The Epoch of Reionization (EoR) is an uncharted era in our Universe's history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic medium. There are many experiments investigating the EoR by tracing the 21cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERA's foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. (in prep.) and supersede results from previously published PAPER analyses.

Carina Cheng Aaron R. Parsons Matthew Kolopanis Daniel C. Jacobs Adrian Liu Saul A. Kohn James E. Aguirre Jonathan C. Pober Zaki S. Ali Gianni Bernardi Richard F. Bradley Chris L. Carilli David R. DeBoer Matthew R. Dexter Joshua S. Dillon Pat Klima David H. E. MacMahon David F. Moore Chuneeta D. Nunhokee William P. Walbrugh Andre Walker

We present limits on the 21cm power spectrum from the Epoch of Reionization (EoR) using data from the 64 antenna configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) analyzed through a power spectrum pipeline independent from previous PAPER analyses. Previously reported results from PAPER have been found to contain significant signal loss (Cheng et al. 2018, arxiv:1810.05175). Several lossy steps from previous PAPER pipelines have not been included in this analysis, namely: delay-based foreground filtering, optimal fringe-rate filtering, and empirical covariance-based estimators. Steps which remain in common with previous analyses include redundant calibration and local sidereal time (LST) binning. The power spectra reported here are effectively the result of applying a linear Fourier transform analysis to the calibrated, LST binned data. This analysis also uses more data than previous publications, including the complete available redshift range of $z \sim 7.5$ to $11$. In previous PAPER analyses, many power spectrum measurements were found to be detections of noncosmological power at levels of significance ranging from two to hundreds of times the theoretical noise. Here, excess power is examined using redundancy between baselines and power spectrum jackknives. The upper limits we find on the 21cm power spectrum from reionization are ($1500$ mK)$^{2}$, ($1900$ mK)$^{2}$, ($280$ mK)$^{2}$, ($200$ mK)$^{2}$, ($380$ mK)$^{2}$, ($300$ mK)$^{2}$ at redshifts $z=10.87,\ 9.93,\ 8.68,\ 8.37,\ 8.13,$ and $7.48$, respectively. For reasons described in Cheng et al. 2018 (arxiv:1810.05175), these limits supersede all previous PAPER results (Ali et al. 2018, arxiv:1502.06016).

Matthew Kolopanis Daniel C. Jacobs Carina Cheng Aaron R. Parsons Saul A. Kohn Jonathan C. Pober James E. Aguirre Zaki S. Ali Gianni Bernardi Richard F. Bradley Christopher L. Carilli David R. DeBoer Matthew Dexter Joshua S. Dillon Joshua Kerrigan Patricia Klima Adrian Liu Dave MacMahon David F. Moore Nithyanandan Thyagarajan Chuneeta Devi Nunhokee William Walbrughp Andre Walker

As machine learning (ML) systems get adopted in more critical areas, it has become increasingly crucial to address the bias that could occur in these systems. Several fairness pre-processing algorithms are available to alleviate implicit biases during model training. These algorithms employ different concepts of fairness, often leading to conflicting strategies with consequential trade-offs between fairness and accuracy. In this work, we evaluate three popular fairness pre-processing algorithms and investigate the potential for combining all algorithms into a more robust pre-processing ensemble. We report on lessons learned that can help practitioners better select fairness algorithms for their models.

Khaled Badran Pierre-Olivier Côté Amanda Kolopanis Rached Bouchoucha Antonio Collante Diego Elias Costa Emad Shihab Foutse Khomh

Through a very careful analysis Kolopanis and collaborators identified a negative power spectrum (PS) systematic. The 21 cm cosmology community has assumed that any observational systematics would add power, as negative PS are non-physical. In addition to the mystery of their origin, negative PS systematics raise the spectre of artificially lowering upper limits on the 21 cm PS. It appears that the source of the negative PS systematics is a subtle interaction between choices in how the PS estimate is calculated and baseline-dependent systematic power. In this paper we present a statistical model of baseline dependent systematics to explore how negative PS systematics can appear and their statistical characteristics. This leads us to recommendations on when and how to consider negative PS systematics when reporting observational 21 cm cosmology upper limits.

Miguel F. Morales Jonathan Pober Bryna J. Hazelton

The 21cm line of neutral hydrogen is a powerful probe of the high-redshift universe (Cosmic Dawn and the Epoch of Reionization), with an unprecedented potential to inform us about key processes of early galaxy formation, the first stars and even cosmology and structure formation, via intensity mapping. It is the subject of a number of current and upcoming low-frequency radio experiments. This paper presents 21cmSense v2.0, which is a Python package that provides a modular framework for calculating the sensitivity of these experiments, in order to enhance the process of their design and forecasting their power for parameter inference. Version 2.0 of 21cmSense has been re-written from the ground up to be more modular and extensible than its venerable predecessor (Pober et al., 2013, 2014), and to provide a more user-friendly interface. The package is freely available both to use and contribute towards at https://github.com/rasg-affiliates/21cmSense.

Steven G. Murray Jonathan Pober Matthew Kolopanis

Treating problems in full general relativity is highly complex and frequently approximate methods are employed to simplify the solution. We present comparative solutions of a infinitesimally thin relativistic, stationary, rigidly rotating disk obtained using the full equations and the approximate approach suggested by Wilson & Mathews. We find that the Wilson-Mathews method has about the same accuracy as the first post-Newtonian approximation.

Willy Kley Gerhard Schaefer

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.

L. Sunil Chandran Mathew C. Francis Rogers Mathew

We establish a thermodynamic limit and Gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces. The results hold for the standard ballistic deposition model as well as the surface relaxation model in the off-lattice setting. The results are proved with the aid of general limit theorems for stabilizing functionals of marked Poisson point processes.

Mathew D. Penrose J. E. Yukich

We present results on NLO-QCD corrections to the process e+ e- --> hadrons via photon-, Z- and graviton-exchange in the context of TeV-scale gravity models. The quantitative impact of these QCD corrections for searches of extra dimensions at a Linear Collider is briefly discussed.

Prakash Mathews V. Ravindran K. Sridhar

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Lal\'in. As a corollary, we also obtain three $q$-series expansions for the dilogarithm.

Mathew D. Rogers