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The application of nonlinear control schemes to electro-hydraulic actuators often requires several alterations in the design of the controllers during their implementation. This is to overcome the challenges that frequently arise from the inherent complexity of such control algorithms owning to model nonlinearities. Moreover, advanced control solutions for this type of systems often introduce input algebraic loops and chatter, which considerably degrade the tracking performance. This study presents a nonlinear control architecture for hydraulic actuators that comprises low-complexity modules, based on well-established designs that facilitate robust high performance in tracking without introducing the aforementioned limitations. Specifically, the proposed solution consists of two variants of a position controller for the hydraulic cylinder and a dynamic input-mapping inversion module to avoid algebraic loops in the control input. The stability of the closed-loop system is analysed using arguments from Lyapunov theory for cascaded non-autonomous nonlinear systems. The effectiveness of the proposed solution is evaluated on a high-fidelity simulator of a wind turbine pitch system. Appropriate quantitative metrics are finally defined to evaluate the closed-loop system performance in comparison to state-of-the-art nonlinear design.

Large Language Models (LLMs) have demonstrated remarkable in-context learning (ICL) capabilities. In this study, we explore a surprising phenomenon related to ICL: LLMs can perform multiple, computationally distinct ICL tasks simultaneously, during a single inference call, a capability we term "task superposition". We provide empirical evidence of this phenomenon across various LLM families and scales and show that this phenomenon emerges even if we train the model to in-context learn one task at a time. We offer theoretical explanations that this capability is well within the expressive power of transformers. We also explore how LLMs internally compose task vectors during superposition. Furthermore, we show that larger models can solve more ICL tasks in parallel, and better calibrate their output distribution. Our findings offer insights into the latent capabilities of LLMs, further substantiate the perspective of "LLMs as superposition of simulators", and raise questions about the mechanisms enabling simultaneous task execution.

This is an index of the contributions by the Giant Radio Array for Neutrino Detection (GRAND) Collaboration to the 10th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities (ARENA 2024, University of Chicago, June 11-14, 2024). The contributions include an overview of GRAND in its present and future incarnations, methods of radio-detection that are being developed for them, and ongoing joint work between the GRAND and BEACON experiments., Comment: Note: To access the list of contributions, please follow the "HTML" link that can be found on the arXiv page

Globular clusters (GCs) are among the oldest objects in the Universe for which an age can be directly measured, thus playing an important cosmological role. This age, on the other hand, depends sensitively on the He abundance, which cannot be reliably measured from spectroscopy in GC stars. Detached eclipsing binaries (DEBs) near the turnoff (TO) point may play an important role in this regard. The aim of this study is to explore the possibility that, by working with differential measurements of stars that comprise a TO binary system, and assuming both stars have the same age and He abundance, one can achieve tighter, more robust, and less model-dependent constraints on the latter two quantities than otherwise possible by working with the absolute parameters of the stars. We compare both absolute and differential parameters of the stars in V69, a TO DEB pair in the GC 47 Tuc, with two different sets of stellar evolutionary tracks, making use of a Monte Carlo technique to estimate its He abundance and age, along with their uncertainties. We find that the relative approach can produce age and He abundance estimates that are in good agreement with those from the literature. We show that our estimates are also less model-dependent, less sensitive to [Fe/H], and more robust to inherent model systematics than those obtained with an absolute approach. On the other hand, the relative analysis finds larger statistical uncertainties than does its absolute counterpart, at least in the case of V69, where both stars have very similar properties. For binary pairs in which one of the components is less evolved than the other, the statistical uncertainty can be reduced. Our study suggests that the method proposed in this work may be useful to robustly constrain the He abundance and ages of GCs., Comment: Accepted for publication in Astronomy & Astrophysics. 14 pages, 11 figures

The operation of upcoming ultra-high-energy cosmic-ray, gamma-ray, and neutrino radio-detection experiments, like the Giant Radio Array for Neutrino Detection (GRAND), poses significant computational challenges involving the production of numerous simulations of particle showers and their detection, and a high data throughput. GRANDlib is an open-source software tool designed to meet these challenges. Its primary goal is to perform end-to-end simulations of the detector operation, from the interaction of ultra-high-energy particles, through -- by interfacing with external air-shower simulations -- the ensuing particle shower development and its radio emission, to its detection by antenna arrays and its processing by data-acquisition systems. Additionally, GRANDlib manages the visualization, storage, and retrieval of experimental and simulated data. We present an overview of GRANDlib to serve as the basis of future GRAND analyses., Comment: 11 pages, 9 figures, plus appendices

