is in agreement with the theoretical prediction. This suggests that the wave number of the excited plasma wave varies with temperature.Comment: 7 pages, 7 figures. Dubna-Nano2008, Accepted for JPCS

Statistics of Solar Wind Electron Breakpoint Energies Using Machine Learning Techniques

Solar wind electron velocity distributions at 1 au consist of a thermal "core" population and two suprathermal populations: "halo" and "strahl". The core and halo are quasi-isotropic, whereas the strahl typically travels radially outwards along the parallel and/or anti-parallel direction with respect to the interplanetary magnetic field. With Cluster-PEACE data, we analyse energy and pitch angle distributions and use machine learning techniques to provide robust classifications of these solar wind populations. Initially, we use unsupervised algorithms to classify halo and strahl differential energy flux distributions to allow us to calculate relative number densities, which are of the same order as previous results. Subsequently, we apply unsupervised algorithms to phase space density distributions over ten years to study the variation of halo and strahl breakpoint energies with solar wind parameters. In our statistical study, we find both halo and strahl suprathermal breakpoint energies display a significant increase with core temperature, with the halo exhibiting a more positive correlation than the strahl. We conclude low energy strahl electrons are scattering into the core at perpendicular pitch angles. This increases the number of Coulomb collisions and extends the perpendicular core population to higher energies, resulting in a larger difference between halo and strahl breakpoint energies at higher core temperatures. Statistically, the locations of both suprathermal breakpoint energies decrease with increasing solar wind speed. In the case of halo breakpoint energy, we observe two distinct profiles above and below 500 km/s. We relate this to the difference in origin of fast and slow solar wind.Comment: Published in Astronomy & Astrophysics, 11 pages, 10 figure

Study of charge-phase diagrams for coupled system of Josephson junctions

Dynamics of stacked intrinsic Josephson junctions (IJJ) in the high-Tc superconductors is theoretically investigated. We calculate the current-voltage characteristics (CVC) of IJJ and study the breakpoint region on the outermost branch of the CVC for the stacks with 9 IJJ. A method for investigation of the fine structure in CVC of IJJ based on the recording the "phase-charge" diagrams is suggested. It is demonstrated that this method reflects the main features of the breakpoint region.Comment: Dubna-Nano2010 conference : http://theor.jinr.ru/~nano10/ will be published online in Journal of Physics: Conference serie