A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by constructing its Schwinger-Keldysh-Galley (SKG) action, including a careful treatment of boundary terms. The construction is based on a doubling of degrees of freedom and independent of a foliation. The action naturally decomposes into a bulk term furnishing Einstein's equations and a boundary term, which is related to conserved quantities, such as the Komar mass. We find that since only trivial connecting conditions must be specified on boundaries, the variational action principle for gravity as an initial value problem is rendered well-posed without the need to add additional boundary terms. The SKG approach to gravity offers a novel and complementary avenue to solve for the metric of spacetime directly from the action, bypassing the governing equations.

In this paper, we use the APOS theoretical framework to validate a hypothetical learning trajectory of the 2D heat equation, a preliminary genetic decomposition that stresses the conceptual understanding of its mathematical formulation. We design questions to probe specific mental constructions of the preliminary genetic decomposition. We interview 8 students in the second year of the B.Sc. enrolled in either engineering, physics or twin (mathematics and physics) majors. Our findings indicate that students engage with many predicted mental constructions. In particular, coordination and encapsulation of two process conceptions of the Laplacian of the temperature improve understanding although it is challenging. Other parts of the genetic decomposition require refinements. These include mental constructions related to the temperature distribution function, heat flow, and the temperature gradient.

Quantum batteries, miniaturized devices able to store and release energy on demand, are promising both because their intrinsic energy and time scales can match those of other quantum technologies and due to the intriguing possibility of achieving super-extensive charging power. While this enhanced scaling is known to appear in several settings, it is generally believed to be forbidden in Wigner-Jordan integrable spin chains charged via quantum-quench protocols. Here, we show that an extended cluster-Ising model, despite belonging to the above category, exhibits super-extensive charging power over wide ranges of system sizes, reaching up to a thousand spins, in proper parameter regimes. This remarkable anomalous scaling is due to a corresponding super-extensive growth of the stored energy, implying that it occurs at large but finite size and cannot persist in the thermodynamic limit. This phenomenon appears robust against finite-temperature effects.

Consecutive topological phase transitions (TPTs) between strongly correlated electronic phases that differ simultaneously in symmetry breaking and topological order are of fundamental interest in condensed matter physics, yet are rarely realized experimentally. We report two consecutive electric-field-driven TPTs at half filling (nu = 1) in angle-aligned MoTe2/WSe2 moire heterobilayers. With increasing out-of-plane displacement field, a geometrically frustrated Mott insulator evolves into a ferromagnetic quantum anomalous Hall (QAH) Mott insulator, i.e., a spin-polarized topological Mott insulator without an observable charge-gap closure, and subsequently into an antiferromagnetic, valley-coherent Mott insulator (VC-AFM) accompanied by a continuous charge-gap collapse and the emergence of a critical metallic state. Layer-resolved magnetic circular dichroism (MCD), magneto-transport, and compressibility measurements jointly determine the phase diagram. The high-field evolution of the antiferromagnetic state reveals a metamagnetic-like transition at a critical field B*, above which a Chern insulating transport response reappears. Our results establish the MoTe2/WSe2 moire platform as a tunable realization of an extended Kane-Mele-Hubbard model hosting sequential correlation-topology-intertwined transitions.

Moiré semiconductors offer flat bands where Coulomb interactions and band topology intertwine, while interlayer coupling plays a central role in forming the moiré potential. However, limited interlayer coupling strength and the lack of efficient tuning methods hinder further exploration of correlated phenomena in moiré semiconductors. Here we introduce a cryogenic dual-gated diamond-anvil platform using helium as a pressure medium, enabling reversible hydrostatic tuning together with magneto-optical spectroscopy in twisted bilayer WSe2. Pressure enhances the moiré potential, redshifts excitons, and stabilizes Stoner ferromagnetism otherwise absent at a 3.1-degree twist. Simultaneously, the half-filled C = 1 Chern insulating state strengthens, exhibiting a reduced saturation field. Moreover, we observe a topological phase transition from a Chern insulator to a Mott insulator at around 2 GPa. First-principles calculations reveal that a Gamma-to-K valence-band-maximum switching drives this transition by converting an Ising-like topological K-valley miniband into a spin-degenerate trivial Gamma miniband. Our findings demonstrate hydrostatic pressure as a powerful, continuous control axis for correlated magnetism and topological band engineering in moiré materials.

