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Background Advancements in Large Language Models (LLMs) hold transformative potential in healthcare, however, recent work has raised concern about the tendency of these models to produce outputs that display racial or gender biases. Although training data is a likely source of such biases, exploration of disease and demographic associations in text data at scale has been limited. Methods We conducted a large-scale textual analysis using a dataset comprising diverse web sources, including Arxiv, Wikipedia, and Common Crawl. The study analyzed the context in which various diseases are discussed alongside markers of race and gender. Given that LLMs are pre-trained on similar datasets, this approach allowed us to examine the potential biases that LLMs may learn and internalize. We compared these findings with actual demographic disease prevalence as well as GPT-4 outputs in order to evaluate the extent of bias representation. Results Our findings indicate that demographic terms are disproportionately associated with specific disease concepts in online texts. gender terms are prominently associated with disease concepts, while racial terms are much less frequently associated. We find widespread disparities in the associations of specific racial and gender terms with the 18 diseases analyzed. Most prominently, we see an overall significant overrepresentation of Black race mentions in comparison to population proportions. Conclusions Our results highlight the need for critical examination and transparent reporting of biases in LLM pretraining datasets. Our study suggests the need to develop mitigation strategies to counteract the influence of biased training data in LLMs, particularly in sensitive domains such as healthcare.

Optical trapping enables precise control of individual particles of different sizes, such as atoms, molecules, or nanospheres. Optical tweezers provide free-space omnidirectional optical trapping of objects in laboratories around the world. As an alternative to standard macroscopic setups based on lenses, which are inherently bound by the diffraction limit, plasmonic and photonic nanostructures promise trapping by near-field optical effects on the extreme nanoscale. However, the practical design of lossless waveguide-coupled nanostructures capable of trapping sub-wavelength-sized particles in all spatial directions has until now proven insurmountable. In this work, we demonstrate an omnidirectional optical trap realized by inverse-designing fabrication-ready integrated dielectric nanocavities. The sub-wavelength optical trap is designed to rely solely on the gradient force and is thus particle-size agnostic. In particular, we show how a trapped particle with a radius of 15 nm experiences a force strong enough to overcome room-temperature thermal fluctuations. Furthermore, through the robust inverse design framework, we tailor manufacturable devices operating at short-wave infrared and near-infrared wavelengths. Our results open a new regime of levitated optical trapping by achieving a deep trapping potential capable of trapping single sub-wavelength particles in all directions using optical gradient forces. We anticipate potentially groundbreaking applications of the optimized optical trapping system for biomolecular analysis in aqueous environments, levitated cavity-optomechanics, and cold atom physics, constituting an important step towards realizing integrated bio-nanophotonics and mesoscopic quantum mechanical experiments.

Neuromorphic computing aims to mimic the architecture and the information processing mechanisms of the mammalian brain, appearing as the only avenue that offers significant energy savings compared to the standard digital computers. Memcapacitive devices (which can change their capacitance between different non-volatile states upon the application of electrical stimulation) can significantly reduce the energy consumption of bioinspired circuitry. In the present work, we study the multimem (memristive and memcapacitive) behavior of devices based on thin films of the topotactic redox La$_{1/2}$Sr$_{1/2}$Mn$_{1/2}$Co$_{1/2}$O$_{3-x}$ (LSMCO) perovskite modified with Sm:Ce$O_2$ (SCO), grown on Nb:SrTiO$_{3}$ with (001) and (110) out of plane orientations. Either the self assembling at the nanoscale of both LSMCO and SCO phases or the doping with Ce(Sm) of the LSMCO perovskite were observed for different fabrication conditions and out of plane orientations. The impact of these changes on the device electrical behavior was determined. The optimum devices resulted those with (110) orientation and Ce(Sm) doping the perovskite. These devices displayed a multimem behavior with robust memcapacitance and significantly lower operation voltages (especially the RESET voltage) in comparison with devices based on pristine LSMCO. In addition, they were able to endure electrical cycling (and the concomitant perovskite topotactic redox transition between oxidized and reduced phases) without suffering nanostructural or chemical changes. We link these properties to an enhanced perovskite reducibility upon Ce(Sm) doping. Our work contributes to increase the reliability of LSMCO based multimem systems and to reduce their operating voltages closer to the 1 V threshold, which are key issues for the development of nanodevices for neuromorphic or in memory computing., Comment: 22 pages, 8 figures

