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Kapranov and Schechtman defined the category FP of factorized perverse sheaves on Sym(C) smooth along the stratification given by multiplicities and with values in a braided monoidal category V. We define for each d\in N the category FP^{\leq d} of factorized perverse sheaves on the disjoint union of Sym^n(C) for n\leq d and the category FP_{\leq d} of factorized perverse sheaves on the open subset of Sym(C) consisting of multi-sets with multiplicities bounded by d. We show that the families (FP^{\leq d})_{d in N} and (FP_{\leq d})_{d in N} fit into systems of categories whose inverse limit is FP, and that for each d the natural restriction functor from FP_{\leq d} to FP^{\leq d} is faithful and compatible with taking the limit. For d=1 we prove that the natural restriction functor is an equivalence and that FP^{\leq 1} and FP_{\leq 1} are equivalent to V.

In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites., Comment: 28 pages

We present a novel microfluidic method to produce quasi-monodisperse bubbles with diameters from tens to very few microns. A gaseous rivulet flows over the shallow groove printed on a T-junction exit channel. The triple contact line delimiting the rivulet is pinned to the groove edges. The rivulet breaks up into bubbles much smaller than the exit channel. When operating under adequate conditions, the flow transitions toward a singular mode where the rivulet remains quasi-static and emits bubbles smaller than the groove width. This allows the production of bubbles with diameters in the 3-5 $\mu$m range, which is preferable for relevant therapeutical applications.

Global sensing enables parameter estimation across arbitrary parameter ranges with a finite number of shots. While various formulations exist, the Bayesian paradigm offers a flexible approach to optimal protocol design under minimal assumptions. However, there are several sets of assumptions capturing the notions of prior ignorance and uninformed estimation, leading to two main approaches: invariance of the prior distribution under specific parameter transformations, and adherence to the geometry of a state space. While the first approach often leads to simpler priors and estimators and is more broadly applicable in adaptive settings, the second can lead to faster posterior convergence in a well-defined measurement setting. We examine the practical consequences of both approaches and show how to apply them in examples of rate and coherence estimation in noisy scenarios. More importantly, by employing the notion of location-isomorphic parameters, we unify the two approaches into a practical and versatile framework for optimal global quantum sensing, detailing when and how each set of assumptions should be employed - a blueprint for the design of quantum sensors., Comment: 17 pages, 5 figures

We investigate the performance of Opticks, an NVIDIA OptiX API 7.5 GPU-accelerated photon propagation compared with a single-threaded Geant4 simulation. We compare the simulations using an improved model of the NEXT-CRAB-0 gaseous time projection chamber. Performance results suggest that Opticks improves simulation speeds by between $58.47\pm{0.02}$ and $181.39\pm{0.28}$ times relative to a CPU-only Geant4 simulation and these results vary between different types of GPU and CPU. A detailed comparison shows that the number of detected photons, along with their times and wavelengths, are in good agreement between Opticks and Geant4., Comment: 12 pages, 8 Figures

Two-dimensional twisted bilayer moir\'e structures provide a versatile material platform for realizing a rich variety of strongly correlated electronic quantum phases intricately coupled with the periodically modulated lattice structures. In this work, we use ultrafast electron diffraction to directly reveal the photoinduced dynamic evolution of the moir\'e superlattice in $2^\circ$ and $57^\circ$ twisted WSe$_2$/MoSe$_2$ heterobilayers. Upon above-band-gap photoexcitation, the moir\'e superlattice diffraction features are enhanced within 1 ps and subsequently suppressed several picoseconds after, accompanied by a collective lattice excitation of a moir\'e phonon mode with sub-THz frequency. This unique response deviates markedly from typical photoinduced lattice heating, and suggests dynamic twisting and untwisting of the local moir\'e chiral structure. We infer large oscillations in the local twist angle, approaching $1^\circ$ peak to trough, that are driven by ultrafast charge carrier excitation and relaxation -- a phenomenon further supported by molecular dynamics simulations. Our findings suggest a novel approach for real-time dynamic reconfiguration of moire superlattices to achieve ultrafast modulation of their strongly correlated behaviors.

Binarity in massive stars has proven to be an important aspect in the their evolution. For Be stars, it might be the cause of their spin up, and thus part of the mechanism behind the formation of their viscous decretion disks. Detecting companions in systems with Be stars is challenging, making it difficult to obtain observational constraints on their binary fraction. We explore the effects of a binary companion in a system with a Be star, from disk formation to quasi steady-state using smoothed particle hydrodynamics (SPH) simulations of coplanar, circular binary systems. High spatial resolution is achieved by adopting particle splitting in the SPH code, as well as a more realistic description of the secondary star and the disk viscosity. The tidal forces considerably affect the Be disk, forming distinct regions in the system, with observational consequences that can be used to infer the presence of a otherwise undetectable companion. With the upgraded code, we can probe a region approximately 4 times larger than previously possible. We describe the configuration and kinematics of each part of the system, and provide a summary of their expected observational signals. Material that enters the Roche lobe of the companion is partially captured by it, forming a rotationally supported, disk-like structure. Material not accreted escapes and forms a circumbinary disk around the system. This is the first work to describe the region beyond the truncation region of the Be disk and its observational consequences with detail. We argue that observational features of previously unclear origin, such as the intermittent shell features and emission features of HR 2142 and HD 55606, originate in areas beyond the truncation region. This new understanding of the behavior of disks in Be binaries will allow not just for better interpretation of existing data, but also for the planning of future observations.

