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Star formation in galaxies is regulated by dynamical and thermal processes. The photoelectric effect on small dust grains usually dominates the heating of the star-forming neutral atomic gas reservoir in metal-rich galaxies, while the lower dust-to-gas mass ratio and the higher luminosity of X-ray sources in metal-poor galaxies suggest that other heating mechanisms may be at play. We calculate the relative contributions of the photoelectric effect, photoionization by UV and X-ray photons, and ionization by cosmic rays to the total heating in a sample of 37 nearby galaxies reaching down to 3% the Milky Way metallicity. We use the statistical code MULTIGRIS together with a grid of Cloudy models propagating radiation from stellar clusters and X-ray sources to the ionized and neutral gas, each galaxy being described as a statistical distribution of many 1D components. Infrared cooling lines from the interstellar medium (ISM) are used as constraints to evaluate the most likely distributions and parameters. We show that the photoelectric effect heating dominates in high-metallicity galaxies (>1/18 the Milky Way value) while cosmic rays and especially photoionization from X-rays become predominant in low-metallicity galaxies. Our models predict reasonably well the X-ray source fluxes in the 0.3-8 keV band using indirect ISM tracers, illustrating that the adopted strategy makes it possible to recover the global intrinsic radiation field properties when X-ray observations are unavailable, for instance in early universe galaxies. Finally, we show that the photoelectric effect heating efficiency on PAHs may be recovered through the [CII]+[OI] / PAH observational proxy only if the other heating mechanisms are accounted for (abridged)., Comment: Submitted to A&A

We study the problem of matching markets with ties, where one side of the market does not necessarily have strict preferences over members at its other side. For example, workers do not always have strict preferences over jobs, students can give the same ranking for different schools and more. In particular, assume w.l.o.g. that workers' preferences are determined by their utility from being matched to each job, which might admit ties. Notably, in contrast to classical two-sided markets with strict preferences, there is no longer a single stable matching that simultaneously maximizes the utility for all workers. We aim to guarantee each worker the largest possible share from the utility in her best possible stable matching. We call the ratio between the worker's best possible stable utility and its assigned utility the \emph{Optimal Stable Share} (OSS)-ratio. We first prove that distributions over stable matchings cannot guarantee an OSS-ratio that is sublinear in the number of workers. Instead, randomizing over possibly non-stable matchings, we show how to achieve a tight logarithmic OSS-ratio. Then, we analyze the case where the real utility is not necessarily known and can only be approximated. In particular, we provide an algorithm that guarantees a similar fraction of the utility compared to the best possible utility. Finally, we move to a bandit setting, where we select a matching at each round and only observe the utilities for matches we perform. We show how to utilize our results for approximate utilities to gracefully interpolate between problems without ties and problems with statistical ties (small suboptimality gaps).

We present a spatially-resolved (~3 pc pix$^{-1}$) analysis of the distribution, kinematics, and excitation of warm H2 gas in the nuclear starburst region of M83. Our JWST/MIRI IFU spectroscopy reveals a clumpy reservoir of warm H2 (> 200 K) with a mass of ~2.3 x 10$^{5}$ Msun in the area covered by all four MRS channels. We additionally use the [Ne II] 12.8 ${\mu}$m and [Ne III] 15.5 ${\mu}$m lines as tracers of the star formation rate, ionizing radiation hardness, and kinematics of the ionized ISM, finding tantalizing connections to the H2 properties and to the ages of the underlying stellar populations. Finally, qualitative comparisons to the trove of public, high-spatial-resolution multiwavelength data available on M83 shows that our MRS spectroscopy potentially traces all stages of the process of creating massive star clusters, from the embedded proto-cluster phase through the dispersion of ISM from stellar feedback., Comment: 21 pages, 11+1 figures; submitted to ApJ

In the strategic multi-armed bandit setting, when arms possess perfect information about the player's behavior, they can establish an equilibrium where: 1. they retain almost all of their value, 2. they leave the player with a substantial (linear) regret. This study illustrates that, even if complete information is not publicly available to all arms but is shared among them, it is possible to achieve a similar equilibrium. The primary challenge lies in designing a communication protocol that incentivizes the arms to communicate truthfully.