This paper presents a novel method to quantify seafarers' good seamanship during navigation scenarios with multi-vessel encounters -- in open and confined waters --, and to compute COLREG's-compliant trajectories for avoiding collision and grounding. The quantification of good seamanship requires knowledge about the state of the vessels (position, heading, and speed) and the surrounding sailing environment. Such information is accessible through the AIS system and the electronic nautical chart. The proposed method evaluates mutual collision risk by examining domain violations of each vessel, and comparing them to the seaman's actions. This results in a comprehensive metric of good seamanship. As risk free actions are not always possible in the resolution of a potential collision and grounding, the method adopts a branch-and-bound scheme to identify achievable maneuvers that minimize the risk. Further, the dynamic nature of vessel speed in congested scenarios is considered, recognizing potential changes in both own and target vessels' forward speeds. The proposed method is experimentally evaluated using historical AIS data and sea charts of Danish waters. This research contributes to the field by providing a more realistic perspective on seamanship in complex maritime environments., Comment: The 15th IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles (CAMS 2024)

This paper addresses the topic of condition monitoring of wind turbine blades and presents a learning-based approach to fault detection. The proposed scheme utilises Principal Components Analysis and Autoencoders to derive data-driven models from root-bending moment and other measurements. The models are trained with real data obtained from a fault-free wind turbine, and then validated on data corresponding to unknown health condition. Online test statistics, employing static thresholds and Generalized Likelihood Ratio tests, are used on residual signals generated by discrepancies between the actual and reconstructed measurements to detect deviations from nominal operation. The efficacy and effectiveness of the proposed methods are demonstrated using real-life data collected from wind turbines experiencing blade faults.

Recent studies have shown that Large Language Models (LLMs) struggle to accurately retrieve information and maintain reasoning capabilities when processing long-context inputs. To address these limitations, we propose a finetuning approach utilizing a carefully designed synthetic dataset comprising numerical key-value retrieval tasks. Our experiments on models like GPT-3.5 Turbo and Mistral 7B demonstrate that finetuning LLMs on this dataset significantly improves LLMs' information retrieval and reasoning capabilities in longer-context settings. We present an analysis of the finetuned models, illustrating the transfer of skills from synthetic to real task evaluations (e.g., $10.5\%$ improvement on $20$ documents MDQA at position $10$ for GPT-3.5 Turbo). We also find that finetuned LLMs' performance on general benchmarks remains almost constant while LLMs finetuned on other baseline long-context augmentation data can encourage hallucination (e.g., on TriviaQA, Mistral 7B finetuned on our synthetic data cause no performance drop while other baseline data can cause a drop that ranges from $2.33\%$ to $6.19\%$). Our study highlights the potential of finetuning on synthetic data for improving the performance of LLMs on longer-context tasks.

Pedestrian trajectory prediction plays a pivotal role in ensuring the safety and efficiency of various applications, including autonomous vehicles and traffic management systems. This paper proposes a novel method for pedestrian trajectory prediction, called multi-stage goal-driven network (MGNet). Diverging from prior approaches relying on stepwise recursive prediction and the singular forecasting of a long-term goal, MGNet directs trajectory generation by forecasting intermediate stage goals, thereby reducing prediction errors. The network comprises three main components: a conditional variational autoencoder (CVAE), an attention module, and a multi-stage goal evaluator. Trajectories are encoded using conditional variational autoencoders to acquire knowledge about the approximate distribution of pedestrians' future trajectories, and combined with an attention mechanism to capture the temporal dependency between trajectory sequences. The pivotal module is the multi-stage goal evaluator, which utilizes the encoded feature vectors to predict intermediate goals, effectively minimizing cumulative errors in the recursive inference process. The effectiveness of MGNet is demonstrated through comprehensive experiments on the JAAD and PIE datasets. Comparative evaluations against state-of-the-art algorithms reveal significant performance improvements achieved by our proposed method., Comment: Paper accepted by 5th International Conference on Computer Vision, Image and Deep Learning (CVIDL 2024)

