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The analysis of longitudinal data gives the chance to observe how unit behaviors change over time, but it also poses series of issues. These have been the focus of a huge literature in the context of linear and generalized linear regression moving also, in the last ten years or so, to the context of linear quantile regression for continuous responses. In this paper, we present lqmix, a novel R package that helps estimate a class of linear quantile regression models for longitudinal data, in the presence of time-constant and/or time-varying, unit-specific, random coefficients, with unspecified distribution. Model parameters are estimated in a maximum likelihood framework, via an extended EM algorithm, and parameters' standard errors are estimated via a block-bootstrap procedure. The analysis of a benchmark dataset is used to give details on the package functions., Comment: 25 pages, 2 figures

Deep learning techniques have become one of the main propellers for solving engineering problems effectively and efficiently. For instance, Predictive Maintenance methods have been used to improve predictions of when maintenance is needed on different machines and operative contexts. However, deep learning methods are not without limitations, as these models are normally trained on a fixed distribution that only reflects the current state of the problem. Due to internal or external factors, the state of the problem can change, and the performance decreases due to the lack of generalization and adaptation. Contrary to this stationary training set, real-world applications change their environments constantly, creating the need to constantly adapt the model to evolving scenarios. To aid in this endeavor, Continual Learning methods propose ways to constantly adapt prediction models and incorporate new knowledge after deployment. Despite the advantages of these techniques, there are still challenges to applying them to real-world problems. In this work, we present a brief introduction to predictive maintenance, non-stationary environments, and continual learning, together with an extensive review of the current state of applying continual learning in real-world applications and specifically in predictive maintenance. We then discuss the current challenges of both predictive maintenance and continual learning, proposing future directions at the intersection of both areas. Finally, we propose a novel way to create benchmarks that favor the application of continuous learning methods in more realistic environments, giving specific examples of predictive maintenance.

Nested regular path queries are used for querying graph databases and RDF triple stores. We propose a new algorithm for evaluating nested regular path queries on a graph from a set of start nodes in combined linear time. We show that this complexity upper bound can be reduced by making it dependent on the size of the query's top-down needed subgraph, a notion that we introduce. For many queries in practice, the top-down needed subgraph is way smaller than the whole graph. Our algorithm is based on a novel compilation schema from nested regular path queries to monadic datalog queries. Its complexity upper bound follows from known properties of top-down datalog evaluation. As an application, we show that our algorithm permits to reformulate in simple terms a variant of a very efficient automata-based algorithm proposed by Maneth and Nguyen that evaluates navigational path queries in datatrees based on indexes and jumping. Moreover, it overcomes some limitations of Maneth and Nguyen's: it is not bound to trees and applies to graphs; it is not limited to forward navigational XPath but can treat any nested regular path query and it can be implemented efficiently without any dedicated techniques, by using any efficient datalog evaluator such as LogicBlox., Comment: In Proceedings ICLP 2022, arXiv:2208.02685

We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms. Our construction recovers the known divisors of minimal moving slope on ${\mathcal A}_g$ for $g\leq 4$, and gives an explicit upper bound for the moving slope of ${\mathcal A}_5$ and a conjectural upper bound for the moving slope of ${\mathcal A}_6$.

Complex Deep Neural Networks such as Capsule Networks (CapsNets) exhibit high learning capabilities at the cost of compute-intensive operations. To enable their deployment on edge devices, we propose to leverage approximate computing for designing approximate variants of the complex operations like softmax and squash. In our experiments, we evaluate tradeoffs between area, power consumption, and critical path delay of the designs implemented with the ASIC design flow, and the accuracy of the quantized CapsNets, compared to the exact functions., Comment: To appear at the ACM/IEEE International Symposium on Low Power Electronics and Design (ISLPED), August 2022, Boston, MA, USA

The gas mass fraction in galaxy clusters is a convenient probe to use in cosmological studies, as it can help derive constraints on a collection of cosmological parameters. It is however subject to various effects from the baryonic physics inside galaxy clusters, which may bias the obtained cosmological constraints. Among different aspects of the baryonic physics, in this paper we focus on the impact of the hydrostatic equilibrium assumption. We analyse the hydrostatic mass bias $B$, constraining a possible mass and redshift evolution of this quantity and its impact on the cosmological constraints. To that end we consider cluster observations of the {\it Planck}-ESZ sample and evaluate the gas mass fraction using X-ray counterpart observations. We show a degeneracy between the redshift dependence of the bias and cosmological parameters. In particular we find a $3.8 \sigma$ evidence for a redshift dependence of the bias when assuming a {\it Planck} prior on $\Omega_m$. On the other hand, assuming a constant mass bias would lead to the extreme large value of $\Omega_m > 0.849$. We however show that our results are entirely dependent on the cluster sample we consider. In particular, the mass and redshift trends that we find for the lowest mass-redshift and highest mass-redshift clusters of our sample are not compatible. Nevertheless, in all the analyses we find a value for the amplitude of the bias that is consistent with $B \sim 0.8$, as expected from hydrodynamical simulations and local measurements, but still in tension with the low value of $B \sim 0.6$ derived from the combination of cosmic microwave background primary anisotropies with cluster number counts., Comment: 24 pages, 14 figures, 6 tables. Accepted in A&A. Baryon fraction table available at http://szcluster-db.ias.u-psud.fr and https://byopic.eu/tools_and_data

