Search

Spherical proportional counters (SPCs) are gaseous particle detectors sensitive to single ionization electrons in their target media, with large detector volumes and low background rates. The $\mbox{NEWS-G}$ collaboration employs this technology to search for low-mass dark matter, having previously performed searches with detectors at the Laboratoire Souterrain de Modane (LSM), including a recent campaign with a 135 cm diameter SPC filled with methane. While in situ calibrations of the detector response were carried out at the LSM, measurements of the mean ionization yield and fluctuations of methane gas in SPCs were performed using a 30 cm diameter detector. The results of multiple measurements taken at different operating voltages are presented. A UV laser system was used to measure the mean gas gain of the SPC, along with $\mathrm{^{37}Ar}$ and aluminum-fluorescence calibration sources. These measurements will inform the energy response model of future operating detectors., Comment: 11 pages, 8 figures

Mueller matrix polarimetry captures essential information about polarized light interactions with a sample, presenting unique challenges for data augmentation in deep learning due to its distinct structure. While augmentations are an effective and affordable way to enhance dataset diversity and reduce overfitting, standard transformations like rotations and flips do not preserve the polarization properties in Mueller matrix images. To this end, we introduce a versatile simulation framework that applies physically consistent rotations and flips to Mueller matrices, tailored to maintain polarization fidelity. Our experimental results across multiple datasets reveal that conventional augmentations can lead to misleading results when applied to polarimetric data, underscoring the necessity of our physics-based approach. In our experiments, we first compare our polarization-specific augmentations against real-world captures to validate their physical consistency. We then apply these augmentations in a semantic segmentation task, achieving substantial improvements in model generalization and performance. This study underscores the necessity of physics-informed data augmentation for polarimetric imaging in deep learning (DL), paving the way for broader adoption and more robust applications across diverse research in the field. In particular, our framework unlocks the potential of DL models for polarimetric datasets with limited sample sizes. Our code implementation is available at github.com/hahnec/polar_augment., Comment: preprint

For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of the ring. Each such function gives rise to a system of local depth conditions which describes the left-hand class in the corresponding cotorsion pair. Furthermore, we show that these cotorsion pairs correspond by explicit duality to hereditary Tor-pairs generated by modules of finite flat dimension., Comment: 27 pages

To search for $\beta\beta0\nu$ decay with unprecedented sensitivity, the R2D2 collaboration is developing a radial time projection chamber with a fiducial mass of half a ton of 136Xe at high pressure. The various approaches implemented to eliminate the radioactive background are presented in terms of detector design, topological recognition of interactions, and event energy reconstruction. The developed tools allow for the disentangling of the sought-after signal from the background, and the projected sensitivity after ten years of data taking yields a half-life limit exceeding $10^{27}$ years, along with a constraint on the effective neutrino mass $m_{\beta\beta}$, sufficient to exclude the inverted mass hierarchy region.

Models for resident infectious diseases, like the SIRS model, may settle into an endemic state with constant numbers of susceptible ($S$), infected ($I$) and recovered ($R$) individuals, where recovered individuals attain a temporary immunity to reinfection. For many infectious pathogens, infection dynamics may also show periodic outbreaks corresponding to a limit cycle in phase space. One way to reproduce oscillations in SIRS models is to include a non-exponential dwell-time distribution in the recovered state. Here, we study a SIRS model with a step-function-like kernel for the immunity time, mapping out the model's full phase diagram. Using the kernel series framework, we are able to identify the onset of periodic outbreaks when successively broadening the step-width. We further investigate the shape of the outbreaks, finding that broader steps cause more sinusoidal oscillations while more uniform immunity time distributions are related to sharper outbreaks occurring after extended periods of low infection activity. Our main results concern recovery distributions characterized by a single dominant timescale. We also consider recovery distributions with two timescales, which may be observed when two or more distinct recovery processes co-exist. Surprisingly, two qualitatively different limit cycles are found to be stable in this case, with only one of the two limit cycles emerging via a standard supercritical Hopf bifurcation.

