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In [ Ge], Bert van Geemen computed the dimension of the space of the fourth power of the theta nullwerte. In [SM2], it has been observe that all linear relations between the $\theta_m^4$ are consequences of the quartic Riemann relations. In this note, we want to give a new proof of these result and extend them.

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (3$\times$2pt) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining $\Lambda$CDM parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure $\Omega_\mathrm{m}=0.300\pm0.017$ and $\sigma_8=0.797\pm0.026$. Compared to constraints from Planck primary CMB anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 ($1.2\sigma$) for the two-parameter difference. We further obtain $S_8\equiv\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5}=0.796\pm0.013$ which is lower than the Planck measurement at the $1.6\sigma$ level. The combined SPT cluster, DES 3$\times$2pt, and Planck datasets mildly prefer a non-zero positive neutrino mass, with a 95% upper limit $\sum m_\nu<0.25~\mathrm{eV}$ on the sum of neutrino masses. Assuming a $w$CDM model, we constrain the dark energy equation of state parameter $w=-1.15^{+0.23}_{-0.17}$ and when combining with Planck primary CMB anisotropies, we recover $w=-1.20^{+0.15}_{-0.09}$, a $1.7\sigma$ difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology., Comment: Submitted to Phys. Rev. D

Eigenstate multifractality, a hallmark of non-interacting disordered metals which can potentially be observed in many-body localized states as well, is characterized by anomalous slow dynamics and appears relevant for many areas of quantum physics from measurement-driven systems to superconductivity. We propose a novel approach to achieve non-ergodic multifractal (NEM) states without disorder by iteratively introducing defects into a crystal lattice, reshaping it from a plain structure into fractal geometry. By comprehensive analysis of the Sierpi\'nski gasket case, we find a robust evidence of the emergence of NEM states that go beyond the conventional classification of quantum states and designate new pathways for quantum transport studies. We discuss potential experimental signatures of these states., Comment: 20 pages, 20 figures

We present an elementary branch and bound algorithm with a simple analysis of why it achieves worstcase optimality for join queries on classes of databases defined respectively by cardinality or acyclic degree constraints. We then show that if one is given a reasonable way for recursively estimating upper bounds on the number of answers of the join queries, our algorithm can be turned into algorithm for uniformly sampling answers with expected running time $O(UP/OUT)$ where $UP$ is the upper bound, $OUT$ is the actual number of answers and $O(\cdot)$ ignores polylogarithmic factors. Our approach recovers recent results on worstcase optimal join algorithm and sampling in a modular, clean and elementary way., Comment: 19 pages, including 17 pages of main text

We assess the capabilities of the LiteBIRD mission to map the hot gas distribution in the Universe through the thermal Sunyaev-Zeldovich (SZ) effect. Our analysis relies on comprehensive simulations incorporating various sources of Galactic and extragalactic foreground emission, while accounting for specific instrumental characteristics of LiteBIRD, such as detector sensitivities, frequency-dependent beam convolution, inhomogeneous sky scanning, and $1/f$ noise. We implement a tailored component-separation pipeline to map the thermal SZ Compton $y$-parameter over 98% of the sky. Despite lower angular resolution for galaxy cluster science, LiteBIRD provides full-sky coverage and, compared to the Planck satellite, enhanced sensitivity, as well as more frequency bands to enable the construction of an all-sky $y$-map, with reduced foreground contamination at large and intermediate angular scales. By combining LiteBIRD and Planck channels in the component-separation pipeline, we obtain an optimal $y$-map that leverages the advantages of both experiments, with the higher angular resolution of the Planck channels enabling the recovery of compact clusters beyond the LiteBIRD beam limitations, and the numerous sensitive LiteBIRD channels further mitigating foregrounds. The added value of LiteBIRD is highlighted through the examination of maps, power spectra, and one-point statistics of the various sky components. After component separation, the $1/f$ noise from LiteBIRD is effectively mitigated below the thermal SZ signal at all multipoles. Cosmological constraints on $S_8=\sigma_8\left(\Omega_{\rm m}/0.3\right)^{0.5}$ obtained from the LiteBIRD-Planck combined $y$-map power spectrum exhibits a 15% reduction in uncertainty compared to constraints from Planck alone. This improvement can be attributed to the increased portion of uncontaminated sky available in the LiteBIRD-Planck combined $y$-map., Comment: 38 pages, 13 figures, abstract shortened. Updated to match version accepted by JCAP