Sliding tasks performed by aerial robots are valuable for inspection and simple maintenance tasks at height, such as non-destructive testing and painting. Although various end-effector designs have been used for such tasks, non-actuated wheel configurations are more frequently applied thanks to their rolling capability for sliding motion, mechanical simplicity, and lightweight design. Moreover, a non-actuated multi-wheel (more than one wheel) configuration in the end-effector design allows the placement of additional equipment e.g., sensors and tools in the center of the end-effector tip for applications. However, there is still a lack of studies on crucial contact conditions during sliding using aerial robots with such an end-effector design. In this article, we investigate the key challenges associated with sliding operations using aerial robots equipped with multiple non-actuated wheels through in-depth analysis grounded in physical experiments. The experimental data is used to create a simulator that closely captures real-world conditions. We propose solutions from both mechanical design and control perspectives to improve the sliding performance of aerial robots. From a mechanical standpoint, design guidelines are derived from experimental data. From a control perspective, we introduce a novel pressure-sensing-based control framework that ensures reliable task execution, even during sliding maneuvers. The effectiveness and robustness of the proposed approaches are then validated and compared using the built simulator, particularly in high-risk scenarios.

Axion-inflation models are a compelling candidate as a mechanism behind the accelerated expansion in the early universe in light of the possibility to embed them in higher dimensional UV complete theories and the exciting prospect of testing them with next-generation cosmological probes. Adding an Abelian gauge sector to axion-inflation models makes for a rich, interesting, phenomenology spanning from primordial black holes to gravitational waves (GWs). Several recent studies employ an approximate analytic (Gaussian) template to characterize the effect of gauge field production on cosmological perturbations. In this work we go beyond such approximation and numerically study particle production and the ensuing scalar and tensor spectra. We find a significant deviation from results based on log-normally distributed vector field excitations. As an important phenomenological application of the improved method, we study the expected chirality and spectral index of the sourced GW background at scales relevant for current and next-generation GW detectors. One striking feature is that of a scale-dependent chirality. We derive a consistency relation between these two observables that can serve as an important tool in identifying key signatures of multi-field dynamics in axion inflation., Comment: 23 pages + Appendices, 9 Figures

Low mass ratio systems (LMR) are a very interesting class of contact eclipsing binaries challenging the theoretical models of stability. These systems are also considered possible progenitors of the rare low-mass optical transients called red novae. In this study, we present the identification of 7 new totally eclipsing LMR systems from Catalina Sky Surveys (CSS) and 77 LMR candidates from the All Sky Automated Survey (ASAS$-$3). Using the available CSS light curves and new multiband observations for CSS$\_$J210228.3$-$031048 and CSS$\_$J231513.$+$345335 with the 2.3 m Aristarchos telescope at Helmos Observatory, we estimate their physical and absolute parameters and investigate their stability and their progenitors. The light curves are analyzed by performing a 2$-$dimension scan on the mass ratio $-$ inclination plane with Phoebe$-$0.31 scripter while the errors are estimated using Monte-Carlo simulations and heuristic scanning of the parameter space. Our analysis revealed that all 9 CSS systems have extreme mass ratios from 0.09 to 0.16. Our statistical analysis of well$-$studied LMR contact binaries shows that LMR systems tend to have warmer and more massive primaries. The investigation of the progenitors of both low and higher-mass ratio systems reveals a trend for the former to originate from higher-mass ancestors. Finally, we investigate the stability condition by calculating the ratio of spin angular momentum to orbital angular momentum and other stability indicators in the context of the reliability of the solutions., Comment: 16 pages, 8 figures

This article provides an overview of the design of nonlinear feedback Cruise Controllers (CCs) for automated vehicles on lane-free roads. The feedback design problem is particularly challenging because of the various state constraints (e.g., collision-free movement, road geometry, speed limits) as well as the nature of the control objective (globally stabilizing distributed controllers that require measurements from neighboring vehicles only). Therefore, the resulting nonlinear control system is defined on an open set (not necessarily diffeomorphic to a linear space) for which the set of desired equilibria is non-compact. The proposed design of the CCs is based on energy-like control Lyapunov functions which combine potential functions with kinetic energy terms and other appropriate penalty terms. The feedback design in the microscopic level is accompanied by the derivation of the corresponding macroscopic traffic flow models. Explicit relations are established between selectable CC features and the obtained macroscopic traffic flow characteristics. This facilitates the active design of efficient traffic flow with desired properties, i.e., the construction of artificial traffic fluids., Comment: 53 pages

