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In this paper, we model the plasma environment of Ganymede by means of a collisionless test particle simulation. By coupling the outputs from a DSMC simulation of Ganymede's exosphere (i.e. number density profiles of neutral species such as $\mathrm{H}$, $\mathrm{H_2}$, $\mathrm{O}$, $\mathrm{HO}$, $\mathrm{H_2O}$, $\mathrm{O_2}$ for which we provide parametrisation) with those of a MagnetoHydroDynamic simulation of the interaction between Ganymede and the Jovian plasma (i.e. electric and magnetic fields), we perform a comparison between simulated ion plasma densities and ion energy spectra with those observed in-situ during 6 close flybys of Ganymede by the Galileo spacecraft. We find that not only our test particle simulation sometimes can well reproduce the in-situ ion number density measurement, but also the dominant ion species during these flybys are $\mathrm{H_2^+}$, $\mathrm{O_2^+}$, and occasionally $\mathrm{H_2O^+}$. Although the observed ion energy spectra cannot be reproduced exactly, the simulated ion energy spectra exhibit similar trends to those observed near the closest approach and near the magnetopause crossings but at lower energies. We show that the neutral exosphere plays an important role in supplying plasma to Ganymede's magnetised environment and that additional mechanisms may be at play to energise/accelerate newborn ions from the neutral exosphere., Comment: accepted for publication in MNRAS

We study the two-dimensional extended Hubbard model on a square lattice and incorporate spin-differentiated nearest neighbor (NN) interactions where the equal-spin ($V_{uu}$) and unequal-spin ($V_{ud}$) terms are independently tuned parameters. We compute single-particle excitations as well as static spin and pairing susceptibilities perturbatively up to the fourth order within the thermodynamic limit and at a finite fixed temperature. By explicitly encoding a ferromagnetic-like NN interaction ($V_{uu} < V_{ud}$), we induce a competition among the uniform $q = (0,0)$, collinear $q = (\pi,0)$, and staggered $q = (\pi,\pi)$ spin excitations. This results in the formation of short-ranged $2\times 2$ ferromagnetic plaquettes arranged in staggered or striped patterns. Kinetic frustration in hopping, both within and between these plaquettes, manifests in single-particle properties, resulting in a reduction of bandwidth and ultimately triggering a Lifshitz transition to quasi-one-dimensional bands. Furthermore, an attractive effective interaction within the localized ferromagnetic plaquette results in the emergence of equal-spin triplet $p$-wave pairing. We demonstrate that sufficiently strong magnetic fluctuations, even at finite length scales, can significantly influence single-particle and pairing properties without breaking translational symmetry. Our approach provides a novel pathway to realize a variety of rich magnetic phases and Fermi surface reconstruction driven by interactions in the absence of explicit geometric frustration., Comment: 10 pages, 9 figures

With today's multi-petawatt lasers, testing quantum electrodynamics (QED) in the strong field regime, where the electric field exceeds the Schwinger critical field in the rest frame of an electron, becomes within reach. Inverse Compton scattering of an intense laser pulse off a high-energy electron beam is the mainstream approach, resulting in the emission of high-energy photons that can decay into Breit-Wheeler electron-positron pairs. Here, we demonstrate experimentally that very high energy photons can be generated in a self-aligned single-laser Compton scattering setup, combining a laser-plasma accelerator and a plasma mirror. Reaching up to the GeV scale, photon emission via nonlinear Compton scattering exhibits a nonclassical scaling in the experiment that is consistent with electric fields reaching up to a fraction $\chi\simeq0.3$ of the Schwinger field in the electron rest frame. These foolproof collisions guaranteed by automatic laser-electron overlap provide a new approach for precise investigations of strong-field QED processes.

The availability of pre-trained models (PTMs) has enabled faster deployment of machine learning across applications by reducing the need for extensive training. Techniques like quantization and distillation have further expanded PTM applicability to resource-constrained IoT hardware. Given the many PTM options for any given task, engineers often find it too costly to evaluate each model's suitability. Approaches such as LogME, LEEP, and ModelSpider help streamline model selection by estimating task relevance without exhaustive tuning. However, these methods largely leave hardware constraints as future work-a significant limitation in IoT settings. In this paper, we identify the limitations of current model recommendation approaches regarding hardware constraints and introduce a novel, hardware-aware method for PTM selection. We also propose a research agenda to guide the development of effective, hardware-conscious model recommendation systems for IoT applications., Comment: Accepted at SERP4IOT'25

We study the maximum and minimum occupancy fraction of the antiferromagnetic Ising model in regular graphs. The minimizing problem is known to determine a computational threshold in the complexity of approximately sampling from the Ising model at a given magnetization, and our results determine this threshold for nearly the entire relevant parameter range in the case $\Delta=3$. A small part of the parameter range lies outside the reach of our methods, and it seems challenging to extend our techniques to larger $\Delta$.

