We derive a small-signal transfer function for a system comprising a virtual synchronous generator (VSG), a synchronous generator (SG), and a load, capturing voltage and frequency dynamics. Using this model, we analyze the sensitivity of SG dynamics to VSG parameters, highlighting trade-offs in choosing virtual inertia and governor lag, the limited effect of damper-winding emulation, and several others.

It is shown that two Banach spaces are linearly isometric if and only if the Gromov--Hausdorff distance between them is finite, in particular, zero. The proof is compilative and relies on results obtained by many researchers on the approximability of almost-surjective almost-isometries by linear surjective isometries. In the finite-dimensional case, previously obtained by I.~Mikhailov, a simpler proof under weaker assumptions is given. In the finite-dimensional case, a criterion for isometry in terms of finite (compact) subsets is also given.

Displacement memory, induced by a wave pulse in a regular black hole spacetime, is studied using geodesic (timelike) separation and geodesic deviation. The presence of the wave pulse in such a black hole is modeled via a function $H(u)$ appearing in a restricted version of a generic Bondi-Sachs type line element. Choosing a sech-squared profile for $H(u)$, we first study (numerically) geodesic separation and geodesic deviation in a flat background. Thereafter, similar investigations are carried out in the presence of the black hole, but in regions far away from the vicinity of the horizon. Our results suggest the presence of a distinct displacement memory effect, which depends on the value of the regularisation parameter $g$ as well as the pulse height. Between different types of regular black holes, one notices parameter-dependent changes in the net displacement memory. Further, a clear difference in the magnitude of displacement memory (at large $u$) in regular and singular black holes is also visible in our numerical results.

We consider a two-dimensional gas of interacting fermions in presence of an external constant magnetic field: the system is extended and homogeneous, and thus assumed to be invariant under magnetic translations. Working within the Hartree-Fock approximation, we analyze the system directly in the thermodynamic limit by solving a self-consistent fixed-point equation for the one-particle density matrix. We prove that, provided that the interactions among fermions are sufficiently weak, there exists a unique one-particle density matrix that solves the self-consistency condition. By choosing the Fermi-Dirac distribution as the function in the fixed-point equation, this approach can describe both positive and zero-temperature cases. At zero temperature and when the chemical potential of the non-interacting system lies in a spectral gap of the free Landau operator, our self-consistent solution is an orthogonal projection (an "interacting" effective Fermi projection). We prove that its integrated density of states varies linearly with the external magnetic field, provided the interaction is weak enough: the slope of this variation is quantized and independent of the interaction. According to the Středa formula, this can be seen as yet another expression of the universality of the quantum Hall effect in weakly interacting systems, at least within the Hartree-Fock approximation.

Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized notion of correlations via arbitrary products is formulated. Remarkably, as a universal property, the connection between such general products and tensor products is established, allowing one to relate generic non-product states to the common notion of entangled states. We construct the set of free operations for general types of products by extending the local-operation-and-classical-communication paradigm, familiar from standard entanglement theory, thereby establishing a resource theory of correlations for general products. A generalization is provided beyond two factors that can be universally related to multipartite entanglement. Applications that highlight the usefulness of the approach are discussed, such as the factorization of fermionic states, the non-local factorization of multi-photon states into single-photon states, and the interesting possibility of understanding prime numbers as a form of single-party entanglement.

The space $\mathcal{G}_n$ of $n$-marked groups provides a natural framework for studying algebraic and geometric invariants under deformation. In general, the growth rate is not continuous on $\mathcal{G}_n$. In this paper, we investigate the subspace $\mathcal{D}_n \subset \mathcal{G}_n$ consisting of $n$-marked Dyer systems, which extend Coxeter systems and include graph products of cyclic groups and right-angled Artin groups. We prove that $\mathcal{D}_n$ is closed in $\mathcal{G}_n$ and introduce a natural partial order on $\mathcal{D}_n$ with respect to which the growth rate is monotonically increasing. As a consequence, the growth rate function $τ: \mathcal{D}_n \to \mathbb{R}_{\geq 1}$ is continuous. The proof combines the solution to the word problem for Dyer systems by Paris and Soergel, the parabolic growth formula by Paris and Varghese, and analytic arguments based on normal convergence and Hurwitz's theorem. This extends the continuity results known for Coxeter systems to the broader class of Dyer systems.