One of the instruments aboard the Sunrise III mission, the Tunable Magnetograph (TuMag), is a tunable imaging spectropolarimeter in visible wavelengths. It is designed to probe the vector magnetic field and the line-of-sight velocity of the photosphere and the lower chromosphere. The quasi-simultaneous observation of two spectral lines provides excellent diagnostic measurements of the magnetic and dynamic coupling in these layers. The key technologies employed for TuMag are an LCVR-based polarimeter and a solid, LiNbO3 Fabry-P\'erot etalon as a spectrometer. However, it also incorporates several innovative features, such as home-made high-sensitivity scientific cameras and a double filter wheel. TuMag can sequentially observe any two out of the three spectral lines of Fe I at 525.02 and 525.06 nm and of Mg I at 517.3 nm. Laboratory measurements have demonstrated outstanding performance, including a wavefront root-mean-square error better than {\lambda}/13 for image quality, a full-width-at-half-maximum of 8.7 pm for the filtergraph transmission profile, and polarimetric efficiencies > 0.54. Here we report on the concept, design, calibration, and integration phases of the instrument, as well as on the data reduction pipeline., Comment: Contains 58 pages and 25 figures; to be published in Solar Physics Topical Collection "The Sunrise III Solar Observatory" (https://link.springer.com/collections/jegdciedig)

This work introduces Salamandra, a suite of open-source decoder-only large language models available in three different sizes: 2, 7, and 40 billion parameters. The models were trained from scratch on highly multilingual data that comprises text in 35 European languages and code. Our carefully curated corpus is made exclusively from open-access data compiled from a wide variety of sources. Along with the base models, supplementary checkpoints that were fine-tuned on public-domain instruction data are also released for chat applications. Additionally, we also share our preliminary experiments on multimodality, which serve as proof-of-concept to showcase potential applications for the Salamandra family. Our extensive evaluations on multilingual benchmarks reveal that Salamandra has strong capabilities, achieving competitive performance when compared to similarly sized open-source models. We provide comprehensive evaluation results both on standard downstream tasks as well as key aspects related to bias and safety.With this technical report, we intend to promote open science by sharing all the details behind our design choices, data curation strategy and evaluation methodology. In addition to that, we deviate from the usual practice by making our training and evaluation scripts publicly accessible. We release all models under a permissive Apache 2.0 license in order to foster future research and facilitate commercial use, thereby contributing to the open-source ecosystem of large language models.

Tuning the chemical potential of a solid to the vicinity of a van Hove singularity (vHS) is a well-established route to discovering emergent quantum phases. In monolayer graphene, the use of electron-donating metal layers has recently emerged as a method to dope the chemical potential to the nearest vHS, as evidenced by Angle-Resolved Photoemission Spectroscopy (ARPES) measurements. In this work, we study the spatial uniformity of the doping from this process using spectroscopic imaging scanning tunneling microscopy (SI-STM). Using molecular beam epitaxy (MBE), we achieve electron doping of graphene on SiC using Ytterbium (Yb-Graphene). We show using in-situ ARPES that the chemical potential is shifted to within 250 meV of the vHS. Using in-situ SI-STM, we establish that there exists significant inhomogeneity in the vHS position in overdoped graphene. We find two separate reasons for this. First, the spatial inhomogeneity of the intercalated Yb leads to local variations in the doping, with a length scale of inhomogeneity set by the screening length of ~ 3 nm. Second, we observe the presence of substitutional Yb dopants in the graphene basal plane. These Yb dopants cause a strong local shift of the doping, along with a renormalization of the quasiparticle amplitude. Theoretical calculations confirm that the Yb impurities effectively change the local potential, thus energetically shifting the position of the van Hove singularity. Our results point to the importance of considering the spatial structure of doping and its inextricable link to electronic structure.

We consider a linear array of trapped ions subjected to local parametric modulation of the trapping potential and continuous laser cooling. In our model, the phase of the parametric modulation varies linearly along the array, breaking time-reversal symmetry and inducing non-trivial topological effects. The linear response to an external force is investigated with the Green's function formalism. We predict the appearance of topological amplification regimes in which the trapped ion array behaves as a directional amplifier of vibrational excitations. The emergence of topological phases is determined by a winding number related to non-Hermitian point-gap topology. Beyond its fundamental interests as a topological driven-dissipative system, our setup can be used for quantum sensing of ultra-weak forces and electric fields. We consider a scheme in which a trapped ion at one edge of the array acts as a sensor of an ultra-weak force, and the vibrational signal gets amplified towards the last trapped ion, which acts as a detector. We consider arrays of 2-30 $^{25}$Mg$^+$ ions, assuming that the detector ion's displacement is measured via fluorescence with a spatial resolution of 200-500 nm, and predict sensitivities as small as 1 yN $\cdot$ Hz$^{-1/2}$. Our system has the advantage that the detected force frequency can be tuned by adjusting the frequency of the periodic drive., Comment: 17 pages, 17 figures

