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GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

Context: Over the last decade, the forestry sector has undergone substantial changes, evolving from a post-2008 financial crisis landscape to incorporating policies favoring sustainable and green alternatives, especially after the 2015 Paris agreement. This evolution was drastically disrupted with the advent of the COVID-19 pandemic in 2020, causing unprecedented interruptions in supply chains, product markets, and data collection. Grasping the aftermath of the COVID-19, regional instances of the forest supply chain sector need synthetic pictures of their present state and future opportunities for emerging wood products and better regional-scale carbon balance. But given the impact of COVID-19 lock-down on data collection, the production of such synthetic pictures has become more complex, yet essential. This was the case for the regional supply chain of the Grand-Est region in France that we studied. Aims: For this study, our aim was to demonstrate that an integrated methodology could provide such synthetic picture even though we sued heterogenous sources of data and different analytical objectives: i.e. (1) retrospectively evaluate the aftermath of COVID-19 pandemic on the supply chain outcomes within the forestry sector; and then (2) retrospectively explore possible options of structural change of regional supply chain that would be required to simultaneously recover from COVID-19 and transit to new objectives in line with the extraction of new bio-molecules from wood biomass, and with the reduction of the regional scale carbon footprint (in line with the IPCC Paris Agreement) Methods: To achieve this, our methodological approach was decomposed into three steps. We first used a Material Flow Analysis (MFA) recently conducted on the forestry sector in the Grand Est region to establish a Sankey diagram (i.e. a schematic representation of industrial sectors and biomass flows along the supply chain) for the pre-Covid-19 period (2014-2018). Then we compared pre-Covid-19 Sankey diagram to the only source of data we could access from the post-Covid-19 period (2020-2021) in order to estimate the impact of Covid-19. Finally, we used as input the reconciled supply chain model into a consequential Wood Product Model (WPMs), called CAT (carbon accounting tool) in order to compare three prospective scenarios: (1) a scenario that projected 2020-2021 Covid-19 conditions and assumed pre-Covid-19 business as usual practices, (2) a scenario illustrating the consequence or rerouting some of the biomass to satisfy the expected increase in pulp and paper production to satisfy the needs of the industry after Covid-19, and (3) a scenario that explored new opportunities in term of extraction of novel bio-molecules by the emerging biochemical wood industry. For every scenario we also evaluated the regional carbon gains and losses that these changes implied. Results: Our study conducted a detailed analysis of the impacts of the COVID-19 pandemic on the forestry sector's supply chain in the Grand Est region, using a dynamic and integrated Wood Product Model. We found significant disruptions during the pandemic period, with notable declines in industrial wood chips and timber hardwood production by 41.8% and 40%, respectively. Conversely, there were substantial increases in fuelwood, timber sawdust, and timber softwood, rising by 14.15%, 44.23%, and 15.29% respectively. These fluctuations underscore the resilience and vulnerabilities within the regional wood supply chain. Our findings also emphasize the potential for strategic rerouting of biomass flows to meet changing industry demands, which could play a crucial role in supporting the sector's recovery and adaptation to post-pandemic conditions. Discussion and conclusion: In addition, our study recognizes the limitations of the current approach combining MFA and WPM and suggests potential areas of enhancement. Ultimately, our findings shed light on the need to develop more integrated analytical methods to provide useful synthetic pictures of regional scale supply chains, when there is a need to adapt it to evolving situations and complex data landscapes.

In many condensed matter systems, long range order emerges at low temperatures as thermal fluctuations subside. In the presence of competing interactions or quenched disorder, however, some systems can show unusual configurations that become more disordered at low temperature, a rare phenomenon known as "inverse melting". Here, we discover an inverse melting of the polar order in a ferroelectric oxide with quenched chemical disorder (BaTi1-xZrxO3) through direct atomic-scale visualization using in situ scanning transmission electron microscopy. In contrast to the clean BaTiO3 parent system in which long range order tracks lower temperatures, we observe in the doped system BaTi1-xZrxO3 that thermally driven fluctuations at high temperature give way to a more ordered state and then to a re-entrant disordered configuration at even lower temperature. Such an inverse melting of the polar order is likely linked to the random field generated by Zr dopants, which modulates the energy landscape arising from the competition between thermal fluctuations and random field pinning potential. These visualizations highlight a rich landscape of order and disorder in materials with quenched disorder, which may be key to understanding their advanced functionalities.

We examine the behavior of the entanglement asymmetry in the ground state of a (1+1)-dimensional conformal field theory with a boundary condition that explicitly breaks a bulk symmetry. Our focus is on the asymmetry of a subsystem $A$ originating from the symmetry-breaking boundary and extending into a semi-infinite bulk. By employing the twist field formalism, we derive a universal expression for the asymmetry, showing that the asymptotic behavior for large subsystems is approached algebraically, with an exponent which is twice the conformal dimension of a boundary condition-changing operator. As a secondary result, we also establish a similar asymptotic behavior for the string order parameter. Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models., Comment: 20 pages, 5 figures

The consecutive magnetic ordering of the Ho and Ru ions in the pyrochlore Ho2Ru2O7 and their interplay are investigated by neutron scattering, magnetic and specific heat measurements. The Ru magnetic moments order at 95 K into an easy-plane antiferromagnetic state, while the Ho moments order at 1.55 K into an unsaturated ferromagnetic state that retains an extensive ground state entropy and present complex spin dynamics throughout the low temperature phase. These unexpected features are analyzed in terms of a fragmented ferromagnetic state equivalent to the pyrochlore kagome ice. Selection of this unusual state relies on a subtle compromise between long-range ferromagnetic interactions between holmium moments and a repulsive cubic field, both mediated by the ruthenium lattice., Comment: 15 pages, 13 figures