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave problems comprise the acoustic and elastic wave equations, with applications in seismic modeling. Motivated by recent Laplace-domain MOR methodologies, we construct reduced bases that approximate the time-domain solution with exponential accuracy. We prove convergence bounds that are explicit and robust with respect to the parameters controlling the Ricker wavelet's shape and width and identify an intrinsic accuracy limit dictated by the wavelet's value at the initial time. In particular, the resulting error bound is independent of the underlying Galerkin discretization space and yields computable criteria for the regime in which exponential convergence is observed.

This review provides an up-to-date account of energy transport in Fermi-Pasta-Ulam-Tsingou (FPUT) chains, a key testbed for nonequilibrium statistical physics. We discuss the transition from the historical puzzle of thermalization to the discovery of anomalous heat transport, where the effective thermal conductivity $κ$ diverges with system size $L$ as $κ\propto L^δ$. The article clarifies the distinction between two universality classes: the FPUT-$αβ$ model, characterized by $δ= 1/3$ and linked to Kardar-Parisi-Zhang (KPZ) physics, and the symmetric FPUT-$β$ model, where numerical and theoretical evidence support $δ= 2/5$. We investigate how finite-size effects - unavoidably induced by the thermostatting protocols - can disguise the asymptotic scaling. Additionally, we analyze the role of conservative noise in preserving hydrodynamic properties and examine how proximity to integrable limits leads to long-lived quasi-particles and, thereby, to diffusive regimes over intermediate spatial scales.

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our techniques are centered on proof terms and condensed detachment, which ties in with approaches to automated first-order proving by proof structure enumeration, and links to Metamath as well as to formulas-as-types. Our methods for generating theorems are based on partitioning the set of proof terms into inductively characterized levels. We study two ideas for improvement: Lemma synthesis by DAG compression of proof term sets and incorporating combinators into proof term construction.

In the era of responsible and sustainable AI, information retrieval and recommender systems must expand their scope beyond traditional accuracy metrics to incorporate environmental sustainability. However, this research line is severely limited by the lack of item-level environmental impact data in standard benchmarks. This paper introduces Eco-Amazon, a novel resource designed to bridge this gap. Our resource consists of an enriched version of three widely used Amazon datasets (i.e., Home, Clothing, and Electronics) augmented with Product Carbon Footprint (PCF) metadata. CO2e emission scores were generated using a zero-shot framework that leverages Large Language Models (LLMs) to estimate item-level PCF based on product attributes. Our contribution is three-fold: (i) the release of the Eco-Amazon datasets, enriching item metadata with PCF signals; (ii) the LLM-based PCF estimation script, which allows researchers to enrich any product catalogue and reproduce our results; (iii) a use case demonstrating how PCF estimates can be exploited to promote more sustainable products. By providing these environmental signals, Eco-Amazon enables the community to develop, benchmark, and evaluate the next generation of sustainable retrieval and recommendation models. Our resource is available at https://doi.org/10.5281/zenodo.18549130, while our source code is available at: http://github.com/giuspillo/EcoAmazon/.

Volatile loss from exoplanetary atmospheres and its possible implications for the longevity of habitable surface conditions is a topic of vigorous debate currently. The vast majority of the habitable zone terrestrial-like exoplanets known to date orbit low-mass M- and K-dwarf stars and are subject to the conditions drastically different to those of terrestrial planets in the Solar System. In particular, they orbit far closer to their host stars than similar planets around G-dwarfs similar to the Sun. Therefore they receive higher X-ray and UV fluxes, even though luminosities of M- and K-dwarfs are lower than those of heavier stars. Furthermore, due to their slower evolution, M-dwarfs retain high activity on the gigayear timescales. The combination of these two effects has led to claims that most terrestrial planets orbiting M-dwarfs may have their atmospheres stripped from the higher X-ray and UV fluxes of their host stars. Opposing this are researchers who point out that volatile inventories for terrestrial exoplanets are ill-constrained, and hence, they may be able to "weather the storm" of these higher X-ray and UV fluxes. In this chapter, we focus on exploring volatile loss in the upper atmospheres of terrestrial planets in our solar system and applications to those in exoplanetary systems around stars of different types.

