679 research outputs found
Generalization of a theorem of Erdos and Renyi on Sidon Sequences
Erd\H os and R\'{e}nyi claimed and Vu proved that for all and for
all , there exists and a sequence of integers
such that the number of ordered representations of any number as a sum of
elements of is bounded by , and such that .
We give two new proofs of this result. The first one consists of an explicit
construction of such a sequence. The second one is probabilistic and shows the
existence of such a that satisfies ,
improving the bound obtained by Vu.
Finally we use the "alteration method" to get a better bound for
, obtaining a more precise estimate for the growth of
sequences.Comment: 12 pages, no figure
Transition temperature and the equation of state from lattice QCD, Wuppertal-Budapest results
The QCD transition is studied on lattices up to . The chiral
condensate is presented as a function of the temperature, and the corresponding
transition temperature is extracted. The equation of state is determined on
lattices with and at some temperature values with . The
pressure and the trace anomaly are presented as functions of the temperature in
the range 100 ...1000 MeV . Using the same configurations we determine the
continuum extrapolated phase diagram of QCD on the plane for small to
moderate chemical potentials. Two transition lines are defined with two
quantities, the chiral condensate and the strange quark number susceptibility.Comment: 4 pages, 2 figures, Proceedings for Quark Matter 201
Topology with Dynamical Overlap Fermions
We perform dynamical QCD simulations with overlap fermions by hybrid
Monte-Carlo method on to lattices. We study the problem of
topological sector changing. A new method is proposed which works without
topological sector changes. We use this new method to determine the topological
susceptibility at various quark masses.Comment: 15 pages, 3 figure
Probe Based Recognition of Targets in Infrared Images
(Also cross-referenced as CAR-TR-693)
A probe based approach is used to recognize objects in a cluttered
background using an infrared imager. A probe is a simple mathematical
function which operates locally on image grey levels and produces an
output that is more directly usable by an algori thm. A directional probe
image is calculated by taking the difference in grey levels between pixels
a set distance apart in a given direction, centered on the probe image
pixel. These probe images contain the information necessary for use by an
object rec ognition algorithm in a readily usable, and mathematically
describable, form. A parametric statistical image background model which
describes the probe images is introduced. The parameters of the probe
image model can be readily estimated from the image. Knowledge of these
parameters, together with target signatures obtained from Computer Aided
Design (CAD) models, allows the likelihood ratio for a given object pose
hypothesis versus the background null hypothesis to be written. The
generalized likelihood ratio test is used to accept one of the object
poses or to choose the null hypothesis. Results of the method applied to
a large set of terrain model board images are presented
Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes
The merger rate of stellar-mass black hole binaries (sBHBs) inferred by the
Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) suggests
the need for an efficient source of sBHB formation. Active galactic nucleus
(AGN) disks are a promising location for the formation of these sBHBs, as well
as binaries of other compact objects, because of powerful torques exerted by
the gas disk. These gas torques cause orbiting compact objects to migrate
towards regions in the disk where inward and outward torques cancel, known as
migration traps. We simulate the migration of stellar mass black holes in an
example of a model AGN disk, using an augmented N-body code that includes
analytic approximations to migration torques, stochastic gravitational forces
exerted by turbulent density fluctuations in the disk, and inclination and
eccentricity dampening produced by passages through the gas disk, in addition
to the standard gravitational forces between objects. We find that sBHBs form
rapidly in our model disk as stellar-mass black holes migrate towards the
migration trap. These sBHBs are likely to subsequently merge on short
time-scales. The process continues, leading to the build-up of a population of
over-massive stellar-mass black holes. The formation of sBHBs in AGN disks
could contribute significantly to the sBHB merger rate inferred by LIGO.Comment: 18 pages, 13 figures, Accepted to Ap
Aberrant septin 9 DNA methylation in colorectal cancer is restricted to a single CpG island.
BACKGROUND: The septin 9 gene (SEPT9) codes for a GTP-binding protein associated with filamentous structures and cytoskeleton formation. SEPT9 plays a role in multiple cancers as either an oncogene or a tumor suppressor gene. Regulation of SEPT9 expression is complex and not well understood; however, hypermethylation of the gene was recently introduced as a biomarker for early detection of colorectal cancer (CRC) and has been linked to cancer of the breast and of the head and neck. Because the DNA methylation landscape of different regions of SEPT9 is poorly understood in cancer, we analyzed the methylation patterns of this gene in distinct cell populations from normal and diseased colon mucosa. METHODS: Laser capture microdissection was performed to obtain homogeneous populations of epithelial and stromal cells from normal, adenomatous, and tumorous colon mucosa. Microdissected samples were analyzed using direct bisulfite sequencing to determine the DNA methylation status of eight regions within and near the SEPT9 gene. Septin-9 protein expression was assessed using immunohistochemistry (IHC). RESULTS: Regions analyzed in SEPT9 were unmethylated in normal tissue except for a methylation boundary detected downstream of the largest CpG island. In adenoma and tumor tissues, epithelial cells displayed markedly increased DNA methylation levels (>80%, p <0.0001) in only one of the CpG islands investigated. SEPT9 methylation in stromal cells increased in adenomatous and tumor tissues (<=50%, p <0.0001); however, methylation did not increase in stromal cells of normal tissue close to the tumor. IHC data indicated a significant decrease (p <0.01) in Septin-9 protein levels in epithelial cells derived from adenoma and tumor tissues; Septin-9 protein levels in stromal cells were low in all tissues. CONCLUSIONS: Hypermethylation of SEPT9 in adenoma and CRC specimens is confined to one of several CpG islands of this gene. Tumor-associated aberrant methylation originates in epithelial cells; stromal cells appear to acquire hypermethylation subsequent to epithelial cells, possibly through field effects. The region in SEPT9 with disease-related hypermethylation also contains the CpGs targeted by a novel blood-based screening test (Epi proColon(R)), providing further support for the clinical relevance of this biomarker
Lattice determination of the critical point of QCD at finite T and \mu
Based on universal arguments it is believed that there is a critical point
(E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which
is of extreme importance for heavy-ion experiments. Using finite size scaling
and a recently proposed lattice method to study QCD at finite \mu we determine
the location of E in QCD with n_f=2+1 dynamical staggered quarks with
semi-realistic masses on lattices. Our result is T_E=160 \pm 3.5 MeV
and \mu_E= 725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained
T_c=172 \pm 3 MeV.Comment: misprints corrected, version to appear in JHE
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