Exciton-polariton condensation occurs at the extrema of the underlying dispersion where the density of states diverges and carriers can naturally accumulate. The existence of multiple such points leads to coupling and competition between the associated modes and dynamical redistribution of the carriers in the dispersion. Here, we directly engineer the above situation via subwavelength periodic patterning of a two-dimensional nanostructure. This leads to multimode condensation into a pair of symmetric condensates that form at high-momenta, accidental-coupling points, and a high-symmetry $\Gamma$-point with a bound-in-the-continuum (BiC) state. The dynamical behaviour of the system reveals the non-simultaneous appearance of these condensates and the interplay of non-trivial gain and relaxation mechanisms. We fully characterise the quasi-static and dynamical regime of this artificial crystal and the properties of the different condensates. This understanding is necessary when band-structure engineering techniques are used to achieve precise control of condensate formation with given energy and momentum.

This paper addresses the critical issue of psychological safety in the design and operation of autonomous vehicles, which are increasingly integrated with artificial intelligence technologies. While traditional safety standards focus primarily on physical safety, this paper emphasizes the psychological implications that arise from human interactions with autonomous vehicles, highlighting the importance of trust and perceived risk as significant factors influencing user acceptance. Through a review of existing safety techniques, the paper defines psychological safety in the context of autonomous vehicles, proposes a risk model to identify and assess psychological risks, and adopts a system-theoretic analysis method. The paper illustrates the potential psychological hazards using a scenario involving a family's experience with an autonomous vehicle, aiming to systematically evaluate situations that could lead to psychological harm. By establishing a framework that incorporates psychological safety alongside physical safety, the paper contributes to the broader discourse on the safe deployment of autonomous vehicle and aims to guide future developments in user-cantered design and regulatory practices.

Gatemons are superconducting qubits resembling transmons, with a gate-tunable semiconducting weak link as the Josephson element. Here, we report a gatemon device featuring an aluminum microwave circuit on a Ge/SiGe heterostructure embedding a Ge quantum well. Owing to the superconducting proximity effect, the high-mobility two-dimensional hole gas confined in this well provides a gate-tunable superconducting weak link between two Al contacts. We perform Rabi oscillation and Ramsey interference measurements, demonstrate the gate-voltage dependence of the qubit frequency, and measure the qubit anharmonicity. We find relaxation times T$_{1}$ up to 119 ns, and Ramsey coherence times T$^{*}_{2}$ up to 70 ns, and a qubit frequency gate-tunable over 3.5 GHz. The reported proof-of-concept reproduces the results of a very recent work [Sagi et al., Nat. Commun. 15, 6400 (2024)] using similar Ge/SiGe heterostructures thereby validating a novel platform for the development of gatemons and parity-protected cos(2$\phi$) qubits.

Within the field of hierarchical modelling, little attention is paid to micro-macro models: those in which group-level outcomes are dependent on covariates measured at the level of individuals within groups. Although such models are perhaps underrepresented in the literature, they have applications in economics, epidemiology, and the social sciences. Despite the strong mathematical similarities between micro-macro and measurement error models, few efforts have been made to apply the much better-developed methodology of the latter to the former. Here, we present a new empirical Bayesian technique for micro-macro data, called FRODO (Functional Regression On Densities of Observations). The method jointly infers group-specific densities for multilevel covariates and uses them as functional predictors in a functional linear regression, resulting in a model that is analogous to a generalized additive model (GAM). In doing so, it achieves a level of generality comparable to more sophisticated methods developed for errors-in-variables models, while further leveraging the larger group sizes characteristic of multilevel data to provide richer information about the within-group covariate distributions. After explaining the hierarchical structure of FRODO, its power and versatility are demonstrated on several simulated datasets, showcasing its ability to accommodate a wide variety of covariate distributions and regression models.

