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Creating a strong clinical practice experience for every teacher at scale requires that three core actors--prep programs, school districts, and states--work together. This framework sets out the six focus areas of clinical practice backed by research and supported by the field as the most important to build a quality clinical practice experience. It further identifies the actions that these core actors can take in each area. Based on survey responses of hundreds of practitioners from teacher prep programs and school districts, the authors learned that while their programs have much to be proud of, they also recognize that they are missing opportunities to deliver an exceptional clinical practice experience. This framework can help the core actors identify the aspects of their clinical practice programs that are already aligned with the evidence and illuminate opportunities to improve.

JWST has revealed a large population of compact, red galaxies at $z>4$ known as Little Red Dots (LRDs). We analyze the spectral energy distributions (SEDs) of 95 LRDs from the JWST PRIMER survey with complete photometric coverage from $1-18\ \mu$m using NIRCam and MIRI imaging, representing the most extensive SED analysis on a large LRD sample with long-wavelength MIRI data. We examine SED models in which either galaxy or active galactic nucleus (AGN) emission dominates the rest-frame UV or optical continuum, extracting physical properties to explore each scenario's implications. In the galaxy-only model, we find massive, dusty stellar populations alongside unobscured, low-mass components, hinting at inhomogeneous obscuration. The AGN-only model indicates dusty, luminous AGNs with low hot dust fractions compared to typical quasars. A hybrid AGN and galaxy model suggests low-mass, unobscured galaxies in the UV, with stellar mass estimates spanning $\sim$2 dex across the different models, underscoring the need for caution in interpreting LRD stellar masses. With MIRI photometry, the galaxy-only model produces stellar masses within cosmological limits, but extremely high stellar mass densities are inferred. The hybrid model infers highly overmassive black holes exceeding those in recently reported high-redshift AGNs, hinting at a partial AGN contribution to the rest-optical continuum or widespread super-Eddington accretion. Our findings highlight the extreme conditions required for both AGN or galaxy dominated scenarios in LRDs, supporting a mixed contribution to the red continuum, or novel scenarios to explain the observed emission., Comment: 22 pages, 10 figures, submitted to ApJ. Machine-readable form of Table 2 available at: https://github.com/geneckleung/lrd_primer_miri

Identifying predictive features from high-dimensional datasets is a major task in biomedical research. However, it is difficult to determine the robustness of selected features. Here, we investigate the performance of randomly chosen features, what we term "random feature baselines" (RFBs), in the context of disease risk prediction from blood plasma proteomics data in the UK Biobank. We begin with two published case studies predicting diagnosis of (1) dementia and (2) hip fracture. RFBs perform similarly to published features of interest (using the same number of proteins, but randomly chosen). We then measure the performance of RFBs for all 607 disease outcomes in the UK Biobank, with various numbers of randomly chosen features, as well as all proteins in the dataset. 114/607 outcomes showed a higher mean AUROC when choosing 5 random features than using all proteins, and the absolute difference in mean AUC was 0.075. 163 outcomes showed a higher mean AUROC when choosing 1000 random features than using all proteins, and the absolute difference in mean AUC was 0.03. Incorporating RFBs should become part of ML practice when feature selection or target discovery is a goal., Comment: Findings paper presented at Machine Learning for Health (ML4H) symposium 2024, December 15-16, 2024, Vancouver, Canada, 5 pages

How small can a set of vertices in the $n$-dimensional hypercube $Q_n$ be if it meets every copy of $Q_d$? The asymptotic density of such a set (for $d$ fixed and $n$ large) is denoted by $\gamma_d$. It is easy to see that $\gamma_d \leq 1/(d+1)$, and it is known that $\gamma_d=1/(d+1)$ for $d \leq 2$, but it was recently shown that $\gamma_d < 1/(d+1)$ for $d \geq 8$. In this paper we show that the latter phenomenon also holds for $d=7$ and $d=6$., Comment: 8 pages

