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We present an update on the analysis of semileptonic $B\rightarrow D^{(*)}$ decays at non-zero recoil. Our computation employs $2 + 1 + 1$ FNAL-MILC ensembles with highly improved staggered quark (HISQ) action for sea and light valence quarks, while the bottom quark is treated using the clover action in the Fermilab interpretation. Simulations are performed across several lattice spacings, ranging approximately from $\sim 0.15$ fm to $\sim 0.06$ fm, and for various quark masses. We will present an overview of the analysis and show some preliminary results for the form factors.

Christoph Scheiner was one of the most outstanding astronomers in the history of the sunspot observations. His book, Rosa Ursina, is the reference work regarding the study of the earliest sunspot records. The sunspot observations compiled by Scheiner in Rosa Ursina and Prodomus, including records made by other observers, forms one of the main references of the observations known for that period; particularly around the 1620s. Thus, his work is crucial to determine the solar activity level of the first solar cycles of the telescopic era. The number of sunspot groups recorded in Scheiner's documentary sources has been included in the existing sunspot group number databases. However, we have detected significant errors in the number of groups currently assigned to Scheiner's records. In this work, we reanalyze the information in Scheiner's source documents. Consequently, the standard 11-yr solar cycle shape for the second solar cycle of the telescopic era, which is not clear in previous studies, now becomes evident. In addition, the highest daily number of groups recorded during this cycle (8 groups) is 20% less than the one included in the existing sunspot group number databases. Using the hypergeometrical probability distribution, we find that solar minima in 2008-2009 and 2018-2019 are comparable to the most probable solar activity level of the minimum around 1632. In particular, the estimated lower limit for the solar activity in 1632 is even comparable with the solar activity level in 2008 and 2018.

The integration of haptics within Augmented Reality may help to deliver an enriched experience, while facilitating the performance of specific actions (e.g. repositioning or resizin ) that are still dependent on the user's skills. This paper gathers the description of a flexible architecture designed to deploy haptically-enabled AR applications. The haptic feedback may be generated through a variety of devices (e.g., wearable, graspable, or mid-air ones), and the architecture facilitates handling the specificity of each. For this reason, it is discussed how to generate a haptic representation of a 3D digital object depending on the application and the target device. Additionally, it is included an analysis of practical, relevant issues that arise when setting up a system to work with specific devices like Head-Mounted Displays (e.g., HoloLens) and mid-air haptic devices (e.g., Ultrahaptics UHK), such as the alignment between the real world and the virtual one. The architecture applicability is demonstrated through the implementation of two applications: Form Inspector and Simon Game, built for HoloLens and iOS mobile phones for visualization and for UHK for mid-air haptics delivery. These applications have been used by nine users to explore the efficiency, meaningfulness, and usefulness of mid-air haptics for form perception, object resizing, and push interaction tasks. Results show that, although mobile interaction is preferred when this option is available, haptics turn out to be more meaningful in identifying shapes when compared to what users initially expect and in contributing to the execution of resizing tasks. Moreover, this preliminary user study reveals that users may be expecting a tailored interface metaphor, not necessarily inspired in natural interaction.

The Maunder Minimum (MM) was a period of prolonged solar activity minimum between 1645 and 1715. Several works have identified a significant number of problematic spotless days in the MM included in existing databases. We have found a list of exact spotless (in the second half of 1709) and spot days (January and August 1709) provided by Johann Heinrich Muller. We computed the most probable value and upper/lower limits of the active day fraction (ADF) from Muller's data using the hypergeometrical probability distribution. Our sample is not strictly random because Muller recorded observations in consecutive days when he observed sunspots. Therefore, our result represents an upper threshold of solar activity for 1709. We compared this result with annual values of the ADF calculated for the Dalton Minimum and the most recent solar cycles. We concluded that it was less active than most years both in the Dalton Minimum and in the most recent solar cycles. Therefore, the solar activity level estimated in this work for 1709 represents robust evidence of low solar activity levels in the MM.

