Papers

Advances in the coding capabilities of LLM agents allow them to inspect and modify their own instructions, tools, and execution procedures. Existing approaches use this ability to search for improved agents through repeated downstream evaluation, which incurs substantial costs and ties the search to the evaluated tasks. We introduce SelfSearch, a reward-free search procedure in which agents modify themselves using records of previous self-improvement episodes. These records capture the reasoning, tool actions, and outcomes of earlier modification attempts, providing concrete experience for improving both task solving and self-modification. Without downstream reward signals during search, SelfSearch improves population-mean success over the initial agent in all six model–benchmark settings, with individual agents gaining up to 11.2 percentage points on Terminal-Bench 2.1. On SWE-bench Multilingual, an agent improves success by 5.0 percentage points while reducing execution cost by 38.5% on tasks solved by both the initial and evolved agents. SelfSearch achieves competitive task success with evaluation-guided search baselines at lower search cost. With only \$4.03 in search cost, it produces a harness that solves 82.0% of Terminal-Bench 2.1 tasks with DeepSeek V4 Flash under the settings of a public nine-harness comparison, matching the top-scoring harness, Codex. These results suggest that experience gained through self-modification can improve agents' downstream capabilities and efficiency.

Let $Q$ be a local ring, $f$ a nonzerodivisor, and $R=Q/(f)$. We characterize weak and Serre liftability of cyclic $R$-modules under suitable hypotheses, obtaining complete-intersection criteria for Serre liftability in small height. We prove that the tensor product of two weakly liftable cyclic modules remains weakly liftable when their first Tor module vanishes, and give sufficient conditions for tensor products to preserve Serre liftability. We construct an Artinian Gorenstein quotient $Q/I$, with $Q$ regular, that is perfect over $R$ and Serre liftable but not weakly liftable to $Q$, showing that the negative answer to a question of Jorgensen persists in this more restrictive setting. Finally, we characterize when a lift induces a lift of the Auslander transpose and obtain a freeness criterion related to the Auslander-Reiten conjecture, recovering a theorem of Ghosh and Samanta.

Motivated by the work of Andrews and El Bachraoui on partitions with repeated smallest parts, Malik and Sarma recently extended this concept to overpartitions. Using generating functions and $q$-series techniques, they established several results, including four identities, and posed the problem of finding combinatorial proofs for these identities. Recently, Baruah, Li, and Mohanta provided combinatorial proofs for three of these identities. In this paper, we present a combinatorial proof of the remaining identity.

Strong-to-weak spontaneous symmetry breaking (SWSSB) is a novel phase transition in mixed states associated with the loss of global charge information. In this work we study fermions with $U(1)$ symmetry under infinite density dephasing and derive the SWSSB properties of the resulting mixed states. Our central observation is that at infinite dephasing every Renyi correlator is exactly the spin-spin correlator of a compact XY model, whose Boltzmann weight is the squared full-counting-statistics generating function of a classical ensemble built from the parent state. For the Renyi-2 correlator it is the full counting statistics of the parent state itself. We complement the infinite dephasing mapping with a novel diagrammatic expansion for the Renyi-1 correlator, applicable to any diagonal mixed state, which computes the couplings of the Renyi-1 XY model. We also study a replica field theory for even Renyi index quantities, applicable at finite dephasing. Our analysis indicates that fully dephased metals display long-range SWSSB in $d\geq 2$, as confirmed numerically and experimentally in $d=2$, and quasi-long-range SWSSB in $d=1$. For insulating parent states both an SWSSB and a trivial phase are possible at infinite dephasing depending on UV details. Long-range SWSSB in $d\geq 3$, or quasi-long-range SWSSB in $d=2$, survives above a nonuniversal, Renyi-index-dependent threshold and is lost when the parent state is deep in the insulating phase, with the exception of quantum Hall insulators which generically have quasi-long-range SWSSB. For even Renyi indices we also determine the stability of the SWSSB phase away from infinite dephasing and derive the universality class of the SWSSB transition.

Internal waves are large-amplitude gravity waves that occur below the ocean surface and propagate along interfaces separating water layers of different densities. Understanding their generation, propagation, and evolution is essential, as these waves play a vital role in the ocean system by contributing to nutrient transport, biological productivity, and the transfer of energy across the ocean and continental shelf. Domain scientists use high-resolution numerical ocean models, to study internal-wave dynamics and associated coastal and nearshore processes on hybrid computational grids. These models generate large-scale, three-dimensional spatiotemporal datasets that capture internal wave flow behavior and interactions with multiple ocean variables. These datasets are generally analyzed using command-line tools with limited interactivity. To address these challenges, we in collaboration with domain scientists designed a task-driven visualization methodology for analyzing multiscale, multivariate flow data on hybrid grids. The framework incorporates a hybrid-grid volumetric reconstruction method, enabling continuous 3D analysis and a coordinated multi-view design that supports interactive exploration of complex flow structures. An insight-based evaluation with domain experts demonstrates that the system enables the identification of previously difficult-to-observe phenomena, including transverse wave propagation, energy transport pathways, and shoaling-driven mixing. Beyond the application domain, our contributions provide generalizable techniques and design principles for visual analysis of multiscale, multivariate flow data on irregular grids.

