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$ $Low density cosmic voids gravitationally lens the cosmic microwave background (CMB), leaving a negative imprint on the CMB convergence $\kappa$. This effect provides insight into the distribution of matter within voids, and can also be used to study the growth of structure. We measure this lensing imprint by cross-correlating the Planck CMB lensing convergence map with voids identified in the Dark Energy Survey Year 3 data set, covering approximately 4,200 deg$^2$ of the sky. We use two distinct void-finding algorithms: a 2D void-finder which operates on the projected galaxy density field in thin redshift shells, and a new code, Voxel, which operates on the full 3D map of galaxy positions. We employ an optimal matched filtering method for cross-correlation, using the MICE N-body simulation both to establish the template for the matched filter and to calibrate detection significances. Using the DES Y3 photometric luminous red galaxy sample, we measure $A_\kappa$, the amplitude of the observed lensing signal relative to the simulation template, obtaining $A_\kappa = 1.03 \pm 0.22$ ($4.6\sigma$ significance) for Voxel and $A_\kappa = 1.02 \pm 0.17$ ($5.9\sigma$ significance) for 2D voids, both consistent with $\Lambda$CDM expectations. We additionally invert the 2D void-finding process to identify superclusters in the projected density field, for which we measure $A_\kappa = 0.87 \pm 0.15$ ($5.9\sigma$ significance). The leading source of noise in our measurements is Planck noise, implying that future data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT) and CMB-S4 will increase sensitivity and allow for more precise measurements.

The exchange bias phenomenon, inherent in exchange-coupled ferromagnetic and antiferromagnetic systems, has intrigued researchers for decades. Van der Waals materials, with their layered structure, provide an optimal platform for probing such physical phenomena. However, achieving a facile and effective means to manipulate exchange bias in pristine van der Waals heterostructures remains challenging. In this study, we investigate the origin of exchange bias in MnPS3/Fe3GeTe2 van der Waals heterostructures. Our work demonstrates a method to modulate unidirectional exchange anisotropy, achieving an unprecedented nearly 1000% variation through simple thermal cycling. Despite the compensated interfacial spin configuration of MnPS3, magneto-transport measurements reveal a huge 170 mT exchange bias at 5 K, the largest observed in pristine van der Waals antiferromagnet-ferromagnet interfaces. This substantial magnitude of the exchange bias is linked to an anomalous weak ferromagnetic ordering in MnPS3 below 40 K. On the other hand, the tunability of exchange bias during thermal cycling is ascribed to the modified arrangement of interfacial atoms and changes in the vdW gap during field cooling. Our findings highlight a robust and easily adjustable exchange bias in van der Waals antiferromagnetic/ferromagnetic heterostructures, presenting a straightforward approach to enhance other interface related spintronic phenomena for practical applications.

Over the past few years, the combination of diffuser and near-field electron ptychography has drawn more attention by its ability to recover large field of view with few diffraction patterns. In this paper, we purpose a novel design and implementation of amplitude diffuser. The amplitude diffuser introduces structures to the illumination while reducing the inelastic scattering. And the amplitude diffuser is implemented at the condenser lens aperture, allowing us to vary the illumination size under the same microscope setup. We demonstrate the reconstruction results under both conventional Transmission Electron Microscopy (TEM) mode as well as Lorentz mode., Comment: Presented in ISCS23

