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We consider an invariant gradient flow for the invariant length functional for co-compact curves in inversive geometry, and prove that solutions exist for all time and converge to loxodromic curves, provided the initial curve is admissible (so that the invariant length element is well defined)., Comment: 18 pages, 3 figures

We introduce a model to describe the interplay between prescribed burning and bushfires based on a system of ordinary differential equations. We show that the system possesses a unique steady-state, whose stability depends on the policy governing prescribed burning. Specifically, a Reactive Policy in which prescribed burning activities are increased in response to bushfire events risks to produce instability and requires an additional feedback control, while a Proactive Policy in which moderate prescribed burning replaces natural bushfires may be more effective to maintain a balanced state. A high regeneration factor is also helpful to ensuring the stability of the equilibrium state. The results presented here should not be regarded as a definitive solution to the issue of prescribed burning, as numerous specific factors must be considered in any comprehensive policymaking approach. Nonetheless, the stability analysis developed in this paper suggests that policies driven primarily by reactive responses to bushfire events may be emotionally charged and prone to instability. These reactive policies would benefit from incorporating feedback control mechanisms. In contrast, strategies based on proactive prescribed burning in moderate quantities, focused on prevention rather than reaction, are likely to be more effective in maintaining long-term ecological stability.

Social media empower distributed content creation by algorithmically harnessing "the social fabric" (explicit and implicit signals of association) to serve this content. While this overcomes the bottlenecks and biases of traditional gatekeepers, many believe it has unsustainably eroded the very social fabric it depends on by maximizing engagement for advertising revenue. This paper participates in open and ongoing considerations to translate social and political values and conventions, specifically social cohesion, into platform design. We propose an alternative platform model that the social fabric an explicit output as well as input. Citizens are members of communities defined by explicit affiliation or clusters of shared attitudes. Both have internal divisions, as citizens are members of intersecting communities, which are themselves internally diverse. Each is understood to value content that bridge (viz. achieve consensus across) and balance (viz. represent fairly) this internal diversity, consistent with the principles of the Hutchins Commission (1947). Content is labeled with social provenance, indicating for which community or citizen it is bridging or balancing. Subscription payments allow citizens and communities to increase the algorithmic weight on the content they value in the content serving algorithm. Advertisers may, with consent of citizen or community counterparties, target them in exchange for payment or increase in that party's algorithmic weight. Underserved and emerging communities and citizens are optimally subsidized/supported to develop into paying participants. Content creators and communities that curate content are rewarded for their contributions with algorithmic weight and/or revenue. We discuss applications to productivity (e.g. LinkedIn), political (e.g. X), and cultural (e.g. TikTok) platforms., Comment: 60 pages

Any well-behaved generative model over a variable $\mathbf{x}$ can be expressed as a deterministic transformation of an exogenous ('outsourced') Gaussian noise variable $\mathbf{z}$: $\mathbf{x}=f_\theta(\mathbf{z})$. In such a model (e.g., a VAE, GAN, or continuous-time flow-based model), sampling of the target variable $\mathbf{x} \sim p_\theta(\mathbf{x})$ is straightforward, but sampling from a posterior distribution of the form $p(\mathbf{x}\mid\mathbf{y}) \propto p_\theta(\mathbf{x})r(\mathbf{x},\mathbf{y})$, where $r$ is a constraint function depending on an auxiliary variable $\mathbf{y}$, is generally intractable. We propose to amortize the cost of sampling from such posterior distributions with diffusion models that sample a distribution in the noise space ($\mathbf{z}$). These diffusion samplers are trained by reinforcement learning algorithms to enforce that the transformed samples $f_\theta(\mathbf{z})$ are distributed according to the posterior in the data space ($\mathbf{x}$). For many models and constraints of interest, the posterior in the noise space is smoother than the posterior in the data space, making it more amenable to such amortized inference. Our method enables conditional sampling under unconditional GAN, (H)VAE, and flow-based priors, comparing favorably both with current amortized and non-amortized inference methods. We demonstrate the proposed outsourced diffusion sampling in several experiments with large pretrained prior models: conditional image generation, reinforcement learning with human feedback, and protein structure generation.