In small area estimation, it is a smart strategy to rely on data measured over time. However, linear mixed models struggle to properly capture time dependencies when the number of lags is large. Given the lack of published studies addressing robust prediction in small areas using time-dependent data, this research seeks to extend M-quantile models to this field. Indeed, our methodology successfully addresses this challenge and offers flexibility to the widely imposed assumption of unit-level independence. Under the new model, robust bias-corrected predictors for small area linear indicators are derived. Additionally, the optimal selection of the robustness parameter for bias correction is explored, contributing theoretically to the field and enhancing outlier detection. For the estimation of the mean squared error (MSE), a first-order approximation and analytical estimators are obtained under general conditions. Several simulation experiments are conducted to evaluate the performance of the fitting algorithm, the new predictors, and the resulting MSE estimators, as well as the optimal selection of the robustness parameter. Finally, an application to the Spanish Living Conditions Survey data illustrates the usefulness of the proposed predictors.

In small area estimation different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models such as the linear mixed effects model or M-quantile regression are often used to improve the precision of survey sample estimates by leveraging auxiliary information for which means or totals are known at the area level. In many applications, the unit-level linkage of records from different sources is probabilistic and potentially error-prone. In this paper, we present adjustments of the small area predictors that are based on either the linear mixed effects model or M-quantile regression to account for the presence of linkage error. These adjustments are developed from a two-component mixture model that hinges on the assumption of independence of the target and auxiliary variable given incorrect linkage. Estimation and inference is based on composite likelihoods and machinery revolving around the Expectation-Maximization Algorithm. For each of the two regression methods, we propose modified small area predictors and approximations for their mean squared errors. The empirical performance of the proposed approaches is studied in both design-based and model-based simulations that include comparisons to a variety of baselines., Comment: total: 46 pages, main: 33 pages, references: 4 pages, technical appendix: 9 pages

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

We determine the maximal dimension of compact subvarieties of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties of dimension $g$, and the maximal dimension of a compact subvariety through a very general point of $\mathcal{A}_g$. This also allows us to draw some conclusions for compact subvarieties of the moduli space of complex curves of compact type., Comment: 36 pages, comments welcome!

Studies of surface brightness fluctuations in the intracluster medium (ICM) present an indirect probe of turbulent properties such as the turbulent velocities, injection scales, and the slope of the power spectrum of fluctuations towards smaller scales. With the advancement of Sunyaev-Zel'dovich (SZ) studies and surveys relative to X-ray observations, we seek to investigate surface brightness fluctuations in a sample of SPT-SZ clusters which also have archival \textit{XMM-Newton} data. Here we present a pilot study of two typical clusters in that sample: SPT-CLJ0232-4421 and SPT-CLJ0638-5358. We infer injection scales larger than 500 kpc in both clusters and Mach numbers $\approx 0.5$ in SPT-CLJ0232-4421 and Mach numbers $\approx 0.6 - 1.6$ in SPT-CLJ0638-5358, which has a known shock. We find hydrostatic bias values for $M_{500}$ less than 0.2 for SPT-CLJ0232-4421 and less than 0.1 for SPT-CLJ0638-5358. These results show the importance to assess its quantitative values via a detailed multiwavelength approach and suggest that the drivers of turbulence may occur at quite larger scales., Comment: Accepted to ApJ; 34 pages, 23 figures, and 14 tables

Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the mean square prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP). Observed Best Prediction (OBP) method has been proposed with the intent to improve on the MSPE over EBLUP. We conduct a Monte Carlo simulation experiment to understand the effect of mispsecification of mean structures on different small area estimators. Our simulation results lead to an unexpected result that OBP may perform very poorly when observational unit level auxiliary variables are used and that OBP can be improved significantly when population means of those auxiliary variables (area level auxiliary variables) are used in the nested error regression model or when a corresponding area level model is used. Our simulation also indicates that the MSPE of OBP in an increasing function of the difference between the sample and population means of the auxiliary variables.

The goal of quantum metrology is to improve measurements' sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup's sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy., Comment: 19 pages, 6 figures

