Memorization in diffusion models is often treated as a global property of the model or dataset. In practice, however, a single diffusion model can simultaneously generate both memorized and novel samples. Which training samples are most likely to be memorized? In this work, we show that memorization is governed by \emph{local data coverage}. Leveraging the connection between diffusion models and kernel density estimation (KDE), we derive a theoretical criterion that predicts whether a point is memorized based on the density of training data in its neighborhood and the size of the training dataset. In the high-dimensional limit, this leads to a sharp, local transition: regions of low coverage are dominated by isolated training samples, which are memorized, while dense regions support interpolation and generalization. We validate these predictions empirically, showing that memorization increases with local sparsity and that diffusion models exhibit a coexistence of memorized and novel samples within the same model. Extending this framework to multi-class settings, we further show that classes with higher intra-class sparsity (and thus lower local coverage) are more strongly memorized. Our results provide a local view of memorization in diffusion models, explaining when and where memorization occurs in terms of data geometry.

Materials discovery increasingly relies on the coordinated use of theory, computation, experiment, data-driven methods, and emerging quantum technologies, yet the full potential of these tools is realised only when they operate within workflows that reflect the complexity of real systems. This perspective summarises current capabilities, limitations, and opportunities across these domains, drawing on contributions from academia, industry, and national laboratories to identify the scientific and structural requirements for more reliable and efficient discovery. Classical simulations provide broad coverage across design spaces, while experimental measurements reveal degradation, heterogeneity, and kinetic processes that determine performance under realistic conditions. Machine learning accelerates exploration when supported by well-curated datasets with clear provenance and uncertainty quantification, and quantum computing offers promising routes into correlated electronic behaviour when aligned with properties that influence engineering decisions. Collectively, these insights highlight the need for reproducible workflows, shared data standards, realistic benchmarks, and a research culture that prepares scientists to work across paradigms. By integrating these methodological and organisational elements, the community can move toward discovery processes that deliver robust predictions, support confident decision making, and shorten the path from conceptual design to deployable materials.

We consider a scenario for dark matter in the Universe, according to which the dark matter sector is comprised by a dark Standard Model sector which interacts only gravitationally with the ordinary Standard Model sector. This dark Standard Model sector is assumed to have the same symmetries as the ordinary Standard Model, with the couplings and the scale of the mirror Standard Model sector being different than the ordinary Standard Model sector. Specifically, the scale of the mirror Standard Model sector will be assumed to be quite higher compared to the ordinary Standard Model. Also the Yukawa couplings among the mirror Higgs and the mirror fermions are assumed to be different from those of the Standard Model and we examine the effects of the different scale and of the different Yukawas on the evolution of the Universe. As we show, a mirror world phase transition occurs at high temperatures of the baryonic Universe, which can be first order or second order, depending on the scale of the Universe and the Yukawa couplings. These are dark phase transitions which occur quite earlier than the real world Standard Model electroweak phase transition. The case of a second order phase transition is quite interesting phenomenologically, since it can potentially have a direct imprint on the spectrum of stochastic gravitational waves for frequencies probed by the future gravitational wave detectors. Also we examine whether this mirror dark matter world can form atoms and as we show in some scenario the high scale mirror dark matter can have both atomic and subatomic particle components. We also give an approximation of the total equation of state of high scale mirror DM and we discuss how high scale mirror DM can reconcile contradicting observations like the Bullet cluster and the Abell 520 cluster.

We prove polynomial bounds on the growth of high Sobolev norms of solutions to the defocusing fractional nonlinear Schrödinger equation with cubic and Hartree-type nonlinearities in two and three dimensions. Our result is based on the upside-down I-method and the method of higher modified energies. The analysis of the fractional case in higher dimensions is possible due to a higher-dimensional analogue of a resonance inequality, which allows us to control the nonresonant frequency contributions.