Augmented Reality (AR) functionalities may be effectively leveraged in collaborative service scenarios (e.g., remote maintenance, on-site building, street gaming, etc.). Standard development cycles for collaborative AR require to code for each specific visualization platform and implement the necessary control mechanisms over the shared assets. This paper describes SARA, an architecture to support cross-platform collaborative Augmented Reality applications based on microservices. The architecture is designed to work over the concept of collaboration models (turn, layer, ownership,hierarchy-based and unconstrained examples) which regulate the interaction and permissions of each user over the AR assets. Thanks to the reusability of its components, during the development of an application, SARA enables focusing on the application logic while avoiding the implementation of the communication protocol, data model handling and orchestration between the different, possibly heterogeneous,devices involved in the collaboration (i.e., mobile or wearable AR devices using different operating systems). To describe how to build an application based on SARA, a prototype for HoloLens and iOS devices has been implemented. the prototype is a collaborative voxel-based game in which several players work real time together on a piece of land, adding or eliminating cubes in a collaborative manner to create buildings and landscapes. Turn-based and unconstrained collaboration models are applied to regulate the interaction, the development workflow for this case study shows how the architecture serves as a framework to support the deployment of collaborative AR services, enabling the reuse of collaboration model components, agnostically handling client technologies.

We present results for the dominant light-quark connected contribution to the long-distance window (LD) of the hadronic vacuum polarization contribution (HVP) to the muon $g-2$ from lattice quantum chromodynamics (QCD). Specifically, with a new determination of the lattice scale on MILC's physical-mass HISQ ensembles, using the $\Omega^-$ baryon mass, we obtain a result of $a^{ll,\,{\mathrm{LD}}}_{\mu}(\mathrm{conn.}) = 401.2(2.3)_{\mathrm{stat}}(3.6)_{\mathrm{syst}}[4.3]_{\mathrm{total}} \times 10^{-10}$. In addition, following up on our recent work on the short- (SD) and intermediate-distance (W) windows, we report updated values for these quantities with this new scale-setting determination. Summing these individual window contributions enables a sub-percent precision determination of the light-quark-connected contribution to HVP of $a^{ll}_{\mu}(\mathrm{conn.}) = 656.2(1.9)_{\mathrm{stat}}(4.0)_{\mathrm{syst}}[4.4]_{\mathrm{total}} \times 10^{-10}$. Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab $g-2$ experiment., Comment: arXiv admin note: text overlap with arXiv:2411.09656

In this paper, the stability of IMEX-BDF methods for delay differential equations (DDEs) is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay, $A$ is a positive definite matrix, but $B$ might be any matrix. First, it is analyzed the case where both matrices diagonalize simultaneously, but the paper focus in the case where the matrices $A$ and $B$ are not simultaneosly diagonalizable. The concept of field of values is used to prove a sufficient condition for unconditional stability of these methods and another condition which also guarantees their stability, but according to the step size. Several numerical examples in which the theory discussed here is applied to DDEs, but also parabolic problems given by partial delay differential equations with a diffusion term and a delayed term are presented., Comment: 25 pages

The first spectroscopy of $^{52}$K was investigated via in-beam $\gamma$-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory after one-proton and one-neutron knockout from $^{53}$Ca and $^{53}$K beams impinging on a 15-cm liquid hydrogen target at $\approx$ 230~MeV/nucleon. The energy level scheme of $^{52}$K was built using single $\gamma$ and $\gamma$-$\gamma$ coincidence spectra. The spins and parities of the excited states were established based on momentum distributions of the fragment after the knockout reaction and based on exclusive cross sections. The results were compared to state-of-the-art shell model calculations with the SDPF-Umod interaction and ab initio IMSRG calculations with chiral effective field theory nucleon-nucleon and three-nucleon forces.