In July 2024, Sunrise completed its third successful science flight. The Sunrise III observatory had been upgraded significantly after the two previous successful flights in 2009 and 2013. Three completely new instruments focus on the small-scale physical processes and their complex interaction from the deepest observable layers in the photosphere up to chromospheric heights. Previously poorly explored spectral regions and lines are exploited to paint a three-dimensional picture of the solar atmosphere with unprecedented completeness and level of detail. The full polarimetric information is captured by all three instruments to reveal the interaction between the magnetic fields and the hydrodynamic processes. Two slit-based spectropolarimeters, the Sunrise UV Spectropolarimeter and Imager (SUSI) and the Sunrise Chromospheric Infrared spectro-Polarimeter (SCIP), focus on the near-ultraviolet and the near-infrared regions respectively, and the imaging spectropolarimeter Tunable Magnetograph (TuMag) simultaneously obtains maps of the full field-of-view of $46 \times 46$ Mm$^2$ in the photosphere and the chromosphere in the visible. The instruments are operated in an orchestrated mode, benefiting from a new Image Stabilization and Light Distribution unit (ISLiD), with the Correlating Wavefront Sensor (CWS) providing the autofocus control and an image stability with a root-mean-square value smaller than 0.005''. A new gondola was constructed to significantly improve the telescope pointing stability, required to achieve uninterrupted observations over many hours. Sunrise III was launched successfully on July 10, 2024, from the Esrange Space Center near Kiruna (Sweden). It reached the landing site between the Mackenzie River and the Great Bear Lake in Canada after a flight duration of 6.5 days. In this paper, we give an overview of the Sunrise III observatory and its instruments., Comment: 67 pages, 25 figures; to be published in Solar Physics Topical Collection "The Sunrise III Solar Observatory" (https://link.springer.com/collections/jegdciedig)

Maximizing the spectral gap through graph rewiring has been proposed to enhance the performance of message-passing graph neural networks (GNNs) by addressing over-squashing. However, as we show, minimizing the spectral gap can also improve generalization. To explain this, we analyze how rewiring can benefit GNNs within the context of stochastic block models. Since spectral gap optimization primarily influences community strength, it improves performance when the community structure aligns with node labels. Building on this insight, we propose three distinct rewiring strategies that explicitly target community structure, node labels, and their alignment: (a) community structure-based rewiring (ComMa), a more computationally efficient alternative to spectral gap optimization that achieves similar goals; (b) feature similarity-based rewiring (FeaSt), which focuses on maximizing global homophily; and (c) a hybrid approach (ComFy), which enhances local feature similarity while preserving community structure to optimize label-community alignment. Extensive experiments confirm the effectiveness of these strategies and support our theoretical insights., Comment: Accepted at ICLR 2025

We explore a minimal scenario where the sole Standard-Model Higgs is responsible for reheating the Universe after inflation, produces a significant background of gravitational waves and maintains the full classical stability of the electroweak vacuum. As the Higgs self-coupling runs toward negative values at high energy scales, a non-minimal interaction with curvature during a stiff background expansion era drives the Higgs fluctuations closer to the instability scale. This curvature-induced tachyonic instability leads to an intense production of Higgs particles, accompanied by a stochastic gravitational-wave background. The characteristic features of such signal can be directly correlated to the inflationary scale, the non-minimal coupling parameter and the top quark Yukawa coupling. We distinguish between three possible scenarios: absolute stability with low top quark masses, potential vacuum instability, and absolute stability with new physics above the instability scale. Our findings suggest that the detection of a peaked background of gravitational waves together with its inflationary tail has the potential to unveil the features of the Higgs effective potential at very high energy scales while providing a minimal explanation for the reheating phase and the emergence of the Standard-Model plasma in the early Universe. Unlike other studies in the literature, the generation of gravitational waves in our scenario does not depend on the quantum instability of the Standard Model vacuum., Comment: 20 pages, 7 figures

Most superconducting mechanisms pair electrons within the same band, forming spin singlets. However, the discovery of multi-band superconductivity has opened new scenarios for pairing, particularly in systems with strong spin-orbit coupling. Here, we reveal inter-band pairing in the superconductor \bipd\ by mapping the amplitude of sub-gap Yu-Shiba-Rusinov (YSR) states around Vanadium adatoms deposited on its surface. The surface of \bipd\ is characterized by spin-helical-like bands near the Fermi level. Scanning tunneling spectroscopy reveals anisotropic YSR amplitude oscillations around the impurity, driven by spin-conserving Bogoliubov quasiparticle interference (BQPI). Analysis of the BQPI patterns at the YSR energy exposes inter-band pairing in this material. Interestingly, only a small subset of all possible inter-band scattering processes observed in the normal state contribute to the BQPI patterns. Combining experimental data and theory, we demonstrate that the observed band selectivity results from the hybridization of the band coupled with the impurity with other bands. Our findings reveal unconventional pairing mechanisms in \bipd\ and highlight the crucial role of spin-orbit interactions in their formation., Comment: 6 pages, 5 figures

This paper focuses on the affective component of a Driver Behavioural Model (DBM), specifically modelling some driver's mental states, such as mental load and active fatigue, which may affect driving performance. We used Bayesian networks (BNs) to explore the dependencies between various relevant variables and estimate the probability that a driver was in a particular mental state based on their physiological and demographic conditions. Through this approach, our goal is to improve our understanding of driver behaviour in dynamic environments, with potential applications in traffic safety and autonomous vehicle technologies.

