The Gaia phase spiral is considered to work as a dynamical clock for dating past perturbations, but some of the previous studies neglected the disc's self-gravity, potentially biasing estimates of the phase spiral's excitation time. We revisit the impact of self-gravitating effects on the evolution of vertical phase spirals and quantify the bias introduced in estimating their excitation time when such effects are ignored. We analysed a high-resolution, self-consistent $N$-body simulation of the MW-Sagittarius dwarf galaxy (Sgr) system, alongside four test particle simulations in potentials constructed from the $N$-body snapshots. In each case, we estimated the winding time of phase spirals by measuring the slope of the density contrast in the vertical angle-frequency space. In the test particle models, the phase spiral begins winding immediately after Sgr's pericentric passage, and the winding time closely tracks the true elapsed time since the Sgr impact. Adding the DM wake yields only a modest (< 100 Myr) reduction of the winding time relative to Sgr alone. By contrast, the self-consistent $N$-body simulation exhibits an initial, coherent vertical oscillation lasting $\gtrsim$ 300 Myr before a clear spiral forms, leading to systematic underestimation of excitation times. An analytical shearing-box model with self-gravity, developed by Widrow (2023), qualitatively reproduces this delay, supporting its origin in the disc's self-gravitating response. Assuming that self-gravity affects phase mixing in the MW to the same degree as the $N$-body model, the lag induced by self-gravity is estimated to be $\sim$ 0.3 Gyr in the solar neighbourhood. Accounting for this delay revises the inferred age of the MW's observed phase spiral to $\sim$0.6-1.2 Gyr, in better agreement with the Sgr's pericentric passage. (shortened for arXiv)

We revisit exact WKB quantization for radial Schrödinger problems from the modern resurgence perspective, with emphasis on how ``physically meaningful'' quantization paths should be chosen and interpreted. Using connection formulae at simple turning points and at regular singular points, we show that the nontrivial-cycle data give the spectrum. In particular, for the $3$-dimensional harmonic oscillator and the $3$-dimensional Coulomb potential, we explicitly compute a closed contour which starts at $+\infty$, bulges into the $r<0$ sector to encircle the origin, and returns to $+\infty$. Also we propose that the appropriate slice of the closed path provides a physical local basis at $r=0$, which is used by an origin-to-$\infty$ open path. Via the change of variables $r=e^x$ ($x\in(-\infty,\infty)$), the origin data are pushed to the boundary condition of convergence at $x\to-\infty$, which renders the equivalence between open-connection and closed-cycle quantization transparent. The Maslov contribution from the regular singularity is incorporated either as a small-circle monodromy which is justified in terms of renormalization group, or, equivalently, as a boundary phase; we also develop an optimized/variational perturbation theory on exact WKB. Our analysis clarifies, in radial settings, how mathematical monodromy data and physical boundary conditions dovetail, thereby addressing recent debates on path choices in resurgence-based quantization.

Music structure analysis (MSA) underpins music understanding and controllable generation, yet progress has been limited by small, inconsistent corpora. We present SongFormer, a scalable framework that learns from heterogeneous supervision. SongFormer (i) fuses short- and long-window self-supervised learning representations to capture both fine-grained and long-range dependencies, and (ii) introduces a learned source embedding to enable training with partial, noisy, and schema-mismatched labels. To support scaling and fair evaluation, we release SongFormDB, the largest MSA corpus to date (over 14k songs spanning languages and genres), and SongFormBench, a 300-song expert-verified benchmark. On SongFormBench, SongFormer sets a new state of the art in strict boundary detection (HR.5F) and achieves the highest functional label accuracy, while remaining computationally efficient; it surpasses strong baselines and Gemini 2.5 Pro on these metrics and remains competitive under relaxed tolerance (HR3F). Code, datasets, and model are open-sourced at https://github.com/ASLP-lab/SongFormer.

Digital media have become central to how labor unions communicate, organize, and sustain collective action. Yet little is known about how unions' online discourse relates to concrete outcomes such as representation elections. This study addresses the gap by combining National Labor Relations Board (NLRB) election data with 158k Facebook posts published by U.S. labor unions between 2015 and 2024. We focused on five discourse frames widely recognized in labor and social movement communication research: diagnostic (identifying problems), prognostic (proposing solutions), motivational (mobilizing action), community (emphasizing solidarity), and engagement (promoting social media interaction). Using a fine-tuned RoBERTa classifier, we systematically annotated unions' posts and analyzed patterns of frame usage around election events. Our findings showed that diagnostic and community frames dominated union communication overall, but that frame usage varied substantially across organizations. Greater use of diagnostic, prognostic, and community frames prior to an election was associated with higher odds of a successful outcome. After elections, framing patterns diverged depending on results: after wins, the use of prognostic and motivational frames decreased, whereas after losses, the use of prognostic and engagement frames increased. By examining variation in message-level framing, the study highlights how communication strategies correlate with organizational success, contributing open tools and data, and complementing prior research in understanding digital communication of unions and social movements.