Free electrons in the interstellar medium refract and diffract radio waves along multiple paths, resulting in angular and temporal broadening of radio pulses that limits pulsar timing precision. We determine multifrequency, multi-epoch scattering times for the large dispersion measure millisecond pulsar J1903+0327 by developing a three component model for the emitted pulse shape that is convolved with a best fit pulse broadening function (PBF) identified from a family of thin-screen and extended-media PBFs. We show that the scattering time, $\tau$, at a fiducial frequency of 1500 MHz changes by approximately 10% over a 5.5yr span with a characteristic timescale of approximately 100 days. We also constrain the spectral index and inner scale of the wavenumber spectrum of electron density variations along this line of sight. We find that the scaling law for $\tau$ vs. radio frequency is strongly affected by any mismatch between the true and assumed PBF or between the true and assumed intrinsic pulse shape. We show using simulations that refraction is a plausible cause of the epoch dependence of $\tau$, manifesting as changes in the PBF shape and $1/e$ time scale. Finally, we discuss the implications of our scattering results on pulsar timing including time of arrival delays and dispersion measure misestimation., Comment: 16 pages, 14 figures, submitted to ApJ

Assistive agents should make humans' lives easier. Classically, such assistance is studied through the lens of inverse reinforcement learning, where an assistive agent (e.g., a chatbot, a robot) infers a human's intention and then selects actions to help the human reach that goal. This approach requires inferring intentions, which can be difficult in high-dimensional settings. We build upon prior work that studies assistance through the lens of empowerment: an assistive agent aims to maximize the influence of the human's actions such that they exert a greater control over the environmental outcomes and can solve tasks in fewer steps. We lift the major limitation of prior work in this area--scalability to high-dimensional settings--with contrastive successor representations. We formally prove that these representations estimate a similar notion of empowerment to that studied by prior work and provide a ready-made mechanism for optimizing it. Empirically, our proposed method outperforms prior methods on synthetic benchmarks, and scales to Overcooked, a cooperative game setting. Theoretically, our work connects ideas from information theory, neuroscience, and reinforcement learning, and charts a path for representations to play a critical role in solving assistive problems., Comment: Conference on Neural Information Processing Systems (NeurIPS), 2024

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC, a highly diverse dataset of abstract reasoning tasks. We train neural models for induction (inferring latent functions) and transduction (directly predicting the test output for a given test input). Our models are trained on synthetic data generated by prompting LLMs to produce Python code specifying a function to be inferred, plus a stochastic subroutine for generating inputs to that function. We find inductive and transductive models solve very different problems, despite training on the same problems, and despite sharing the same neural architecture.

Proximal policy optimization (PPO) is a widely-used algorithm for on-policy reinforcement learning. This work offers an alternative perspective of PPO, in which it is decomposed into the inner-loop estimation of update vectors, and the outer-loop application of updates using gradient ascent with unity learning rate. Using this insight we propose outer proximal policy optimization (outer-PPO); a framework wherein these update vectors are applied using an arbitrary gradient-based optimizer. The decoupling of update estimation and update application enabled by outer-PPO highlights several implicit design choices in PPO that we challenge through empirical investigation. In particular we consider non-unity learning rates and momentum applied to the outer loop, and a momentum-bias applied to the inner estimation loop. Methods are evaluated against an aggressively tuned PPO baseline on Brax, Jumanji and MinAtar environments; non-unity learning rates and momentum both achieve statistically significant improvement on Brax and Jumanji, given the same hyperparameter tuning budget.