The Nancy Grace Roman Space Telescope is capable of delivering an unprecedented all-sky, high-spatial resolution, multi-epoch infrared map to the astronomical community. This opportunity arises in the midst of numerous ground- and space-based surveys that will provide extensive spectroscopy and imaging together covering the entire sky (such as Rubin/LSST, Euclid, UNIONS, SPHEREx, DESI, SDSS-V, GALAH, 4MOST, WEAVE, MOONS, PFS, UVEX, NEO Surveyor, etc.). Roman can uniquely provide uniform high-spatial-resolution (~0.1 arcsec) imaging over the entire sky, vastly expanding the science reach and precision of all of these near-term and future surveys. This imaging will not only enhance other surveys, but also facilitate completely new science. By imaging the full sky over two epochs, Roman can measure the proper motions for stars across the entire Milky Way, probing 100 times fainter than Gaia out to the very edge of the Galaxy. Here, we propose NANCY: a completely public, all-sky survey that will create a high-value legacy dataset benefiting innumerable ongoing and forthcoming studies of the universe. NANCY is a pure expression of Roman's potential: it images the entire sky, at high spatial resolution, in a broad infrared bandpass that collects as many photons as possible. The majority of all ongoing astronomical surveys would benefit from incorporating observations of NANCY into their analyses, whether these surveys focus on nearby stars, the Milky Way, near-field cosmology, or the broader universe., Comment: Submitted to the call for white papers for the Roman Core Community Survey (June 16th, 2023), and to the Bulletin of the AAS

Metallic/intermetalic materials with BCC structures hold an intrinsic instability due to phonon softening along [110] dirrection, causing BCC to lower-symmetry phases transformation when the BCC structures are thermally or mechanically stressed. Fe50Rh50 binary system is one of the exceptional BCC structures (ordered-B2) that has not been yet showing such transformation upon application of thermal stress, although mechanical deformation results in B2 to disordered FCC (gamma) and L10 phases transformation. Here, a comprehensive transmission electron microscopy (TEM) study is conducted on thermally-stressed samples of Fe50Rh50 aged at water and liquid nitrogen from 1150 degree C and 1250 degree C. The results show that, samples quenched from 1150 degree C into water and liquid nitrogen show presence of 1/4{110} and 1/2{110} satellite reflections, the latter of which is expected from phonon dispersion curves obtained by density functional theory calculation. Therefore, it is believed that Fe50Rh50 maintains the B2 structure that is in premartensite state. Once Fe50Rh50 is quenched from 1250 degree C into liquid nitrogen, formation of two short-range ordered tetragonal phases with various c/a ratios (~1.15 and 1.4) is observed in line with phases formed from mechanically deformed (30%) sample. According to our observations, an accurate atomistic shear model ({110}<1-10>) is presented that describes the martensitic transformation of B2 to these tetragonal phases. These findings offer implications useful for understanding of magnetic and physical characteristics of metallic/intermetallic materials.

This work investigates the effect of copper substitution on the magnetic properties of SmCo$_{5}$ thin films synthesized by molecular beam epitaxy. A series of thin films with varying concentrations of Cu were grown under otherwise identical conditions to disentangle structural and compositional effects on the magnetic behavior. The combined experimental and theoretical studies show that Cu substitution at the Co$_{3g}$ sites not only stabilizes the formation of the SmCo$_{5}$ structure but enhances magnetic anisotropy and coercivity. Density functional theory calculations indicate that Sm(Co$_4$Cu$_{3g}$)$_5$ possesses a higher single-ion anisotropy as compared to pure SmCo$_{5}$. In addition, X-ray magnetic circular dichroism reveals that Cu substitution causes an increasing decoupling of the Sm 4\textit{f} and Co 3\textit{d} moments. Scanning transmission electron microscopy confirms predominantly SmCo$_{5}$ phase formation and reveals nanoscale inhomogeneities in the Cu and Co distribution. Our study based on thin film model systems and advanced characterization as well as modeling reveals novel aspects of the complex interplay of intrinsic and extrinsic contributions to magnetic hysteresis in rare earth-based magnets, \textit{i.e.} the combination of increased intrinsic anisotropy due to Cu substitution and the extrinsic effect of inhomogeneous elemental distribution of Cu and Co.