PAC-Bayesian and Sample Compress learning frameworks are instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that outputs the parameters of a downstream predictor from a dataset input. The originality of our approach lies in the investigated hypernetwork architectures that encode the dataset before decoding the parameters: (1) a PAC-Bayesian encoder that expresses a posterior distribution over a latent space, (2) a Sample Compress encoder that selects a small sample of the dataset input along with a message from a discrete set, and (3) a hybrid between both approaches motivated by a new Sample Compress theorem handling continuous messages. The latter theorem exploits the pivotal information transiting at the encoder-decoder junction to compute generalization guarantees for each downstream predictor obtained by our meta-learning scheme., Comment: Accepted at the NeurIPS 2024 workshop on Compression in Machine Learning

In this work, we provide upper bounds on the risk of mixtures of experts by imposing local differential privacy (LDP) on their gating mechanism. These theoretical guarantees are tailored to mixtures of experts that utilize the one-out-of-$n$ gating mechanism, as opposed to the conventional $n$-out-of-$n$ mechanism. The bounds exhibit logarithmic dependence on the number of experts, and encapsulate the dependence on the gating mechanism in the LDP parameter, making them significantly tighter than existing bounds, under reasonable conditions. Experimental results support our theory, demonstrating that our approach enhances the generalization ability of mixtures of experts and validating the feasibility of imposing LDP on the gating mechanism.

As small radiation fields play an ever-increasing role in radiation therapy, accurate dosimetry of these fields becomes critical to ensure high quality dose calculation and treatment optimization. The PRB-0002, a new plastic scintillation detector (PSD) part of the Hyperscint RP-200 dosimetric platform from Medscint, can potentially facilitate small field measurements. In this work our objective is twofold: first we perform a detailed characterization of the field output correction factors of the PRB-0002 over a wide range of field sizes; second we demonstrate how this PSD can be used to determine the field output correction factors for other small field detectors. Uncertainties were carefully considered and a detailed uncertainty budget is provided. EGSnrc Monte Carlo simulations were conducted to determine the impact of detector composition, surrounding materials, dose averaging within the sensitive volume as well as ionization quenching. From these simulations, the field output correction factors of this PSD were determined. Then, by experimental comparisons, field output correction factors for 2 solid state detectors and 3 small volume ion chambers were. With PRB-0002, the material composition was found to be balanced with the ionization quenching making the field output correction factor near unity. For fields between 0.6 $\times$ 0.6 and 30 $\times$ 30~cm$^2$, the field output correction factors of the PRB-0002 were between 1.002 and 0.999 with a total uncertainty of 0.5 %. Analysis of the uncertainty budget showed that an overall uncertainty of 0.59% can be achieved for a 1 $\times$ 1~cm$^2$ using PRB-0002. We conclude that PRB-0002 is a near-ideal detector for small field dosimetry. Furthermore, it can be used to experimentally determine the field output correction factors of other dosimeters with great accuracy.

A search for proton decay into $e^+/\mu^+$ and a $\eta$ meson has been performed using data from a 0.373 Mton$\cdot$year exposure (6050.3 live days) of Super-Kamiokande. Compared to previous searches this work introduces an improved model of the intranuclear $\eta$ interaction cross section, resulting in a factor of two reduction in uncertainties from this source and $\sim$10\% increase in signal efficiency. No significant data excess was found above the expected number of atmospheric neutrino background events resulting in no indication of proton decay into either mode. Lower limits on the proton partial lifetime of $1.4\times\mathrm{10^{34}~years}$ for $p\rightarrow e^+\eta$ and $7.3\times\mathrm{10^{33}~years}$ for $p\rightarrow \mu^+\eta$ at the 90$\%$ C.L. were set. These limits are around 1.5 times longer than our previous study and are the most stringent to date.

Plant morphological traits, their observable characteristics, are fundamental to understand the role played by each species within their ecosystem. However, compiling trait information for even a moderate number of species is a demanding task that may take experts years to accomplish. At the same time, massive amounts of information about species descriptions is available online in the form of text, although the lack of structure makes this source of data impossible to use at scale. To overcome this, we propose to leverage recent advances in large language models (LLMs) and devise a mechanism for gathering and processing information on plant traits in the form of unstructured textual descriptions, without manual curation. We evaluate our approach by automatically replicating three manually created species-trait matrices. Our method managed to find values for over half of all species-trait pairs, with an F1-score of over 75%. Our results suggest that large-scale creation of structured trait databases from unstructured online text is currently feasible thanks to the information extraction capabilities of LLMs, being limited by the availability of textual descriptions covering all the traits of interest.