We present a new semi-analytical model for the evolution of galaxies and supermassive black holes (SMBHs) that is based on the extended Press-Schechter formalism and phenomenological modelling of star formation. The model yields BH mass-stellar mass relations that reproduce both the JWST and pre-JWST observations. If the efficiency for BH mergers is high the JWST data prefer light seeds while the pre-JWST data prefers heavy seeds. The fit improves for a smaller merger efficiency, $O(0.1)$, for which both data prefer heavy seeds, while also accommodating the PTA GW background data., Comment: 5 pages, 4 figures

Broadly intelligent agents should form task-specific abstractions that selectively expose the essential elements of a task, while abstracting away the complexity of the raw sensorimotor space. In this work, we present Neuro-Symbolic Predicates, a first-order abstraction language that combines the strengths of symbolic and neural knowledge representations. We outline an online algorithm for inventing such predicates and learning abstract world models. We compare our approach to hierarchical reinforcement learning, vision-language model planning, and symbolic predicate invention approaches, on both in- and out-of-distribution tasks across five simulated robotic domains. Results show that our approach offers better sample complexity, stronger out-of-distribution generalization, and improved interpretability., Comment: In submission

We introduce a multi-turn benchmark for evaluating personalised alignment in LLM-based AI assistants, focusing on their ability to handle user-provided safety-critical contexts. Our assessment of ten leading models across five scenarios (each with 337 use cases) reveals systematic inconsistencies in maintaining user-specific consideration, with even top-rated "harmless" models making recommendations that should be recognised as obviously harmful to the user given the context provided. Key failure modes include inappropriate weighing of conflicting preferences, sycophancy (prioritising user preferences above safety), a lack of attentiveness to critical user information within the context window, and inconsistent application of user-specific knowledge. The same systematic biases were observed in OpenAI's o1, suggesting that strong reasoning capacities do not necessarily transfer to this kind of personalised thinking. We find that prompting LLMs to consider safety-critical context significantly improves performance, unlike a generic 'harmless and helpful' instruction. Based on these findings, we propose research directions for embedding self-reflection capabilities, online user modelling, and dynamic risk assessment in AI assistants. Our work emphasises the need for nuanced, context-aware approaches to alignment in systems designed for persistent human interaction, aiding the development of safe and considerate AI assistants., Comment: Submitted to ICLR 2025 on 01/10/2024

Interfacial energy dissipation during stick-slip motion of a liquid drop on a non-conductive polymer substrate is shown to lead to an irreversible increase in electrical charge. This previously unobserved phenomenon occurs during surface wetting, in contrast to the previously reported charge separation mechanism that occurs during dewetting. Understanding this electrification mechanism will facilitate the design of energy harvesters and aid the development of risk mitigation strategies for electrostatic buildup in liquid flow across a wide range of industrial applications.

Scanning helium microscopy (SHeM) is an emerging technique that uses a beam of neutral atoms to image and analyse surfaces. The low energies ($\sim$64 meV) and completely non-destructive nature of the probe particles provide exceptional sensitivity for studying delicate samples and thin devices, including 2D materials. To date, around five such instruments have been constructed and are described in the literature. All represent the first attempts at SHeM construction in different laboratories, and use a single detection device. Here, we describe our second generation microscope, which is the first to offer multi-detector capabilities. The new instrument builds on recent research into SHeM optimisation and incorporates many improved design features over our previous instrument. We present measurements that highlight some of the unique capabilities the instrument provides, including 3D surface profiling, alternative imaging modes, and simultaneous acquisition of images from a mixed species beam.

Ultrawide bandgap (UWBG) semiconductors are promising for next-generation power electronics, largely attributed to their substantial bandgap and exceptional breakdown electric field. Rutile GeO2 (r-GeO2) emerges as a promising alternative, particularly because of its ambipolar dopability. However, research on r-GeO2 is still in its infancy, and further investigation into its structural properties is essential for enhancing epilayer quality. In our previous work, we identified distinct surface morphologies; square-patterned and smooth regions of epitaxial r-GeO2 films grown on r-TiO2 (001) substrates using metal-organic chemical vapor deposition (MOCVD).This research employs transmission electron microscopy (TEM) to investigate the structural characteristics of the material. The findings indicate that the square-patterned regions are crystalline, whereas the smooth regions exhibit amorphous properties. The measured lattice spacing in the (110) plane is 0.324 nm, slightly exceeding the theoretical value of 0.312 nm. This discrepancy suggests the presence of tensile strain in the r-GeO2 film, resulting from lattice mismatch or thermal expansion differences with the substrate. We also observed a threading dislocation density of 1.83*10^9 cm-2, consisting of 11.76% screw-type, 29.41% edge-type, 55.89% mixed-type dislocations, and 2.94% planar defects. These findings offer valuable insights into the growth mechanisms and defect characteristics of r-GeO2., Comment: 19 pages, 5 figures

