Papers

We consider vacuum spatially homogeneous models in Hořava-Lifshitz gravity, which are expected to describe generic singularities for these modified gravity theories. These models perturb the well-known Bianchi models in general relativity (GR) by a parameter $v\in (0,1)$, in which GR occurs at $v=1/2$. We show that all periodic heteroclinic chains of Bianchi type II orbits are robust for small perturbations of GR, i.e. they exist for any $v\approx 1/2$. Moreover, we prove the existence of a stable manifold for each heteroclinic chain within a Cantor set for the supercritical case, $v\in (1/2,1)$. In particular, we discuss the heteroclinic chains of periods three and four in detail.

(Abridged) Baryonic feedback is expected to transform cuspy dark-matter (DM) haloes into cores, but direct observational links between inner DM slopes and galaxy star-formation histories (SFHs) remain limited. We investigate and quantify the connection between halo inner slopes and baryonic assembly histories in a large sample of intermediate-z galaxies. We analyse 375 galaxies at 0.1<z<1.43 spanning 7<log(Mstar/Msun)<11.2 using 3D forward modelling of MUSE kinematics and disk-halo decompositions with mass-dependent (DC14-based) and generalised Navarro-Frenk-White (gNFW) halo profiles. Stellar population parameters are inferred from multi-band Spectral Energy Distribution fitting of UV-to-MIR photometry using a non-parametric SFH model. Bayesian model comparison shows that the DC14-based halo density profiles are statistically preferred over gNFW for a substantial fraction of the sample. The inferred inner slopes from gNFW fits nevertheless follow the DC14 expectation and reproduce the expected dependence on the stellar-to-halo mass ratio, despite this not being explicitly imposed. Partial correlation coefficient and random forest regression analyses consistently identify stellar mass (or, equivalently, the stellar-to-halo mass ratio) as the primary driver of the inner density slope, a result that holds robustly even when the analysis is restricted to the gNFW fits. In contrast, SFH-related quantities (e.g. formation time and 'burstiness' indicators) exhibit no independent predictive power on the DM halo inner slope once the dependence on stellar mass is accounted for. Cored systems preferentially occupy lower-mass, more bursty bins with later assembly times, whereas cuspy systems are associated with higher stellar masses, lower star formation activity, and earlier assembly epochs, in agreement with theoretical expectations of stellar-feedback-induced cores.

A theorem of Landau and Ramanujan states that almost all integers are not sums of two squares (when ordered by their absolute value). Equivalently, almost all integers are not norms from the Gaussian rationals $\mathbb{Q}(i)$. In this paper, we prove a version of this norm result for elliptic curves $E$. Let $E$ be an elliptic curve over a number field $K$ with complex multiplication, such that $K$ contains the endomorphism ring of $E$. For a fixed non-torsion point $P \in E(K)$ and an abelian extension $L/K$, we show that subject to a technical condition, the $y$-coordinate of almost all multiples of $P$ does not belong to the norm group of $L$. The proof is an adaptation of an argument of Bhakta et al. , whose main tools are elliptic divisibility sequences and a sieve technique known as the elliptic sieve. To account for the points in $E(K)$ arising from the additional endomorphisms, we apply the elliptic sieve to elliptic nets, a higher-rank generalisation of elliptic divisibility sequences. This approach demonstrates the possibility of applying the elliptic sieve to $\mathbb{Z}$–linear combination of points on elliptic curves and the usefulness of elliptic nets to counting problems on elliptic curves.

Advection-diffusion plays an essential role in transport phenomena such as atmospheric and cloud dynamics. Improved forecasting of cloud motion, in turn, enhances solar power production forecasts and facilitates the integration of additional photovoltaic (PV) sources into the power grid. However, both classical numerical models and emerging deep learning approaches face challenges when applied to spatially irregular sensor networks such as those formed by weather stations. In this work, we adopt a graph signal processing perspective and model advection-diffusion particles as signals on a graph to capture the dynamics of these processes. We introduce a Physics-Informed Graph Neural Network (PING) for forecasting future advection-diffusion particle concentrations on irregular grids. The model incorporates a discretized advection-diffusion equation as a soft constraint in the loss function to guide learning toward physically consistent solutions. This model is on par with state of the art models on synthetic and real transport phenomena datasets, including sea surface temperature and cloud index datasets. Furthermore, the PING model is successfully coupled with models for forecasting PV power production. This hybrid approach leverages data fusion from ground-based sensors at PV stations and satellite images with cloud concentration to improve the accuracy of intra-day PV power production.