Two-dimensional van der Waals (vdW) heterostructures are an attractive platform for studying exchange bias due to their defect free and atomically flat interfaces. Chromium thiophosphate (CrPS4), an antiferromagnetic material, possesses uncompensated magnetic spins in a single layer, rendering it a promising candidate for exploring exchange bias phenomena. Recent findings have highlighted that naturally oxidized vdW ferromagnetic Fe3GeTe2 exhibits exchange bias, attributed to the antiferromagnetic coupling of its ultrathin surface oxide layer (O-FGT) with the underlying unoxidized Fe3GeTe2. Anomalous Hall measurements are employed to scrutinize the exchange bias within the CrPS4/(O-FGT)/Fe3GeTe2 heterostructure. This analysis takes into account the contributions from both the perfectly uncompensated interfacial CrPS4 layer and the interfacial oxide layer. Intriguingly, a distinct and non-monotonic exchange bias trend is observed as a function of temperature below 140 K. The occurrence of exchange bias induced by a 'pre-set field' implies that the prevailing phase in the polycrystalline surface oxide is ferrimagnetic Fe3O4. Moreover, the exchange bias induced by the ferrimagnetic Fe3O4 is significantly modulated by the presence of the van der Waals antiferromagnetic CrPS4 layer, forming a heterostructure, along with additional iron oxide phases within the oxide layer. These findings underscore the intricate and complex nature of exchange bias in van der Waals heterostructures, highlighting their potential for tailored manipulation and control.

We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated algebraic theories. We describe syntax and semantics for three classes of algebraic theories: finitary quotient inductive-inductive theories, their infinitary generalization, and finally higher inductive-inductive theories. In each case, an algebraic signature is a typing context or a closed type in a specific type theory.

The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In this work, we observe that two-level type theory (2LTT), a system originally devised for the purpose of developing synthetic homotopy theory, also serves as a system for staged compilation with dependent types. 2LTT has numerous good properties for this use case: it has a concise specification, well-behaved model theory, and it supports a wide range of language features both at the object and the meta level. First, we give an overview of 2LTT's features and applications in staging. Then, we present a staging algorithm and prove its correctness. Our algorithm is "staging-by-evaluation", analogously to the technique of normalization-by-evaluation, in that staging is given by the evaluation of 2LTT syntax in a semantic domain. The staging algorithm together with its correctness constitutes a proof of strong conservativity of 2LLT over the object theory. To our knowledge, this is the first description of staged compilation which supports full dependent types and unrestricted staging for types.

The Dark Energy Spectroscopic Instrument (DESI) survey will measure large-scale structures using quasars as direct tracers of dark matter in the redshift range 0.92.1. We present several methods to select candidate quasars for DESI, using input photometric imaging in three optical bands (g, r, z) from the DESI Legacy Imaging Surveys and two infrared bands (W1, W2) from the Wide-field Infrared Explorer (WISE). These methods were extensively tested during the Survey Validation of DESI. In this paper, we report on the results obtained with the different methods and present the selection we optimized for the DESI main survey. The final quasar target selection is based on a Random Forest algorithm and selects quasars in the magnitude range 16.599% purity for a nominal effective exposure time of ~1000s. With a 310 per sq. deg. target density, the main selection allows DESI to select more than 200 QSOs per sq. deg. (including 60 quasars with z>2.1), exceeding the project requirements by 20%. The redshift distribution of the selected quasars is in excellent agreement with quasar luminosity function predictions., Comment: 21 pages, 21 figures, typos corrected, references added

Current pulse driven Neel vector rotation in metallic antiferromagnets is one of the most promising concepts in antiferromagnetic spintronics. We show microscopically that the Neel vector of epitaxial thin films of the prototypical compound Mn2Au can be reoriented reversibly in the complete area of cross shaped device structures using single current pulses. The resulting domain pattern with aligned staggered magnetization is long term stable enabling memory applications. We achieve this switching with low heating of 20 K, which is promising regarding fast and efficient devices without the need for thermal activation. Current polarity dependent reversible domain wall motion demonstrates a Neel spin-orbit torque acting on the domain walls., Comment: 9 pages, 9 figures