We discuss probabilistic measures of concordance between two probability distributions based on the expected misclassification rate (EMR). The focus is on comparing a given reference distribution with other distributions in a parametrised class, and optimising concordance by identifying parameter values maximising EMR or a regularised variant. EMR is a practical and decision-theoretically meaningful measure, and its optimisation has direct interpretation as a Bayesian decision analysis with a bounded utility function. We explore theoretical properties of EMR, discuss relationships with other measures including Küllback-Leibler divergence, and recognise that its optimisation has a synthetic Bayesian emulation interpretation that aids understanding and specification of regularisation penalties. A main area of methodology is in mixture synthesis where the parametrised family is a discrete mixture of given distributions. A detailed example comes from scenario forecasting in macroeconomic policy settings, a key applied area motivating the new methodology. Theoretical developments underlie efficient numerical optimisation and analysis is easily implemented using direct Monte Carlo simulation.

Recently, the Turán problem for graphs with bounded clique number has attracted considerable attention. Since a graph can be regarded as a signed graph without negative edges, it is natural to extend the study of such Turán-type problems to signed graphs. With this motivation, we investigate the Turán-type problem for unbalanced $C_{2k+1}^{-}$-free signed graphs with bounded clique number. In fact, we establish a general result via the classical stability theorem. Specifically, for sufficiently large $n$ and a color-critical graph $F$, we determine the maximum number of edges among all $n$-vertex $C_{2k+1}^{-}$-free unbalanced signed graphs whose underlying graphs are $F$-free.

The Sachs-Wolfe (SW) effect, arising from large-scale structures in the universe, modifies the frequencies of gravitational waves (GWs) sourced by a cosmological background. We show that for backgrounds with $\Omega_{\rm GW}\gtrsim 10^{-10}$, this effect imprints anisotropies and spectral distortions that can be detectable with a network of space-based interferometers (such as LISA + Taiji) and, if not taken into account, may bias the estimate of the theoretical model of the GW background. The effect is particularly enhanced in the high-frequency end of the spectrum. The SW-induced anisotropies and spectral distortions present in a GW background sourced at primordial times will correlate with the SW signature present in the CMB. Any detection of a cross-correlation between the GW anisotropies and the CMB at large scales is therefore a smoking gun for confirming the primordial nature of the background.

Achieving nonvolatile and multistate manipulation of charge-spin conversion, including the Edelstein effect (EE) and spin Hall effect (SHE), is crucial for high-density spintronic memory. Here, we propose a mechanism to simultaneously control both EE and SHE in two-dimensional ferroelectric bilayers, where interlayer-parallel and interlayer-antiparallel polarization configurations can coexist. Symmetry analysis shows that in the interlayer-parallel states, reversal of the total polarization switches the sign of the EE, whereas changing to an interlayer-antiparallel configuration suppresses the EE to zero, enabling electrically switchable current-induced spin accumulation among three distinct states, which could be used for ternary logic operations. Meanwhile, the magnitude of the SHE can be tuned by switching between two different classes of polarization configurations, namely interlayer-parallel and interlayer-antiparallel configurations. Using first-principles calculations, we demonstrate this mechanism in bilayer metallic ferroelectric PtBi2, where both interlayer-parallel and interlayer-antiparallel polarization configurations are energetically stable. The EE coefficient in interlayer-parallel states, which can be reversed by polarization switching, arises from competing electron- and hole-pocket contributions near the Fermi surface. The intrinsic SHE coefficients originate from spin Berry curvature that can be reshaped by polarization configuration variation and Fermi-level tuning. Our results establish ferroelectric bilayers as an all-in-one platform for electrically programmable charge-spin conversion.

Freedom of Information (FOI) laws aim to increase government transparency, yet existing assessments focus mainly on legal compliance and procedural outcomes, leaving organizational behavior underexamined. As FOI processes are increasingly mediated through digital information systems, public response data offer traces of how organizations handle requests and disclosures in practice. This paper develops and evaluates a pattern-based approach that uses such data to signal transparency-impeding behavior across government agencies and over time. Drawing on prior literature, we identify nine recurring behavioral patterns that undermine transparency. Using a dataset of 15,277 Dutch FOI dossiers comprising 139,449 documents, we operationalize and evaluate measurable indicators for six of these patterns, demonstrating that they enable systematic comparison of disclosure practices across agencies and over time. Expert interviews with researchers, journalists, and civil servants confirm the interpretability and practical usefulness of the indicators for investigative prioritization, comparative research, and transparency oversight.