Recent results of ground-based telescopes, giving high-quality measurements of the CMB temperature power spectrum on small scales motivate the need for an accurate model of foregrounds, which dominate the primary signal at these multipoles. In a previous work, we have shown that cosmological information could be retrieved from the power spectrum of the thermal SZ effect. In this work, we introduce a physically motivated model of the Epoch of Reionisation in the cosmological analysis of CMB data, which is coherent on all scales. In particular, at high multipoles, the power spectrum of the kinetic SZ (kSZ) effect is inferred from a set of cosmological and reionisation parameters by a machine-learning algorithm. First including an asymmetric parameterisation of the reionisation history in the Planck 2018 data analysis, we retrieve a value of the optical depth consistent with previous results, but stemming from a completely different history of reionisation in which the first luminous sources light up as early as $z=15$. Considering the latest small-scale data from the SPT and letting the cosmology free to vary, we find that including the new cosmology-dependent SZ spectra helps tighten the constraints on their amplitudes by breaking their degeneracy. We report a $5\sigma$ measurement of the kSZ signal at $\ell=3000$, $\mathcal{D}_{3000}^\mathrm{kSZ} = 3.4^{+0.5}_{-0.3}\,\mu\mathrm{K}^2$ at the 68% confidence level, marginalised over cosmology, as well as an upper limit on the patchy signal from reionisation $\mathcal{D}_{3000}^\mathrm{pkSZ}<1.6~\mu\mathrm{K}^2$ (95% C.L.). Additionally, we find that the SPT data favour slightly earlier reionisation scenarios than Planck, leading to $\tau = 0.062 ^{+0.012}_{-0.015}$ and a reionisation midpoint $z_\mathrm{re} = 7.9^{+1.1}_{-1.3}$ (68% C.L.), which is in line with constraints from high-redshift quasars and galaxies., Comment: The code used to estimate the kSZ and tSZ power spectra from cosmological parameters can be found at https://szdb.osups.universite-paris-saclay.fr/. This paper is the second of a series of two (the first one is arXiv:2109.03272)

In this paper we propose a flexible nested error regression small area model with high dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area specific estimating equations method that allows appropriate pooling of a large number of areas in estimating small area specific model parameters. We propose a parametric bootstrap and jackknife method to estimate not only the mean squared errors but also other commonly used uncertainty measures such as standard errors and coefficients of variation. We conduct both modelbased and design-based simulation experiments and real-life data analysis to evaluate the proposed methodology

We provide the first combined cosmological analysis of South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the $\nu \Lambda$CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find $\alpha_{\text{SZ}} = 1.49_{-0.10}^{+0.07}$ and $(1-b)_{\text{SZ}} = 0.69_{-0.14}^{+0.07}$ respectively. The results for the mass slope show a $\sim 4 \, \sigma$ departure from the self-similar evolution, $\alpha_{\text{SZ}} \sim 1.8$. This shift is mainly driven by the matter density value preferred by SPT data, $\Omega_m = 0.30 \pm 0.03$, lower than the one obtained by Planck data alone, $\Omega_m = 0.37_{-0.06}^{+0.02}$. The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, $(1-b) \sim 0.8$, and with results required by the Planck cosmic microwave background cosmology, $(1-b) \sim 0.6$. From this analysis, we obtain a new catalog of Planck cluster masses $M_{500}$. We estimate the ratio between the published Planck $M_{\text{SZ}}$ masses and our derived masses $M_{500}$, as a "measured mass bias", $(1-b)_M$. We analyse the mass, redshift and detection noise dependence of $(1-b)_M$, finding an increasing trend towards high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass high-mass, low-z high-z regimes., Comment: 22 pages, 10 figures, the catalogs can be found at http://pole.uchicago.edu/public/data/sptplanck_cluster