Self-assembled quantum dots based on III-V semiconductors have excellent properties for applications in quantum optics. However, the presence of a 2D wetting layer which forms during the Stranski-Krastanov growth of quantum dots can limit their performance. Here, we investigate wetting layer formation during quantum dot growth by the alternative droplet epitaxy technique. We use a combination of photoluminescence excitation spectroscopy, lifetime measurements, and transmission electron microscopy to identify the presence of an InGaAs wetting layer in these droplet epitaxy quantum dots, even in the absence of distinguishable wetting layer photoluminescence. We observe that increasing the amount of Ga deposited on a GaAs (100) surface prior to the growth of InGaAs quantum dots leads to a significant reduction in the emission wavelength of the wetting layer to the point where it can no longer be distinguished from the GaAs acceptor peak emission in photoluminescence measurements.

The role of the crystal lattice, temperature and magnetic field for the spin structure formation in the 2D van der Waals magnet Fe5GeTe2 is a key open question. Using Lorentz transmission electron microscopy, we experimentally observe topological spin structures up to room temperature in the metastable pre-cooling and stable post-cooling phase of Fe5GeTe2. Over wide temperature and field ranges, skyrmionic magnetic bubbles form without preferred chirality, which is indicative of a centrosymmetric crystal structure. In the pre-cooling phase, these bubbles are observable even without the application of an external field, while in the post-cooling phase, a transformation from bubble domains to stripe domains is seen. To understand the magnetic order in Fe5GeTe2 we compare macroscopic magnetometry characterization results with microscopic density functional theory calculation. Our results show that even up to room temperature, topological spin structures can be stabilized in centrosymmetric van der Waals magnets., Comment: 25 pages, 10 figures

The recent emergence of magnetic van der Waals materials allows for the investigation of current induced magnetization manipulation in two dimensional materials. Uniquely, Fe3GeTe2 has a crystalline structure that allows for the presence of bulk spin-orbit torques (SOTs), that we quantify in a Fe3GeTe2 flake. From the symmetry of the measured torques, we identify the current induced effective fields using harmonic analysis and find dominant bulk SOTs, which arise from the symmetry in the crystal structure. Our results show that Fe3GeTe2 uniquely can exhibit bulk SOTs in addition to the conventional interfacial SOTs enabling magnetization manipulation even in thick single layers without the need for complex multilayer engineering., Comment: 19 pages 4 figures

Iron and its alloys have made modern civilisation possible, with metallic meteorites providing one of the human's earliest sources of usable iron as well as providing a window into our solar system's billion-year history. Here highest-resolution tools reveal the existence of a previously hidden FeNi nanophase within the extremely slowly cooled metallic meteorite NWA 6259. This new nanophase exists alongside Ni-poor and Ni-rich nanoprecipitates within a matrix of tetrataenite, the uniaxial, chemically ordered form of FeNi. The ferromagnetic nature of the nanoprecipitates combined with the antiferromagnetic character of the FeNi nanophases give rise to a complex magnetic state that evolves dramatically with temperature. These observations extend and possibly alter our understanding of celestial metallurgy, provide new knowledge concerning the archetypal Fe-Ni phase diagram and supply new information for the development of new types of sustainable, technologically critical high-energy magnets., Comment: 10 pages, 5 figures

Filamentary textures can take the form of braided, rope-like superstructures in nonlinear media such as plasmas and superfluids. The formation of similar superstructures in solids has been predicted, for example from flux lines in superconductors. However, their observation has proved challenging. Here, we use electron microscopy and numerical methods to reveal braided superstructures of magnetic skyrmions in thin crystals of B20-type FeGe. Their discovery opens the door to applications of rich topological landscapes of geometric braids in magnetic solids., Comment: 6 pages, 3 figures