Radio-interferometry (RI) observes the sky at unprecedented angular resolutions, enabling the study of several far-away galactic objects such as galaxies and black holes. In RI, an array of antennas probes cosmic signals coming from the observed region of the sky. The covariance matrix of the vector gathering all these antenna measurements offers, by leveraging the Van Cittert-Zernike theorem, an incomplete and noisy Fourier sensing of the image of interest. The number of noisy Fourier measurements -- or visibilities -- scales as $\mathcal O(Q^2B)$ for $Q$ antennas and $B$ short-time integration (STI) intervals. We address the challenges posed by this vast volume of data, which is anticipated to increase significantly with the advent of large antenna arrays, by proposing a compressive sensing technique applied directly at the level of the antenna measurements. First, this paper shows that beamforming -- a common technique of dephasing antenna signals -- usually used to focus some region of the sky, is equivalent to sensing a rank-one projection (ROP) of the signal covariance matrix. We build upon our recent work arXiv:2306.12698v3 [eess.IV] to propose a compressive sensing scheme relying on random beamforming, trading the $Q^2$-dependence of the data size for a smaller number $N_{\mathrm p}$ ROPs. We provide image recovery guarantees for sparse image reconstruction. Secondly, the data size is made independent of $B$ by applying $N_{\mathrm m}$ Bernoulli modulations of the ROP vectors obtained for the STI. The resulting sample complexities, theoretically derived in a simpler case without modulations and numerically obtained in phase transition diagrams, are shown to scale as $\mathcal O(K)$ where $K$ is the image sparsity. This illustrates the potential of the approach.

Jupiter's icy moon Ganymede has a tenuous exosphere produced by sputtering and possibly sublimation of water ice. To date, only atomic hydrogen and oxygen have been directly detected in this exosphere. Here, we present observations of Ganymede's CO$_2$ exosphere obtained with the James Webb Space Telescope. CO$_2$ gas is observed over different terrain types, mainly over those exposed to intense Jovian plasma irradiation, as well as over some bright or dark terrains. Despite warm surface temperatures, the CO$_2$ abundance over equatorial subsolar regions is low. CO$_2$ vapor has the highest abundance over the north polar cap of the leading hemisphere, reaching a surface pressure of 1 pbar. From modeling we show that the local enhancement observed near 12 h local time in this region can be explained by the presence of cold traps enabling CO$_2$ adsorption. However, whether the release mechanism in this high-latitude region is sputtering or sublimation remains unclear. The north polar cap of the leading hemisphere also has unique surface-ice properties, probably linked to the presence of the large atmospheric CO2 excess over this region. These CO2 molecules might have been initially released in the atmosphere after the radiolysis of CO$_2$ precursors, or from the sputtering of CO$_2$ embedded in the H$_2$O ice bedrock. Dark terrains (regiones), more widespread on the north versus south polar regions, possibly harbor CO$_2$ precursors. CO$_2$ molecules would then be redistributed via cold trapping on ice-rich terrains of the polar cap and be diurnally released and redeposited on these terrains. Ganymede's CO$_2$ exosphere highlights the complexity of surface-atmosphere interactions on Jupiter's icy Galilean moons., Comment: 21 pages, 21 figures, Accepted as a Letter in Astronomy and Astrophysics

We introduce a novel mathematical framework for analyzing neural networks using tools from quiver representation theory. This framework enables us to quantify the similarity between a new data sample and the training data, as perceived by the neural network. By leveraging the induced quiver representation of a data sample, we capture more information than traditional hidden layer outputs. This quiver representation abstracts away the complexity of the computations of the forward pass into a single matrix, allowing us to employ simple geometric and statistical arguments in a matrix space to study neural network predictions. Our mathematical results are architecture-agnostic and task-agnostic, making them broadly applicable. As proof of concept experiments, we apply our results for the MNIST and FashionMNIST datasets on the problem of detecting adversarial examples on different MLP architectures and several adversarial attack methods. Our experiments can be reproduced with our \href{https://github.com/MarcoArmenta/Hidden-Activations-are-not-Enough}{publicly available repository}.