With the growing interest in Multimodal Recommender Systems (MRSs), collecting high-quality datasets provided with multimedia side information (text, images, audio, video) has become a fundamental step. However, most of the current literature in the field relies on small- or medium-scale datasets that are either not publicly released or built using undocumented processes. In this paper, we aim to fill this gap by releasing M3L-10M and M3L-20M, two large-scale, reproducible, multimodal datasets for the movie domain, obtained by enriching with multimodal features the popular MovieLens-10M and MovieLens-20M, respectively. By following a fully documented pipeline, we collect movie plots, posters, and trailers, from which textual, visual, acoustic, and video features are extracted using several state-of-the-art encoders. We publicly release mappings to download the original raw data, the extracted features, and the complete datasets in multiple formats, fostering reproducibility and advancing the field of MRSs. In addition, we conduct qualitative and quantitative analyses that showcase our datasets across several perspectives. This work represents a foundational step to ensure reproducibility and replicability in the large-scale, multimodal movie recommendation domain. Our resource can be fully accessed at the following link: https://zenodo.org/records/18499145, while the source code is accessible at https://github.com/giuspillo/M3L_10M_20M.

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital images by modifying local structures via structuring elements (SEs), while cubical homology captures global topological features such as connected components and loop structures within images. Building on the GUDHI package for persistent homology (PH) computation on cubical complexes, we propose the MMPersistence library, which integrates MM operations with diverse SEs and PH computation to extract multiscale persistence information. By employing SEs of different shapes to construct topological filtrations, the proposed MM-based PH framework encodes both spatial and morphological characteristics of digital images, providing richer local geometric information than conventional cubical homology alone and establishing a unified foundation for analyzing digital images that integrates topological insight with morphological image processing techniques.

Context. Hot Jupiters are ideal natural laboratories to investigate atmospheric composition and dynamics. However, high-resolution transmission spectroscopy is currently limited by our capability of removing planet-occulted line-distortion (POLD) contamination from the signal. Aims. In this paper, we aim to characterize the transmission spectrum of WASP-31 b from two and a half transits observed with the ESPRESSO spectrograph at the VLT. Methods. The Rossiter-McLaughlin (RM) signature was analyzed using the RM "revolutions" method. Before extracting the transmission spectrum of the planet, we corrected the dataset for telluric lines using molecfit and further modeled the POLD deformations using EvE. Results. We confirm the planet low sky-projected spin-orbit angle from previous studies and further refine its value to $λ= -0.09^{+0.31}_{-0.32}$ deg. We do not detect any species (including previously detected species such as K or CrH) in the planetary atmosphere. In most cases the non-detections are due to the strong POLDs contamination or lack of observable lines in the ESPRESSO wavelength range, and so previous detections cannot be ruled out. Conclusions. Planet-occulted line-distortion contamination continues to be the main limitation of high-resolution transmission spectroscopy for species present in both the star and the planet, hindering atmospheric detections even with state-of-the-art models, in particular for planets with a low sky-projected spin-orbit angle. Developing advanced techniques to isolate planetary signatures is of utmost importance in the advent of ELT-like observations.

This work presents a fully coupled, multiphysics computational framework for predicting the thermo-chemical material response of thermal protection systems in inductively coupled plasma (ICP) wind tunnels. The framework integrates a high-fidelity Navier-Stokes plasma solver, an electromagnetic field solver, and a discontinuous-Galerkin material response solver using a partitioned coupling strategy. This enables an ab initio, end-to-end simulation of the 350 kW Plasmatron X facility at the University of Illinois Urbana-Champaign (UIUC), including plasma generation, electromagnetic heating, near-wall thermochemistry, and time-accurate material ablation. The model captures key ICP physics such as vortex-mode recirculation, Joule-heating-driven plasma formation, and Lorentz-force-induced flow confinement, and accurately predicts the transition from subsonic to supersonic jet behavior at low pressures. Validation against cold-wall calorimetry and graphite ablation experiments shows that predicted stagnation-point heat fluxes fall well within experimental uncertainty, while fully coupled simulations accurately reproduce measured stagnation temperature histories and recession rates with errors below 12% and 10%, respectively. Remaining discrepancies during early transient heating are attributed to uncertainties in power-coupling efficiency, equilibrium ablation modeling, and material property datasets. Overall, the framework demonstrates strong predictive capability for ICP wind tunnel environments and provides a foundation for improved design, interpretation, and planning of hypersonic material testing campaigns.

