A framework for evaluating statistical dependencies and rank correlations in power law graphs

We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. To the best of our knowledge, this is the first attempt to apply the well developed theory of regular variation to graph data. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between different graph parameters, such as in-degree and PageRank. Based on the proposed methodology, we suggest a new measure for rank correlations. Unlike most known methods, this measure is especially sensitive to rank permutations for topranked nodes. Using this method, we demonstrate that the PageRank ranking is not sensitive to moderate changes in the damping factor

Stability of Multiplanetary Systems in Star Clusters

Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct $N$-body simulations of four planetary systems models in three different star cluster environments with respectively N=2k, 8k and 32k stars. In each cluster, an ensemble of initially identical planetary systems are assigned to solar-type stars with $\sim 1 M_{\odot}$ and evolved for 50~Myr. We found that following the depletion of protoplanetary disks, external perturbations and planet-planet interactions are two driving mechanisms responsible for the destabilization of planetary systems. The planet survival rate varies from $\sim 95\%$ in the N=2k cluster to $\sim 60\%$ in the N=32k cluster, which suggests that most planetary systems can indeed survive in low-mass clusters, except in the central regions. We also find that planet ejections through stellar encounters are cumulative processes, as only $\sim 3\%$ of encounters are strong enough to excite the eccentricity by $\Delta e \geq 0.5$. Short-period planets can be perturbed through orbit crossings with long-period planets. When taking into account planet-planet interactions, the planet ejection rate nearly doubles, and therefore multiplicity contributes to the vulnerability of planetary systems. In each ensemble, $\sim 0.2\%$ of planetary orbits become retrograde due to random directions of stellar encounters. Our results predict that young low-mass star clusters are promising sites for next-generation planet surveys, yet low planet detection rates are expected in dense globular clusters such as 47 Tuc. Nevertheless, planets in denser stellar environments are likely to have shorter orbital periods, which enhances their detectability.Comment: 19 pages, 13 figures, 4 tables, accepted for publication in MNRA

Achievable performance of blind policies in heavy traffic

For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system load. Moreover, it is verified that this bound is tight in heavy traffic, up to a constant multiplicative factor. We obtain this result by combining techniques from two disparate areas: competitive analysis and applied probability

Science and poetry: poems as an educational tool for biology teaching

Contains fulltext : 253566.pdf (Publisher’s version ) (Open Access

Dynamical Interactions and the Black Hole Merger Rate of the Universe

Binary black holes can form efficiently in dense young stellar clusters, such as the progenitors of globular clusters, via a combination of gravitational segregation and cluster evaporation. We use simple analytic arguments supported by detailed N-body simulations to determine how frequently black holes born in a single stellar cluster should form binaries, be ejected from the cluster, and merge through the emission of gravitational radiation. We then convolve this ``transfer function'' relating cluster formation to black hole mergers with (i) the distribution of observed cluster masses and (ii) the star formation history of the universe, assuming that a significant fraction gcl of star formation occurs in clusters and that a significant fraction gcand of clusters undergo this segregation and evaporation process. We predict future ground--based gravitational wave (GW) detectors could observe ~500 (gcl/0.5) (gcand/0.1) double black hole mergers per year, and the presently operating LIGO interferometer would have a chance (50%) at detecting a merger during its first full year of science data. More realistically, advanced LIGO and similar next-generation gravitational wave observatories provide unique opportunities to constrain otherwise inaccessible properties of clusters formed in the early universe.Comment: 4 pages, 2 figures. To appear in PRD Rapid Communication

Gargantuan chaotic gravitational three-body systems II. Dependence on angular momentum and astrophysical scale

Recently we estimated that about 5 percent of supermassive black hole triple systems are fundamentally unpredictable. These gargantuan chaotic systems are able to exponentially magnify Planck length perturbations to astronomical scales within their interaction timescale. These results were obtained in the zero angular momentum limit, which we naively expected to be the most chaotic. Here, we generalise to triple systems with arbitrary angular momenta by systematically varying the initial virial ratio. We find the surprising result that increasing the angular momentum enhances the chaotic properties of triples. This is not only explained by the longer life times, allowing for a prolonged exponential growth, but also the maximum Lyapunov exponent itself increases. For the ensemble of initially virialised triple systems, we conclude that the percentage of unpredictable supermassive black hole triples increases to about 30 percent. A further increase up to about 50 percent is reached when considering triples on smaller astrophysical scales. Fundamental unpredictability is thus a generic feature of chaotic, self-gravitating triple populations.Comment: 13 pages, 11 figures, 2 tables. Submitted to MNRA