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_\mu$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain $a^{ll,\,{\mathrm{SD}}}_{\mu}(\mathrm{conn.}) = 48.116(16)(94)[96] \times 10^{-10}$ and $a^{ll,\,{\mathrm{W}}}_{\mu}(\mathrm{conn.}) = 207.06(17)(63)[66] \times 10^{-10}$. We use Bayesian model averaging combined with a global bootstrap to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a^{{\mathrm{SD}}}_{\mu} = 69.01(2)(21)[21] \times 10^{-10}$ and $a^{{\mathrm{W}}}_{\mu} = 236.57(20)(94)[96] \times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavour-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model., Comment: 435 pages, 53 Figures, 190 tables. arXiv admin note: substantial text overlap with arXiv:2111.09849, arXiv:1902.08191, some corrections and updated references

Gaze target detection aims at determining the image location where a person is looking. While existing studies have made significant progress in this area by regressing accurate gaze heatmaps, these achievements have largely relied on access to extensive labeled datasets, which demands substantial human labor. In this paper, our goal is to reduce the reliance on the size of labeled training data for gaze target detection. To achieve this, we propose AL-GTD, an innovative approach that integrates supervised and self-supervised losses within a novel sample acquisition function to perform active learning (AL). Additionally, it utilizes pseudo-labeling to mitigate distribution shifts during the training phase. AL-GTD achieves the best of all AUC results by utilizing only 40-50% of the training data, in contrast to state-of-the-art (SOTA) gaze target detectors requiring the entire training dataset to achieve the same performance. Importantly, AL-GTD quickly reaches satisfactory performance with 10-20% of the training data, showing the effectiveness of our acquisition function, which is able to acquire the most informative samples. We provide a comprehensive experimental analysis by adapting several AL methods for the task. AL-GTD outperforms AL competitors, simultaneously exhibiting superior performance compared to SOTA gaze target detectors when all are trained within a low-data regime. Code is available at https://github.com/francescotonini/al-gtd., Comment: Accepted to ACM Multimedia 2024

While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric behavior of Poisson structures, such as the presence of symplectic leaves with varying dimensions. In this paper, we propose a general approach for the construction of geometric integrators on any Poisson manifold based on independent geometric and dynamic sources of approximation. The novel geometric approximation is obtained by adapting structural results about symplectic realizations of general Poisson manifolds. We also provide an error analysis for the resulting methods and illustrative applications.

Multi-object tracking (MOT) endeavors to precisely estimate the positions and identities of multiple objects over time. The prevailing approach, tracking-by-detection (TbD), first detects objects and then links detections, resulting in a simple yet effective method. However, contemporary detectors may occasionally miss some objects in certain frames, causing trackers to cease tracking prematurely. To tackle this issue, we propose BUSCA, meaning `to search', a versatile framework compatible with any online TbD system, enhancing its ability to persistently track those objects missed by the detector, primarily due to occlusions. Remarkably, this is accomplished without modifying past tracking results or accessing future frames, i.e., in a fully online manner. BUSCA generates proposals based on neighboring tracks, motion, and learned tokens. Utilizing a decision Transformer that integrates multimodal visual and spatiotemporal information, it addresses the object-proposal association as a multi-choice question-answering task. BUSCA is trained independently of the underlying tracker, solely on synthetic data, without requiring fine-tuning. Through BUSCA, we showcase consistent performance enhancements across five different trackers and establish a new state-of-the-art baseline across three different benchmarks. Code available at: https://github.com/lorenzovaquero/BUSCA., Comment: Accepted at ECCV 2024. Code available at https://github.com/lorenzovaquero/BUSCA

The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in $^{53}$Ca and $^{55}$Ca, populated from \ts{54,56}Ca($p,pn$) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum $l$ assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)\,keV in $^{53}$Ca and 6000(250)\,keV in $^{55}$Ca indicate a significant $l$\, =\,3 component, providing the first experimental evidence for the $\nu 0f_{7/2}$ single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the $\nu 0f_{7/2}$ orbital in $^{55}$Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and \textit{ab initio} calculations and diverge markedly from the experimental distributions in the nickel isotones at $Z=28$., Comment: 13 pages, 7 figures