We consider the case of axion-like particles (ALPs) during inflation. When coupled to a non-Abelian gauge sector via a Chern-Simons term, ALPs support an intriguing, testable, phenomenology with very distinctive features including chiral primordial gravitational waves. For sufficiently small values of the gauge vev and coupling, scalar perturbations in the gauge sector exhibit a known instability. We harness the power of such instability for primordial black hole (PBH) generation. In the case of an axion-inflaton, one is dynamically driven into a strong-backreaction regime that crosses the instability band thereby sourcing a peaked scalar spectrum leading to PBH production and the related scalar-induced gravitational waves. Remarkably, this dynamics is largely insensitive to the initial conditions and the shape of the potential, highlighting the universal nature of the sourcing mechanism. In the case of spectator ALPs one can identify the parameter space that sets off the strong backreaction regime and the ensuing features. We show that spectator ALP models may also access the scalar instability region without triggering strong backreaction., Comment: 10 pages, 8 figures

We study the impact of gravitational wave memory on the distribution of far away light sources in the sky. For the first time we compute the built up of small, but permanent tensor distortions of the metric over cosmological time-scales using realistic models of compact binary coalescences (CBCs) whose rate of occurrence is extrapolated at $z\sim {\cal O}(1)$. This allows for a consistent computation of the random-walk like evolution of gravitational wave memory which, in turn, is used to estimate the overall shape and magnitude of astrometric deflections of far away sources of light. We find that for pulsar or quasar proper motions, the near-Earth contribution to the astrometric deflections dominates the result and the deflection is analogous to a stochastic gravitational wave memory background that is generally subdominant to the primary stochastic gravitational wave background. We find that this contribution can be within the reach of future surveys such as Theia. Finally, we also study the deviation of the presently observed angular distribution of quasars from perfect isotropy, which arises from the slow build-up of gravitational wave memory over the entire history of the universe. In this case, we find that astrometric deflections depend on the entire light trajectory from the source to the Earth, yielding a quadruple pattern whose magnitude is unlikely to be within reach of the next generation of astrometric surveys due to shot noise and cosmic variance limitations., Comment: 17 Pages, 8 Figures

The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to different assessment of situation at two approaching vessels. This may lead to high-risk conditions and could cause collision. This article considers decision making under uncertainty and suggests a novel method for probabilistic interpretation of vessel encounters that is explainable and provides a measure of uncertainty in the evaluation. The method is equally useful for decision support on a manned bridge as on Marine Autonomous Surface Ships (MASS) where it provides input for automated navigation. The method makes formal safety assessment and validation feasible. We obtain a resilient algorithm for machine interpretation of COLREGs under uncertainty and show its efficacy by simulations., Comment: Submitted to IEEE Transactions on Intelligent Transportation Systems

Nanoscience at times can seem out of reach to the developing world and the general public, with much of the equipment expensive and knowledge seemingly esoteric to nonexperts. Using only cheap, everyday household items, accessible research with real applications can be shown. Here, graphene suspensions were produced using pencil lead, tap water, kitchen appliances, soaps and coffee filters, with a childrens glue based graphene nanocomposite for highly sensitive pulse measurements demonstrated.

In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles., Comment: 34 pages, 19 figures

Wind energy is the leading non-hydro renewable technology. Increasing reliability is a key factor in reducing the downtime of high-power wind turbines installed in remote off-shore places, where maintenance is costly and less reactive. Defects in the pitch system are responsible for up to 20% of a wind turbine downtime.Thus, monitoring such defects is essential for avoiding it. This paper presents a generic assessment of the diagnosis capabilities in hydraulic pitch systems, which are used in high-power wind turbines. A mathematical model of the non-linear system dynamics is presented along with a description of the most frequent faults that occur. Structural analysis is used to assess which defects can be detected in the pitch system. The structural properties are furthermore explored to investigate the possibility of reducing the amount of sensors without compromising the fault diagnosis capabilities. Robustness to model uncertainty is finally addressed and generic principles for estimating the detectable magnitude of wear and tear are presented.