We explore a novel variant of the classical prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that the competitive ratio between the expected optimal performance of the online decision maker compared to that of a prophet, who uses the average of the top $\ell$ items, must be greater than $\ell/c_{\ell}$, with $c_{\ell}$ the solution to an integral equation. We prove that this lower bound is larger than $1-1/(\exp(\ell)-1)$. This implies that the bound converges exponentially fast to $1$ as $\ell$ grows. In particular, the bound for $\ell=2$ is $2/c_{2} \approx 0.966$ which is much closer to $1$ than the classical bound of $0.745$ for $\ell=1$. Additionally, the proposed algorithm can be extended to a more general scenario, where the decision maker is permitted to select $k$ items. This subsumes the $k$ multi-unit i.i.d. prophet problem and provides the current best asymptotic guarantees, as well as enables broader understanding in the more general framework. Finally, we prove a nearly tight competitive ratio when only static threshold policies are allowed.

We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the limiting tree. For this purpose, we introduce and study unimodular matchings on weighted unimodular random trees as well as a notion of optimality for these objects. In this context, we prove that, in law, there is a unique optimal unimodular matching for a given unimodular tree. We then prove that this law is the local limit of the sequence of matchings of maximal weight. Along the way, we also show that this law is characterised by an equation derived from a message passing algorithm., Comment: 54 pages, 19 figures

We present a pioneering spatially-resolved, multi-phase gas abundance study on the blue compact dwarf galaxy NGC~5253, targeting 10 star-forming (SF) clusters inside six FUV HST/COS pointings with co-spatial optical VLT/MUSE observations throughout the galaxy. The SF regions span a wide range of ages (1--15 Myr) and are distributed at different radii (50 -- 230 pc). We performed robust absorption-line profile fitting on the COS spectra, covering 1065--1430 \AA\ in the FUV, allowing an accurate computation of neutral-gas abundances for 13 different ions sampling 8 elements. These values were then compared with the ionized-gas abundances, measured using the direct method on MUSE integrated spectra inside analog COS apertures. Our multi-phase, spatially resolved comparisons find abundances which are lower in the neutral gas than the ionized gas by 0.22 dex, 0.80 dex and 0.58 dex for log(O/H), log(N/H) and log(N/O), respectively. We modeled the chemical abundance distributions and evaluated correlations as a function of radius and age. It was found that while N, O and N/O abundances decrease as a function of age in the ionized gas, they increase with age in the neutral gas. No strong correlations for N, O or N/O were observed as a function of radius. The N/O and N/H offsets between the phases were found to decrease with age, providing evidence that chemical enrichment happens differentially, first in the ionized-gas phase around 2--5 Myrs (due to N-rich Wolf-Rayet stars) and then mixing out into the cold neutral gas on longer timescales of 10--15 Myr., Comment: 40 pages, 14 Figures. Revised version submitted to ApJ

How should an expert send forecasts to maximize her utility subject to passing a calibration test? We consider a dynamic game where an expert sends probabilistic forecasts to a decision maker. The decision maker uses a calibration test based on past outcomes to verify the expert's forecasts. We characterize the optimal forecasting strategy by reducing the dynamic game to a static persuasion problem. A distribution of forecasts is implementable by a calibrated strategy if and only if it is a mean-preserving contraction of the distribution of conditionals (honest forecasts). We characterize the value of information by comparing what an informed and uninformed expert can attain. Moreover, we consider a decision maker who uses regret minimization, instead of the calibration test, to take actions. We show that the expert can achieve the same payoff against a regret minimizer as under the calibration test, and in some instances, she can achieve strictly more., Comment: The conference version of this work has been accepted to the Twenty-Fifth ACM Conference on Economics and Computation (EC'24)

BlueMUSE is a blue-optimised, medium spectral resolution, panoramic integral field spectrograph under development for the Very Large Telescope (VLT). With an optimised transmission down to 350 nm, spectral resolution of R$\sim$3500 on average across the wavelength range, and a large FoV (1 arcmin$^2$), BlueMUSE will open up a new range of galactic and extragalactic science cases facilitated by its specific capabilities. The BlueMUSE consortium includes 9 institutes located in 7 countries and is led by the Centre de Recherche Astrophysique de Lyon (CRAL). The BlueMUSE project development is currently in Phase A, with an expected first light at the VLT in 2031. We introduce here the Top Level Requirements (TLRs) derived from the main science cases, and then present an overview of the BlueMUSE system and its subsystems fulfilling these TLRs. We specifically emphasize the tradeoffs that are made and the key distinctions compared to the MUSE instrument, upon which the system architecture is built., Comment: 20 pages, 10 figures, proceedings of the SPIE astronomical telescopes and instrumentation conference, Yokohama, 16-21 June

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The goal of the seller is to design a pricing strategy that collects as much revenue as possible. We focus on two different valuation models. The first assumes that valuations linearly depend on the context and are further distorted by noise. Under minor regularity assumptions, our algorithm achieves an optimal regret bound of $\tilde{\mathcal{O}}(T^{2/3})$, improving the existing results. The second model removes the linearity assumption, requiring only that the expected buyer valuation is $\beta$-H\"older in the context. For this model, our algorithm obtains a regret $\tilde{\mathcal{O}}(T^{d+2\beta/d+3\beta})$, where $d$ is the dimension of the context space.

