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In this paper, we study a Liouville-type theorem for the stationary fractional quasi-geostrophic equation in various dimensions. Indeed, our analysis focuses on dimensions n = 2, 3, 4 and we explore the uniqueness of weak solutions for this fractional system. We demonstrate here that, under some specific Lebesgue integrability information, the only admissible solution to the stationary fractional quasi-geostrophic system is the trivial one and this result provides a comprehensive understanding of how the dimension in connection to the fractional power of the Laplacian influences the uniqueness properties of weak solutions.

To enhance the ionization yield of liquid argon time projection chambers (LArTPC) used in dark matter and neutrino experiments it was proposed the use of dopants in LAr, with ionization energies below the scintillation threshold of Ar. While dual-phase LArTPCs have excellent sensitivity to single ionization electrons, their compatibility with photosensitive dopants is hindered by gas-phase electroluminescence photons ionizing the dopants, leading to a positive feedback loop. This can be addressed by optically decoupling the gaseous and liquid phases with a barrier that transmits electrons. A possible solution relies on the use of a pair of structures based on Gaseous Electron Multipliers(GEMs) with misaligned holes. Rather than amplifying electron signals in gas pockets within their holes, their holes will be filled with LAr and a low biasing voltage, so that incident drifting electrons are drawn into the holes but not amplified. Instead, amplification will occur in the gas phase above the structures. Its core element is a GEM-like structure machined from polyethylene naphthalate(PEN). Since PEN scintillates in the visible spectrum, the risk of increased radioactivity due to the larger mass compared to traditional wire grids is negated by the potential to veto its own radioactivity. As such, these structures may also be a useful alternative to wire grids. In this work, we report the newest developments on the production of GEM-like structures using laser-based techniques, namely the manufacture of the first batch PEN and PMMA-based GEM-like structures. This process allows low-cost, reproducible fabrication of a high volume of such structures. In addition to being a low radioactive technique, we expect that it will allow the scaling up of the production of these structures at a reduced cost. First tests indicate good electrical stability, while the performance assessment is still ongoing., Comment: 4 pages, 3 figures, 1 table, conference LRT2024

X-ray imaging is an invaluable tool for noninvasive analysis in many fields ranging from basic science to medicine and security. The development of low-dose large area imaging solutions still represents an important challenge for various applications. One solution to the imaging of large areas lies in the development of novel computational imaging systems that can overcome the limitations imposed by hardware, relying instead on numerical processing power. The single-pixel detector, depending on the application, may offer a competitive edge over conventional cameras (being a cheaper alternative to the multi-pixelated solutions). In addition, the single-pixel detector can be used to achieve improved detection efficiency, faster timing response, and good spatial resolution with low radiation dose. Moreover, this technique enables detectors to image through diffuse mediums, increasing the image quality at significant depths, solving the depth penetration issues of other imaging methods. In this work, we explore the application of single-pixel imaging techniques to produce two-dimensional images with high temporal resolution (only if the process is reproducible and the conditions are static), using only a single detector (bucket detector). The setup, based on the application of Hadamard patterns, showed promising results, proving the ability of the system to acquire images using thin PLA based masks (up to 5 mm thickness). Both simulation, using GEANT 4, and experimental setup, based on a time projection chamber (TPC), used in this work to demonstrate this technique will be reported here along with the first results., Comment: 17 pages, 13 figures and 3 tables, paper

The Xenon-Argon Technology (X-ArT) collaboration presents a study on the dynamics of pure and xenon-doped liquid argon (LAr) scintillation. Using two types of silicon photomultipliers sensitive to different wavelength ranges, we identify a long-lived extreme ultraviolet (EUV) radiative component that enhances the light yield. This component is present in both pure and xenon-doped LAr, becoming more pronounced at higher xenon concentrations, where it complements the traditional collisional energy transfer process. To explain this mechanism, we develop a comprehensive model of the Xe-doped LAr scintillation process that integrates both collisional and radiative contributions. Additionally, we investigate how xenon doping affects LAr scintillation light yield and pulse shape discrimination. Finally, we hypothesize that the EUV component may explain the emission of spurious electrons, a known challenge in light dark matter searches using noble liquids. By characterizing the scintillation dynamics in Xe-doped LAr, identifying the long-lived EUV component, and exploring the potential origin of spurious electrons, this work lays the groundwork for optimizing detector performance and advancing the design and sensitivity of future noble liquids particle detectors., Comment: 20 pages, 11 figures

The Elo rating system is a popular and widely adopted method for measuring the relative skills of players or teams in various sports and competitions. It assigns players numerical ratings and dynamically updates them based on game results and a model parameter. Assuming random games, this leads to a Markov chain for the evolution of the ratings of the $N$ players in the league. Despite its widespread use, little is known about the large-time behaviour of this process. Aiming to fill this gap, in this article we prove that the process has a unique equilibrium to which it converges in an almost-sure sense and in Wasserstein metrics. Moreover, we show important properties of the stationary distribution, such as finiteness of an exponential moment, full support, and quantitative convergence to the players' true skills as the update parameter decreases. We also provide Monte Carlo simulations that illustrate some of these properties and offer new insights., Comment: 24 pages, 4 figures