Probabilistic programs often trade accuracy for efficiency, and thus may, with a small probability, return an incorrect result. It is important to obtain precise bounds for the probability of these errors, but existing verification approaches have limitations that lead to error probability bounds that are excessively coarse, or only apply to first-order programs. In this paper we present Eris, a higher-order separation logic for proving error probability bounds for probabilistic programs written in an expressive higher-order language. Our key novelty is the introduction of error credits, a separation logic resource that tracks an upper bound on the probability that a program returns an erroneous result. By representing error bounds as a resource, we recover the benefits of separation logic, including compositionality, modularity, and dependency between errors and program terms, allowing for more precise specifications. Moreover, we enable novel reasoning principles such as expectation-preserving error composition, amortized error reasoning, and error induction. We illustrate the advantages of our approach by proving amortized error bounds on a range of examples, including collision probabilities in hash functions, which allow us to write more modular specifications for data structures that use them as clients. We also use our logic to prove correctness and almost-sure termination of rejection sampling algorithms. All of our results have been mechanized in the Coq proof assistant using the Iris separation logic framework and the Coquelicot real analysis library., Comment: Camera ready version with appendix

We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, $g_c$. In the competitive regime $g_c$ serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct., Comment: 20 pages, 6 figures

Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs written in languages with specific syntactic patterns for looping. In this paper, we consider almost-sure termination for higher-order probabilistic programs with general references. This combination of features allows for recursion and looping to be encoded through a variety of patterns. Therefore, rather than developing proof rules for reasoning about particular recursion patterns, we instead propose an approach based on proving refinement between a higher-order program and a simpler probabilistic model, in such a way that the refinement preserves termination behavior. By proving a refinement, almost-sure termination behavior of the program can then be established by analyzing the simpler model. We present this approach in the form of Caliper, a higher-order separation logic for proving termination-preserving refinements. Caliper uses probabilistic couplings to carry out relational reasoning between a program and a model. To handle the range of recursion patterns found in higher-order programs, Caliper uses guarded recursion, in particular the principle of L\"ob induction. A technical novelty is that Caliper does not require the use of transfinite step indexing or other technical restrictions found in prior work on guarded recursion for termination-preservation refinement. We demonstrate the flexibility of this approach by proving almost-sure termination of several examples, including first-order loop constructs, a random list generator, treaps, and a sampler for Galton-Watson trees that uses higher-order store. All the results have been mechanized in the Coq proof assistant.

Evidence suggests that different prompts lead large language models (LLMs) to generate responses with varying quality. Yet, little is known about prompts' effects on response quality in healthcare domains. In this exploratory study, we address this gap, focusing on a specific healthcare domain: dementia caregiving. We first developed an innovative prompt template with three components: (1) system prompts (SPs) featuring 4 different roles; (2) an initialization prompt; and (3) task prompts (TPs) specifying different levels of details, totaling 12 prompt combinations. Next, we selected 3 social media posts containing complicated, real-world questions about dementia caregivers' challenges in 3 areas: memory loss and confusion, aggression, and driving. We then entered these posts into GPT-4, with our 12 prompts, to generate 12 responses per post, totaling 36 responses. We compared the word count of the 36 responses to explore potential differences in response length. Two experienced dementia care clinicians on our team assessed the response quality using a rating scale with 5 quality indicators: factual, interpretation, application, synthesis, and comprehensiveness (scoring range: 0-5; higher scores indicate higher quality).

The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integrable hierarchies are then classified in terms of a decomposition of the underlying affine Lie algebra $\hat {\cal{G}} $ into graded subspaces defined by a grading operator $Q$. In this paper we shall discuss explicitly the simplest case of the affine $\hat {sl}(2)$ Kac-Moody algebra within the principal gradation given rise to the KdV and mKdV hierarchies and extend to supersymmetric models. It is known that the positive mKdV sub-hierachy is associated to some positive odd graded abelian subalgebra with elements denoted by $E^{(2n+1)}$. Each of these elements in turn, defines a time evolution equation according to time $t=t_{2n+1}$. An interesting observation is that for negative grades, the zero curvature representation allows both, even or odd sub-hierarchies. In both cases, the flows are non-local leading to integro-differential equations. Whilst positive and negative odd sub-hierarchies admit zero vacuum solutions, the negative even admits strictly non-zero vacuum solutions. Soliton solutions can be constructed by gauge transforming the zero curvature from the vacuum into a non trivial configuration (dressing method). Inspired by the dressing transformation method, we have constructed a gauge-Miura transformation mapping mKdV into KdV flows. Interesting new results concerns the negative grade sector of the mKdV hierarchy in which a double degeneracy of flows (odd and its consecutive even) of mKdV are mapped into a single odd KdV flow. These results are extended to supersymmetric hierarchies based upon the affine $\hat {sl}(2,1)$ super-algebra., Comment: 22 pages Latex

