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Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence assumption for MDS and MSRD codes. We also prove that the same integer sequences appear as sequences of greedy weights of linear block codes, rank-metric codes, and sum-rank metric codes. Finally, we characterize the integer sequences which appear as sequences of relative generalized weights (respectively, relative greedy weights) of linear block codes., Comment: 19 pages

We consider the problem of unfair discrimination between two groups and propose a pre-processing method to achieve fairness. Corrective methods like statistical parity usually lead to bad accuracy and do not really achieve fairness in situations where there is a correlation between the sensitive attribute S and the legitimate attribute E (explanatory variable) that should determine the decision. To overcome these drawbacks, other notions of fairness have been proposed, in particular, conditional statistical parity and equal opportunity. However, E is often not directly observable in the data, i.e., it is a latent variable. We may observe some other variable Z representing E, but the problem is that Z may also be affected by S, hence Z itself can be biased. To deal with this problem, we propose BaBE (Bayesian Bias Elimination), an approach based on a combination of Bayes inference and the Expectation-Maximization method, to estimate the most likely value of E for a given Z for each group. The decision can then be based directly on the estimated E. We show, by experiments on synthetic and real data sets, that our approach provides a good level of fairness as well as high accuracy.

We report on the results obtained with the global CUPID-0 background model, which combines the data collected in the two measurement campaigns for a total exposure of 16.6 kg$\times$yr. We identify with improved precision the background sources in the region of interest for neutrinoless double $\beta$-decay, making more solid the foundations for the background budget of the next-generation CUPID experiment. Relying on the excellent data reconstruction, we measure the two-neutrino double $\beta$-decay half-life of $^{82}$Se with unprecedented accuracy: $T_{1/2}^{2\nu} = [8.69 \pm 0.05 \textrm{(stat.)}~^{+0.09}_{-0.06} \textrm{(syst.)}] \times 10^{19}~\textrm{yr}$.

The MacWilliams' Extension Theorem is a classical result by Florence Jessie MacWilliams. It shows that every linear isometry between linear block-codes endowed with the Hamming distance can be extended to a linear isometry of the ambient space. Such an extension fails to exist in general for rank-metric codes, that is, one can easily find examples of linear isometries between rank-metric codes which cannot be extended to linear isometries of the ambient space. In this paper, we explore to what extent a MacWilliams' Extension Theorem may hold for rank-metric codes. We provide an extensive list of examples of obstructions to the existence of an extension, as well as a positive result., Comment: 12 pages

Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this chapter is to present the mathematical theory of sum-rank metric codes, paying special attention to the $\mathbb{F}_q$-linear case in which different sizes of matrices are allowed. We provide a comprehensive overview of the main results in the area. In particular, we discuss invariants, optimal anticodes, and MSRD codes. In the last section, we concentrate on $\mathbb{F}_{q^m}$-linear codes.

CUPID is a next-generation bolometric experiment aiming at searching for neutrinoless double-beta decay with ~250 kg of isotopic mass of $^{100}$Mo. It will operate at $\sim$10 mK in a cryostat currently hosting a similar-scale bolometric array for the CUORE experiment at the Gran Sasso National Laboratory (Italy). CUPID will be based on large-volume scintillating bolometers consisting of $^{100}$Mo-enriched Li$_2$MoO$_4$ crystals, facing thin Ge-wafer-based bolometric light detectors. In the CUPID design, the detector structure is novel and needs to be validated. In particular, the CUORE cryostat presents a high level of mechanical vibrations due to the use of pulse tubes and the effect of vibrations on the detector performance must be investigated. In this paper we report the first test of the CUPID-design bolometric light detectors with NTD-Ge sensors in a dilution refrigerator equipped with a pulse tube in an above-ground lab. Light detectors are characterized in terms of sensitivity, energy resolution, pulse time constants, and noise power spectrum. Despite the challenging noisy environment due to pulse-tube-induced vibrations, we demonstrate that all the four tested light detectors comply with the CUPID goal in terms of intrinsic energy resolution of 100 eV RMS baseline noise. Indeed, we have measured 70--90 eV RMS for the four devices, which show an excellent reproducibility. We have also obtained outstanding energy resolutions at the 356 keV line from a $^{133}$Ba source with one light detector achieving 0.71(5) keV FWHM, which is -- to our knowledge -- the best ever obtained when compared to $\gamma$ detectors of any technology in this energy range., Comment: Prepared for submission to JINST; 16 pages, 7 figures, and 1 table