The video game industry comprises a vast, continuously evolving landscape of themes and genres. For studios and publishers that navigate this competitive market, understanding the structural dynamics and temporal evolution of specific game categories is crucial for identifying viable entry points. In this paper, we introduce Games Mapper, a novel analytical tool based on the Mapper algorithm from topological data analysis. Unlike traditional clustering techniques, Games Mapper captures the continuous topological relationships between datasets over time (or other guiding variables). We extend the standard algorithm with an automated cluster labelling method, ensuring highly interpretable and interactive visualisations of genre evolution. To demonstrate the efficacy of our approach, we present a comprehensive case study on Simulation games released on Steam between 2015 and 2025. Games Mapper autonomously segments the genre into coherent, persistent subgenres, and captures dynamic market shifts. Ultimately, we provide a scalable, generalisable tool for researchers and industrials to unravel complex market structures and track the evolution of the Steam ecosystem.

We present a bond-operator theory (BOT) for analytical consideration of the $t$-$J$ model and its extensions with longer-rage hopping terms. This technique is based on previously suggested representation of electron operators via localized spins 1/2 and spinless Fermi-operators of mobile holons which requires no constraint between them. We introduce a representation of operators of spins, holons, and electrons in (extended) unit cell containing several lattice sites via a zoo of Bose- and Fermi-operators acting in the Hilbert space of all quantum states of the whole unit cell. BOT provides a regular expansion of physical quantities in powers of $1/n$ using conventional diagrammatic technique, where $n\ge1$ is the maximum number of introduced quasiparticles (bosons and fermions) which can occupy a unit cell. The suggested representation reproduces commutation algebra of all operators at any $n>0$ and allows to consider both magnetically ordered and disordered phases. Some elementary excitations described in the BOT by separate bosons or fermions appear in common approaches as bound states of conventional quasiparticles. In particular, there are two-hole bound states (Cooper pairs of two holes) which are described within the BOT by separate bosons. We discuss in detail properties of the $t$-$J$ model on the square lattice with no more than two holes (polarons). Although the expansion parameter $1/n$ is not small in the physically meaningful case of $n=1$, we obtain a good quantitative agreement with previous numerical findings at $n=1$ even in the first order in $1/n$ after taking into account a few simple diagrams. Self-consistent calculations in the first order in $1/n$ bring our results to a very good quantitative agreement with previous numerical findings of the ground state energy, staggered magnetization, and spectra of magnons, polarons, and lowest-energy two-hole bound states.

The Geometric Dilution of Precision (GDoP) characterizes the noise sensitivity of a Time-Difference-of-Arrival (TDoA) localization system, but does not capture every way the analytical multilateration solution can become ill-conditioned. We introduce a complementary geometry-quality metric $\kappa$, the leading coefficient of the closed-form TDoA solver's quadratic, and derive its $N$-dimensional generalization through a vectorized formulation. Two closed-form algebraic identities relate $\kappa$ to the Jacobian determinant of the measurement model and to the quadratic's discriminant, establishing that the system exhibits exactly two distinct singularity loci: branch divergence and the Jacobian/branch-merge locus flagged by GDoP. A Cramér--Rao-bound-linked closed form for the noise sensitivity $\sigma_\kappa$ under the standard Gaussian ToA model is validated against Monte Carlo to 2% median relative error. An empirical atlas over a dimensionless geometry parameter space confirms both identities at machine precision and shows that $\kappa$-bad regions and GDoP-bad regions are non-trivially disjoint in target space, establishing the two metrics as genuinely complementary. A case study on a four-node operational array, with per-sensor time of arrival (ToA) noise estimated empirically from Automatic Dependent Surveillance Broadcast (ADS-B)-paired over-the-air captures, shows that the theory-predicted threshold and a Monte-Carlo-measured operational threshold agree on the per-subsystem ordering at the deployment noise level. Their ratio is approximately constant across the three two-dimensional subsystems, serving as a deployment-specific calibration constant between the algebraic $\kappa$-noise floor and the downstream operational threshold, analogous in spirit to the standard relation linking GDoP to the circular error probable.

