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Antiferromagnets that display very small stray magnetic field are ideal for spintronic applications. Of particular interest are non-collinear, chiral antiferromagnets of the type Mn3X (X=Sn, Ge), which display a large magnetotransport response that is correlated with their antiferromagnetic ordering. The ability to read out and manipulate this ordering is crucial for their integration into spintronic devices. These materials exhibit a tiny unbalanced magnetic moment such that a large external magnetic field can, in principle, be used to set the material into a single antiferromagnetic domain. However, in thin films of Mn3Sn, we find that such fields induce only a partial magnetic ordering. By detecting two orthogonal in-plane components of the magnetic order vector, we find that the non-switchable fraction has a unidirectional anisotropy. This also enables us to visualize switching along multiple easy axes in Mn3Sn. Studying the switching at the nanoscale allows us to correlate the pining behavior to crystal grain boundaries in the Mn3Sn nanowire structures.

The anomalous Nernst effect (ANE) gives rise to an electrical response transverse to the magnetization and an applied temperature gradient in a magnetic metal. A nanoscale temperature gradient can be generated by the use of a laser beam applied to the apex of an atomic force microscope tip, thereby allowing for spatially-resolved ANE measurements beyond the optical diffraction limit. Such a method has been used previously to map in-plane magnetized magnetic textures. However, the spatial distribution of the out-of-plane temperature gradient, which is needed to fully interpret such an ANE-based imaging, was not studied. We therefore use a well-known magnetic texture, a magnetic vortex core, to demonstrate the reliability of the ANE method for the imaging of magnetic domains with nanoscale resolution. Moreover, since the ANE signal is directly proportional to the temperature gradient, we can also consider the inverse problem and deduce information about the nanoscale temperature distribution. Our results together with finite element modeling indicate that besides the out-of-plane temperature gradients, there are even larger in-plane temperature gradients. Thus we extend the ANE imaging to study out-of-plane magnetization in a racetrack nano-wire by detecting the ANE signal generated by in-plane temperature gradients. In all cases, a spatial resolution of about 80 nm is obtained. These results are significant for the rapidly growing field of thermo-electric imaging of antiferromagnetic spintronic device structures.

Galaxy cluster abundance measurements provide a classic test of cosmology. They are most sensitive to the evolved amplitude of fluctuations, usually expressed as $S_8 = \sigma_8\sqrt{\Omega_m/0.3}$. Thus, abundance constraints exhibit a strong degeneracy between $\sigma_8$ and $\Omega_{\rm m}$, as do other similar low-redshift tests such as cosmic shear. The mass distribution in the infall region around galaxy clusters, where material is being accreted from the surrounding field, also exhibits a cosmological dependence, but in this case it is nearly orthogonal to the $S_8$ direction in the $\Omega_m$--$\sigma_8$ plane, making it highly complementary to halo abundance or cosmic shear studies. We explore how weak lensing measurements of the infall region might be used to complement abundance studies, considering three different tests. The splashback radius is a prominent feature of the infall region; we show that detection of this feature in lensing data from the Euclid survey could independently constrain $\Omega_{\rm m}$ and $\sigma_8$ to $\pm 0.05$. Another feature, the depletion radius where the bias reaches a minimum, also shows cosmological dependence, though it is challenging to observe in practice. The strongest constraints come from direct measurements of the shear profile in the infall region at $2$--$4\,r_{200{\rm c}}$. Combining the latter with abundance constraints such as those reported from SRG$/$eROSITA should reduce the area of the error contours by an estimated factor of $1.2$ using a sample of clusters observed by the UNIONS survey, or a factor of $3$ using clusters observed by the Euclid Wide survey over a broader range of redshift., Comment: 14 pages, 10 figures

Cosmological parameters such as $\Omega_{\rm{M}}$ and $\sigma_{8}$ can be measured indirectly using various methods, including galaxy cluster abundance and cosmic shear. These measurements constrain the composite parameter $S_{8}$, leading to degeneracy between $\Omega_{\rm{M}}$ and $\sigma_{8}$. However, some structural properties of galaxy clusters also correlate with cosmological parameters, due to their dependence on a cluster's accretion history. In this work, we focus on the splashback radius, an observable cluster feature that represents a boundary between a cluster and the surrounding Universe. Using a suite of cosmological simulations with a range of values for $\Omega_{\rm{M}}$ and $\sigma_{8}$, we show that the position of the splashback radius around cluster-mass halos is greater in cosmologies with smaller values of $\Omega_{\rm{M}}$ or larger values of $\sigma_{8}$. This variation breaks the degeneracy between $\Omega_{\rm{M}}$ and $\sigma_{8}$ that comes from measurements of the $S_{8}$ parameter. We also show that this variation is, in principle, measurable in observations. As the splashback radius can be determined from the same weak lensing analysis already used to estimate $S_{8}$, this new approach can tighten low-redshift constraints on cosmological parameters, either using existing data, or using upcoming data such as that from Euclid and LSST., Comment: 12 pages, 7 figures, 1 table, accepted for publication in ApJ

Numerous metrics exist to quantify the dynamical state of galaxy clusters, both observationally and within simulations. Many of these correlate strongly with one another, but it is not clear whether all of these measures probe the same intrinsic properties. In this work, we use two different statistical approaches -- principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) -- to investigate which dynamical properties of a cluster are in fact the best descriptors of its dynamical state. We use measurements taken directly from The Three Hundred suite of galaxy cluster simulations, as well as morphological properties calculated using mock X-ray and SZ maps of the same simulated clusters. We find that four descriptions of dynamical state naturally arise, and although correlations exist between these, a given cluster can be "dynamically relaxed" according to all, none, or some of these four descriptions. These results demonstrate that it is highly important for future observational and theoretical studies to consider in which sense clusters are dynamically relaxed. Cluster dynamical states are complex and multi-dimensional, and so it is not meaningful to classify them simply as "relaxed" and "unrelaxed" based on a single linear scale., Comment: 18 pages, 7 figures, 3 tables, accepted for publication in MNRAS

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of $D^\times$ on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of $D^\times$ to $G^0$-finite $\text{GL}_n(F)$-equivariant vector bundles with connection on $\Omega$, the $(n-1)$-dimensional Drinfeld symmetric space.

Event-based structured light systems have recently been introduced as an exciting alternative to conventional frame-based triangulation systems for the 3D measurements of diffuse surfaces. Important benefits include the fast capture speed and the high dynamic range provided by the event camera - albeit at the cost of lower data quality. So far, both low-accuracy event-based as well as high-accuracy frame-based 3D imaging systems are tailored to a specific surface type, such as diffuse or specular, and can not be used for a broader class of object surfaces ("mixed reflectance scenes"). In this paper, we present a novel event-based structured light system that enables fast 3D imaging of mixed reflectance scenes with high accuracy. On the captured events, we use epipolar constraints that intrinsically enable decomposing the measured reflections into diffuse, two-bounce specular, and other multi-bounce reflections. The diffuse objects in the scene are reconstructed using triangulation. Eventually, the reconstructed diffuse scene parts are used as a "display" to evaluate the specular scene parts via deflectometry. This novel procedure allows us to use the entire scene as a virtual screen, using only a scanning laser and an event camera. The resulting system achieves fast and motion-robust (14Hz) reconstructions of mixed reflectance scenes with < 500 $\mu$m accuracy. Moreover, we introduce a "superfast" capture mode (250Hz) for the 3D measurement of diffuse scenes.

Dark matter haloes grow at a rate that depends on the value of the cosmological parameters $\sigma_8$ and $\Omega_{\rm m}$ through the initial power spectrum and the linear growth factor. While halo abundance is routinely used to constrain these parameters, through cluster abundance studies, the halo growth rate is not. In recent work, we proposed constraining the cosmological parameters using observational estimates of the overall dynamical "age" of clusters, expressed, for instance, by their half-mass assembly redshift $z_{50}$. Here we explore the prospects for using the instantaneous growth rate, as estimated from the halo merger rate, from the average growth rate over the last dynamical time, or from the fraction of systems with recent episodes of major growth. We show that the merger rate is mainly sensitive to the amplitude of fluctuations $\sigma_8$, while the rates of recent growth provide constraints in the $\Omega_{\rm m}$-$\sigma_8$ plane that are almost orthogonal to those provided by abundance studies. Data collected for forthcoming cluster abundance studies, or studies of the galaxy merger rate in current and future galaxy surveys, may thus provide additional constraints on the cosmological parameters complementary to those already derived from halo abundance., Comment: 16 pages, 12 figures, 1 table and two figures in appendix

Dwarf galaxies are important tracers of small-scale cosmological structure, yet much of our knowledge about these systems comes from the limited sample of dwarf galaxies within the Local Group. To make a comprehensive inventory of dwarf populations in the local Universe, we require effective methods for deriving distance estimates for large numbers of faint, low surface brightness objects. Here we test the surface brightness fluctuation (SBF) method, traditionally applied to brighter early-type galaxies, on a sample of 20 nearby dwarf galaxies detected in the COSMOS field. These objects are partially resolved in HST ACS images, and have confirmed redshift distances in the range 17-130 Mpc. We discuss the many model choices required in applying the SBF method, and explore how these affect the final distance estimates. Amongst other variations on the method, when applying the SBF method, we alter the standard equation to include a term accounting for the power spectrum of the background, greatly improving our results. For the most robust modelling choices, we find a roughly Gaussian SBF signal that correlates linearly with distance out to distances of 50-100 Mpc, but with only a fraction of the power expected. At larger distances, there is excess power relative to that predicted, probably from undetected point sources. Overall, obtaining accurate SBF distances to faint, irregular galaxies remains challenging, but may yet prove possible with the inclusion of more information about galaxy properties and point source populations, and the use of more advanced techniques., Comment: 18 pages, 26 figures, accepted by MNRAS

A growing body of evidence suggests that the central density of cuspy dark matter subhaloes is conserved in minor mergers. However, empirical models of subhalo evolution, calibrated from simulations, often assume a drop in the central density. Since empirical models of subhaloes are used in galaxy-galaxy lensing studies and dark matter annihilation calculations, we explore the consequences of assuming different subhalo models. We find that dark matter annihilation calculations are very sensitive to the assumed subhalo mass profile, and different models can give more than a magnitude difference in the J-factor and boost factor in individual haloes. On the other hand, the shear and convergence profiles used in galaxy-galaxy lensing are sensitive to the initial profile assumed (e.g., NFW versus Einato) but are otherwise well-approximated by a simple model in which the original profile is sharply truncated. We conclude that since the innermost parts of haloes are difficult to resolve in simulations, it is important to have a theoretical understanding of how subhaloes evolve to make accurate predictions of the dark matter annihilation signal., Comment: 13 figures. To be submitted to JCAP

Let $\Omega^d$ be the $d$-dimensional Drinfeld symmetric space for a finite extension $F$ of $\mathbb{Q}_p$. Let $\Sigma^1$ be a geometrically connected component of the first Drinfeld covering of $\Omega^d$ and let $\mathbb{F}$ be the residue field of the unique degree $d+1$ unramified extension of $F$. We show that the natural homomorphism determined by the second Drinfeld covering from the group of characters of $(\mathbb{F}, +)$ to $\text{Pic}(\Sigma^1)[p]$ is injective. In particular, $\text{Pic}(\Sigma^1)[p] \neq 0$. We also show that all vector bundles on $\Omega^1$ are trivial, which extends the classical result that $\text{Pic}(\Omega^1) = 0$., Comment: v2: minor typos corrected

When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the available information to extract the wisdom of the crowd. A linear opinion pool has been widely used, whereby the combining is applied to the probability predictions of the distributional forecasts. However, it has been argued that this will tend to deliver overdispersed distributional forecasts, prompting the combination to be applied, instead, to the quantile predictions of the distributional forecasts. Results from different applications are mixed, leaving it as an empirical question whether to combine probabilities or quantiles. In this paper, we present an alternative approach. Looking at the distributional forecasts, combining the probability forecasts can be viewed as vertical combining, with quantile forecast combining seen as horizontal combining. Our alternative approach is to allow combining to take place on an angle between the extreme cases of vertical and horizontal combining. We term this angular combining. The angle is a parameter that can be optimized using a proper scoring rule. We show that, as with vertical and horizontal averaging, angular averaging results in a distribution with mean equal to the average of the means of the distributions that are being combined. We also show that angular averaging produces a distribution with lower variance than vertical averaging, and, under certain assumptions, greater variance than horizontal averaging. We provide empirical support for angular combining using weekly distributional forecasts of COVID-19 mortality at the national and state level in the U.S., Comment: 47 pages, 16 figures

A real number is a rule that, when provided with a rational interval, answers Yes or No depending on if the real number ought to be considered to be in the given interval. Since the goal is to define the real numbers, this can only motivate the definition of which rules should be considered a real number. The rule must satisfy five properties and any rule that does so we call an oracle. Three of the properties ensure that we do not have multiple oracles representing the same real number. The other two properties ensure that the oracle does narrow down to a single real number. The most important property is the Separating property which ensures that if we divide a Yes interval into two parts, then one part is a Yes interval while the other is a No interval; the exception is if the division point, which is a rational number, happens to be the desired real number in which case both intervals are Yes intervals. We explore various examples and algorithms in using oracles in addition to establishing that the oracles do, in fact, form the field of real numbers. The concept of a Family of Overlapping, Notionally Shrinking Intervals is defined and found to be an essential tool in working with oracle arithmetic. Mediant approximations, which are related to continued fraction representations, naturally arise from an oracle perspective. We also compare and contrast with other common definitions of real numbers, such as Cauchy sequences and Dedekind cuts, in which the conclusion is that the oracle perspective is somewhat of a master map to the other definitions. We do an explicit example to contrast oracle arithmetic with decimal arithmetic and continued fraction arithmetic., Comment: 101 pages, project home: https://github.com/jostylr/Reals-as-Oracles

A new definition of a real number is that it is a rule which says Yes or No based on whether the real number ought to be in a given rational interval. This is a teaser paper for formalizing, exploring, and generalizing this definition. The full exploration is given in the paper "Defining Real Numbers as Oracles"., Comment: 4 pages, project home: https://github.com/jostylr/Reals-as-Oracles/

High-throughput screening techniques are commonly used to obtain large quantities of data in many fields of biology. It is well known that artifacts arising from variability in the technical execution of different experimental batches within such screens confound these observations and can lead to invalid biological conclusions. It is therefore necessary to account for these batch effects when analyzing outcomes. In this paper we describe RxRx1, a biological dataset designed specifically for the systematic study of batch effect correction methods. The dataset consists of 125,510 high-resolution fluorescence microscopy images of human cells under 1,138 genetic perturbations in 51 experimental batches across 4 cell types. Visual inspection of the images alone clearly demonstrates significant batch effects. We propose a classification task designed to evaluate the effectiveness of experimental batch correction methods on these images and examine the performance of a number of correction methods on this task. Our goal in releasing RxRx1 is to encourage the development of effective experimental batch correction methods that generalize well to unseen experimental batches. The dataset can be downloaded at https://rxrx.ai.