The layer stacking morphology in nanocarbons is paramount for achieving new properties and outperforming applications. Here, we demonstrate that graphene quantum dots (GQDs) retain crystallinity and a stacking structure from CVD graphene grown on Ni foam. Our results reveal that GQD subdomains comprise a few-layer graphene structure in the AB -- AB and ABC -- ABC stacking configuration. HR-TEM images along with a multiple-approach characterization (XRD, XPS, UV-vis, AFM, and ATR-IR) exhibit 3.0 to 8.0 nm crystalline GQDs with 2-6 graphene layers thick indicating a disk-shape structure. The UV-vis profiles show changes in color of the dispersion (from colorless to red) during and after the electrochemistry, suggesting a systematic electrooxidation of graphene into smaller, highly crystalline, and more complex sp2/sp3 structures. Importantly, a control experiment performed under the same conditions but with a graphitic rod exhibited large, polydisperse, and multilayer carbon structures. This work demonstrates a relatively easy electrochemical synthesis to obtain GQDs which retain the pristine and, in turn, distinctive structure of graphene grown on Ni foam., Comment: 33 pages

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to \infty$ and at least one between $P/D^K$, $N/D^L$ remains finite., Comment: 11 pages + appendix, 4 figures. Comments are welcome

Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some extent. Our method is elementary and works well for many models of random polynomials, with gaussian or non-gaussian coefficients., Comment: arXiv admin note: text overlap with arXiv:2008.04111, arXiv:1912.12051

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding., Comment: 21 pages, 18 figures, submitted to Monthly Notices of the Royal Astronomical Society

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of $\pi$ character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with anti-parallel spins coupled through a conformational dependent interaction. The 2-OS molecule is a protected derivative of the Chichibabin's diradical, featuring a non-planar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule's magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs for a new class of all-carbon spin-crossover materials., Comment: 8 pages in the main manuscript, including 4 figures, 21 pages in the supporting info, including 19 figures

There are two key paradigms for non-equilibrium dynamics: on the one hand, aging towards an equilibrium state that cannot be reached on reasonable timescales; on the other, external driving that can lead to non-equilibrium steady states. We explore how these two mechanisms interact, by studying the behaviour of trap models, which are paradigmatic descriptions of slow glassy dynamics, when driven by trajectory bias towards high or low activity. To diagnose whether the driven systems continue to age, we establish a framework for mapping the biased dynamics to a Markovian time evolution with time-dependent transition rates. We find that the original aging dynamics reacts in two qualitatively distinct ways to the driving: it can be destroyed by driving of any nonzero strength (fragile aging), whereby the dynamics either reaches an active steady state or effectively freezes; or it can persist within a finite range of driving strengths around the undriven case (robust aging). This classification into fragile and robust aging could form the basis for distinguishing different universality classes of aging dynamics., Comment: 26 pages, 9 figures

Sensitive wide-field observations of polarized thermal emission from interstellar dust grains will allow astronomers to address key outstanding questions about the life cycle of matter and energy driving the formation of stars and the evolution of galaxies. Stratospheric balloon-borne telescopes can map this polarized emission at far-infrared wavelengths near the peak of the dust thermal spectrum - wavelengths that are inaccessible from the ground. In this paper we address the sensitivity achievable by a Super Pressure Balloon (SPB) polarimetry mission, using as an example the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) Observatory. By launching from Wanaka, New Zealand, BLAST Observatory can obtain a 30-day flight with excellent sky coverage - overcoming limitations of past experiments that suffered from short flight duration and/or launch sites with poor coverage of nearby star-forming regions. This proposed polarimetry mission will map large regions of the sky at sub-arcminute resolution, with simultaneous observations at 175, 250, and 350 $\mu m$, using a total of 8274 microwave kinetic inductance detectors. Here, we describe the scientific motivation for the BLAST Observatory, the proposed implementation, and the forecasting methods used to predict its sensitivity. We also compare our forecasted experiment sensitivity with other facilities., Comment: Published in PASP