The Milky Way is a complex ecosystem, for which we can obtain detailed observations probing the physical mechanisms determining the interstellar medium. For a detailed comparison with observations, and to provide theories for missing observables, we need to model the Milky Way as closely as possible. However, details of the Galactic structure are not fully defined by observations, raising the need for more generalized models. With the Rhea simulations we present a set of Milky Way like simulations, containing detailed physics of the interstellar medium, as well as star formation and stellar feedback. We conduct two simulations that differ in the gravitational potential: one fitted to several structural details derived from observations, the other just reproducing the most basic quantities. We find little difference in the overall morphology except for the bar region, which funnels gas towards the Galactic inner region and therefore prevents quenching in the center. Despite differences with galacto-centric radius, the global star formation rate is almost identical in both setups. A spiral arm potential does not influence properties of groups of formed stars. A bar potential, however, lowers size and formation time of those groups. We therefore conclude for a spiral arm potential to have little influence on star formation in the Galaxy, except for producing long-lived spiral structures instead of transient ones. A Galactic bar potential has noticeable influence on star formation mainly within the innermost 2.5kpc., Comment: 26 pages, 19 figures, submitted to A&A. See additional Rhea companion paper Kjellgren et al. today on astro-ph

Background: When developing a clinical prediction model using time-to-event data, previous research focuses on the sample size to minimise overfitting and precisely estimate the overall risk. However, instability of individual-level risk estimates may still be large. Methods: We propose a decomposition of Fisher's information matrix to examine and calculate the sample size required for developing a model that aims for precise and fair risk estimates. We propose a six-step process which can be used before data collection or when an existing dataset is available. Steps (1) to (5) require researchers to specify the overall risk in the target population at a key time-point of interest; an assumed pragmatic 'core model' in the form of an exponential regression model; the (anticipated) joint distribution of core predictors included in that model; and the distribution of any censoring. Results: We derive closed-form solutions that decompose the variance of an individual's estimated event rate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to calculate and examine uncertainty distributions around individual risk estimates and misclassification probabilities for specified sample sizes. We provide an illustrative example in breast cancer and emphasise the importance of clinical context, including risk thresholds for decision making, and examine fairness concerns for pre- and post-menopausal women. Lastly, in two empirical evaluations, we provide reassurance that uncertainty interval widths based on our approach are close to using more flexible models. Conclusions: Our approach allows users to identify the (target) sample size required to develop a prediction model for time-to-event outcomes, via the pmstabilityss module. It aims to facilitate models with improved trust, reliability and fairness in individual-level predictions., Comment: arXiv admin note: text overlap with arXiv:2407.09293

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,700 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 27 pages, 6 figures

Many applications, including medical diagnostics, sonar and navigation rely on the detection of acoustic waves. Photonic hydrophones demonstrate comparable sensitivity to piezoelectric-based hydrophones, but with significantly reduced size, weight and power requirements. In this paper we demonstrate a micron-sized free-standing silicon photonic hydrophone. We demonstrate sensitivity on the order of $\sim$mPa/$\sqrt{\textrm{Hz}}$ from 10-200 kHz, with a minimum detectable pressure of 145 $\mu$Pa/$\sqrt{\textrm{Hz}}$ at 22 kHz. We also deployed our hydrophone in a wave flume to evaluate its suitability for underwater measurement and communication. Our hydrophone matches the sensitivity of commercial hydrophones, but is many orders of magnitude smaller in volume, which could enable high spatial resolution imaging of micron-sized acoustic features (i.e., living cell vibrations). Our hydrophone could also be used in underwater communication and imaging applications., Comment: 11 pages, 5 figures