Safe reinforcement learning (RL) is a promising approach for many real-world decision-making problems where ensuring safety is a critical necessity. In safe RL research, while expected cumulative safety constraints (ECSCs) are typically the first choices, chance constraints are often more pragmatic for incorporating safety under uncertainties. This paper proposes a \textit{flipping-based policy} for Chance-Constrained Markov Decision Processes (CCMDPs). The flipping-based policy selects the next action by tossing a potentially distorted coin between two action candidates. The probability of the flip and the two action candidates vary depending on the state. We establish a Bellman equation for CCMDPs and further prove the existence of a flipping-based policy within the optimal solution sets. Since solving the problem with joint chance constraints is challenging in practice, we then prove that joint chance constraints can be approximated into Expected Cumulative Safety Constraints (ECSCs) and that there exists a flipping-based policy in the optimal solution sets for constrained MDPs with ECSCs. As a specific instance of practical implementations, we present a framework for adapting constrained policy optimization to train a flipping-based policy. This framework can be applied to other safe RL algorithms. We demonstrate that the flipping-based policy can improve the performance of the existing safe RL algorithms under the same limits of safety constraints on Safety Gym benchmarks., Comment: Accepted to NeurIPS 2024

The NEWS-G direct detection experiment uses spherical proportional counters to search for light dark matter candidates. New results from a 10 day physics run with a $135\,\mathrm{cm}$ in diameter spherical proportional counter at the Laboratoire Souterrain de Modane are reported. The target consists of $114\,\mathrm{g}$ of methane, providing sensitivity to dark matter spin-dependent coupling to protons. New constraints are presented in the mass range $0.17$ to $1.2\,\mathrm{GeV/c^2}$, with a 90% confidence level cross-section upper limit of $30.9\,\mathrm{pb}$ for a mass of $0.76\,\mathrm{GeV/c^2}$., Comment: 7 pages, 3 figures

We propose an extension of the reinforcement learning architecture that enables moral decision-making of reinforcement learning agents based on normative reasons. Central to this approach is a reason-based shield generator yielding a moral shield that binds the agent to actions that conform with recognized normative reasons so that our overall architecture restricts the agent to actions that are (internally) morally justified. In addition, we describe an algorithm that allows to iteratively improve the reason-based shield generator through case-based feedback from a moral judge., Comment: 8 pages, 2 figures, Workshop paper accepted to FEAR24 (IFM Workshop)

In this paper, we present a novel method to compute the determinant of a link using Fourier-Hadamard transforms of Boolean functions. We also investigate the determinant of centrally symmetric links (a special class of strong achiral links). In particular, we show that the determinant of a centrally symmetric link with an even number of components is equals zero.

Locomotion may be induced on three levels. On a classical level, actuators and limbs follow the sequence of open-loop top-down control signals they receive. Limbs may move alternatively on their own, which implies that interlimb coordination must be mediated either by the body or via decentralized inter-limb signaling. In this case, when embodiment is present, two types of controllers are conceivable for the actuators of the limbs, local pacemaker circuits and control principles based on self-organized embodiment. The latter, self-organized control, is based on limit cycles and chaotic attractors that emerge within the feedback loop composed of controller, body, and environment. For this to happen, the sensorimotor loop must be locally closed, e.g. via propriosensation. Here we review the progress made within the framework of self-organized embodiment, with a particular focus on the concept of attractoring. This concept characterizes situations when sets of attractors combining discrete and continuous spectra are available as motor primitives for higher-order control schemes, such as kick control. In particular, we show that a simple generative principle allows for the robust formulation of self-organized embodiment. Based on the recurrent alternation between measuring the actual status of an actuator and providing a target for the actuator to achieve in the next step, we find that the mechanism leads to compliant locomotion for a range of simulated and real-world robots, which include barrel- and sphere-shaped agents, as well as wheeled and legged robots., Comment: Contains embedded links to videos illustrating emerging locomotion, 16 pages, 6 figures

This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set for constraint tightening with the help of the computation of the minimal robust positively invariant set, the chance constraints are guaranteed, assuming only the mean and covariance of the disturbance distribution are given. The resulting online optimization problem is a standard strictly quadratic programming, just like in conventional model predictive control with recursive feasibility and stability guarantees and is simple to implement. A numerical example is provided to illustrate the proposed method., Comment: This paper was accepted for publication in CDC 2024

Attention involves comparing query and key vectors in terms of a scalar product, $\mathbf{Q}^T\mathbf{K}$, together with a subsequent softmax normalization. Classicaly, parallel/orthogonal/antiparallel queries and keys lead to large/intermediate/small attention weights. Here we study expressive attention (EA), which is based on $(\mathbf{Q}^T\mathbf{K})^2$, the squared dot product. In this case attention is enhanced when query and key are either parallel or antiparallel, and suppressed for orthogonal configurations. For a series of autoregressive prediction tasks, we find that EA performs at least as well as the standard mechanism, dot-product attention (DPA). Increasing task complexity, EA is observed to outperform DPA with increasing margins, which also holds for multi-task settings. For a given model size, EA manages to achieve 100\% performance for a range of complexity levels not accessible to DPA.