Accurately quantifying the ionizing photon production efficiency ($\xi_\rm{ion}$) of $z>6$ star-forming galaxies (SFGs) is necessary to understand their contribution to reionization. We investigate the ionizing properties of N=289 SFGs selected at $z=6.9-7.6$ from the JWST Cycle-1 imaging programmes; PRIMER and JADES. We use BAGPIPES to consistently infer the equivalent widths of their [OIII]+$\rm{H\beta}$ emission lines ($W_\lambda$) and their physical properties. To supplement our high-redshift galaxies, we measure $W_\lambda$ photometrically for a sample of N=253 $z=3.2-3.6$ SFGs selected from the VANDELS spectroscopic survey. Comparing these samples, we find a strong apparent redshift evolution in their median $W_\lambda$, increasing from $W_\lambda =310\pm25\,\r{A}$ in VANDELS to $W_\lambda =630\pm30\,\r{A}$ in our JWST-based sample. In the JWST sample at $z>7$, we find that $W_\lambda$ correlates with both stellar mass and UV luminosity, with high-mass, $M_{ UV}-$faint galaxies producing systematically weaker emission lines. Moreover, we discover a departure from the standard log-normal shape of the $W_\lambda$ distribution, characterised by a more pronounced tail at lower $W_\lambda$, consistent with increasingly bursty star formation. Using $W_\lambda$ as a proxy for $\xi_\rm{ion}$, and UV spectral slope as a proxy for LyC escape fraction ($f_\rm{esc}$), we find a minority of galaxies with high $\xi_\rm{ion}$ and $f_\rm{esc}$ (e.g., $\rm{log(\xi_{ion}/erg^{-1}Hz})\sim25.6$ and $f_\rm{esc}\sim0.15$). However, we find that the LyC photon budget at $z>7$ is dominated by galaxies with more moderate output, close to the sample median of $\rm{log(\xi_{ion}/erg^{-1}Hz})\sim25.3$ and $f_\rm{esc}\sim0.05$. This is consistent with estimates for the number of LyC photons required to power reionization at $z>7$, with no evidence for over or under-production., Comment: 18 pages, 9 figures + 1 appendix. Submitted to MNRAS

Kidney transplantation is the preferred treatment for end-stage renal disease, yet the scarcity of donors and inefficiencies in allocation systems create major bottlenecks, resulting in prolonged wait times and alarming mortality rates. Despite their severe scarcity, timely and effective interventions to prevent non-utilization of life-saving organs remain inadequate. Expedited out-of-sequence placement of hard-to-place kidneys to centers with the highest likelihood of utilizing them has been recommended in the literature as an effective strategy to improve placement success. Nevertheless, current attempts towards this practice is non-standardized and heavily rely on the subjective judgment of the decision-makers. This paper proposes a novel data-driven, machine learning-based ranking system for allocating hard-to-place kidneys to centers with a higher likelihood of accepting and successfully transplanting them. Using the national deceased donor kidney offer and transplant datasets, we construct a unique dataset with donor-, center-, and patient-specific features. We propose a data-driven out-of-sequence placement policy that utilizes machine learning models to predict the acceptance probability of a given kidney by a set of transplant centers, ranking them accordingly based on their likelihood of acceptance. Our experiments demonstrate that the proposed policy can reduce the average number of centers considered before placement by fourfold for all kidneys and tenfold for hard-to-place kidneys. This significant reduction indicates that our method can improve the utilization of hard-to-place kidneys and accelerate their acceptance, ultimately reducing patient mortality and the risk of graft failure. Further, we utilize machine learning interpretability tools to provide insights into factors influencing the kidney allocation decisions.