Ultrafast laser excitation of carriers in semiconductors often results in the creation of fully symmetric coherent optical phonons, typically understood in terms of a thermalized transient carrier population. We test this understanding with systematic measurements and first-principles calculations of the photon-energy dependence of ultrafast-laser-driven coherent phonon generation in tellurium, using excitation wavelengths around the electronic band gap. We observe that, contrary to the expectations of models assuming a thermalized carrier population, the coherent amplitude of the fully symmetric $A_1$ mode changes only weakly when tuning wavelength across the band gap. The measured spectral dependence is instead reproduced by a transition-resolved prethermal force weighted by optical matrix elements and band- and momentum-dependent $A_1$ deformation potentials. Fitting this model to the data yields an excited transition state lifetime of a few femtoseconds. These results identify transition selectivity, rather than a thermalized total carrier density, as a key factor controlling coherent-phonon generation in semiconductors excited near a band gap.

State-to-state rate coefficients for inelastic molecular collisions are essential inputs for non-local thermodynamic equilibrium radiative transfer models, yet their computation using quantum scattering methods is prohibitive for large molecules and highly excited rotational states. We investigate the ability of artificial neural networks to extend existing datasets of collisional excitation rate coefficients without performing additional scattering calculations. A multilayer perceptron model was trained using molecular quantum numbers, level energies, energy gaps, and kinetic temperature as descriptors, and optimized on logarithmic rate coefficients. The model was tested on diverse collision systems ranging from simple diatomic molecules (CO, SiO) to open-shell species (SO), small asymmetric tops (H$_2$O, SO$_2$), and complex organic molecules (benzonitrile and vinyl cyanide) colliding with H$_2$ molecules or He atoms. Extrapolations were performed toward higher rotational levels, higher temperatures, and combinations of both. For most systems, predictions of rate coefficients involving previously unseen rotational states yielded mean error factors between 1.1 and 1.5, with the dominant rate coefficients generally reproduced more accurately than weaker transitions. Temperature extrapolations proved particularly successful, while combined extrapolations in temperature and rotational levels remained accurate to within a factor of two in most cases. The prediction quality depends on the interplay between dataset size, temperature range, molecular complexity, and the presence of clear collisional propensity rules. Overall, the approach demonstrates that machine learning can provide a practical route to extending collisional datasets for astrophysical applications, especially for large molecules for which additional quantum-scattering calculations are computationally demanding.

Goodman proved a lower bound on triangle counts which, in graphon language, states that every graphon of edge density $p$ has triangle density at least $2p^2-p$. Bennett, Dudek, Lidický, and Pikhurko established the corresponding bound for $C_5$, determining its minimum density at every Turán density $p=1-1/k$ with an integer $k\ge3$. We extend this bound to every odd cycle in the dense regime: for every odd integer $m\ge3$ and every graphon $W$ with edge density $p\ge2/3$, $t(C_m, W) \ge p^m-p(1-p)^{m-1}.$ For $2/3\le p<1$, equality holds precisely for balanced complete $k$-partite graphons with an integer $k\ge3$, up to graphon equivalence, and we establish qualitative stability at these densities. In the same density range, we also strengthen Kim and Lee's density-sensitive commonality inequality for odd cycles by adding the nonnegative term $t(P_{m-1},1-W)-(1-p)^{m-1}$ to the lower bound, where $P_{m-1}$ is the path with $m-1$ edges. To prove the main results, we develop a spectral excursion expansion and use Dirichlet averaging to reduce the resulting polynomial inequalities in arbitrarily many spectral variables to a one-variable problem. We prove the one-variable inequality through a uniform inequality comparing odd and even moments of shifted Gamma random variables. We also formalise the odd-cycle lower-bound theorem in Lean 4.