We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding their use in future studies. This discussion considers several choices related to the metric used to quantify these distances. We explore the differences between the various options, using a combination of analytical studies and simulated minimum-bias and multi-jet events. Making judicious choices when defining the metric and reference geometry can improve sensitivity to interesting signal features and reduce sensitivity to non-perturbative effects in QCD. The goal of this article is to provide a 'field guide' that can inform how choices made when defining a manifold distance can be tailored for the analysis at-hand., Comment: 28 pages, 15 figures

Ganymede's aurora are the product of complex interactions between its intrinsic magnetosphere and the surrounding Jovian plasma environment and can be used to derive both atmospheric composition and density. In this study, we analyzed a time-series of Ganymede's optical aurora taken with Keck I/HIRES during eclipse by Jupiter on 2021-06-08 UTC, one day after the Juno flyby of Ganymede. The data had sufficient signal-to-noise in individual 5-minute observations to allow for the first high cadence analysis of the spatial distribution of the aurora brightness and the ratio between the 630.0 and 557.7 nm disk-integrated auroral brightnesses -- a quantity diagnostic of the relative abundances of O, O$_2$ and H$_2$O in Ganymede's atmosphere. We found that the hemisphere closer to the centrifugal equator of Jupiter's magnetosphere (where electron number density is highest) was up to twice as bright as the opposing hemisphere. The dusk (trailing) hemisphere, subjected to the highest flux of charged particles from Jupiter's magnetosphere, was also consistently almost twice as bright as the dawn (leading) hemisphere. We modeled emission from simulated O$_2$ and H$_2$O atmospheres during eclipse and found that if Ganymede hosts an H$_2$O sublimation atmosphere in sunlight, it must collapse on a faster timescale than expected to explain its absence in our data given our current understanding of Ganymede's surface properties., Comment: 20 pages, 13 figures, 7 tables

The rapid advancement of machine learning technologies raises questions about the security of machine learning models, with respect to both training-time (poisoning) and test-time (evasion, impersonation, and inversion) attacks. Models performing image-related tasks, e.g. detection, and classification, are vulnerable to adversarial attacks that can degrade their performance and produce undesirable outcomes. This paper introduces a novel technique for anomaly detection in images called 2DSig-Detect, which uses a 2D-signature-embedded semi-supervised framework rooted in rough path theory. We demonstrate our method in adversarial settings for training-time and test-time attacks, and benchmark our framework against other state of the art methods. Using 2DSig-Detect for anomaly detection, we show both superior performance and a reduction in the computation time to detect the presence of adversarial perturbations in images.

Rydberg atom electric field sensors are tunable quantum sensors that can perform sensitive radio frequency (RF) measurements. Their qualities have piqued interest at longer wavelengths where their small size compares favorably to impedance-matched antennas. Here, we compare the signal detection sensitivity of cm-scale Rydberg sensors to similarly sized room-temperature electrically small antennas with active and passive receiver backends. We present and analyze effective circuit models for each sensor type, facilitating a fair sensitivity comparison for cm-scale sensors. We calculate that contemporary Rydberg sensor implementations are less sensitive than unmatched antennas with active amplification. However, we find that idealized Rydberg sensors operating with a maximized atom number and at the standard quantum limit may perform well beyond the capabilities of antenna-based sensors at room temperature, the sensitivities of both lying below typical atmospheric background noise., Comment: 6 pages, 3 figures

The difficulty of monitoring biodiversity at fine scales and over large areas limits ecological knowledge and conservation efforts. To fill this gap, Species Distribution Models (SDMs) predict species across space from spatially explicit features. Yet, they face the challenge of integrating the rich but heterogeneous data made available over the past decade, notably millions of opportunistic species observations and standardized surveys, as well as multimodal remote sensing data. In light of that, we have designed and developed a new European-scale dataset for SDMs at high spatial resolution (10--50m), including more than 10k species (i.e., most of the European flora). The dataset comprises 5M heterogeneous Presence-Only records and 90k exhaustive Presence-Absence survey records, all accompanied by diverse environmental rasters (e.g., elevation, human footprint, and soil) traditionally used in SDMs. In addition, it provides Sentinel-2 RGB and NIR satellite images with 10 m resolution, a 20-year time series of climatic variables, and satellite time series from the Landsat program. In addition to the data, we provide an openly accessible SDM benchmark (hosted on Kaggle), which has already attracted an active community and a set of strong baselines for single predictor/modality and multimodal approaches. All resources, e.g., the dataset, pre-trained models, and baseline methods (in the form of notebooks), are available on Kaggle, allowing one to start with our dataset literally with two mouse clicks.