Optical topologies in the form of Skyrmions have attracted significant interest of late, where their integer Skyrmion number has been shown to be robust to complex media. Here we create the first fractional Skyrmions by structuring light as a vectorial superposition of non-integer orbital angular momentum. We unravel the map structure to reveal a new phenomenon, the abrupt transition jumps in skyrmion number, which serves to reinforce the integer nature of skyrmion topologies. Our experimental demonstration agrees well with simulation, opening a new spectrum of optical topologies to explore, with exciting possibilities in optical communication and sensing.

We show that for non-conjugate subgroups $G_1$ and $G_2$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_1$ and $G_2$ are not isomorphic. This allows us to show that $\mathbb Z$-coset equivalent subgroups of a finite group are not necessarily isomorphic, answering a question of Dipendra Prasad. We also indicate connections to profinite rigidity, anabelian geometry, mapping class groups, and non-arithmetic lattices in Lie groups.

We provide a detailed analysis of the non-twisting subcase of the large class of type D black holes with a non-aligned electromagnetic field, presented recently in [H. Ovcharenko and J. Podolsky, Phys. Rev. D 112 (2025) 064076]. We show that such exact solutions split into two main subclasses that (after a suitable re-parametrization) can be interpreted as either the uncharged Schwarzschild or C-metric in the external Bertotti-Robinson (BR) spacetime with geometry ${\mathrm{AdS}_2\times\mathrm{S}_2}$, or as the charged Reissner-Nordstrom black hole accelerating in the external BR electromagnetic field. The distinction between these two subclasses is determined by the parameter $r_0$ that encodes relations between the external Maxwell field (given by the non-aligned components of the Faraday tensor ${Φ_0=Φ_2}$) and the Maxwell field created by the charge of the black hole (given by the aligned component $Φ_1$). Namely, if ${r_0=0}$ then the electromagnetic field is fully determined by ${Φ_0=Φ_2}$, and one gets the C-metric in the BR universe (including also the non-accelerating Schwarzschild-BR black hole). But if ${r_0\neq 0}$ then the electromagnetic field is independently determined by both the external BR field and the field of a black hole itself, and this can be interpreted as the Reissner-Nordstrom black hole accelerating in the Bertotti-Robinson spacetime. Even though such an interpretation of the spacetime family is quite simple, it contains a lot of subtleties (e.g. the no-charge limit of the RN-BR spacetime, the non-trivial dependence on the signs of the mass and charge of a black hole, extreme black holes, and others) which we carefully investigate in this work. We also show the explicit relation to solutions previously found by Van den Bergh and Carminati, and we discuss the connection to the Alekseev-Garcia and Alexeev solutions.

An Amplitude-Encoded Quantum Genetic Algorithm (AEQGA) has been developed to minimize $χ^2$ functions of different cosmological probes (Supernovae Type Ia, Baryon Acoustic Oscillations, Cosmic Microwave Background Radiation), to find the best-fit value for two cosmological parameters, namely the Hubble Constant and the density matter content of the Universe today. Our main aim is to pave the way to testing the adoption of quantum optimization in the inference of the cosmological parameters that describe the universe evolution. AEQGA computes the merit function classically, and then uses a quantum circuit to entangle the population and perform crossover and mutation operations. The results show consistency with the isocontours of the objective functions. We then tested the general behavior of AEQGA as a function of its hyperparameters and compared it with a second quantum genetic algorithm found in the literature as well as with classical algorithms, finding consistent results.

Today we design wireless networks using mathematical models that govern communication in different propagation environments. We rely on measurement campaigns to deliver parametrized propagation models, and on the 3GPP standards process to optimize model-based performance, but as wireless networks become more complex this model-based approach is losing ground. Mobile Network Operators (MNOs) are counting on Artificial Intelligence (AI) to transform wireless by increasing spectral efficiency, reducing signaling overhead, and enabling continuous network innovation through software upgrades. They may also be interested in new use cases like integrated sensing and communications (ISAC). All we need is an AI-native physical layer, so why not simply tailor the offline AI algorithms that have revolutionized image and natural language processing to the wireless domain? We argue that these algorithms rely on off-line training that is precluded by the sub-millisecond speeds at which the wireless interference environment changes. We present an alternative architecture, a universal neural receiver based on convolution, which governs transmit and receive signal processing of any signal in any part of the wireless spectrum. Our neural receiver is designed to invert convolution, and we separate the question of which convolution to invert from the actual deconvolution. The neural network that performs deconvolution is very simple, and we configure this network by setting weights based on domain knowledge. By telling our neural network what we know, we avoid extensive offline training. By developing a universal receiver, we hope to simplify discussions about the proper choice of waveform for different use cases in the international standards. Since the receiver architecture is largely independent of technologies introduced at the base station, we hope to increase the rate of innovation in wireless.