Nature has always inspired scientists and engineers to understand the underlying mechanism leading to optimal design in bio-inspired dynamics. This study presents a computational framework for optimizing undulatory swimming profiles using a combination of Design-by-Morphing and Bayesian optimization strategies. The swimming profile are expressed by morphing five baseline bio-inspired profiles using Design-by-Morphing to create an exploratory design space. The optimization objective is to find the optimal swimming profile, wavelength and undulation frequency to maximize propulsive efficiency. The optimized swimming profiles demonstrate a marked improvement in propulsive efficiency relative to the reference anguilliform and carangiform modes. The best-performing optimized cases achieve peak efficiencies in the range of 49-57\% over a broad range of kinematic conditions, representing an overall enhancement of 16-35\% compared to reference anguilliform and carangiform modes. The improved performance is attributed to favorable surface stress distributions and enhanced energy recovery mechanisms. A detailed force decomposition reveals that the optimal swimmer minimizes resistive drag and maximizes constructive work contributions, particularly in the anterior and posterior body regions. Spatial and temporal work decomposition indicates a strategic redistribution of input and recovered energy, enhancing performance while reducing energetic cost relative to propulsive force. These findings demonstrate that morphing-based parametric design, when guided by surrogate-assisted optimization, offers a powerful framework for discovering energetically efficient swimming gaits, with significant implications for the design of autonomous underwater propulsion systems and the broader field of bio-inspired locomotion.

Qualitative research offers deep insights into human experiences, but its processes, such as coding and thematic analysis, are time-intensive and laborious. Recent advancements in qualitative data analysis (QDA) tools have introduced AI capabilities, allowing researchers to handle large datasets and automate labor-intensive tasks. However, qualitative researchers have expressed concerns about AI's lack of contextual understanding and its potential to overshadow the collaborative and interpretive nature of their work. This study investigates researchers' preferences among three degrees of delegation of AI in QDA (human-only, human-initiated, and AI-initiated coding) and explores factors influencing these preferences. Through interviews with 16 qualitative researchers, we identified efficiency, ownership, and trust as essential factors in determining the desired degree of delegation. Our findings highlight researchers' openness to AI as a supportive tool while emphasizing the importance of human oversight and transparency in automation. Based on the results, we discuss three factors of trust in AI for QDA and potential ways to strengthen collaborative efforts in QDA and decrease bias during analysis.

This Letter reports the observation of $W^{+}W^{-}γ$ triboson production in 140 fb$^{-1}$ of data collected by the ATLAS detector from proton--proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV at the LHC. Events with an opposite-charge $eμ$ pair, a high transverse-momentum photon, and significant missing transverse momentum are considered. The observed (expected) significance of the signal is 5.9 (6.0) standard deviations. The measured fiducial cross-section, defined for the $W^{+}W^{-}γ\to e^{\pm}μ^{\mp}ν\barνγ$ final state is 6.2 $\pm$ 0.8 (stat.) $\pm$ 0.6 (sys.) fb, in good agreement with the Standard Model prediction of 6.1$^{\,+1.0}_{-0.7}$ fb. Constraints on the Wilson coefficients of 13 dimension-8 operators describing physics beyond the Standard Model through anomalous quartic gauge-boson couplings are derived using the effective field theory framework.

Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart: the classical Fisher information matrix (CFIM). It is known that averaging the classical Fisher information matrix over Haar-random measurement bases yields $\mathbb{E}_{U\simμ_H}[F^U(\boldsymbolθ)] = \frac{1}{2}Q(\boldsymbolθ)$ for pure states in $\mathbb{C}^N$. In this paper, we review this identity by revealing its connection to covariant measurement in quantum metrology. Furthermore, we go beyond this and obtain the exact variance of CFIM ($O(N^{-1})$), estimate its moment, and establish non-asymptotic concentration bounds ($\exp(-Θ(N)t^2)$), demonstrating that using few random measurement bases is sufficient to approximate the QFIM accurately in high-dimensional settings. This work establishes a solid theoretical foundation for efficient quantum natural gradient methods via randomized measurements.