We present multi-epoch R-band imaging and long-slit spectroscopy of the dynamically new comet C/2024 E1 (Wierzchos) during its pre-perihelion phase, spanning heliocentric distances from 4.5 to 2.3 au. The most prominent fluorescence emissions in the visible wavelength range are detected. We measure production rates of CN, C$_2$, and C$_3$, while no significant NH$_2$ signal is identified. In our dataset, CN became detectable at 3.48 au, and C$_3$ and C$_2$ at 2.80 au. The mean ratios $\log\mathrm{C}_2/\mathrm{CN} = 0.00 \pm 0.07$ and $\log\mathrm{C}_3/\mathrm{CN} = -1.03 \pm 0.09$ place the comet in an intermediate taxonomic regime between typical and carbon-depleted populations. Dust production rates, ejection velocities, and particle size distributions are constrained using a Monte Carlo dust tail model that reproduces the observed coma morphology. The dust population is characterized by a power-law size distribution with an exponent of $\sim -3.5$, and particle sizes ranging from 1~$\mu$m to 4~mm. The inferred initial ejection velocities span from $\sim$20$ m $s$^{-1}$ to $\sim$100$ m $s$^{-1}$. We use the empirical relation between CN and OH to estimate the water production rate and derive the dust-to-gas mass ratio for heliocentric distances $r_{\rm{h}} \lesssim 3$ au, where water sublimation is expected to dominate the activity regime. The dust-to-gas mass ratio remains consistently above unity, ranging from $\sim$1 to 3 depending on the choice of scale lengths and the CN--OH conversion factor. This result characterizes C/2024 E1 as a ``dust-rich'' comet, where the mass loss is dominated by the refractory component rather than volatiles.

We develop classical density functional learning to address fluids with truncated pairwise interparticle interactions in three-dimensional spherical geometry. Simulation data for systems with randomized repulsive pair potentials provide the basis for supervised training of a neural metadensity functional, thereby making efficient use of results for radial distribution functions in the bulk fluid via the test particle route. Specifically, we develop spherical local learning in order to represent the one-body direct correlation functional in terms of a neural network, which captures spatial curvature effects as well as the metadensity functional dependence on the thermally scaled pair potential. The framework yields efficient access to inhomogeneous structuring and related physical phenomena that occur in fluids and general solvents when adsorbed against curved solutes and confined inside of spherical and planar cavities. Test particle setups facilitate accurate prediction of the bulk fluid pair structure and verification of thermodynamic test particle sum rules via functional line integration. Applying the metadensity functional for Henderson inversion allows one to infer accurately the pair potential from the bulk radial distribution function. We address implications of the geometrical setup for two-body quantities and obtain the two-body direct correlation functional from automatic differentiation. For the hard sphere fluid, we confirm metadensity functional predictions against results from a standard neural density functional with fixed pair potential as well as to an analytic functional as given by fundamental measure theory. Simulation results provide further reference and corroborate reliable results of the spherical neural metadensity functional across a broad range of applications.

Building upon the semi-implicit multilevel spectral deferred correction (SI-MLSDC) method introduced by Pfister and Stiller [38], this work presents a 1D space-time adaptive high-order method combining discontinuous Galerkin spectral element discretizations with multilevel spectral deferred corrections. The proposed approach enables genuine arbitrary-order accuracy in space and time while dynamically balancing spatial and temporal discretization errors to reduce computational cost. A key contribution is the development of a novel temporal error estimator that in combination with a spectral error estimator in space provides a reliable basis for adaptive refinement decisions. The error estimator is compared with two alternative refinement criteria to assess their impact on accuracy, computational efficiency and their suitability for complex this http URL performance of the adaptive method is demonstrated for nonlinear conservation laws ranging from Burgers' equation to the Euler equations. Numerical results show substantial runtime reductions while maintaining the desired accuracy. In particular, significant computational savings are achieved for Burgers' equation, and challenging benchmark problems such as the Shu-Osher shock-fluctuation benchmark. These results demonstrate the potential of adaptive SI-MLSDC methods for efficient high-order space-time adaptive simulations of complex flow problems.

The classification and enumeration of short mesh patterns have emerged as two central directions in the area. We make substantial progress on both fronts. We construct an involution and a bijection that establish distributional equivalences for two classes of length-$2$ mesh patterns, thereby resolving a conjecture from 2019 and a recent conjecture. As a consequence, the best known upper bounds for the numbers of distribution-equivalence and Wilf-equivalence classes drop to $106$ and $47$, respectively. Combined with the known lower bounds of 105 and 46, conjectured to be exact, these results leave both classifications hinging on a single distribution-equivalence question conjectured in 2019, whose resolution would at once settle the remaining Wilf-equivalence case. We further conjecture that this unresolved equidistribution also holds for involutions, a subclass of all permutations. We also determine the distributions of three additional classes of length-$2$ mesh patterns through a detailed structural analysis. Our work combines bijective techniques with generating-function methods, yielding new insights into the structure and enumeration of short mesh patterns.