We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization $\hat{f}$ of a Lipschitz map $f:M\to N$ is Dunford-Pettis if and only if it is Radon-Nikod\'ym if and only if it does not fix any copy of $L_1$. We also identify and study the corresponding metric property of $f$, which is a natural extension of the curve-flatness introduced in [arXiv:2103.09370]. Further, we show that $\hat{f}$ is compact if and only if it does not fix any copy of $\ell_1$., Comment: 37 pages

We report the detection of water vapor associated with main-belt comet 358P/PANSTARRS on UT 2024 January 8-9 using the NIRSPEC instrument aboard JWST. We derive a water production rate of Q(H2O)=(5.0+/-0.2)x10^25 molecules/s, marking only the second direct detection of sublimation products of any kind from a main-belt comet, after 238P/Read. Similar to 238P, we find a remarkable absence of hypervolatile species, finding Q(CO2)<7.6x10^22 molecules/s, corresponding to Q(CO2)/Q(H2O)<0.2%. Upper limits on CH3OH and CO emission are also estimated. Photometry from ground-based observations show that the dust coma brightened and faded slowly over ~250 days in 2023-2024, consistent with photometric behavior observed in 2012-2013, but also indicate a ~2.5x decline in the dust production rate between these two periods. Dynamical dust modeling shows that the coma's morphology as imaged by JWST's NIRCAM instrument on 2023 November 22 can be reproduced by asymmetric dust emission from a nucleus with a mid-range obliquity (~80 deg) with a steady-state mass loss rate of ~0.8 kg/s. Finally, we find similar Afrho-to-gas ratios of log10(Afrho/Q(H2O))=-24.8+/-0.2 for 358P and log10(Afrho/QH2O)=-24.4+/-0.2 for 238P, suggesting that Afrho could serve as an effective proxy for estimating water production rates in other active main-belt comets. The confirmation of water vapor outgassing in both main-belt comets observed by JWST to date reinforces the use of recurrent activity near perihelion as an indicator of sublimation-driven activity in active asteroids., Comment: 32 pages, 13 figures. Accepted for publication in The Planetary Science Journal

The theory of interfacial properties in liquid-liquid or liquid-vapour systems is nearly 200 years old. The advent of computational tools has greatly advanced the field, mainly through the use of Molecular Dynamics simulations. Despite the successes and advances in the theory of interfacial phenomena for liquid-liquid systems, the study of solid-liquid interfaces remains a challenge both theoretically and experimentally. The main reason why the treatment of solid-liquid systems has fallen behind that of liquid-liquid systems is that there are complications that arise whenever an interface involving solid systems is considered involving both theory of the solid-liquid interface and the calculations using MD simulations. An example of the former is that, contrary to the liquid-liquid case, the interfacial properties of solids depend on the lattice orientation. The main complications in these calculations arise from the fact that for solids the ``mechanical route'' cannot be used. To overcome this problem, several numerical approaches were proposed. The main purpose of this review is to provide an overview of these different methodologies and to discuss their strengths and weaknesses. We classify these methodologies into two main groups: direct and indirect methods. Direct methods are those that can calculate directly the properties of interfaces, while in indirect approaches the properties of the interface are not the primary result of the simulations. We also included a discussion on the origin of the difficulties in considering solid interfaces from a thermodynamic point of view. In the second part of the review, we discuss two key related topics: nucleation theory and curved interfaces. They both represent an important problem in the study of interfaces and in the context of solid-liquid ones for which the research is still extremely active., Comment: 111 pages, 14 figures

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing more tailorable light-matter interactions in general. In this paper, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of $2\pi\cdot1.45~ \rm MHz$ we achieve $\langle n \rangle = 1.3 \pm 1.1$ in $500~\mu \rm s$ and cooling rates of ${\sim}0.3 \, \rm quanta/\mu s$. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a simple model. Cooling is fast and power-efficient, with improved performance compared to simulated operation under the corresponding running wave configuration., Comment: 16 pages, 11 figures

Trapped ions are a promising modality for quantum systems, with demonstrated utility as the basis for quantum processors and optical clocks. However, traditional trapped-ion systems are implemented using complex free-space optical configurations, whose large size and susceptibility to vibrations and drift inhibit scaling to large numbers of qubits. In recent years, integrated-photonics-based systems have been demonstrated as an avenue to address the challenge of scaling trapped-ion systems while maintaining high fidelities. While these previous demonstrations have implemented both Doppler and resolved-sideband cooling of trapped ions, these cooling techniques are fundamentally limited in efficiency. In contrast, polarization-gradient cooling can enable faster and more power-efficient cooling and, therefore, improved computational efficiencies in trapped-ion systems. While free-space implementations of polarization-gradient cooling have demonstrated advantages over other cooling mechanisms, polarization-gradient cooling has never previously been implemented using integrated photonics. In this paper, we design and experimentally demonstrate key polarization-diverse integrated-photonics devices and utilize them to implement a variety of integrated-photonics-based polarization-gradient-cooling systems, culminating in the first experimental demonstration of polarization-gradient cooling of a trapped ion by an integrated-photonics-based system. By demonstrating polarization-gradient cooling using an integrated-photonics-based system and, in general, opening up the field of polarization-diverse integrated-photonics-based devices and systems for trapped ions, this work facilitates new capabilities for integrated-photonics-based trapped-ion platforms.

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras.

Today, cheap numerical hardware offers huge amounts of parallel computing power, much of which is used for the task of fitting neural networks to data. Adoption of this hardware to accelerate statistical Markov chain Monte Carlo (MCMC) applications has been much slower. In this chapter, we suggest some patterns for speeding up MCMC workloads using the hardware (e.g., GPUs, TPUs) and software (e.g., PyTorch, JAX) that have driven progress in deep learning over the last fifteen years or so. We offer some intuitions for why these new systems are so well suited to MCMC, and show some examples (with code) where we use them to achieve dramatic speedups over a CPU-based workflow. Finally, we discuss some potential pitfalls to watch out for.