Let $x_1,\dots,x_{n}$ be a fixed sequence of real numbers. At each stage, pick $k$ integers $\{I_{i}\}_{1\leq i \leq k}$ uniformly at random without replacement and then for each $i \in \{1,2,\dots,k\}$ replace $x_{I_i}$ by $(x_{I_1}+x_{I_2}+\dots+x_{I_k})/k$. It is easy to observe that all the co-ordinates converge to $(x_1+\dots+x_n)/n$. In this article, we extend the result of \cite{chatterjee2019note} by establishing order of decay of the expected $L^{2}$ distance. Furthermore, we establish the mixing time to be in between $\frac{n}{k \log k}\log n$ and $\frac{n}{k-1}\log n$.

In this paper, we prove some new \(q\)-series identities connecting \(4\)-regular partitions and partitions with distinct even parts with largest part being odd. We also define three new partition functions with distinct even parts except the largest part which is even, and prove identities connecting the three partitions with \(4\)-regular partitions. Moreover, we also offer some congruence for the three newly defined partitions.

We develop a framework for calculating nucleon-deuteron scattering using strict perturbation theory for treating subleading interactions in chiral effective field theory (ChEFT). Rather than using direct evaluations in the distorted-wave expansion, our approach solves a hierarchy of integral equations to obtain subleading scattering amplitudes. A benchmark with the wave packet continuum-discretization is performed. This framework benefits from the fact that the renormalization-group invariance chiral forces involves only a limited number of two-body partial waves at leading order. We use it to calculate nucleon-deuteron elastic scattering differential cross sections and analyzing powers up to next-to-leading order.

We study the task of quantum state exclusion, focusing on antidistinguishability and its generalization to $x$-antidistinguishability, under global measurements and local operations with classical communication (LOCC). We also introduce weak and strong notions of antidistinguiahbaility ($x$-antidistinguishability) depending on whether all states or all $x$-tuples are exhaustively eliminated. Our results reveal striking differences between state exclusion and the more familiar task of state discrimination. In particular, we show that LOCC antidistinguishability of multipartite product states is symmetric with respect to the initiating party but this symmetry breaks down for higher-order $x$-antidistinguishability. Most notably, we establish a manifestation of \emph{nonlocality without entanglement} in the context of state exclusion: we prove that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, demonstrating that three is the minimal number of states required for this phenomenon. We further extend this separation to $2$-antidistinguishability and present example exhibiting the same type of nonlocality. At last, we provide an antidistinguishable tripartite product states that are not LOCC antidistinguishable across any bipartition, which ensures the phenomenon of \emph{genuine nonlocality without entanglement} in this framework.

The ARCADIA INFN R&D project developed a Fully Depleted Monolithic Active Pixel Sensor (FD-MAPS) using a customized LFoundry 110 nm CIS process. The first in-beam characterization of the ARCADIA Main Demonstrator 3 (MD3) sensor with 200 $μ$m active thickness has been performed at the Fermilab Test Beam Facility with a 120 GeV proton beam. The Device Under Test (DUT) is tested with a trigger-less telescope composed of two ARCADIA MD3 tracking planes. This early study investigates the effect of the front-end parameters on the tracking performance.

Household size impacts the spread of respiratory infectious diseases: Larger households tend to boost transmission by acquiring external infections more frequently and subsequently transmitting them back into the community. Furthermore, mandatory interventions primarily modulate contagion between households rather than within them. We developed an approach to quantify the role of household size in epidemics by separating within-household from out-household transmission, and found that household size explains 41% of the variability in cumulative COVID-19 incidence across 34 European countries (95% confidence interval: [15%, 46%]). The contribution of households to the overall dynamics can be quantified by a boost factor that increases with the effective household size, implying that countries with larger households require more stringent interventions to achieve the same levels of containment. This suggests that households constitute a structural (dis-)advantage that must be considered when designing and evaluating mitigation strategies.