Consider the annulus $\mathbb{A}_r=\{z\in\mathbb{C}:r^{-1}<|z|<r\}$ for $r>1$ and the quantum annulus \[ Q\mathbb{A}_r=\{T:\ T \text{ is an invertible operator and} \ \|T\|, \|T^{-1}\|\leq r\}. \] McCullough and Pascoe proved that $T\in Q\mathbb{A}_r$ if and only if $\beta(T^*,T)=(r^2+r^{-2})-T^*T-(T^*T)^{-1}\ge0$. We call an invertible operator $T$ a quantum annulus unitary if $\beta(T^*,T)=0$. In this article, we construct an explicit doubly commuting $d$-tuple of quantum annulus unitaries that simultaneously extends a given doubly commuting $d$-tuple of operators in $Q\mathbb{A}_r$. We introduce the notion of a regular quantum annulus unitary dilation and show that the dilation arising from our construction is regular. As an application of the dilation theorem, we show that $\overline{\mathbb A}_r$ is a complete $K_t$-spectral set for operators in $Q\mathbb{A}_r$ and $\overline{\mathbb{A}}_r^d$ is a complete $K_{dc}^{(d)}$-spectral set for doubly commuting $d$-tuples of operators in $Q\mathbb{A}_r$, where \[ K_t=2\left(1+\frac{2r^2}{(r^2+1)\sqrt{r^4-1}}\right) \quad \text{and} \quad K_{dc}^{(d)}=\left[2\left(1+\frac{2r^2}{(r^2+1)\sqrt{r^4-1}}\right)\right]^d. \] We further prove that every doubly commuting tuple of operators in $Q\mathbb{A}_r$ is similar to a commuting tuple having $\overline{\mathbb{A}}_r^{d}$ as a complete spectral set. In addition, we establish bounds for the optimal spectral constants and show that they converge to $2^d$ as $r\to\infty$. We also obtain an alternative characterization of operators in $Q\mathbb{A}_r$ and quantum annulus unitaries, and prove that $\overline{\mathbb{A}}_r^d$ is a $K$-spectral set for a subclass of commuting $d$-tuples in $Q\mathbb{A}_r$.

Photon-number-resolving (PNR) detectors are essential components of photonic quantum technologies, yet thus far, no practical metric exists to certify how many photons they can genuinely resolve in a single measurement. Here we introduce an operational framework for quantifying the capability of a PNR detector to distinguish between different numbers of photons, i.e. its genuine resolution. In turn, we develop a practical and scalable protocol for certifying the genuine resolution of a detector, which is based on coherent state probes. We apply the method to a 28-pixel photon-number-resolving superconducting nanowire single-photon detector (PNR-SNSPD) and certify genuine four-outcome resolution. Our work highlights the critical requirements in terms of detector efficiency towards achieving high genuine resolution. This approach provides an operational benchmark for PNR detectors and fills a crucial gap in the characterization of photonic quantum devices.

We conduct two three-dimensional hydrodynamic simulations of the jittering-jets explosion mechanism (JJEM) of core-collapse supernova (CCSN), launching three pairs of inclined opposite jets into the core of an enveloped-stripped stellar model, and reproduce some morphological features of observed CCSN remnants (CCSNRs) that a single pair of jets or instabilities alone cannot reproduce. We launch the three pairs of jets within about a second, and follow the ejecta for more than 10 seconds until after shock breakout. Our main findings are: (1) Although the jets are choked deep inside the star, they manage to form a pronounced multipolar (point-symmetric) morphology. (2) Instabilities and vortices resulting from the jet-star interaction form small clumps and narrow filaments, some of which form point-symmetric morphology, resembling some observed CCSNRs. (3) The most energetic jet of one simulation forms a large low-density blowout ahead of the ejecta, with filaments dragging behind it, resembling the blowout of the Cygnus Loop. (4) The inner ejecta presents two symmetry axes along two of the three jet axes: one of a pair of rings and one of a pair of nozzles, resembling the structure of the point-symmetric SNR J0450.4-7050. (5) The three pairs of jets compress two dense blocks between their axes. The blocks exhibit a Doppler-shift bipolar outflow highly inclined to the morphological axes along the jet axes. The inclined Doppler-bipolar outflow and morphology axis resembles the CCSNRe W49B and SNR G292.0+1.8. Our study supports the claim that the JJEM is the primary explosion mechanism of CCSNe.

