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Testing possible variations in fundamental constants of nature is a crucial endeavor in observational cosmology. This paper investigates potential cosmological variations in the fine structure constant ($\alpha$) through a non-parametric approach, using galaxy cluster observations as the primary cosmological probe. We employ two methodologies based on galaxy cluster gas mass fraction measurements derived from X-ray and Sunyaev-Zeldovich observations, along with luminosity distances from type Ia supernovae. We also explore how different values of the Hubble constant ($H_0$) impact the variation of $\alpha$ across cosmic history. When using the Planck satellite's $H_0$ observations, a constant $\alpha$ is ruled out at approximately the 3$\sigma$ confidence level for $z \lesssim 0.5$. Conversely, employing local estimates of $H_0$ restores agreement with a constant $\alpha$., Comment: 10 pages, 3 figures, I table. Accepted by the The European Physical Journal C

Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first derive novel metrics that balance accuracy in factual and counterfactual questions, capturing a more complete view of the reasoning abilities of language models than traditional factual-only based metrics. Second, we propose several fine-tuning approaches that aim to elicit better reasoning mechanisms, in the sense of the proposed metrics. Finally, we evaluate the performance of the fine-tuned language models in a variety of realistic scenarios. In particular, we investigate to what extent our fine-tuning approaches systemically achieve better generalization with respect to the base models in several problems that require, among others, inductive and deductive reasoning capabilities.

Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.

Recent advances in AI have been significantly driven by the capabilities of large language models (LLMs) to solve complex problems in ways that resemble human thinking. However, there is an ongoing debate about the extent to which LLMs are capable of actual reasoning. Central to this debate are two key probabilistic concepts that are essential for connecting causes to their effects: the probability of necessity (PN) and the probability of sufficiency (PS). This paper introduces a framework that is both theoretical and practical, aimed at assessing how effectively LLMs are able to replicate real-world reasoning mechanisms using these probabilistic measures. By viewing LLMs as abstract machines that process information through a natural language interface, we examine the conditions under which it is possible to compute suitable approximations of PN and PS. Our research marks an important step towards gaining a deeper understanding of when LLMs are capable of reasoning, as illustrated by a series of math examples.

In this work, we obtain Hubble constant ($H_0$) estimates by using two galaxy cluster gas mass fraction measurement samples, Type Ia supernovae luminosity distances, and the validity of the cosmic distance duality relation. Notably, the angular diameter distance (ADD) to each galaxy cluster in the samples is determined by combining its gas mass fraction measurement with galaxy clustering observations, more precisely, the $\Omega_b/\Omega_m$ ratio. Such a combination results in a $H_0$ estimate that is independent of a specific cosmological framework. In one of the samples, the gas fraction measurements were calculated in spherical shells at radii near $r_{\rm 2500}$ (44 data points), while in the other (103 data points) the measurements were calculated within $ r_{\rm 500}$. We find $H_0=72.7^{+6.3}_{-5.6}$ km/s/Mpc at 68\% CL for the joint analysis of these data sets. We also investigate the impact on the $H_0$ determination by exploring the precision and number of gas mass fraction data by performing a data Monte Carlo simulation. Our simulations show that future measurements could achieve a precision of up to 5\% for $H_0$., Comment: 9 pages, 5 figures. H0 estimate updated with joint analysis of the two gas mass fraction samples

It is well-known that Einstein's equations constrain only the total energy-momentum tensor of the cosmic substratum, without specifying the characteristics of its individual constituents. Consequently, cosmological models featuring distinct decompositions within the dark sector, while sharing identical values for the sum of dark components' energy-momentum tensor, remain indistinguishable when assessed through observables based on distance measurements. Notably, it has been already demonstrated that cosmological models with dynamical descriptions of dark energy, characterized by a time-dependent equation of state (EoS), can always be mapped into a model featuring a decaying vacuum ($w=-1$) coupled with dark matter. We explore the possibility of breaking this degeneracy by using measurements of the gas mass fraction observed in massive and relaxed galaxy clusters. This data is particularly interesting for this purpose because it isolates the matter contribution, possibly allowing the degeneracy breaking. We study the particular case of the $w$CDM model with its interactive counterpart. We compare the results obtained from both descriptions with a non-parametric analysis obtained through Gaussian Process. Even though the degeneracy may be broken from the theoretical point of view, we find that current gas mass fraction data seems to be insufficient for a final conclusion about which approach is favored, even when combined with SNIa, BAO and CMB., Comment: 14+2 pages, 4+4 figures, 3+1 tables. Comments are welcome

Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs -- even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches., Comment: To appear in the 3rd Conference on Causal Learning and Reasoning (CLeaR 2024)

Large language models (LLMs) are powerful AI tools that can generate and comprehend natural language text and other complex information. However, the field lacks a mathematical framework to systematically describe, compare and improve LLMs. We propose Hex a framework that clarifies key terms and concepts in LLM research, such as hallucinations, alignment, self-verification and chain-of-thought reasoning. The Hex framework offers a precise and consistent way to characterize LLMs, identify their strengths and weaknesses, and integrate new findings. Using Hex, we differentiate chain-of-thought reasoning from chain-of-thought prompting and establish the conditions under which they are equivalent. This distinction clarifies the basic assumptions behind chain-of-thought prompting and its implications for methods that use it, such as self-verification and prompt programming. Our goal is to provide a formal framework for LLMs that can help both researchers and practitioners explore new possibilities for generative AI. We do not claim to have a definitive solution, but rather a tool for opening up new research avenues. We argue that our formal definitions and results are crucial for advancing the discussion on how to build generative AI systems that are safe, reliable, fair and robust, especially in domains like healthcare and software engineering., Comment: 4 figures, 18 pages

The rapid digitization of real-world data offers an unprecedented opportunity for optimizing healthcare delivery and accelerating biomedical discovery. In practice, however, such data is most abundantly available in unstructured forms, such as clinical notes in electronic medical records (EMRs), and it is generally plagued by confounders. In this paper, we present TRIALSCOPE, a unifying framework for distilling real-world evidence from population-level observational data. TRIALSCOPE leverages biomedical language models to structure clinical text at scale, employs advanced probabilistic modeling for denoising and imputation, and incorporates state-of-the-art causal inference techniques to combat common confounders. Using clinical trial specification as generic representation, TRIALSCOPE provides a turn-key solution to generate and reason with clinical hypotheses using observational data. In extensive experiments and analyses on a large-scale real-world dataset with over one million cancer patients from a large US healthcare network, we show that TRIALSCOPE can produce high-quality structuring of real-world data and generates comparable results to marquee cancer trials. In addition to facilitating in-silicon clinical trial design and optimization, TRIALSCOPE may be used to empower synthetic controls, pragmatic trials, post-market surveillance, as well as support fine-grained patient-like-me reasoning in precision diagnosis and treatment., Comment: 6 Figures, 22 Pages, 3 Tables

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes the class of morphisms of schemes for which the conclusion of the aforementioned Theorem holds. The key is giving a weaker definition of locally finitely presented morphisms.

Recent advances in immunomics have shown that T-cell receptor (TCR) signatures can accurately predict active or recent infection by leveraging the high specificity of TCR binding to disease antigens. However, the extreme diversity of the adaptive immune repertoire presents challenges in reliably identifying disease-specific TCRs. Population genetics and sequencing depth can also have strong systematic effects on repertoires, which requires careful consideration when developing diagnostic models. We present an Adaptive Immune Repertoire-Invariant Variational Autoencoder (AIRIVA), a generative model that learns a low-dimensional, interpretable, and compositional representation of TCR repertoires to disentangle such systematic effects in repertoires. We apply AIRIVA to two infectious disease case-studies: COVID-19 (natural infection and vaccination) and the Herpes Simplex Virus (HSV-1 and HSV-2), and empirically show that we can disentangle the individual disease signals. We further demonstrate AIRIVA's capability to: learn from unlabelled samples; generate in-silico TCR repertoires by intervening on the latent factors; and identify disease-associated TCRs validated using TCR annotations from external assay data.