Viscous electron flow exhibits exotic signatures such as superballistic conduction. Bending the geometry of the device is a must to observe hydrodynamic effects. To this end, we build three antidot graphene superlattices with different hole diameters. We measure their electrical properties at various temperatures and under the effect of a perpendicular magnetic field. We find an enhanced superballistic effect, suggesting the effectiveness of the geometry at bending the electron flow. In addition, superballistic conduction behaves non-monotonically with the magnetic field, which is related with the ballistic-hydrodynamic transition. We also analyze the device resistance as a function of the size of the antidot superlattice to find characteristic scaling laws describing the different transport regimes. We prove that the antidot superlattice is a convenient geometry for realizing hydrodynamic flow, and the experiment provides valuable explanations for the technologically relevant effects of superballistic conduction and scaling laws.

The existing large scale weak lensing surveys typically reserve the best seeing conditions for a certain optical band to minimize shape measurement errors and maximize the number of usable background galaxies. This is because most popular shear measurement methods contain explicit or implicit thresholds on the galaxy-to-PSF (point spread function) size ratio, below which their shape measurement errors increase abruptly. Using the DECaLS data, we have previously demonstrated that the Fourier\_Quad method performs very well on poorly resolved galaxy images in general. It is therefore a ready tool for shear measurement with multi-band images regardless of their seeing conditions. In this paper, we apply the Fourier\_Quad pipeline on the multi-band images from the third public data release of the Hyper Suprime-Cam Subaru Strategic Program. We show that the shear catalogs from the five optical bands (g/r/i/z/y) all pass the field-distortion test with very high accuracy. Using the LOWZ and CMASS galaxies as foreground lenses, we show that the errorbar in the galaxy-galaxy lensing measurement can be decreased by factors around 15\% by combining shear catalogs from different bands. This indicates that it is worthful to do multi-bands shear measurements for a better shear statistics., Comment: 14 pages, 12 figures

We study the sedimentation of U-shaped circular disks in the Stokes limit of vanishing inertia. We simulate the flow past such disks using a finite-element-based solution of the 3D Stokes equations, accounting for the integrable singularities that develop along their edges. We show that the purely vertical sedimentation of such disks in their upright- [upside-down-] U orientation is unstable to perturbations about their pitching [rolling] axes. The instability is found to depend only weakly on the size of the container in which the disks sediment, allowing us to analyse their behaviour based on the resistance matrix which governs the evolution of the disk's six rigid-body degrees of freedom in an unbounded fluid. We show that the governing equations can be reduced to two ODEs which describe the disk's inclination against the direction of gravity. A phase-plane analysis, results of which are in good agreement with experiments, reveals that the two instabilities generally cause the disk to sediment along complex spiral trajectories while it alternates between pitching- and rolling-dominated motions. The chirality of the trajectories is set by the initial conditions rather than the (non-chiral) shape of the disk. For certain initial orientations, the disk retains its inclination and sediments along a perfectly helical path. The observed behaviour is fundamentally different from that displayed by flat circular disks which sediment without any reorientation. We therefore study the effect of variations in the disk's curvature to show how in the limit of vanishing curvature the behaviour of a flat disk is recovered., Comment: 27 pages, 12 figures

Transition metal dichalcogenides (TMDs) are ideal systems for two-dimensional (2D) optoelectronic applications, owing to their strong light-matter interaction and various band gap energies. New techniques to modify the crystallographic phase of TMDs have recently been discovered, allowing the creation of lateral heterostructures and the design of all-2D circuitry. Thus far, the potential benefits of phase-engineered TMD devices for optoelectronic applications are still largely unexplored. The dominant mechanisms involved in the photocurrent generation in these systems remain unclear, hindering further development of new all-2D optoelectronic devices. Here, we fabricate locally phase-engineered MoTe$_{2}$ optoelectronic devices, creating a metal (1T') semiconductor (2H) lateral junction and unveil the main mechanisms at play for photocurrent generation. We find that the photocurrent originates from the 1T'-2H junction, with a maximum at the 2H MoTe$_{2}$ side of the junction. This observation, together with the non-linear IV-curve, indicates that the photovoltaic effect plays a major role on the photon-to-charge current conversion in these systems. Additionally, the 1T'-2H MoTe$_{2}$ heterojunction device exhibits a fast optoelectronic response over a wavelength range of 700 nm to 1100 nm, with a rise and fall times of 113 $\mu$s and 110 $\mu$s, two orders of magnitude faster when compared to a directly contacted 2H MoTe$_{2}$ device. These results show the potential of local phase-engineering for all-2D optoelectronic circuitry.

