A Bayesian method for pulsar template generation

Extracting Times of Arrival from pulsar radio signals depends on the knowledge of the pulsars pulse profile and how this template is generated. We examine pulsar template generation with Bayesian methods. We will contrast the classical generation mechanism of averaging intensity profiles with a new approach based on Bayesian inference. We introduce the Bayesian measurement model imposed and derive the algorithm to reconstruct a "statistical template" out of noisy data. The properties of these "statistical templates" are analysed with simulated and real measurement data from PSR B1133+16. We explain how to put this new form of template to use in analysing secondary parameters of interest and give various examples: We implement a nonlinear filter for determining ToAs of pulsars. Applying this method to data from PSR J1713+0747 we derive ToAs self consistently, meaning all epochs were timed and we used the same epochs for template generation. While the average template contains fluctuations and noise as unavoidable artifacts, we find that the "statistical template" derived by Bayesian inference quantifies fluctuations and remaining uncertainty. This is why the algorithm suggested turns out to reconstruct templates of statistical significance from ten to fifty single pulses. A moving data window of fifty pulses, taking out one single pulse at the beginning and adding one at the end of the window unravels the characteristics of the methods to be compared. It shows that the change induced in the classical reconstruction is dominated by random fluctuations for the average template, while statistically significant changes drive the dynamics of the proposed method's reconstruction. The analysis of phase shifts with simulated data reveals that the proposed nonlinear algorithm is able to reconstruct correct phase information along with an acceptable estimation of the remaining uncertainty.Comment: 21 pages, 16 figures, submitted to MNRA

On Timing Model Extraction and Hierarchical Statistical Timing Analysis

In this paper, we investigate the challenges to apply Statistical Static Timing Analysis (SSTA) in hierarchical design flow, where modules supplied by IP vendors are used to hide design details for IP protection and to reduce the complexity of design and verification. For the three basic circuit types, combinational, flip-flop-based and latch-controlled, we propose methods to extract timing models which contain interfacing as well as compressed internal constraints. Using these compact timing models the runtime of full-chip timing analysis can be reduced, while circuit details from IP vendors are not exposed. We also propose a method to reconstruct the correlation between modules during full-chip timing analysis. This correlation can not be incorporated into timing models because it depends on the layout of the corresponding modules in the chip. In addition, we investigate how to apply the extracted timing models with the reconstructed correlation to evaluate the performance of the complete design. Experiments demonstrate that using the extracted timing models and reconstructed correlation full-chip timing analysis can be several times faster than applying the flattened circuit directly, while the accuracy of statistical timing analysis is still well maintained

An independent test on the local position invariance of gravity with the triple pulsar PSR J0337+1715

We design a direct test of the local position invariance (LPI) in the post-Newtonian gravity, using the timing observation of the triple pulsar, PSR J0337+1715. The test takes advantage of the large gravitational acceleration exerted by the outer white dwarf to the inner neutron star -- white dwarf binary. Using machine-precision three-body simulations and dedicated Markov-chain Monte Carlo (MCMC) techniques with various sampling strategies and noise realizations, we estimate that the Whitehead's parameter could have already been limited to $|\xi| \lesssim 0.4$ (95\% CL), with the published timing data spanning from January 2012 to May 2013. The constraint is still orders of magnitude looser than the best limit, yet it is able to independently falsify Whitehead's gravity theory where $\xi=1$. In addition, the new test is immune to extra assumptions and involves full dynamics of a three-body system with a strongly self-gravitating neutron star.Comment: 14 pages, 4 figures; Classical and Quantum Gravity, in pres