Much of the research on the interpretability of deep neural networks has focused on studying the visual features that maximally activate individual neurons. However, recent work has cast doubts on the usefulness of such local representations for understanding the behavior of deep neural networks because individual neurons tend to respond to multiple unrelated visual patterns, a phenomenon referred to as "superposition". A promising alternative to disentangle these complex patterns is learning sparsely distributed vector representations from entire network layers, as the resulting basis vectors seemingly encode single identifiable visual patterns consistently. Thus, one would expect the resulting code to align better with human perceivable visual patterns, but supporting evidence remains, at best, anecdotal. To fill this gap, we conducted three large-scale psychophysics experiments collected from a pool of 560 participants. Our findings provide (i) strong evidence that features obtained from sparse distributed representations are easier to interpret by human observers and (ii) that this effect is more pronounced in the deepest layers of a neural network. Complementary analyses also reveal that (iii) features derived from sparse distributed representations contribute more to the model's decision. Overall, our results highlight that distributed representations constitute a superior basis for interpretability, underscoring a need for the field to move beyond the interpretation of local neural codes in favor of sparsely distributed ones.

This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the strong instability of standing waves associated with ground state solutions in the $L^2$-supercritical case. The presence of a doping profile causes several difficulties, especially in examining geometric shapes of fibering maps along an $L^2$-invariant scaling curve. Furthermore, the classical approach by Berestycki-Cazenave for the strong instability cannot be applied to our problem due to a remainder term caused by the doping profile. To overcome these difficulties, we establish a new energy inequality associated with the $L^2$-invariant scaling and adopt the strong instability result developed by Fukaya-Ohta(2018). When the doping profile is a characteristic function supported on a bounded smooth domain, some geometric quantities related to the domain, such as the mean curvature, are responsible for the strong instability of standing waves., Comment: arXiv admin note: substantial text overlap with arXiv:2411.02103; text overlap with arXiv:2409.01842

This paper introduces a data-driven approach to estimate precipitation rates from Synthetic Aperture Radar (SAR) at a spatial resolution of 200 meters per pixel. It addresses previous challenges related to the collocation of SAR and weather radar data, specifically the misalignment in collocations and the scarcity of rainfall examples under strong wind. To tackle these challenges, the paper proposes a multi-objective formulation, introducing patch-level components and an adversarial component. It exploits the full NEXRAD archive to look for potential co-locations with Sentinel-1 data. With additional enhancements to the training procedure and the incorporation of additional inputs, the resulting model demonstrates improved accuracy in rainfall estimates and the ability to extend its performance to scenarios up to 15 m/s., Comment: 36 pages, 13 figures

Human excrement composting (HEC) is a sustainable strategy for human excrement (HE) management that recycles nutrients and mitigates health risks while reducing reliance on freshwater, fossil fuels, and fertilizers. We present a comprehensive microbial time series analysis of HEC and show that the initial gut-like microbiome of HEC systems transitions to a microbiome similar to soil and traditional compost in fifteen biological replicates tracked weekly for one year., Comment: Main text: 9 pages, 2 figures; Extended data: 10 figures; Supplemental Text: 32 pages, 8 figures, 2 tables

In this paper, we present a dynamic semantic clustering approach inspired by the Chinese Restaurant Process, aimed at addressing uncertainty in the inference of Large Language Models (LLMs). We quantify uncertainty of an LLM on a given query by calculating entropy of the generated semantic clusters. Further, we propose leveraging the (negative) likelihood of these clusters as the (non)conformity score within Conformal Prediction framework, allowing the model to predict a set of responses instead of a single output, thereby accounting for uncertainty in its predictions. We demonstrate the effectiveness of our uncertainty quantification (UQ) technique on two well known question answering benchmarks, COQA and TriviaQA, utilizing two LLMs, Llama2 and Mistral. Our approach achieves SOTA performance in UQ, as assessed by metrics such as AUROC, AUARC, and AURAC. The proposed conformal predictor is also shown to produce smaller prediction sets while maintaining the same probabilistic guarantee of including the correct response, in comparison to existing SOTA conformal prediction baseline.

Myosin motors are fundamental biological actuators, powering diverse mechanical tasks in eukaryotic cells via ATP hydrolysis. Recent work revealed that myosin's velocity-dependent detachment rate can bridge actomyosin dynamics to macroscale Hill muscle predictions. However, the influence of this microscale unbinding, which we characterize by a dimensionless parameter $\alpha$, on macroscale energetic flows-such as power consumption, output and efficiency-remains elusive. Here we develop an analytical model of myosin dynamics that relates unbinding rates $\alpha$ to energetics. Our model agrees with published in-vivo muscle data and, furthermore, uncovers a performance-efficiency tradeoff governed by $\alpha$. To experimentally validate the tradeoff, we build HillBot, a robophysical model of Hill's muscle that mimics nonlinearity. Through HillBot, we decouple $\alpha$'s concurrent effect on performance and efficiency, demonstrating that nonlinearity drives efficiency. We compile 136 published measurements of $\alpha$ in muscle and myoblasts to reveal a distribution centered at $\alpha^* = 3.85 \pm 2.32$. Synthesizing data from our model and HillBot, we quantitatively show that $\alpha^*$ corresponds to a class of generalist actuators that are both relatively powerful and efficient, suggesting that the performance-efficiency tradeoff underpins the prevalence of $\alpha^*$ in nature. We leverage these insights and propose a nonlinear variable-impedance protocol to shift along a performance-efficiency axis in robotic applications., Comment: 23 pages, 6 figures. PDF of supplemental information available in zip download

This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the existence of ground state solutions by considering the minimization problem on a Nehari-Pohozaev set. The presence of a doping profile causes several difficulties, especially in the proof of the uniqueness of a maximum point of a fibering map. A key ingredient is to establish the energy inequality. We also establish the relation between ground state solutions and $L^2$-constraint minimizers. When the doping profile is a characteristic function supported on a bounded smooth domain, some geometric quantities related to the domain, such as the mean curvature,are responsible for the existence of ground state solutions.