This paper presents a general method to construct Poisson integrators, i.e., integrators that preserve the underlying Poisson geometry. We assume the Poisson manifold is integrable, meaning there is a known local symplectic groupoid for which the Poisson manifold serves as the set of units. Our constructions build upon the correspondence between Poisson diffeomorphisms and Lagrangian bisections, which allows us to reformulate the design of Poisson integrators as solutions to a certain PDE (Hamilton-Jacobi). The main novelty of this work is to understand the Hamilton-Jacobi PDE as an optimization problem, whose solution can be easily approximated using machine learning related techniques. This research direction aligns with the current trend in the PDE and machine learning communities, as initiated by Physics- Informed Neural Networks, advocating for designs that combine both physical modeling (the Hamilton-Jacobi PDE) and data., Comment: 5 pages, 5 figures

The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wavefunctions with expedited convergence toward exact solutions. These advancements culminate in shallower circuits and, as demonstrated, reduced measurement requirements. This research delineates these enhancements and assesses their performance across mono, di, and tridimensional arrangements of H4 models, as well as in the water molecule. Ultimately, this work attests to the viability of physically-motivated strategies in fortifying ADAPT-VQE's efficiency, marking a significant stride in quantum chemistry simulations.

We compute the vector, scalar, and tensor form factors for the $B\to \pi$, $B\to K$, and $B_s\to K$ amplitudes, which are needed to describe semileptonic $B$-meson decay rates for both the charged and neutral current cases. We use the highly improved staggered quark (HISQ) action for the sea and light valence quarks. The bottom quark is described by the clover action in the Fermilab interpretation. Simulations are carried out on $N_f = 2+1+1$ MILC HISQ ensembles at approximate lattice spacings from $0.15$ fm down to $0.057$ fm. We present blinded preliminary results for the form factors., Comment: 10 pages, 5 figures, proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31 - August 4, 2023, Fermilab, USA

We present an update for results on $B$-meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration's gauge ensembles with lattice spacings down to $\sim$0.03 fm, allows the $b$ quark to be treated with the same discretization as the lighter quarks. The talk will focus on updated results for $B_{(s)} \to D_{(s)}$, $B_{(s)} \to K$ scalar and vector form factors., Comment: Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA

Objective: To analyze the current scientific knowledge and research lines focused on environmentally sustainable health systems, including the role of nurses. Background: There seem to be differences between creating interventions focused on environmentally sustainable health systems, including nurses, and the scarcity of research on this topic, framed on the Sustainable Development Goals. Methods: A bibliometric analysis was carried out, via three databases (Web of Science, Scopus, and Pubmed), and the guideline recommendations were followed to select bibliometric data. Results: The search resulted in 159 publications, significantly increasing the trends from 2017 to 2021 (p=0.028). The most relevant countries in this area were the United States of America, the United Kingdom, and Sweden. Also, the top articles were from relevant journals, indexed in Journal Citation Report, and the first and the second quartile linked to the nursing field and citations (p<0.001). Conclusion: Education is key to achieving environmentally sustainable health systems via institutions and policies. Implications for nursing management: There is a lack of experimental data and policies on achieving or maintaining environmentally sustainable health care systems, indicating that nurses have an important role and should be consulted and included in decision-making policies regarding sustainability in the healthcare systems., Comment: 9 pages,4 figures,2 tables