We show the improvement to cosmological constraints from galaxy cluster surveys with the addition of CMB-cluster lensing data. We explore the cosmological implications of adding mass information from the 3.1$\sigma$ detection of gravitational lensing of the cosmic microwave background (CMB) by galaxy clusters to the Sunyaev-Zel'dovich (SZ) selected galaxy cluster sample from the 2500 deg$^2$ SPT-SZ survey and targeted optical and X-ray followup data. In the $\Lambda$CDM model, the combination of the cluster sample with the Planck power spectrum measurements prefers $\sigma_8 \left(\Omega_m/0.3 \right)^{0.5} = 0.831 \pm 0.020$. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether or not the 3.1$\sigma$ CMB-cluster lensing measurement is included. We then forecast the impact of CMB-cluster lensing measurements with future cluster catalogs. Adding CMB-cluster lensing measurements to the SZ cluster catalog of the on-going SPT-3G survey is expected to improve the expected constraint on the dark energy equation of state $w$ by a factor of 1.3 to $\sigma(w) = 0.19$. We find the largest improvements from CMB-cluster lensing measurements to be for $\sigma_8$, where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty on $\sigma_8$ by factors of 2.4 and 3.6 for SPT-3G and CMB-S4 respectively., Comment: Comments are welcome

The gas mass fraction in galaxy clusters is a convenient tool to use in the context of cosmological studies. Indeed this quantity allows to constrain the universal baryon fraction $\Omega_b/\Omega_m$, as well as other parameters like the matter density $\Omega_m$, the Hubble parameter $h$ or the Equation of State of Dark Energy $w$. This gas mass fraction is also sensitive to baryonic effects that need to be taken into account, and that translate into nuisance parameters. Two of them are the depletion factor $\Upsilon$, and the hydrostatic mass bias $B = (1 - b)$. The first one describes how baryons are depleted in clusters with respect to the universal baryon fraction, while the other encodes the bias coming from the fact that the mass is deduced from X-ray observations under the hypothesis of hydrostatic equilibrium. We will show preliminary results, obtained using the {\it Planck}-ESZ clusters observed by XMM-{\it Newton}, on both cosmological and cluster parameters. We will notably discuss the investigation on a possible redshift dependence of the mass bias, which is considered to be non-existent in hydrodynamic simulations based on $\Lambda$-CDM, and compare our results with other studies., Comment: To appear in the Proceedings of the International Conference entitled "mm Universe @ NIKA2", Rome (Italy), June 2021, EPJ Web of conferences

In this talk I focus on how the modelling of the mass-observable relation and the halo mass function can impact the accuracy and precision of cosmological constraints inferred from galaxy clusters. I present a new analysis of clusters detected in mm wavelengths by the Planck satellite, highlighting the need of an improved description and calibration for the mass-observable relation., Comment: To appear in the Proceedings of the International Conference entitled "mm Universe at NIKA2", Rome (Italy), June 2021, EPJ Web of conferences

Small scale CMB angular power spectrum contains not only primordial CMB information but also many contaminants coming from secondary anisotropies. Most of the latter depend on the cosmological model but are often marginalised over. We propose a new analysis of the SPT data focusing on the cosmological contribution of the thermal Sunyaev Zel'dovich (tSZ) effect. We model the tSZ angular spectrum with the halo model and train a random forest algorithm to speed up its computation. We show that using the cosmological information of the tSZ on top of the primordial CMB one contained in SPT data bring more constraints on cosmological parameters. We also combine for the first time Planck tSZ angular power spectrum with SPT ones to put further constraints. This proof of concept study shows how much a proper modelling of the foregrounds in the cosmological analyses is needed., Comment: To appear in the Proceedings of the International Conference entitled "mm Universe @ NIKA2", Rome (Italy), June 2021, EPJ Web of conferences

We constructed a new all-sky Compton parameter map (y-map) of the thermal Sunyaev-Zel'dovich (tSZ) effect from the 100 to 857 GHz frequency channel maps delivered within the Planck data release 4. The improvements in terms of noise and systematic effects translated into a y-map with a noise level smaller by ~7% compared to the maps released in 2015, and with significantly reduced survey stripes. The produced 2020 y-map is also characterized by residual foreground contamination, mainly due to thermal dust emission at large angular scales and to CIB and extragalactic point sources at small angular scales. Using the new Planck data, we computed the tSZ angular power spectrum and found that the tSZ signal dominates the y-map in the multipole range, 60 < l < 600. We performed the cosmological analysis with the tSZ angular power spectrum and found S8=0.764+0.015-0.018(stat)+0.031-0.016(sys), including systematic uncertainties from a hydrostatic mass bias and pressure profile model. The S8 value may differ by +-0.016 depending on the hydrostatic mass bias model and by +0.021 depending on the pressure profile model used for the analysis. The obtained value is fully consistent with recent KiDS and DES weak-lensing observations. While our result is slightly lower than the Planck CMB one, it is consistent with the latter within 2 sigma., Comment: 14 pages, 17 figures, Accepted for publication in MNRAS

We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.