Prophet inequalities are fundamental optimal stopping problems, where a decision-maker observes sequentially items with values sampled independently from known distributions, and must decide at each new observation to either stop and gain the current value or reject it irrevocably and move to the next step. This model is often too pessimistic and does not adequately represent real-world online selection processes. Potentially, rejected items can be revisited and a fraction of their value can be recovered. To analyze this problem, we consider general decay functions $D_1,D_2,\ldots$, quantifying the value to be recovered from a rejected item, depending on how far it has been observed in the past. We analyze how lookback improves, or not, the competitive ratio in prophet inequalities in different order models. We show that, under mild monotonicity assumptions on the decay functions, the problem can be reduced to the case where all the decay functions are equal to the same function $x \mapsto \gamma x$, where $\gamma = \inf_{x>0} \inf_{j \geq 1} D_j(x)/x$. Consequently, we focus on this setting and refine the analyses of the competitive ratios, with upper and lower bounds expressed as increasing functions of $\gamma$., Comment: Accepted as a conference paper at NeurIPS 2024

Bilateral trade models the problem of facilitating trades between a seller and a buyer having private valuations for the item being sold. In the online version of the problem, the learner faces a new seller and buyer at each time step, and has to post a price for each of the two parties without any knowledge of their valuations. We consider a scenario where, at each time step, before posting prices the learner observes a context vector containing information about the features of the item for sale. The valuations of both the seller and the buyer follow an unknown linear function of the context. In this setting, the learner could leverage previous transactions in an attempt to estimate private valuations. We characterize the regret regimes of different settings, taking as a baseline the best context-dependent prices in hindsight. First, in the setting in which the learner has two-bit feedback and strong budget balance constraints, we propose an algorithm with $O(\log T)$ regret. Then, we study the same set-up with noisy valuations, providing a tight $\widetilde O(T^{\frac23})$ regret upper bound. Finally, we show that loosening budget balance constraints allows the learner to operate under more restrictive feedback. Specifically, we show how to address the one-bit, global budget balance setting through a reduction from the two-bit, strong budget balance setup. This established a fundamental trade-off between the quality of the feedback and the strictness of the budget constraints.

Inspired by sequential budgeted allocation problems, we study the online matching problem with budget refills. In this context, we consider an online bipartite graph G=(U,V,E), where the nodes in $V$ are discovered sequentially and nodes in $U$ are known beforehand. Each $u\in U$ is endowed with a budget $b_{u,t}\in \mathbb{N}$ that dynamically evolves over time. Unlike the canonical setting, in many applications, the budget can be refilled from time to time, which leads to a much richer dynamic that we consider here. Intuitively, adding extra budgets in $U$ seems to ease the matching task, and our results support this intuition. In fact, for the stochastic framework considered where we studied the matching size built by Greedy algorithm on an Erd\H{o}s-R\'eyni random graph, we showed that the matching size generated by Greedy converges with high probability to a solution of an explicit system of ODE. Moreover, under specific conditions, the competitive ratio (performance measure of the algorithm) can even tend to 1. For the adversarial part, where the graph considered is deterministic and the algorithm used is Balance, the $b$-matching bound holds when the refills are scarce. However, when refills are regular, our results suggest a potential improvement in algorithm performance. In both cases, Balance algorithm manages to reach the performance of the upper bound on the adversarial graphs considered.

The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be reduced to specific instances, due to cost or data limitations. Our investigation focuses on scenarios where predictions for only $B$ job sizes out of $n$ are available to the algorithm. We first establish near-optimal lower bounds and algorithms in the case of perfect predictions. Subsequently, we present a learning-augmented algorithm satisfying the robustness, consistency, and smoothness criteria, and revealing a novel tradeoff between consistency and smoothness inherent in the scenario with a restricted number of predictions., Comment: Accepted as a conference paper at ICML 2024