Markov Decision Processes (MDPs) offer a fairly generic and powerful framework to discuss the notion of optimal policies for dynamic systems, in particular when the dynamics are stochastic. However, computing the optimal policy of an MDP can be very difficult due to the curse of dimensionality present in solving the underlying Bellman equations. Model Predictive Control (MPC) is a very popular technique for building control policies for complex dynamic systems. Historically, MPC has focused on constraint satisfaction and steering dynamic systems towards a user-defined reference. More recently, Economic MPC was proposed as a computationally tractable way of building optimal policies for dynamic systems. When stochsaticity is present, economic MPC is close to the MDP framework. In that context, Economic MPC can be construed as attractable heuristic to provide approximate solutions to MDPs. However, there is arguably a knowledge gap in the literature regarding these approximate solutions and the conditions for an MPC scheme to achieve closed-loop optimality. This chapter aims to clarify this approximation pedagogically, to provide the conditions for MPC to deliver optimal policies, and to explore some of their consequences.

In this chapter, we report on our experience with domestic flexible electric energy demand based on a regular commercial (HVAC)-based heating system in a house. Our focus is on investigating the predictability of the energy demand of the heating system and of the thermal response when varying the heating system settings. Being able to form such predictions is crucial for most flexible demand algorithms. We will compare several methods for predicting the thermal and energy response, which either gave good results or which are currently promoted in the literature for controlling buildings. We will report that the stochasticity of a house response is -- in our experience -- the main difficulty in providing domestic flexible demand from heating. The experiments were carried out on a regular house in Norway, equipped with four air-to-air Mitsubishi heat pumps and a high-efficiency balanced ventilation system. The house was equipped with multiple IoT-based climate sensors, real-time power measurement, and the possibility to drive the HVAC system via the IoT. The house is operating on the spot market (Nord Pool NO3) and is exposed to a peak energy demand penalty. Over a period of three years, we have collected data on the house (temperatures, humidity, air quality), real-time power and hourly energy consumption, while applying various flexible demand algorithms responding to the local energy costs. This has produced large variations in the settings of the heating system and energy demand, resulting in rich data for investigating the house response. This chapter aims at providing important insights on providing flexible demand from houses in cold climates.

The factors contributing to the persistence and stability of life are fundamental for understanding complex living systems. Organisms are commonly challenged by harsh and fluctuating environments that are suboptimal for growth and reproduction, which can lead to extinction. Species often contend with unfavorable and noisy conditions by entering a reversible state of reduced metabolic activity, a phenomenon known as dormancy. Here, we develop Spore Life, a model to investigate the effects of dormancy on population dynamics. It is based on Conway's Game of Life, a deterministic cellular automaton where simple rules govern the metabolic state of an individual based on the metabolic state of its neighbors. For individuals that would otherwise die, Spore Life provides a refuge in the form of an inactive state. These dormant individuals (spores) can resuscitate when local conditions improve. The model includes a parameter alpha that controls the survival probability of spores, interpolating between Game of Life (alpha = 0) and Spore Life (alpha = 1), while capturing stochastic dynamics in the intermediate regime (0 < alpha < 1). In addition to identifying the emergence of unique periodic configurations, we find that spore survival increases the average number of active individuals and buffers populations from extinction. Contrary to expectations, the stabilization of the population is not the result of a large and long-lived seed bank. Instead, the demographic patterns in Spore Life only require a small number of resuscitation events. Our approach yields novel insight into what is minimally required for the emergence of complex behaviors associated with dormancy and the seed banks that they generate.

In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme on the real system trajectories. However, these predictions may not accurately capture the real system dynamics, for e.g., due to stochasticity, resulting in sub-optimal control policies. This lack of optimality is a critical issue in case of problems with economic objectives. We address this by providing sufficient conditions on the underlying prediction scheme such that a Predictive Controller can achieve closed-loop optimality. However, these conditions do not readily extend to Data-Driven Predictive Control. In this context of closed-loop optimality, we conclude that the factor distinguishing the approaches within Data-Driven Predictive Control is if they can be cast as a sequential decision-making process or not, rather than the dichotomy of model-based vs. model-free. Furthermore, we show that the conventional approach of improving the prediction accuracy from data may not guarantee optimality.