Magnetic high entropy alloys (HEAs) are a new category of high-performance magnetic materials, with multi-component concentrated compositions and complex multi-phase structures. Although there have been numerous reports of their interesting magnetic properties, there is very limited understanding about the interplay between their hierarchical multi-phase structures and their local magnetic structures. By employing high spatial resolution correlative magnetic, structural and chemical studies, we reveal the influence of a hierarchically decomposed B2 + A2 structure in an AlCo0.5Cr0.5FeNi HEA on the formation of magnetic vortex states within individual A2 (disordered BCC) precipitates, which are distributed in an ordered B2 matrix that is weakly ferromagnetic. Non-magnetic or weakly ferromagnetic B2 precipitates in large magnetic domains of the A2 phase, and strongly magnetic Fe-Co-rich interphase A2 regions, are also observed. These results provide important insight into the origin of coercivity in this HEA, which can be attributed to a complex magnetization process that includes the successive reversal of magnetic vortices.

In type theories, universe hierarchies are commonly used to increase the expressive power of the theory while avoiding inconsistencies arising from size issues. There are numerous ways to specify universe hierarchies, and theories may differ in details of cumulativity, choice of universe levels, specification of type formers and eliminators, and available internal operations on levels. In the current work, we aim to provide a framework which covers a large part of the design space. First, we develop syntax and semantics for cumulative universe hierarchies, where levels may come from any set equipped with a transitive well-founded ordering. In the semantics, we show that induction-recursion can be used to model transfinite hierarchies, and also support lifting operations on type codes which strictly preserve type formers. Then, we consider a setup where universe levels are first-class types and subject to arbitrary internal reasoning. This generalizes the bounded polymorphism features of Coq and at the same time the internal level computations in Agda.

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to initiate and control their motion has opened a new field of research, skyrmionics, that aims at using skyrmions as information carriers for data storage and manipulation. Recent advances in skyrmionics prompt for a thorough understanding of the detailed three-dimensional (3D) spin texture of a skyrmion including skyrmion-skyrmion interactions and their coupling to surfaces and interfaces. These properties crucially affect application-related aspects such as the stability and mobility of skyrmions in confined structures. To date, however, experimental techniques to measure the three-dimensional spin texture with nanometer resolution are largely missing. We therefore adapt holographic vector field electron tomography to the problem and report on the first quantitative reconstruction of the 3D spin texture of skyrmions with sub-10 nanometer resolution. The reconstructed textures reveal a variety of previously unseen local deviations from a homogeneous Bloch character within the skyrmion tubes (SkTs), details of the collapse of the skyrmion texture at surfaces, and a correlated modulation of the SkT in FeGe along their tube axes. The quantitative 3D data of the magnetic induction also allow to experimentally confirm some principles of skyrmion formation by deriving spatially resolved maps of the magnetic energy density across these magnetic solitons.

The characteristic microstructure of Sm(Co,Fe,Cu,Zr)$_z$ alloys with SmCo$_5$ cell walls in Sm$_2$Co$_{17}$ cells, all intersected by Zr-rich platelets, makes them some of the best performing high-temperature permanent magnets. Plentiful research has been performed to tailor the microstructure at the nanoscale, but due to its complexity many questions remain unanswered about the effect of the individual phases on the magnetic performance at different temperatures. Here, we explore this mechanism effect for three different Sm(Co,Fe,Cu,Zr)$_z$ alloys by deploying high-resolution magnetic imaging via in-situ transmission electron microscopy and three-dimensional chemical analysis using atom probe tomography. We show that their microstructures differ in terms of SmCo$_5$ cell-wall and Z-phase size and density, as well as the Cu concentration in the cell walls, and demonstrate how these features influence the magnetic domain size and density and thus form different magnetic textures. Moreover, we illustrate that the dominant coercivity mechanism at room temperature is domain-wall pinning and show that magnets with a denser cell-wall network, a steeper Cu gradient across the cell-wall boundary, and thinner Z-phase platelets have a higher coercivity. We also show that the coercivity mechanism at high temperatures is domain-wall nucleation at the cell walls. Increasing the Cu concentration inside the cell walls decreases the transition temperature between pinning and nucleation, significantly decreasing the coercivity with increasing temperature. We therefore provide a detailed explanation of how the microstructure on the atomic to nanoscale directly affects the magnetic performance and provide detailed guidelines for an improved design of Sm(Co,Fe,Cu,Zr)$_z$ magnets., Comment: 14 pages, 9 figures