Confining electromagnetic fields inside an optical cavity can enhance the light-matter coupling between quantum materials embedded inside the cavity and the confined photon fields. When the interaction between the matter and the photon fields is strong enough, even the quantum vacuum field fluctuations of the photons confined in the cavity can alter the properties of the cavity-embedded solid-state materials at equilibrium and room temperature. This approach to engineering materials with light avoids fundamental issues of laser-induced transient matter states. To clearly differentiate this field from phenomena in driven systems, we call this emerging field cavity materials engineering. In this review, we first present theoretical frameworks, especially, ab initio methods, for describing light-matter interactions in solid-state materials embedded inside a realistic optical cavity. Next, we overview a few experimental breakthroughs in this domain, detailing how the ground state properties of materials can be altered within such confined photonic environments. Moreover, we discuss state-of-the-art theoretical proposals for tailoring material properties within cavities. Finally, we outline the key challenges and promising avenues for future research in this exciting field., Comment: 75 pages, 8 figures

The rapid aging of the global population has highlighted the need for technologies to support elderly, particularly in healthcare and emotional well-being. Facial expression recognition (FER) systems offer a non-invasive means of monitoring emotional states, with applications in assisted living, mental health support, and personalized care. This study presents a systematic review of deep learning-based FER systems, focusing on their applications for the elderly population. Following a rigorous methodology, we analyzed 31 studies published over the last decade, addressing challenges such as the scarcity of elderly-specific datasets, class imbalances, and the impact of age-related facial expression differences. Our findings show that convolutional neural networks remain dominant in FER, and especially lightweight versions for resource-constrained environments. However, existing datasets often lack diversity in age representation, and real-world deployment remains limited. Additionally, privacy concerns and the need for explainable artificial intelligence emerged as key barriers to adoption. This review underscores the importance of developing age-inclusive datasets, integrating multimodal solutions, and adopting XAI techniques to enhance system usability, reliability, and trustworthiness. We conclude by offering recommendations for future research to bridge the gap between academic progress and real-world implementation in elderly care.

Attosecond spectroscopy of materials has provided invaluable insight into light-driven coherent electron dynamics. However, attosecond spectroscopies have so far been focused on weakly-correlated materials. As a result, the behavior of strongly-correlated systems is largely unknown at sub- to few-femtosecond timescales, even though it is typically the realm at which electron-electron interactions operate. Here we conduct attosecond-resolved experiments on the correlated insulator nickel oxide, and compare its response to a common band insulator, revealing fundamentally different behaviors. The results, together with state-of-the art time-dependent $\textit{ab initio}$ calculations, show that the correlated system response is governed by a laser-driven quench of electron correlations. The evolution of the on-site electronic interaction is measured here at its natural timescale, marking the first direct measurement of Hubbard $U$ renormalization in NiO. It is found to take place within a few femtoseconds, after which structural changes slowly start to take place. The resulting picture sheds light on the entire light-induced response of a strongly-correlated system, from attosecond to long-lived effects.

We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the Euclidean setting with no dependence on geometric constants, like the minimum curvature. Building on this, we develop algorithms for g-convex, g-concave smooth min-max problems on Hadamard manifolds. Notably, one method nearly matches the gradient oracle complexity of the lower bound for Euclidean problems, for the first time.

We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in (Pedregosa et al., 2020), but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments.

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering practical stopping criteria. We present a new Frank-Wolfe algorithm utilizing an optimistic framework and provide a primal-dual convergence proof. Additionally, we propose a generalized short-step strategy aimed at optimizing a computable primal-dual gap. Interestingly, this new generalized short-step strategy is also applicable to gradient descent algorithms beyond Frank-Wolfe methods. As a byproduct, our work revisits and refines primal-dual techniques for analyzing Frank-Wolfe algorithms, achieving tighter primal-dual convergence rates. Empirical results demonstrate that our optimistic algorithm outperforms existing methods, highlighting its practical advantages.

We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.

We present the discovery of twelve metal-poor and distant pre-main sequence (PMS) candidates in the dwarf irregular galaxy Wolf-Lundmark-Melotte (WLM)~968 kpc away, at a present-day metallicity of [Fe/H] around $-$0.9. These candidates have masses between 1.25-5 M$_{\odot}$, with ages <10 Myr, and exhibit significant near-infrared excesses at 2.5 and 4.3 $\mu$m. They are concentrated within a cluster roughly 10 pc (2'') across situated in the HII region [HM95]-9. These are the most distant and metal-poor PMS stars known, and can offer new quantitative insights into star formation at low-metallicities., Comment: Accepted for publication in ApJ Letters. Comments welcome. 6 pages, 4 figures, and 1 table

In this paper, we introduce holiAtlas, a holistic, multimodal and high-resolution human brain atlas. This atlas covers different levels of details of the human brain anatomy, from the organ to the substructure level, using a new dense labelled protocol generated from the fusion of multiple local protocols at different scales. This atlas has been constructed averaging images and segmentations of 75 healthy subjects from the Human Connectome Project database. Specifically, MR images of T1, T2 and WMn (White Matter nulled) contrasts at 0.125 $mm^{3}$ resolution that were nonlinearly registered and averaged using symmetric group-wise normalisation to construct the atlas. At the finest level, the holiAtlas protocol has 350 different labels derived from 10 different delineation protocols. These labels were grouped at different scales to provide a holistic view of the brain at different levels in a coherent and consistent manner. This multiscale and multimodal atlas can be used for the development of new ultra-high resolution segmentation methods that can potentially leverage the early detection of neurological disorders., Comment: 22 pages

The optical selection rules endorsed by symmetry are crucial for understanding the optical properties of quantum materials and the associated ultrafast spectral phenomena. Herein, we introduce momentum-resolved Floquet optical selection rules using the group theory to elucidate the pump-probe photoemission spectral distributions of monolayer black phosphorus (BP), which are governed by the symmetries of both the material and the lasers. Using time-dependent density functional theory (TDDFT), we further investigate the dynamical evolution of Floquet(-Volkov) states in the photoemission spectra of monolayer BP, revealing their spectral weights at specific momenta for each sideband. These observations are comprehensively explained by the proposed Floquet optical selection rules. Our framework not only clarifies experimental photoemission spectra but also uncovers novel characteristics under different pump-probe configurations. Our results are expected to deepen the understanding of light-induced ultrafast spectra in BP and can be further extended to other Floquet systems.