The current experiments searching for neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay also collect large statistics of Standard Model allowed two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay events. These can be used to search for Beyond Standard Model (BSM) physics via $2\nu\beta\beta$ decay spectral distortions. $^{100}$Mo has a natural advantage due to its relatively short half-life, allowing higher $2\nu\beta\beta$ decay statistics at equal exposures compared to the other isotopes. We demonstrate the potential of the dual read-out bolometric technique exploiting a $^{100}$Mo exposure of 1.47 kg $\times$ y, acquired in the CUPID-Mo experiment at the Modane underground laboratory (France). We set limits on $0\nu\beta\beta$ decays with the emission of one or more Majorons, on $2\nu\beta\beta$ decay with Lorentz violation, and $2\nu\beta\beta$ decay with a sterile neutrino emission. In this analysis, we investigate the systematic uncertainty induced by modeling the $2\nu\beta\beta$ decay spectral shape parameterized through an improved model, an effect never considered before. This work motivates searches for BSM processes in the upcoming CUPID experiment, which will collect the largest amount of $2\nu\beta\beta$ decay events among the next-generation experiments.

We study the extremes of variable speed branching Brownian motion (BBM) where the time-dependent "speed functions", which describe the time-inhomogeneous variance, converge to the identity function. We consider general speed functions lying strictly below their concave hull and piecewise linear, concave speed functions. In the first case, the log-correction for the order of the maximum depends only on the rate of convergence of the speed function near 0 and 1 and exhibits a smooth interpolation between the correction in the i.i.d. case, $\frac{1}{2\sqrt{2}} \ln t$, and that of standard BBM, $\frac{3}{2\sqrt{2}} \ln t$. In the second case, we describe the order of the maximum in dependence of the form of speed function and show that any log-correction larger than $\frac{3}{2\sqrt{2}} \ln t$ can be obtained. In both cases, we prove that the limiting law of the maximum and the extremal process essentially coincide with those of standard BBM, using a first and second moment method which relies on the localisation of extremal particles. This extends the results of Bovier and Hartung for two-speed BBM., Comment: 45 pages, 2 figures

As part of the R2D2 (Rare Decays with Radial Detector) R&D, the use of a gas detector with a spherical or cylindrical cathode, equipped with a single anode and operating at high pressure, was studied for the search of rare phenomena such as neutrinoless double-beta decay. The presented measurements were obtained with a cylindrical detector, covering gas pressures ranging from 1 to 10 bar in argon and 1 to 6 bar in xenon, using both a point-like source of $^{210}$Po (5.3 MeV $\alpha$ ) and a diffuse source of $^{222}$Rn (5.5 MeV $\alpha$). Analysis and interpretation of the data were developed using the anodic current waveform. Similar detection performances were achieved with both gases, and comparable energy resolutions were measured with both sources. As long as the purity of the gas was sufficient, no significant degradation of the measured energy was observed by increasing the pressure. At the highest operating pressure, an energy resolution better than 1.5% full-width at half-maximum (FWHM) was obtained for both gaseous media, although optimal noise conditions were not reached.

Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that the uncertainties are independent of the state. However, this assumption falls short in many real-world applications, where uncertainties are state-dependent, referred to as contextual uncertainties. This paper formulates the problem of computing probabilistic reachable sets of stochastic nonlinear states with contextual uncertainties by seeking minimum-volume polynomial sublevel sets with contextual chance constraints. The formulated problem cannot be solved by the existing sample-based approximation method since the existing methods do not consider the conditional probability densities. To address this, we propose a consistent sample approximation of the original problem by leveraging the conditional density estimation and resampling. The obtained approximate problem is a tractable optimization problem. Additionally, we prove the almost uniform convergence of the proposed sample-based approximation, showing that it gives the optimal solution almost consistently with the original ones. Through a numerical example, we evaluate the effectiveness of the proposed method against existing approaches, highlighting its capability to significantly reduce the bias inherent in sample-based approximation without considering a conditional probability density.