Pt-based electrocatalysts are the primary choice for fuel cells due to their superior oxygen reduction reaction (ORR) activity. To enhance ORR performance and durability, extensive studies have investigated transition metal alloying, doping, and shape control to optimize the three key governing factors for ORR: geometry, local chemistry, and strain of their surface and subsurface. However, systematic optimization remains incomplete, as it requires an atomic-scale understanding of these factors and their dynamics over potential cycling, as well as their relationship to ORR activity. Here, we implement neural network-assisted atomic electron tomography to measure the 3D atomic structural dynamics and their effects on the functional degradation of PtNi alloy catalysts. Our results reveal that PtNi catalysts undergo shape changes, surface alloying, and strain relaxation during cycling, which can be effectively mitigated by Ga doping. By combining geometry, local chemistry, and strain analysis, we calculated the changes in ORR activity over thousands of cycles and observed that Ga doping leads to higher initial activity and greater stability. These findings offer a pathway to understanding 3D atomic structural dynamics and their relation to ORR activity during cycling, paving the way for the systematic design of durable, high-efficiency nanocatalysts., Comment: 45 pages, 4 main figures, 15 supplementary figures

We report the results of a spectroscopic survey of candidate T subdwarfs identified by the Backyard Worlds: Planet 9 program. Near-infrared spectra of 31 sources with red $J-W2$ colors and large $J$-band reduced proper motions show varying signatures of subsolar metallicity, including strong collision-induced H$_2$ absorption, obscured methane and water features, and weak K I absorption. These metallicity signatures are supported by spectral model fits and 3D velocities, indicating thick disk and halo population membership for several sources. We identify three new metal-poor T subdwarfs ([M/H] $\lesssim$ $-$0.5), CWISE J062316.19+071505.6, WISEA J152443.14$-$262001.8, and CWISE J211250.11-052925.2; and 19 new "mild" subdwarfs with modest metal deficiency ([M/H] $\lesssim$ $-$0.25). We also identify three metal-rich brown dwarfs with thick disk kinematics. We provide kinematic evidence that the extreme L subdwarf 2MASS J053253.46+824646.5 and the mild T subdwarf CWISE J113010.07+313944.7 may be part of the Thamnos population, while the T subdwarf CWISE J155349.96+693355.2 may be part of the Helmi stream. We define a metallicity classification system for T dwarfs that adds mild subdwarfs (d/sdT), subdwarfs (sdT), and extreme subdwarfs (esdT) to the existing dwarf sequence. We also define a metallicity spectral index that correlates with metallicities inferred from spectral model fits and iron abundances from stellar primaries of benchmark T dwarf companions. This expansion of the T dwarf classification system supports investigations of ancient, metal-poor brown dwarfs now being uncovered in deep imaging and spectroscopic surveys., Comment: 82 pages, 19 figures, accepted to ApJS

Salt clouds are predicted to be common on warm exoplanets, but their optical properties are uncertain. The Exoplanet Cloud Ensemble Scattering System (ExCESS), a new apparatus to measure the scattering intensity and degree of linear polarization (DOLP) for an ensemble of particles, is introduced here and used to study the light scattering properties of KCl cloud analogs. ExCESS illuminates particles with a polarized laser beam (532 nm) and uses a photomultiplier tube detector to sweep the plane of illumination. Scattering measurements for KCl particles were collected for three size distributions representative of modeled clouds for the warm exoplanet GJ 1214b. Our measurements show that Lorenz-Mie calculations, commonly used to estimate the light scattering properties of assumedly spherical cloud particles, offer an inaccurate depiction of cubic and cuboid shaped KCl particles. All of our measurements indicate that Lorenz-Mie scattering overestimates the backscattering intensity of our cloud analogs and incorrectly predicts the scattering at mid-phase angles (~90 degrees) and preferential polarization state of KCl scattered light. Our results align with the general scattering properties of non-spherical particles and underscore the importance of further understanding the effects that such particles will have on radiative transfer models of exoplanet atmospheres and reflected light observations of exoplanets by the upcoming Nancy Grace Roman Space Telescope and Habitable Worlds Observatory., Comment: Published in the Planetary Science Journal

When we experience a visual stimulus as beautiful, how much of that experience derives from perceptual computations we cannot describe versus conceptual knowledge we can readily translate into natural language? Disentangling perception from language in visually-evoked affective and aesthetic experiences through behavioral paradigms or neuroimaging is often empirically intractable. Here, we circumnavigate this challenge by using linear decoding over the learned representations of unimodal vision, unimodal language, and multimodal (language-aligned) deep neural network (DNN) models to predict human beauty ratings of naturalistic images. We show that unimodal vision models (e.g. SimCLR) account for the vast majority of explainable variance in these ratings. Language-aligned vision models (e.g. SLIP) yield small gains relative to unimodal vision. Unimodal language models (e.g. GPT2) conditioned on visual embeddings to generate captions (via CLIPCap) yield no further gains. Caption embeddings alone yield less accurate predictions than image and caption embeddings combined (concatenated). Taken together, these results suggest that whatever words we may eventually find to describe our experience of beauty, the ineffable computations of feedforward perception may provide sufficient foundation for that experience.

Fetching techniques from Generalised Geometry and Exceptional Field Theory, we develop a new method to identify consistent subsectors of four-dimensional gauged maximal supergravities that possess a (locally) geometric embedding in type IIB or 11D supergravity. We show that a subsector that is invariant under a structure group $\textrm{G}_\textrm{S} \subset \textrm{E}_{7(7)}$ can define a consistent truncation, even when $\textrm{G}_\textrm{S}$ is not part of the symmetry of the gauged maximal supergravity. As an illustration of the method, type IIB supergravity on $\textrm{S}^{1} \times \textrm{S}^{5}$ is shown to admit a consistent truncation to pure $\mathcal{N}=4$, $D=4$ gauged supergravity. Explicit uplift formulae are presented which provide a type IIB alternative to the M-theory embedding constructed by Cvetic, Lu and Pope $25$ years ago., Comment: 9 pages

The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form $\nu^{\otimes\mathbb N}$ where $\nu$ is a measure on $[0,1]$. Recently, Jahel--Tsankov generalized this theorem showing that under conditions on $M$, the group $\operatorname{Aut}(M)$ is de Finetti, i.e. $\operatorname{Aut}(M)$-invariant measures on $[0,1]^M$ are mixtures of measures of the form $\nu^{\otimes M}$ where $\nu$ is a measure on $[0,1]$. In this note, we give an example of a non-de Finetti non-Archimedean group.

Particle collisions at accelerators such as the Large Hadron Collider, recorded and analyzed by experiments such as ATLAS and CMS, enable exquisite measurements of the Standard Model and searches for new phenomena. Simulations of collision events at these detectors have played a pivotal role in shaping the design of future experiments and analyzing ongoing ones. However, the quest for accuracy in Large Hadron Collider (LHC) collisions comes at an imposing computational cost, with projections estimating the need for millions of CPU-years annually during the High Luminosity LHC (HL-LHC) run \cite{collaboration2022atlas}. Simulating a single LHC event with \textsc{Geant4} currently devours around 1000 CPU seconds, with simulations of the calorimeter subdetectors in particular imposing substantial computational demands \cite{rousseau2023experimental}. To address this challenge, we propose a conditioned quantum-assisted deep generative model. Our model integrates a conditioned variational autoencoder (VAE) on the exterior with a conditioned Restricted Boltzmann Machine (RBM) in the latent space, providing enhanced expressiveness compared to conventional VAEs. The RBM nodes and connections are meticulously engineered to enable the use of qubits and couplers on D-Wave's Pegasus-structured \textit{Advantage} quantum annealer (QA) for sampling. We introduce a novel method for conditioning the quantum-assisted RBM using \textit{flux biases}. We further propose a novel adaptive mapping to estimate the effective inverse temperature in quantum annealers. The effectiveness of our framework is illustrated using Dataset 2 of the CaloChallenge \cite{calochallenge}., Comment: 26 pages, 10 figures, 8 appendices

In this paper, we introduce the Diff-Instruct*(DI*), a data-free approach for building one-step text-to-image generative models that align with human preference while maintaining the ability to generate highly realistic images. We frame human preference alignment as online reinforcement learning using human feedback (RLHF), where the goal is to maximize the reward function while regularizing the generator distribution to remain close to a reference diffusion process. Unlike traditional RLHF approaches, which rely on the KL divergence for regularization, we introduce a novel score-based divergence regularization, which leads to significantly better performances. Although the direct calculation of this divergence remains intractable, we demonstrate that we can efficiently compute its \emph{gradient} by deriving an equivalent yet tractable loss function. Remarkably, with Stable Diffusion V1.5 as the reference diffusion model, DI* outperforms \emph{all} previously leading models by a large margin. When using the 0.6B PixelArt-$\alpha$ model as the reference diffusion, DI* achieves a new record Aesthetic Score of 6.30 and an Image Reward of 1.31 with only a single generation step, almost doubling the scores of the rest of the models with similar sizes. It also achieves an HPSv2 score of 28.70, establishing a new state-of-the-art benchmark. We also observe that DI* can improve the layout and enrich the colors of generated images.

The thermal Sunyaev-Zel'dovich effect (tSZ) is a sensitive probe of cosmology, as it traces the abundance of galaxy clusters and groups in the late-time Universe. Upcoming cosmic microwave background experiments such as the Simons Observatory (SO) and CMB-S4 will provide low-noise and high-resolution component-separated tSZ maps covering a large sky fraction. The tSZ signal is highly non-Gaussian; therefore, higher-order statistics are needed to optimally extract information from these maps. In this work, we study the cosmological constraining power of several tSZ statistics -- Minkowski functionals (MFs), peaks, minima, and moments -- that have yielded promising results in capturing non-Gaussian information from other cosmological data. Using a large suite of halo-model-based tSZ simulations with varying $\Omega_{c}$ and $\sigma_{8}$ (154 cosmologies and over $800, 000$ maps, each $10.5\times10.5$ deg$^{2}$), we show that by combining these observables, we can achieve $\approx 29\times$ tighter constraints compared to using the tSZ power spectrum alone in an idealized noiseless case, with the MFs dominating the constraints. We show that much of the MF constraining power arises from halos below the detection threshold of cluster surveys, suggesting promising synergies with cluster-count analyses. Finally, we demonstrate that these statistics have the potential to deliver tight constraints even in the presence of noise. For example, using post-component-separation tSZ noise expected for SO, we obtain $\approx1.6\times$ and $\approx1.8\times$ tighter constraints than the power spectrum with MFs and all statistics combined, respectively. We show that the constraints from MFs approach the noiseless case for white-noise levels $\lesssim 1 \,\, \mu$K-arcmin., Comment: 30 pages, 23 figures

We demonstrate that architectures which traditionally are considered to be ill-suited for a task can be trained using inductive biases from another architecture. Networks are considered untrainable when they overfit, underfit, or converge to poor results even when tuning their hyperparameters. For example, plain fully connected networks overfit on object recognition while deep convolutional networks without residual connections underfit. The traditional answer is to change the architecture to impose some inductive bias, although what that bias is remains unknown. We introduce guidance, where a guide network guides a target network using a neural distance function. The target is optimized to perform well and to match its internal representations, layer-by-layer, to those of the guide; the guide is unchanged. If the guide is trained, this transfers over part of the architectural prior and knowledge of the guide to the target. If the guide is untrained, this transfers over only part of the architectural prior of the guide. In this manner, we can investigate what kinds of priors different architectures place on untrainable networks such as fully connected networks. We demonstrate that this method overcomes the immediate overfitting of fully connected networks on vision tasks, makes plain CNNs competitive to ResNets, closes much of the gap between plain vanilla RNNs and Transformers, and can even help Transformers learn tasks which RNNs can perform more easily. We also discover evidence that better initializations of fully connected networks likely exist to avoid overfitting. Our method provides a mathematical tool to investigate priors and architectures, and in the long term, may demystify the dark art of architecture creation, even perhaps turning architectures into a continuous optimizable parameter of the network., Comment: Under Review; 24 pages, 9 figures; Project page and code is at https://untrainable-networks.github.io/