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to implement traffic-responsiveness. In this paper, we take a novel perspective and show that it is possible to use the already necessary sensing infrastructure to estimate the uncertain quantities in real time. Specifically, resorting to the store-and-forward model, we design a novel network-wide traffic-responsive strategy that estimates the occupancy and exogenous demand in each link, i.e., entering (exiting) vehicle flows at the origins (destinations) of the network or within links, in real time. Borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback-feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations for the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.

Contemporary process industries are constantly confronted with volatile market conditions that jeopardise their financial sustainability. While mature markets transition to oligopoly structures, the supply chain operation should adapt to a more customer-centric focus. Key issues related to the modelling and impact of the related contractual agreements between firms and customers remain largely unexplored. In the present work, we examine the problem of fair customer allocation in oligopolies under different contractual agreements within a multi-period setting. We consider an ensemble of contract types that vary in terms of pricing mechanisms and duration. The role of fairness is examined following the social welfare and Nash bargaining scheme. In the latter case, the overall problem is formulated as an MINLP. For its efficient solution we employ a piecewise linearisation strategy based on special-ordered sets. The impact of the different fairness schemes on the optimal customer allocation is evaluated via two case studies from the industrial gases market.

The formulation of a measurement theory for relativistic quantum field theory (QFT) has recently been an active area of research. In contrast to the asymptotic measurement framework that was enshrined in QED, the new proposals aim to supply a measurement framework for measurements in local spacetime regions. This paper surveys episodes in the history of quantum theory that contemporary researchers have identified as precursors to their own work and discusses how they laid the groundwork for current approaches to local measurement theory for QFT., Comment: 17 pages, 1 figure, to be published in EPJ H Special Issue "History for Physics: Contextualizing modern developments in the foundations of quantum theory"

Controlling automated vehicles on large lane-free roundabouts is challenging because of the geometrical complexity and frequent conflicts among entering, rotating, and exiting vehicles. This paper proposes a comprehensive methodology to control the vehicles within the roundabout and the connected road branches. The developed real-time vehicle movement strategy relies on offline-computed wide overlapping movement corridors, one for each Origin-Destination (OD) movement, which delineate the admissible movement zones of corresponding OD vehicles. Also, space-dependent desired orientations are determined by destination, so as to mitigate potential vehicle conflicts and reduce trip distance. A distributed (per vehicle) movement control strategy, using two nonlinear feedback controllers (NLFC), for circular and straight movements, respectively, is employed to navigate each vehicle within the respective OD corridor toward its destination, accounting for the desired orientation and avoiding collisions with other vehicles; while boundary controllers guarantee that the corridor boundaries will not be violated, and the exit will not be missed. As an overly complicated case study, we consider the famous roundabout of Place Charles de Gaulle in Paris, featuring a width of 38 m and comprising a dozen of bidirectional radial streets, hence a total of 144 ODs. The pertinence and effectiveness of the presented method is verified via microscopic simulation and evaluation of macroscopic data., Comment: 16 pages, 21 figures, 1 table, and 47 equations

Prostate cancer patients who undergo prostatectomy are closely monitored for recurrence and metastasis using routine prostate-specific antigen (PSA) measurements. When PSA levels rise, salvage therapies are recommended to decrease the risk of metastasis. However, due to the side effects of these therapies and to avoid over-treatment, it is important to understand which patients and when to initiate these salvage therapies. In this work, we use the University of Michigan Prostatectomy registry Data to tackle this question. Due to the observational nature of this data, we face the challenge that PSA is simultaneously a time-varying confounder and an intermediate variable for salvage therapy. We define different causal salvage therapy effects defined conditionally on different specifications of the longitudinal PSA history. We then illustrate how these effects can be estimated using the framework of joint models for longitudinal and time-to-event data. All proposed methodology is implemented in the freely-available R package JMbayes2.