In reinforcement learning (RL), agents sequentially interact with changing environments while aiming to maximize the obtained rewards. Usually, rewards are observed only after acting, and so the goal is to maximize the expected cumulative reward. Yet, in many practical settings, reward information is observed in advance -- prices are observed before performing transactions; nearby traffic information is partially known; and goals are oftentimes given to agents prior to the interaction. In this work, we aim to quantifiably analyze the value of such future reward information through the lens of competitive analysis. In particular, we measure the ratio between the value of standard RL agents and that of agents with partial future-reward lookahead. We characterize the worst-case reward distribution and derive exact ratios for the worst-case reward expectations. Surprisingly, the resulting ratios relate to known quantities in offline RL and reward-free exploration. We further provide tight bounds for the ratio given the worst-case dynamics. Our results cover the full spectrum between observing the immediate rewards before acting to observing all the rewards before the interaction starts., Comment: Accepted to NeurIPS 2024 as spotlight

We investigate notions of group fairness in bipartite matching markets involving agents and jobs, where agents are grouped based on sensitive attributes. Employing a geometric approach, we characterize how many agents can be matched in each group, showing that the set of feasible matchings forms a (discrete) polymatroid. We show how we can define weakly-fair matchings geometrically, for which poly-matroid properties imply that they are maximal. Next, we focus on strong fairness notions (inspired by group-fairness metrics in machine learning), where each group gets their exact same fraction of their entitlement, and we explore the Price of Fairness (PoF), i.e., the loss in optimality when imposing such fairness constraints. Importantly, we advocate for the notion of opportunity fairness, where a group entitlement is the maximum number of agents that can be matched without the presence of other competing groups. We show that the opportunity PoF is bounded independently of the number of agents and jobs, but may be linear in the number of groups. Finally, we provide improved bounds with additional structural properties, or with stochastic graphs.

The combination of lightly supervised pre-training and online fine-tuning has played a key role in recent AI developments. These new learning pipelines call for new theoretical frameworks. In this paper, we formalize core aspects of weakly supervised and active learning with a simple problem: the estimation of the mode of a distribution using partial feedback. We show how entropy coding allows for optimal information acquisition from partial feedback, develop coarse sufficient statistics for mode identification, and adapt bandit algorithms to our new setting. Finally, we combine those contributions into a statistically and computationally efficient solution to our problem.

Randomizing the mapping of addresses to cache entries has proven to be an effective technique for hardening caches against contention-based attacks like Prime+Prome. While attacks and defenses are still evolving, it is clear that randomized caches significantly increase the security against such attacks. However, one aspect that is missing from most analyses of randomized cache architectures is the choice of the replacement policy. Often, only the random- and LRU replacement policies are investigated. However, LRU is not applicable to randomized caches due to its immense hardware overhead, while the random replacement policy is not ideal from a performance and security perspective. In this paper, we explore replacement policies for randomized caches. We develop two new replacement policies and evaluate a total of five replacement policies regarding their security against Prime+Prune+Probe attackers. Moreover, we analyze the effect of the replacement policy on the system's performance and quantify the introduced hardware overhead. We implement randomized caches with configurable replacement policies in software and hardware using a custom cache simulator, gem5, and the CV32E40P RISC-V core. Among others, we show that the construction of eviction sets with our new policy, VARP-64, requires over 25-times more cache accesses than with the random replacement policy while also enhancing overall performance.

Context. Multi-wavelength studies of galaxies and galactic nuclei allow us to build a relatively more complete picture of the interstellar medium (ISM), especially in the dusty regions of starburst galaxies. An understanding of the physical processes in nearby galaxies can assist in the study of more distant sources at higher redshifts, which cannot be resolved. Aims. We aimed to use observations presented in the first part of this series of papers to model the physical conditions of the ISM in the nuclear region of NGC 253, in order to obtain primary parameters such as gas densities and metallicities. From the created model we further calculated secondary parameters such as gas masses of the different phases, and estimated the fraction of [C II] 158 um from the different phases, which allowed us to probe the nuclear star-formation rate. Methods. To compare theory with our observations we used MULTIGRIS, a probabilistic tool that determines probabilities for certain ISM parameters from a grid of Cloudy models together with a set of spectroscopic lines. Results. We find that the hypothetical active galactic nucleus within NGC 253 has only a minor impact compared to the starburst on the heating of the ISM as probed by the observed lines. We characterise the ISM and obtain parameters such as a solar metallicity, a mean density of ~230cm-3 , an ionisation parameter of log U = -3, and an age of the nuclear cluster of ~2 Myr. Furthermore, we estimate the masses of the ionised (3.8 x 10^6 M_sol ), neutral atomic (9.1 x 10^6 M_sol ), and molecular (2.0 x 10^8 M_sol ) gas phases as well as the dust mass (1.8 x 10^6 M_sol ) in the nucleus of NGC 253., Comment: Accepted for publication in A&A; 15 pages, 10 Figures, 6 Tables