Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

Gene expression patterns unveil a new level of molecular heterogeneity in colorectal cancer.

The recognition that colorectal cancer (CRC) is a heterogeneous disease in terms of clinical behaviour and response to therapy translates into an urgent need for robust molecular disease subclassifiers that can explain this heterogeneity beyond current parameters (MSI, KRAS, BRAF). Attempts to fill this gap are emerging. The Cancer Genome Atlas (TGCA) reported two main CRC groups, based on the incidence and spectrum of mutated genes, and another paper reported an EMT expression signature defined subgroup. We performed a prior free analysis of CRC heterogeneity on 1113 CRC gene expression profiles and confronted our findings to established molecular determinants and clinical, histopathological and survival data. Unsupervised clustering based on gene modules allowed us to distinguish at least five different gene expression CRC subtypes, which we call surface crypt-like, lower crypt-like, CIMP-H-like, mesenchymal and mixed. A gene set enrichment analysis combined with literature search of gene module members identified distinct biological motifs in different subtypes. The subtypes, which were not derived based on outcome, nonetheless showed differences in prognosis. Known gene copy number variations and mutations in key cancer-associated genes differed between subtypes, but the subtypes provided molecular information beyond that contained in these variables. Morphological features significantly differed between subtypes. The objective existence of the subtypes and their clinical and molecular characteristics were validated in an independent set of 720 CRC expression profiles. Our subtypes provide a novel perspective on the heterogeneity of CRC. The proposed subtypes should be further explored retrospectively on existing clinical trial datasets and, when sufficiently robust, be prospectively assessed for clinical relevance in terms of prognosis and treatment response predictive capacity. Original microarray data were uploaded to the ArrayExpress database (http://www.ebi.ac.uk/arrayexpress/) under Accession Nos E-MTAB-990 and E-MTAB-1026. © 2013 Swiss Institute of Bioinformatics. Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland

Region of magnetic dominance near a rotating black hole

This is a brief contribution in which a simplified criterion of the relevance of the test-particle approximation describing motion of material near a magnetized black hole is discussed. Application to processes of the dissipative collimation of astronomical jets (as proposed by de Felice and Curir, 1992) is mentioned.Comment: 11 pages, to appear in General Relativity and Gravitation, also available (with additional illustrations) at http://otokar.troja.mff.cuni.cz/user/karas/au_www/karas/papers.ht

Electron-Positron Pairs in Hot Accretion Flows and Thin Disk Coronae

We investigate equilibrium accretion flows dominated by $e^+ e^-$ pairs. We consider one- and two-temperature accretion disk coronae above a thin disk, as well as hot optically thin two-temperature accretion flows without an underlying thin disk; we model the latter in the framework of advection-dominated accretion flows (ADAFs). In all three cases we include equipartition magnetic fields. We confirm the previous result that the equilibrium density of pairs in two-temperature ADAFs is negligible; and show that the inclusion of magnetic fields and the corresponding synchrotron cooling reduces the pair density even further. Similarly, we find that pairs are unimportant in two-temperature coronae. Even when the corona has significantly enhanced heating by direct transfer of viscous dissipation in the thin disk to the corona, the inefficient Coulomb coupling between protons and electrons acts as a bottleneck and prevents the high compactness required for pair-dominated solutions. Only in the case of a one-temperature corona model do we find pair-dominated thermal equilibria. These pair-dominated solutions occur over a limited range of optical depth and temperature.Comment: 38 pages, including 10 figures, LaTeX; to appear in Ap

INTEGRAL and Swift/XRT observations of the source PKS 0208-512

The active galaxy PKS 0208-512, detected at lower energies by COMPTEL, has been claimed to be a MeV blazar from EGRET. We report on the most recent INTEGRAL observations of the blazar PKS 0208-512, which are supplemented by Swift ToO observations. The high energy X-ray and gamma-ray emission of PKS 0208-512 during August - December 2008 has been studied using 682 ks of INTEGRAL guest observer time and ~ 56 ks of Swift/XRT observations. These data were collected during the decay of a gamma-ray flare observed by Fermi/LAT. At X-ray energies (0.2 - 10 keV) PKS 0208-512 is significantly detected by Swift/XRT, showing a power-law spectrum with a photon index of ~ 1.64. Its X-ray luminosity varied by roughly 30% during one month. At hard X-/soft gamma-ray energies PKS 0208-512 shows a marginally significant (~ 3.2 sigma) emission in the 0.5-1 MeV band when combining all INTEGRAL/SPI data. Non-detections at energies below and above this band by INTEGRAL/SPI may indicate intrinsic excess emission. If this possible excess is produced by the blazar, one possible explanation could be that its jet consists of an abundant electron-positron plasma, which may lead to the emission of an annihilation radiation feature. Assuming this scenario, we estimate physical parameters of the jet of PKS 0208-512.Comment: accepted for publication in A&

Suzaku Observations of Luminous Quasars: Revealing the Nature of High-Energy Blazar Emission in Quiescent States