The localized states in the band gap of amorphous phase change alloys like Ge$_2$Sb$_2$Te$_5$ control the electrical conduction via the Poole-Frenkel mechanism. Understanding the origin of in-gap states and their evolution in time during aging of the glass is therefore important for the control of the resistance drift in phase change memory devices. Here, we use a machine learning interatomic potential to generate several models of Ge$_2$Sb$_2$Te$_5$ whose electronic structure is then analyzed within density functional theory with a hybrid functional. A detailed statistical analysis of the structural motifs on which the in-gap states are localized, reveals that the vast majority of in-gap states involve wrong bonds (homopolar or Ge-Sb bonds) often accompanied by Ge in tetrahedral configurations or overcoordinated Ge and Sb atoms. Metadynamics simulations mimicking glass aging support the picture that structural relaxations lead to the depletion of in-gap states and then to an increase of resistance. The simulations thus provide important insights for the mitigation of the resistance drift in phase change memory devices.

The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects. Unfortunately, dissipative properties tend to deteriorate in numerical computations, especially in nonlinear systems. Discrete gradient methods can help mitigate this problem. In this paper, we present a class of structure-preserving time discretization schemes based on discrete gradients for a special class of systems that are dissipative with respect to a quadratic supply rate.

We have investigated the electronic structure of Ba4Ir3O10 within the density-functional theory (DFT) using the generalized gradient approximation while considering strong Coulomb correlations (GGA+U) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. Ba4Ir3O10 has a quasi-2D structure composed of buckled sheets, which constitute corner-connected Ir3O12 trimers containing three distorted face-sharing IrO6 octahedra. The Ir atoms are distributed over two symmetrically inequivalent sites: the center of the trimer (Ir1) and its two tips (Ir2). The Ir1 - Ir2 distance within the trimer is quite small and equals to 2.58 A at low temperature. As a result, the clear formation of bonding and antibonding states at the Ir1 site occurs. The large bonding-antibonding splitting stabilizes the dyz-orbital-dominant antibonding state of t2g holes and produces a wide energy gap at the Fermi level. However, the energy gap opens up only with taking into account strong Coulomb correlations at the Ir2 site. Therefore, we have quite a unique situation when the insulating state is driven by both the dimerization at the Ir1 site and Mott insulating behavior at the Ir2 one. We have investigated resonant inelastic x-ray scattering (RIXS) spectra at the Ir L3 edge. The calculated results are in good agreement with experimental data. The RIXS spectrum possesses several sharp features below 2.1 eV corresponding to transitions within the Ir t2g levels. The excitation located from 2.1 to 4.6 eV is due to t2g to eg and O2p to t2g transitions. The wide structure situated at 6.2-12 eV appears due to charge transfer and O2p to eg transitions. We have also presented comprehensive theoretical calculations of the RIXS spectrum at the oxygen K edge.

Ultrasound-matter interactions underpin numerous biomedical and soft-matter applications, yet simulating these phenomena is challenging due to the large separation of viscous and sonic time scales. Continuum methods capture large-scale wave propagation but cannot resolve microscale interactions, while particle-based approaches offer molecular resolution but struggle with efficiency and stability at larger scales. We introduce a particle-based virtual ultrasound machine that uses a novel smoothed dissipative particle dynamics variant with an implicit pressure solver and a negative-pressure stabilization scheme, required to mimic acoustic propagation across MHz-GHz frequencies. We demonstrate its capabilities by modeling the acoustophoresis of encapsulated microbubbles, a key mechanism in ultrasound-mediated drug delivery. Beyond this application, the approach establishes a generalizable platform for simulating wave-matter interactions in soft and biological materials, opening new directions for computational studies of acoustics-driven phenomena in science and engineering.

Primordial black holes (PBHs) formed in the early Universe evaporate via Hawking radiation and constitute a generic source of stochastic gravitational waves. Existing studies of gravitational wave production from evaporating PBHs typically assume vacuum evaporation, neglecting the fact that PBHs in the early Universe are embedded in a hot thermal plasma. In this work, we investigate gravitational wave production from primordial black holes whose evaporation is thermally influenced by their surrounding environment. We adopt a thermal evaporation framework in which interactions with the ambient plasma modify the effective decay rate of the black hole, leading to enhanced mass loss at early times and a redistribution of the evaporation history compared to the standard non-thermal vacuum case. Since graviton emission is intrinsically tied to the evaporation history of PBHs, these thermal effects play a crucial role in determining the timing and spectral properties of the resulting stochastic gravitational wave background. Our results provide a consistent framework for incorporating thermal effects into gravitational wave production from evaporating primordial black holes and set the stage for a detailed analysis of their observational signatures.

