Densification and Structural Transitions in Networks that Grow by Node Copying

We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When $p<\frac{1}{2}$, this algorithm generates sparse networks, in which the average node degree is finite. A power-law degree distribution also arises, with a non-universal exponent whose value is determined by a transcendental equation in $p$. In the sparse regime, the network is "normal", e.g., the relative fluctuations in the number of links are asymptotically negligible. For $p\geq \frac{1}{2}$, the emergent networks are dense (the average degree increases with the number of nodes $N$) and they exhibit intriguing structural behaviors. In particular, the $N$-dependence of the number of $m$-cliques (complete subgraphs of $m$ nodes) undergoes $m-1$ transitions from normal to progressively more anomalous behavior at a $m$-dependent critical values of $p$. Different realizations of the network, which start from the same initial state, exhibit macroscopic fluctuations in the thermodynamic limit---absence of self averaging. When linking to second neighbors of the target node can occur, the number of links asymptotically grows as $N^2$ as $N\to\infty$, so that the network is effectively complete as $N\to \infty$.Comment: 15 pages, 12 figure

Secondary periodicities of microbursts of TeV gamma rays from the Crab pulsar

Observations were made during the past several years on the Crab pulsar using the Ooty atmospheric Cerenkov array with the aim of detecting possible emission of ultra high energy gamma rays by the pulsar. During the course of these observations, it was found that the Crab pulsar emits TeV gamma rays in bursts of short duration. The microbursts of TeV gamma rays from the Crab pulsar, which were seen in the data of at least three years, also reveal interesting secondary periodicities. It was noticed at first that some bursts could be connected with the others that occurred during the same night or during the next two nights with integral number of cycles of periods 43 + or - 1 minute. Ten possible periods in the vicinity of 43 minutes were determined for all the combinations of bursts for each year. The best values of periods thus obtained were different from year to year. But when, instead of the real time, the number of Crab cycles elapsed between the bursts was used as the unit of time, two values of burst periods - 77460 and 77770 Crab cycles - were found to be significant in the data of at least two years. A Monte Carlo simulation using 1500 trial periods chosen randomly within + or - 5 minutes of the original burst period did not reveal any value of the period as significant

Observations on TeV gamma rays from Geminga and PSR 0950+08

The Geminga (2 CG 195+04) which exhibits a periodicity with a period of 59 to 60 s in its emission of X-rays, GeV gamma rays and TeV gamma rays was studied. During the winter of 1984 to 1985, this object was observed to see if it emits TeV gamma rays with a periodicity approx 60 s. The observations were carried out at two different sites separated by 11 Km with the Ooty Atmospheric Cerenkov Array split into two parts. Data were collected during clear moonless nights for a total duration of 15.3 hours spread over 2 months. Since the first time derivative of period is believed to be large and uncertain. The total data are subdivided into segments of duration not more than 3 days each to steer clear of the effects of P in the phase analysis. If TeV gamma ray signals are seen in each of these segments, it is possible to derive P from observed data

A CLEAN-based Method for Deconvolving Interstellar Pulse Broadening from Radio Pulses

Multipath propagation in the interstellar medium distorts radio pulses, an effect predominant for distant pulsars observed at low frequencies. Typically, broadened pulses are analyzed to determine the amount of propagation-induced pulse broadening, but with little interest in determining the undistorted pulse shapes. In this paper we develop and apply a method that recovers both the intrinsic pulse shape and the pulse broadening function that describes the scattering of an impulse. The method resembles the CLEAN algorithm used in synthesis imaging applications, although we search for the best pulse broadening function, and perform a true deconvolution to recover intrinsic pulse structre. As figures of merit to optimize the deconvolution, we use the positivity and symmetry of the deconvolved result along with the mean square residual and the number of points below a given threshold. Our method makes no prior assumptions about the intrinsic pulse shape and can be used for a range of scattering functions for the interstellar medium. It can therefore be applied to a wider variety of measured pulse shapes and degrees of scattering than the previous approaches. We apply the technique to both simulated data and data from Arecibo observations.Comment: 9 pages, 6 figures, Accepted for publication in the Astrophysical Journa

1.57 μm InGaAsP/InP surface emitting lasers by angled focus ion beam etching

The characteristics of 1.57 μm InGaAsP/InP surface emitting lasers based on an in-plan ridged structure and 45° beam deflectors defined by angled focused ion beam (FIB) etching are reported. With an externally integrated beam deflector, threshold currents and emission spectra identical to conventional edge emitting lasers are achieved. These results show that FIB etching is a very promising technique for the definition of high quality mirrors and beam deflectors on semiconductor heterostructures for a variety of integrated optoelectronic devices

Pulsed emission of TeV gamma rays from Vela pulsar

The Ooty atmospheric Cerenkov array, consisting of 10 parabolic mirrors of 0.9 m diameter and 8 of 1.5 m diameter, was used for observations on the Vela pulsar to see if it emits gamma rays in the TeV energy range. During the winter of 1984-85, the array was split into two parts: (1) consisting wholly of the smaller mirrors, and (2) wholly of the bigger mirrors. The two arrays were operated at two different sites to distinguish a marginally significant genuine pulsar signal from spurious signals produced trivially by chance fluctuations in the background rates. All the mirrors were pointed at the celestial object to track it for durations of the order of 1 to 6 hours during clear moonless nights. The event time data is analyzed to detect a possible pulsed emission of TeV gamma rays using the contemporaneous pulsar elements on the basis of their radio observations on the Vela pulsar. Results from the analyses of observations made during the winters of 1982-83 and 1984-85 on steady pulsed emission and on possible transient emission is presented