In the length-constrained minimum spanning tree (MST) problem, we are given an $n$-node edge-weighted graph $G$ and a length constraint $h \geq 1$. Our goal is to find a spanning tree of $G$ whose diameter is at most $h$ with minimum weight. Prior work of Marathe et al.\ gave a poly-time algorithm which repeatedly computes maximum cardinality matchings of minimum weight to output a spanning tree whose weight is $O(\log n)$-approximate with diameter $O(\log n)\cdot h$. In this work, we show that a simple random sampling approach recovers the results of Marathe et al. -- no computation of min-weight max-matchings needed! Furthermore, the simplicity of our approach allows us to tradeoff between the approximation factor and the loss in diameter: we show that for any $\epsilon \geq 1/\operatorname{poly}(n)$, one can output a spanning tree whose weight is $O(n^\epsilon / \epsilon)$-approximate with diameter $O(1/\epsilon)\cdot h$ with high probability in poly-time. This immediately gives the first poly-time $\operatorname{poly}(\log n)$-approximation for length-constrained MST whose loss in diameter is $o(\log n)$.

Field-effect devices constructed by stacking flakes of van der Waals (vdW) materials, with hexagonal boron nitride (hBN) playing the role of gate dielectric, often exhibit virtually no hysteresis in their characteristics. This permits exquisitely detailed studies of diverse gate-voltage-tuned phenomena in vdW devices. Recently, however, a dramatic form of gate hysteresis, sometimes called the "gate doesn't work" (GDW) or "electron ratchet" effect, has been seen in certain individual vdW devices that seem otherwise unexceptional. When it occurs, this hysteresis phenomenon is striking and robust, yet it is difficult to reliably reproduce between devices and, largely as a result, its origin remains disputed. Most devices where it has been seen have a bilayer graphene channel and nominal rotational alignment between the graphene and hBN, which has engendered explanations based on properties of bilayer graphene combined with moir\'e effects. Here, we report our studies of the phenomenon observed in devices that have multilayer graphene channels. We find that the effect can occur in devices with graphite channels that have many more than two graphene layers, in which case it is unambiguously associated with just one surface of the graphite. It can also survive to room temperature, occur in the absence of intentional rotational alignment with hBN, persist when a monolayer of WSe2 is inserted between the graphene and hBN, and exhibit continuous relaxation on timescales of hours or longer. These observations impose strong constraints on the origin of this puzzling phenomenon, which has exciting potential applications if it can be mastered., Comment: 7 pages, 4 figures, 12 supplementary information figures, 1 supplementary information table

Radio-quiet Seyfert galaxies have been detected in GeV gamma-rays by the Fermi Large Area Telescope (LAT), but the origin of much of this emission is unclear. We consider the nearby example, the Seyfert galaxy GRS 1734-292, which exhibits weak starburst and jet activities that are insufficient to explain the observed gamma-ray flux. With the first detailed multi-wavelength study of this source, we demonstrate that an active galactic nucleus (AGN) disk wind can account for its gamma-ray emission. Using a lepto-hadronic emission model based on a shocked ambient medium and a shocked wind region created by an AGN accretion disk wind, we identify two viable scenarios that are consistent with the Fermi-LAT data and multi-wavelength observations: a hadronic pp-dominated scenario and a leptonic external Compton-dominated scenario. Both of these show that future observations with the Cherenkov Telescope Array (CTA) and the Southern Wide-field Gamma-ray Observatory (SWGO) could detect TeV emission from a disk wind in GRS 1734-292. Such a detection would substantially improve our understanding of cosmic ray acceleration efficiency in AGN disk wind systems, and would establish radio-quiet Seyfert galaxies as cosmic ray accelerators capable of reaching ultra-high energies., Comment: 8 pages, 2 figures, 1 table

