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 $h \ge 2$ and for all $\epsilon > 0$, there exists $g = g_h(\epsilon)$ and a sequence of integers $A$ such that the number of ordered representations of any number as a sum of $h$ elements of $A$ is bounded by $g$, and such that $|A \cap [1,x]| \gg x^{1/h - \epsilon}$. 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 $g$ that satisfies $g_h(\epsilon) \ll \epsilon^{-1}$, improving the bound $g_h(\epsilon) \ll \epsilon^{-h+1}$ obtained by Vu. Finally we use the "alteration method" to get a better bound for $g_3(\epsilon)$, obtaining a more precise estimate for the growth of $B_3[g]$ 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 $N_t=16$. 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 $N_t=6,8,10$ and at some temperature values with $N_t=12$. 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 $\mu-T$ 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 $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3\times 16$ 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 $L_t=4$ 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