An array of twelve 0.28 kg lithium molybdate (LMO) low-temperature bolometers equipped with 16 bolometric Ge light detectors, aiming at optimization of detector structure for CROSS and CUPID double-beta decay experiments, was constructed and tested in a low-background pulse-tube-based cryostat at the Canfranc underground laboratory in Spain. Performance of the scintillating bolometers was studied depending on the size of phonon NTD-Ge sensors glued to both LMO and Ge absorbers, shape of the Ge light detectors (circular vs. square, from two suppliers), in different light collection conditions (with and without reflector, with aluminum coated LMO crystal surface). The scintillating bolometer array was operated over 8 months in the low-background conditions that allowed to probe a very low, $\mu$Bq/kg, level of the LMO crystals radioactive contamination by $^{228}$Th and $^{226}$Ra., Comment: Prepared for submission to JINST; 23 pages, 9 figures, and 4 tables

New-generation direct searches for low mass dark matter feature detection thresholds at energies well below 100 eV, much lower than the energies of commonly used X-ray calibration sources. This requires new calibration sources with sub-keV energies. When searching for nuclear recoil signals, the calibration source should ideally cause mono-energetic nuclear recoils in the relevant energy range. Recently, a new calibration method based on the radiative neutron capture on $^{182}$W with subsequent de-excitation via single $\gamma$-emission leading to a nuclear recoil peak at 112 eV was proposed. The CRESST-III dark matter search operated several CaWO$_{4}$-based detector modules with detection thresholds below 100 eV in the past years. We report the observation of a peak around the expected energy of 112 eV in the data of three different detector modules recorded while irradiated with neutrons from different AmBe calibration sources. We compare the properties of the observed peaks with Geant-4 simulations and assess the prospects of using this for the energy calibration of CRESST-III detectors., Comment: 8 pages, 4 figures; submitted to Phys. Rev. D

In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages of the stream IFT from a computational point of view, and provide a few example applications where its use turns out to be valuable.

Accurate planning of transcatheter aortic implantation (TAVI) is important to minimize complications, and it requires anatomic evaluation of the aortic root (AR), commonly done through 3D computed tomography (CT) image analysis. Currently, there is no standard automated solution for this process. Two convolutional neural networks (CNNs) with 3D U-Net architectures (model 1 and model 2) were trained on 310 CT scans for AR analysis. Model 1 performed AR segmentation and model 2 identified the aortic annulus and sinotubular junction (STJ) contours. Results were validated against manual measurements of 178 TAVI candidates. After training, the two models were integrated into a fully automated pipeline for geometric analysis of the AR. The trained CNNs effectively segmented the AR, annulus and STJ, resulting in mean Dice scores of 0.93 for the AR, and mean surface distances of 1.16 mm and 1.30 mm for the annulus and STJ, respectively. Automatic measurements were in good agreement with manual annotations, yielding annulus diameters that differed by 0.52 [-2.96, 4.00] mm (bias and 95% limits of agreement for manual minus algorithm). Evaluating the area-derived diameter, bias and limits of agreement were 0.07 [-0.25, 0.39] mm. STJ and sinuses diameters computed by the automatic method yielded differences of 0.16 [-2.03, 2.34] and 0.1 [-2.93, 3.13] mm, respectively. The proposed tool is a fully automatic solution to quantify morphological biomarkers for pre-TAVI planning. The method was validated against manual annotation from clinical experts and showed to be quick and effective in assessing AR anatomy, with potential for time and cost savings.

We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some properties of these invariants and compare them with other invariants of convolutional codes which appear in the literature., Comment: 13 pages, submitted

We present limits on the spin-independent interaction cross section of dark matter particles with silicon nuclei, derived from data taken with a cryogenic calorimeter with 0.35 g target mass operated in the CRESST-III experiment. A baseline nuclear recoil energy resolution of $(1.36\pm 0.05)$ eV$_{\text{nr}}$, currently the lowest reported for macroscopic particle detectors, and a corresponding energy threshold of $(10.0\pm 0.2)$ eV$_{\text{nr}}$ have been achieved, improving the sensitivity to light dark matter particles with masses below 160 MeV/c$^2$ by a factor of up to 20 compared to previous results. We characterize the observed low energy excess, and we exclude noise triggers and radioactive contaminations on the crystal surfaces as dominant contributions., Comment: 8 pages, 5 figures; precised the position of the calibration source in Fig. 1; extended the discussion about the observed energy spectrum; added the DM limit curve to ancillary files. Published in Phys. Rev. D