Star Formation in the vicinity of Nuclear Black Holes: Young Stellar Objects close to Sgr A*

It is often assumed that the strong gravitational field of a super-massive black hole disrupts an adjacent molecular cloud preventing classical star formation in the deep potential well of the black hole. Yet, young stars have been observed across the entire nuclear star cluster of the Milky Way including the region close ($<$0.5~pc) to the central black hole, Sgr A*. Here, we focus particularly on small groups of young stars, such as IRS 13N located 0.1 pc away from Sgr A*, which is suggested to contain about five embedded massive young stellar objects ($<$1 Myr). We perform three dimensional hydrodynamical simulations to follow the evolution of molecular clumps orbiting about a $4\times10^6~M_{\odot}$ black hole, to constrain the formation and the physical conditions of such groups. The molecular clumps in our models assumed to be isothermal containing 100 $M_{\odot}$ in $<$0.2 pc radius. Such molecular clumps exist in the circumnuclear disk of the Galaxy. In our highly eccentrically orbiting clump, the strong orbital compression of the clump along the orbital radius vector and perpendicular to the orbital plane causes the gas densities to increase to values higher than the tidal density of Sgr A*, which are required for star formation. Additionally, we speculate that the infrared excess source G2/DSO approaching Sgr A* on a highly eccentric orbit could be associated with a dust enshrouded star that may have been formed recently through the mechanism supported by our models.Comment: 18 pages, 11 figures, accepted for publication in MNRA

Hyperfast pulsars as the remnants of massive stars ejected from young star clusters

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of ~1100 km/s, which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole, and (iii) a single star and a hard binary intermediate-mass black hole. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of 10^6 -10^7 stars pc^{-3}. Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.Comment: 11 pages, 6 figures, 1 table, accepted to MNRA

Het Nieuwe Telen Anthurium: Ontwerpen en doorrekenen van een energiezuinig teeltconcept

“Het Nieuwe Telen” is substantieel energiezuiniger telen, met inzet van technieken om de warmtevraag te beperken en een optimaal teeltklimaat te handhaven. In diverse gewassen heeft het toepassen van verschillende elementen uit “Het Nieuwe Telen” geleid tot een substantiële verlaging van het energieverbruik en tegelijkertijd tot een verbetering van de kwaliteit bij gelijkblijvende productie. Anthuriumtelers zien in Het Nieuwe Telen ook interessante maatregelen voor hun gewas, die zouden kunnen bijdragen aan het verlagen van het energiegebruik en tegelijkertijd aan het oplossen van diverse kwaliteitsproblemen die zich in de huidige teeltwijze voordoen. De huidige teeltwijze kenmerkt zich door een, in vergelijking met andere teelten, laag energiegebruik. De lage bloemprijzen van de afgelopen jaren hebben ervoor gezorgd dat het besparen op de kosten (energie en arbeid) belangrijker is geworden dan de productie of de kwaliteit.In overleg met een groep telers en voorlichters uit diverse regio’s en uit België is een “referentieteelt” omschreven, met nadruk op energieverbruik en twee kwaliteitsaspecten: blauwverkleuring en glazigheid na de oogst (productkwaliteit) en rek van de internodia (gewaskwaliteit). Vervolgens zijn in een paar werkbijeenkomsten allerlei mogelijkheden besproken om energie te besparen met aandacht voor de genoemde kwaliteitsaspecten. Het energieverbruik van de meest kansrijke mogelijkheden is na selectie berekend met behulp van een kasklimaatmodel; de te verwachten effecten op de kwaliteit zijn met behulp van uit de literatuur beschikbare gegevens geanalyseerd. Het onderzoek is door Productschap Tuinbouw en Ministerie van LNV binnen het programma Kas als Energiebron gefinancier