We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.

This study presents a combined experimental and computational investigation of an oloid shaped particle settling in a quiescent fluid. The oloid, a unique convex shape with anisotropic geometry, provides a distinctive model for exploring how a particle's shape and orientation affect its settling dynamics. The settling oloids are tracked experimentally for Galileo numbers $48 \leq \text{Ga} \leq 5.4 \cdot 10^3$, using two particle sizes ($D_{\text{eq}}$ = 21.6 mm, and $D_{\text{eq}}$ = 10.8 mm). The density ratio between the particle and fluid $\Gamma$ = $\frac{\rho_p}{\rho_f}$ ranges from $1.11 \leq \Gamma \leq 1.30$ in the experiments. Computationally, the Galileo numbers $10 \leq \text{Ga} \leq 100$ are simulated, with $\Gamma = 2$. The experimental findings and numerical results are in good agreement, and give a consistent idea of the oloid settling dynamics. Our results indicate two distinct falling modes for the oloid, separated by Galileo number. The stable mode is characterised by a preferential orientation, with a rotation around the vertical axis, whereas the tumbling mode has randomly distributed orientation and rotation statistics. We characterise the falling velocity, orientation, and rotation dynamics of the oloids over a range of Galileo numbers. Additionally, the influence of the initial orientation is revealed to determine the rotation dynamics at low Galileo numbers.

Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each step. This study improves IRK efficiency by leveraging parallelism to decouple stage computations and reduce communication overhead, specifically we stably decouple a perturbed version of the stage system of equations and recover the exact solution by solving a Sylvester matrix equation with an explicitly known low-rank right-hand side. Two IRK families -- symmetric methods and collocation methods -- are analyzed, with extensions to nonlinear problems using a simplified Newton method. Implementation details, shared memory parallel code, and numerical examples, particularly for ODEs from spatially discretized PDEs, demonstrate the efficiency of the proposed IRK technique.

e-ASTROGAM (enhanced ASTROGAM) is a breakthrough Observatory space mission, with a detector composed by a Silicon tracker, a calorimeter, and an anticoincidence system, dedicated to the study of the non-thermal Universe in the photon energy range from 0.3 MeV to 3 GeV - the lower energy limit can be pushed to energies as low as 150 keV for the tracker, and to 30 keV for calorimetric detection. The mission is based on an advanced space-proven detector technology, with unprecedented sensitivity, angular and energy resolution, combined with polarimetric capability. Thanks to its performance in the MeV-GeV domain, substantially improving its predecessors, e-ASTROGAM will open a new window on the non-thermal Universe, making pioneering observations of the most powerful Galactic and extragalactic sources, elucidating the nature of their relativistic outflows and their effects on the surroundings. With a line sensitivity in the MeV energy range one to two orders of magnitude better than previous generation instruments, e-ASTROGAM will determine the origin of key isotopes fundamental for the understanding of supernova explosion and the chemical evolution of our Galaxy. The mission will provide unique data of significant interest to a broad astronomical community, complementary to powerful observatories such as LIGO-Virgo-GEO600-KAGRA, SKA, ALMA, E-ELT, TMT, LSST, JWST, Athena, CTA, IceCube, KM3NeT, and LISA.

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

We present the first results from an all-sky all-frequency (ASAF) search for an anisotropic stochastic gravitational-wave background using the data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. Upper limit maps on broadband anisotropies of a persistent stochastic background were published for all observing runs of the LIGO-Virgo detectors. However, a broadband analysis is likely to miss narrowband signals as the signal-to-noise ratio of a narrowband signal can be significantly reduced when combined with detector output from other frequencies. Data folding and the computationally efficient analysis pipeline, {\tt PyStoch}, enable us to perform the radiometer map-making at every frequency bin. We perform the search at 3072 {\tt{HEALPix}} equal area pixels uniformly tiling the sky and in every frequency bin of width $1/32$~Hz in the range $20-1726$~Hz, except for bins that are likely to contain instrumental artefacts and hence are notched. We do not find any statistically significant evidence for the existence of narrowband gravitational-wave signals in the analyzed frequency bins. Therefore, we place $95\%$ confidence upper limits on the gravitational-wave strain for each pixel-frequency pair, the limits are in the range $(0.030 - 9.6) \times10^{-24}$. In addition, we outline a method to identify candidate pixel-frequency pairs that could be followed up by a more sensitive (and potentially computationally expensive) search, e.g., a matched-filtering-based analysis, to look for fainter nearly monochromatic coherent signals. The ASAF analysis is inherently independent of models describing any spectral or spatial distribution of power. We demonstrate that the ASAF results can be appropriately combined over frequencies and sky directions to successfully recover the broadband directional and isotropic results.