We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid classical-quantum models. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network -- including the disentangled MPO -- runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (i) an explicitly disentangling variational method leveraging standard tensor-network optimization techniques, and (ii) an implicitly disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.

In this paper we study the theory of multi-knotoids in the annulus and in the torus, building up from the theory of planar knotoids to the theory of toroidal knotoids through the theory of annular knotoids. We introduce the concept of lifted annular and toroidal knotoids and examine inclusion relations arising naturally from the topology of the supporting manifolds. We also introduce the concept of mixed knotoids as special cases of planar knotoids, containing a fixed unknot for representing the thickened annulus or a fixed Hopf link for representing the thickened torus. We then extend the Turaev loop bracket for planar knotoids to bracket polynomials for annular and for toroidal knotoids, whose universal analogues recover the Kauffman bracket knotoid skein modules of the thickened annulus and the thickened torus.

We show that the neutral current data of the MINOS and MINOS+ experiments can provide information on the axial neutral current non-standard interactions of neutrinos with the $u$ and $d$ quarks; {\it i.e.,} on $ε_{αβ}^{Aq}$. We derive bounds on the $ee$, $eτ$ and $ττ$ components of these couplings and show that the MINOS(+) bounds on $ε^{Aq}_{eτ}$ and $ε^{Aq}_{ττ}$ are currently the world leading ones. The bound on the isospin singlet case, $ε^{Au}_{ττ}=ε^{Ad}_{ττ}$ is of particular interest because while this isospin singlet NSI is theoretically motivated, it was practically unconstrained before these results.

Gaia has recently revealed a population of over 20 compact objects in wide astrometric binaries, while LIGO-Virgo-KAGRA (LVK) have observed around 100 compact object binaries as gravitational-wave (GW) mergers. Despite belonging to different systems, the compact objects discovered by both Gaia and the LVK follow a multimodal mass distribution, with a global maximum at neutron star (NS) masses ($\sim 1$-$2\,M_\odot$) and a secondary local maximum at black hole (BH) masses $\sim10\,M_\odot$. However, the relative dearth of objects, or ``mass gap," between these modes is more pronounced among the wide binaries observed by Gaia compared to the GW population, with $9^{+10}_{-6}\%$ of GW component masses falling between $2.5$--$5\,M_\odot$ compared to $\lesssim5\%$ of Gaia compact objects. We explore whether this discrepancy can be explained by the natal kicks received by low-mass BHs. GW progenitor binaries may be more likely to survive natal kicks, because the newborn BH has a more massive companion and/or is in a tighter binary than Gaia progenitor binaries. We compare the survival probabilities of Gaia and GW progenitor binaries as a function of natal kick strength and pre-supernova binary parameters, and map out the parameter space and kick strength required to disrupt the progenitor binaries leading to low-mass BHs in Gaia systems more frequently than those in GW systems.

QFT vector models are a newly developed approach to quantum gravity, which are based on induced gravity in discrete spacetimes. Here we review some basic definitions and properties of these models and point out directions for future research.

Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $\{ X, \langle .,. \rangle \}$ be a full Hilbert $A$-module. Then any bijective bounded module morphism $T$, for which every norm-closed $A$-submodule of $X$ is invariant, is of the form $T=d \cdot {\rm id}_X$ where $d \in Z(M(A))$ is invertible. As an example of a merely injective bounded module operator with that preserver property serves $T =d \cdot {\rm id}_X$ where $|d| \in Z(M(A))$ has a positive spectrum, but not bounded away from zero. The same assertions are true if the restriction on the C*-submodules to be norm-closed is dropped. From a different point of view, for two given strongly Morita equivalent C*-algebras $A$ and $B$ and a Hilbert $B$-$A$ bimodule $\{ X, \langle .,. \rangle \}$ with faithful compact right action of $B$, for any two two-sided norm-closed ideals $I \in A$, $J \in B$, any full compatible norm-closed Hilbert $J$-$I$ subbimodule of $X$ is invariant for any left bounded $B$-module operator and any right bounded $A$-module operator. So these subsets of submodules of $X$ cannot rule out any bounded module operator as a non-preserver of that subset collection, however any single element of this subset collection is preserved by any bounded module operator on $X$. For any $B$-$A$ imprimitivity bimodule both the C*-valued inner product values are always preserved by bijective bounded module operators $T$ on $X$ iff $T= u \cdot {\rm id}_X$ for a unitary element $u\in Z(M(A))$.

A variety of mechanisms in the early Universe lead to the generation of gravitational waves (GWs). We introduce here a novel source of GWs generated by vacuum fluctuations after inflation. Given that gravitons are minimally coupled particles, their quantum creation takes place during inflation, but is absent in an unperturbed Universe during the radiation-dominated epoch, since they behave as conformally coupled particles. However, the presence of inhomogeneities breaks the conformal flatness of the metric, allowing scalar metric perturbations to induce the quantum production of gravitons. We compute the resulting GW spectrum from this mechanism for different models of the primordial scalar power spectrum. We find that this GW signal peaks around the GHz frequency range, distinguishing it from other astrophysical and cosmological backgrounds and underscoring the need for detectors sensitive to these high frequencies.

Motivation: Protein folding is a dynamic process during which a protein's amino acid sequence undergoes a series of 3-dimensional (3D) conformational changes en route to reaching a native 3D structure; the resulting 3D structural conformations are called folding intermediates. While data on native 3D structures are abundant, data on 3D structures of non-native intermediates remain sparse, due to limitations of current technologies for experimental determination of 3D structures. Yet, analyzing folding intermediates is crucial for understanding folding dynamics and misfolding-related diseases. Hence, we search the literature for available (experimentally and computationally obtained) 3D structural data on folding intermediates, organizing the data in a centralized resource. Additionally, we assess whether existing methods, designed for predicting native structures, can also be utilized to predict structures of non-native intermediates. Results: Our literature search reveals six studies that provide 3D structural data on folding intermediates (two for post-translational and four for co-translational folding), each focused on a single protein, with 2-4 intermediates. Our assessment shows that an established method for predicting native structures, AlphaFold2, does not perform well for non-native intermediates in the context of co-translational folding; a recent study on post-translational folding concluded the same for even more existing methods. Yet, we identify in the literature recent pioneering methods designed explicitly to predict 3D structures of folding intermediates by incorporating intrinsic biophysical characteristics of folding dynamics, which show promise. This study assesses the current landscape and future directions of the field of 3D structural analysis of protein folding dynamics.

The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new research areas including open quantum many-body systems, non-equilibrium condensed matter, and the possibility to test its limits in driven-open quantum simulators, call for a critical revision of its regimes of applicability. In this pedagogical review, we re-examine the folklore surrounding its three standard approximations (Born, Markov, and Rotating Wave Approximation), as we build our narrative by employing a series of examples and case studies accessible to any reader with a solid background on the fundamentals of quantum mechanics. As a synthesis of our work, we offer a checklist that contrasts common lore with refined expectations, offering a practical guideline for assessing the breakdown of the Lindblad framework in the problem at hand.

Aided by the tools and outlook provided by modern classification theory, we take a new look at the Brown-Voiculescu entropy of endomorphisms of nuclear C*-algebras. In particular, we introduce `coloured' versions of noncommutative topological entropy suitable for C*-algebras A of finite nuclear dimension or finite decomposition rank. In the latter case, assuming further that A is simple, separable, unital, satisfies the UCT and has finitely many extremal traces, we prove a variational type principle in terms of quasidiagonal approximations relative to this finite set of traces. Building on work of Kerr, we also show that infinite entropy occurs generically among endomorphisms and automorphisms of certain classifiable C*-algebras that function as noncommutative spaces of observables of topological manifolds.

Motivated by recent developments in the field of multilevel quantum batteries, we present the model of a quantum device for energy storage with anharmonic level spacing, based on a superconducting circuit in the transmon regime. It is charged via the sequential interaction with a collection of identical and independent ancillary two-level systems. By means of a numerical analysis we show that, in case these ancillas are coherent, this kind of quantum battery can achieve remarkable performances for what it concerns the control of the stored energy and its extraction in regimes of parameters within reach in nowadays quantum circuits.

We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion theories with factorization systems and categorical Galois structures. We describe several examples of these torsion theories, in the dual of elementary toposes, in varieties of universal algebras used as models for non-classical logic, and in coslices of the category of abelian groups.

Accurate prediction of crop yield is critical for supporting food security, agricultural planning, and economic decision-making. However, yield forecasting remains a significant challenge due to the complex and nonlinear relationships between weather variables and crop production, as well as spatial heterogeneity across agricultural regions. We propose DSNet, a deep neural network architecture that integrates functional and scalar predictors with spatially varying coefficients and spatial random effects. The method is designed to flexibly model spatially indexed functional data, such as daily temperature curves, and their relationship to variability in the response, while accounting for spatial correlation. DSNet mitigates the curse of dimensionality through a low-rank structure inspired by the spatially varying functional index model (SVFIM). Through comprehensive simulations, we demonstrate that DSNet outperforms state-of-the-art functional regression models for spatial data, when the functional predictors exhibit complex structure and their relationship with the response varies spatially in a potentially nonstationary manner. Application to corn yield data from the U.S. Midwest demonstrates that DSNet achieves superior predictive accuracy compared to both leading machine learning approaches and parametric statistical models. These results highlight the model's robustness and its potential applicability to other weather-sensitive crops.

We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the plane is replaced by some function with the same homogeneity. We show how several convexity properties of the generalized Keplerian orbits appear in this context. We describe the generalized hodographs.

Optimizing conflicting molecular properties while strictly adhering to complex 3D structural constraints constitutes a challenging Constrained Multi-Objective Optimization Problem (CMOP). Traditional Evolutionary Algorithms (EAs) destroy chemical valency in 3D space, whereas 3D diffusion models act as rigid generators requiring costly retraining for novel objectives. To bridge this gap, we propose a progressive algorithmic suite. First, we introduce the Evolutionary-Guided Diffusion (EGD) operator, which executes crossover and mutation at an optimally calibrated noise level, leveraging a pre-trained denoising network to project chimeric states back onto the valid chemical manifold. Second, to combat the severe loss of molecular structural diversity inherent in traditional EMO frameworks, we design a Structure-Aware Environmental Selection (SAES) mechanism that explicitly enforces structural distinctiveness. Finally, synergizing EGD and SAES, we develop the Diffusion-based Evolutionary Molecular Optimization (DEMO) framework for CMOPs. To safely navigate disjoint feasible regions, DEMO employs a tri-population architecture with distinct goals: exploring novel chemical scaffolds, refining partially assembled intermediates, and fine-tuning perfectly feasible elite molecules. Extensive experiments across single-property targeting, unconstrained MOPs, multi-fragment CMOPs, and 3D protein-ligand docking demonstrate that our method comprehensively outperforms state-of-the-art baselines and traditional EMO frameworks. Operating entirely zero-shot, this suite consistently discovers highly diverse, chemically valid Pareto frontiers.

Understanding the intricate interplay between distinct quantum resources is a fundamental prerequisite for rigorously characterizing the boundary between classical and quantum technologies. Among the vast landscape of quantum resources, entanglement, magic, and coherence have arguably attracted the most intense investigation. However, while universally recognized as the core drivers of quantum advantage, our understanding of their structural interplay remains fragmented and compartmentalized. In this work, we introduce an indicator called {\em bra-ket entanglement} (BKE) defined in the operator vectorization space to bridge all three quantum resources. Specifically, we show that BKE governs a resource dependence transition in the generation of entanglement: in the low-BKE regime, the growth of entanglement is dominated by coherence, largely independent of magic. However, as BKE increases, the dependence on coherence will gradually be replaced by a dependence on magic. Consequently, in the high-BKE regime, entanglement generation becomes dominated by magic, largely independent of coherence. These results are built on a series of new entropy-theoretic relations and are verified through numerical experiments. We also discuss implications of our results for the resource transitions in classical simulations of mixed states and marginal probabilities and for relating different classical simulation methods.

We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices when all agents have path-independent choice functions. This result answers an open question of Blair~\cite{blair1988lattice}. In the process, we introduce new tools to reason on general lattices for optimization purposes: the \emph{partial representation} of a lattice, which partially extends Birkhoff's representation theorem to non-distributive lattices; the \emph{distributive closure} of a lattice, which gives such a partial representation; and \emph{join constraints}, which can be added to the distributive closure to obtain a representation for the original lattice. Then, we use these techniques to show that the minimum cost stable matching problem under the same standard assumptions on choice functions is NP-hard, by establishing a connection with antimatroid theory.

We present an explicit and exact solution to the governing equations describing the vertical structure of the Arctic Ocean region centred around the North Pole. The solution describes a stratified water column with three constant-density regions: a motionless bottom layer, a middle layer -- the halocline -- described by nonhydrostatic, near-inertial Pollard waves, and an upper layer presenting a mean current and a wave motion associated with the one in the halocline layer.

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first consider approximate posteriors in which the means vary and the posterior covariance is kept fixed, for all possible realisations of the data simultaneously. We give necessary and sufficient conditions for these approximating posteriors to be equivalent to the exact posterior. For such approximations, we measure the data-averaged approximation error with the Kullback-Leibler, Rényi and Amari $α$-divergences for $α\in(0,1)$, and the Hellinger distance. With the loss in Kullback-Leibler and Rényi divergences, we find the optimal approximations and formulate an equivalent condition for their uniqueness, extending the work in finite dimensions of Spantini et al. (SIAM J. Sci. Comput. 2015). We then consider joint low-rank approximation of the mean and covariance. For the reverse Kullback-Leibler divergence, the optimal approximations of the mean and of the covariance yield an optimal joint approximation of the mean and covariance. We interpret one such joint approximation in terms of an optimal projector in parameter space, and show that this approximation amounts to solving a Bayesian inverse problem with projected forward model. Extensive numerical examples demonstrate some of our theoretical findings.

In large-scale UAV swarms, dynamically executing machine learning tasks can pose significant challenges due to network volatility and the heterogeneous resource constraints of each UAV. Traditional approaches often rely on centralized orchestration to partition tasks among nodes. However, these methods struggle with communication bottlenecks, latency, and reliability when the swarm grows or the topology shifts rapidly. To overcome these limitations, we propose a fully distributed, diffusive metric-based approach for split computing in UAV swarms. Our solution introduces a new iterative measure, termed the aggregated gigaflops, capturing each node's own computing capacity along with that of its neighbors without requiring global network knowledge. By forwarding partial inferences intelligently to underutilized nodes, we achieve improved task throughput, lower latency, and enhanced energy efficiency. Further, to handle sudden workload surges and rapidly changing node conditions, we incorporate an early-exit mechanism that can adapt the inference pathway on-the-fly. Extensive simulations demonstrate that our approach significantly outperforms baseline strategies across multiple performance indices, including latency, fairness, and energy consumption. These results highlight the feasibility of large-scale distributed intelligence in UAV swarms and provide a blueprint for deploying robust, scalable ML services in diverse aerial networks.

Understanding plasma self-magnetization is one of the fundamental challenges in both laboratory and astrophysical plasmas. Self-magnetization can modify the plasma transport properties, altering the dynamical evolution of plasmas. Multiple high-energy-density (HED) experiments have observed the formation of ion-scale magnetic filaments of megagauss strength, though their origin remains debated. Here, we conduct 2D collisional particle-in-cell (PIC) simulations with a laser ray-tracing module for a fully self-consistent simulation of the plasma ablation, expansion, and magnetization. The simulations use a planar geometry, effectively suppressing the Biermann magnetic fields, to focus on anisotropy-driven instabilities. The laser intensity is varied between $10^{13}$ and $10^{14}$ W/$\rm cm^2$, which is relevant to HED and inertial fusion experiments where collisions must be considered. We find that above a critical intensity, the plasma rapidly self-magnetizes via an expansion-driven Weibel process, producing plasma beta of 100 ($β= 8πk_B n_eT_e/B^2$) and Hall parameter $ω_{\rm ce}τ_{e}>1$ within the first few hundred picoseconds. The magnetic field is sufficiently strong to modify plasma heat transport, and simulations with artificially suppressed magnetic field show noticeably different temperature profiles.

We study the long-time behavior of small and large solutions to a broad class of nonlinear Dirac-type equations. Our results are classified in 1D massless and massive cases, 3D general and $n$ dimensional in generality. In the 1D massless case we prove that any globally defined solution converges to zero as time tends to infinity, within a spatial region expanding at a rate proportional to $ t \log^{-2} t$. This result holds without assumptions on the smallness of initial data or specific power of nonlinearity, ruling out the existence of standing breather-like or solitary wave structures in this regime. In the 1D massive case, solitary waves are known to exist. Introducing new virial identities adapted to the Dirac's distinctive algebra, we prove that there are ``holomorphic'' odd nonlinearities under which globally defined small odd solutions decay to zero on spatial compact sets as time tends to infinity. This result is extended to the 3D case under boundedness of the $H^1$ norm but without requiring the parity condition on the data, giving decay proofs for an important class of nonlinear Dirac models, and opening the door to the future use of virial identities to prove asymptotic stability of well-chosen Dirac solitary waves. Finally, in higher dimensions $ n \geq 1$, we prove the $L^2$ decay for global solutions of nonlinear Dirac equations in the ``exterior light-cone'' region. This confirms the non-existence of breathers and other solutions propagating faster than the speed of light. Our proofs rely on carefully constructed weighted virial identities.