Liquidity provision in automated market makers is typically analyzed at the pool level, implicitly assuming LP homogeneity. This aggregate view can hide how liquidity provision outcomes differ between LP strategies, particularly as concentrated liquidity AMM designs operating on high-performance blockchains allow liquidity to be actively repositioned around trades. We develop a markout-based framework to decompose Uniswap LP profitability into active and passive components using two complementary methods: a LIFO subtraction method that matches short-lived mint-burn positions and attributes swap-level markouts by liquidity share; and an infinitesimal LP benchmark that estimates the performance of a fully passive, always-in-range marginal LP directly from the AMM price path. We apply these methods to Uniswap v2, v3, and v4 pools on Ethereum, Arbitrum, and Base chains, and find passive profitability can materially differ from aggregate pool profitability. In Uniswap v2, with liquidity distributed evenly and active LP behavior nearly absent, the overall and passive markouts are almost the same. In contrast, concentrated-liquidity pools have a systematic active-passive gap: passive LPs tend to underperform aggregate pool-level measures. The gap is wider on Ethereum than on L2s, consistent with active liquidity provision being more useful when block times and ordering conditions allow LPs to react to incoming flow. In general, passive LPs perform better on higher fee pools. The LIFO and infinitesimal estimates are generally consistent directionally across most pools, providing evidence of the robustness of the decomposition. The results suggest that adverse selection in AMMs is not evenly distributed among LPs, with important implications for LP strategy, fee-tier design and measurement of DEX market quality.

We analyze circular-orbit stability, epicyclic resonances, relativistic precession, and quasi-periodic-oscillation (QPO) constraints in the constant-curvature vacuum sector of metric $f(R)$ gravity. The Schwarzschild–(anti-)de~Sitter and Kerr–(anti-)de~Sitter backgrounds are characterized by curvature $R_0$ satisfying the algebraic trace equation. We derive stationary-coordinate-time orbital and epicyclic frequencies and determine stable timelike circular-orbit domains. Positive curvature confines stable motion between innermost and outermost stable circular orbits, which merge at a critical curvature, and permits two resonance radii for suitable frequency ratios. Negative curvature allows stable motion to arbitrarily large radii, with $\Omega_\theta/\Omega_r\rightarrow1/2$, compared with unity in the asymptotically flat limit. We determine the $3{:}2$, $2{:}1$, and $3{:}1$ resonance branches and signed nodal precession, recovering the Lense–Thirring limit. We also evaluate angular-momentum-weighted rigid-flow precession and viscous alignment, with the outermost stable orbit bounding positive-curvature flows. A Bayesian Markov chain Monte Carlo analysis combining the simultaneous GRO J1655–40 QPO triplet with an independent dynamical-mass measurement yields $R_0M^2=-5.57^{+12.94}_{-16.15}\times10^{-4}$ at $68\%$ credibility, conditional on the geodesic relativistic-precession prescription and adopted time normalization. Kerr remains allowed, with negligible fit improvement from nonzero curvature. Doubling the mass uncertainty broadens the curvature interval by approximately $2.1$; removing the mass likelihood reveals an extended, prior-dependent degeneracy. This is therefore a joint QPO and dynamical-mass constraint, with no significant evidence for departure from Kerr.

Given an $n\times n$ symmetric matrix $M$ with largest eigenvalue $\lambda_1\geq 0$, it is easy to show that the solution of the optimisation problem $\max_{v\in [-1,1]^n}v^TMv$ is at most $\lambda_1 n$. We prove the following converse: if every $n'\times n'$ principal submatrix of $M$ has maximal eigenvalue at least $\lambda$, then $\max_{v\in [-1,1]^n}v^TMv\geq \lambda(n-n'+1)$. This allows us to lift results about the second largest and the smallest eigenvalue of graphs to the (a priori more difficult) setting of positive discrepancy and MaxCut. Using this new connection, we prove that every $n$-vertex $m$-edge graph that is far from a disjoint union of cliques has a cut of size at least $m/2+n^{5/4-o(1)}$, which is sharp up to the $o(1)$-term. Moreover, we prove that every $d$-regular $n$-vertex graph has bisection width at most $dn/4-\Omega_{\varepsilon}(d^{1/3}n)$ for $d\leq (1-\varepsilon)n/2$, which is optimal for $d=\Omega(n)$. This confirms a conjecture of Räty, Sudakov and Tomon.

In the context of the rapidly growing field of galactic exoplanet population studies, we present an exoplanet simulator capable of generating synthetic populations for millions of stars in a few seconds (Padois et al., 2025). Our framework combines observed exoplanet detections with the latest planetary formation models, incorporating dependencies between host star properties and planet occurrence rates, orbital period distributions, and other key demographic features. However, many model parameters remain uncertain and model-dependent. To constrain some of the most critical ones, we couple our simulator with simulation-based inference (SBI): we define a set of 44 free parameters describing the population of different planet types (occurrence rates, mass-period distribution, mass-radius relation, etc.), run millions of simulations sampling from broad prior distributions, simulate their detectability by Kepler, and train a machine-learning algorithm to learn the relationships between input parameters and the resulting "observed" synthetic populations. The best-fit parameters are then inferred by comparing model outputs to real observations, for which we adopt the Kepler confirmed planet catalogue as our reference dataset, since it provides the largest homogeneous sample from a single facility. We present preliminary results for the planet occurrence rate as a function of stellar mass and metallicity, across different planet types, along with constraints on several key simulation parameters such as the orbital period distribution and the inclination dispersion within planetary systems. These refined parameters enable us to refine our yield predictions for upcoming exoplanet detection missions, including PLATO, Roman, and HAYDN.

Tabular machine learning typically relies on per-dataset workflows, fitting tree ensembles or running AutoML searches from scratch for every task. We present TabFM, a 400M-parameter tabular foundation model that formulates supervised tabular prediction as in-context learning. TabFM produces calibrated zero-shot predictions in a single forward pass without task-specific tuning. Trained entirely on synthetic tables generated from structural causal models, TabFM learns general tabular representations that transfer zero-shot to real-world tasks. Across all 51 benchmark datasets in TabArena (38 classification and 13 regression), zero-shot TabFM ranks first among default tabular foundation models and outperforms tuned AutoML pipelines. Two extensions over the same frozen weights improve performance further on both tracks: multi-view feature expansion with ensembling and post-hoc calibration (TabFM+), and LLM-guided, dataset-specific data processing and feature engineering (TabFM-Auto).

As the input dimension $n$ grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck for function approximation: both rule count and parameter count grow exponentially with $n$. Traditional LCSs partition the $n$-dimensional input space directly, requiring $\mathcal{O}(m^n)$ rules for adequate coverage, where $m$ is the per-variable resolution. This article breaks from this paradigm by reorganizing rules dimension-wise, guided by the Kolmogorov-Arnold representation theorem: any continuous $n$-dimensional function can be expressed as a finite superposition of one-dimensional functions. The proposed Kolmogorov-Arnold Classifier System (KACS) decomposes the target function into one-dimensional subproblems and assigns a dedicated ruleset to each, reducing the worst-case rule count from $\mathcal{O}(m^n)$ to $\mathcal{O}(mn^2)$ and replacing $n$-dimensional local models with one-dimensional models requiring only two parameters per rule, independent of $n$. We also provide the first constructive proof that an LCS, namely KACS, is a universal approximator for continuous functions on compact domains. Evaluated against a direct $n$-dimensional input space partitioning approach under otherwise identical conditions, KACS achieves competitive accuracy in many settings while using only 2% to 40% of the parameters. Our implementation is available at https://github.com/YNU-NakataLab/KACS.

Network reconstruction from partial information is usually performed at the same resolution level at which constraints are observable. This becomes problematic when only coarse-grained information is available, while the relevant process occurs at a finer scale. Here we employ the multiscale model of weighted networks introduced in a companion paper and turn it into a probabilistic framework for reconstructing weighted networks across arbitrary aggregation levels. The model is built to preserve its functional form under coarse-graining, so that global parameters calibrated on an observable aggregate layer can be transferred to finer layers without refitting. We test the method on two empirical systems with different aggregation mechanisms. In the International Trade Network, countries are aggregated into geographic macro-regions and the observed coarse-grained layer is used to infer the underlying country-level network. In the Dutch production network, sectoral flows are reconstructed across the hierarchical industrial classification, using coarser sectoral layers to infer finer ones. In both geographical and sectoral settings, we benchmark our genuinely multiscale reconstruction method against a state-of-the-art weighted reconstruction model calibrated directly at the target resolution, and therefore using additional information available at the same (finer) scale at which performance is evaluated. Remarkably, despite this informational disadvantage, our method recovers the fine-scale binary structure with high accuracy, improving precision, specificity, accuracy and maximum degree-error diagnostics, while remaining nearly equivalent in sensitivity.

