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We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`{e}che's multivariable Tauberian theorem. We also give the lower bound of the exponent of $\log$ factor in the conjecture of Jutila. As an application, we give a lower bound of a weighted average of shifted moments of quadratic Dirichlet $L$-functions., Comment: 14 pages

Each year, the European Space Agency (ESA) organizes challenges for university students, from BSc to PhD levels. The ESA Concurrent Engineering Challange 2024 was hosted by four Concurrent Design Facilites (CDF) across Europe: ESEC Galazia, ISAE SUPAERO, the University of Athens, and the University of Portsmouth. A total of 102 students participated in the event. Over five days, students worked on a feasibility study for a space mission, simulating ESA's design session at ESTEC, the ESA headquarters. Students were divided into specializes groups based on their backgrounds, reflecting ESA's concurrent engineering teams. This paper discusses the design of subsystems by students, their trade-off results, and the outcomes of the CDF study. It highlights the effectiveness of concurrent engineering, which enabled rapid and efficient results even from non-esxpert teams. The future development roadmap and lessons learned are also presented. The students used CDP4-Comet software within the replicated ESA CDF, resulting in the PEDRO-V mission proposal: Planetary Exploration Deployment and Research Operation - Venus. The teams collaboratively defined the Concept of Operations, identified actors, worst-case scenarios, use cases, and activities. Their output included a list of requirements, a draft product breakdown structure, and key subsystems information. The concurrent engineering process led to continuous improvement and convergence of key parameters. This approach proved to be effective by aligning different teams' solutions and comparing them to similar missions. The PEDRO-V mission feasibility was confirmed, demonstrating the potential of concurrent engineering in accademic settings for space missions. (summarized with AI), Comment: ESA SECESA 2024 Conference, Strasbourg (France), 8 pages

We substitute individual Pt atoms into monolayer MoS$_2$ and study the resulting atomic structures with single-sideband (SSB) ptychography supported by ab initio simulations. We demonstrate that while high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) imaging provides excellent Z-contrast, distinguishing some defect types such as single and double sulfur vacancies remains challenging due to their low relative contrast difference. However, SSB with its nearly linear Z-contrast and high phase sensitivity enables reliable identification of these defect configurations as well as various Pt dopant structures at significantly lower electron doses. Our findings uncover the precise atomic placement and highlight the potential of SSB ptychography for detailed structural analysis of dopant-modified 2D materials while minimizing beam-induced damage, offering new pathways for understanding and engineering atomic-scale features in 2D systems.

Accurate computational ptychographic phase reconstructions are enabled by fast direct-electron cameras with high dynamic ranges used for four-dimensional scanning transmission electron microscopy (4D-STEM). The availability of open software packages is making such analyses widely accessible, and especially when implemented in Python, easy to compare in terms of computational efficiency and reconstruction quality. In this contribution, I reconstruct atomic phase shifts from convergent-beam electron diffraction maps of pristine monolayer graphene, which is an ideal dose-robust uniform phase object, acquired on a Dectris ARINA detector installed in a Nion UltraSTEM 100 operated at 60 keV with a focused-probe convergence semi-angle of 34 mrad. For two different recorded maximum scattering angle settings, I compare a range of direct and iterative open-source phase reconstruction algorithms, evaluating their computational efficiency and tolerance to reciprocal-space binning and real-space thinning of the data. The quality of the phase images is assessed by quantifying the variation of atomic phase shifts using a robust parameter-based method revealing an overall agreement with some notable differences in the absolute magnitudes and the variation of the phases. Although such variation is not a major issue when analyzing data with many identical atoms, it does put limits on what level of precision can be relied upon for unique sites such as defects or dopants, which also tend to be more dose-sensitive. Overall, these findings and the accompanying open data and code provide useful guidance for the sampling required for desired levels of phase precision, and suggest particular care is required when relying on electron ptychography for quantitative analyses of atomic-scale electromagnetic properties., Comment: 17 pages, 8 figures

In some scenarios, the dark matter relic abundance is set by the semi-annihilation of two dark matter particles into one dark matter particle and one Standard Model particle. These semi-annihilations might still be occurring today in the Galactic Center at a significant rate, generating a flux of boosted dark matter particles. We investigate the possible signals of this flux component in direct detection and neutrino experiments for sub-GeV dark matter masses. We show that for typical values of the semi-annihilation cross-section, the sensitivity of current experiments to the spin-independent dark matter-proton scattering cross-section can be several orders of magnitude larger than current constraints from cosmic-ray boosted dark matter. We also argue that the upcoming DARWIN and DUNE experiments may probe scattering cross-sections as low as $10^{-37}\,{\rm cm}^2$ for masses between 30 MeV and 1 GeV., Comment: 12 pages, 2 figures