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these endeavours. This leads to fruitful CD-FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with fruitful weights determined by the relative sizes of the median- and quantile-FIC scores. And Mrs. Jones is pregnant.

We investigate the nonequilibrium dynamics of the nearest-neighbour Ising model subjected to stochastic resetting, where the system is intermittently returned to an initial configuration with magnetisation $m_0$, with the inter-reset times drawn from the power law distribution $ατ_0^α/ τ^{α+1}$. The heavy-tailed resets generate magnetisation distributions that differ significantly from both equilibrium dynamics and the previously studied Ising model with exponentially distributed reset times. In two dimensions, for $T > T_C$, we find a quasi-ferro state for all $α$, marked by a double-peaked distribution that diverges at $m=0$ and $m=m_0$; no steady state exists for $α< 1$, while a stationary state emerges for $α> 1$. For $T < T_C$, power law resetting produces two distinct regimes separated by a crossover exponent $α^* = 1-c$: a single-peak ferromagnetic phase localised at $m_{eq}$ for $α< α^*$, and a dual-peak ferromagnetic phase with divergences at $m_{eq}$ and $m_0$ for $α> α^*$. Analytic results in one and two dimensions, supported by simulations, yield a rich phase diagram in the $(T,α)$ plane and reveal how heavy-tailed resetting generates nonequilibrium phases very different from those seen in the case of exponential resetting.

We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate that the existence of such a measure depends sensitively on the structure of the drift and diffusion terms, as well as on the chosen discretization scheme of the underlying stochastic dynamics. To ground our discussion, we draw motivation from phenomenological models in statistical theories of turbulence, where geometric Brownian motion serves as a classical example. To address situations where the standard invariant measure fails to exist, we heuristically explore the concept of infinite ergodicity, a notion recently introduced in the context of statistical physics for drift-diffusion stochastic processes.

Background: Neutron reactions off lithium isotopes up to 50 MeV are important for nuclear data science, around the International Fusion Material Irradiation Facility (IFMIF) facility in particular. Purpose: We aim at constructing a semi-microscopic reaction model that describes neutron elastic scattering off $^6$Li up to 50 MeV taking the breakup channels of $^6$Li into account. Methods: We adopt the continuum-discretized coupled-channels method (CDCC) with an $α+p+n$ three-body model of $^6$Li. We employ the $g$-matrix effective interaction by Jeukenne, Lejeune, and Mahaux (JLM). The renormalization factors of the real and imaginary parts of the JLM interaction are treated as free parameters. Results: The renormalization parameter of the real part of the JLM interaction is found to be constant ($=1.1$), whereas that for the imaginary part has a smooth energy dependence. The four-body CDCC calculation with these parameters well describes the angular distributions of both proton and neutron elastic scatterings as well as the neutron total cross section and proton total reaction cross section. The applicable energy range is found to be from 7 MeV to 50 MeV. Conclusions: We have constructed a reliable reaction model for describing nucleon-$^6$Li scattering between 7 MeV and 50 MeV. This model can directly be applied to inelastic scattering and break reactions for $^6$Li with the help of the complex scaling method.

Social media has billions of users, but we still do not fully understand why users prefer one platform over another. Establishing new platforms among already popular competitors is difficult. Prior research has richly documented people's experiences within individual platforms, yet situating those experiences within the entirety of a user's social media experience remains challenging. What platforms have people used, and why have they transitioned between them? We collected data from a quota-based sample of 1,000 U.S. participants. We introduce the concept of \emph{Social Media Journeys} to study the entirety of their social media experiences systematically. We identify push and pull factors across the social media landscape. We also show how different generations adopted social media platforms based on personal needs. With this work, we advance HCI by moving towards holistic perspectives when discussing social media technology, offering new insights for platform design, governance, and regulation.

Nearest neighbor search on high-dimensional vectors is fundamental in modern AI and database systems. In many real-world applications, queries involve constraints on multiple numeric attributes, giving rise to range-filtering approximate nearest neighbor search (RFANNS). While there exist RFANNS indexes for single-attribute range predicates, extending them to the multi-attribute setting is nontrivial and often ineffective. In this paper, we propose KHI, an index for multi-attribute RFANNS that combines an attribute-space partitioning tree with HNSW graphs attached to tree nodes. A skew-aware splitting rule bounds the tree height by $O(\log n)$, and queries are answered by routing through the tree and running greedy search on the HNSW graphs. Experiments on four real-world datasets show that KHI consistently achieves high query throughput while maintaining high recall. Compared with the state-of-the-art RFANNS baseline, KHI improves QPS by $2.46\times$ on average and up to $16.22\times$ on the hard dataset, with larger gains for smaller selectivity, larger $k$, and higher predicate cardinality.

Quantum architectures based on neutral atoms have gained significant attention in recent years as specialized computational machines due to their ability to directly encode the independent set constraint on graphs, exploiting the Rydberg blockade mechanism. In this work, we address the Drone Delivery Packing Problem via a hybrid quantum-classical framework leveraging a neutral-atom quantum processing unit (QPU). We reformulate the optimization task as a graph-partitioning problem based on the independent sets (ISs) of a scheduling graph that encodes delivery incompatibilities. Each partition corresponds to deliveries assigned to a single drone, with the objective of minimizing the total number of partitions. While the ISs represent time-feasible schedules, battery-duration constraints are enforced through a classical post-processing routine. This methodology enables the recovery of optimal delivery schedules, provided a sufficient number of samples is collected from the QPU to resolve the solution space. We benchmark the hybrid workflow through numerical emulations and demonstrate its effectiveness on Pasqal's Fresnel QPU, reporting hardware experiments with configurations of up to 100 atoms.

For a static and spherically symmetric spacetime, we investigate the class of exact solutions that arise when two fundamental geometric constraints are imposed simultaneously: the Karmarkar's condition and the vanishing of the Weyl tensor. These conditions restrict the curvature in such a way that the spacetime becomes conformally flat and belongs to the family of embedding class-I solutions. Even though the subsequent solutions namely, the Schwarzschild interior solution and the de Sitter solution are well known, the novelty of our presentation is that these solutions are shown to be a direct consequence of the imposed geometric constraints. The physical matter composition becomes highly constrained by the associated geometry under such conditions. The Schwarzschild interior solution describes the spacetime of an incompressible fluid sphere while the de Sitter solution corresponds to a vacuum energy dominated configuration. Interestingly, pressure anisotropy as well as `complexity factor' vanish identically once the Karmarkar's condition and the conformal flatness conditions are applied simultaneously. As these two geometric constraints alone are sufficient to determine the background spacetime uniquely, Karmarkar's condition might not be a suitable method for the development of realistic stellar models in a conformally flat spacetime unless one invokes other factors into consideration such as time-dependent metric potentials.

The geometric dimension $g$ of a Vector Addition System with States (VASS) is the dimension of the vector space generated by cycles in the VASS; this parameter refines the standard dimension $d$, the number of counters. Recently, it was discovered that the fastest-known algorithm for solving the reachability problem for VASS has the same complexity in terms of $g$ as in terms of $d$. This suggests that the geometric dimension may in fact be a more adequate parameter for measuring the complexity of VASS reachability problems. We initiate a more systematic study of the geometric dimension. We discuss differences between two parameters: the geometric dimension and the SCC dimension. Our main technical result states that classical results about the coverability and boundedness problems can be improved from dimension $d$ to geometric dimension $g$. Namely, coverability is witnessed by runs of length $n^{2^{\mathcal{O}(g)}}$ instead of $n^{2^{\mathcal{O}(d)}}$, and unboundedness can be witnessed by runs of length $n^{2^{\mathcal{O}(g\log g)}}$ instead of $n^{2^{\mathcal{O}(d\log d )}}$, where $n$ is the size of the instance. We also study integer reachability and simultaneous unboundedness in VASS parameterised by the geometric dimension.

This chapter develops the concept of \textbf{meekly $SC^*$-normality}, a novel generalization of the classical notion of normality in topology. The proposed framework simultaneously broadens $SC^*$-normality and other established forms of normality, offering a unified perspective on generalized separation axioms. Fundamental properties are systematically derived, several equivalent characterizations are obtained, and the relationships between meekly $SC^*$-normal spaces and a range of existing normal-type spaces are rigorously analyzed. By establishing these structural connections, the chapter not only enriches the theory of generalized closed sets and separation axioms but also opens new directions for further research in advanced topological studies.