We report the discovery of BD+05$\,$4868$\,$Ab, a transiting exoplanet orbiting a bright ($V=10.16$) K-dwarf (TIC 466376085) with a period of 1.27 days. Observations from NASA's Transiting Exoplanet Survey Satellite (TESS) reveal variable transit depths and asymmetric transit profiles that are characteristic of comet-like tails formed by dusty effluents emanating from a disintegrating planet. Unique to BD+05$\,$4868$\,$Ab is the presence of prominent dust tails in both the trailing and leading directions that contribute to the extinction of starlight from the host star. By fitting the observed transit profile and analytically modeling the drift of dust grains within both dust tails, we infer large grain sizes ($\sim1-10\,\mu$m) and a mass loss rate of $10\,M_{\rm \oplus}\,$Gyr$^{-1}$, suggestive of a lunar-mass object with a disintegration timescale of only several Myr. The host star is probably older than the Sun and is accompanied by an M-dwarf companion at a projected physical separation of 130 AU. The brightness of the host star, combined with the planet's relatively deep transits ($0.8-2.0\%$), presents BD+05$\,$4868$\,$Ab as a prime target for compositional studies of rocky exoplanets and investigations into the nature of catastrophically evaporating planets., Comment: 24 pages, 17 figures. Submitted to AAS Journals

Evolutionary sparse learning (ESL) uses a supervised machine learning approach, Least Absolute Shrinkage and Selection Operator (LASSO), to build models explaining the relationship between a hypothesis and the variation across genomic features (e.g., sites) in sequence alignments. ESL employs sparsity between and within the groups of genomic features (e.g., genomic loci) by using sparse-group LASSO. Although some software packages are available for performing sparse group LASSO, we found them less well-suited for processing and analyzing genome-scale data containing millions of features, such as bases. MyESL software fills the need for open-source software for conducting ESL analyses with facilities to pre-process the input hypotheses and large alignments, make LASSO flexible and computationally efficient, and post-process the output model to produce different metrics useful in functional or evolutionary genomics. MyESL can take phylogenetic trees and sequence alignments as input and transform them into numeric responses and features, respecetively. The model outputs are processed into user-friendly text and graphical files. The computational core of MyESL is written in C++, which offers model building with or without group sparsity, while the pre- and post-processing of inputs and model outputs is performed using customized functions written in Python. One of its applications in phylogenomics showcases the utility of MyESL. Our analysis of empirical genome-scale datasets shows that MyESL can build evolutionary models quickly and efficiently on a personal desktop, while other computational packages were unable due to their prohibitive requirements of computational resources and time. MyESL is available for Python environments on Linux and distributed as a standalone application for Windows and macOS. It is available from https://github.com/kumarlabgit/MyESL.

We predict the Fried physical frailty phenotype health deficits (FPFP5: slow gait, weakness, weight loss, low activity, and exhaustion) using two measures of frailty: frailty index (FI) or frailty phenotype (FP). The FP theorizes that the FPFP5 are mutually dependent through shared etiology and positive feedbacks, so that the total number of FPFP5 deficits (NFPFP5) should be highly predictive of existing deficits. Alternatively, the FI theorizes that strong mutual dependencies exist between \emph{all} age-related health deficits, so that the FI would be more predictive. We investigated predictive models of FPFP5 using FI or NFPFP5 in the Health and Retirement Study (HRS), the English Longitudinal Study of Aging (ELSA), and the National Health and Nutrition Examination Survey (NHANES). We find that the FI, chronological age, and current deficit state are all important predictors of future FPFP5 deficits. Notably, the FI consistently out-performed NFPFP5, raising questions regarding FPFP5 causal connections and how best to measure the physical component of frailty. We discuss implications for both FPFP5 forecasting, and inference when data are missing or incomplete., Comment: main text: 13 pages (including ref), 5 figures and 3 tables. supplemental: 19 pages