We develop a quantum-classical hierarchical equations of motion (QC-HEOM) approach for simulating non-Markovian open quantum systems. The method combines the ensemble-averaged classical path reference of the quantum-classical path integral formalism with a hierarchy of auxiliary quantum influence functionals. By incorporating thermal fluctuations through an ensemble average over reference trajectories, the hierarchy is required to represent only the residual quantum memory associated with the imaginary part of the bath response function. Consequently, unlike conventional hierarchical equations of motion, QC-HEOM does not require Matsubara or Padé expansions of the thermal kernel and exhibits only weak temperature dependence of the hierarchy size. Furthermore, because thermal fluctuations are supplied through reference classical trajectories, the framework naturally extends beyond harmonic baths and enables the incorporation of anharmonic and molecular environments through externally generated trajectories. We derive the formalism and demonstrate its exactness for a harmonic bath. Applications to an asymmetric spin-boson model and the seven-site Fenna--Matthews--Olson complex illustrate the accuracy of QC-HEOM. It reproduces benchmark quasi-adiabatic path integral and hierarchical equations of motion results while requiring substantially fewer auxiliary objects, particularly at low temperatures. These results establish QC-HEOM as an efficient framework for treating residual quantum memory in quantum-classical descriptions of open-system dynamics. The separation of thermal fluctuations from residual quantum memory through the use of Wigner trajectories provides an approximate route toward hierarchical treatments of complex anharmonic environments that are inaccessible to conventional HEOM approaches.

This paper presents a search for semi-visible Higgs boson decays in final states with a photon ($\gamma$) and missing transverse momentum $p_T^{miss}$. The analysis is optimised for the gluon-gluon fusion production channel and exploits a novel trigger deployed in 2023, with reduced thresholds down to 50 GeV on the photon transverse momentum ($p_T^{\gamma}$) and 70 GeV on the $p_T^{miss}$, in combination with a selection on the transverse mass of the $p_T^{miss}$-$\gamma$ system ($m_T$) above 80 GeV. The results are interpreted in terms of Higgs boson decays into a $\gamma$ and a dark photon $\gamma_d$ ($H \to \gamma \gamma_d$). The analysis is performed using 135 fb$^{-1}$ of Run 3 data collected by ATLAS in 2023 and 2024. A boosted decision tree is used to identify events with misreconstructed primary vertices, which can affect the $p_T^{miss}$ calculation. Data-driven methods are employed to estimate the backgrounds from jets and electrons misidentified as photons, while the backgrounds with genuine photons are taken from Monte Carlo simulations, normalised to data in control regions with muons. A binned maximum-likelihood fit to the $m_T$ distribution is performed to evaluate the compatibility of the observed data with the Standard Model expectation. No significant excess is observed over the Standard Model prediction, and an observed (expected) upper limit on the branching ratio of $H \to \gamma \gamma_d$ of 1.4% (1.2%) is obtained at 95% confidence level. Combining this result with previous Run 2 searches improves the observed (expected) upper limit to 0.9% (0.9%).

In this paper, we prove lower bounds for the Gaussian-weighted \(L^2\)-curvature integral of embedded self-shrinkers. The proof combines normal coordinate functions with weighted Poincaré inequalities arising from first-eigenvalue estimates of Ding--Xin and Brendle--Tsiamis. For closed self-shrinkers, the estimate gives an explicit lower bound in terms of entropy and, together with the entropy gap theorem of Colding--Ilmanen--Minicozzi--White, yields a strict curvature gap for nonspherical closed shrinkers. In dimension two, we combine this estimate with the classification theorem and entropy gap theorem of Bernstein--Wang to obtain the corresponding gap statement for complete embedded self-shrinkers with polynomial volume growth.

