Search

We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of [Johansson and Linusson 2007]. In particular, we give a uniform proof of an exponential upper bound for the number of alternating sign matrices classically avoiding one of twelve particular patterns, and a super-exponential lower bound for all other single-pattern avoidance classes. We also show that for any fixed integer $k$, there is an exponential upper bound for the number of alternating sign matrices that classically avoid any single permutation pattern and contain precisely $k$ negative ones. Finally, we prove that there must be at most $3$ negative ones in an alternating sign matrix which classically avoids both $2143$ and $3412$, and we exactly enumerate the number of them with precisely $3$ negative ones.

This paper presents the first search for dark matter axions with mass in the ranges 76.56 to 76.82 $\mu$eV and 79.31 to 79.53 $\mu$eV using a prototype setup for the MAgnetized Disk and Mirror Axion eXperiment (MADMAX). The experimental setup employs a dielectric haloscope consisting of three sapphire disks and a mirror to resonantly enhance the axion-induced microwave signal within the magnetic dipole field provided by the 1.6 T Morpurgo magnet at CERN. Over 14.5 days of data collection, no axion signal was detected. A 95% CL upper limit on the axion-photon coupling strength down to $|g_{a\gamma}| \sim 2 \times 10^{-11} \mathrm{GeV}^{-1}$ is set in the targeted mass ranges, surpassing previous constraints, assuming a local axion dark matter density $\rho_{a}$ of $0.3~\mathrm{GeV}/\mathrm{cm}^3$. This study marks the first axion dark matter search using a dielectric haloscope.

We report the first result from a dark photon dark matter search in the mass range from ${78.62}$ to $83.95~\mathrm{\mu eV}/c^2$ with a dielectric haloscope prototype for MADMAX (Magnetized Disc and Mirror Axion eXperiment). Putative dark photons would convert to observable photons within a stack consisting of three sapphire disks and a mirror. The emitted power of this system is received by an antenna and successively digitized using a low-noise receiver. No dark photon signal has been observed. Assuming unpolarized dark photon dark matter with a local density of $\rho_{\chi}=0.3~\mathrm{GeV/cm^3}$ we exclude a dark photon to photon mixing parameter $\chi > 3.0 \times 10^{-12}$ over the full mass range and $\chi > 1.2 \times 10^{-13}$ at a mass of $80.57~\mathrm{\mu eV}/c^2$ with a 95\% confidence level. This is the first physics result from a MADMAX prototype and exceeds previous constraints on $\chi$ in this mass range by up to almost three orders of magnitude., Comment: v1

MADMAX, a future experiment to search for axion dark matter, is based on a novel detection concept called the dielectric haloscope. It consists of a booster composed of several dielectric disks positioned with $\mu$m precision. A prototype composed of one movable disk was built to demonstrate the mechanical feasibility of such a booster in the challenging environment of the experiment: high magnetic field to convert the axions into photons and cryogenic temperature to reduce the thermal noise. It was tested both inside a strong magnetic field up to 1.6 T and at cryogenic temperatures down to 35K. The measurements of the velocity and positioning accuracy of the disk are shown and are found to match the MADMAX requirements., Comment: 14 pages, 9 figures

The reciprocity approach is a powerful method to determine the expected signal power of axion haloscopes in a model-independent way. Especially for open and broadband setups like the MADMAX dielectric haloscope the sensitivity to the axion field is difficult to calibrate since they do not allow discrete eigenmode analysis and are optically too large to fully simulate. The central idea of the reciprocity approach is to measure a reflection-induced test field in the setup instead of trying to simulate the axion-induced field. In this article, the reciprocity approach is used to determine the expected signal power of a dish antenna and a minimal dielectric haloscope directly from measurements. The results match expectations from simulation but also include important systematic effects that are too difficult to simulate. In particular, the effect of antenna standing waves and higher order mode perturbations can be quantified for the first time in a dielectric haloscope., Comment: v2, updated to match journal version, 18 pages, 10 figures

Axion haloscopes search for dark matter axions from the galactic halo, most commonly by measuring a power excess sourced by the axion effective current density. Constraining axion parameters from detection or lack thereof requires estimating the expected signal power. Often, this is done by studying the response of the haloscope to a known, but different, source current density, for example via a reflection measurement. However, only in the special case when both sources induce the same electromagnetic fields, do the quantities derived from a reflection measurement adequately describe the setup during an axion measurement. While this might be valid for the traditional resonant cavity haloscope, new broadband or open designs like dish antennas or dielectric haloscopes cannot make this assumption. A more general relation between axion- and reflection-induced fields is needed. In this article, we use the Lorentz reciprocity theorem to derive an expression for the axion signal power which instead of the unmeasurable axion-induced fields depends on the measurable reflection-induced fields. This entirely circumvents the need to know the response of the haloscope to the unknown axion source. It applies to a wide variety of haloscopes including resonant cavities, dielectric haloscopes, and broadband dish antennas., Comment: 13 pages, 4 figures; v2: minor changes to match published version

