7,664 research outputs found
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 genomic maps as sequences of gene markers, the
objective of \msr{d} is to find subsequences, one subsequence of each
genomic map, such that the total length of syntenic blocks in these
subsequences is maximized. For any constant , a polynomial-time
2d-approximation for \msr{d} was previously known. In this paper, we show that
for any , \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 . In particular, we show that
\msr{d} is NP-hard to approximate within . From the other
direction, we show that the previous 2d-approximation for \msr{d} can be
optimized into a polynomial-time algorithm even if 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
n/
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
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