246,173 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
New Supporting Evidence for the Overdensity of Galaxies around the Radio-Loud Quasar SDSS J0836+0054 at z =5.8
Recently, Zheng et al. (2005) found evidence for an overdensity of galaxies
around a radio-loud quasar, SDSS J0836+0054, at z=5.8 (a five arcmin
region). We have examined our deep optical imaging data (B, V, r', i', z', and
NB816) taken with the Suprime-Cam on the Subaru Telescope. The NB816
narrow-band filter (lambda_c = 815 nm and nm) is suitable
for searching for Ly emitters at . We have found a new
strong Ly emitter at close to object B identified by
Zheng et al. Further, the non detection of the nine objects selected by Zheng
et al. (2005) in our B, V, and r' images provides supporting evidence that they
are high-z objects.Comment: 5 pages, 1 figure, accepted for PAS
Comment on ``Deterministic equations of motion and phase ordering dynamics''
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase
ordering dynamics in the microcanonical model displays unusual scaling
laws. We show here, performing more careful numerical investigations, that
Zheng only observed transient dynamics mostly due to the corrections to scaling
introduced by lattice effects, and that Ising-like (model A) phase ordering
actually takes place at late times. Moreover, we argue that energy conservation
manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure
Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
Let E be an unbounded open (or closed) domain in Euclidean space of dimension
greater or equal to two. We present conservativeness criteria for (possibly
reflected) diffusions with state space E that are associated to fairly general
perturbed divergence form operators. Our main tool is a recently extended
forward and backward martingale decomposition, which reduces to the well-known
Lyons-Zheng decomposition in the symmetric case.Comment: Corrected typos, minor modification
Regulation of G protein-coupled receptors by palmitoylation and cholesterol
Due to their membrane location, G protein-coupled receptors (GPCRs) are subject to regulation by soluble and integral membrane proteins as well as membrane components, including lipids and sterols. GPCRs also undergo a variety of post-translational modifications, including palmitoylation. A recent article by Zheng et al. in BMC Cell Biology demonstrates cooperative roles for receptor palmitoylation and cholesterol binding in GPCR dimerization and G protein coupling, underlining the complex regulation of these receptors
Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
In this paper, we consider the stochastic optimal control problems under
G-expectation. Based on the theory of backward stochastic differential
equations driven by G-Brownian motion, which was introduced in [10.11], we can
investigate the more general stochastic optimal control problems under
G-expectation than that were constructed in [28]. Then we obtain a generalized
dynamic programming principle and the value function is proved to be a
viscosity solution of a fully nonlinear second-order partial differential
equation.Comment: 25 page
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