Inapproximability of maximal strip recovery

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \ge 2$, a polynomial-time 2d-approximation for \msr{d} was previously known. In this paper, we show that for any $d \ge 2$, \msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating \msr{d} for all $d \ge 2$. In particular, we show that \msr{d} is NP-hard to approximate within $\Omega(d/\log d)$. From the other direction, we show that the previous 2d-approximation for \msr{d} can be optimized into a polynomial-time algorithm even if $d$ is not a constant but is part of the input. We then extend our inapproximability results to several related problems including \cmsr{d}, \gapmsr{\delta}{d}, and \gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) and the Proceedings of the 4th International Frontiers of Algorithmics Workshop (FAW 2010

The First Ground Level Enhancement Event of Solar Cycle 24: Direct Observation of Shock Formation and Particle Release Heights

We report on the 2012 May 17 Ground Level Enhancement (GLE) event, which is the first of its kind in Solar Cycle 24. This is the first GLE event to be fully observed close to the surface by the Solar Terrestrial Relations Observatory (STEREO) mission. We determine the coronal mass ejection (CME) height at the start of the associated metric type II radio burst (i.e., shock formation height) as 1.38 Rs (from the Sun center). The CME height at the time of GLE particle release was directly measured from a STEREO image as 2.32 Rs, which agrees well with the estimation from CME kinematics. These heights are consistent with those obtained for cycle-23 GLEs using back-extrapolation. By contrasting the 2012 May 17 GLE with six other non-GLE eruptions from well-connected regions with similar or larger flare size and CME speed, we find that the latitudinal distance from the ecliptic is rather large for the non-GLE events due to a combination of non-radial CME motion and unfavorable solar B0 angle, making the connectivity to Earth poorer. We also find that the coronal environment may play a role in deciding the shock strength.Comment: 16 pages, 4 figures, 1 tabl

Some combinatorial problems

AbstractThere are many interesting and sophisticated problems posed in the IMO, Putnam and domestic Olympiads. Some of these problems have deep mathematical background, nice generalizations, and lead to new areas of research in combinatorics. We investigate several topics in this category and mention some results and open problems

Ground Level Enhancement in the 2014 January 6 Solar Energetic Particle Event

We present a study of the 2014 January 6 solar energetic particle (SEP) event, which produced a small ground level enhancement (GLE), making it the second GLE of this unusual solar cycle 24. This event was primarily observed by the South Pole neutron monitors (increase of ~2.5%) whereas a few other neutron monitors recorded smaller increases. The associated coronal mass ejection (CME) originated behind the western limb and had the speed of 1960 km/s. The height of the CME at the start of the associated metric type II radio burst, which indicates the formation of a strong shock, was measured to be 1.61 Rs using a direct image from STEREO-A/EUVI. The CME height at the time of GLE particle release (determined using the South Pole neutron monitor data) was directly measured as 2.96 Rs, from the STEREO-A/COR1 white-light observations. These CME heights are consistent with those obtained for the GLE71, the only other GLE of the current cycle as well as cycle-23 GLEs derived using back-extrapolation. GLE72 is of special interest because it is one of the only two GLEs of cycle 24, one of the two behind-the-limb GLEs and one of the two smallest GLEs of cycles 23 and 24

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

BMB activity defines refractory and competent hair follicle populations during the propagation of regenerative waves

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De-leptonization and Non-Axisymmetric Instabilities in Core Collapse Supernovae

The timescale of de-leptonization by neutrino loss and associated contraction of a proto-neutron star is short compared to the time to progagate a shock through the helium core of a massive star, and so the de-leptonization phase does not occur in the vacuum of space, but within the supernova ambiance whether or not there has been a successful explosion. Dynamical non-axisymmetric instabilities (NAXI) are predicted for sufficiently strongly differentially rotating proto-neutron stars. Some modes are unstable for small values of the ratio of rotational kinetic energy to binding energy, T/|W| > 0.01. The NAXI are likely to drive magnetoacoustic waves into the surrounding time-dependent density structure. These waves represent a mechanism of the dissipation of the free energy of differential rotation of the proto-neutron star, and the outward deposition of this energy may play a role in the supernova explosion process. We estimate the power produced by this process and the associated timescale and discuss the possible systematics of the de-leptonization phase in this context. A likely possibility is that the proto-neutron star will spin down through these effects before de-leptonization and produce substantial but not excessive energy input.Comment: 15 pages, 1 figure, accepted for publication in the Astrophysical Journa

The Evolving Radio Photospheres of Long-Period Variable Stars

Observations with the Karl G. Jansky Very Large Array at 46 GHz (7 mm) have been used to measure the size and shape of the radio photospheres of four long-period variable stars: R Leonis (R Leo), IRC+10216 (CW Leo), chi Cygni (chi Cyg), and W Hydrae (W Hya). The shapes of the stars range from nearly round to ellipticities of ~0.15. Comparisons with observations taken several years earlier show that the photospheric parameters (mean diameter, shape, and/or flux density) of each of the stars have changed over time. Evidence for brightness asymmetries and non-uniformities across the radio surfaces are also seen in the visibility domain and in images obtained using a sparse modeling image reconstruction technique. These trends may be explained as manifestations of large-scale irregular convective flows on the stellar surface, although effects from non-radial pulsations cannot be excluded. Our data also allow a new evaluation of the proper motion of IRC+10216. Our measurement is in agreement with previous values obtained from radio wavelength measurements, and we find no evidence of statistically significant astrometric perturbations from a binary companion.Comment: 15 pages; accepted to A