Lipolysis is a life-essential metabolic process, which supplies fatty acids stored in lipid droplets to the body in order to match the demands of building new cells and providing cellular energy. In this paper, we present a first mathematical modelling approach for lipolysis, which takes into account that the involved enzymes act on the surface of lipid droplets. We postulate an active region near the surface where the substrates are within reach of the surface-bound enzymes and formulate a system of reaction-diffusion PDEs, which connect the active region to the inner core of lipid droplets via interface conditions. We establish two numerical discretisations based on finite element method and isogeometric analysis, and validate them to perform reliably. Since numerical tests are best performed on non-zero explicit stationary state solutions, we introduce and analyse a model, which describes besides lipolysis also a reverse process (yet in a physiologically much oversimplified way). The system is not coercive such that establishing well-posedness is a non-standard task. We prove the unique existence of global and equilibrium solutions. We establish exponential convergence to the equilibrium solutions using the entropy method. We then study the stationary state model and compute explicitly for radially symmetric solutions. Concerning the finite element methods, we show numerically the linear and quadratic convergence of the errors with respect to the $H^{1}$- and $L^{2}$-norms, respectively. Finally, we present numerical simulations of a prototypical PDE model of lipolysis and illustrate that ATGL clustering on lipid droplets can significantly slow down lipolysis.

While Large Language Models (LLMs) excel at generating human-like text, aligning their outputs with complex, qualitative goals like pedagogical soundness remains a significant challenge. Standard reinforcement learning techniques often rely on slow and expensive LLM-as-a-judge evaluations or on brittle, keyword-based metrics like ROUGE, which fail to capture the semantic essence of a high-quality explanation. In this work, we introduce a novel approach to reward shaping within the Group Relative Policy Optimisation (GRPO) framework. Our central contribution is the use of a small, efficient encoder-only transformer as a semantic reward model. This model provides a dense, semantically rich reward signal based on the cosine similarity between a generated explanation and a ground-truth reference, guiding the policy towards explanations that are not just factually correct but also structurally and conceptually aligned with expert reasoning. We apply this method to the task of training a model for the Italian medical-school entrance examinations, following standard domain-adaptive continued pre-training (CPT) and supervised fine-tuning (SFT). Our results demonstrate that GRPO with our proposed semantic reward significantly improves explanation faithfulness and clarity over a strong SFT baseline, showcasing the power of using lightweight encoder models for nuanced reward shaping in complex generation tasks

The distribution of close-in exoplanets is shaped by the interplay between atmospheric and dynamical processes. The Neptunian Desert, Ridge, and Savanna illustrate the sensitivity of these worlds to such processes, making them ideal to disentangle their roles. Determining how many Neptunes were brought close-in by early disk-driven migration (DDM; maintaining primordial spin-orbit alignment) or late high-eccentricity migration (HEM; generating large misalignments) is essential to understand how much atmosphere they lost. We propose a unified view of the Neptunian landscape to guide its exploration, speculating that the Ridge is a hot spot for evolutionary processes. Low-density Neptunes would mainly undergo DDM, getting fully eroded at shorter periods than the Ridge, while denser Neptunes would be brought to the Ridge and Desert by HEM. We embark on this exploration via ATREIDES, which relies on spectroscopy and photometry of 60 close-in Neptunes, their reduction with robust pipelines, and their interpretation through internal structure, atmospheric, and evolutionary models. We carried out a systematic RM census with VLT/ESPRESSO to measure the distribution of 3D spin-orbit angles, correlate its shape with system properties and thus relate the fraction of aligned-misaligned systems to DDM, HEM, and atmospheric erosion. Our first target, TOI-421c, lies in the Savanna with a neighboring sub-Neptune TOI-421b. We measured their 3D spin-orbit angles (Psib = 57+11-15 deg; Psic = 44.9+4.4-4.1 deg). Together with the eccentricity and possibly large mutual inclination of their orbits, this hints at a chaotic dynamical origin that could result from DDM followed by HEM. ATREIDES will provide the community with a wealth of constraints for formation and evolution models. We welcome collaborations that will contribute to pushing our understanding of the Neptunian landscape forward.

Large language models (LLMs) show increasing potential in education, yet benchmarks for non-English languages in specialized domains remain scarce. We introduce MedBench-IT, the first comprehensive benchmark for evaluating LLMs on Italian medical university entrance examinations. Sourced from Edizioni Simone, a leading preparatory materials publisher, MedBench-IT comprises 17,410 expert-written multiple-choice questions across six subjects (Biology, Chemistry, Logic, General Culture, Mathematics, Physics) and three difficulty levels. We evaluated diverse models including proprietary LLMs (GPT-4o, Claude series) and resource-efficient open-source alternatives (<30B parameters) focusing on practical deployability. Beyond accuracy, we conducted rigorous reproducibility tests (88.86% response consistency, varying by subject), ordering bias analysis (minimal impact), and reasoning prompt evaluation. We also examined correlations between question readability and model performance, finding a statistically significant but small inverse relationship. MedBench-IT provides a crucial resource for Italian NLP community, EdTech developers, and practitioners, offering insights into current capabilities and standardized evaluation methodology for this critical domain.

Periodically time-varying media, known as photonic time crystals (PTCs), provide a promising platform for observing unconventional wave phenomena. We analyze the scattering of electromagnetic waves from spatially finite PTCs using the multispectral Floquet scattering matrix, which naturally incorporates the frequency-mixing processes intrinsic to such systems. For dispersionless, real, and time-periodic permittivities, this matrix is pseudounitary. Here we demonstrate that this property leads to multiple symmetry-breaking transitions: for increasing driving strength, scattering matrix eigenvalues lying on the unit circle (unbroken symmetry regime) meet at exceptional points (EPs), where they break up into inverse complex conjugate pairs (broken symmetry regime). We identify the symmetry operator associated with these transitions and show that, in time-symmetric systems, it corresponds to the time-reversal operator. Remarkably, at the parametric resonance condition, one eigenvalue vanishes while its partner diverges, signifying simultaneous coherent perfect absorption (CPA) and lasing. Since our approach relies solely on the Floquet scattering matrix, it is not restricted to a specific geometry but instead applies to any periodically time-varying scattering system. To illustrate this universality, we apply our method to a variety of periodically time-modulated structures, including slabs, spheres, and metasurfaces. In particular, we show that using quasi-bound states in the continuum resonances sustained by a metasurface, the CPA and lasing conditions can be attained for a minimal modulation strength of the permittivity. Our results pave the way for engineering time-modulated photonic systems with tailored scattering properties, opening new avenues for dynamic control of light in next-generation optical devices.

We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the models' rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses.

The AU Microscopii planetary system is only 24 Myr old, and its geometry may provide clues about the early dynamical history of planetary systems. Here, we present the first measurement of the Rossiter-McLaughlin effect for the warm sub-Neptune AU Mic c, using two transits observed simultaneously with the European Southern Observatory's (ESO's) Very Large Telescope (VLT)/Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO), CHaracterising ExOPlanet Satellite (CHEOPS), and Next-Generation Transit Survey (NGTS). After correcting for flares and for the magnetic activity of the host star, and accounting for transit-timing variations, we find the sky-projected spin-orbit angle of planet c to be in the range $\lambda_c=67.8_{-49.0}^{+31.7}$\,degrees (1-$\sigma$). We examine the possibility that planet c is misaligned with respect to the orbit of the inner planet b ($\lambda_b=-2.96_{-10.30}^{+10.44}$\,degrees), and the equatorial plane of the host star, and discuss scenarios that could explain both this and the planet's high density, including secular interactions with other bodies in the system or a giant impact. We note that a significantly misaligned orbit for planet c is in some degree of tension with the dynamical stability of the system, and with the fact that we see both planets in transit, though these arguments alone do not preclude such an orbit. Further observations would be highly desirable to constrain the spin-orbit angle of planet c more precisely.

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a biventricular rabbit model, with promising results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.

We present the discovery and characterization of two warm mini-Neptunes transiting the K3V star TOI-815 in a K-M binary system. Analysis of the spectra and rotation period reveal it to be a young star with an age of $200^{+400}_{-200}$Myr. TOI-815b has a 11.2-day period and a radius of 2.94$\pm$0.05$\it{R_{\rm\mathrm{\oplus}}}$ with transits observed by TESS, CHEOPS, ASTEP, and LCOGT. The outer planet, TOI-815c, has a radius of 2.62$\pm$0.10$\it{R_{\rm\mathrm{\oplus}}}$, based on observations of three non-consecutive transits with TESS, while targeted CHEOPS photometry and radial velocity follow-up with ESPRESSO were required to confirm the 35-day period. ESPRESSO confirmed the planetary nature of both planets and measured masses of 7.6$\pm$1.5 $\it{M_{\rm \mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=1.64$^{+0.33}_{-0.31}$gcm$^{-3}$) and 23.5$\pm$2.4$\it{M_{\rm\mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=7.2$^{+1.1}_{-1.0}$gcm$^{-3}$) respectively. Thus, the planets have very different masses, unlike the usual similarity of masses in compact multi-planet systems. Moreover, our statistical analysis of mini-Neptunes orbiting FGK stars suggests that weakly irradiated planets tend to have higher bulk densities compared to those suffering strong irradiation. This could be ascribed to their cooler atmospheres, which are more compressed and denser. Internal structure modeling of TOI-815b suggests it likely has a H-He atmosphere constituting a few percent of the total planet mass, or higher if the planet is assumed to have no water. In contrast, the measured mass and radius of TOI-815c can be explained without invoking any atmosphere, challenging planetary formation theories. Finally, we infer from our measurements that the star is viewed close to pole-on, which implies a spin-orbit misalignment at the 3$\sigma$ level.

There is lattice evidence that the QCD matter above the chiral restoration temperature Tch and below the deconfinement temperature Td, called stringy fluid, is characterized by an approximate chiral spin symmetry, which is a symmetry of confinement in QCD with light quarks. The energy density, pressure and entropy density in the stringy fluid scale as Nc^1, which is in contrast to the Nc^0 scaling in the hadron gas and to the Nc^2 scaling in the quark-gluon plasma. Here we clarify the origin of the Nc^1 scaling. We employ a solvable field-theoretical large $N_c$ chirally symmetric and confining model. In vacuum the confining potential induces a spontaneous breaking of chiral symmetry. The mesons are spatially localized states of quarks and antiquarks. Still in the confining regime the system undergoes the chiral restoration phase transition at $T_{ch}$ because of Paili blocking of the quark levels required for the existence of the quark condensate, by the thermal excitation of quarks and antiquarks. The same Paili blocking leads to a delocalization of the color singlet low-spin meson-like states that become infinitely large in the chiral limit. Consequently the stringy fluid represents a very dense medium of the overlapping huge color-singlet low-spin quark-antiquark systems. The Bethe-Salpeter equation that determines the rest-frame excitation energies of the color-singlet quark-antiquark system is Nc-independent both in vacuum and in the medium in the confining regime. The excitation energy of the quark-antiquark color-singlet systems scales as Nc^0, i.e. as meson mass in vacuum. The Nc^1 scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.

Artificial intelligence (AI) technologies (re-)shape modern life, driving innovation in a wide range of sectors. However, some AI systems have yielded unexpected or undesirable outcomes or have been used in questionable manners. As a result, there has been a surge in public and academic discussions about aspects that AI systems must fulfill to be considered trustworthy. In this paper, we synthesize existing conceptualizations of trustworthy AI along six requirements: 1) human agency and oversight, 2) fairness and non-discrimination, 3) transparency and explainability, 4) robustness and accuracy, 5) privacy and security, and 6) accountability. For each one, we provide a definition, describe how it can be established and evaluated, and discuss requirement-specific research challenges. Finally, we conclude this analysis by identifying overarching research challenges across the requirements with respect to 1) interdisciplinary research, 2) conceptual clarity, 3) context-dependency, 4) dynamics in evolving systems, and 5) investigations in real-world contexts. Thus, this paper synthesizes and consolidates a wide-ranging and active discussion currently taking place in various academic sub-communities and public forums. It aims to serve as a reference for a broad audience and as a basis for future research directions.

The existence of non-zero neutrino masses points to the likely existence of multiple SM neutral fermions. When such states are heavy enough that they cannot be produced in oscillations, they are referred to as Heavy Neutral Leptons (HNLs). In this white paper we discuss the present experimental status of HNLs including colliders, beta decay, accelerators, as well as astrophysical and cosmological impacts. We discuss the importance of continuing to search for HNLs, and its potential impact on our understanding on key fundamental questions, and additionally we outline the future prospects for next-generation future experiments or upcoming accelerator run scenarios.

Tomographic techniques are vital in modern medicine, allowing doctors to observe patients' interior features. Individual steps in the measurement process are modeled by `single projection operators' $p$. These are line integral operators over a collection of curves that covers the regions of interest. Then, the entire measurement process can be understood as a finite collection of such single projections, and thus be modeled by an $N$-projections operator $P=(p_1,\dots,p_N)$. The most well-known example of an $N$-projections operator is the restriction of the Radon transform to finitely many projection angles. Characterizations of the range of $N$-projections operators are of intrinsic mathematical interest and can also help in practical applications such as geometric calibration, motion detection, or model parameter identification. In this work, we investigate the range of projection pair operators $\mathcal{P}$ in the plane, i.e., operators formed by two projections ($N=2$) applied to functions in $\mathbb{R}^2$. We find that the set of annihilators to $\mathrm{rg}(\mathcal{P})$ that are regular distributions contains at most one dimension and a range condition can be explicitly determined by what we refer to as `kernel conditions'. With this tool, we examine the exponential fanbeam transform for which no range conditions were known, finding that no (regular) range condition exists, and therefore, arbitrary data can be approximated in an $L^2$ sense by projections of smooth functions. We also illustrate the use of this theory on a mixed parallel-fanbeam projection pair operator.

We review observations of solar activity, geomagnetic variation, and auroral visibility for the extreme geomagnetic storm on 1872 February 4. The extreme storm (referred to here as the Chapman-Silverman storm) apparently originated from a complex active region of moderate area (\approx 500 {\mu}sh) that was favorably situated near disk center (S19° E05°). There is circumstantial evidence for an eruption from this region at 9--10 UT on 1872 February 3, based on the location, complexity, and evolution of the region, and on reports of prominence activations, which yields a plausible transit time of \approx29 hr to Earth. Magnetograms show that the storm began with a sudden commencement at \approx14:27 UT and allow a minimum Dst estimate of £ -834 nT. Overhead aurorae were credibly reported at Jacobabad (British India) and Shanghai (China), both at 19°.9 in magnetic latitude (MLAT) and 24°. 2 in invariant latitude (ILAT). Auroral visibility was reported from 13 locations with MLAT below |20|° for the 1872 storm (ranging from |10°. 0|--|19°. 9| MLAT) versus one each for the 1859 storm (|17°. 3| MLAT) and the 1921 storm (|16.°2| MLAT). The auroral extension and conservative storm intensity indicate a magnetic storm of comparable strength to the extreme storms of 1859 September (25°.1 \pm 0°.5 ILAT and -949 \pm 31 nT) and 1921 May (27°.1 ILAT and -907 \pm 132 nT), which places the 1872 storm among the three largest magnetic storms yet observed.

We provide an exact analytical solution of the single-particle Schrödinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The resulting dynamics exhibit self-similar behavior, with a structure reminiscent of the domain wall melting problem, albeit characterized by a nontrivial time-dependent length scale and phase. Building on this solution, we derive hydrodynamic predictions for the evolution of particle density, current, and entanglement entropy along the chain. In the special case of a sudden quench, the system develops a breathing interface region, which may be interpreted as a realization of Wannier-Stark localization, as previously suggested on the basis of hydrodynamic arguments.

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.

The proliferation of misinformation necessitates scalable, automated fact-checking solutions. Yet, current benchmarks often overlook multilingual and topical diversity. This paper introduces a novel, dynamically extensible data set that includes 61,514 claims in multiple languages and topics, extending existing datasets up to 2024. Through a comprehensive evaluation of five prominent Large Language Models (LLMs), including GPT-4o, GPT-3.5 Turbo, LLaMA 3.1, and Mixtral 8x7B, we identify significant performance gaps between different languages and topics. While overall GPT-4o achieves the highest accuracy, it declines to classify 43% of claims. Across all models, factual-sounding claims are misclassified more often than opinions, revealing a key vulnerability. These findings underscore the need for caution and highlight challenges in deploying LLM-based fact-checking systems at scale.

We investigate the formation of musical preferences of millions of users of the NetEase Cloud Music (NCM), one of the largest online music platforms in China. We combine the methods from complex networks theory and information sciences within the context of Big Data analysis to unveil statistical patterns and community structures underlying the formation and evolution of musical preference behaviors. Our analyses address the decay patterns of music influence, users' sensitivity to music, age and gender differences, and their relationship to regional economic indicators. Employing community detection in user-music bipartite networks, we identified eight major cultural communities in the population of NCM users. Female users exhibited higher within-group variability in preference behavior than males, with a major transition occurring around the age of 25. Moreveor, the musical tastes and the preference diversity measures of women were also more strongly associated with economic factors. However, in spite of the highly variable popularity of music tracks and the identified cultural and demographic differences, we observed that the evolution of musical preferences over time followed a power-law-like decaying function, and that NCM listeners showed the highest sensitivity to music released in their adolescence, peaking at the age of 13. Our findings suggest the existence of universal properties in the formation of musical tastes but also their culture-specific relationship to demographic factors, with wide-ranging implications for community detection and recommendation system design in online music platforms.

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM).