Subset feedback vertex set is fixed parameter tractable

The classical Feedback Vertex Set problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. Feedback Vertex Set has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider a more general and difficult version of the problem, named Subset Feedback Vertex Set (SUBSET-FVS in short) where an instance comes additionally with a set S ? V of vertices, and we ask for a set of at most k vertices that hits all simple cycles passing through S. Because of its applications in circuit testing and genetic linkage analysis SUBSET-FVS was studied from the approximation algorithms perspective by Even et al. [SICOMP'00, SIDMA'00]. The question whether the SUBSET-FVS problem is fixed-parameter tractable was posed independently by Kawarabayashi and Saurabh in 2009. We answer this question affirmatively. We begin by showing that this problem is fixed-parameter tractable when parametrized by |S|. Next we present an algorithm which reduces the given instance to 2^k n^O(1) instances with the size of S bounded by O(k^3), using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem. These two facts allow us to give a 2^O(k log k) n^O(1) time algorithm solving the Subset Feedback Vertex Set problem, proving that it is indeed fixed-parameter tractable.Comment: full version of a paper presented at ICALP'1

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

Climate services for health: from global observations to local interventions

Despite the wealth of available climate data available, there is no consensus on the most appropriate product choice for health impact modelling and how this influences downstream climate-health decisions. We discuss challenges related to product choice, highlighting the importance of considering data biases and co-development of climate services between different sectors

Evidence for an intermediate-mass black hole in the globular cluster NGC 6624

PSR B1820$-$30A is located in the globular cluster NGC 6624 and is the closest known pulsar to the centre of any globular cluster. We present more than 25 years of high-precision timing observations of this millisecond pulsar and obtain four rotational frequency time derivative measurements. Modelling these higher-order derivatives as being due to orbital motion, we find solutions which indicate that the pulsar is in either a low-eccentricity ($0.33\lesssim e\lesssim0.4$) smaller orbit with a low mass companion (such as a main sequence star, white dwarf, neutron star, or stellar mass black hole) or a high-eccentricity ($e\gtrsim0.9$) larger orbit with a massive companion. The cluster mass properties and the observed properties of 4U 1820$-$30 and the other pulsars in the cluster argue against the low-eccentricity possibility. The high-eccentricity solution reveals that the pulsar is most likely orbiting around an intermediate-mass black hole (IMBH) of mass $> 7,500$~M$_\odot$ located at the cluster centre. A gravitational model for the globular cluster, which includes such a central black hole (BH), predicts an acceleration that is commensurate with that measured for the pulsar. It further predicts that the model-dependent minimum mass of the IMBH is $\sim60,000$~M$_\odot$. Accounting for the associated contribution to the observed period derivative indicates that the $\gamma$-ray efficiency of the pulsar should be between 0.08 and 0.2. Our results suggest that other globular clusters may also contain central black holes and they may be revealed by the study of new pulsars found sufficiently close to their centres. Note that we found an erratum in Section 5 and thus, the $\sim$60,000~M$_\odot$ mass mentioned above has to be replaced by the correct model-dependent mass limit of $\sim$20,000~M$_\odot$. See the erratum appended.Comment: 15 pages, 10 figures, Accepted by MNRAS on 23 February 2017. Erratum was accepted by MNRAS on 17 May 201

