A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

Calibration of the EDGES High-Band Receiver to Observe the Global 21-cm Signature from the Epoch of Reionization

The EDGES High-Band experiment aims to detect the sky-average brightness temperature of the $21$-cm signal from the Epoch of Reionization (EoR) in the redshift range $14.8 \gtrsim z \gtrsim 6.5$. To probe this redshifted signal, EDGES High-Band conducts single-antenna measurements in the frequency range $90-190$ MHz from the Murchison Radio-astronomy Observatory in Western Australia. In this paper, we describe the current strategy for calibration of the EDGES High-Band receiver and report calibration results for the instrument used in the $2015-2016$ observational campaign. We propagate uncertainties in the receiver calibration measurements to the antenna temperature using a Monte Carlo approach. We define a performance objective of $1$~mK residual RMS after modeling foreground subtraction from a fiducial temperature spectrum using a five-term polynomial. Most of the calibration uncertainties yield residuals of $1$~mK or less at $95\%$ confidence. However, current uncertainties in the antenna and receiver reflection coefficients can lead to residuals of up to $20$ mK even in low-foreground sky regions. These dominant residuals could be reduced by 1) improving the accuracy in reflection measurements, especially their phase 2) improving the impedance match at the antenna-receiver interface, and 3) decreasing the changes with frequency of the antenna reflection phase.Comment: Updated to match version accepted by Ap

Radio Astronomy

Contains reports on three research projects.National Aeronautics and Space Administration (Grant NsG-419)National Aeronautics and Space Administration (Grant NsG-250-62)U. S. Air Force under Contract AF 19(628)-500Lincoln Laboratory, Purchase Order DDL BB-10

Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization

Preliminary results are presented from a simple, single-antenna experiment designed to measure the all-sky radio spectrum between 100 and 200 MHz. The system used an internal comparison-switching scheme to reduce non-smooth instrumental contaminants in the measured spectrum to 75 mK. From the observations, we place an initial upper limit of 450 mK on the relative brightness temperature of the redshifted 21 cm contribution to the spectrum due to neutral hydrogen in the intergalactic medium (IGM) during the epoch of reionization, assuming a rapid transition to a fully ionized IGM at a redshift of 8. With refinement, this technique should be able to distinguish between slow and fast reionization scenarios. To constrain the duration of reionization to dz > 2, the systematic residuals in the measured spectrum must be reduced to 3 mK.Comment: Submitted to ApJ. 9 pages including 6 figure