We deal with negative square moments of Dirichlet $L$-functions. Summing over characters modulo $q$, we obtain an asymptotic formula for the negative second moment of $L(1,\chi)$ involving conductors. As an application, we give the improved lower bound on the success probability of the algorithm which recovers a short generator of the input generator of a principal ideal sampled from a specific Gaussian distribution in cyclotomic number fields., Comment: 21 pages, 1 table

This study presents the first observation of a mixed mode of charge transfer during an upward positive flash, which was initiated from the S\"antis Tower in Switzerland. High-speed camera footage, along with current and electric field measurements, revealed a downward-propagating recoil leader connecting to the grounded current-carrying plasma channel at a junction height of < 1 km above the tip of the tower. This event triggered the "return stroke"-like main pulse associated with Type 1 upward positive flashes, leading us to propose a mixed mode of charge transfer (normally observed in upward negative flashes) as the physical mechanism at play. Furthermore, the observed pulse shared characteristics with both mixed-mode and M-component -type initial continuous current (ICC) pulses, challenging existing classification criteria, and supporting the notion of a singular mode of charge transfer with a range of junction-dependent pulse characteristics, as opposed to two distinct modes. The recoil leader itself was accompanied by a sequence of fast electric field pulses indicative of step-like propagation, also an observational first. These findings contribute to improving our understanding of the mechanisms of charge transfer in upward lightning flashes.

People feel attached to places that are meaningful to them, which psychological research calls "place attachment." Place attachment is associated with self-identity, self-continuity, and psychological well-being. Even small cues, including videos, images, sounds, and scents, can facilitate feelings of connection and belonging to a place. Telepresence robots that allow people to see, hear, and interact with a remote place have the potential to establish and maintain a connection with places and support place attachment. In this paper, we explore the design space of robotic telepresence to promote place attachment, including how users might be guided in a remote place and whether they experience the environment individually or with others. We prototyped a telepresence robot that allows one or more remote users to visit a place and be guided by a local human guide or a conversational agent. Participants were 38 university alumni who visited their alma mater via the telepresence robot. Our findings uncovered four distinct user personas in the remote experience and highlighted the need for social participation to enhance place attachment. We generated design implications for future telepresence robot design to support people's connections with places of personal significance., Comment: Proceedings of the 29th ACM/IEEE International Conference on Human Robot Interaction (HRI 2025)

Minimal dark matter is an attractive candidate for dark matter because it is stabilized without the need to impose additional symmetries. It is known that the mass of the $SU(2)_L$ quintuplet fermion dark matter is predicted to be around 14 TeV, based on the thermal production mechanism. In this work, we embed the quintuplet dark matter within non-supersymmetric $SU(5)$ grand unified theories. We find that two pairs of colored sextet fermions are required at the $\mathcal{O}(1-10)~\mathrm{TeV}$ scale to achieve gauge coupling unification, with the unification scale near the reduced Planck scale. These colored sextet fermions become metastable because their interactions are suppressed by the unification scale. Our model can be tested through comprehensive searches for colored sextet fermions in collider experiments, as well as through indirect and direct detection methods for minimal dark matter., Comment: 13 pages, 1 figure

Solving the inverse problem in spiral galaxies, that allows the derivation of the spatial distribution of dust, gas and stars, together with their associated physical properties, directly from panchromatic imaging observations, is one of the main goals of this work. To this end we used radiative transfer models to decode the spatial and spectral distribution of the nearby face-on galaxies M101 and NGC 3938. In both cases we provide excellent fits to the surface-brightness distributions derived from GALEX, SDSS, 2MASS, Spitzer and Herschel imaging observations. Together with previous results from M33, NGC 628, M51 and the Milky Way, we obtain a small statistical sample of modelled nearby galaxies that we analyse in this work. We find that in all cases Milky Way-type dust with Draine-like optical properties provide consistent and successful solutions. We do not find any "submm excess", and no need for modified dust-grain properties. Intrinsic fundamental quantities like star-formation rates (SFR), specific SFR (sSFR), dust opacities and attenuations are derived as a function of position in the galaxy and overall trends are discussed. In the SFR surface density versus stellar mass surface density space we find a structurally resolved relation (SRR) for the morphological components of our galaxies, that is steeper than the main sequence (MS). Exception to this is for NGC 628, where the SRR is parallel to the MS., Comment: 31 pages

