Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

On Possible Measurement of Gravitational Interaction Parameters on Board a Satellite

The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is discussed and further developed. Various particle trajectories near a heavy ball are numerically simulated. Some basic sources of error are analysed. The $G$ measurement procedure is modelled by noise insertion to a ``true'' trajectory. It is concluded that the present knowledge of $G, \alpha$ (for $\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of magnitude.Comment: (only two misprints on title page) 7 page

Recovering rearranged cancer chromosomes from karyotype graphs

BACKGROUND: Many cancer genomes are extensively rearranged with highly aberrant chromosomal karyotypes. Structural and copy number variations in cancer genomes can be determined via abnormal mapping of sequenced reads to the reference genome. Recently it became possible to reconcile both of these types of large-scale variations into a karyotype graph representation of the rearranged cancer genomes. Such a representation, however, does not directly describe the linear and/or circular structure of the underlying rearranged cancer chromosomes, thus limiting possible analysis of cancer genomes somatic evolutionary process as well as functional genomic changes brought by the large-scale genome rearrangements. RESULTS: Here we address the aforementioned limitation by introducing a novel methodological framework for recovering rearranged cancer chromosomes from karyotype graphs. For a cancer karyotype graph we formulate an Eulerian Decomposition Problem (EDP) of finding a collection of linear and/or circular rearranged cancer chromosomes that are determined by the graph. We derive and prove computational complexities for several variations of the EDP. We then demonstrate that Eulerian decomposition of the cancer karyotype graphs is not always unique and present the Consistent Contig Covering Problem (CCCP) of recovering unambiguous cancer contigs from the cancer karyotype graph, and describe a novel algorithm CCR capable of solving CCCP in polynomial time. We apply CCR on a prostate cancer dataset and demonstrate that it is capable of consistently recovering large cancer contigs even when underlying cancer genomes are highly rearranged. CONCLUSIONS: CCR can recover rearranged cancer contigs from karyotype graphs thereby addressing existing limitation in inferring chromosomal structures of rearranged cancer genomes and advancing our understanding of both patient/cancer-specific as well as the overall genetic instability in cancer

Vertical structure of recent arctic warming from observed data and reanalysis products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10584-011-0192-8Spatiotemporal patterns of recent (1979–2008) air temperature trends are evaluated using three reanalysis datasets and radiosonde data. Our analysis demonstrates large discrepancies between the reanalysis datasets, possibly due to differences in the data assimilation procedures as well as sparseness and inhomogeneity of high-latitude observations. We test the robustness of Arctic tropospheric warming based on the ERA-40 dataset. ERA-40 Arctic atmosphere temperatures tend to be closer to the observed ones in terms of root mean square error compare to other reanalysis products used in the article. However, changes in the ERA-40 data assimilation procedure produce unphysical jumps in atmospheric temperatures, which may be the likely reason for the elevated tropospheric warming trend in 1979-2002. NCEP/NCAR Reanalysis show that the near-surface upward temperature trend over the same period is greater than the tropospheric trend, which is consistent with direct radiosonde observations and inconsistent with ERA-40 results. A change of sign in the winter temperature trend from negative to positive in the late 1980s is documented in the upper troposphere/lower stratosphere with a maximum over the Canadian Arctic, based on radiosonde data. This change from cooling to warming tendency is associated with weakening of the stratospheric polar vortex and shift of its center toward the Siberian coast and possibly can be explained by the changes in the dynamics of the Arctic Oscillation. This temporal pattern is consistent with multi-decadal variations of key Arctic climate parameters like, for example, surface air temperature and oceanic freshwater content. Elucidating the mechanisms behind these changes will be critical to understanding the complex nature of high-latitude variability and its impact on global climate change.acceptedVersio

MODERNIZATION OF RUSSIAN HEALT PROTECTION SYSTEM SOLVES THE PROBLEM OF RENDERING QUALITY MEDICAL AID TO POPULATION

Last two dozen years, permanent growth of death rate and decrease birth rate take place in Russia. To great extent, this is owing to inadequate health protection system. The practice of personal payments for medical services in amounts unattainable for overwhelming majority of thepopulation grows. RF President’s Administration sets an example: cardiologist’s advice in their clinics costs 40 times more that according to obligatory medical insurance rates. 84% of the country citizens do not approve this approach and consider it socially unjust. An important national project aimed at modernization of the health protection system started in 2011. Non-private medical establishments are to be equipped with up-to-date equipment, modern information systems and medical service standards based on CRM system adopted in developed countries; salaries of health personnel are to be increased

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde