A Rapid X-ray Flare from Markarian 501

We present X-ray observations of the BL Lacertae (BL Lac) object Markarian 501 (Mrk 501), taken with the Rossi X-ray Timing Explorer in 1998 May as part of a multi-wavelength campaign. The X-ray light curve shows a very rapid flare in which the 2-10 keV flux increased by ~60% in <200 seconds. This rapid rise is followed by a drop-off in the 2-10 keV flux of ~40% in <600 seconds. The 10-15 keV variation in this flare is roughly a factor of two on similar time-scales. During the rise of the flare, the 3-15 keV spectral index hardened from 2.02 +/- 0.03 to 1.87 +/- 0.04, where it remained during the decay of the flare. This is the fastest variation ever seen in X-rays from Mrk 501 and among the fastest seen at any wavelength for this object. The shift in the energy at which the spectral power peaks (from 30 keV during the flare) is also among the most rapid shifts seen from this object. This flare occurs during an emission state (2-10 keV flux approximately 1.2e-10 erg cm^-2 s^-1) that is approximately 25% of the peak flux observed in 1997 April from this object but which is still high compared to its historical average X-ray flux. The variations in the hardness ratio are consistent with the low energy variations leading those at high energies during the development and decay of the flare. This pattern is rare among high frequency peaked BL Lac objects like Mrk 501, but has been seen recently in two other TeV emitting BL Lacs, Mrk 421 and PKS 2155-304. The hard lag is consistent with a flare dominated by the acceleration time-scale for a simple relativistic shock model of flaring.Comment: 11 pages, 3 figures, accepted for publication in Astrophys. J. Letter

On surfaces with p_g=2, q=1 and K^2=5

We consider minimal surfaces of general type with $p_g = 2$, $q = 1$ and $K^2 = 5$. We provide a stratification of the corresponding moduli space and we give some bounds for the number and the dimensions of its irreducible components.Comment: 25 pages. To appear in Rendiconti del Circolo Matematico di Palerm

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies

We have used data from the TeV gamma-ray flare associated with the active galaxy Markarian 421 observed on 15 May 1996 to place bounds on the possible energy-dependence of the speed of light in the context of an effective quantum gravitational energy scale. The possibility of an observable time dispersion in high energy radiation has recently received attention in the literature, with some suggestions that the relevant energy scale could be less than the Planck mass and perhaps as low as 10^16 GeV. The limits derived here indicate this energy scale to be in excess of 4x10^16 GeV at the 95% confidence level. To the best of our knowledge, this constitutes the first convincing limit on such phenomena in this energy regime.Comment: 6 pages, including 2 figure

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Disrupting resilient criminal networks through data analysis: The case of sicilian mafia

Compared to other types of social networks, criminal networks present particularly hard challenges, due to their strong resilience to disruption, which poses severe hurdles to LawEnforcement Agencies (LEAs). Herein, we borrow methods and tools from Social Network Analysis (SNA) to (i) unveil the structure and organization of Sicilian Mafia gangs, based on two real-world datasets, and (ii) gain insights as to how to efficiently reduce the Largest Connected Component (LCC) of two networks derived from them. Mafia networks have peculiar features in terms of the links distribution and strength, which makes them very different from other social networks, and extremely robust to exogenous perturbations. Analysts also face difficulties in collecting reliable datasets that accurately describe the gangs' internal structure and their relationships with the external world, which is why earlier studies are largely qualitative, elusive and incomplete. An added value of our work is the generation of two realworld datasets, based on raw data extracted from juridical acts, relating to a Mafia organization that operated in Sicily during the first decade of 2000s. We created two different networks, capturing phone calls and physical meetings, respectively. Our analysis simulated different intervention procedures: (i) arresting one criminal at a time (sequential node removal); and (ii) police raids (node block removal). In both the sequential, and the node block removal intervention procedures, the Betweenness centrality was the most effective strategy in prioritizing the nodes to be removed. For instance, when targeting the top 5% nodes with the largest Betweenness centrality, our simulations suggest a reduction of up to 70% in the size of the LCC. We also identified that, due the peculiar type of interactions in criminal networks (namely, the distribution of the interactions' frequency), no significant differences exist between weighted and unweighted network analysis. Our work has significant practical applications for perturbing the operations of criminal and terrorist networks

Geometric and homological finiteness in free abelian covers

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of Riemann surfaces and complements of hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201

Correlated variability of Mkn 421 at X-ray and TeV wavelengths on timescales of hours

Mkn 421 was observed for about two days with BeppoSAX, prior to and partly overlapping the start of a 1 week continuous exposure with ASCA in April 1998, as part of a world-wide multiwavelength campaign. A pronounced, well defined, flare observed in X-rays was also observed simultaneously at TeV energies by the Whipple Observatory's 10 m gamma-ray telescope. These data provide the first evidence that the X-ray and TeV intensities are well correlated on time-scales of hours.Comment: 4 pages, 1 figure, presented at the VERITAS Workshop on the TeV Astrophysics of Extragalactic Object