The $M1$ transition strengths between excited $2^+$ states of the neutron-rich, radioactive nuclide $^{132}$Te have been studied through direct lifetime measurements using the Doppler-shift attenuation method in a two-neutron transfer reaction on a $^{130}$Te target. An unambiguous identification of the lowest-lying mixed-symmetry $2^+$ state has been achieved on the basis of the large $B(M1;2^+_2\rightarrow2^+_1$)=0.18(2) $\mu_\mathrm{N}^2$ transition strength, in agreement with shell-model calculations. Results are compared to the shell model, and the analysis of both, data and calculations, unambiguously identifies the second-excited $2^+$ state of $^{132}$Te as the one-quadrupole phonon mixed-symmetry state of this isotope. A lowering of the energy and $B(M1;2^+_\mathrm{ms}\rightarrow 2^+_1)$ strength within the $N$=80 isotones toward the $Z$=50 shell closure is observed, which goes alongside with the lowering of the $E2$ collectivity approaching the magic proton shell.

We measure the two-dimensional elastic modulus $E^\text{2D}$ of atomically clean defect-engineered graphene with a known defect distribution and density in correlated ultra-high vacuum experiments. The vacancies are introduced via low-energy (< 200 eV) Ar ion irradiation and the atomic structure is obtained via semi-autonomous scanning transmission electron microscopy and image analysis. Based on atomic force microscopy nanoindentation measurements, a decrease of $E^\text{2D}$ from 286 to 158 N/m is observed when measuring the same graphene membrane before and after an ion irradiation-induced vacancy density of $1.0\times 10^{13}$ cm$^{-2}$. This decrease is significantly greater than what is predicted by most theoretical studies and in stark contrast to some measurements presented in the literature. With the assistance of atomistic simulations, we show that this softening is mostly due to corrugations caused by local strain at vacancies with two or more missing atoms, while the influence of single vacancies is negligible. We further demonstrate that the opposite effect can be measured when surface contamination is not removed before defect engineering, Comment: 16 pages, 10 figures

Interferometry of atomic matter waves is an essential tool in fundamental sciences [1-5] and for applied quantum sensors [6-10]. The sensitivity of interferometers scales with the momentum separation of the diffracted matter waves, leading to the development of large-momentum transfer beam splitters [11,12]. However, despite decades of research, crystalline gratings used since the first atomic diffraction experiments are still unmatched regarding momentum transfer [13]. So far, diffraction through such gratings has only been reported for subatomic particles, but never for atoms. Here, we answer to this century-old challenge by demonstrating diffraction of helium and hydrogen atoms at kiloelectronvolt energies through single-layer graphene at normal incidence. Despite the atoms' high kinetic energy and coupling to the electronic system of graphene, we observe diffraction patterns featuring coherent scattering of up to eight reciprocal lattice vectors. Diffraction in this regime is possible due to the short interaction time of the projectile with the atomically-thin crystal, limiting the momentum transfer to the grating. Our demonstration is the atomic counterpart of the first transmission experiments with electrons by Thomson and Reid [14,15], unlocking new potentials in atom diffraction. We expect our findings to inspire studies of decoherence in an uncharted energy regime and the development of new matter-wave-based sensors.

Density functional theory with linear combination of atomic orbitals (LCAO) basis sets is useful for studying large atomic systems, especially when it comes to computationally highly demanding time-dependent dynamics. We have implemented the Ehrenfest molecular dynamics (ED) method with the approximate approach of Tomfohr and Sankey within the projector augmented-wave code GPAW. We apply this method to small molecules as well as larger periodic systems, and elucidate its limits, advantages, and disadvantages in comparison to the existing implementation of Ehrenfest dynamics with a real-space grid representation. For modest atomic velocities, LCAO-ED shows satisfactory accuracy at a much reduced computational cost. This method will be particularly useful for modeling ion irradiation processes that require large amounts of vacuum in the simulation cell.