These notes are based on lectures given at the XIX Modave School on Mathematical Physics and present an introduction to Exceptional Field Theory. We cover the standard Kaluza-Klein reductions on tori, with applications to supergravity. We review the supergravity action of type IIA/IIB and eleven-dimensional supergravities. We motivate the appearance of the hidden symmetry groups $\mathrm{E}_{d(d)}$ through the lens of string dualities. We explore the construction and properties of $\mathrm{E}_{7(7)}$-ExFT and review other $\mathrm{E}_{d(d)}$-ExFT for $3\leq d\leq 8$, as well as double field theories. These notes conclude with some applications of ExFT to consistent truncations., Comment: 89 pages + references, 6 figures. Lecture notes from XIX Modave Summer School in Mathematical Physics, 2023

Low-metallicity environments are subject to inefficient cooling. They also have low dust-to-gas ratios and therefore less efficient photoelectric (PE) heating than in solar-neighbourhood conditions, where PE heating is one of the most important heating processes in the warm neutral interstellar medium (ISM). We perform magneto-hydrodynamic simulations of stratified ISM patches with a gas metallicity of 0.02 Z$_\odot$ as part of the SILCC project. The simulations include non-equilibrium chemistry, heating, and cooling of the low-temperature ISM as well as anisotropic cosmic ray (CR) transport, and stellar tracks. We include stellar feedback in the form of far-UV and ionising (FUV and EUV) radiation, massive star winds, supernovae, and CR injection. From the local CR energy density, we compute a CR heating rate that is variable in space and time. In this way, we can compare the relative impact of PE and CR heating on the metal-poor ISM and find that CR heating can dominate over PE heating. Models with a uniform CR ionisation rate suppress or severely delay star formation, since they provide a larger amount of energy to the ISM due to CR heating. Models with a variable CR ionisation rate form stars predominantly in pristine regions with low PE heating and CR ionisation rates where the metal-poor gas is able to cool efficiently. Because of the low metallicity, the amount of formed stars in all runs is not enough to trigger outflows of gas from the mid-plane., Comment: submitted to MNRAS

The high electron temperature in galaxy clusters ($>1\,$keV or $>10^7\,$K) leads to corrections at the level of a few percent in their thermal Sunyaev-Zeldovich effect signatures. Both the size and frequency dependence of these corrections, which are known as relativistic temperature corrections, depend upon the temperature of the objects. In this work we exploit this effect to measure the average temperature of a stack of Compton-$y$ selected clusters. Specifically, we apply the "spectroscopic method" and search for the temperature that best fits the clusters' signal measured at frequencies from 30 to 545 GHz by the Atacama Cosmology Telescope and Planck satellite. We measure the average temperature of clusters detected in the ACT maps to be $8.5\pm 2.4\,$keV, with an additional systematic error of comparable amplitude dominated by passband uncertainty. Upcoming surveys, such as the Simons Observatory and CMB-S4, have the potential to dramatically improve upon these measurements and thereby enable precision studies of cluster temperatures with millimeter observations. The key challenge for future observations will be mitigating instrumental systematic effects, which already limit this analysis., Comment: 21 pages with 17 figures

metasnf is an R package that enables users to apply meta clustering, a method for efficiently searching a broad space of cluster solutions by clustering the solutions themselves, to clustering workflows based on similarity network fusion (SNF). SNF is a multi-modal data integration algorithm commonly used for biomedical subtype discovery. The package also contains functions to assist with cluster visualization, characterization, and validation. This package can help researchers identify SNF-derived cluster solutions that are guided by context-specific utility over context-agnostic measures of quality., Comment: 72 pages, 22 figures, submitted to Journal of Statistical Software

For an odd prime $p$, we determine the $p$-primary component of the Farrell cohomology of the pure mapping class groups of a non orientable surface of genus $p$ with $k\geqslant 1$ marked points. To do this, we classify conjugacy classes of subgroups of order $p$ of the pure mapping class group of a non orientable surface of any genus with marked points. This is obtained by extending the notion of topological equivalence for surface kernel epimorphisms of non Euclidean crystallographic groups, adapting it to the setting of surfaces with marked points., Comment: 26 pages, 2 figures

Aberration correction is an important aspect of modern high-resolution scanning transmission electron microscopy. Most methods of aligning aberration correctors require specialized sample regions and are unsuitable for fine-tuning aberrations without interrupting on-going experiments. Here, we present an automated method of correcting first- and second-order aberrations called BEACON which uses Bayesian optimization of the normalized image variance to efficiently determine the optimal corrector settings. We demonstrate its use on gold nanoparticles and a hafnium dioxide thin film showing its versatility in nano- and atomic-scale experiments. BEACON can correct all first- and second-order aberrations simultaneously to achieve an initial alignment and first- and second-order aberrations independently for fine alignment. Ptychographic reconstructions are used to demonstrate an improvement in probe shape and a reduction in the target aberration.

Let $W$ be a finite group generated by reflections of a lattice $M$. If a lattice polytope $P \subset M \otimes_{\mathbb Z}\mathbb R$ is preserved by $W$, then we show that the quotient of the projective toric variety $X_P$ by $W$ is isomorphic to the toric variety $X_{P \cap D}$, where $D$ is a fundamental domain for the action of $W$. This answers a question of Horiguchi-Masuda-Shareshian-Song, and recovers results of Blume, of the second author, and of Gui-Hu-Liu., Comment: comments welcome!

