Search

Galaxy sizes are a key parameter to distinguishing between different galaxy types and morphologies, reflecting their formation and assembly histories. Several methods define galaxy boundaries, often relying on light concentration or isophotal densities. However, these approaches were often constrained by observational limitations and did not necessarily provide a clear physical boundary for galaxy outskirts. With modern deep imaging surveys, a new physically motivated definition has emerged using the radial position of the star formation threshold as the galaxy size, approximated by the stellar mass density contour at 1 Msun pc^-2 (R_1). We test this definition using three state-of-the-art hydrodynamical simulation suites, analyzing stellar surface density profiles across a wide range of stellar masses and redshifts. We measure the galaxy sizes according to this new definition and compare them with the most traditional size metric, the stellar half-mass radius. Our analysis demonstrates that the R_1-M_star relation exhibits consistent behaviour across both low and high-stellar mass galaxies, with remarkably low scatter. This relation is independent of redshift and holds across the three different cosmological hydrodynamical simulation suites, highlighting its robustness to variations in galaxy formation models. Furthermore, we explore the connection between a galaxy's total mass within R1 and its stellar mass, finding very little scatter in this relation. This suggests that R1 could serve as a reliable observational tracer for the galaxy's dynamical mass. The size-stellar mass relation proposed provides a reliable and physically motivated method for defining the outskirts of galaxies. This method remains consistent not only at z=0 but also throughout the evolutionary history of galaxies, offering a robust and meaningful framework for galaxy evolution studies., Comment: 11 pages, 8 figures, 1 table and 3 appendices

Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR are reported.

In the first part of this paper I will describe my work together with Lars and in the second part I will give a look at some of Lars's oldest papers., Comment: 11 pages, to appear in the memorial volume for Lars Brink, added more details in the derivation of Weinberg infrared singularities from superstring theory

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions., Comment: Collection of summaries of twelve topical panel discussions and individual thoughts of speakers and panelists, Nordita Scientific Program "Quantum Gravity: from gravitational EFTs to UV complete approaches". 63 pages + references, no figures - V2: typos fixed, references and one contribution added

Due to poor observational constraints on the low-mass end of the subhalo mass function, the detection of dark matter (DM) subhalos on sub-galactic scales would provide valuable information about the nature of DM. Stellar wakes, induced by passing DM subhalos, encode information about the mass of the inducing perturber and thus serve as an indirect probe for the DM substructure within the Milky Way (MW). Our aim is to assess the viability and performance of deep learning searches for stellar wakes in the Galactic stellar halo caused by DM subhalos of varying mass. We simulate massive objects (subhalos) moving through a homogeneous medium of DM and star particles, with phase-space parameters tailored to replicate the conditions of the Galaxy at a specific distance from the Galactic center. The simulation data is used to train deep neural networks with the purpose of inferring both the presence and mass of the moving perturber, and assess subhalo detectability in varying conditions of the Galactic stellar and DM halos. We find that our binary classifier is able to infer the presence of subhalos, showing non-trivial performance down to a subhalo mass of $5 \times 10^7 \rm \, M_\odot$. We also find that our binary classifier is generalisable to datasets describing subhalo orbits at different Galactocentric distances. In a multiple-hypothesis case, we are able to discern between samples containing subhalos of different masses. Out of the phase-space observables available to us, we conclude that overdensity and velocity divergence are the most important features for subhalo detection performance.

Cosmological hydrodynamical simulations provide valuable insights on galaxy evolution when coupled with observational data. Comparisons with real galaxies are typically performed via scaling relations of model fitting. Here we follow an alternative approach based on the spectral variance in a model-independent way. We build upon the work presented in Sharbaf et al. (2023) that studied the covariance of high quality SDSS continuum-subtracted spectra in a relatively narrow range of velocity dispersion (100-150 km/s). Here the same analysis is applied to synthetic data from the EAGLE and Illustris TNG100 simulations, to assess the ability of these runs to mimic real galaxies. The real and simulated spectra are consistent regarding spectral variance, although with subtle differences that can inform the implementation of subgrid physics. Spectral fitting done a posteriori on stacks segregated with respect to latent space reveals that the first principal component (PC1) is predominantly influenced by the stellar age distribution, with an underlying age-metallicity degeneracy. Good agreement is found regarding star formation prescriptions but there is disagreement with AGN feedback, that also affects the subset of quiescent galaxies. We show a substantial difference in the implementation of the AGN subgrid, regarding central black hole seeding, that could lead to the mismatch. Differences are manifest between these two simulations in the star formation histories stacked with respect to latent space. We emphasise that this methodology only relies on the spectral variance to assess whether simulations provide a true representation of galaxy formation., Comment: Submitted to MNRAS. 27 pages including supplementary material. Comments welcome

We study algebraic shifting of uniform hypergraphs and finite simplicial complexes in the exterior algebra with respect to matrices which are not necessarily generic. Several questions raised by Kalai (2002) are addressed. For instance, it turns out that the combinatorial shifting of Erd\H{o}s$\unicode{x2013}$Ko$\unicode{x2013}$Rado (1961) arises as a special case. Moreover, we identify a sufficient condition for partial shifting to preserve the Betti numbers of a simplicial complex; examples show that this condition is sharp.

Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency limit, retaining an exact dependence on the kinematics of the massive objects. This allows us to study independently the ultrarelativistic or massless limit, where we find agreement with the literature, and the small-deflection or post-Minkowskian (PM) limit, where we provide explicit results up to $\mathcal{O}(G^5)$. These confirm that the high-velocity limit of a given PM order is smoothly connected to the corresponding massless result whenever the latter is analytic in the Newton constant $G$. We also provide explicit expressions for the waveforms to order $\omega^{-1}$, $\log\omega$, $\omega(\log\omega)^2$ in the soft limit, $\omega\to0$, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type $\omega^{n-1}(\log\omega)^{n}$ with $n\ge 3$., Comment: 42 pages + references. V2: Presentation expanded and improved. We include several new results based on the resummed waveform that captures all leading logarithms for a background $2\to2$ hard process. V3: Matches the published version

We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain. Its core feature involves the (general Legendre transform of the) cumulant generating function of the Whittle likelihood score, as obtained using an approximated distribution of the periodogram ordinates. We present a testing algorithm that significantly expands the applicability of the state-of-the-art saddlepoint test, while maintaining the numerical accuracy of the saddlepoint approximation. Additionally, we demonstrate connections between our findings and three other prevalent frequency domain approaches: the bootstrap, empirical likelihood, and exponential tilting. Numerical examples using both simulated and real data illustrate the advantages and accuracy of our methodology.

We introduce a classical version of the loop corrected soft graviton theorem and we use it to compute the universal part of the one-loop (2PM) waveform up to sub-subleading order in the energy $\omega$ of the emitted graviton for spinless black-hole scattering. In particular, we compute the action of the soft operators on the classically resummed four-point amplitude, that can be written in terms of the exponential of the eikonal phase (and is therefore non-perturbative in the Newton's constant $G_N$) and then we perform the usual PM expansion in powers of $G_N$ . We find perfect agreement with the existing 2PM literature at the orders $\omega^{-1}$, $\log\omega$ and $\omega\log^2\omega$, which are universal. Furthermore, we use this method to compute the universal part of the $\omega\log\omega$ contribution to the 2PM waveform. Even if in the present analysis we limit ourselves to compute the soft 2PM waveform, our general formulae can be used to extract all universal PM orders of the terms connected with the infrared divergences, once the impulse at the corresponding precision is known. Our approach, based on the resummed eikonal amplitude, gives a unified picture of the various computations of the classical soft graviton behaviour that are present in the literature since the seminal paper by Weinberg in 1965., Comment: 41 pages, 1 figure. Minor typos have been corrected with respect to the v1 and there is a more careful comparison with existing literature

We characterise the intra-cluster light (ICL) in ensembles of full-physics cluster simulations from The Three Hundred project, a suite of 324 hydrodynamical resimulations of cluster-sized halos. We identify the ICL as those stellar particles bound to the potential of the cluster itself, but not to any of its substructures, and separate the brightest cluster galaxy (BCG) by means of a fixed 50 kpc aperture. We find the total BCG+ICL mass to be in agreement with state-of-the-art observations of galaxy clusters. The ICL mass fraction of our clusters is between 30 and 50 per cent of the total stellar mass within $R_{500}$, while the BCG represents around 10 percent. We further find no trend of the ICL fraction with cluster halo mass, at least not in the range $[0.2,3]\cdot10^{15}h^{-1}M_\odot$ considered here. For the dynamical state, characterised both by theoretical estimators and by the recent merging history of the cluster, there is a clear correlation, such that more relaxed clusters and those that have undergone fewer recent mergers have a higher ICL fraction. Finally, we investigate the possibility of using the ICL to explore the dark matter (DM) component of galaxy clusters. We compute the volumetric density profile for the DM and ICL components and show that, up to $R_{500}$, the ratio between the two can be described by a power law. Working with the velocity dispersion profiles instead, we show that the ratio can be fit by a straight line. Providing the parameters of these fits, we show how the ICL can be used to infer DM properties., Comment: 18 pages, 14 figures. Accepted for publication in Astronomy & Astrophysics

Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call it General Spatio-Temporal Factor Model (GSTFM). First, we provide the probabilistic and mathematical underpinning needed for the representation of a random field as the sum of two components: the common component (driven by a small number $q$ of latent factors) and the idiosyncratic component (mildly cross-correlated). We show that the two components are identified as $n\to\infty$. Second, we propose an estimator of the common component and derive its statistical guarantees (consistency and rate of convergence) as $\min(n, S, T )\to\infty$. Third, we propose an information criterion to determine the number of factors. Estimation makes use of Fourier analysis in the frequency domain and thus we fully exploit the information on the spatio-temporal covariance structure of the whole panel. Synthetic data examples illustrate the applicability of GSTFM and its advantages over the extant generalized dynamic factor model that ignores the spatial correlations.

We describe a generic JSON based file format which is suitable for computations in computer algebra. This is implemented in the computer algebra system OSCAR, but we also indicate how it can be used in a different context.

We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each node is real-valued and varies in time as each new edge, encoding an outcome like a win or loss, raises or lowers the node's estimated strength or prestige, as is often observed in real scenarios including sequences of games, tournaments, or interactions in animal hierarchies. Our method works by solving a linear system of equations and requires only one parameter to be tuned. As a result, the corresponding algorithm is scalable and efficient. We test our method by evaluating its ability to predict interactions (edges' existence) and their outcomes (edges' directions) in a variety of applications, including both synthetic and real data. Our analysis shows that in many cases our method's performance is better than existing methods for predicting dynamic rankings and interaction outcomes., Comment: 17 pages, 9 figures

Motivated by conceptual problems in quantum theories of gravity, the gravitational eikonal approach, inspired by its electromagnetic predecessor, has been successfully applied to the transplanckian energy collisions of elementary particles and strings since the late eighties, and to string-brane collisions in the past decade. After the direct detection of gravitational waves from black-hole mergers, most of the attention has shifted towards adapting these methods to the physics of black-hole encounters. For such systems, the eikonal exponentiation provides an amplitude-based approach to calculate classical gravitational observables, thus complementing more traditional analytic methods such as the Post-Newtonian expansion, the worldline formalism, or the Effective-One-Body approach. In this review we summarize the main ideas and techniques behind the gravitational eikonal formalism. We discuss how it can be applied in various different physical setups involving particles, strings and branes and then we mainly concentrate on the most recent developments, focusing on massive scalars minimally coupled to gravity, for which we aim at being as self-contained and comprehensive as possible., Comment: 215 pages, 19 figures. v2: published version

Recently, the scientific community has questioned the statistical reproducibility of many empirical results, especially in the field of machine learning. To contribute to the resolution of this reproducibility crisis, we propose a theoretically sound methodology for comparing the performance of a set of algorithms. We exemplify our methodology in Deep Reinforcement Learning (Deep RL). The performance of one execution of a Deep RL algorithm is a random variable. Therefore, several independent executions are needed to evaluate its performance. When comparing algorithms with random performance, a major question concerns the number of executions to perform to ensure that the result of the comparison is theoretically sound. Researchers in Deep RL often use less than 5 independent executions to compare algorithms: we claim that this is not enough in general. Moreover, when comparing more than 2 algorithms at once, we have to use a multiple tests procedure to preserve low error guarantees. We introduce AdaStop, a new statistical test based on multiple group sequential tests. When used to compare algorithms, AdaStop adapts the number of executions to stop as early as possible while ensuring that enough information has been collected to distinguish algorithms that have different score distributions. We prove theoretically that AdaStop has a low probability of making a (family-wise) error. We illustrate the effectiveness of AdaStop in various use-cases, including toy examples and Deep RL algorithms on challenging Mujoco environments. AdaStop is the first statistical test fitted to this sort of comparisons: it is both a significant contribution to statistics, and an important contribution to computational studies performed in reinforcement learning and in other domains.

Kernel methods provide a powerful framework for non parametric learning. They are based on kernel functions and allow learning in a rich functional space while applying linear statistical learning tools, such as Ridge Regression or Support Vector Machines. However, standard kernel methods suffer from a quadratic time and memory complexity in the number of data points and thus have limited applications in large-scale learning. In this paper, we propose Snacks, a new large-scale solver for Kernel Support Vector Machines. Specifically, Snacks relies on a Nystr\"om approximation of the kernel matrix and an accelerated variant of the stochastic subgradient method. We demonstrate formally through a detailed empirical evaluation, that it competes with other SVM solvers on a variety of benchmark datasets., Comment: 6 pages

This paper is written for a Festschrift in honour of Professor Marc Hallin and it proposes some developments on quantile regression. We connect our investigation to Marc's scientific production and we present some theoretical and methodological advances for quantiles estimation in non standard settings. We split our contributions in two parts. The first part is about conditional quantiles estimation for nonstationary time series. The second part is about conditional quantiles estimation for the analysis of multivariate independent data in the presence of possibly large dimensional covariates. Monte Carlo studies illustrate numerically the performance of our methods and compare them to some extant techniques.

