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We detail the the REACH radiometric system designed to enable measurements of the 21-cm neutral hydrogen line. Included is the radiometer architecture and end-to-end system simulations as well as a discussion of the challenges intrinsic to highly-calibratable system development. Following this, we share laboratory results based on the calculation of noise wave parameters utilising an over-constrained least squares approach demonstrating a calibration RMSE of 80 mK for five hours of integration on a custom-made source with comparable impedance to that of the antenna used in the field. This paper therefore documents the state of the calibrator and data analysis in December 2022 in Cambridge before shipping to South Africa., Comment: 30 pages, 19 figures

Observations of the 21-cm line from primordial hydrogen promise to be one of the best tools to study the early epochs of the Universe: the Dark Ages, the Cosmic Dawn, and the subsequent Epoch of Reionization. In 2018, the EDGES experiment caught the attention of the cosmology community with a potential detection of an absorption feature in the sky-averaged radio spectrum centred at 78 MHz. The feature is deeper than expected, and, if confirmed, would call for new physics. However, different groups have re-analyzed the EDGES data and questioned the reliability of the signal. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is a sky-averaged 21-cm experiment aiming at improving the current observations by tackling the issues faced by current instruments related to residual systematic signals in the data. The novel experimental approach focuses on detecting and jointly explaining these systematics together with the foregrounds and the cosmological signal using Bayesian statistics. To achieve this, REACH features simultaneous observations with two different antennas, an ultra wideband system (redshift range 7.5 to 28), and a receiver calibrator based on in-field measurements. Simulated observations forecast percent-level constraints on astrophysical parameters, potentially opening up a new window to the infant Universe., Comment: Publication date: 21 July 2022

In safety-critical applications of reinforcement learning such as healthcare and robotics, it is often desirable to optimize risk-sensitive objectives that account for tail outcomes rather than expected reward. We prove the first regret bounds for reinforcement learning under a general class of risk-sensitive objectives including the popular CVaR objective. Our theory is based on a novel characterization of the CVaR objective as well as a novel optimistic MDP construction.

Following the reported detection of an absorption profile associated with the 21~cm sky-averaged signal from the Cosmic Dawn by the EDGES experiment in 2018, a number of experiments have been set up to verify this result. This paper discusses the design process used for global 21~cm experiments, focusing specifically on the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). This experiment will seek to understand and compensate for systematic errors present using detailed modelling and characterization of the instrumentation. There is detailed the quantitative figures of merit and numerical modelling used to assist the design process of the REACH dipole antenna (one of the 2 antenna designs for REACH Phase I). This design process produced a 2.5:1 frequency bandwidth dipole. The aim of this design was to balance spectral smoothness and low impedance reflections with the ability to describe and understand the antenna response to the sky signal to inform the critically important calibration during observation and data analysis., Comment: 32 pages, 30 figures, to be submitted to the Journal of Astronomical Instrumentation

Andrews, Lewis and Lovejoy introduced the partition function $PD(n)$ as the number of partitions of $n$ with designated summands. A bipartition of $n$ is an ordered pair of partitions $(\pi_1, \pi_2)$ with the sum of all of the parts being $n$. In this paper, we introduce a generalized crank named the $pd$-crank for bipartitions with designated summands and give some inequalities for the $pd$-crank of bipartitions with designated summands modulo 2 and 3. We also define the $pd$-crank moments weighted by the parity of $pd$-cranks $\mu_{2k,bd}(-1,n)$ and show the positivity of $(-1)^n\mu_{2k,bd}(-1,n)$. Let $M_{bd}(m,n)$ denote the number of bipartitions of $n$ with designated summands with $pd$-crank $m$. We prove a monotonicity property of $pd$-cranks of bipartitions with designated summands and find that the sequence $\{M_{bd}(m,n)\}_{|m|\leq n}$ is unimodal for $n\not= 1,5,7$., Comment: 17 pages

Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behaviour of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes., Comment: Selected for Viewpoint in Physics; PRL Editor's Suggestion

Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of noninteracting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems., Comment: The original version has been split into two parts. This first part focuses on order vs. correlation. The second part, about finite-size scaling, will be included in a separate paper. 15 pages, 6 figures, 1 table, 5 videos