Infrared small target detection is often used in different civilian and military applications to detect static or moving targets in scenes like in ground, air and sea surveillance. First valuable research has emerged since 30 years ago and the two last decades witnessed very significant publications in this field following the rise of low-rank and sparse decomposition (model-based methods) and deep learning models (data-based methods). Furthermore, several surveys can be found in the literature but none of them addresses an overall review in this field. In this context, the aim of this paper is to provide a complete survey of the traditional and recent approaches in infrared small target detection. First, we categorize the different approaches found in the literature in terms of the modeling models, i.e mathematical models, machine learning models and signal processing models. Then, we have discussed them in terms of the critical situations that they claim to handle. Furthermore, we present the available resources, datasets and libraries. Then, we conclude with several promising directions for future research. For the sake of reading, this survey is divided into two parts: 1) "Traditional and Recent Approaches for Infrared Small Target Detection : Overview, Challenges and Perspectives (Part 1)" about conventional and low-rank and sparse decomposition (model-based methods), and 2) "Traditional and Recent Approaches for Infrared Small Target Detection : Overview, Challenges and Perspectives (Part 2)" about deep learning models (data-based methods).

Identifying influential nodes is a fundamental task in complex network analysis, with applications in epidemic control, information diffusion, and network robustness. Existing centrality-based and learning-based methods often provide limited integration of structural information across different network scales. To address this limitation, we propose CSBA-Net, for Cross-Scale Structural BiGRU Attention Network, a multi-scale structural representation learning framework that jointly captures local, community-level, and global structural patterns. The extracted representations are processed by CNNs and integrated through a BiGRU with multi-head self-attention to model dependencies across structural scales. Influential-node scores are learned through regression using SIR-based diffusion simulations as reference targets. We conduct experiments on 24 real-world and 12 synthetic networks from social, biological, technological, and knowledge domains, and show that CSBA-Net achieves Kendall's tau=0.802, Spearman's rho=0.943, NDCG10 =0.898, and NDCG20 =0.916, outperforming the considered centrality-, CNN-, and GNN-based baselines. The results demonstrate the effectiveness of combining complementary structural scales for accurate influential-node ranking across diverse network structures.

This paper proposes a novel analytical method for resource adequacy assessment in renewable rich power systems. The approach begins by applying the stress strength method to estimate two key resource adequacy indices: loss of load expectation (LOLE) and expected energy not supplied (EENS). This method requires defining the probability distribution functions (PDFs) for both the generation side and the load side. The load is assumed to follow a normal probability distribution, while the generation side probability distribution is derived from the combined PDFs of conventional, wind, and solar power sources. The approach models the cumulative impact of uncertainties on resource adequacy using the central limit theorem (CLT), and improves accuracy with a cumulant based Gram Charlier expansion when the CLT alone is insufficient. The effectiveness of the proposed method is validated through Monte Carlo simulations conducted on the IEEE single area and multi-area RTS-96 test systems. The results demonstrate that the proposed method achieves a substantial reduction in computational time, which is crucial in the context of operational planning, without sacrificing accuracy. Furthermore, its performance improves as renewable penetration increases, making it particularly suitable for future power systems operation and planning.

We study Dirac mini-stars in modified $R^2$ gravity, where gravity is sourced by both linear and nonlinear spinor fields. Two-dimensional (2D) and three-dimensional (3D) profiles of the mini-star mass are constructed as functions of the spinor frequency (for the 2D profiles) and the central value of the spinor field (for the 3D profiles) in general relativity and modified gravity for various values of the spinor nonlinearity parameter. We show that the modification of gravity alters the properties of these configurations, while increasing the nonlinearity parameter within the framework of $R^2$ gravity significantly changes the profiles of the spinor and metric functions, the effective energy density, and the dependence of the total mass on the oscillation frequency. The most pronounced changes occur at large values of the nonlinearity parameter.

Autonomous research agents must acquire and reason over evidence within a limited budget. Yet relevant sources can remain uninspected or unused, leaving a gap between retrieval coverage and the evidence that informs research. The challenge is to align fast local judgments with changing evidence needs and feed their findings back into research decisions. We introduce JevGPT, a dual-system architecture for autonomous research that couples fast evidence processing with deliberative research planning. System Two sets evidence objectives and integrates findings, while System One locates support, assesses relevance, and guides further inspection. Independent source judgments run in parallel; selected original passages inform the next research step. Experiments on fixed-corpus question answering and document ranking show that JevGPT achieves leading task performance, with faster completion and lower cost than comparably effective research agents. Evidence analysis shows broader source inspection and greater coverage of supporting documents in the research loop, highlighting efficient evidence processing as a route to more capable autonomous research.