A substantial fraction of the cosmic baryons is expected to hide in the form of diffuse warm-hot intergalactic medium (WHIM), the majority of which resides in the filaments of the Cosmic Web and has proven very difficult to detect due to its low density. Close to galaxy clusters, the filament gas is affected by the cluster's gravitational potential and attains substantial infall velocities, eventually undergoing a termination shock which may boost its X-ray signal. We aim to identify the optimal locations of the enhanced X-ray emission and absorption arising from cluster-filament interactions, as well as improve our understanding of the various physical processes affecting the WHIM as it approaches the cluster. We applied the DisPerSE filament finder to the galaxy distribution in the surroundings of a Coma-like ($M_{200} \sim 10^{15.4}~{\rm M}_{\odot}$) simulated C-EAGLE galaxy cluster. We characterised the thermodynamic properties of the gas in such filaments as well as their dependence on distance from the cluster, and provided a physical interpretation for the results. The identified filaments account for $\sim 50$% of the hot WHIM ($T > 10^{5.5}$ K) in the cluster vicinity. The filament gas is in approximate free-fall all the way down to $\sim 2 \ r_{200}$ from the cluster, at which stage it begins to slow down due to the increasing pressure of the ambient gas. The deceleration is accompanied by the conversion of gas bulk kinetic energy into heat and the increase of density and temperature from the general Cosmic Web level of $\rho \sim 10\rho_{\rm av}$ and $T = 10^5-10^6$ K towards $\rho \sim 100\rho_{\rm av}$ and $T = 10^7-10^8$ K near the cluster boundary. We conclude that the detection of the cosmic filaments of galaxies around clusters may provide a practical observational avenue for locating the densest and hottest phase of the missing baryons., Comment: 20 pages, 16 figures, accepted for publication in A&A

Endogeneity, i.e. the dependence of noise and covariates, is a common phenomenon in real data due to omitted variables, strategic behaviours, measurement errors etc. In contrast, the existing analyses of stochastic online linear regression with unbounded noise and linear bandits depend heavily on exogeneity, i.e. the independence of noise and covariates. Motivated by this gap, we study the over- and just-identified Instrumental Variable (IV) regression, specifically Two-Stage Least Squares, for stochastic online learning, and propose to use an online variant of Two-Stage Least Squares, namely O2SLS. We show that O2SLS achieves $\mathcal O(d_{x}d_{z}\log^2 T)$ identification and $\widetilde{\mathcal O}(\gamma \sqrt{d_{z} T})$ oracle regret after $T$ interactions, where $d_{x}$ and $d_{z}$ are the dimensions of covariates and IVs, and $\gamma$ is the bias due to endogeneity. For $\gamma=0$, i.e. under exogeneity, O2SLS exhibits $\mathcal O(d_{x}^2 \log^2 T)$ oracle regret, which is of the same order as that of the stochastic online ridge. Then, we leverage O2SLS as an oracle to design OFUL-IV, a stochastic linear bandit algorithm to tackle endogeneity. OFUL-IV yields $\widetilde{\mathcal O}(\sqrt{d_{x}d_{z}T})$ regret that matches the regret lower bound under exogeneity. For different datasets with endogeneity, we experimentally show efficiencies of O2SLS and OFUL-IV.

Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it is sensitive to outliers and it may not be even defined when the underlying model has infinite moments. To cope with these problems, first we consider a robust version of the primal transportation problem and show that it defines the {robust Wasserstein distance}, $W^{(\lambda)}$, depending on a tuning parameter $\lambda > 0$. Second, we illustrate the link between $W_1$ and $W^{(\lambda)}$ and study its key measure theoretic aspects. Third, we derive some concentration inequalities for $W^{(\lambda)}$. Fourth, we use $W^{(\lambda)}$ to define minimum distance estimators, we provide their statistical guarantees and we illustrate how to apply the derived concentration inequalities for a data driven selection of $\lambda$. Fifth, we provide the {dual} form of the robust optimal transportation problem and we apply it to machine learning problems (generative adversarial networks and domain adaptation). Numerical exercises provide evidence of the benefits yielded by our novel methods.