Context. Studying pulsating stars in clusters opens a new window onto stellar physics. Gravity-mode (g-mode) pulsators in open clusters allow us to measure their near-core rotation rates and, together with cluster age and mass constraints, test angular momentum transport in stars above about 1.5 solar masses. Aims. We aim to detect g-mode pulsations in member stars of the young open cluster NGC 3532, about 300 Myr old, and to measure their near-core rotation rates and internal properties. Methods. We used TESS photometry to extract light curves of NGC 3532 members. The observed g-mode period spacings allow us to measure near-core rotation rates and the asymptotic period spacing, Pi0. We also fitted isochrones to the colour-magnitude diagrams of NGC 3532 and NGC 2516 to refine the cluster ages and obtain stellar masses. Results. We constrain the observed instability region of young gamma Doradus members from a blue edge at about 7760 K to a red edge at about 7070 K, while some hotter g-mode pulsators are also seen. The near-core rotation rates show a rotation-mass relation similar to that in NGC 2516: below 1.6 solar masses, the rotation rate increases with mass, whereas above 1.6 solar masses the NGC 3532 stars reach a plateau at about 2.8 d^-1. This mass may mark a threshold between different rotational spin-down mechanisms. Existing evolutionary models with angular momentum transport imply that these g-mode pulsators were born rotating above 55 percent of the critical value. Our simplified models, assuming spherical symmetry, angular momentum conservation, and rigid internal rotation, suggest that either mass-dependent initial rotation rates are required, or that minor angular momentum loss still operates above 1.6 solar masses. Finally, our Pi0 measurements reveal a discrepancy with theoretical predictions for some pulsators, as also found in the younger cluster NGC 2516.

Synchronous online teaching environments pose specific challenges for the analysis of pedagogical activity as teaching takes place via videoconferencing platforms and interactions are multimodal. While pedagogical orchestration has been extensively studied in the context of face-to-face courses and at the level of instructional design, the analysis of teaching in videoconferencing environments remains under-explored and insufficiently instrumented in terms of methodology. This article proposes a multimodal observation grid designed to analyze the instrumentalised pedagogical orchestration of teachers during synchronous online classes. Based on theories of pedagogical orchestration, multimodality and professional gestures of teachers, this grid identifies a set of observable indicators related to communicational gestures, posture, gaze and the management of digital tools. These indicators are structured and ranked in order of priority according to their observability and analytical relevance. They are operationalised to consider the constraints associated with data that can be analysed in videoconference class contexts. The proposed grid aims to provide a reproducible methodological framework for the analysis of instrumental pedagogical orchestration, with a view to future empirical validation.

Recent advances in cold atom manipulation enable the study of many-body systems where short-range interactions between neighboring atoms coexist with long-range interactions mediated by photons. Such a combination of interactions makes a theoretical approach challenging beyond mean-field methods. In this work, we develop a neural quantum state based approach to study these systems numerically. We introduce a neural-network architecture capable of handling hybrid Hilbert spaces with large local bosonic dimensions in strongly interacting spin-photon systems. We benchmark this approach on a model of a two-dimensional lattice of Rydberg atoms coupled to a photon mode. The superradiant ground states found in the large spin-photon coupling regime allow us to demonstrate the efficiency of the method in the presence of high photon occupation. Furthermore, the ability to capture spin-spin and spin-photon correlations leads us to observe quantitative deviations in the ground state phase boundaries with respect to mean-field theory. The method extends to other systems with a similar hybrid Hilbert space structure, such as spin-phonon systems, and provides a scalable framework for investigating their ground state properties.

Using two distinct approaches, we derive a universal expression for the leading finite-volume effects of the smeared vector-vector spectral density (proportional to the smeared hadronic $R$-ratio) in a periodic cubic spatial volume of side length $L$. First, building on the results of previous work for finite-volume effects on Euclidean two-point functions, we show that the $L$ dependence is exponentially suppressed for a certain class of smearing kernels, and that the leading effects can be expressed universally in terms of the pion form factor. The same representation is then derived starting from the Lellouch-Lüscher-Meyer expression for the spectral decomposition of the correlator. The results may prove useful for controlling the $L \to \infty$ extrapolation of smeared spectral densities, in particular by defining a scaling regime in which the finite-volume effects are dominated by the leading terms in a large $L$ expansion and thus can be reliably estimated. To illustrate this point, we also present numerical estimates based on various kernels and models of particle interactions. Despite focusing on the vector channel, our derivation defines a general framework applicable to other cases as well.