We consider a parametric nonautonomous $(p, q)$-equation with unbalanced growth as follows \begin{align*} \left\{ \begin{aligned} &-\Delta_p^\alpha u(z)-\Delta_q u(z)=\lambda \vert u(z)\vert^{\tau-2}u(z)+f(z, u(z)), \quad \quad \hbox{in }\Omega,\\ &u|_{\partial \Omega}=0, \end{aligned} \right. \end{align*} where $\Omega \subseteq \mathbb{R}^N$ be a bounded domain with Lispchitz boundary $\partial\Omega$, $\alpha \in L^{\infty}(\Omega)\backslash \{0\}$, $a(z)\geq 0$ for a.e. $z \in \Omega$, $ 1<\tau< q0$. In the reaction there is a parametric concave term and a perturbation $f(z, x)$. Under the minimal conditions on $f(z, 0)$, which essentially restrict its growth near zero, by employing variational tools, truncation and comparison techniques, as well as critical groups, we prove that for all small values of the parameter $\lambda>0$, the problem has at least three nontrivial bounded solutions (positive, negative, nodal), which are ordered and asymptotically vanish as $\lambda \rightarrow 0^{+}$.

The sky is the limit with regards to the societal impact nanomaterials can have on our lives. However, in this study we show that their potential is out of this world. The planet Mars has an abundant source of calcium sulfate minerals and in our work, we show that these deposits can be the basis of transformative nanomaterials to potentially support future space endeavors. Through a scalable eco-friendly liquid processing technique performed on two common terrestrial gypsum, our simple method presented a cost-efficient procedure to yield the commercially valuable intermediate phase of gypsum, known as bassanite. Through the liquid exfoliation of bassanite powders, suspensions of large aspect ratio anhydrite nanobelts with long-term stability were characterized through scanning electron microscopy and Raman spectroscopy. Transmission electron microscopy showed nanobelts to have a mesocrystal structure, with distinct nanoparticle constituents making up the lattice. Unexpectedly, anhydrite nanobelts had remarkable electronic properties, namely a bandgap that was easily tuned between semiconducting (~2.2 eV) and insulating (~4 eV) behaviors through dimensional control measured via atomic force microscopy. To demonstrate the application potential of our nanobelts; optoelectronic, electrochemical and nanocomposite measurements were made. For the hydrogen evolution reaction and mechanical reinforcement, selenite-based anhydrite nanobelts displayed superlative performances.

Forward complete systems are guaranteed to have solutions that exist globally for all positive time. In this paper, a relaxed Lyapunov-like condition for forward completeness is presented for finite-dimensional systems defined on open sets that does not require boundedness of the Lyapunov-like function along the solutions of the system. The corresponding condition is then exploited for the design of autonomous two-dimensional movement, with focus on lane-free cruise controllers for automated vehicles described by the bicycle kinematic model. The derived feedback laws (cruise controllers) are decentralized and can account for collision avoidance, roads of variable width, on-ramps and off-ramps as well as different desired speed for each vehicle., Comment: 30 pages, 9 figures

Let $\mathscr{L}$ be either the Laplace--Beltrami operator, its shift without spectral gap, or the distinguished Laplacian on a symmetric space of noncompact type $\mathbb{X}$ of arbitrary rank. We consider the heat equation, the fractional heat equation, and the Caffarelli--Silvestre extension problem associated with $\mathscr{L}$, and in each of these cases we characterize the weights $v$ on $\mathbb{X}$ for which the solution converges pointwise a.e. to the initial data when the latter is in $L^{p}(v)$, $1\leq p < \infty$. As a tool, we also establish vector-valued weak type $(1,1)$ and $L^{p}$ estimates ($1

We demonstrate that the recently announced signal for a stochastic gravitational wave background (SGWB) from pulsar timing array (PTA) observations, if attributed to new physics, is compatible with primordial GW production due to axion-gauge dynamics during inflation. More specifically we find that axion-$U(1)$ models may lead to sufficient particle production to explain the signal while simultaneously source some fraction of sub-solar mass primordial black holes (PBHs) as a signature. Moreover there is a parity violation in GW sector, hence the model suggests chiral GW search as a concrete target for future. We further analyze the axion-$SU(2)$ coupling signatures and find that in the low/mild backreaction regime, it is incapable of producing PTA evidence and the tensor-to-scalar ratio is low at the peak, hence it overproduces scalar perturbations and PBHs., Comment: 2 figures, total 8 pages, published in PLB