Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding.

Hugh Garsden Philip Bull Mike Wilensky Zuhra Abdurashidova Tyrone Adams James E. Aguirre Paul Alexander Zaki S. Ali Rushelle Baartman Yanga Balfour Adam P. Beardsley Lindsay M. Berkhout Gianni Bernardi Tashalee S. Billings Judd D. Bowman Richard F. Bradley Jacob Burba Steven Carey Chris L. Carilli Kai-Feng Chen Carina Cheng Samir Choudhuri David R. DeBoer Eloy de Lera Acedo Matt Dexter Joshua S. Dillon Scott Dynes Nico Eksteen John Ely Aaron Ewall-Wice Nicolas Fagnoni Randall Fritz Steven R. Furlanetto Kingsley Gale-Sides Bharat Kumar Gehlot Abhik Ghosh Brian Glendenning Adelie Gorce Deepthi Gorthi Bradley Greig Jasper Grobbelaar Ziyaad Halday Bryna J. Hazelton Jacqueline N. Hewitt Jack Hickish Tian Huang Daniel C. Jacobs Alec Josaitis Austin Julius MacCalvin Kariseb Nicholas S. Kern Joshua Kerrigan Honggeun Kim Piyanat Kittiwisit Saul A. Kohn Matthew Kolopanis Adam Lanman Paul La Plante Adrian Liu Anita Loots Yin-Zhe Ma David H. E. MacMahon Lourence Malan Cresshim Malgas Keith Malgas Bradley Marero Zachary E. Martinot Andrei Mesinger Mathakane Molewa Miguel F. Morales Tshegofalang Mosiane Steven G. Murray Abraham R. Neben Bojan Nikolic Chuneeta Devi Nunhokee Hans Nuwegeld Aaron R. Parsons Robert Pascua Nipanjana Patra Samantha Pieterse Yuxiang Qin Eleanor Rath Nima Razavi-Ghods Daniel Riley James Robnett Kathryn Rosie Mario G. Santos Peter Sims Saurabh Singh Dara Storer Hilton Swarts Jianrong Tan Nithyanandan Thyagarajan Pieter van Wyngaarden Peter K. G. Williams Zhilei Xu Haoxuan Zheng

Two theorems are presented concerning the Miquel point configuration, when the operative points on the sides of the triangle are the feet of Cevians,

Christopher Bradley

A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.

Christopher Bradley

A construction is given of five Hagge circles complete with supporting calculations.

Christopher Bradley

We prove that it is always possible to find a permutation $p$ on the set $\{1,...,n\}$ such that $c+p(c)$ is prime for all $c \in \{1,...,n\}.$

Paul Bradley

Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".

Richard C. Bradley

PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired comparisons. The PageRank algorithm ranks nodes according to their importance in a network. Whereas Bradley-Terry scores are computed via maximum likelihood estimation, PageRanks are derived from the stationary distribution of a Markov chain. More recent work has shown maximum likelihood estimates for the Bradley-Terry model may be approximated from such a limiting distribution, an interesting connection that has been discovered and rediscovered over the decades. Here we show - through relatively simple mathematics - a connection between paired comparisons and PageRank that exploits the quasi-symmetry property of the Bradley-Terry model. This motivates a novel interpretation of Bradley-Terry scores as 'scaled' PageRanks, and vice versa, with direct implications for citation-based journal ranking metrics.

David Antony Selby

A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first studied by Zermelo in 1929 and rediscovered by Bradley and Terry in 1952. One obvious area of application for such a model is sporting events, and in particular Major League Baseball. With this in mind, we describe a hierarchical Bayesian version of Bradley-Terry suitable for use in ranking and prediction problems, and compare results from these application domains to standard maximum likelihood approaches. Our Bayesian methods outperform the MLE-based analogues, while being simple to construct, implement, and interpret.

Gabriel C. Phelan John T. Whelan

The Bradley-Terry model is widely used for pairwise comparison data analysis. In this paper, we analyze the asymptotic behavior of the maximum likelihood estimator of the Bradley-Terry model in its logistic parameterization, under a general class of linear identifiability constraints. We show that the constraint requiring the Bradley-Terry scores for all compared objects to sum to zero minimizes the sum of the variances of the estimated scores, and recommend using this constraint in practice.

Weichen Wu Brian W. Junker Nynke M. D. Niezink

Rejoinder to ``Least angle regression'' by Efron et al. [math.ST/0406456]

Bradley Efron Trevor Hastie Iain Johnstone Robert Tibshirani