Optical-uv spectrum and proper motion of the middle-aged pulsar b1055-52

PSRB1055-52 is a middle-aged (~535 kyr) radio, X-ray, and gamma-ray pulsar showing X-ray thermal emission from the neutron star (NS) surface. A candidate optical counterpart to PSRB1055-52 was proposed by Mignani and coworkers based on Hubble Space Telescope (HST) observations performed in 1996, in one spectral band only. We report on HST observations of this field carried out in 2008, in four spectral bands. The astrometric and photometric analyses of these data confirm the identification of the proposed candidate as the pulsar's optical counterpart. Similarly to other middle-aged pulsars, its optical-UV spectrum can be described by the sum of a power-law (PLO) component, presumably emitted from the pulsar magnetosphere, and a Rayleigh-Jeans (RJ) component emitted from the NS surface. The spectral index of the PLO component, alpha_O=1.05+/-0.34, is larger than for other pulsars with optical counterparts. The RJ component, with the brightness temperature TO=(0.66+/-0.10) d_350**2 R_O,13**-2 MK (where d_350 and R_O,13 are the distance to the pulsar in units of 350 pc and the radius of the emitting area in units of 13 km), shows a factor of 4 excess with respect to the extrapolation of the X-ray thermal component into the UV-optical. This hints that the RJ component is emitted from a larger, colder area, and suggests that the distance to the pulsar is smaller than previously thought. From the absolute astrometry of the HST images we measured the pulsar coordinates with a position accuracy of 0.15". From the comparison with previous observations we measured the pulsar proper motion, mu = 42+/-5 mas/yr, which corresponds to a transverse velocity V_t = (70+/-8) d_350 km/s.Comment: 12 pages, 5 figures, accepted for publication on Astrophysical Journal, (Fig1a available at http://www.mssl.ucl.ac.uk/~rm2/

Potassium limitation of forest productivity – Part 2: CASTANEA-MAESPA-K shows a reduction in photosynthesis rather than a stoichiometric limitation of tissue formation

Potassium (K) availability constrains forest productivity. Brazilian eucalypt plantations are a good example of the K limitation of wood production. Here, we built upon a previously described model (CASTANEA-MAESPA-K) and used it to understand whether the simulated decline in C source under K deficiency was sufficient to explain the K limitation of wood productivity in Brazilian eucalypt plantations. We developed allocation schemes for both C and K and included these in CASTANEA-MAESPA-K. Neither direct limitations of the C-sink activity nor direct modifications of the C allocation by K availability were included in the model. Simulation results show that the model was successful in replicating the observed patterns of wood productivity limitation by K deficiency. Simulations also show that the response of net primary productivity (NPP) is not linear with increasing K fertilisation. Simulated stem carbon use and water use efficiencies decreased with decreasing levels of K availability. Simulating a direct stoichiometric limitation of NPP or wood growth was not necessary to reproduce the observed decline of productivity under K limitation, suggesting that K stoichiometric plasticity could be different to that of N and P. Confirming previous results from the literature, the model simulated an intense recirculation of K in the trees, suggesting that retranslocation processes were essential for tree functioning. Optimal K fertilisation levels calculated by the model were similar to nutritional recommendations currently applied in Brazilian eucalypt plantations, paving the way for validation of the model at a larger scale and of this approach for developing decision-making tools to improve fertilisation practices.</p

The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches

The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95% confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1%), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black-hole binaries with circular orbits.Comment: Accepted for publication by the Monthly Notices of the Royal Astronomical Societ

Three Millisecond Pulsars in FERMI LAT Unassociated Bright Sources

We searched for radio pulsars in 25 of the non-variable, unassociated sources in the Fermi LAT Bright Source List with the Green Bank Telescope at 820 MHz. We report the discovery of three radio and gamma-ray millisecond pulsars (MSPs) from a high Galactic latitude subset of these sources. All of the pulsars are in binary systems, which would have made them virtually impossible to detect in blind gamma-ray pulsation searches. They seem to be relatively normal, nearby (<=2 kpc) millisecond pulsars. These observations, in combination with the Fermi detection of gamma-rays from other known radio MSPs, imply that most, if not all, radio MSPs are efficient gamma-ray producers. The gamma-ray spectra of the pulsars are power-law in nature with exponential cutoffs at a few GeV, as has been found with most other pulsars. The MSPs have all been detected as X-ray point sources. Their soft X-ray luminosities of ~10^{30-31} erg/s are typical of the rare radio MSPs seen in X-rays.Comment: Accepted for publication in ApJ Letter