We present the results from the Suzaku X-ray observations of five flat-spectrum radio quasars (FSRQs), namely PKS0208-512, Q0827+243, PKS1127-145, PKS1510-089 and 3C 454.3. All these sources were additionally monitored simultaneously or quasi-simultaneously by the Fermi satellite in gamma-rays and the Swift UVOT in the UV and optical bands, respectively. We constructed their broad-band spectra covering the frequency range from 10^14 Hz up to 10^25 Hz, and those reveal the nature of high-energy emission of luminous blazars in their low-activity states. The analyzed X-ray spectra are well fitted by a power-law model with photoelectric absorption. In the case of PKS0208-512, PKS1127-145, and 3C 454.3, the X-ray continuum showed indication of hard-ening at low-energies. Moreover, when compared with the previous X-ray observations, we see a significantly increasing contribution of low-energy photons to the total X-ray fluxes when the sources are getting fainter. The same behavior can be noted in the Suzaku data alone. A likely explanation involves a variable, flat-spectrum component produced via inverse-Compton (IC) emission, plus an additional, possibly steady soft X-ray component prominent when the source gets fainter. This soft X-ray excess is represented either by a steep powerlaw (photon indices Gamma ~ 3 - 5) or a blackbody-type emission with temperatures kT ~ 0.1-0.2 keV. We model the broad-band spectra spectra of the five observed FSRQs using synchrotron self-Compton (SSC) and/or external-Compton radiation (ECR) models. Our modeling suggests that the difference between the low and high-activity states in luminous blazars is due to the different total kinetic power of the jet, most likely related to varying bulk Lorentz factor of the outflow within the blazar emission zone.Comment: 36 pages, 8 figures, 11 tables. Accepted for publication in the Astrophysical Journal

High-Energy Neutrinos from Photomeson Processes in Blazars

An important radiation field for photomeson neutrino production in blazars is shown to be the radiation field external to the jet. Assuming that protons are accelerated with the same power as electrons and injected with a -2 number spectrum, we predict that km^2 neutrino telescopes will detect about 1-to-several neutrinos per year from flat spectrum radio quasars (FSRQs) such as 3C 279. The escaping high-energy neutron and photon beams transport inner jet energy far from the black-hole engine, and could power synchrotron X-ray jets and FR II hot spots and lobes.Comment: revised paper (minor revisions), accepted for publication in PR

Fermi Gamma-ray Space Telescope Observations of Recent Gamma-ray Outbursts from 3C 454.3

The flat spectrum radio quasar 3C~454.3 underwent an extraordinary outburst in December 2009 when it became the brightest gamma-ray source in the sky for over one week. Its daily flux measured with the Fermi Large Area Telescope at photon energies E>100 MeV reached F = 22+/-1 x 10^-6 ph cm^-2 s^-1, representing the highest daily flux of any blazar ever recorded in high-energy gamma-rays. It again became the brightest source in the sky in 2010 April, triggering a pointed-mode observation by Fermi. The correlated gamma-ray temporal and spectral properties during these exceptional events are presented and discussed. The main results show flux variability over time scales less than 3 h and very mild spectral variability with an indication of gradual hardening preceding major flares. No consistent loop pattern emerged in the gamma-ray spectral index vs flux plane. A minimum Doppler factor of ~ 15 is derived, and the maximum energy of a photon from 3C 454.3 is ~ 20 GeV. The spectral break at a few GeV is inconsistent with Klein-Nishina softening from power-law electrons scattering Ly_alpha line radiation, and a break in the underlying electron spectrum in blazar leptonic models is implied.Comment: submitted to the Astrophysical Journa

EPTAS and Subexponential Algorithm for Maximum Clique on Disk and Unit Ball Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Cliqe on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics ’90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show that the disjoint union of two odd cycles is never the complement of a disk graph nor of a unit (3-dimensional) ball graph. From that fact and existing results, we derive a simple QPTAS and a subexponential algorithm running in time 2O˜(n2/3) for Maximum Cliqe on disk and unit ball graphs. We then obtain a randomized EPTAS for computing the independence number on graphs having no disjoint union of two odd cycles as an induced subgraph, bounded VC-dimension, and linear independence number. This, in combination with our structural results, yields a randomized EPTAS for Max Cliqe on disk and unit ball graphs. Max Cliqe on unit ball graphs is equivalent to finding, given a collection of points in R3, a maximum subset of points with diameter at most some fixed value. In stark contrast, Maximum Cliqe on ball graphs and unit 4-dimensional ball graphs, as well as intersection graphs of filled ellipses (even close to unit disks) or filled triangles is unlikely to have such algorithms. Indeed, we show that, for all those problems, there is a constant ratio of approximation which cannot be attained even in time 2n1−ε, unless the Exponential Time Hypothesis fails

PKS 1502+106: a new and distant gamma-ray blazar in outburst discovered by the Fermi Large Area Telescope

The Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope discovered a rapid (about 5 days duration), high-energy (E >100 MeV) gamma-ray outburst from a source identified with the blazar PKS 1502+106 (OR 103, S3 1502+10, z=1.839) starting on August 05, 2008 and followed by bright and variable flux over the next few months. Results on the gamma-ray localization and identification, as well as spectral and temporal behavior during the first months of the Fermi all-sky survey are reported here in conjunction with a multi-waveband characterization as a result of one of the first Fermi multi-frequency campaigns. The campaign included a Swift ToO (followed up by 16-day observations on August 07-22, MJD 54685-54700), VLBA (within the MOJAVE program), Owens Valley (OVRO) 40m, Effelsberg-100m, Metsahovi-14m, RATAN-600 and Kanata-Hiroshima radio/optical observations. Results from the analysis of archival observations by INTEGRAL, XMM-Newton and Spitzer space telescopes are reported for a more complete picture of this new gamma-ray blazar.Comment: 17 pages, 11 figures, accepted for The Astrophysical Journa