We present the properties of a massive, large, dusty, metal-rich, star-forming galaxy at z_spec=6.73. GOODSN-100182 was observed with JWST/NIRSpec as part of the AURORA survey, and is also covered by public multi-wavelength HST and JWST imaging. While the large mass of GOODSN-100182 (~10^10 M_sun) was indicated prior to JWST, NIRCam rest-optical imaging now reveals the presence of an extended disk (r_eff~1.5 kpc). In addition, the NIRSpec R~1000 spectrum of GOODSN-100182 includes the detection of a large suite of rest-optical nebular emission lines ranging in wavelength from [OII]3727 up to [NII]6583. The ratios of Balmer lines suggest significant dust attenuation (E(B-V)_gas=0.40+0.10/-0.09), consistent with the red rest-UV slope inferred for GOODSN-100182 (beta=-0.50+/-0.09). The star-formation rate based on dust-corrected H-alpha emission is log(SFR(H-alpha)/ M_sun/yr)=2.02+0.13/-0.14, well above the z~7 star-forming main sequence in terms of specific SFR. Strikingly, the ratio of [NII]6583/H-alpha emission suggests almost solar metallicity, as does the ratio ([OIII]5007/H-beta)/([NII]6583/H-alpha) and the detection of the faint [FeII]4360 emission feature, whereas the [OIII]5007/[OII]3727 ratio suggests roughly 50% solar metallicity. Overall, the excitation and ionization properties of GOODSN-100182 more closely resemble those of typical star-forming galaxies at z~2-3 rather than z~7. Based on public spectroscopy of the GOODS-N field, we find that GOODSN-100182 resides within a significant galaxy overdensity, and is accompanied by a spectroscopically-confirmed neighbor galaxy. GOODSN-100182 demonstrates the existence of mature, chemically-enriched galaxies within the first billion years of cosmic time, whose properties must be explained by galaxy formation models., Comment: 16 pages, 13 figures, submitted to ApJ

Measurements monitoring the inductive coupling between oscillating radio-frequency magnetic fields and objects of interest create versatile platforms for non-destructive testing. The benefits of ultra low frequency measurements, i.e., below 3 kHz, are sometimes outweighed by the fundamental and technical difficulties related to operating pick-up coils or other field sensors in this frequency range. Inductive measurements with the detection based on a two-photon interaction in rf atomic magnetometers address some of these issues, as the sensor gains an uplift in its operational frequency. The developments reported here integrate the fundamental and applied aspects of the two-photon process in magnetic induction measurements. In this paper, all spectral components of the two-photon process are identified, which result from the non-linear interactions between the rf fields and atoms. A method for the retrieval of the two-photon phase information, which is critical for inductive measurements, is also demonstrated. Furthermore, a self-compensation configuration is introduced, whereby high contrast measurements of defects can be obtained due to the sensor's insensitivity to the primary field, including using simplified instrumentation for this configuration by producing two rf fields with a single rf coil., Comment: 10 pages, 9 figures

We give a density condition for when, subject to a necessary parity condition, an eulerian graph or digraph may be cellularly embedded in an orientable surface so that it has exactly two faces, each bounded by an euler circuit, one of which may be specified in advance. More generally, suppose that every vertex in an $n$-vertex eulerian digraph (loops and multiple arcs allowed) has at least $(4n+2)/5$ neighbors, and specify any decomposition of the arcs into disjoint directed circuits (closed trails). We show that such a digraph has an orientable embedding in which the given circuits are facial walks and there are exactly one or two other faces. This embedding then has maximum genus relative to the given circuits being facial walks. When there is only one other face, it is necessarily bounded by an euler circuit. Consequently, if the numbers of vertices and edges have the same parity, a sufficiently dense digraph $D$ with a given directed euler circuit $T$ has an orientable embedding with exactly two faces, each bounded by an euler circuit, one of which is $T$. These results for digraphs give analogous results for graphs as immediate corollaries. The main theorem encompasses several special cases in the literature, such as when the digraph is a tournament., Comment: 32 pages, 12 figures