We investigate the post-inflationary evolution of a non-minimally coupled inflaton field in scalar-tensor theories, framed within the flexible framework of Einstein-Cartan gravity. By focusing on a class of simplified Higgs-like scenarios, we simulate the transition from the end of inflation to the formation of oscillons using fully-fledged 3+1 classical lattice simulations. Once oscillons form, we extract their profiles and perform 1+1 simulations to evolve their radial equations. Our findings reveal that these oscillons, unlike typical cases in the literature, are relatively short-lived, due to the presence of self interactions at small field values. The radiation produced by this novel type of oscillons can quickly lead to a radiation-dominated Universe, even in the absence of additional fields or interactions. Finally, we leverage our results to derive precise predictions for the inflationary observables and the produced spectrum of gravitational waves associated with oscillon formation. Significantly, our study establishes also an upper bound on the duration of the heating phase in Einstein-Cartan Higgs inflation scenarios., Comment: 29 pages, 10 figures

We develop symmetric Cartan calculus, an analogue of classical Cartan calculus for symmetric differential forms. We first show that the analogue of the exterior derivative, the symmetric derivative, is not unique and its different choices are parametrized by torsion-free affine connections. We use a choice of symmetric derivative to generate the symmetric bracket and the symmetric Lie derivative, and give geometric interpretations of all of them. By proving the structural identities and describing the role of affine morphisms, we reveal an unexpected link of symmetric Cartan calculus with the Patterson-Walker metric, which we recast as a direct analogue of the canonical symplectic form on the cotangent bundle. We show that, in the light of the Patterson-Walker metric, symmetric Cartan calculus becomes a complete analogue of classical Cartan calculus. As an application of this new framework, we introduce symmetric cohomology, which involves Killing tensors, or, in the case of the Levi-Civita connection, Killing vector fields. We characterize the Levi-Civita connections of $\mathrm{S}^1$ in terms of symmetric cohomology and develop further techniques., Comment: 58 pages, 1 figure, Section 7 about further techniques for symmetric cohomology has been added

A universal methodology for coding-decoding the complex amplitude field of an imaged sample in coherent microscopy is presented, where no restrictions on any of the two interferometric beams are required. Thus, the imaging beam can be overlapped with, in general, any other complex amplitude distribution and, in particular, with a coherent and shifted version of itself considering two orthogonal directions. The complex field values are retrieved by a novel Cepstrum-based algorithm, named as Spatial-Shifting Cepstrum (SSC), based on a weighted subtraction of the Cepstrum transform in the cross-correlation term of the object field spectrum in addition with the generation of a complex pupil from the combination of the information retrieved from different holographic recordings (one in horizontal and one in vertical direction) where one of the interferometric beams is shifted 1 pixel. As a result, the field of view is tripled since the complex amplitudes of the three interferometric fields involved in the process are retrieved. Proof-of-concept validation of this methodology, named as Cepstrum-based Interferometric Microscopy (CIM), is provided considering an off-axis holographic configuration for retrieving the cross-correlation of the two interferometric complex amplitude fields in a compact quasi-common path Michelson interferometric configuration. Experimental results for different types of phase samples (resolution test targets for step-by-step calibration and demonstration as well as fixed biosamples) are included.

In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as heat generation due to external sources. Additionally, the thermal contact resistance at the interfaces between each pair of materials is taken into account. The problem is mathematically modeled, and explicit analytical solutions are derived using Fourier techniques. A convergent finite difference scheme is also formulated to simulate specific cases. The solution is consistent with previous results. A numerical example is provided, demonstrating the coherence between the obtained results and the physical behavior of the problem. This work was recently published for a two-layer body; the generalization to m-layer bodies allows for conclusions that enhance the theoretical understanding of heat transfer in multilayer materials and may contribute to improving the thermal design of multilayer engineering systems., Comment: 24 Pages, 4 Figures, 3 Tables, 4 Appendices. arXiv admin note: substantial text overlap with arXiv:2410.19018

In this paper, we present a human-based computation approach for the analysis of peripheral blood smear (PBS) images images in patients with Sickle Cell Disease (SCD). We used the Mechanical Turk microtask market to crowdsource the labeling of PBS images. We then use the expert-tagged erythrocytesIDB dataset to assess the accuracy and reliability of our proposal. Our results showed that when a robust consensus is achieved among the Mechanical Turk workers, probability of error is very low, based on comparison with expert analysis. This suggests that our proposed approach can be used to annotate datasets of PBS images, which can then be used to train automated methods for the diagnosis of SCD. In future work, we plan to explore the potential integration of our findings with outcomes obtained through automated methodologies. This could lead to the development of more accurate and reliable methods for the diagnosis of SCD