We describe the design of a Thomson scattering (TS) diagnostic to be used on the SMall Aspect Ratio Tokamak (SMART). SMART is a spherical tokamak being commissioned in Spain that aims to explore positive triangularity (PT) and negative triangularity (NT) plasma scenarios at a low aspect ratio. The SMART TS diagnostic is designed to enable a wide range of electron temperature (1 eV to 1 keV) and density (0.5 - 10 $\times 10^{19} ~\rm{m^{ - 3}}$) measurements. A 2Joule laser operating at 1064 nm will be used to probe the electron temperature and density of the plasma. The laser is capable of operating in the burst mode at 1kHz, 2kHz, and 4kHz to investigate fast phenomena or at $30$ Hz to study 1 sec (or more) long discharges. The scattered light will be collected over an angular range of 60-120 degrees at 28 spatial points in the midplane covering the core region and edge plasma on both the low-field side (LFS) and the high-field side (HFS). Simulation data is used to determine the optimum location of Thomson scattering measurement points to effectively resolve the edge pedestal in the LFS and HFS regions under different triangularity conditions. Each scattering signal will be spectrally resolved on five wavelength channels of a polychromator to obtain the electron temperature measurement. We will also present a method to monitor in-situ laser alignment in the core during calibrations and plasma operations., Comment: Five pages and six figures

By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this approach we study the Bethe lattice and evaluate the second order self-energy for which reliable benchmarks exist. We show that, when evaluating diagrams on the Matsubara axis, the analytic sums of pole representations are extremely precise. We point out the absence of a numerical sign problem in the evaluation, and explore the application of the same procedure for real-frequency evaluation of diagrams. We find that real-frequency results are subject to noise that is controlled at low temperatures and can be mitigated at additional computational expense. We further demonstrate the utility of this approach by evaluating dynamical mean-field and bold diagrammatic self-consistency schemes at both second and fourth order and compare to benchmarks where available., Comment: 10 pages, 8 figures

Modern physics experiments rely on precise timing provided by programmable digital pulse generators. In many experimental control systems, this role is filled by custom devices built on Field Programmable Gate Arrays (FPGAs). While highly flexible and performant, these systems can be difficult to scale to very large systems due to cost and complexity. Recent advances in microcontroller systems allows these much simpler systems to fill the role of digital pulse generators. Here we demonstrate one such alternative based on the Raspberry Pi Pico microcontroller which allows for timing resolution down to 7.5 ns with a minimum pulse width of of 37.5 ns., Comment: 9 pages, 5 figures

This work introduces a new approach to building crash-safe file systems for persistent memory. We exploit the fact that Rust's typestate pattern allows compile-time enforcement of a specific order of operations. We introduce a novel crash-consistency mechanism, Synchronous Soft Updates, that boils down crash safety to enforcing ordering among updates to file-system metadata. We employ this approach to build SquirrelFS, a new file system with crash-consistency guarantees that are checked at compile time. SquirrelFS avoids the need for separate proofs, instead incorporating correctness guarantees into the typestate itself. Compiling SquirrelFS only takes tens of seconds; successful compilation indicates crash consistency, while an error provides a starting point for fixing the bug. We evaluate SquirrelFS against state of the art file systems such as NOVA and WineFS, and find that SquirrelFS achieves similar or better performance on a wide range of benchmarks and applications.

We present a systematic study of the interaction, doping, and layer dependence of the $d_{x^2-y^2}$-wave pairing susceptibility of the Hubbard model for a stacked 2D square lattice. We perform a multi-index perturbative expansion up to fourth-order to obtain coefficients in powers of the Hubbard $U$, the inter-layer $V$, and the pair-hopping $J$ interactions. We evaluate the vertex diagrams that contribute to the pairing susceptibility for $\ell= 2,3, 4$ layered models in the $U$-$V$-$J$ interaction space. This provides unprecedented access to the pairing amplitudes, allowing us to identify the processes that enhance or reduce pairing. We distinguish pairing within the diagonal channel, $P^{\parallel}_{d}$, and off-diagonal channel, $P^{\perp}_{d}$, and find that, in the absence of $J$, the qualitative behavior of the layered system is equivalent to the single-layer model. In the presence of $J$, we show that pairing is enhanced sublinearly with increasing $\ell$ and is primarily mediated by the $P^{\perp}_{d}$ component and find which coefficients and diagram sets are responsible. Finally, we construct a generalized $\ell$-dependent equation for $ P^{\perp}_{d}$ to speculate pairing beyond $\ell=4$., Comment: 21 pages, 9 figures in the main text, 10 figures in the supplemental material (appended)

This report presents a short summary of the activities of the "Standard Model" working group for the "Physics at TeV Colliders" workshop (Les Houches, France, 12-30 June, 2023)., Comment: Proceedings of the Standard Model Working Group of the 2023 Les Houches Workshop, Physics at TeV Colliders, Les Houches 12-30 June 2023. 48 pages