Radio-loud quasars at high redshift (z > 4) are rare objects in the Universe and rarely observed with Very Long Baseline Interferometry (VLBI). But some of them have flux density sufficiently high for monitoring of their apparent position. The instability of the astrometric positions could be linked to the astrophysical process in the jetted active galactic nuclei in the early Universe. Regular observations of the high-redshift quasars are used for estimating their apparent proper motion over several years. We have undertaken regular VLBI observations of several high-redshift quasars at 2.3 GHz (S band) and 8.4 GHz (X band) with a network of five radio telescopes: 40-m Yebes (Spain), 25-m Sheshan (China), and three 32-m telescopes of the Quasar VLBI Network (Russia) -- Svetloe, Zelenchukskaya, and Badary. Additional facilities joined this network occasionally. The sources have also been observed in three sessions with the European VLBI Network (EVN) in 2018--2019 and one Long Baseline Array (LBA) experiment in 2018. In addition, several experiments conducted with the Very Long Baseline Array (VLBA) in 2017--2018were used to improve the time sampling and the statistics. Based on these 37 astrometric VLBI experiments between 2017 and 2021, we estimated the apparent proper motions of four quasars: 0901+697, 1428+422, 1508+572, and 2101+600.

Probing the solar corona is crucial to study the coronal heating and solar wind acceleration. However, the transient and inhomogeneous solar wind flows carry large-amplitude inherent Alfven waves and turbulence, which make detection more difficult. We report the oscillation and propagation of the solar wind at 2.6 solar radii (Rs) by observation of China Tianwen and ESA Mars Express with radio telescopes. The observations were carried out on Oct.9 2021, when one coronal mass ejection (CME) passed across the ray paths of the telescope beams. We obtain the frequency fluctuations (FF) of the spacecraft signals from each individual telescope. Firstly, we visually identify the drift of the frequency spikes at a high spatial resolution of thousands of kilometers along the projected baselines. They are used as traces to estimate the solar wind velocity. Then we perform the cross-correlation analysis on the time series of FF from different telescopes. The velocity variations of solar wind structure along radial and tangential directions during the CME passage are obtained. The oscillation of tangential velocity confirms the detection of streamer wave. Moreover, at the tail of the CME, we detect the propagation of an accelerating fast field-aligned density structure indicating the presence of magnetohydrodynamic waves. This study confirm that the ground station-pairs are able to form particular spatial projection baselines with high resolution and sensitivity to study the detailed propagation of the nascent dynamic solar wind structure., Comment: 13 pages, 9 figures

We prove that given a planar embedding of a graph in the sphere the expansion of the graph structure by predicates encoding separation of vertices by simple cycles of the graph is dp-minimal.

Astrometric positions of radio-emitting active galactic nuclei (AGNs) can be determined with sub-milliarcsec accuracy using very long baseline interferometry (VLBI). The usually small apparent proper motion of distant extragalactic targets allow us to realize the fundamental celestial reference frame with VLBI observations. However, long-term astrometric monitoring may reveal extreme changes in some AGN positions. Using new VLBI observations in 2018-2021, we show here that four extragalactic radio sources (3C48, CTA21, 1144+352, 1328+254) have a dramatic shift in their positions by 20-130 milliarcsec over two decades. For all four sources, the apparent positional shift is caused by their radio structure change., Comment: Accepted for publication in MNRAS

We prove that no subgroup of the group of boundary-fixing homeomorphisms of a compact surface whose action on the interior of the surface is sufficiently transitive can be Roelcke precompact with the topology inherited from the compact-open topology.

Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode invariance of the integrand under a set of bijective transformations in the input domain, in particular some unitary transformations, such as rotations, axis-flips, or point symmetries. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.