The CRESST experiment employs cryogenic calorimeters for the sensitive measurement of nuclear recoils induced by dark matter particles. The recorded signals need to undergo a careful cleaning process to avoid wrongly reconstructed recoil energies caused by pile-up and read-out artefacts. We frame this process as a time series classification task and propose to automate it with neural networks. With a data set of over one million labeled records from 68 detectors, recorded between 2013 and 2019 by CRESST, we test the capability of four commonly used neural network architectures to learn the data cleaning task. Our best performing model achieves a balanced accuracy of 0.932 on our test set. We show on an exemplary detector that about half of the wrongly predicted events are in fact wrongly labeled events, and a large share of the remaining ones have a context-dependent ground truth. We furthermore evaluate the recall and selectivity of our classifiers with simulated data. The results confirm that the trained classifiers are well suited for the data cleaning task., Comment: 12 pages, 8 figures, 6 tables

We present the first search for the Majoron-emitting modes of the neutrinoless double $\beta$ decay ($0\nu\beta\beta\chi_0$) using scintillating cryogenic calorimeters. We analysed the CUPID-0 Phase I data using a Bayesian approach to reconstruct the background sources activities, and evaluate the potential contribution of the $^{82}$Se $0\nu\beta\beta\chi_0$. We considered several possible theoretical models which predict the existence of a Majoron-like boson coupling to the neutrino. The energy spectra arising from the emission of such bosons in the neutrinoless double $\beta$ decay have spectral indices $n=$ 1, 2, 3 or 7. We found no evidence of any of these decay modes, setting a lower limit (90% of credibility interval) on the half-life of 1.2 $\times$ 10$^{23}$ yr in the case of $n=$ 1, 3.8 $\times$ 10$^{22}$ yr for $n=$ 2, 1.4 $\times$ 10$^{22}$ yr for $n=$ 3 and 2.2 $\times$ 10$^{21}$ yr for $n=$ 7. These are the best limits on the $0\nu\beta\beta\chi_0$ half-life of the $^{82}$Se, and demonstrate the potentiality of the CUPID-0 technology in this field.

Code comments are important artifacts in software systems and play a paramount role in many software engineering (SE) tasks related to maintenance and program comprehension. However, while it is widely accepted that high quality matters in code comments just as it matters in source code, assessing comment quality in practice is still an open problem. First and foremost, there is no unique definition of quality when it comes to evaluating code comments. The few existing studies on this topic rather focus on specific attributes of quality that can be easily quantified and measured. Existing techniques and corresponding tools may also focus on comments bound to a specific programming language, and may only deal with comments with specific scopes and clear goals (e.g., Javadoc comments at the method level, or in-body comments describing TODOs to be addressed). In this paper, we present a Systematic Literature Review (SLR) of the last decade of research in SE to answer the following research questions: (i) What types of comments do researchers focus on when assessing comment quality? (ii) What quality attributes (QAs) do they consider? (iii) Which tools and techniques do they use to assess comment quality?, and (iv) How do they evaluate their studies on comment quality assessment in general? Our evaluation, based on the analysis of 2353 papers and the actual review of 47 relevant ones, shows that (i) most studies and techniques focus on comments in Java code, thus may not be generalizable to other languages, and (ii) the analyzed studies focus on four main QAs of a total of 21 QAs identified in the literature, with a clear predominance of checking consistency between comments and the code. We observe that researchers rely on manual assessment and specific heuristics rather than the automated assessment of the comment quality attributes.

We analyze to what extent final users can infer information about the level of protection of their data when the data obfuscation mechanism is a priori unknown to them (the so-called ''black-box'' scenario). In particular, we delve into the investigation of two notions of local differential privacy (LDP), namely {\epsilon}-LDP and R\'enyi LDP. On one hand, we prove that, without any assumption on the underlying distributions, it is not possible to have an algorithm able to infer the level of data protection with provable guarantees; this result also holds for the central versions of the two notions of DP considered. On the other hand, we demonstrate that, under reasonable assumptions (namely, Lipschitzness of the involved densities on a closed interval), such guarantees exist and can be achieved by a simple histogram-based estimator. We validate our results experimentally and we note that, on a particularly well-behaved distribution (namely, the Laplace noise), our method gives even better results than expected, in the sense that in practice the number of samples needed to achieve the desired confidence is smaller than the theoretical bound, and the estimation of {\epsilon} is more precise than predicted.