Determining stress and strain in a component of a fusion power plant involves defining boundary conditions for the mechanical equilibrium equations, implying the availability of a full reactor model for defining those conditions. To address this fundamental challenge of reactor design, a finite element method (FEM) model for the Mega-Ampere Spherical Tokamak Upgrade (MAST-U) fusion tokamak, operating at the Culham Campus of UKAEA, has been developed and applied to assess mechanical deformations, strain, and stress in the full tokamak structure, taken as a proxy for a fusion power plant. The model, handling 127 million finite elements using about 800 processors in parallel, illustrates the level of fidelity of structural simulations of a complex nuclear device made possible by the modern supercomputing systems. The model predicts gravitational and atmospheric pressure-induced deformations in broad agreement with observations, and enables computing the spectrum of acoustic vibrations of a tokamak, arising from mechanical disturbances like an earthquake or a plasma disruption. We introduce the notion of the density of stress to characterise the distribution of stress in the entire solid body of the tokamak, and to predict the magnitude and locations of stress concentrations. The model enables defining computational requirements for simulating a whole operating fusion power plant, and provides a digital foundation for the assessment of reactor performance as well as for specifying the relevant materials testing programme.

Adam Smith's inquiry into the emergence and stability of the self-organization of the division of labor in commodity production and exchange is considered using statistical equilibrium methods from statistical physics. We develop a statistical equilibrium model of the distribution of independent direct producers in a hub-and-spoke framework that predicts both the center of gravity of producers across lines of production as well as the endogenous fluctuations between lines of production that arise from Smith's concept of "perfect liberty". The ergodic distribution of producers implies a long-run balancing of "advantages to disadvantages" across lines of employment and gravitation of market prices around Smith's natural prices.

We present a sample of 50 H-alpha detected broad-line active galactic nuclei (BLAGN) at redshifts 3.50), independent of the contributions of emission lines to the broadband photometry. We construct the black hole (BH) mass function at 3.5

We argue that dielectric haloscopes like MADMAX, originally designed for detecting axion dark matter, are also very promising gravitational wave detectors. Operated in resonant mode at frequencies around $\mathcal{O}(10\,\text{GHz})$, these detectors benefit from enhanced gravitational wave to photon conversion at the surfaces of a stack of thin dielectric disks. Since the gravitational wave is relativistic, there is an additional enhancement of the signal compared to the axion case due to increased conversion probability of gravitational waves to photons in the vacuum between the disks. A gravitational wave search using a dielectric haloscope imposes stringent requirements on the disk thickness and placement, but relaxed requirements on the disk smoothness. An advantage is the possibility of a broadband or hybrid resonant/broadband operation mode, which extends the frequency range down to $\mathcal{O}(100\,\text{MHz})$. We show that strain sensitivities down to $10^{-21} \text{Hz}^{-1/2} \times (10\,\text{GHz}/f)$ will be possible in the coming years for the broadband setup, while a resonant setup optimized for gravitational waves could even reach $3\times 10^{-23} \text{Hz}^{-1/2} \times (10\,\text{GHz}/f)$ with current technology., Comment: 12 + 8 pages, 6 + 3 figures

Let $g\colon L\rightarrow L$ be an atoroidal, endperiodic map on an infinite type surface $L$ with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, $g$ is isotopic to a spun pseudo-Anosov map $f$. We show that spun pseudo-Anosov maps minimize the number of periodic points of period $n$ for sufficiently high $n$ over all maps in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor. We also show that the same theorem holds for atoroidal Handel--Miller maps when you only consider periodic points that lie in the intersection of the stable and unstable laminations., Comment: 13 pages, 3 figures

We show that if $\mathcal{A} \subset {[n] \choose n/2}$ with measure bounded away from zero and from one, then the $\Omega(\sqrt{n})$-iterated upper shadows of $\mathcal{A}$ and $\mathcal{A}^c$ intersect in a set of positive measure. This confirms (in a strong form) a conjecture of Friedgut. It can be seen as a stability result for the Kruskal--Katona theorem., Comment: Minor corrections. 8 pages