Energy is a critical driver of modern economic systems. Accurate energy price forecasting plays an important role in supporting decision-making at various levels, from operational purchasing decisions at individual business organizations to policy-making. A significant body of literature has looked into energy price forecasting, investigating a wide range of methods to improve accuracy and inform these critical decisions. Given the evolving landscape of forecasting techniques, the literature lacks a thorough empirical comparison that systematically contrasts these methods. This paper provides an in-depth review of the evolution of forecasting modeling frameworks, from well-established econometric models to machine learning methods, early sequence learners such LSTMs, and more recent advancements in deep learning with transformer networks, which represent the cutting edge in forecasting. We offer a detailed review of the related literature and categorize forecasting methodologies into four model families. We also explore emerging concepts like pre-training and transfer learning, which have transformed the analysis of unstructured data and hold significant promise for time series forecasting. We address a gap in the literature by performing a comprehensive empirical analysis on these four family models, using data from the EU energy markets, we conduct a large-scale empirical study, which contrasts the forecasting accuracy of different approaches, focusing especially on alternative propositions for time series transformers.

In this talk, we discuss the phenomenology of radiative 3-loop seesaw models. The 3-loop suppression allows the new particles to have masses at the TeV scale, along with relatively large Yukawa couplings, while retaining consistency with neutrino masses and mixing, as observed in neutrino oscillation experiments. This leads to a rich phenomenology, especially in searches for charged lepton flavor violation, where the models predict sizable rates, well within future experimental reach. The models provide viable fermionic or scalar dark matter candidates, as is typical within the scotogenic paradigm. We discuss specific realizations in which the W-mass anomaly and the baryon asymmetry of the Universe can be accommodated, while complying with current constraints imposed by electroweak precision observables, charged-lepton flavor violation and neutrinoless double-beta decay., Comment: 6 pages, 4 figures. Talk given at the 42nd International Conference on High Energy Physics - ICHEP2024 (18-24 July 2024, Prague, Czech Republic)

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time., Comment: Corresponding author: S. Doeleman

Here, we report on the measurements of the $\gamma$-ray strength functions and nuclear level densities of ${}^{112,114}$Sn performed for the first time at the 9~MV Tandem accelerator facilities at IFIN-HH using the Oslo method. We extract thermodynamic properties and gross and fine properties of the pygmy dipole resonance for systematic comparison in the chain of Sn isotopes. The results are compared with microscopic models implemented in the TALYS reaction code and the fully microscopic quasiparticle-phonon model for the underlying nuclear structure of the dipole strength in ${}^{112,114}$Sn. The quasiparticle-phonon model results show the importance of complex configurations to the low-energy dipole response in the pygmy dipole resonance energy region. The experimental data are further included in the cross-section and reaction rate calculations for the $(\mathrm{n},\gamma)$ reaction of the $p$-process nuclei ${}^{112,114}$Sn showing a significant increase in reaction rates at high temperatures compared to existing nuclear databases., Comment: 21 pages, 17 figures

In recent years there have been a growing interest in online auditing of information flow over social networks with the goal of monitoring undesirable effects, such as, misinformation and fake news. Most previous work on the subject, focus on the binary classification problem of classifying information as fake or genuine. Nonetheless, in many practical scenarios, the multi-class/label setting is of particular importance. For example, it could be the case that a social media platform may want to distinguish between ``true", ``partly-true", and ``false" information. Accordingly, in this paper, we consider the problem of online multiclass classification of information flow. To that end, driven by empirical studies on information flow over real-world social media networks, we propose a probabilistic information flow model over graphs. Then, the learning task is to detect the label of the information flow, with the goal of minimizing a combination of the classification error and the detection time. For this problem, we propose two detection algorithms; the first is based on the well-known multiple sequential probability ratio test, while the second is a novel graph neural network based sequential decision algorithm. For both algorithms, we prove several strong statistical guarantees. We also construct a data driven algorithm for learning the proposed probabilistic model. Finally, we test our algorithms over two real-world datasets, and show that they outperform other state-of-the-art misinformation detection algorithms, in terms of detection time and classification error., Comment: 42 pages

We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class $VII$ surfaces., Comment: The paper is published

The multipole expansion can be formulated in spherical and Cartesian coordinates. By constructing an explicit map linking both formulations in isotropic media, we discover a lack of equivalence between them in anisotropic media. In isotropic media, the Cartesian multipole tensor can be reduced to a spherical tensor containing fewer independent components. In anisotropic media, however, the loss of propagation symmetry prevents this reduction. Consequently, non-harmonic sources radiate fields that can be projected onto a finite set of Cartesian multipole moments but require potentially infinitely many spherical moments. For harmonic sources, the link between the two approaches provides a systematic way to construct the spherical multipole expansion from the Cartesian one. The lack of equivalence between both approaches results in physically significant effects wherever the field propagation includes the Laplace operator. We demonstrate this issue in an electromagnetic radiation inverse problem in anisotropic media, including an analysis of a large-anisotropy regime and an introduction to vector spherical harmonics. We show that the use of the Cartesian approach increases the efficiency and interpretability of the model. The proposed approach opens the door to a broader application of the multipole expansion in anisotropic media., Comment: 23 pages, 5 figures

The Blandford-Znajek (BZ) process is steady electromagnetic energy release from rotating black holes (BHs) along magnetic field lines threading them and widely believed to drive relativistic jets. This process is successfully demonstrated in general relativistic magnetohydrodynamic (MHD) simulations with the coordinate system regular on the event horizon, in which the outward Poynting flux on the horizon is considered to reduce BH energy. Meanwhile, alternative pictures for the BH energy reduction that invoke infall of negative energy objects were also discussed, although all of the proposed definitions of the negative energy and/or its infall velocity were ambiguous. We revisit the mechanism of BH energy reduction in the BZ process under the ideal MHD condition by utilizing the coordinate system singular on the horizon, in which the falling membrane of past accreted matter should exist above the horizon. We find that the Poynting flux is produced at the boundary between the falling membrane and the magnetically-dominated inflow, and the front of the inflow creates the negative electromagnetic energy, which reduces the rotational energy of spacetime. We also clarify that the poloidal electric current does not form a closed circuit within the magnetically-dominated flow. Previous interpretations of the BZ process and possibilities of violation of ideal MHD condition and BH charging are also discussed., Comment: 17 pages, 4 figures; accepted for publication in PTEP

Traumatic brain injury (TBI) can cause a range of cognitive and communication challenges that negatively affect social participation in both face-to-face interactions and computer-mediated communication. In particular, individuals with TBI report barriers that limit access to participation on social media platforms. To improve access to and use of social media for users with TBI, we introduce the Social Media Accessibility and Rehabilitation Toolkit (\textbf{SMART-TBI}). The toolkit includes five aids (Writing Aid, Interpretation Aid, Filter Mode, Focus Mode, and Facebook Customization) designed to address the cognitive and communicative needs of individuals with TBI. We asked eight users with moderate-severe TBI and five TBI rehabilitation experts to evaluate each aid. Our findings revealed potential benefits of aids and areas for improvement, including the need for psychological safety, privacy control, and balancing business and accessibility needs; and overall mixed reactions among the participants to AI-based aids., Comment: In Proceedings The 26th International ACM SIGACCESS Conference on Computers and Accessibility (ASSETS'24)

We report the first observation of the nearby giant radio galaxy NGC 315 using a global VLBI array consisting of 22 radio antennas located across five continents, including high-sensitivity stations, at 22 GHz. Utilizing the extensive $(u,v)$-coverage provided by the array, coupled with the application of a recently developed super-resolution imaging technique based on the regularized maximum likelihood method, we were able to transversely resolve the NGC 315 jet at parsec scales for the first time. Previously known for its central ridge-brightened morphology at similar scales in former VLBI studies, the jet now clearly exhibits a limb-brightened structure. This finding suggests an inherent limb-brightening that was not observable before due to limited angular resolution. Considering that the jet is viewed at an angle of $\sim50^\circ$, the observed limb-brightening is challenging to reconcile with the magnetohydrodynamic models and simulations, which predict that the Doppler-boosted jet edges should dominate over the non-boosted central layer. The conventional jet model that proposes a fast spine and a slow sheath with uniform transverse emissivity may pertain to our observations. However, in this model, the relativistic spine would need to travel at speeds of $\Gamma\gtrsim6.0-12.9$ along the de-projected jet distance of (2.3-10.8) $\times 10^3$ gravitational radii from the black hole. We propose an alternative scenario that suggests higher emissivity at the jet boundary layer, resulting from more efficient particle acceleration or mass loading onto the jet edges, and consider prospects for future observations with even higher angular resolution., Comment: 25 pages, 12 figures, 1 table, accepted for publication in the Astrophysical Journal Letters

It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma ``An essentially saturated surface not of K\"ahler-type", {\em Bull. of the LMS}, 40(5):845--854, 2008], require studying finite unramified covers of OT-manifolds., Comment: The paper is published

The electrocardiogram (ECG) is a ubiquitous diagnostic test. Conventional task-specific ECG analysis models require large numbers of expensive ECG annotations or associated labels to train. Transfer learning techniques have been shown to improve generalization and reduce reliance on labeled data. We present ECG-FM, an open foundation model for ECG analysis, and conduct a comprehensive study performed on a dataset of 1.66 million ECGs sourced from both publicly available and private institutional sources. ECG-FM adopts a transformer-based architecture and is pretrained on 2.5 million samples using ECG-specific augmentations and contrastive learning, as well as a continuous signal masking objective. Our transparent evaluation includes a diverse range of downstream tasks, where we predict ECG interpretation labels, reduced left ventricular ejection fraction, and abnormal cardiac troponin. Affirming ECG-FM's effectiveness as a foundation model, we demonstrate how its command of contextual information results in strong performance, rich pretrained embeddings, and reliable interpretability. Due to a lack of open-weight practices, we highlight how ECG analysis is lagging behind other medical machine learning subfields in terms of foundation model adoption. Our code is available at https://github.com/bowang-lab/ECG-FM/., Comment: 22 pages, 7 figures, 10 tables

We present a study of the scattering of a monochromatic helical laser beam, described by a Laguerre-Gauss solution of the Maxwell equations, on an electron sheet, initially at rest in the focal plane of the laser; the interaction is described in the framework of a local plane wave approximation. We calculate the scattered electromagnetic field observed in an arbitrary point at a large distance from the laser focal spot, by adding coherently the contributions of each electron in the electron sheet. Due to the interference effects, the radiation is emitted only into the forward direction, within a narrow cone, and it has a spatial structure that we analyze theoretically and numerically. For circularly polarized incident fields, the structure is also helical, with a helical index which depends on the helical index of the incident radiation and the harmonic order. These structures can be observed experimentally, as each harmonic order is emitted with a different frequency, and within cones of different opening angles. Our findings are in agreement with experimental results in the literature which demonstrate the generation of OAM carrying photons by radiation scattering on electrons.

While the traditional formulation of machine learning tasks is in terms of performance on average, in practice we are often interested in how well a trained model performs on rare or difficult data points at test time. To achieve more robust and balanced generalization, methods applying sharpness-aware minimization to a subset of worst-case examples have proven successful for image classification tasks, but only using deep neural networks in a scenario where the most difficult points are also the least common. In this work, we show how such a strategy can dramatically break down under more diverse models, and as a more robust alternative, instead of typical sharpness we propose and evaluate a training criterion which penalizes poor loss concentration, which can be easily combined with loss transformations such as CVaR or DRO that control tail emphasis.

The afterglows of gamma-ray bursts are non-thermal electron synchrotron emissions from relativistic shocks. The origin of strong magnetic field in the emission region remains elusive, and two field amplification mechanisms via the plasma kinetic and magnetohydrodynamic instabilities have been discussed. The polarimetric observations are a powerful probe to distinguish these two mechanisms. So far, most theoretical works have focused on the former mechanism and constructed afterglow polarization models with microscopic-scale turbulence whose coherence length is much smaller than the thickness of the blast wave. In this work, focusing on the latter mechanism, we utilize our semi-analytic model of the synchrotron polarization with large-scale turbulence whose coherence length is comparable to the thickness of the blast wave to investigate the effect of magnetic field anisotropy and the observer viewing angle. We find that the polarization in our large-scale turbulence model can exhibit both behaviors characteristic of the microscopic-scale turbulence model and those not seen in the microscopic-scale model. Then we find that the large-scale model could explain all the polarimetric observational data to date that seem to be forward shock emission. We also examine the effect of ordered-field component, and find that polarization degree and polarization angle constant in time are realized only when the energy density ratio of the ordered and fluctuated components is $\gtrsim 50$. In this case, however, the polarization degree is much higher than the observed values., Comment: Submitted to ApJ, comments welcome

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.

We study the moduli stacks of slope-semistable torsion-free coherent sheaves that admit reflexive, respectively locally free, Seshadri graduations on a smooth projective variety. We show that they are open in the stack of coherent sheaves and that they admit good moduli spaces when the field characteristic is zero. In addition, in the locally free case we prove that the resulting moduli space is a quasi-projective scheme., Comment: v2: Added remarks 3.1 and 3.2 on openness in the analytic case, small notational change