CRESST is a leading direct detection sub-$\mathrm{GeVc}^{-2}$ dark matter experiment. During its second phase, cryogenic bolometers were used to detect nuclear recoils off the $\mathrm{CaWO}_4$ target crystal nuclei. The previously established electromagnetic background model relies on secular equilibrium (SE) assumptions. In this work, a validation of SE is attempted by comparing two likelihood-based normalisation results using a recently developed spectral template normalisation method based on Bayesian likelihood. We find deviations from SE; further investigations are necessary to determine their origin., Comment: Part of special issue: ICRM-LLRMT22 8th International Conference on Radionuclide Metrology - Low Level Radioactivity Measurement and Techniques, 6 pages, 3 figures

In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Hamming metric. In this paper, we propose a new definition of generalized weights of convolutional codes, that takes into account the underlying module structure of the code. We derive the basic properties of our generalized weights and discuss the relation with the previous definition. We establish upper bounds on the weight hierarchy of MDS and MDP codes and show that that, depending on the code parameters, some or all of the generalized weights of MDS codes are determined by the length, rank, and internal degree of the code. We also prove an anticode bound for convolutional codes and define optimal anticodes as the codes which meet the anticode bound. Finally, we classify optimal anticodes and compute their weight hierarchy.

The CRESST experiment observes an unexplained excess of events at low energies. In the current CRESST-III data-taking campaign we are operating detector modules with different designs to narrow down the possible explanations. In this work, we show first observations of the ongoing measurement, focusing on the comparison of time, energy and temperature dependence of the excess in several detectors. These exclude dark matter, radioactive backgrounds and intrinsic sources related to the crystal bulk as a major contribution., Comment: 10 pages, 5 figures; to be published in IDM2022 proceedings; corrected several minor typos

In the past decades, numerous experiments have emerged to unveil the nature of dark matter, one of the most discussed open questions in modern particle physics. Among them, the CRESST experiment, located at the Laboratori Nazionali del Gran Sasso, operates scintillating crystals as cryogenic phonon detectors. In this work, we present first results from the operation of two detector modules which both have 10.46 g LiAlO$_2$ targets in CRESST-III. The lithium contents in the crystal are $^6$Li, with an odd number of protons and neutrons, and $^7$Li, with an odd number of protons. By considering both isotopes of lithium and $^{27}$Al, we set the currently strongest cross section upper limits on spin-dependent interaction of dark matter with protons and neutrons for the mass region between 0.25 and 1.5 GeV/c$^2$., Comment: 9 pages, 8 figures

CUPID-0, an array of Zn$^{82}$Se cryogenic calorimeters, was the first medium-scale demonstrator of the scintillating bolometers technology. The first project phase (March 2017 - December 2018) allowed the most stringent limit on the neutrinoless double beta decay half-life of the isotope of interest, $^{82}$Se, to be set. After a six months long detector upgrade, CUPID-0 began its second and last phase (June 2019 - February 2020). In this letter, we describe the search for neutrinoless double beta decay of $^{82}$Se with a total exposure (phase I + II) of 8.82 kg$\times$yr of isotope. We set a limit on the half-life of $^{82}$Se to the ground state of $^{82}$Kr of T$^{0\nu}_{1/2}$($^{82}$Se)$>$ 4.6$\times \mathrm{10}^{24}$ yr (90\% credible interval), corresponding to an effective Majorana neutrino mass m$_{\beta\beta} <$ (263 -- 545) meV. We also set the most stringent lower limits on the neutrinoless decays of $^{82}$Se to the 0$_1^+$, 2$_1^+$ and 2$_2^+$ excited states of $^{82}$Kr, finding 1.8$\times$10$^{23}$ yr, 3.0$\times$10$^{23}$ yr, 3.2$\times$10$^{23}$ yr (90$\%$ credible interval) respectively.