André planes of order $q^t$ can be constructed from the Desarguesian plane $PG(2,q^t)$ using a process that involves replacing André nets. This article constructs ovals in André planes of order $q^t$, $q$ even and $t$ prime that are inherited from conics of the Desarguesian plane $PG(2,q^t)$. Further, it is shown that certain conics do not inherit to arcs under the process of André replacement.

Chiroptical sensing is central to gain fundamental insight into electronic, vibrational and rotational degrees of freedom of chiral molecules, and is a cornerstone for nanomedicine and drug discovery platforms. Current chiral sensing technologies to assess the enantiomeric imbalance of chiral pharmaceutical compounds are sensitive to ml volumes but are time-consuming and cannot be integrated on a chip, thus creating a major bottleneck for drug discovery and nanomedicine. Here, we propose a novel chiroptical sensing approach based on optical rectification in a photonic micro-cavity filled by a drug solution with nl volume. We theoretically demonstrate that, upon optical excitation by intense pulsed laser light, such a nonlinear effect produces a chirally-sensitive nV voltage burst at the electrically-gated micro-cavity boundaries, with sign depending solely on the drug enantiomeric imbalance. Our results shed light on the potential of optical rectification as a robust platform for innovative lab-on-a-chip devices enabling chiral sensing with nl sensitivity.

High-fidelity simulations are increasingly adopted, due to advances in computational power and methods such as Direct Numerical Simulation (DNS) and hybrid Large-Eddy Simulation (LES). These approaches are particularly valuable for unsteady flows around complex geometries at high Reynolds numbers; however they still require careful experimental validation. Planar and stereo Particle Image Velocimetry (PIV) are widely used for measurements but limited by measurement-plane selection and their ability to capture vortices shapes and trajectories. This motivates the growing interest in volumetric techniques, historically difficult to implement in industrial settings. Recent advances in Particle Tracking Velocimetry (PTV) for measuring flows over large volumes make this approach suitable for validating numerical simulations of complex this http URL study compares volumetric PTV measurements against high-fidelity LES to assess the capabilities and limitations for industrial flows. The aim is to establish a benchmark PTV dataset for motorsport aerodynamics using the Shake-The-Box algorithm. The experiment was carried out in the 10x5 wind tunnel at Imperial College London equipped with a rolling road for ground effect simulation and capable of testing up to 50% scale F1 model. Volumetric PTV measurements were performed downstream of the open-source Imperial Front Wing (IFW) at Re=74896. Results are compared with planar PIV studies and implicit LES simulation using spectral h/p elements in Nektar++. This work addresses open questions in the literature concerning the wake of the IFW. Good quantitative agreement is observed in the wake topology. A previously unreported vortex is identified which has the key role of preventing the merging of other dominant structures. These results demonstrate the suitability of PTV and STB for industrial applications while providing a benchmark dataset for the IFW.

We report multiwavelength observations of EP240305a, an uncatalogued X-ray transient detected by the Einstein Probe on March 5, 2024. The source exhibits distinct characteristics across the X-ray, optical, near-infrared, and radio bands. The soft X-ray observations show two significant flares lasting ~100-250 s, accompanied by rapid flux decay in a few days, and the optical and near-infrared data reveal a faint, candidate counterpart. In contrast, the radio observations expose a long-term spectral evolution from a self-absorbed to an optically thin state within two months, implying discrete jet ejection. We compare EP240305a with known classes of X-ray transients and find that it is unlikely to be associated with long-timescale transients such as jetted tidal disruption events or X-ray binaries. Its properties also disfavor a short-timescale stellar flare origin. Although the absence of optical spectroscopy prevents a redshift determination, the source exhibits properties similar to those of gamma-ray-dark gamma-ray burst-like transients, which may be associated with relativistic jets viewed off-axis or with choked jets. The discovery of EP240305a, along with other uncataloged transients detected by the Einstein Probe, underscores the scientific potential of highly sensitive X-ray survey telescopes and rapid-response multiwavelength follow-up observations in exploring the nature of atypical astronomical transients.