Iron meteorite falls are rare compared to stony meteorites, and until recently no iron meteorite had a reliably determined pre-atmospheric orbit. This changed on 2020 November 7, when a bright fireball was observed across Sweden and neighboring regions, with optical, acoustic, and seismic detections extending up to 665 km from the trajectory. After a month-long recovery effort, a 13.8 kg iron meteorite was discovered near Ådalen, representing the first instrumentally recorded and recovered fall of its type and the first iron meteorite with a derivable heliocentric orbit; the event also exhibited the lowest terminal height measured for a well-documented fireball. We combine optical, infrasound, and seismic data to reconstruct the luminous trajectory and employ a Monte Carlo model to simulate the dark flight phase and predicted strewn field, while also investigating the plausibility of a ricochet prior to final deposition. Our analysis identifies distinct aerodynamic properties of iron meteoroids compared to stony bodies, including the influence of streamlined shapes and deep regmaglypts on drag and flight stability, underscoring the need to incorporate iron-specific parameters into entry models to constrain atmospheric dynamics and improve recovery predictions for future events.

The zone abstraction, widely adopted for its notable practical efficiency, is the de facto standard in the verification of Timed Automata (TA). Nonetheless, region-based abstractions have been shown to outperform zones in specific subclasses of TA. To complement and support mature zone-based tools, we introduce TARZAN, a C++ region-based verification library for TA. The algorithms implemented in TARZAN use a novel region abstraction that tracks the order in which clocks become unbounded. This additional ordering induces a finer partitioning of the state space, enabling backward algorithms to avoid the combinatorial explosion associated with enumerating all ordered partitions of unbounded clocks, when computing immediate delay predecessor regions. We validate TARZAN by comparing forward reachability results against the state-of-the-art tools Uppaal and TChecker. The experiments confirm that zones excel when TA have large constants and strict guards. In contrast, TARZAN exhibits superior performance on closed TA and TA with punctual guards. Finally, we demonstrate the efficacy of our backward algorithms, establishing a foundation for region-based analysis in domains like Timed Games, where backward exploration is essential.

A precision measurement of the photoionization of pure sodium and potassium nanoparticles isolated in a beam enabled an accurate determination of their work functions as a function of temperature. In addition to resolving and quantifying the initial gradual decrease of the work function with temperature, which is associated with thermal expansion, the experiment revealed that the work function then undergoes a distinct drop both in magnitude and in slope that signifies the onset of nanoparticle melting. This establishes that a structural phase transition can be detected via a high-resolution measurement of the photoemission threshold. The melting temperature of nanoparticles with diameters of 7-9 nm is reduced by nearly 100 K relative to the bulk value. This suppression aligns with predictions from the Gibbs-Thomson equation which describes finite-size phase transitions.

This study examines the evolution of a grassroots, volunteer-driven peer-to-peer (P2P) educational initiative from an emergency response to the 2023 Türkiye earthquake into a sustainable ecosystem that operated for over two years and supported 300+ middle-school learners with 40+ volunteer tutors. Employing an interpretive case study approach, we triangulated data from participant observation, focus groups, questionnaires, and collaborative visioning workshops to investigate the socio-technical dynamics enabling long-term resilience in a fully online, nonreciprocal far-peer tutoring setting. Our findings reveal that while age proximity fosters trust and open communication, it also poses challenges for tutors who must balance peer rapport with instructional authority. Volunteer engagement is driven primarily by intrinsic motives - educational impact and community belonging - while optional micro-earning is envisioned as a practical enabler for long-term sustainability. Tutees report significant gains in confidence, self-expression, and accelerated comprehension, attributing these outcomes to personalized, interactive sessions within a "family-like" safe space that combines academic instruction with socio-emotional support. Notably, tutees view tutors as aspirational role models and express strong intentions to return as tutors themselves, envisioning a self-regenerating cycle of intergenerational reciprocity that carries knowledge and solidarity from generation to generation. Both cohorts call for a dedicated platform featuring integrated scheduling, personalization, feedback, and quality assurance mechanisms. We synthesize these insights into theory-informed implications and five design principles for sustainable P2P learning ecosystems at scale.