The exploration of ultrafast phenomena is a frontier of condensed matter research, where the interplay of theory, computation, and experiment is unveiling new opportunities for understanding and engineering quantum materials. With the advent of advanced experimental techniques and computational tools, it has become possible to probe and manipulate nonequilibrium processes at unprecedented temporal and spatial resolutions, providing insights into the dynamical behavior of matter under extreme conditions. These capabilities have the potential to revolutionize fields ranging from optoelectronics and quantum information to catalysis and energy storage. This Roadmap captures the collective progress and vision of leading researchers, addressing challenges and opportunities across key areas of ultrafast science. Contributions in this Roadmap span the development of ab initio methods for time-resolved spectroscopy, the dynamics of driven correlated systems, the engineering of materials in optical cavities, and the adoption of FAIR principles for data sharing and analysis. Together, these efforts highlight the interdisciplinary nature of ultrafast research and its reliance on cutting-edge methodologies, including quantum electrodynamical density-functional theory, correlated electronic structure methods, nonequilibrium Green's function approaches, quantum and ab initio simulations.

Nonograms are logic puzzles in which cells in a grid must be colored or left blank according to the numbers that are located in its headers. In this study, we analyze different techniques to solve this type of logical problem using an Heuristic Algorithm, Genetic Algorithm, and Heuristic Algorithm with Neural Network. Furthermore, we generate a public dataset to train the neural networks. We published this dataset and the code of the algorithms. Combination of the heuristic algorithm with a neural network obtained the best results. From state of the art review, no previous works used neural network to solve nonograms, nor combined a network with other algorithms to accelerate the resolution process.

The study of regular black holes and black hole mimickers as alternatives to standard black holes has recently gained significant attention, driven both by the need to extend general relativity to describe black hole interiors, and by recent advances in observational technologies. Despite considerable progress in this field, significant challenges remain in identifying and characterizing physically well-motivated classes of regular black holes and black hole mimickers. This report provides an overview of these challenges, and outlines some of the promising research directions -- as discussed during a week-long focus programme held at the Institute for Fundamental Physics of the Universe (IFPU) in Trieste from November 11th to 15th, 2024., Comment: 39 pages, 3 figures

Spot-size converters are key for efficient coupling of light between waveguides of different sizes. While adiabatic tapers are well suited for small size differences, they become impractically long for expansion factors around x100 which are often required when coupling integrated waveguides and free-space beams. Evanescent couplers and bragg deflectors can be used in this scenario, but their operation is inherently limited in bandwidth. Here we propose a solution based on a parabolic dielectric interface that couples light from a 0.5 um-wide waveguide to a 285 um-wide waveguide, i.e. an expansion factor of x570. We experimentally demonstrate an unprecedented bandwidth of more than 380 nm with insertion losses below 0.35 dB. We furthermore provide analytical expressions for the design of such parabolic spot-size-converters for arbitrary expansion factors.

Coherent manipulation of lattice vibrations using ultrafast light pulses enables access to nonequilibrium 'hidden' phases with designed functionalities in quantum materials. However, expanding the understanding of nonlinear light-phonon interaction mechanisms remains crucial for developing new strategies. Here, we report re-entrant ultrafast phase transitions in SrTiO3 driven by intense terahertz excitation. As the terahertz field increases, the system transitions from the quantum paraelectric (QPE) ground state to an intermediate ferroelectric phase, and then unexpectedly reverts to a QPE state above ~500 kV/cm. The latter hidden QPE phase exhibits distinct lattice dynamics compared to the initial phases, highlighting activated antiferrodistortive phonon modes. Aided by first-principles dynamical calculations, we identify the mechanism for these complex behaviors as a superposition of multiple coherently excited eigenstates of the polar soft mode. Our results reveal a previously uncharted quantum facet of SrTiO3 and open pathways for harnessing high-order excitations to engineer quantum materials in the ultrafast regime., Comment: 18 pages, 4 figures

We perform extensive simulations of the two-dimensional cavity-coupled electron gas in a modulating potential as a minimal model for cavity quantum materials. These simulations are enabled by a newly developed quantum-electrodynamical (QED) auxiliary-field quantum Monte Carlo method. We present a procedure to greatly reduce finite-size effects in such calculations. Based on our results, we show that a modified version of weak-coupling perturbation theory is remarkably accurate for a large parameter region. We further provide a simple parameterization of the light-matter correlation energy as a functional of the cavity parameters and the electronic density. These results provide a numerical foundation for the development of the QED density functional theory, which was previously reliant on analytical approximations, to allow quantitative modeling of a wide range of systems with light-matter coupling., Comment: 6 pages, 3 figures

This paper studies the relationship between the student's abilities in the second year of high school and the infrastructural endowment in all Italian municipalities, using spatial Bayesian modelling. Municipal student scores are obtained by averaging standardized and spatially homogeneous indicators of student outcomes provided by the Invalsi Institute for two subjects, Italian and Mathematics. Given the nature of the data, we employ a multilevel regression model assuming a bivariate Intrinsic Conditionally Autoregressive (ICAR) latent effect to explain the spatial variability and account for the correlation between the two subjects. Bayesian model estimation is obtained by the Integrated Nested Laplace Approximation (INLA), implemented in the \texttt{R-INLA} package. We find that alongside a significant association with the current state of school infrastructure and facilities, spatially structured latent effects are still necessary to explain the different student outcomes across municipalities.