One of the most energetic events in the Universe are core-collapse Supernovae (SNe), where almost all the star's binding energy is released as neutrinos. These particles are direct probes of the processes occurring in the stellar core and provide unique insights into the gravitational collapse. RES-NOVA will revolutionize how we detect neutrinos from astrophysical sources, by deploying the first ton-scale array of cryogenic detectors made from archaeological lead. Pb offers the highest neutrino interaction cross-section via coherent elastic neutrino-nucleus scattering (CE$\nu$NS). Such process will enable RES-NOVA to be equally sensitive to all neutrino flavors. For the first time, we propose to use archaeological Pb as sensitive target material in order to achieve an ultra-low background level in the region of interest (\textit{O}(1keV)). All these features make possible the deployment of the first cm-scale neutrino telescope for the investigation of astrophysical sources. In this contribution, we will characterize the radiopurity level and the performance of a small-scale proof-of-principle detector of RES-NOVA, consisting in a PbWO$_4$ crystal made from archaeological-Pb operated as cryogenic detector.

The Cryogenic Underground Observatory for Rare Events (CUORE) is the most sensitive experiment searching for neutrinoless double-beta decay ($0\nu\beta\beta$) in $^{130}\text{Te}$. CUORE uses a cryogenic array of 988 TeO$_2$ calorimeters operated at $\sim$10 mK with a total mass of 741 kg. To further increase the sensitivity, the detector response must be well understood. Here, we present a non-linear thermal model for the CUORE experiment on a detector-by-detector basis. We have examined both equilibrium and dynamic electro-thermal models of detectors by numerically fitting non-linear differential equations to the detector data of a subset of CUORE channels which are well characterized and representative of all channels. We demonstrate that the hot-electron effect and electric-field dependence of resistance in NTD-Ge thermistors alone are inadequate to describe our detectors' energy dependent pulse shapes. We introduce an empirical second-order correction factor in the exponential temperature dependence of the thermistor, which produces excellent agreement with energy-dependent pulse shape data up to 6 MeV. We also present a noise analysis using the fitted thermal parameters and show that the intrinsic thermal noise is negligible compared to the observed noise for our detectors., Comment: 34 pages, 14 figures, 6 tables

The Cryogenic Underground Observatory for Rare Events (CUORE) at Laboratori Nazionali del Gran Sasso of INFN in Italy is an experiment searching for neutrinoless double beta (0$\nu\beta\beta$) decay. Its main goal is to investigate this decay in $^{130}$Te, but its ton-scale mass and low background make CUORE sensitive to other rare processes as well. In this work, we present our first results on the search for \nbb decay of $^{128}$Te, the Te isotope with the second highest natural isotopic abundance. We find no evidence for this decay, and using a Bayesian analysis we set a lower limit on the $^{128}$Te \nbb decay half-life of T$_{1/2} > 3.6 \times 10^{24}$ yr (90\% CI). This represents the most stringent limit on the half-life of this isotope, improving by over a factor 30 the previous direct search results, and exceeding those from geochemical experiments for the first time.

Can one tell if an ideal is radical just by looking at the degrees of the generators? In general, this is hopeless. However, there are special collections of degrees in multigraded polynomial rings, with the property that any multigraded ideal generated by elements of those degrees is radical. We call such a collection of degrees a radical support. In this paper, we give a combinatorial characterization of radical supports. Our characterization is in terms of properties of cycles in an associated labelled graph. We also show that the notion of radical support is closely related to that of Cartwright-Sturmfels ideals. In fact, any ideal generated by multigraded generators whose multidegrees form a radical support is a Cartwright-Sturmfels ideal. Conversely, a collection of degrees such that any multigraded ideal generated by elements of those degrees is Cartwright-Sturmfels is a radical support., Comment: 11 pages, 7 figures

CUORE is a large scale cryogenic experiment searching for neutrinoless double beta decay ($0\nu\beta\beta$) in $^{130}$Te. The CUORE detector is made of natural tellurium, providing the possibility of rare event searches on isotopes other than $^{130}$Te. In this work we describe a search for neutrinoless positron emitting electron capture ($0\nu\beta^+EC$) decay in $^{120}$Te with a total TeO$_2$ exposure of 355.7 kg $\cdot$ yr, corresponding to 0.2405 kg $\cdot$ yr of $^{120}$Te. Albeit $0 \nu \beta\beta$ with two final state electrons represents the most promising channel, the emission of a positron and two 511-keV $\gamma$s make $0\nu\beta^+EC$ decay signature extremely clear. To fully exploit the potential offered by the detector modularity we include events with different topology and perform a simultaneous fit of five selected signal signatures. Using blinded data we extract a median exclusion sensitivity of $3.4 \cdot 10^{22}$ yr at 90% Credibility Interval (C.I.). After unblinding we find no evidence of $0\nu\beta^+EC$ signal and set a 90% C.I. Bayesian lower limit of $2.9 \cdot 10^{22}$ yr on $^{120}$Te half-life. This result improves by an order of magnitude the existing limit from the combined analysis of CUORE-0 and Cuoricino.

