Complexity transitions in global algorithms for sparse linear systems over finite fields

We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to changes in performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary to the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.Comment: 23 pages, 8 figure

Detection of Contact Binaries Using Sparse High Phase Angle Lightcurves

We show that candidate contact binary asteroids can be efficiently identified from sparsely sampled photometry taken at phase angles >60deg. At high phase angle, close/contact binary systems produce distinctive lightcurves that spend most of the time at maximum or minimum (typically >1mag apart) brightness with relatively fast transitions between the two. This means that a few (~5) sparse observations will suffice to measure the large range of variation and identify candidate contact binary systems. This finding can be used in the context of all-sky surveys to constrain the fraction of contact binary near-Earth objects. High phase angle lightcurve data can also reveal the absolute sense of the spin.Comment: 4 pages, 4 figures, 1 table. Accepted for publication in ApJ

A search for magnetic fields on central stars in planetary nebulae

One of the possible mechanisms responsible for the panoply of shapes in planetary nebulae is the presence of magnetic fields that drive the ejection of ionized material during the proto-planetary nebula phase. Therefore, detecting magnetic fields in such objects is of key importance for understanding their dynamics. Still, magnetic fields have not been detected using polarimetry in the central stars of planetary nebulae. Circularly polarized light spectra have been obtained with the Focal Reducer and Low Dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory and the Intermediate dispersion Spectrograph and Imaging System at the William Herschel Telescope. Nineteen planetary nebulae spanning very different morphology and evolutionary stages have been selected. Most of central stars have been observed at different rotation phases to point out evidence of magnetic variability. In this paper, we present the result of two observational campaigns aimed to detect and measure the magnetic field in the central stars of planetary nebulae on the basis of low resolution spectropolarimetry. In the limit of the adopted method, we can state that large scale fields of kG order are not hosted on the central star of planetary nebulae.Comment: Paper accepted to be published in Astronomy and Astrophysics on 20/01/201

Number of loops of size h in growing scale-free networks

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.Comment: 4 pages, 3 figure

Mean-Field and Anomalous Behavior on a Small-World Network

We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous scaling is found in the width of the mean-field region, as well as in the mean-field amplitudes. Finally, we consider non-equilibrium processes.Comment: 4 pages, 0 figures; reference adde

The ultracool dwarf DENIS-P J104814.7-395606. Chromospheres and coronae at the low-mass end of the main-sequence

We have obtained an XMM-Newton observation and a broad-band spectrum from the ultraviolet to the near infrared with X-Shooter for one of the nearest M9 dwarfs, DENIS-P J1048-3956 (4pc). We integrate these data by a compilation of activity parameters for ultracool dwarfs from the literature with the aim to advance our understanding of these objects by comparing them to early-M type dwarf stars and the Sun. Our deep XMM-Newton observation has led to the first X-ray detection of DENIS-P J1048-3956 (log Lx = 25.1) as well as the first measurement of its V band brightness (V = 17.35mag). Flux-flux relations between X-ray and chromospheric activity indicators are here for the first time extended into the regime of the ultracool dwarfs. The approximate agreement of DENIS-P J1048-3956 and other ultracool dwarfs with flux-flux relations for early-M dwarfs suggests that the same heating mechanisms work in the atmospheres of ultracool dwarfs, albeit weaker as judged from their lower fluxes. The observed Balmer decrements of DENIS-P J1048-3956 are compatible with optically thick plasma in LTE at low, nearly photospheric temperature or optically thin LTE plasma at 20000K. Describing the decrements with CaseB recombination requires different emitting regions for Halpha and the higher Balmer lines. The high observed Halpha/Hbeta flux ratio is also poorly fitted by the optically thin models. We derive a similarly high value for the Halpha/Hbeta ratio of vB10 and LHS2065 and conclude that this may be a characteristic of ultracool dwarfs. We add DENIS-P J1048-3956 to the list of ultracool dwarfs detected in both the radio and the X-ray band. The Benz-Guedel relation between radio and X-ray luminosity of late-type stars is well-known to be violated by ultracool dwarfs. We speculate on the presence of two types of ultracool dwarfs with distinct radio and X-ray behavior.Comment: accepted for publication in Astronomy & Astrophysic