Fisher Formalism For Anisotropic Gravitational-Wave Background Searches With Pulsar Timing Arrays

Pulsar timing arrays (PTAs) are currently the only experiments directly sensitive to gravitational waves with decade-long periods. Within the next five to ten years, PTAs are expected to detect the stochastic gravitational-wave background (SGWB) collectively sourced by inspiraling supermassive black hole binaries. It is expected that this background is mostly isotropic, and current searches focus on the monopole part of the SGWB. Looking ahead, anisotropies in the SGWB may provide a trove of additional information on both known and unknown astrophysical and cosmological sources. In this paper, we build a simple yet realistic Fisher formalism for anisotropic SGWB searches with PTAs. Our formalism is able to accommodate realistic properties of PTAs and allows simple and accurate forecasts. We illustrate our approach with an idealized PTA consisting of identical, isotropically distributed pulsars. In a companion paper, we apply our formalism to current PTAs and show that it can be a powerful tool to guide and optimize real data analysis

An Optimal Algorithm for Online Freeze-Tag

In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, each frozen robot is not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than 7/3 for online freeze-tag, and posed the question of whether an O(1)-competitive algorithm exists. We provide a (1+?2)-competitive algorithm for online time-dependent freeze-tag, and show that this is the best possible: there does not exist an algorithm which achieves a lower competitive ratio on every metric space

The beamformer and correlator for the Large European Array for Pulsars

The Large European Array for Pulsars combines Europe's largest radio telescopes to form a tied-array telescope that provides high signal-to-noise observations of millisecond pulsars (MSPs) with the objective to increase the sensitivity of detecting low-frequency gravitational waves. As part of this endeavor we have developed a software correlator and beamformer which enables the formation of a tied-array beam from the raw voltages from each of telescopes. We explain the concepts and techniques involved in the process of adding the raw voltages coherently. We further present the software processing pipeline that is specifically designed to deal with data from widely spaced, inhomogeneous radio telescopes and describe the steps involved in preparing, correlating and creating the tied-array beam. This includes polarization calibration, bandpass correction, frequency dependent phase correction, interference mitigation and pulsar gating. A link is provided where the software can be obtained.Comment: 10 pages, 6 figures, accepted for publication in Astronomy and Computin

Combinatorics of Local Search: An Optimal 4-Local Hall\u27s Theorem for Planar Graphs

Local search for combinatorial optimization problems is becoming a dominant algorithmic paradigm, with several papers using it to resolve long-standing open problems. In this paper, we prove the following `4-local\u27 version of Hall\u27s theorem for planar graphs: given a bipartite planar graph G = (B, R, E) such that |N(B\u27)| >= |B\u27| for all |B\u27| <= 4, there exists a matching of size at least |B|/4 in G; furthermore this bound is tight. Besides immediately implying improved bounds for several problems studied in previous papers, we find this variant of Hall\u27s theorem to be of independent interest in graph theory