Optical variability has proven to be an effective way of detecting AGNs in imaging surveys, lasting from weeks to years. In the present work we test its use as a tool to identify AGNs in the VST multi-epoch survey of the COSMOS field, originally tailored to detect supernova events. We make use of the multi-wavelength data provided by other COSMOS surveys to discuss the reliability of the method and the nature of our AGN candidates. Our selection returns a sample of 83 AGN candidates; based on a number of diagnostics, we conclude that 67 of them are confirmed AGNs (81% purity), 12 are classified as supernovae, while the nature of the remaining 4 is unknown. For the subsample of AGNs with some spectroscopic classification, we find that Type 1 are prevalent (89%) compared to Type 2 AGNs (11%). Overall, our approach is able to retrieve on average 15% of all AGNs in the field identified by means of spectroscopic or X-ray classification, with a strong dependence on the source apparent magnitude. In particular, the completeness for Type 1 AGNs is 25%, while it drops to 6% for Type 2 AGNs. The rest of the X-ray selected AGN population presents on average a larger r.m.s. variability than the bulk of non variable sources, indicating that variability detection for at least some of these objects is prevented only by the photometric accuracy of the data. We show how a longer observing baseline would return a larger sample of AGN candidates. Our results allow us to assess the usefulness of this AGN selection technique in view of future wide-field surveys.

The analytical continuation of correlation functions from imaginary to real time is a crucial step in lattice gauge theories, and it challenges our ability to derive non-perturbative predictions from lattice simulations. We review aspects of this "inverse problem", which has driven both theoretical and algorithmic advancements in recent years, opening new promising avenues for non-perturbative studies of the Standard Model and beyond. The focus of this proceeding will be on variations of Backus-Gilbert and Bayesian methods.

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant states, etc. Hence the need to develop theories that ensure the existence of structures such as invariant tori or periodic orbits and device efficient computational methods. In this work we concentrate on the existence of invariant tori for the specific case of dissipative systems known as "conformally symplectic" systems, which have the property that they transform the symplectic form into a multiple of itself. To give explicit examples of conformally symplectic systems, we will present two different models: a discrete system, the standard map, and a continuous system, the spin-orbit problem. In both cases we will consider the conservative and dissipative versions, that will help to highlight the differences between the symplectic and conformally symplectic dynamics. For such dissipative systems we will present a KAM theorem in an a-posteriori format. The method of proof is based on extending geometric identities originally developed in [39] for the symplectic case. Besides leading to streamlined proofs of KAM theorem, this method provides a very efficient algorithm which has been implemented. Coupling an efficient numerical algorithm with an a-posteriori theorem, we have a very efficient way to provide rigorous estimates close to optimal. Indeed, the method gives a criterion (the Sobolev blow up criterion) that allows to compute numerically the breakdown. We will review this method as well as an extension of J. Greene's method and present the results in the conservative and dissipative standard maps. Computing close to the breakdown, allows to discover new mathematical phenomena such as the "bundle collapse mechanism".

We present the first spectroscopic abundance determination of iron, alpha-elements (Si, Ca and Ti) and sodium for the Mira variable V1 in the metal-rich globular cluster NGC 5927. We use high-resolution (R~ 28,000), high signal-to-noise ratio (~200) spectra collected with WINERED, a near-infrared (NIR) spectrograph covering simultaneously the wavelength range 0.91--1.35 micron. The effective temperature and the surface gravity at the pulsation phase of the spectroscopic observation were estimated using both optical (V) and NIR time-series photometric data. We found that the Mira is metal-rich ([Fe/H]=-0.55 \pm 0.15) and moderately alpha-enhanced ([alpha/Fe]=0.15 \pm 0.01, sigma=0.2). These values agree quite well with the mean cluster abundances based on high-resolution optical spectra of several cluster red giants available in the literature ([Fe/H]=-0.47 \pm 0.06, [alpha/Fe]=+0.24 \pm 0.05). We also found a Na abundance of +0.35 \pm 0.20 that is higher than the mean cluster abundance based on optical spectra (+0.18 \pm 0.13). However, the lack of similar spectra for cluster red giants and that of corrections for departures from local-thermodynamical equilibrium prevents us from establishing whether the difference is intrinsic or connected with multiple populations. These findings indicate a strong similarity between optical and NIR metallicity scales in spite of the difference in the experimental equipment, data analysis and in the adopted spectroscopic diagnostics.

In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with the default event. We specialize it for some volatility models and we provide price approximations, based on the representation formula. We study numerically their accuracy, comparing the results with Monte Carlo simulations, and we run a theoretical study of the error. We also introduce a seminal study of roughness influence on the claim's price.

Stellar bars are key structures in disc galaxies, driving angular momentum redistribution and influencing processes such as bulge growth and star formation. Quantifying the bar fraction as a function of redshift and stellar mass is therefore important for constraining the physical processes that drive disc formation and evolution across the history of the Universe. Leveraging the unprecedented resolution and survey area of the Euclid Q1 data release combined with the Zoobot deep-learning model trained on citizen-science labels, we identify 7711 barred galaxies with $M_* \gtrsim 10^{10}M_\odot$ in a magnitude-selected sample I_E < 20.5 spanning $63.1 deg^2$. We measure a mean bar fraction of $0.2-0.4$, consistent with prior studies. At fixed redshift, massive galaxies exhibit higher bar fractions, while lower-mass systems show a steeper decline with redshift, suggesting earlier disc assembly in massive galaxies. Comparisons with cosmological simulations (e.g., TNG50, Auriga) reveal a broadly consistent bar fraction, but highlight overpredictions for high-mass systems, pointing to potential over-efficiency in central stellar mass build-up in simulations. These findings demonstrate Euclid's transformative potential for galaxy morphology studies and underscore the importance of refining theoretical models to better reproduce observed trends. Future work will explore finer mass bins, environmental correlations, and additional morphological indicators.

The Euclid Wide Survey (EWS) is expected to identify of order $100\,000$ galaxy-galaxy strong lenses across $14\,000$deg$^2$. The Euclid Quick Data Release (Q1) of $63.1$deg$^2$ Euclid images provides an excellent opportunity to test our lens-finding ability, and to verify the anticipated lens frequency in the EWS. Following the Q1 data release, eight machine learning networks from five teams were applied to approximately one million images. This was followed by a citizen science inspection of a subset of around $100\,000$ images, of which $65\%$ received high network scores, with the remainder randomly selected. The top scoring outputs were inspected by experts to establish confident (grade A), likely (grade B), possible (grade C), and unlikely lenses. In this paper we combine the citizen science and machine learning classifiers into an ensemble, demonstrating that a combined approach can produce a purer and more complete sample than the original individual classifiers. Using the expert-graded subset as ground truth, we find that this ensemble can provide a purity of $52\pm2\%$ (grade A/B lenses) with $50\%$ completeness (for context, due to the rarity of lenses a random classifier would have a purity of $0.05\%$). We discuss future lessons for the first major Euclid data release (DR1), where the big-data challenges will become more significant and will require analysing more than $\sim300$ million galaxies, and thus time investment of both experts and citizens must be carefully managed.

Severi varieties are the parameter spaces for curves with prescribed homology class and genus on a smooth surface. We describe their limits along degenerations of surfaces, with a view towards the enumeration of curves. This includes a complete proof of the Caporaso-Harris recursive formula, with all the necessary background on deformations of curves and singularities.

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, CDO pricing, and empirical analysis of green loan portfolios.

The energy density of the Universe is dominated by dark energy and dark matter, two mysterious components which pose some of the most important questions in fundamental science today. Euclid is a high-precision survey mission designed to answer these questions by mapping the geometry of the dark Universe. Euclid's Visible-NIR imaging and spectroscopy of the entire extragalactic sky will further produce extensive legacy science for various fields of astronomy. Over the 2008-2009 period, Euclid has been the object of an ESA Assessment Phase in which the study of the Euclid Imaging instrument was under the responsibility of the Euclid Imaging Consortium (EIC). The EIC Science Book presents the studies done by the EIC science working groups in the context of this study phase. We first give a brief description of the Euclid mission and of the imaging instrument and surveys. We then summarise the primary and legacy science which will be achieved with the Euclid imaging surveys, along with the simulations and data handling scheme which have been developed to optimise the instrument and ensure its science performance.

Chemical oxidation of multilayer graphene grown on silicon carbide yields films exhibiting reproducible characteristics, lateral uniformity, smoothness over large areas, and manageable chemical complexity, thereby opening opportunities to accelerate both fundamental understanding and technological applications of this form of graphene oxide films. Here, we investigate the vertical inter-layer structure of these ultra-thin oxide films. X-ray diffraction, atomic force microscopy, and IR experiments show that the multilayer films exhibit excellent inter-layer registry, little amount (<10%) of intercalated water, and unexpectedly large interlayer separations of about 9.35 Å. Density functional theory calculations show that the apparent contradiction of "little water but large interlayer spacing in the graphene oxide films" can be explained by considering a multilayer film formed by carbon layers presenting, at the nanoscale, a non-homogenous oxidation, where non-oxidized and highly oxidized nano-domains coexist and where a few water molecules trapped between oxidized regions of the stacked layers are sufficient to account for the observed large inter-layer separations. This work sheds light on both the vertical and intra-layer structure of graphene oxide films grown on silicon carbide, and more in general, it provides novel insight on the relationship between inter-layer spacing, water content, and structure of graphene/graphite oxide materials.

Relics of ancient accretion events experienced by the Milky Way are predominantly located within the stellar halo of our Galaxy. However, debris from different objects display overlapping distributions in dynamical spaces, making it extremely challenging to properly disentangle their contribution to the build-up of the Galaxy. To shed light on this chaotic context, we started a program aimed at the homogeneous chemical tagging of the local halo of the Milky Way, focusing on the component in retrograde motion, since this is expected to host a large fraction of stars accreted from past mergers. The A Walk on the Retrograde Side (WRS) project targets retrograde halo stars in the Solar Neighborhood having accurate $6$-D phase space information available, measuring the precise chemical abundance of several chemical elements from high-resolution spectroscopy. In this first paper, we present the project and the analysis of high-resolution spectra obtained with UVES at VLT and PEPSI at LBT for $186$ stars. Accurate radial velocity and chemical abundance of several elements have been obtained for all the target stars. In particular we focus on the chemical composition of a specific subset of substructures identified dynamically in the literature. Our study reveals that two among the more recently discovered structures in the retrograde halo, namely Antaeus / L-RL$64$ and ED-$3$, have identical chemical patterns and similar integrals of motion, suggesting a common origin. In turn, the abundance patterns of this unified system differ from that of Gaia-Enceladus, confirming that it is an independent structure. Finally, Sequoia exhibits a different chemistry with respect to that of Gaia-Enceladus at \mathrm{[Fe/H]} &lt; -1.5 dex, showcasing an excess of stars with lower Mg and Ca in the common metallicity range.

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the M\"obius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.

We measured the impact of long-range exponentially decaying intra-areal lateral connectivity on the scaling and memory occupation of a distributed spiking neural network simulator compared to that of short-range Gaussian decays. While previous studies adopted short-range connectivity, recent experimental neurosciences studies are pointing out the role of longer-range intra-areal connectivity with implications on neural simulation platforms. Two-dimensional grids of cortical columns composed by up to 11 M point-like spiking neurons with spike frequency adaption were connected by up to 30 G synapses using short- and long-range connectivity models. The MPI processes composing the distributed simulator were run on up to 1024 hardware cores, hosted on a 64 nodes server platform. The hardware platform was a cluster of IBM NX360 M5 16-core compute nodes, each one containing two Intel Xeon Haswell 8-core E5-2630 v3 processors, with a clock of 2.40 G Hz, interconnected through an InfiniBand network, equipped with 4x QDR switches.