iResum: a new paradigm for resumming gravitational wave amplitudes

We introduce a new, resummed, analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections $f_{\ell m}$ of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform multipoles, both for a test-mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much closer to the corresponding "exact" functions (obtained solving numerically the Teukolsky equation) up to the light-ring, than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical/analytical agreement at the last-stable-orbit, and a well-controlled behavior up to the light-ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with Numerical Relativity (NR) data shows that the analytical/numerical fractional disagreement at merger, without NR-calibration of the EOB waveform, is generically reduced by iResum, from a $40\%$ of the usual approach to just a few percents. This suggests that EOBNR waveform models for coalescing BBHs may be improved using iResum amplitudes.Comment: 6 pages, 7 figures. Improved discussion for the comparable-mass cas

Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity

We compute and analyze the gravitational waveform emitted to future null infinity by a system of two black holes in the large mass ratio limit. We consider the transition from the quasi-adiabatic inspiral to plunge, merger, and ringdown. The relative dynamics is driven by a leading order in the mass ratio, 5PN-resummed, effective-one-body (EOB), analytic radiation reaction. To compute the waveforms we solve the Regge-Wheeler-Zerilli equations in the time-domain on a spacelike foliation which coincides with the standard Schwarzschild foliation in the region including the motion of the small black hole, and is globally hyperboloidal, allowing us to include future null infinity in the computational domain by compactification. This method is called the hyperboloidal layer method, and is discussed here for the first time in a study of the gravitational radiation emitted by black hole binaries. We consider binaries characterized by five mass ratios, $\nu=10^{-2,-3,-4,-5,-6}$, that are primary targets of space-based or third-generation gravitational wave detectors. We show significative phase differences between finite-radius and null-infinity waveforms. We test, in our context, the reliability of the extrapolation procedure routinely applied to numerical relativity waveforms. We present an updated calculation of the gravitational recoil imparted to the merger remnant by the gravitational wave emission. As a self consistency test of the method, we show an excellent fractional agreement (even during the plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the gravitational wave angular momentum flux computed at null infinity. New results concerning the radiation emitted from unstable circular orbits are also presented.Comment: 22 pages, 18 figures. Typos corrected. To appear in Phys. Rev.

Adjunct hexagonal array token Petri nets and hexagonal picture languages

Adjunct Hexagonal Array Token Petri Net Structures (AHPN) are re- cently introduced hexagonal picture generating devices which extended the Hexag- onal Array Token Petri Net Structures . In this paper we consider AHPN model along with a control feature called inhibitor arcs and compare it with some ex- pressive hexagonal picture generating and recognizing models with respect to the generating power

Iso-array rewriting P systems with context-free iso-array rules

A new computing model called P system is a highly distributed and parallel theoretical model, which is proposed in the area of membrane computing. Ceterchi et al. initially proposed array rewriting P systems by extending the notion of string rewriting P systems to arrays (2003). A theoretical model for picture generation using context-free iso-array grammar rules and puzzle iso-array grammar rules are introduced by Kalyani et al. (2004, 2006). Also iso-array rewriting P systems for iso-picture languages have been studied by Annadurai et al. (2008). In this paper we consider the context-free iso-array rules and context-free puzzle iso-array rules in iso-array rewriting P systems and examine the generative powers of these P systems

Gigahertz-Peaked Spectrum Radio Sources in Nearby Galaxies

There is now strong evidence that many low-luminosity AGNs (LLAGNs) contain accreting massive black holes and that the nuclear radio emission is dominated by parsec-scale jets launched by these black holes. Here, we present preliminary results on the 1.4 GHz to 667 GHz spectral shape of a well-defined sample of 16 LLAGNs. The LLAGNs have a falling spectrum at high GHz frequencies. Several also show a low-frequency turnover with a peak in the 1-20 GHz range. The results provide further support for jet dominance of the core radio emission. The LLAGNs show intriguing similarities with gigahertz-peaked spectrum (GPS) sources.Comment: 6 pages, to appear in ASP Conference series, 2002, Vol. 25

Brief Announcement: Automating and Mechanising Cutoff Proofs for Parameterized Verification of Distributed Protocols

We propose a framework to automate and mechanize simulation-based proofs of cutoffs for parameterized verification of distributed protocols. We propose a strategy to derive the simulation relation given the cutoff instance and encode the correctness of the simulation relation as a formula in first-order logic. We have successfully applied our approach on a number of distributed protocols

Automating and Mechanizing Cutoff-based Verification of Distributed Protocols

Distributed protocols are generally parametric and can be executed on a system with any number of nodes, and hence proving their correctness becomes an infinite state verification problem. The most popular approach for verifying distributed protocols is to find an inductive invariant which is strong enough to prove the required safety property. However, finding inductive invariants is known to be notoriously hard, and is especially harder in the context of distributed protocols which are quite complex due to their asynchronous nature. In this work, we investigate an orthogonal cut-off based approach to verifying distributed protocols which sidesteps the problem of finding an inductive invariant, and instead reduces checking correctness to a finite state verification problem. The main idea is to find a finite, fixed protocol instance called the cutoff instance, such that if the cutoff instance is safe, then any protocol instance would also be safe. Previous cutoff based approaches have only been applied to a restricted class of protocols and specifications. We formalize the cutoff approach in the context of a general protocol modeling language (RML), and identify sufficient conditions which can be efficiently encoded in SMT to check whether a given protocol instance is a cutoff instance. Further, we propose a simple static analysis-based algorithm to automatically synthesize a cut-off instance. We have applied our approach successfully on a number of complex distributed protocols, providing the first known cut-off results for many of them.Comment: 27 page

Shuffle on array languages generated by array grammars

Motivated by the studies done by G. Siromoney et al. (1973) and Alexan- dru Mateescu et al. (1998) we examine the language theoretic results related to shuf- fle on trajectories by making use of Siromoney array grammars such as (R : R)AG, (R : C F )AG, (C F : R)AG, (C F : C F )AG, (C S : R)AG, (C S : C S)AG and (C F : C S)AG which are more powerful than the Siromoney matrix grammars (1972) and are used to make digital pictures