Stochastic differential equation (SDE) models can reproduce trajectories while missing temporal dependence. We compare residual-based scores from a held-out path with scores from paths simulated by a fitted implementation, keeping fitted parameters, simulation rules and the scoring rule fixed. We give conditions for Monte Carlo calibration and bound conditional rejection error by the gap between conditional score CDFs. Residuals use zero-noise centres and covariance approximations that track noise propagation over observation intervals; report residuals also include reporting variation. Residual weights affect sensitivity and the influence of fitting error. For a quadratic energy score in a linear example with singular true covariance, whitening with nonsingular fitted covariance matrices leaves a nonvanishing score-CDF gap as nonzero coefficient estimates approach the truth. A fixed positive-definite weighting matrix makes the gap vanish. In a controlled SIR experiment using reference paths simulated at fitted parameters, adding susceptible-state endpoints to training or downweighting a low-variance residual reduces null rejection. A separate comparison using reference paths simulated at the true parameter shows reduced sensitivity to added susceptible-coordinate noise after downweighting. An exploratory weekly-report application incorporates reporting and reconstruction into reference simulations, revealing excess correlation between squared residuals in Czechia and persistently negative residuals in Finland.

We study the regularity of the free boundary for a multi-phase obstacle-type problem associated to quadrature domains, which arises from the minimization of the energy $$J(U,F):= \int_{B_1} (\frac 1 2 |\nabla U|^2 + F \cdot U)dx$$ among all competitors $U=(u^1,\ldots, u^N)$ with non-negative components $u^i \geq 0$ with disjoint supports, and constant forcing terms $f^i>0.$ We focus on the geometry of the free boundary at points where at least three distinct components meet (triple junctions).

Pain is one of the most common and clinically important symptoms, reflecting disease onset, progression, and treatment response. However, pain is difficult to accurately capture and interpret from medical text, as its expression varies across languages, documentation types, and patient demographics, and is often embedded in terminology, negation, temporality, and contextual descriptions. Existing pain-related studies remain largely monolingual or limited to narrow clinical settings. In this study, we introduce PAINT, a multilingual framework for studying pain representation across medical exams and real-world clinical texts. PAINT includes nine pain-focused dataset partitions spanning English, Spanish, Portuguese, and Japanese, with clinician annotations in all four languages. We curated a structured schema covering pain relevance, pain presence, anatomical location, pain descriptors, and demographic information. To capture multilingual pain representations, we leverage large language models (LLMs) and adopt an ensemble strategy to improve performance. Ten clinicians across four languages validate the labels: the ensemble reaches macro-F1 of 0.91-1.00 on pain relevance and pain presence and 92-100% accuracy on demographics, with inter-annotator $\kappa$ of 0.82-1.00. We release the WorldMedQA-Pain ensemble labels, the extraction pipeline, validation scripts, and clinician annotation sheets for publicly licensed corpora, providing a foundation for pain-centered clinical NLP and for studying pain documentation across languages and healthcare contexts.

The Radon transforms on Grassmannians define two families of geometric operators on convex bodies when applied to their projection functions. On the one hand, these are Minkowski's projection body maps and on the other hand these operators coincide on origin-symmetric bodies with the mean section body maps introduced by Goodey and Weil in 1992. Over the past two decades various sharp isoperimetric inequalities for projection bodies were shown to also hold for mean section bodies. However, an analogue of Lutwak's log-concavity inequalities for the intrinsic volumes of projection bodies remained open for mean section bodies. We establish new Aleksandrov–Fenchel inequalities for averages of certain mixed volumes and apply them to show that also all the intrinsic volumes of mean section bodies are indeed log-concave.