Model Predictive Control (MPC) is effective at generating safe control strategies in constrained scenarios, at the cost of computational complexity. This is especially the case in robots that require high sampling rates and have limited computing resources. Differentiable Predictive Control (DPC) trains offline a neural network approximation of the parametric MPC problem leading to computationally efficient online control laws at the cost of losing safety guarantees. DPC requires a differentiable model, and performs poorly when poorly conditioned. In this paper we propose a system decomposition technique based on relative degree to overcome this. We also develop a novel safe set generation technique based on the DPC training dataset and a novel event-triggered predictive safety filter which promotes convergence towards the safe set. Our empirical results on a quadcopter demonstrate that the DPC control laws have comparable performance to the state-of-the-art MPC whilst having up to three orders of magnitude reduction in computation time and satisfy safety requirements in a scenario that DPC was not trained on., Comment: 8 Pages, 6 figures

The international collaboration designing and constructing the Deep Underground Neutrino Experiment (DUNE) at the Long-Baseline Neutrino Facility (LBNF) has developed a two-phase strategy toward the implementation of this leading-edge, large-scale science project. The 2023 report of the US Particle Physics Project Prioritization Panel (P5) reaffirmed this vision and strongly endorsed DUNE Phase I and Phase II, as did the European Strategy for Particle Physics. While the construction of the DUNE Phase I is well underway, this White Paper focuses on DUNE Phase II planning. DUNE Phase-II consists of a third and fourth far detector (FD) module, an upgraded near detector complex, and an enhanced 2.1 MW beam. The fourth FD module is conceived as a "Module of Opportunity", aimed at expanding the physics opportunities, in addition to supporting the core DUNE science program, with more advanced technologies. This document highlights the increased science opportunities offered by the DUNE Phase II near and far detectors, including long-baseline neutrino oscillation physics, neutrino astrophysics, and physics beyond the standard model. It describes the DUNE Phase II near and far detector technologies and detector design concepts that are currently under consideration. A summary of key R&D goals and prototyping phases needed to realize the Phase II detector technical designs is also provided. DUNE's Phase II detectors, along with the increased beam power, will complete the full scope of DUNE, enabling a multi-decadal program of groundbreaking science with neutrinos.

This article is devoted to the mathematical study of a new Navier-Stokes-alpha model with a nonlinear filter equation. For a given indicator function, this filter equation was first considered by W. Layton, G. Rebholz, and C. Trenchea to select eddies for damping based on the understanding of how nonlinearity acts in real flow problems. Numerically, this nonlinear filter equation was applied to the nonlinear term in the Navier-Stokes equations to provide a precise analysis of numerical diffusion and error estimates. Mathematically, the resulting alpha-model is described by a doubly nonlinear parabolic-elliptic coupled system. We therefore undertake the first theoretical study of this system by considering periodic boundary conditions in the spatial variable. Specifically, we address the existence and uniqueness of weak Leray-type solutions, their rigorous convergence to weak Leray solutions of the classical Navier-Stokes equations, and their long-time dynamics through the concept of the global attractor and some upper bounds for its fractal dimension. Handling the nonlinear filter equation together with the well-known nonlinear transport term makes certain estimates delicate, particularly when deriving upper bounds on the fractal dimension. For the latter, we adapt techniques developed for hyperbolic-type equations., Comment: 45 pages

We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated based on the opinion of the second (the ``persuader''). We derive the mean-field kinetic equation describing the large population limit of the model, and we provide several quantitative results establishing convergence to the unique equilibrium distribution. Surprisingly, in some range of the model parameters, the support of the equilibrium distribution exhibits a fractal structure. This provides a new mathematical description for the so-called opinion fragmentation phenomenon., Comment: 23 pages, 4 figures

Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive Control (DPC), a physics-informed machine learning methodology. We base our model on the Macroscopic Fundamental Diagram (MFD) and the Networked Macroscopic Fundamental Diagram (NMFD), offering a simplified representation of citywide traffic networks. Our approach ensures compliance with system constraints by construction. In empirical comparisons with existing state-of-the-art Model Predictive Control (MPC) methods, our approach demonstrates a 4 order of magnitude reduction in computation time and an up to 37% improvement in traffic performance. Furthermore, we assess the robustness of our controller to scenario shifts and find that it adapts well to changes in traffic patterns. This work proposes more efficient traffic control methods, particularly in large-scale urban networks, and aims to mitigate emissions and alleviate congestion in the future., Comment: 8 Figures, 1 Table