The control of domain walls is central to nearly all magnetic technologies, particularly for information storage and spintronics. Creative attempts to increase storage density need to overcome volatility due to thermal fluctuations of nanoscopic domains and heating limitations. Topological defects, such as solitons, skyrmions, and merons, may be much less susceptible to fluctuations, owing to topological constraints, while also being controllable with low current densities. Here, we present the first evidence for soliton/soliton and soliton/antisoliton domain walls in the hexagonal chiral magnet Mn1/3NbS2 that respond asymmetrically to magnetic fields and exhibit pair-annihilation. This is important because it suggests the possibility of controlling the occurrence of soliton pairs and the use of small fields or small currents to control nanoscopic magnetic domains. Specifically, our data suggest that either soliton/soliton or soliton/antisoliton pairs can be stabilized by tuning the balance between intrinsic exchange interactions and long-range magnetostatics in restricted geometries, Comment: 8 pages, 4 figures

The proposal that very small N\'eel skyrmions can form in SrRuO$_3$/SrIrO$_3$ epitaxial bilayers and that the electric field-effect can be used to manipulate these skyrmions in gated devices strongly stimulated the recent research of SrRuO$_3$ heterostructures. A strong interfacial Dzyaloshinskii-Moriya interaction, combined with the breaking of inversion symmetry, was considered as the driving force for the formation of skyrmions in SrRuO$_3$/SrIrO$_3$ bilayers. Here, we investigated nominally symmetric heterostructures in which an ultrathin ferromagnetic SrRuO$_3$ layer is sandwiched between large spin-orbit coupling SrIrO$_3$ layers, for which the conditions are not favorable for the emergence of a net interfacial Dzyaloshinskii-Moriya interaction. Previously the formation of skyrmions in the asymmetric SrRuO$_3$/SrIrO$_3$ bilayers was inferred from anomalous Hall resistance loops showing humplike features that resembled topological Hall effect contributions. Symmetric SrIrO$_3$/SrRuO$_3$/SrIrO$_3$ trilayers do not show hump anomalies in the Hall loops. However, the anomalous Hall resistance loops of symmetric multilayers, in which the trilayer is stacked several times, do exhibit the humplike structures, similar to the asymmetric SrRuO$_3$/SrIrO$_3$ bilayers. The origin of the Hall effect loop anomalies likely resides in unavoidable differences in the electronic and magnetic properties of the individual SrRuO$_3$ layers rather than in the formation of skyrmions.

Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of type theories and constructive definitions of real, ordinal and surreal numbers. We develop new metatheory for large QIITs, large elimination, recursive equations and infinitary constructors. As in prior work, we describe QIITs using a type theory where each context represents a QIIT signature. However, in our case the theory of signatures can also describe its own signature, modulo universe sizes. We bootstrap the model theory of signatures using self-description and a Church-coded notion of signature, without using complicated raw syntax or assuming an existing internal QIIT of signatures. We give semantics to described QIITs by modeling each signature as a finitely complete CwF (category with families) of algebras. Compared to the case of finitary QIITs, we additionally need to show invariance under algebra isomorphisms in the semantics. We do this by modeling signature types as isofibrations. Finally, we show by a term model construction that every QIIT is constructible from the syntax of the theory of signatures.