We provide a new scaling relation between $Y_{\text{SZ}}$, the integrated Sunyaev-Zeldovich signal and $M_{500}^{Y_{\text{X}}}$, the cluster mass derived from X-ray observations, using a sample of clusters from the Planck Early Sunyaev-Zeldovich (ESZ) catalogue observed in X-rays by Chandra, and compare it to the results of the Planck collaboration obtained from XMM-Newton observations of a subsample of the ESZ. We calibrated a mass bias on a subset of the Planck cosmological cluster sample using published weak-lensing data from CCCP and MENeaCS, for the new scaling relation as well as that from the Planck collaboration. We propose a novel method to account for selection effects and find a mass bias of $(1-b)=0.89\pm0.04$ for the Chandra-calibrated scaling relation, and $(1-b)=0.76\pm0.04$ for the XMM-Newton-calibrated scaling relation. We apply the scaling relations we derived to the full Planck cosmological cluster sample and obtain identical cosmological constraints regardless of the X-ray sample used, with $\sigma_8 =0.77\pm0.02$, $\Omega_m=0.31\pm0.02$, and $S_8= \sigma_8 \sqrt{\Omega_m / 0.3}=0.78\pm0.02$. We also provide constraints with a redshift evolution of the scaling relation fitted from the data instead of fixing it to the self-similar value. We find a redshift evolution significantly deviating from the self-similar value, leading to a higher value of $S_8=0.81\pm0.02$. We compare our results to those from various cosmological probes, and find that our $S_8$ constraints are competitive with the tightest constraints from the literature. When assuming a self-similar redshift evolution, our constraints are in agreement with most late-time probes and in tension with constraints from the CMB primary anisotropies. When relaxing the assumption of redshift evolution and fitting it to the data, we find no significant tension with results from either late-time probes or the CMB., Comment: 21 pages, 20 figures, accepted by A&A

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range $0.25-1.78$ over a total sky area of 5,200 deg$^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6

We present a catalog of 689 galaxy cluster candidates detected at significance $\xi>4$ via their thermal Sunyaev-Zel'dovich (SZ) effect signature in 95 and 150 GHz data from the 500-square-degree SPTpol survey. We use optical and infrared data from the Dark Energy Camera and the Wide-field Infrared Survey Explorer (WISE) and \spitzer \ satellites, to confirm 544 of these candidates as clusters with $\sim94\%$ purity. The sample has an approximately redshift-independent mass threshold at redshift $z>0.25$ and spans $1.5 \times 10^{14} < M_{500c} < 9.1 \times 10^{14}$ $M_\odot/h_{70}$ \ and $0.031$. We use external radio data from the Sydney University Molonglo Sky Survey (SUMSS) to estimate contamination to the SZ signal from synchrotron sources. The contamination reduces the recovered $\xi$ by a median value of 0.032, or $\sim0.8\%$ of the $\xi=4$ threshold value, and $\sim7\%$ of candidates have a predicted contamination greater than $\Delta \xi = 1$. With the exception of a small number of systems $(<1\%)$, an analysis of clusters detected in single-frequency 95 and 150 GHz data shows no significant contamination of the SZ signal by emission from dusty or synchrotron sources. This cluster sample will be a key component in upcoming astrophysical and cosmological analyses of clusters. The SPTpol millimeter-wave maps and associated data products used to produce this sample are available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html, and the NASA LAMBDA website. An interactive sky server with the SPTpol maps and Dark Energy Survey data release 2 images is also available at NCSA https://skyviewer.ncsa.illinois.edu., Comment: Matches version accepted by OJA. 19 pages + references, 14 figures, cluster candidate table provided in Appendix. Data products available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html and an interactive sky server at https://skyviewer.ncsa.illinois.edu

Given a conjunctive query $Q$ and a database $D$, a direct access to the answers of $Q$ over $D$ is the operation of returning, given an index $k$, the $k$-th answer for some order on its answers. While this problem is #P-hard in general with respect to combined complexity, many conjunctive queries have an underlying structure that allows for a direct access to their answers for some lexicographical ordering that takes polylogarithmic time in the size of the database after a polynomial time precomputation. Previous work has precisely characterised the tractable classes and given fine-grained lower bounds on the precomputation time needed depending on the structure of the query. In this paper, we generalise these tractability results to the case of signed conjunctive queries, that is, conjunctive queries that may contain negative atoms. Our technique is based on a class of circuits that can represent relational data. We first show that this class supports tractable direct access after a polynomial time preprocessing. We then give bounds on the size of the circuit needed to represent the answer set of signed conjunctive queries depending on their structure. Both results combined together allow us to prove the tractability of direct access for a large class of conjunctive queries. On the one hand, we recover the known tractable classes from the literature in the case of positive conjunctive queries. On the other hand, we generalise and unify known tractability results about negative conjunctive queries -- that is, queries having only negated atoms. In particular, we show that the class of $\beta$-acyclic negative conjunctive queries and the class of bounded nest set width negative conjunctive queries admit tractable direct access., Comment: 48 pages, 11 figures

We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at $z=0.25$ to 10% at $z=0.95$, to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multi-observable likelihood for the Sunyaev-Zel'dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset., Comment: Accepted for publication in Phys. Rev. D. arXiv v2 corresponds to published article