Distribution shift is a common situation in machine learning tasks, where the data used for training a model is different from the data the model is applied to in the real world. This issue arises across multiple technical settings: from standard prediction tasks, to time-series forecasting, and to more recent applications of large language models (LLMs). This mismatch can lead to performance reductions, and can be related to a multiplicity of factors: sampling issues and non-representative data, changes in the environment or policies, or the emergence of previously unseen scenarios. This brief focuses on the definition and detection of distribution shifts in educational settings. We focus on standard prediction problems, where the task is to learn a model that takes in a series of input (predictors) $X=(x_1,x_2,...,x_m)$ and produces an output $Y=f(X)$., Comment: Learning Engineering Virtual Institute

In volume-filtered Euler-Lagrange simulations of particle-laden flows, the fluid forces acting on a particle are estimated using reduced models, which rely on the knowledge of the local undisturbed flow for that particle. Since the two-way coupling between the particle and the fluid creates a local flow perturbation, the filtered fluid velocity interpolated to the particle location must be corrected prior to estimating the fluid forces, so as to subtract the contribution of this perturbation and recover the local undisturbed flow with good accuracy. In this manuscript, we present a new model for estimating a particle's self-induced flow disturbance that accounts for its transient development and for inertial effects related to finite particle Reynolds numbers. The model also does not require the direction of the momentum feedback to align with the direction of the particle's relative velocity, allowing force contributions other than the steady drag force to be considered. It is based upon the linearization of the volume-filtered equations governing the particle's self-induced flow disturbance, such that their solution can be expressed as a linear combination of regularized transient Stokeslet contributions. Tested on a range of numerical cases, the model is shown to consistently estimate the particle's self-induced flow disturbance with high accuracy both in steady and highly transient flow environments, as well as for finite particle Reynolds numbers.

Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network information. However, the required extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experiment that selects a sub-population in the first stage and restricts treatment rollout to this sub-population in the second stage. We explore the role of clustering in the first stage by analyzing the bias and variance of a polynomial interpolation-style estimator under this experimental design. Bias increases with the number of edges cut in the clustering of the interference network, but variance depends on qualities of the clustering that relate to homophily and covariate balance. There is a tension between clustering objectives that minimize the number of cut edges versus those that maximize covariate balance across clusters. Through simulations, we explore a bias-variance trade-off and compare the performance of the estimator under different clustering strategies., Comment: 35 pages, 5 Tables, 14 figures

Today, cloud workloads are essentially opaque to the cloud platform. Typically, the only information the platform receives is the virtual machine (VM) type and possibly a decoration to the type (e.g., the VM is evictable). Similarly, workloads receive little to no information from the platform; generally, workloads might receive telemetry from their VMs or exceptional signals (e.g., shortly before a VM is evicted). The narrow interface between workloads and platforms has several drawbacks: (1) a surge in VM types and decorations in public cloud platforms complicates customer selection; (2) essential workload characteristics (e.g., low availability requirements, high latency tolerance) are often unspecified, hindering platform customization for optimized resource usage and cost savings; and (3) workloads may be unaware of potential optimizations or lack sufficient time to react to platform events. In this paper, we propose a framework, called Workload Intelligence (WI), for dynamic bi-directional communication between cloud workloads and cloud platform. Via WI, workloads can programmatically adjust their key characteristics, requirements, and even dynamically adapt behaviors like VM priorities. In the other direction, WI allows the platform to programmatically inform workloads about upcoming events, opportunities for optimization, among other scenarios. Because of WI, the cloud platform can drastically simplify its offerings, reduce its costs without fear of violating any workload requirements, and reduce prices to its customers on average by 48.8%.

Polyethylene naphthalate (PEN) foils have been demonstrated as a wavelength shifter suitable for operation in liquid argon. At the same time, wavelength shifting efficiency of technical grades of PEN, commercially available on the market, is lower than that of tetraphenyl butadiene (TPB). This paper reports on an R&D program focused on exploring the intrinsic limitations of PEN and optimizing it for the highest achievable wavelength shifting efficiency., Comment: Proceedings of LIght Detection In Noble Elements - LIDINE 2023

We address the issue of inequivalent Fock representations in Quantum Field Theory in a curved homogenous and anisotropic background, namely Kantowski-Sachs spacetime. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.

This introductory report outlines the challenges of postsecondary completion, the variable value provided by a postsecondary pathway, and the corresponding cost and debt. Together, these challenges create an inequitable, ineffective, and unsustainable U.S. postsecondary system in which individuals are increasingly reluctant to participate or return. After exploring the challenges, the authors propose three enablers of choice that people from systemically marginalized communities too often do not have access to -- and that could be the basis for transforming the postsecondary system: (1) information; (2) the social capital of navigation; and (3) versatile, inclusive, high-quality postsecondary pathway options. [The Suder Foundation provided financial support for this work.]