A Fishburn permutation is a permutation which avoids the bivincular pattern $(231, \{1\}, \{1\})$, while an ascent sequence is a sequence of nonnegative integers in which each entry is less than or equal to one more than the number of ascents to its left. Fishburn permutations and ascent sequences are linked by a bijection $g$ of Bousquet-M\'elou, Claesson, Dukes, and Kitaev. We write $F_n(\sigma_1,\ldots,\sigma_k)$ to denote the set of Fishburn permutations of length $n$ which avoid each of $\sigma_1,\ldots,\sigma_k$ and we write $A_n(\alpha_1,\ldots,\alpha_k)$ to denote the set of ascent sequences which avoid each of $\alpha_1,\ldots,\alpha_k$. We settle a conjecture of Gil and Weiner by showing that $g$ restricts to a bijection between $F_n(3412)$ and $A_n(201)$. Building on work of Gil and Weiner, we use elementary techniques to enumerate $F_n(123)$ with respect to inversion number and number of left-to-right maxima, obtaining expressions in terms of $q$-binomial coefficients, and to enumerate $F_n(123,\sigma)$ for all $\sigma$. We use generating tree techniques to study the generating functions for $F_n(321, 1423)$, $F_n(321,3124)$, and $F_n(321,2143)$ with respect to inversion number and number of left-to-right maxima. We use these results to show $|F_n(321,1423)| = |F_n(321,3124)| = F_{n+2} - n - 1$, where $F_n$ is a Fibonacci number, and $|F_n(321,2143)| = 2^{n-1}$. We conclude with a variety of conjectures and open problems., Comment: 41 pages, 4 figures

How do we know how much we know? Quantifying uncertainty associated with our modelling work is the only way we can answer how much we know about any phenomenon. With quantitative science now highly influential in the public sphere and the results from models translating into action, we must support our conclusions with sufficient rigour to produce useful, reproducible results. Incomplete consideration of model-based uncertainties can lead to false conclusions with real world impacts. Despite these potentially damaging consequences, uncertainty consideration is incomplete both within and across scientific fields. We take a unique interdisciplinary approach and conduct a systematic audit of model-related uncertainty quantification from seven scientific fields, spanning the biological, physical, and social sciences. Our results show no single field is achieving complete consideration of model uncertainties, but together we can fill the gaps. We propose opportunities to improve the quantification of uncertainty through use of a source framework for uncertainty consideration, model type specific guidelines, improved presentation, and shared best practice. We also identify shared outstanding challenges (uncertainty in input data, balancing trade-offs, error propagation, and defining how much uncertainty is required). Finally, we make nine concrete recommendations for current practice (following good practice guidelines and an uncertainty checklist, presenting uncertainty numerically, and propagating model-related uncertainty into conclusions), future research priorities (uncertainty in input data, quantifying uncertainty in complex models, and the importance of missing uncertainty in different contexts), and general research standards across the sciences (transparency about study limitations and dedicated uncertainty sections of manuscripts)., Comment: 40 Pages (including supporting information), 3 Figures, 2 Boxes, 1 Table

Long, Reid, and Thistlewaite have shown that some groups generated by representations of the $\Delta 334$ triangle group in $SL_3({\mathbb Z})$ are thin, while the status of others is unknown. In this paper we take a new approach: for each group we introduce a new graph that captures information about representations of $\Delta 334$ in the group. We provide examples of our graph for a variety of groups, and we use information about the graph for $SL_3({\mathbb Z}/2{\mathbb Z})$ to show that the chromatic number of the graph for $SL_3({\mathbb Z})$ is at most eight. By generating a portion of the graph for $SL_3({\mathbb Z})$ we show its chromatic number is at least four; we conjecture it is equal to four., Comment: 9 pages, 3 figures

We present 3D calculations for dielectric haloscopes such as the currently envisioned MADMAX experiment. For ideal systems with perfectly flat, parallel and isotropic dielectric disks of finite diameter, we find that a geometrical form factor reduces the emitted power by up to $30\,\%$ compared to earlier 1D calculations. We derive the emitted beam shape, which is important for antenna design. We show that realistic dark matter axion velocities of $10^{-3} c$ and inhomogeneities of the external magnetic field at the scale of $10\,\%$ have negligible impact on the sensitivity of MADMAX. We investigate design requirements for which the emitted power changes by less than $20\,\%$ for a benchmark boost factor with a bandwidth of $50\,{\rm MHz}$ at $22\,{\rm GHz}$, corresponding to an axion mass of $90\,\mu{\rm eV}$. We find that the maximum allowed disk tilt is $100\,\mu{\rm m}$ divided by the disk diameter, the required disk planarity is $20\,\mu{\rm m}$ (min-to-max) or better, and the maximum allowed surface roughness is $100\,\mu{\rm m}$ (min-to-max). We show how using tiled dielectric disks glued together from multiple smaller patches can affect the beam shape and antenna coupling., Comment: 25 pages, 12 figures; added detail, updated references, matches published version

Axions and axion-like particles are excellent low-mass dark matter candidates. The MADMAX experiment aims to directly detect galactic axions with masses between $40\,\mu{\rm eV}$ and $400\,\mu{\rm eV}$ by using the axion-induced emission of electromagnetic waves from boundaries between materials of different dielectric constants under a strong magnetic field. Combining many such surfaces, this emission can be significantly enhanced (boosted) using constructive interference and resonances. We present a first proof of principle realization of such a booster system consisting of a copper mirror and up to five sapphire disks. The electromagnetic response of the system is investigated by reflectivity measurements. The mechanical accuracy, calibration process of unwanted reflections and the repeatability of a basic tuning algorithm to place the disks are investigated. We find that for the presented cases the electromagnetic response in terms of the group delay predicted by one-dimensional calculations is sufficiently realized in our setup. The repeatability of the tuning is at the percent level, and would have small impact on the sensitivity of such a booster., Comment: 10 pages, 12 figures; minor changes, introduction and references expanded, matches published version

Chroma from luma (CfL) prediction is a new and promising chroma-only intra predictor that models chroma pixels as a linear function of the coincident reconstructed luma pixels. In this paper, we present the CfL predictor adopted in Alliance Video 1 (AV1), a royalty-free video codec developed by the Alliance for Open Media (AOM). The proposed CfL distinguishes itself from prior art not only by reducing decoder complexity, but also by producing more accurate predictions. On average, CfL reduces the BD-rate, when measured with CIEDE2000, by 5% for still images and 2% for video sequences., Comment: 8 pages