Galaxy cluster number counts are an important probe to constrain cosmological parameters. One of the main ingredients of the analysis, along with accurate estimates of the clusters' masses, is the selection function, and in particular the completeness, associated to the cluster sample one is considering. Incorrectly characterising this function can lead to biases in the cosmological constraints. In this work, we want to study the completeness of the Planck cluster catalog, estimating the clusters' probability of detection in a realistic setting using hydrodynamical simulations. In particular, we probe the case in which the cluster model assumed in the detection method differs from the shape and profiles of true galaxy clusters. We create around 9000 images of the Sunyaev-Zel'dovich effect from galaxy clusters from the IllustrisTNG simulation, and use a Monte-Carlo injection method to estimate the completeness function. We study the impact of having different cluster pressure profiles, as well as that of complex cluster morphologies on the detection process. We find that the cluster profile has a significant effect on the completeness, with clusters with steeper profiles producing a higher completeness than ones with flatter profiles. We also show that cluster morphologies have small impact on the completeness, finding that elliptical clusters have slightly lower probability of detection with respect to spherically symmetric ones. Finally, we investigate the impact of a different completeness function on a cosmological analysis with cluster number counts, showing a shift in the constraints on $\Omega_m$ and $\sigma_8$ that lies in the same direction as the one driven by the mass bias., Comment: 13 pages, 12 figures. Submitted to A&A

We present an extension to a Sunyaev-Zel'dovich Effect (SZE) selected cluster catalog based on observations from the South Pole Telescope (SPT); this catalog extends to lower signal-to-noise than the previous SPT-SZ catalog and therefore includes lower mass clusters. Optically derived redshifts, centers, richnesses and morphological parameters together with catalog contamination and completeness statistics are extracted using the multi-component matched filter algorithm (MCMF) applied to the S/N>4 SPT-SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalog. The main catalog contains 811 sources above S/N=4, has 91% purity and is 95% complete with respect to the original SZE selection. It contains 50% more total clusters and twice as many clusters above z=0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalog completeness. As an example, we provide two subsamples with S/N>4.25 and S/N>4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N>4.5 has 98% purity and 96% completeness, and will be included in a combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations., Comment: 16 pages, 17 figures, submitted to MNRAS

Magnetic skyrmions are vortex-like quasiparticles characterized by long lifetime and remarkable topological properties. That makes them a promising candidate for the role of information carriers in magnetic information storage and processing devices. Although considerable progress has been made in studying skyrmions in classical systems, little is known about the quantum case: quantum skyrmions cannot be directly observed by probing the local magnetization of the system, and the notion of topological protection is elusive in the quantum realm. Here, we explore the potential robustness of quantum skyrmions in comparison to their classical counterparts. We theoretically analyze the dynamics of a quantum skyrmion subject to local projective measurements and demonstrate that the properties of the skyrmionic quantum state change very little upon external perturbations. We further show that by performing repetitive measurements on a quantum skyrmion, it can be completely stabilized through an analog of the quantum Zeno effect., Comment: 7+eps pages, 7 figures; v2: fixed mistake in the definition of rescaled time \tau after Eq.(6)

We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.

In this paper, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber's function. To assess the impact of changes in the covariates across the entire unconditional distribution of the responses, we extend the work of Firpo et al. (2009) by running a mean regression of the recentered influence function on the explanatory variables. We discuss the estimation procedure and establish the asymptotic properties of the derived estimators. A data-driven procedure is also presented to select the tuning constant of the Huber's function. The validity of the proposed methodology is explored with simulation studies and through an application using the Survey of Household Income and Wealth 2016 conducted by the Bank of Italy.

In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of $\hat{\rho}_{\mathbf{\theta}}$ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high post-processing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in $\hat{\rho}_{\mathbf{\theta}} \, ^{\otimes n}$ into $m

We study various naturally defined subvarieties of the moduli space ${\mathcal A}_g$ of complex principally polarized abelian varieties (ppav) in a neighborhood of the locus of products of $g$ elliptic curves. In this neighborhood, we obtain a local description for the locus of hyperelliptic curves, reproving the recent result of Shepherd-Barron that the hyperelliptic locus is locally given by tridiagonal matrices. We further reprove and generalize to arbitrary genus the recent result of Agostini and Chua showing that the locus of Jacobians of genus 5 curves with a theta-null is an irreducible component of the locus of ppav with a theta-null such that the singular locus of the theta divisor at the corresponding two-torsion point has tangent cone of rank at most 3. We further show that the locus of ppav such that the gradient vanishes, for some odd theta characteristic, locally has codimension $g$ near the diagonal. Finally, we obtain new results on the locus where the rank of the Hessian of the theta function at a two-torsion point that lies on the theta divisor is equal to 2., Comment: v2: only corrected TeX, to disable showkeys

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.