We exhibit a one-parameter family of first-order real elliptic systems on the plane whose ellipticity constant degenerates to zero as $δ\to 0$, with condition number $κ= O(δ^{-2})$. For any fixed elliptic solver operating at finite precision, the parameter $δ$ can be chosen small enough to defeat the solver; no uniform numerical scheme based on the ellipticity constant alone can handle the entire family. Despite this, every member of the family is explicitly solvable -- and its initial value problem well posed -- by elementary means once a transport-theoretic invariant is identified. The cost of the transport solution is independent of $δ$. The example serves as a cautionary tale: the ellipticity constant alone does not determine the practical difficulty of a first-order PDE. Before invoking an elliptic solver, one should compute the transport obstruction $G$; its vanishing -- or smallness -- signals structure that standard elliptic methods miss entirely.

The growing complexity of healthcare systems requires advanced computational models for real-time monitoring, secure data exchange, and intelligent decision-making. Digital Twins (DTs) provide virtual representations of physical healthcare entities, enabling continuous patient monitoring and personalized care. However, classical DT frameworks face limitations in scalability, computational efficiency, and security. Recent studies have introduced Quantum Digital Twins (QDTs) to enhance performance through quantum computing, addressing challenges such as quantum-resistant security and efficient task offloading in healthcare environments. Despite these advances, most existing QDT models remain constrained by fundamental challenges related to quantum hardware limitations, hybrid classical-quantum system integration, cloud-based quantum access, scalability, and clinical trust. This paper provides a comprehensive review of QDTs for healthcare, with a particular focus on identifying and analyzing the key challenges that currently hinder their real-world adoption. Furthermore, it outlines critical research directions and enabling strategies aimed at advancing the development of secure, reliable, and clinically viable quantum digital twin systems for next-generation healthcare applications.

The model of the attention economy, where content producers compete for the attention of users, relies on two key forces: information supply and demand. This study leverages the feedback loop between these forces to develop a method for detecting and quantifying information voids, i.e., periods in which little or no reliable information is available on a given topic. Using a case study on COVID-19 vaccines rollout in six European countries, and drawing on data from multiple platforms including Facebook, Google, Twitter, Wikipedia, and online news outlets, we examine how information voids emerge, persist and correlate with a decline in the proportion of high-quality information circulating online. By conceptualising information voids as a specific regime of information spreading, we also quantify their counterpart, information overabundance, which constitute a central component of the current definition of infodemic. We show that information voids are associated with a higher prevalence of misinformation, thus representing problematic hotspots in which individuals are more likely to be misled by low-quality online content. Overall, our findings provide empirical support for the inclusion of information voids in mechanistic explanations of misinformation emergence.

We analyze numerically the performance of Quantum Reservoir Computing (QRC) for statistical and financial problems. We use a reservoir composed of two superconducting islands coupled via their charge degrees of freedom. The key non-linear elements that provide the reservoir with rich and complex dynamics are the Josephson junctions that connect each island to the ground. We show that QRC implemented in this circuit can accurately classify complex probability distributions, including those with heavy tails, and identify regimes in correlated time series, such as periods of high volatility generated by standard econometric models. We find QRC to outperform some of the best classical methods when the amount of information is limited. This demonstrates its potential to be a noise-resilient quantum learning approach capable of tackling real-world problems within currently available superconducting platforms. We further discuss how to improve our QRC algorithm in real superconducting hardware to benefit from a much larger Hilbert space.

We study the problem of prescribing the Gaussian curvature on the disk and the geodesic curvature on its boundary via a conformal change of the metric. In this paper the case of negative Gaussian curvature is treated, a regime for which the bubbling behavior of approximate solutions is not so well understood. This is due to the possible appearance of blow-up solutions with diverging length and area. We give an existence result under assumptions on the curvatures which are somewhat natural, in view of some obstructions inherent to the problem. Our strategy is variational and relies on the study of certain families of approximated problems. By performing a refined blow-up analysis for solutions with bounded Morse index, we conclude compactness.