The standard cosmological paradigm narrates a reassuring story of a universe currently dominated by an enigmatic dark energy component. Disquietingly, its universal explaining power has recently been challenged by, above all, the $\sim4\sigma$ tension in the values of the Hubble constant. Another, less studied anomaly is the repeated observation of integrated Sachs-Wolfe imprints $\sim5\times$ stronger than expected in the $\Lambda$CDM model from R>100 $Mpc/h$ super-structures. Here we show that the inhomogeneous AvERA model of emerging curvature is capable of telling a plausible albeit radically different story that explains both observational anomalies without dark energy. We demonstrate that while stacked imprints of R>100 $Mpc/h$ supervoids in cosmic microwave background temperature maps can discriminate between the AvERA and $\Lambda$CDM models, their characteristic differences may remain hidden using alternative void definitions and stacking methodologies. Testing the extremes, we then also show that the CMB Cold Spot can plausibly be explained in the AvERA model as an ISW imprint. The coldest spot in the AvERA map is aligned with multiple low-$z$ supervoids with R>100 $Mpc/h$ and central underdensity $\delta_{0}\approx-0.3$, resembling the observed large-scale galaxy density field in the Cold Spot area. We hence conclude that the anomalous imprint of supervoids may well be the canary in the coal mine, and existing observational evidence for dark energy should be re-interpreted to further test alternative models., Comment: 16 pages, 9 figures, accepted by MNRAS

There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and normalisation. One option is to embed the syntax deeply, by using inductive definitions in a proof assistant. However, in this case the handling of definitional equalities becomes technically challenging. Alternatively, we can reuse conversion checking in the metatheory by shallowly embedding the object theory. In this paper, we consider the standard model of a type theoretic object theory in Agda. This model has the property that all of its equalities hold definitionally, and we can use it as a shallow embedding by building expressions from the components of this model. However, if we are to reason soundly about the syntax with this setup, we must ensure that distinguishable syntactic constructs do not become provably equal when shallowly embedded. First, we prove that shallow embedding is injective up to definitional equality, by modelling the embedding as a syntactic translation targeting the metatheory. Second, we use an implementation hiding trick to disallow illegal propositional equality proofs and constructions which do not come from the syntax. We showcase our technique with very short formalisations of canonicity and parametricity for Martin-L\"of type theory. Our technique only requires features which are available in all major proof assistants based on dependent type theory., Comment: 36 pages, to be presented at the 13th International Conference on Mathematics of Program Construction (MPC 2019)

Higher inductive-inductive types (HIITs) generalize inductive types of dependent type theories in two ways. On the one hand they allow the simultaneous definition of multiple sorts that can be indexed over each other. On the other hand they support equality constructors, thus generalizing higher inductive types of homotopy type theory. Examples that make use of both features are the Cauchy real numbers and the well-typed syntax of type theory where conversion rules are given as equality constructors. In this paper we propose a general definition of HIITs using a small type theory, named the theory of signatures. A context in this theory encodes a HIIT by listing the constructors. We also compute notions of induction and recursion for HIITs, by using variants of syntactic logical relation translations. Building full categorical semantics and constructing initial algebras is left for future work. The theory of HIIT signatures was formalised in Agda together with the syntactic translations. We also provide a Haskell implementation, which takes signatures as input and outputs translation results as valid Agda code.

The most powerful magnets for high temperature applications are Sm-Co-based alloys with a microstructure that combines magnetically soft and hard regions. The microstructure consists of a dense domain-wall-pinning network that endows the material with remarkable magnetic hardness. A precise understanding of the coupling between magnetism and microstructure is essential for enhancing the performance of Sm-Co magnets, but experiments and theory have not yet converged to a unified model. Here, we combine transmission electron microscopy, atom probe tomography, and nanometer-resolution off-axis electron holography with micromagnetic simulations to show that the magnetization processes in Sm-Co magnets result from an interplay between curling instabilities and pinning effects at the intersections between magnetically soft and hard regions. We also find that topologically non-trivial magnetic domains separated by a complex network of domain walls play a key role in the magnetic state. Our findings reveal a previously hidden aspect of magnetism and provide insight into the full potential of high-performance magnetic materials.