We propose a new analysis of small scale CMB data by introducing the cosmological dependency of the foreground signals, focusing first on the thermal Sunyaev-Zel'dovich (tSZ) power spectrum, derived from the halo model. We analyse the latest observations by the South Pole Telescope (SPT) of the high-$\ell$ power (cross) spectra at 90, 150 and 220 GHz, as the sum of CMB and tSZ signals, both depending on cosmological parameters, and remaining contaminants. In order to perform faster analyses, we propose a new tSZ modelling based on machine learning algorithms (namely Random Forest). We show that the additional information contained in the tSZ power spectrum tightens constraints on cosmological and tSZ scaling relation parameters. We combine for the first time the Planck tSZ data with SPT high-$\ell$ to derive even stronger constraints. Finally, we show how the amplitude of the remaining kSZ power spectrum varies depending on the assumptions made on both tSZ and cosmological parameters., Comment: Accepted in A&A, Random Forest code for tSZ spectra computation is available on IAS SZ portal SZDB: https://szdb.osups.universite-paris-saclay.fr/

A subvariety of a quasi-projective complex variety $X$ is called ``universally irreducible'' if its preimage inside the universal cover of $X$ is irreducible. In this paper we investigate sufficient conditions for universal irreducibility. We consider in detail complete intersection subvarieties of small codimension inside Siegel moduli spaces of any finite level. Moreover we show that, for $g\geq 3$, every Siegel modular form is the product of finitely many irreducible analytic functions on the Siegel upper half-space $\mathbb{H}_g$. We also discuss the special case of singular theta series of weight $\frac{1}{2}$ and of Schottky forms., Comment: 37 pages. Final version. Accepted for publication on Crelle

SWELTO -- Space WEather Laboratory in Turin Observatory is a conceptual framework where new ideas for the analysis of space-based and ground-based data are developed and tested. The input data are (but not limited to) remote sensing observations (EUV images of the solar disk, Visible Light coronagraphic images, radio dynamic spectra, etc...), in situ plasma measurements (interplanetary plasma density, velocity, magnetic field, etc...), as well as measurements acquired by local sensors and detectors (radio antenna, fluxgate magnetometer, full-sky cameras, located in OATo). The output products are automatic identification, tracking, and monitoring of solar stationary and dynamic features near the Sun (coronal holes, active regions, coronal mass ejections, etc...), and in the interplanetary medium (shocks, plasmoids, corotating interaction regions, etc...), as well as reconstructions of the interplanetary medium where solar disturbances may propagate from the Sun to the Earth and beyond. These are based both on empirical models and numerical MHD simulations. The aim of SWELTO is not only to test new data analysis methods for future application for Space Weather monitoring and prediction purposes, but also to procure, test and deploy new ground-based instrumentation to monitor the ionospheric and geomagnetic responses to solar activity. Moreover, people involved in SWELTO are active in outreach to disseminate the topics related with Space Weather to students and the general public.

Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of High Temperature Superconducting materials (Extended Sachdev-Ye-Kitaev (SYK) models). Our hydrodynamical approach to the marginal Fermi liquid emerging out of the interaction, identifies the low energy collective excitations of the system in its coherent phase. These neutral excitations diffuse in the lattice, but the diffusion is heavily hindered by coupling to the pseudo Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. A critical temperature for superconductivity arises in the electron liquid,in case these excitations are assumed to mediate an attractive Cooper-pairing, in the electron liquid, which is not BCS-like., Comment: 37 pages, 12 figures, corrects few ambiguities, some typos and adds 3 references

Commutative properties in formal languages pose problems at the frontier of computer science, computational linguistics and computational group theory. A prominent problem of this kind is the position of the language $O_n$, the language that contains the same number of letters $a_i$ and $\bar a_i$ with $1\leq i\leq n$, in the known classes of formal languages. It has recently been shown that $O_n$ is a Multiple Context-Free Language (MCFL). However the more precise conjecture of Nederhof that $O_n$ is an MCFL of dimension $n$ was left open. We present two proofs of this conjecture, both relying on tools from algebraic topology. On our way, we prove a variant of the necklace splitting theorem.

M-quantile regression is a general form of quantile-like regression which usually utilises the Huber influence function and corresponding tuning constant. Estimation requires a nuisance scale parameter to ensure the M-quantile estimates are scale invariant, with several scale estimators having previously been proposed. In this paper we assess these scale estimators and evaluate their suitability, as well as proposing a new scale estimator based on the method of moments. Further, we present two approaches for estimating data-driven tuning constant selection for M-quantile regression. The tuning constants are obtained by i) minimising the estimated asymptotic variance of the regression parameters and ii) utilising an inverse M-quantile function to reduce the effect of outlying observations. We investigate whether data-driven tuning constants, as opposed to the usual fixed constant, for instance, at c=1.345, can improve the efficiency of the estimators of M-quantile regression parameters. The performance of the data-driven tuning constant is investigated in different scenarios using model-based simulations. Finally, we illustrate the proposed methods using a European Union Statistics on Income and Living Conditions data set., Comment: 30 pages, 6 figures