Neuro-oncological surgery is the primary brain cancer treatment, yet it faces challenges with gliomas due to their invasiveness and the need to preserve neurological function. Hence, radical resection is often unfeasible, highlighting the importance of precise tumor margin delineation to prevent neurological deficits and improve prognosis. Imaging Mueller polarimetry, an effective modality in various organ tissues, seems a promising approach for tumor delineation in neurosurgery. To further assess its use, we characterized the polarimetric properties by analysing 45 polarimetric measurements of 27 fresh brain tumor samples, including different tumor types with a strong focus on gliomas. Our study integrates a wide-field imaging Mueller polarimetric system and a novel neuropathology protocol, correlating polarimetric and histological data for accurate tissue identification. An image processing pipeline facilitated the alignment and overlay of polarimetric images and histological masks. Variations in depolarization values were observed for grey and white matter of brain tumor tissue, while differences in linear retardance were seen only within white matter of brain tumor tissue. Notably, we identified pronounced optical axis azimuth randomization within tumor regions. This study lays the foundation for machine learning-based brain tumor segmentation algorithms using polarimetric data, facilitating intraoperative diagnosis and decision making., Comment: 12 pages, 9 figures. This work has been submitted to the IEEE for possible publication

Wide-field imaging Mueller polarimetry is a revolutionary, label-free, and non-invasive modality for computer-aided intervention: in neurosurgery it aims to provide visual feedback of white matter fibre bundle orientation from derived parameters. Conventionally, robust polarimetric parameters are estimated after averaging multiple measurements of intensity for each pair of probing and detected polarised light. Long multi-shot averaging, however, is not compatible with real-time in-vivo imaging, and the current performance of polarimetric data processing hinders the translation to clinical practice. A learning-based denoising framework is tailored for fast, single-shot, noisy acquisitions of polarimetric intensities. Also, performance-optimised image processing tools are devised for the derivation of clinically relevant parameters. The combination recovers accurate polarimetric parameters from fast acquisitions with near-real-time performance, under the assumption of pseudo-Gaussian polarimetric acquisition noise. The denoising framework is trained, validated, and tested on experimental data comprising tumour-free and diseased human brain samples in different conditions. Accuracy and image quality indices showed significant improvements on testing data for a fast single-pass denoising versus the state-of-the-art and high polarimetric image quality standards. The computational time is reported for the end-to-end processing. The end-to-end image processing achieved real-time performance for a localised field of view. The denoised polarimetric intensities produced visibly clear directional patterns of neuronal fibre tracts in line with reference polarimetric image quality standards; directional disruption was kept in case of neoplastic lesions. The presented advances pave the way towards feasible oncological neurosurgical translations of novel, label free, interventional feedback.

BINGO is a project aiming to set the grounds for large-scale bolometric neutrinoless double-beta-decay experiments capable of investigating the effective Majorana neutrino mass at a few meV level. It focuses on developing innovative technologies (a detector assembly, cryogenic photodetectors and active veto) to achieve a very low background index, of the order of $10^{-5}$ counts/(keV kg yr) in the region of interest. The BINGO demonstrator, called MINI-BINGO, is designed to investigate the promising double-beta-decay isotopes $^{100}$Mo and $^{130}$Te and it will be composed of Li$_2$MoO$_4$ and TeO$_2$ crystals coupled to bolometric light detectors and surrounded by a Bi$_4$Ge$_3$O$_{12}$-based veto. This will allow us to reject a significant background in bolometers caused by surface contamination from $\alpha$-active radionuclides by means of light yield selection and to mitigate other sources of background, such as surface contamination from $\beta$-active radionuclides, external $\gamma$ radioactivity, and pile-up due to random coincidence of background events. This paper describes an R\&D program towards the BINGO goals, particularly focusing on the development of an innovative assembly designed to reduce the passive materials within the line of sight of the detectors, which is expected to be a dominant source of background in next-generation bolometric experiments. We present the performance of two prototype modules -- housing four cubic (4.5-cm side) Li$_2$MoO$_4$ crystals in total -- operated in the Canfranc underground laboratory in Spain within a facility developed for the CROSS double-beta-decay experiment., Comment: Submitted to Nucl. Instr. Meth. A; 28 pages, 11 figures, 4 tables

In this paper, we report on a tabletop experiment studying neutron scattering in a Spherical Proportional Counter using an Am-Be source. Systematic studies were carried out to investigate the effect of gas mixture, pressure, operating voltage, and sphere size on the drift time-rise time relationship of the signal in a spherical proportional counter. Our experimental results showed good agreement with MagBoltz simulations. These findings are a crucial step towards measuring the quenching factor in gases using a neutron beam for the New Experiments With Spheres-Gas (NEWS-G) experiment and has important implications for the development of neutron detection techniques and their potential applications in nuclear and particle physics.