Photo-detection is a fundamental component of experimental photonics, yet theoretical models often treat detectors solely in the photon-number basis, neglecting other relevant degrees of freedom such as spectral characteristics. We present a complete quantum process model for physically realistic photodetection that incorporates both photon-number effects and frequency-dependent detector response, described through explicitly derived Kraus operators in the operator-sum representation. This formalism accommodates realistic inefficiencies, models detection within finite spectral windows, and can be directly substituted for idealized models in quantum optical analyses. The model leads to identifying the suitable detection window of the detectors relative to the spectral distribution of incident photons and conversely, in order to maximize the observability of quantum effects.

Motivated by a recent work of G. Knese [Canad. Math. Bull., 2026], we introduce the operator-valued Schur-Agler class in infinitely many variables, consisting of functions whose restrictions to every finite-dimensional polydisk lie in the operator-valued Schur-Agler class. We first establish an operator-valued analogue of Montel's theorem and, using it as a key ingredient, establish an Agler decomposition and a realization formula for functions in this class. The series in the Agler decomposition converges in the strong operator topology, and we show that this convergence cannot, in general, be strengthened to norm convergence. The realization formula yields a holomorphic extension of every function in the operator-valued Schur-Agler class to $\mathrm{Ball}(\ell^\infty)$, the open unit ball of $\ell^\infty$. Finally, as an application, we prove an Agler-Pick interpolation theorem in infinitely many variables.

We study the task allocation problem, where our goal is to develop an online algorithm that efficiently distributes tasks among workers based on their computational performance. This task is challenging since computation times are random and non-stationary in practice. Recent works have introduced different online algorithms to address this problem. One of them is Adaptive Task Allocation (ATA), a bandit-style algorithm. However, previous theoretical guarantees leave substantial room for improvement, and existing methods are designed only for stationary computation times. Using new proof techniques, our work establishes an improved analysis of ATA with better gap-dependent and gap-independent regret guarantees, improving upon all previous approaches. We also introduce a new method, Sliding Window Adaptive Task Allocation (SW-ATA), designed for more practical non-stationary environments. Finally, we prove new lower bounds in both the stationary and non-stationary settings.

This work presents a data-driven load-surrogate modelling framework for real-time control of floating offshore wind farms. The proposed methodology uses mid-fidelity simulations performed with OpenFAST and FAST.Farm together with MLife fatigue analysis to generate Damage Equivalent Load (DEL) datasets of floating wind turbines under wake steering conditions. A two-stage surrogate modelling approach is adopted: first, a Feed-Forward Neural Network (FFNN) is trained using data from simulations of a single floating wind turbine, while a second stage corrects the residual error between the FFNN predictions and FAST.Farm simulations using either Gaussian Process Regression (GPR) or an additional FFNN. The results show that the proposed framework can estimate DELs with errors generally below 15% for tower base bending moment, blade root bending moment, yaw bearing moment, and fairlead tension, while maintaining computational times compatible with real-time applications. The study also highlights the challenges related to generalization of the load-surrogate model under varying environmental and control conditions, especially for large floating wind farms. Overall, the proposed methodology demonstrates the potential of surrogate-based DEL estimation for load-aware floating wind farm control applications.

The James Webb Space Telescope has unlocked uncharted territory for the study of early black holes, enabling the detection of fainter and smaller black holes at larger cosmological distances than previously possible. Compared to nearby massive black holes, they are characterised by several unexpected attributes, such as their multi-wavelength properties or their relation to their host galaxies. These observational findings challenge our understanding of the past evolution of present-day supermassive black holes, and provide novel anchor points to constrain theoretical models of black hole formation and growth. This review summarises our current understanding of the observed properties of newly discovered, active black holes in the early Universe, discusses the status of mass measurements and the relation to their hosts, as well as open questions and future prospects.

Third-party skills can expose LLM agents to malicious instructions hidden by encoding. We introduce Ciphered Skill Injection (CSI), which embeds such instructions in skill files for agents to decode and follow. We evaluate Caesar and layered variants across eight models and 139 injection-task pairs, separating instruction recovery from attack success. In the primary setting with shortened skills, the variants achieve attack success rates of up to 47.5% and 40.3%, respectively. Successful decoding does not guarantee attack success, and layering has model-dependent effects. The tested skill scanners rarely flag injected skills. These findings highlight the risk of promoting decoded, untrusted content into actionable instructions.