The study of the extreme weather space events is important for a technological dependent society. Extreme Value Theory could be decisive to characterize those extreme events in order to have the knowledge to make decisions in technological, economic and social matters, in all fields with possible impacts. In this work, the hourly values of the Dst geomagnetic index has been studied for the period 1957-2014 using the peaks-over-threshold technique. The shape parameter obtained from the fit of the generalized Pareto distribution to the extreme values of the |Dst| index leads to a negative value implying an upper bound for this time series. This result is relevant, because the estimation of this limit for the extreme values lead to 850 nT as the highest expected value for this geomagnetic index. Thus, from the previous characterization of the Carrington geomagnetic storm and our results, it could be considered the worst case scenario., Comment: 12 pages, 5 figures

Cold dark matter axions produced in the post-inflationary Peccei-Quinn symmetry breaking scenario serve as clear targets for their experimental detection, since it is in principle possible to give a sharp prediction for their mass once we understand precisely how they are produced from the decay of global cosmic strings in the early Universe. In this paper, we perform a dedicated analysis of the spectrum of axions radiated from strings based on large scale numerical simulations of the cosmological evolution of the Peccei-Quinn field on a static lattice. Making full use of the massively parallel code and computing resources, we executed the simulations with up to $11264^3$ lattice sites, which allows us to improve our understanding of the dependence on the parameter controlling the string tension and thus give a more accurate extrapolation of the numerical results. We found that there are several systematic effects that have been overlooked in previous works, such as the dependence on the initial conditions, contaminations due to oscillations in the spectrum, and discretisation effects, some of which could explain the discrepancy in the literature. We confirmed the trend that the spectral index of the axion emission spectrum increases with the string tension, but did not find a clear evidence of whether it continues to increase or saturates to a constant at larger values of the string tension due to the severe discretisation effects. Taking this uncertainty into account and performing the extrapolation with a simple power law assumption on the spectrum, we find that the dark matter mass is predicted in the range of $m_a \approx 95$-$450\,\mu\mathrm{eV}$., Comment: 52 pages, 46 figures; revised version of the manuscript, accepted for publication in JCAP

After 30 years since the beginning of the Global Positioning System (GPS), or, more generally, Global Navigation Satellite System (GNSS) meteorology, this technique has proven to be a reliable method for retrieving atmospheric water vapor; it is low-cost, weather independent, with high temporal resolution and is highly accurate and precise. GNSS ground-based networks are becoming denser, and the first stations installed have now quite long time-series that allow the study of the temporal features of water vapor and its relevant role inside the climate system. In this review, the different GNSS methodologies to retrieve atmospheric water vapor content re-examined, such as tomography, conversion of GNSS tropospheric delay to water vapor estimates, analyses of errors, and combinations of GNSS with other sources to enhance water vapor information. Moreover, the use of these data in different kinds of studies is discussed. For instance, the GNSS technique is commonly used as a reference tool for validating other water vapor products (e.g., radiosounding, radiometers onboard satellite platforms or ground-based instruments). Additionally, GNSS retrievals are largely used in order to determine the high spatio-temporal variability and long-term trends of atmospheric water vapor or in models with the goal of determining its notable influence on the climate system (e.g., assimilation in numerical prediction, as input to radiative transfer models, study of circulation patterns, etc., Comment: 29 pages, 3 figures

In this work we study Beltrami fields with non-constant proportionality factor on $\mathbb{R}^3$. More precisely, we analyze the existence of vector fields $X$ satisfying the equations $curl(X)=fX$ and $div(X)=0$ for a given $f\in C^\infty(\mathbb R^3)$ in a neighborhood of a point $p\in\mathbb{R}^3$. Since the regular case has been treated previously, we focus on the case where $p$ is a non-degenerate critical point of $f$. We prove that for a generic Morse function $f$, the only solution is the trivial one $X\equiv 0$ (here generic refers to explicit arithmetic properties of the eigenvalues of the Hessian of $f$ at $p$). Our results stem from the introduction of algebraic obstructions, which are discussed in detail throughout the paper., Comment: 26 pages