We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as "ModMax" electrodynamics. This family of theories is the only one that preserves all the symmetries of Maxwell's theory, having applications in the study of regular black hole solutions and supersymmetry. The purpose of this article is three-fold. Firstly, we study the initial-value problem of ModMax and show, by means of a simple geometric criterion, that such a theory admits a well-posed formulation. Secondly, we prove a series of geometric inequalities relating energy, charge, angular momentum, and size in ModMax. The validity of these bounds gives strong evidence of a universal inequality conjectured by Bekenstein for macroscopic systems. Finally, we perform the first stable numerical simulations of ModMax in the highly nonlinear regime, and verify an inequality between energy, size and angular momentum in bounded domains., Comment: 16 pages, 3 figures

Recent studies of organic molecular solids are highlighted by their complex phase diagram and light-induced phenomena, such as Mott insulator, spin liquid phase, and superconductivity. However, a discrepancy between experimental observation and first-principle calculation on the $\kappa$-(BEDT-TTF)$_2$X family inhibits understanding their properties. Here, we revisit the electronic structure of $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ with the recently developed DFT+GOU method to correct the energy level of molecular orbital states in the molecular solid. Our work reveals that the insulating electronic structure of $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ originates from the energy gap between the highest occupied and the lowest unoccupied molecular orbital states of the BEDT-TTF dimers, that are the periodic unit of the molecular solid. We verify that our calculation result provides consistent band gap, optical conductivity, and evolution of the metal-insulator transition as a function of pressure with experimental observations. Especially, the superconducting dome of $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, which originates from the flat band state at the Fermi level, is reproduced. Additionally, we constructed a new low-energy lattice model based on the ability of electronic structure data that can be used to address many-body physics, such as quantum spin liquid and double-holon dynamics. Our provides a deeper understanding of the complex phase diagram and various light-induced phenomena in the $\kappa$-(BEDT-TTF)$_2$X family and the other complex organic molecular solids., Comment: 4 figures

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties of uniformly convex regularizers, turns an optimization algorithm for H\"older smooth convex losses into a uniformly stable learning algorithm with optimal statistical risk bounds on the excess risk, up to a constant factor depending on $p$. Achieving a black-box reduction for uniform stability was posed as an open question by (Attia and Koren, 2022), which had solved the Euclidean case $p=2$. We explore applications that leverage non-Euclidean geometry in addressing binary classification problems., Comment: 33 pages, no figures

The recent observation of superconductivity in the vicinity of insulating or Fermi surface reconstructed metallic states has established twisted bilayers of WSe$_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries and topology. In this work, we study the emergence of electronic ordering in twisted WSe$_2$ driven by gate-screened Coulomb interactions. Our first-principles treatment begins by constructing moir\'e Wannier orbitals that faithfully capture the bandstructure and topology of the system and project the gate-screened Coulomb interaction onto them. Using unbiased functional renormalization group calculations, we find an interplay between intervalley-coherent antiferromagnetic order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near the displacement field-tunable van-Hove singularity. Our microscopic approach establishes incommensurate intervalley-coherent antiferromagnetic spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta = 5.08^{\circ}$ twisted WSe$_2$ and demonstrates that nesting properties of the Fermi surface sheets near the higher-order van-Hove point cause an asymmetric density dependence of the spin ordering as the density is varied across the van-Hove line, in good agreement with experimental observations. We show how the region of superconducting and magnetic order evolves within the two-dimensional phase space of displacement field and electronic density as twist angle is varied between $4^{\circ} \dots 5^{\circ}$., Comment: 11 pages, 6 figures

Ordinal Classification (OC) is a machine learning field that addresses classification tasks where the labels exhibit a natural order. Unlike nominal classification, which treats all classes as equally distinct, OC takes the ordinal relationship into account, producing more accurate and relevant results. This is particularly critical in applications where the magnitude of classification errors has implications. Despite this, OC problems are often tackled using nominal methods, leading to suboptimal solutions. Although decision trees are one of the most popular classification approaches, ordinal tree-based approaches have received less attention when compared to other classifiers. This work conducts an experimental study of tree-based methodologies specifically designed to capture ordinal relationships. A comprehensive survey of ordinal splitting criteria is provided, standardising the notations used in the literature for clarity. Three ordinal splitting criteria, Ordinal Gini (OGini), Weighted Information Gain (WIG), and Ranking Impurity (RI), are compared to the nominal counterparts of the first two (Gini and information gain), by incorporating them into a decision tree classifier. An extensive repository considering 45 publicly available OC datasets is presented, supporting the first experimental comparison of ordinal and nominal splitting criteria using well-known OC evaluation metrics. Statistical analysis of the results highlights OGini as the most effective ordinal splitting criterion to date. Source code, datasets, and results are made available to the research community., Comment: 34 pages, 4 figures, 6 tables