We investigate the influence of decay rates on the dynamics of three-dimensional gene regulatory networks modeled by nonlinear differential equations with logistic sigmoidal regulatory functions. Particular attention is paid to the existence, location, and stability of equilibrium points in systems involving numerous interacting parameters. An explicit analytical representation of a central equilibrium is obtained under suitable relations between the regulatory weights, thresholds, and decay coefficients, allowing its location to be determined without solving the corresponding nonlinear algebraic system numerically. General formulas for the characteristic polynomial of the linearized system are derived, and spectral conditions for instability are established for several classes of regulatory interactions. We demonstrate how variations in decay rates can change the number and stability of equilibria, transform oscillatory dynamics, and influence the emergence or suppression of complicated attractors. The possibility of chaotic behavior is investigated through eigenvalue configurations, Lyapunov exponents, and the Kaplan-Yorke dimension. Numerical examples illustrate the sensitivity of the dynamics to decay parameters, including the suppression of previously observed chaotic behavior. The results provide an analytical framework for investigating equilibrium configurations, stability transitions, and complex dynamics in parametrized gene regulatory networks.

Wearable fall detection is hampered by rare fall events, scarce labeled IMU data, and the cost of training deep models on large, imbalanced corpora. Existing methods either rely on hand-crafted features with shallow classifiers, which limits learning from raw signals, or train deep networks on full datasets that require re-sampling to counter class skew and demand substantial data and compute. To address this, we propose a novel Fall detection framework via Normalized-gradient and Embedding matched Synthetic Time-frequency condensation, dubbed FALLNEST, a data-centric approach that distills large, imbalanced IMU datasets into tiny, class-balanced synthetic training sets. Building on dual-domain time-series condensation (CondTSC), FALLNEST introduces a fall-specific 7-channel input with accelerometer vector magnitude, class-balanced K-Means initialization, and normalized gradient matching with gradient clipping, combined with MMD-based embedding alignment and multi-view Fourier-domain augmentation, so that class balance arises from the condensed set itself rather than from re-sampling. We evaluate on SisFall, KFall, and MobiFall using strict subject-wise splits and naturally imbalanced test sets, reporting accuracy, Macro-F1, and PR-AUC over five seeds. A 102K-parameter TinyCNN trained on only 32 to 146 synthetic windows (about only 1% of the training windows) reaches 93.5-95.8% mean accuracy and 0.89-0.98 PR-AUC, with standard deviations of 1.0-1.7% in accuracy, demonstrating the efficacy of our approach.

We study spectral measures of one-dimensional quasiperiodic Schrödinger operators. For subcritical Schrödinger operator with Diophantine frequency, we prove sharp measurable-set bounds, answering a question of Avila and Jitomirskaya \cite{AJ}; we prove optimal Fourier decay and the sharp decay order of the time-averaged quantum return probability, confirming a conjecture of Aloisio, Carvalho, and de Oliveira \cite{ACO} and a prediction of Zhong and Mosseri \cite{ZhongMosseri}. For the subcritical almost Mathieu operator, we establish summable square-root envelopes for the spectral density, with an optimal density-one formulation of the lower bound, thereby answering a question of Avila \cite{Aqi}. These results follow from a general theorem for reflectionless measures under a summable square-root Craig-type condition. We establish an exact residue expansion of the squared Borel transform, which connects local density blow-up with long-time averaged return probabilities: the endpoint residues determine both the square-root edge profiles and the leading coefficient of the time-averaged return probability.

We study stochastic contextual bandits with an unknown context-lumpable structure. The $S$ contexts are partitioned into $r$ blocks, and every arm has the same mean reward across contexts in the same block. Under arbitrary context distributions and without separation assumptions, we design an algorithm with expected regret $\widetilde{O}(\sqrt{r(S+K)T})$, matching the lower bound of Lee et al. (2023) up to logarithmic factors and improving their previous upper bound by a factor of $r$. The algorithm operates over dyadic accuracy levels, using a baseline policy and confidence-based early stopping to control exploration. It then performs cross-context elimination: since rewards are identical within a block, one selected arm eliminates all surviving records from that block, requiring at most $r$ selections at each level. Multi-scale exploration assigns finer accuracies to frequent blocks and coarser accuracies to rare blocks, yielding a near-optimal arm for every block while keeping the weighted policy error small.