Machine learning models are widely used, but can also often be wrong. Users would benefit from a reliable indication of whether a given output from a given model should be trusted, so a rational decision can be made whether to use the output or not. For example, outputs can be associated with a confidence measure; if this confidence measure is strongly associated with likelihood of correctness, then the model is said to be well-calibrated. A well-calibrated confidence measure can serve as a basis for rational, graduated decision-making on how much review and care is needed when using generated code. Calibration has so far been studied in mostly non-generative (e.g. classification) settings, especially in software engineering. However, generated code can quite often be wrong: Given generated code, developers must decide whether to use directly, use after varying intensity of careful review, or discard model-generated code. Thus, calibration is vital in generative settings. We make several contributions. We develop a framework for evaluating the calibration of code-generating models. We consider several tasks, correctness criteria, datasets, and approaches, and find that, by and large, generative code models we test are not well-calibrated out of the box. We then show how calibration can be improved using standard methods, such as Platt scaling. Since Platt scaling relies on the prior availability of correctness data, we evaluate the applicability and generalizability of Platt scaling in software engineering, discuss settings where it has good potential for practical use, and settings where it does not. Our contributions will lead to better-calibrated decision-making in the current use of code generated by language models, and offers a framework for future research to further improve calibration methods for generative models in software engineering., Comment: Published in ICSE'25

With the increasing number of fast-electric vehicle charging stations (fast-EVCSs) and the popularization of information technology, electricity price competition between fast-EVCSs is highly expected, in which the utilization of public and/or privacy-preserved information will play a crucial role. Self-interest electric vehicle (EV) users, on the other hand, try to select a fast-EVCS for charging in a way to maximize their utilities based on electricity price, estimated waiting time, and their state of charge. While existing studies have largely focused on finding equilibrium prices, this study proposes a personalized dynamic pricing policy (PeDP) for a fast-EVCS to maximize revenue using a reinforcement learning (RL) approach. We first propose a multiple fast-EVCSs competing simulation environment to model the selfish behavior of EV users using a game-based charging station selection model with a monetary utility function. In the environment, we propose a Q-learning-based PeDP to maximize fast-EVCS' revenue. Through numerical simulations based on the environment: (1) we identify the importance of waiting time in the EV charging market by comparing the classic Bertrand competition model with the proposed PeDP for fast-EVCSs (from the system perspective); (2) we evaluate the performance of the proposed PeDP and analyze the effects of the information on the policy (from the service provider perspective); and (3) it can be seen that privacy-preserved information sharing can be misused by artificial intelligence-based PeDP in a certain situation in the EV charging market (from the customer perspective).

In this paper we evaluated the performance of a reconfigurable intelligent surface tested with a fifth generation signal provided by a commercial fifth generation base station. We adopted a reverberation chamber as a real life propagating environment. Tests were conducted at the millimeter wave frequency range. This measurement campaign was carried out under the H2020 European project RISE-6G and a collaboration program between TIM S.p.A., Nokia and Universit\`a Politecnica delle Marche., Comment: Accepted at EuCAP 2024

Let $R$ be a commutative noetherian ring. We prove that the class of modules of projective dimension bounded by $k$ is of finite type if and only if $R$ satisfies Serre's condition $(S_k)$. In particular, this answers positively a question of Bazzoni and Herbera in the specific setting of a Gorenstein ring. Applying similar techniques, we also show that the $k$-dimensional version of the Govorov-Lazard Theorem holds if and only if $R$ satisfies the "almost" Serre condition $(C_{k+1})$.

Let $p$ be a prime, $W$ the ring of Witt vectors of a perfect field $k$ of characteristic $p$ and $\zeta$ a primitive $p$th root of unity. We introduce a new notion of calculus over $W$ that we call absolute calculus. It may be seen as a singular version of the $q$-calculus used in previous work, in the sense that the role of the coordinate is now played by $q$ itself. We show that what we call a weakly nilpotent absolute connection on a finite free module is equivalent to a prismatic vector bundle on $W[\zeta]$. As a corollary of a theorem of Bhatt and Scholze, we finally obtain that an absolute connection with a frobenius structure on a finite free module is equivalent to a lattice in a crystalline representation. We also consider the case of de Rham prismatic crystals as well as Hodge-Tate prismatic crystals.