Current experiments to search for broken lepton-number symmetry through the observation of neutrinoless double-beta decay ($0\mathrm{\nu\beta\beta}$) provide the most stringent limits on the Majorana nature of neutrinos and the effective Majorana neutrino mass ($m_{\beta\beta}$). The next-generation experiments will focus on the sensitivity to the $0\mathrm{\nu\beta\beta}$ half-life of $\mathcal{O}(10^{27}$--$10^{28}$~years$)$ and $m_{\beta\beta}\lesssim15$~meV, which would provide complete coverage of the so-called Inverted Ordering region of the neutrino mass parameter space. By taking advantage of recent technological breakthroughs, new, future calorimetric experiments at the 1-ton scale can increase the sensitivity by at least another order of magnitude, exploring the large fraction of the parameter space that corresponds to the Normal neutrino mass ordering. In case of a discovery, such experiments could provide important insights toward a new understanding of the mechanism of $0\mathrm{\nu\beta\beta}$. We present here a series of projects underway that will provide advancements in background reduction, cryogenic readout, and physics searches beyond $0\mathrm{\nu\beta\beta}$, all moving toward the next-to-next generation CUPID-1T detector., Comment: contribution to Snowmass 2021

RES-NOVA is a newly proposed experiment for the detection of neutrinos from astrophysical sources, mainly Supernovae, using an array of cryogenic detectors made of PbWO$_4$ crystals produced from archaeological Pb. This unconventional material, characterized by intrinsic high radiopurity, enables to achieve low-background levels in the region of interest for the neutrino detection via Coherent Elastic neutrino-Nucleus Scattering (CE$\nu$NS). This signal lies at the detector energy threshold, O(1 keV), and it is expected to be hidden by naturally occurring radioactive contaminants of the crystal absorber. Here, we present the results of a radiopurity assay on a 0.84 kg PbWO$_4$ crystal produced from archaeological Pb operated as a cryogenic detector. The crystal internal radioactive contaminations are: $^{232}$Th $<$40 $\mu$Bq/kg, $^{238}$U $<$30 $\mu$Bq/kg, $^{226}$Ra 1.3 mBq/kg and $^{210}$Pb 22.5 mBq/kg. We present also a background projection for the final experiment and possible mitigation strategies for further background suppression. The achieved results demonstrate the feasibility of realizing this new class of detectors., Comment: New analysis with high statistic

Many low-threshold experiments observe sharply rising event rates of yet unknown origins below a few hundred eV, and larger than expected from known backgrounds. Due to the significant impact of this excess on the dark matter or neutrino sensitivity of these experiments, a collective effort has been started to share the knowledge about the individual observations. For this, the EXCESS Workshop was initiated. In its first iteration in June 2021, ten rare event search collaborations contributed to this initiative via talks and discussions. The contributing collaborations were CONNIE, CRESST, DAMIC, EDELWEISS, MINER, NEWS-G, NUCLEUS, RICOCHET, SENSEI and SuperCDMS. They presented data about their observed energy spectra and known backgrounds together with details about the respective measurements. In this paper, we summarize the presented information and give a comprehensive overview of the similarities and differences between the distinct measurements. The provided data is furthermore publicly available on the workshop's data repository together with a plotting tool for visualization., Comment: 44 pages, 20 figures; Editors: A. Fuss, M. Kaznacheeva, F. Reindl, F. Wagner; updated copyright statements and funding information

It is well-known that the dimension of optimal anticodes in the rank-metric is divisible by the maximum m between the number of rows and columns of the matrices. Moreover, for a fixed k divisible by m, optimal rank-metric anticodes are the codes with least maximum rank, among those of dimension k. In this paper, we study the family of rank-metric codes whose dimension is not divisible by m and whose maximum rank is the least possible for codes of that dimension, according to the Anticode bound. As these are not optimal anticodes, we call them quasi optimal anticodes (qOACs). In addition, we call dually qOAC a qOAC whose dual is also a qOAC. We describe explicitly the structure of dually qOACs and compute their weight distributions, generalized weights, and associated q-polymatroids.