Three-dimensional femtoscopy probes the space-time structure of particle-emitting sources in relativistic heavy-ion collisions. The collision-energy dependence of Lévy source parameters may reveal the evolution of strongly interacting matter and possible signatures of the QCD phase diagram. We previously studied the excitation function of three-dimensional Lévy source parameters for pion pairs in Au+Au collisions with EPOS4, analyzing the pair-distance distribution \(D(\rho)\) through one-dimensional projections. Here, we analyze the full three-dimensional source distribution and correlation function directly. We construct \(D(\rho_{\rm out},\rho_{\rm side},\rho_{\rm long})\) as a 3D histogram, transform it into \(C(q_{\rm out},q_{\rm side},q_{\rm long})\) using a Fast Fourier Transform, and fit the correlation function with the analytic Lévy formula. This approach can reduce biases arising when one-dimensional projections are used to describe a non-elliptical source. We apply the method across the RHIC Beam Energy Scan range and compare the extracted energy dependence with results from the projection-based method and recent UrQMD calculations. We focus on the out-side observables \(R_{\rm diff}^{2}=R_{\rm out}^{2}-R_{\rm side}^{2}\) and \(R_{\rm out}/R_{\rm side}\), whose different energy dependences in EPOS4 and UrQMD may illuminate the roles of emission duration and source dynamics. This work establishes a direct three-dimensional framework for comparison with future femtoscopic measurements and for exploring possible non-monotonic structures associated with the QCD phase diagram.

On-policy self-distillation (OPSD) has emerged as a popular training paradigm for LLMs, providing dense, token-level supervision by aligning a model's own distribution with the distribution induced by privileged information. However, existing OPSD methods derive supervision solely from privileged information of the same instance, leaving inter-instance supervision largely unexplored. We propose Lookahead Self-Distillation (LEAD), which introduces inter-instance distillation by allowing the teacher to first learn from other on-policy rollouts before teaching the student. LEAD constructs lookahead teachers through virtual RL updates on disjoint subsets of on-policy rollouts, and uses each teacher to provide cross-group token-level supervision for the other subset. To reconcile the complementary yet potentially conflicting signals from OPSD and RLVR, we introduce harmonious modulation, which adaptively modulates the GRPO advantage based on the agreement between the two signals. Extensive experiments on scientific reasoning and interactive-agent benchmarks show that LEAD achieves the best in-domain average performance across model scales while maintaining out-of-domain generalization comparable to GRPO.

Cloud droplets respond to turbulent motion with finite inertia and settle under gravity, while condensation and evaporation change their sizes. The nonuniform accumulation of cloud droplets in turbulent flows, known as preferential concentration, has attracted sustained interest because it affects droplet collision and coalescence rates. We develop an analytical theory that quantifies the coupled effects of droplet inertia, gravitational settling, and phase change on concentration changes. Applying this theory to simulations of two-dimensional homogeneous thermal convection reveals that phase change markedly enhances preferential concentration in this flow, primarily through spatial differences in settling speed. These differences arise because droplets experience different thermodynamic histories along their trajectories and thus acquire different sizes. Droplet transport further increases this settling contribution by rearranging droplets of different sizes. Fluid deformation partly offsets this enhancement by thinning concentration structures, reducing the preferential concentration measured at a fixed spatial scale.

Turbulent annular Poiseulle flow is commonly encountered in various engineering applications, such as heat exchangers. The effects of the inner wall transverse curvature on the flowfield, characterised by the ratio of inner and outer radii $\eta = R_{i}/R_{o}$, have been studied previously using Direct Numerical Simulations (DNS). Scale-resolving simulations based on a Reynolds-Averaged Navier Stokes framework offer a potentially cheaper alternative to traditional Large Eddy Simulations (LES); however it is not clear if such models are able to capture the turbulence anisotropy in the turbulent annular pipe flow. In the present study, turbulent annular Poiseulle flow at $Re_{D_{h}} = 8900$ is performed with the Partially-Averaged Navier Stokes (PANS) model, a variable-resolution turbulence model that is based on the conventional RANS modelling. The ability of the PANS model to capture the effects of the transverse wall curvature is found to be comparable with DNS and other RANS-based scale-resolving approaches despite its relative simplicity and reduced computational cost.