Flux pumping was achieved in recent hybrid scenario experiments in the ASDEX Upgrade (AUG) tokamak, which is characterized by a sawtooth-free helical quiescent state and the anomalous radial redistribution of toroidal current density and poloidal magnetic flux. In this article, the self-regulation mechanism of the AUG core plasma during flux pumping is investigated at realistic parameters using the JOREK code based on the two-temperature, nonlinear, full magnetohydrodynamic (MHD) model. A key milestone in AUG flux pumping modelling is achieved by quantitatively reproducing the clamped current density and safety factor profiles in the plasma core, demonstrating the effectiveness of the dynamo effect in sustaining the flux pumping state. The dynamo term, that is of particular interest, is primarily generated by the pressure-gradient driven m/n = 1/1 quasi-interchange-like MHD instability. The work systematically extrapolates the parameter regimes of flux pumping from the above AUG base case by scanning dissipation coefficients and plasma beta. The simulation results reveal bifurcated plasma behaviours at different Hartmann numbers, including distinct states such as flux pumping (helical core with a flat current density), sawteeth (periodic kink-cycling), single crash (without subsequent cycle), and quasi-stationary magnetic island (peaked current density). Transitions from marginal flux pumping state to sawteeth are observed in long-term simulations. The relationships between system dissipation, plasma beta, and different plasma states are carefully analyzed. For practical purposes, the potential operational window for flux pumping, as determined by plasma density and temperature, is estimated. The modelling efforts advance the understanding of flux pumping and facilitate the development of a fast surrogate model for efficient evaluation of flux pumping.

In this manuscript, we study the Schrödinger cat state transfer in a quantum optical version of Newton's cradle in non-Markovian environment. Based on a non-Markovian master equation, we show that the cat state can be transferred purely through the memory effect of the non-Markovian common environment, even without any direct couplings between neighbor cavities. The mechanism of the environment induced cat state transfer is analyzed both analytically and numerically to demonstrate that the transfer is a unique phenomenon in non-Markovian regime. From this example, the non-Markovian environment is shown to be qualitatively different from the Markovian environment reflected by the finite versus zero residue coherence. Besides, we also show the influence of environmental parameters are crucial for the transfer. We hope the cat state transfer studied in this work may shed more light on the fundamental difference between non-Markovian and Markovian environments.

We examine static and dynamic social network structure in 176 villages within the Copan Department of Honduras across two data waves (2016, 2019), using detailed data on multiplex networks for 20,232 individuals enrolled in a longitudinal survey. These networks capture friendship, health advice, financial help, and adversarial relationships, allowing us to show how cooperation and conflict jointly shape social structure. Using node-level network measures derived from near-census sociocentric village networks, we leverage mixed-effects zero-inflated negative binomial models to assess the influence of individual attributes, such as gender, marital status, education, religion, and indigenous status, and of village characteristics, on the dynamics of social networks over time. We complement these node-level models with dyadic assortativity (odds-ratio-based homophily) and community-level measures to describe how sorting by key attributes differs across network types and between waves. Our results demonstrate significant assortativity based on gender and religion, particularly within health and financial networks. Across networks, gender and religion exhibit the most consistent assortative mixing. Additionally, community-level assortativity metrics indicate that educational and financial factors increasingly influence social ties over time. Our findings provide insights into how personal attributes and community dynamics interact to shape network formation and socio-economic relationships in rural settings over time.

The development of data science expertise requires tacit, process-oriented skills that are difficult to teach directly. This study addresses the resulting challenge of empirically understanding how the problem-solving processes of experts and novices differ. We apply a multi-level sequence analysis to 440 Jupyter notebooks from a public dataset, mapping low-level coding actions to higher-level problem-solving practices. Our findings reveal that experts do not follow fundamentally different transitions between data science phases than novices (e.g., Data Import, EDA, Model Training, Visualization). Instead, expertise is distinguished by the overall workflow structure from a problem-solving perspective and cell-level, fine-grained action patterns. Novices tend to follow long, linear processes, whereas experts employ shorter, more iterative strategies enacted through efficient, context-specific action sequences. These results provide data science educators with empirical insights for curriculum design and assessment, shifting the focus from final products toward the development of the flexible, iterative thinking that defines expertise-a priority in a field increasingly shaped by AI tools.

Let $X$ be a mildly singular Fano variety such that the tangent sheaf is a direct sum. We show that the direct factors are algebraically integrable, so the infinitesimal decomposition induces a product structure on a quasi-étale cover of $X$.