We investigate a terahertz (THz) gas sensing platform based on all-dielectric metasurfaces that support quasi-bound states in the continuum (quasi-BIC) with both electric and magnetic dipole resonances. The structure is designed to achieve the first Kerker condition, minimizing backscattering and maximizing light-matter interaction, which significantly enhances the sensitivity of the sensor. By optimizing structural parameters, this metasurface selectively resonates at characteristic absorption frequencies of target gases, facilitating detection even at low concentrations. We validate the approach using two gases with strong but distinct THz absorption profiles: hydrogen cyanide (HCN) and sulfur dioxide (SO2). Furthermore, the free-standing design maximizes gas interaction on both sides of the metasurface, eliminating substrate-induced losses and enabling a reduced physical footprint. Our findings indicate that this metasurface outperforms standard THz sensing approaches in terms of compactness and sensitivity per path length unit, obtaining the same detection threshold as sensing in free space with a path length between 2 and 3 orders of magnitude shorter, underscoring its potential for industrial applications where the available space for sensing can be limited., Comment: 12 pages, 5 figures

Leaf-cutting ants, notorious for causing defoliation in commercial forest plantations, significantly contribute to biomass and productivity losses, impacting forest producers in Brazil. These ants construct complex underground nests, highlighting the need for advanced monitoring tools to extract subsurface information across large areas. Synthetic Aperture Radar (SAR) systems provide a powerful solution for this challenge. This study presents the results of electromagnetic simulations designed to detect leaf-cutting ant nests in industrial forests. The simulations modeled nests with 6 to 100 underground chambers, offering insights into their radar signatures. Following these simulations, a field study was conducted using a drone-borne SAR operating in the P-band. A helical flight pattern was employed to generate high-resolution ground tomography of a commercial eucalyptus forest. A convolutional neural network (CNN) was implemented to detect ant nests and estimate their sizes from tomographic data, delivering remarkable results. The method achieved an ant nest detection accuracy of 100%, a false alarm rate of 0%, and an average error of 21% in size estimation. These outcomes highlight the transformative potential of integrating Synthetic Aperture Radar (SAR) systems with machine learning to enhance monitoring and management practices in commercial forestry., Comment: 8 pages, 22 figures, 4 tables

Finding players with similar profiles is an important problem in sports such as football. Scouting for new players requires a wealth of information about the available players so that similar profiles to that of a target player can be identified. However, information about the position of the players in the field is seldom used. For this reason, a novel approach based on spatial data analysis is introduced to produce a spatial similarity index that can help to identify similar players. The use of this new spatial similarity index is illustrated to identify similar players using spatial data from the Spanish competition "La Liga", season 2019-2020.

The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and injective dimension, respectively. For a local ring $R$ and finitely generated $R$-modules $M$ and $N$, we provide conditions involving quasi-homological dimensions where the equality $\sup \lbrace i\geq 0: \operatorname{Ext}_R^i(M,N)\not=0 \rbrace =\operatorname{depth} R-\operatorname{depth} M$, which we call Ischebeck's formula, holds. One of the results in this direction generalizes a well-known result of Ischebeck concerning modules of finite injective dimension, considering the quasi-injective dimension. On the other hand, we establish an inequality relating the quasi-projective dimension of a finitely generated module to its grade and introduce the concept of a quasi-perfect module as a natural generalization of a perfect module. We prove several results for this new concept similar to the classical results. Additionally, we provide a formula for the grade of finitely generated modules with finite quasi-injective dimension over a local ring, as well as grade inequalities for modules of finite quasi-projective dimension. In our study, Cohen-Macaulayness criteria are also obtained., Comment: 20 pages, comments and suggestions are welcome

This paper considers a broadcast multiple-input multiple-output (MIMO) network with multiple users and simultaneous wireless information and power transfer (SWIPT). In this scenario, it is assumed that some users are able to harvest power from radio frequency (RF) signals to recharge batteries through wireless power transfer from the transmitter, while others are served simultaneously with data transmission. The criterion driving the optimization and design of the system is based on the weighted sum rate for the users being served with data. At the same time, constraints stating minimum per-user harvested powers are included in the optimization problem. This paper derives the structure of the optimal transmit covariance matrices in the case where both types of users are present simultaneously in the network, particularizing the results to the cases where either only harvesting nodes or only information users are to be served. The tradeoff between the achieved weighted sum rate and the powers harvested by the user terminals is analyzed and evaluated using the rate-power (R-P) region. Finally, we propose a two-stage user grouping mechanism that decides which users should be scheduled to receive information and which users should be configured to harvest energy from the RF signals in each particular scheduling period, this being one of the main contributions of this paper., Comment: Paper accepted to be published at EURASIP Journal on Wireless Communications and Networking, https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/s13638-019-1460-y

Federated Learning (FL) has emerged as a solution for distributed model training across decentralized, privacy-preserving devices, but the different energy capacities of participating devices (system heterogeneity) constrain real-world implementations. These energy limitations not only reduce model accuracy but also increase dropout rates, impacting on convergence in practical FL deployments. In this work, we propose LeanFed, an energy-aware FL framework designed to optimize client selection and training workloads on battery-constrained devices. LeanFed leverages adaptive data usage by dynamically adjusting the fraction of local data each device utilizes during training, thereby maximizing device participation across communication rounds while ensuring they do not run out of battery during the process. We rigorously evaluate LeanFed against traditional FedAvg on CIFAR-10 and CIFAR-100 datasets, simulating various levels of data heterogeneity and device participation rates. Results show that LeanFed consistently enhances model accuracy and stability, particularly in settings with high data heterogeneity and limited battery life, by mitigating client dropout and extending device availability. This approach demonstrates the potential of energy-efficient, privacy-preserving FL in real-world, large-scale applications, setting a foundation for robust and sustainable pervasive AI on resource-constrained networks.