1,860 research outputs found
Algorithmic and Hardness Results for the Colorful Components Problems
In this paper we investigate the colorful components framework, motivated by
applications emerging from comparative genomics. The general goal is to remove
a collection of edges from an undirected vertex-colored graph such that in
the resulting graph all the connected components are colorful (i.e., any
two vertices of the same color belong to different connected components). We
want to optimize an objective function, the selection of this function
being specific to each problem in the framework.
We analyze three objective functions, and thus, three different problems,
which are believed to be relevant for the biological applications: minimizing
the number of singleton vertices, maximizing the number of edges in the
transitive closure, and minimizing the number of connected components.
Our main result is a polynomial time algorithm for the first problem. This
result disproves the conjecture of Zheng et al. that the problem is -hard
(assuming ). Then, we show that the second problem is -hard,
thus proving and strengthening the conjecture of Zheng et al. that the problem
is -hard. Finally, we show that the third problem does not admit
polynomial time approximation within a factor of for
any , assuming (or within a factor of , assuming ).Comment: 18 pages, 3 figure
Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system
This manuscript extends the analysis of a much studied singularly perturbed
three-component reaction-diffusion system for front dynamics in the regime
where the essential spectrum is close to the origin. We confirm a conjecture
from a preceding paper by proving that the triple multiplicity of the zero
eigenvalue gives a Jordan chain of length three. Moreover, we simplify the
center manifold reduction and computation of the normal form coefficients by
using the Evans function for the eigenvalues. Finally, we prove the unfolding
of a Bogdanov-Takens bifurcation with symmetry in the model. This leads to
stable periodic front motion, including stable traveling breathers, and these
results are illustrated by numerical computations.Comment: 39 pages, 7 figure
Exchange Bias Induced by the Fe3O4 Verwey transition
We present a study of the exchange bias in different configurations of V2O3
thin films with ferromagnetic layers. The exchange bias is accompanied by a
large vertical shift in the magnetization. These effects are only observed when
V2O3 is grown on top of Ni80Fe20 permalloy. The magnitude of the vertical shift
is as large as 60% of the total magnetization which has never been reported in
any system. X-Ray diffraction studies show that the growth conditions promote
the formation of a ferrimagnetic Fe3O4 interlayer. The change in the easy
magnetization axis of Fe3O4 across the Verwey transition at 120 K is correlated
with the appearance of exchange bias and vertical shift in magnetization. Both
phenomena disappear above 120 K, indicating for the first time a direct
relationship between the magnetic signature of the Verwey transition and
exchange bias.Comment: Accepted for publication Physical Review
Review of the Laguerre-Gauss mode technology research program at Birmingham
Gravitational wave detectors from the advanced generation onwards are
expected to be limited in sensitivity by thermal noise of the optics, making
the reduction of this noise a key factor in the success of such detectors. A
proposed method for reducing the impact of this noise is to use higher-order
Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently
used fundamental mode. We present here a synopsis of the research program
undertaken by the University of Birmingham into the suitability of LG mode
technology for future gravitational wave detectors. This will cover our
previous and current work on this topic, from initial simulations and table-top
LG mode experiments up to implementation in a prototype scale suspended cavity
and high-power laser bench
Fungal Peptaibiotics: Assessing Potential Meteoritic Amino Acid Contamination
The presence of non-protein alpha-dialkyl-amino acids such as alpha-aminoisobutyric acid (alpha-A1B) and isovaline (Iva), which are relatively rare in the terrestrial biosphere, has long been used as an indication of the indigeneity of meteoritic amino acids, however, the discovery of alpha-AIB in peptides producers by a widespread group of filamentous fungi indicates the possibility of a terrestrial biotic source for the alpha-AIB observed in some meteorites. The alpha-AIB-containing peptides produced by these fungi are dubbed peptaibiotics. We measured the molecular distribution and stable carbon and nitrogen isotopic ratios for amino acids found in the total hydrolysates of four biologically synthesized peptaibiotics. We compared these aneasurenetts with those from the CM2 carbonaceous chondrite Murchison and from three Antarctic CR2 carbonaceous chondrites in order to understand the peptaibiotics as a potential source of meteoritic contamination
Diffusive stability for periodic metric graphs
Analysis and Stochastic
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