We study the convex-concave bilinear saddle-point problem $\min_x \max_y f(x) + y^\top Ax - g(y)$, where both, only one, or none of the functions $f$ and $g$ are strongly convex, and suitable rank conditions on the matrix $A$ hold. The solution of this problem is at the core of many machine learning tasks. By employing tools from operator theory, we systematically prove the contractivity (in turn, the linear convergence) of several first-order primal-dual algorithms, including the Chambolle-Pock method. Our approach results in concise and elegant proofs, and it yields new convergence guarantees and tighter bounds compared to known results.

We study the co-evolution of black holes (BHs) and their host galaxies in the ASTRID and Illustris-TNG300 cosmological simulations and the Dark Sage Semi-Analytic Model (SAM), focusing on the evolution of the BH mass - stellar mass ($M_{\rm BH}-M_*$) relation. Due to differences in the adopted sub-grid modeling of BH seeding, dynamics, and feedback, the models differ in their predicted redshift evolution of the $M_{\rm BH}-M_*$ relation. We find that it is the interplay between the star formation rate (SFR) and the black hole accretion rate (BHAR) which drives the evolution of the mean relation. We define a quantity $\mathcal{R}$, the ratio between the specific BHAR and SFR (i.e. $\mathcal{R} \equiv\ $sBHAR/sSFR), and demonstrate that it is $\mathcal{R}$ that governs the evolution of individual sources in the $M_{\rm BH}-M_*$ plane. The efficiency of BH growth versus stellar mass growth in the sSFR-sBHAR plane reflects the partitioning of gas between fueling star formation versus BH accretion. This partitioning depends on the implementation of BH dynamics and the nature of how AGN feedback quenches galaxies. In the cosmological simulations (ASTRID and Illustris-TNG300), the BHAR and SFR are intrinsically linked, resulting in a tight $M_{\rm BH}-M_*$ correlation, while the Dark Sage SAM produces a significantly larger scatter. We discuss these results in the context of recently discovered over-massive BHs and massive quenched galaxies at high redshift by the James Webb Space Telescope., Comment: 17 pages, 8 figures. Submitted to ApJ. Comments welcome

Quantum states exhibiting single-particle entanglement (SPE) can encode and process quantum information more robustly than their multi-particle analogs. Understanding the vulnerability and resilience of SPE to disorder is therefore crucial. This letter investigates phase, coin, and position disorder via discrete-time quantum walks on odd and even cyclic graphs to study their effect on SPE. The reduction in SPE is insignificant for low levels of phase or coin disorder, showing the resilience of SPE to minor perturbations. However, SPE is seen to be more vulnerable to position disorder. We analytically prove that maximally entangled single-particle states (MESPS) at time step $t=1$ are impervious to phase disorder regardless of the choice of the initial state. Further, MESPS at timestep $t=1$ is also wholly immune to coin disorder for phase-symmetric initial states. Position disorder breaks odd-even parity and distorts the physical time cone of the quantum walker, unlike phase or coin disorder. SPE saturates towards a fixed value for position disorder, irrespective of the disorder strength at large timestep $t$. Furthermore, SPE can be enhanced with moderate to significant phase or coin disorder strengths at specific time steps. Interestingly, disorder can revive single-particle entanglement from absolute zero in some instances, too. These results are crucial in understanding single-particle entanglement evolution and dynamics in a lab setting., Comment: 17 pages, 14 figures

In network settings, interference between units makes causal inference more challenging as outcomes may depend on the treatments received by others in the network. Typical estimands in network settings focus on treatment effects aggregated across individuals in the population. We propose a framework for estimating node-wise counterfactual means, allowing for more granular insights into the impact of network structure on treatment effect heterogeneity. We develop a doubly robust and non-parametric estimation procedure, KECENI (Kernel Estimation of Causal Effect under Network Interference), which offers consistency and asymptotic normality under network dependence. The utility of this method is demonstrated through an application to microfinance data, revealing the impact of network characteristics on treatment effects.

Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the next query point through binary accept/reject recommendations (labels). Experts' labels are often costly, requiring efficient use of their efforts, and can at the same time be unreliable, requiring careful adjustment of the degree to which any expert is trusted. We introduce the first principled approach that provides two key guarantees. (1) Handover guarantee: similar to a no-regret property, we establish a sublinear bound on the cumulative number of experts' binary labels. Initially, multiple labels per query are needed, but the number of expert labels required asymptotically converges to zero, saving both expert effort and computation time. (2) No-harm guarantee with data-driven trust level adjustment: our adaptive trust level ensures that the convergence rate will not be worse than the one without using advice, even if the advice from experts is adversarial. Unlike existing methods that employ a user-defined function that hand-tunes the trust level adjustment, our approach enables data-driven adjustments. Real-world applications empirically demonstrate that our method not only outperforms existing baselines, but also maintains robustness despite varying labelling accuracy, in tasks of battery design with human experts., Comment: Accepted to NeurIPS 2024 as a spotlight

The fraction of dwarf galaxies hosting central, intermediate-mass black holes (IMBHs) at low redshifts is an important observational probe of black hole seeding at high redshift. Detections of nuclear accretion signatures in dwarf galaxies provides strong evidence for the presence of these IMBHs. We develop a Bayesian model to infer the black hole occupation fraction assuming a broken power law Eddington ratio distribution function. Our approach accounts for non-detections, incompleteness, and contamination from star-forming-related emission. We apply this model to galaxies with X-ray data from the Chandra Source Catalog at distances $<50$ Mpc, radio data from the VLA Sky Survey at $< 50$ Mpc, and optical variability data from the Palomar Transient Factory at $z<0.055$. We find a black hole occupation fraction of at least $90$ percent at stellar masses of $M_{\star}=10^8~M_{\odot}$ and at least $39$ percent at $M_{\star} = 10^7~M_{\odot}$ (95\% confidence intervals). We show the resulting black hole mass function. These constraints on the IMBH population have implications for the Laser Interferometer Space Antenna (LISA) mission and for cosmological models of black hole seeding and growth. We also constrain the extremely low luminosity end ($L_{\rm{bol}}\lesssim10^{40}$ erg s$^{-1}$) of the AGN luminosity functions at $z=0$. Our AGN luminosity functions are broadly consistent with an extrapolation of the shallow slope of the AGN luminosity functions from previous work., Comment: accepted for publication in ApJ

We consider 3-Majority, a probabilistic consensus dynamics on a complete graph with $n$ vertices, each vertex starting with one of $k$ initial opinions. At each discrete time step, a vertex $u$ is chosen uniformly at random. The selected vertex $u$ chooses three neighbors $v_1,v_2,v_3$ uniformly at random with replacement and takes the majority opinion held by the three, where ties are broken in favor of the opinion of $v_3$. The main quantity of interest is the consensus time, the number of steps required for all vertices to hold the same opinion. This asynchronous version turns out to be considerably harder to analyze than the synchronous version and so far results have only been obtained for $k=2$. Even in the synchronous version the results for large $k$ are far from tight. In this paper we prove that the consensus time is $\tilde{\Theta}( \min(nk,n^{1.5}) )$ for all $k$. These are the first bounds for all $k$ that are tight up to a polylogarithmic factor., Comment: Symposium on Discrete Algorithms (SODA25)

The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long range ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-$\mathbf{k}$ magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single and multi-$\mathbf{k}$ variants., Comment: accepted in (IUCr) Acta Crystallographica Section B, 8 Figures, 7 Tables

Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate-scale quantum (NISQ) devices due to limited qubit resources and noise. In this paper, we propose an efficient framework for simulating open quantum systems on NISQ hardware by leveraging a time-perturbative Kraus operator representation of the system's dynamics. Our approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. We demonstrate the efficiency of our method by simulating quantum channels, such as the continuous-time Pauli channel and damped harmonic oscillators, on NISQ trapped-ion hardware, including IonQ Harmony and Quantinuum H1-1. Additionally, we introduce hardware-agnostic error mitigation techniques, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. Our results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus-based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term., Comment: 18 pages, 12 figures

Based on the analysis of a large number of high-fidelity nonlinear gyrokinetic simulations, we propose a novel strategy to improve confinement in tokamak plasmas by combining up-down asymmetric flux surface shaping with the Low Momentum Diffusivity (LMD) regime. We show that the intrinsic momentum flux driven by up-down asymmetry creates strong flow shear in the LMD regime that can significantly reduce energy transport, increasing the critical gradient by up to $25\%$. In contrast to traditional methods for generating flow shear, such as neutral beam injection, this approach requires no external momentum source and is expected to scale well to large fusion devices. The experimental applicability of this strategy in spherical tokamaks is addressed via simulations by considering actual equilibria from MAST and a preliminary equilibrium from SMART., Comment: 7 pages, 5 figures

The lattice of flats $\mathcal L_M$ of a matroid $M$ is combinatorially well-behaved and, when $M$ is realizable, admits a geometric model in the form of a "matroid Schubert variety". In contrast, the lattice of flats of a polymatroid exhibits many combinatorial pathologies and admits no similar geometric model. We address this situation by defining the lattice $\mathcal L_P$ of "combinatorial flats" of a polymatroid $P$. Combinatorially, $\mathcal L_P$ exhibits good behavior analogous to that of $\mathcal L_M$: it is graded, determines $P$ when $P$ is simple, and is top-heavy. When $P$ is realizable over a field of characteristic 0, we show that $\mathcal L_P$ is modelled by a "polymatroid Schubert variety". Our work generalizes a number of results of Ardila-Boocher and Huh-Wang on matroid Schubert varieties; however, the geometry of polymatroid Schubert varieties is noticeably more complicated than that of matroid Schubert varieties. Many natural questions remain open., Comment: 24 pages, 3 figures, comments welcome!

The Horn inequalities characterise the possible spectra of triples of $n$-by-$n$ Hermitian matrices $A+B=C$. We study integral inequalities that arise as limits of Horn inequalities as $n \to \infty$. These inequalities are parametrised by the points of an infinite-dimensional convex body, the asymptotic Horn system $\mathscr{H}$, which can be regarded as a topological closure of the countable set of Horn inequalities for all finite $n$. We prove three main results. The first shows that arbitrary points of $\mathscr{H}$ can be well approximated by specific sets of finite-dimensional Horn inequalities. The second is a quantitative result on the redundancy of the Horn inequalities in an infinite-dimensional setting. Concretely, the Horn inequalities for finite $n$ are indexed by certain sets $T^n_r$ with $1 \le r \le n-1$; we show that if $(n_k)_{k \ge 1}$ and $(r_k)_{k \ge 1}$ are any sequences such that $(r_k / n_k)_{k \ge 1}$ is a dense subset of $(0,1)$, then the Horn inequalities indexed by the sets $T^{n_k}_{r_k}$ are sufficient to imply all of the others. Our third main result shows that $\mathscr{H}$ has a remarkable self-characterisation property. Namely, membership in $\mathscr{H}$ is determined by the very inequalities corresponding to the points of $\mathscr{H}$ itself. To illuminate this phenomenon, we sketch a general theory of sets that characterise themselves in the sense that they parametrise their own membership criteria, and we consider the question of what further information would be needed in order for this self-characterisation property to determine the Horn inequalities uniquely., Comment: 35 pages, 2 figures. This version: strengthened Theorem 2.3, added several remarks and corollaries

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time., Comment: Corresponding author: S. Doeleman