Brain networks characterize structural and functional relationships among brain regions and support research on cognition, brain disorders, and brain-computer interfaces. Their time-varying topology and higher-order spatiotemporal dependencies are not adequately represented by conventional static networks. Existing tools primarily focus on static connectomes and provide limited integration of dynamic network modeling with modern graph and sequence learning methods. We present BrainNet Studio, an integrated toolkit for static and dynamic brain network analysis. It provides a unified workflow encompassing network construction, feature extraction, predictive modeling, candidate biomarker identification, visualization, and assisted interpretation. The toolkit integrates 27 algorithms, including deep learning, graph neural networks, and spatiotemporal sequence models, to support classification and the identification of discriminative brain regions and connections. A large language model generates researcher-verifiable summaries of functional connectivity, structural connectivity, and structure-function coupling at individual and group levels. Within a consistent computational framework, users can configure analytical tasks, compare methods, inspect outputs, and extend functionality without repeatedly assembling application-specific pipelines. BrainNet Studio provides a practical and extensible platform for connectome analysis in cognitive neuroscience, exploratory studies of brain disorders, and brain-computer interfaces. The toolkit is publicly available at https://github.com/xbrainnet/Brainnet-Studio.

Observing the earliest stages of high-mass star formation in the mid-infrared (mid-IR) is challenging because the extinction is high and the resolution limited. Millimeter vibrationally and torsionally excited transitions of several molecules have been proposed as indirect probes of local mid-IR radiation fields around young stellar objects (YSOs). We investigate the excitation and spatial distribution of torsionally excited methanol ($\mathrm{CH_3OH}$) in 12 high-mass star-forming clumps in different evolutionary stages, assessing their potential as tracers of the mid-IR luminosity of embedded protostars. We analyzed rotational transitions of methanol within the same torsionally excited states $v_\mathrm{t}$$\geq$1 in the Atacama Large Millimeter/submillimeter Array (ALMA) 890 $\mathrm{\mu m}$ observations and compared them with Spitzer 24 $\mathrm{\mu m}$ data by plotting line luminosities normalized by methanol abundance against mid-IR luminosities. The torsionally excited methanol emission is generally compact and systematically coincident with ALMA dust continuum peaks and 24 $\mathrm{\mu m}$ emission, even in faint sources. The only clump without an IR counterpart also shows no $v_\mathrm{t}$$\geq$1 emission, supporting radiative pumping as the dominant excitation mechanism. We found a promising power-law trend between $v_\mathrm{t}$$\geq$1 methanol lines and 24 $\mathrm{\mu m}$ luminosities, largely independent of the methanol abundance. $\mathrm{CH_3OH}$ $v_\mathrm{t}$$\geq$1 transitions appear to be promising tracers of local mid-IR radiation fields of embedded protostars, providing core-scale information even in highly extincted regions. As a pilot study, our results suggest that extending our study to a larger statistical sample is crucial for testing and improving this method.

The GlueX experiment in Hall D at Jefferson Lab enables studies of the light meson spectrum in $\gamma p$ interactions with a linearly polarized photon beam. GlueX aims in particular to search for hybrid mesons that have exotic quantum numbers and therefore cannot be classified as conventional hadrons. We present the search for the $\pi_1(1600)$ meson by means of a partial-wave analysis of the $\pi^{+}\pi^{-}\pi^{-}$ system produced off the $\Delta^{++}$-baryon. Data with the selected three-pion final state are fitted in bins of $m_{3\pi}$ as coherent sums of partial-wave amplitudes defined in the reflectivity basis. The properties of $a_{2}^{-}(1320)$ production are investigated through the extracted signal in the $\rho\,\pi^{-}$ $D$-waves. In this analysis, the overall $m_{3\pi}$ lineshape will be extracted for each of the model contributions. The main interest lies in establishing the existence of a resonant $1^{-+}$ contribution in the $\rho\,\pi^{-}$ $P$-wave configuration.

Complex tasks inherently couple workflow structure, agent responsibility, collaboration, and memory access: task regions delimit responsibility and tool scope, cross-region dependencies give rise to handoffs, and ownership boundaries delimit private and selectively shared memory. Existing methods can jointly optimize agent and communication structures, yet such optimization does not by itself require responsibility, handoff, and memory boundaries to remain consistent with task dependencies. We term this requirement topological coherence. We introduce TOCOMAS, a Topology-Coherent Multi-Agent System. TOCOMAS grounds a task graph in tool interfaces, organizes compatible task nodes into reusable responsibility domains, and derives dependency-induced and profile-conditioned collaboration together with boundary-regulated memory visibility. During online self-evolution, TOCOMAS proposes coupled changes to agent, collaboration, and memory policies, retaining for subsequent tasks only candidates that satisfy structural constraints and improve evaluated reward. Across BBEH, WorkBench, SWE-Bench-Verified, and CoMemBench, TOCOMAS improves task success over baselines across backbones. CoMemBench also shows gains over the self-evolving baseline in verified progress, handoffs, and memory isolation.

Reduced walking speed in people with multiple sclerosis (MS) is associated with an increased risk of falls. However, virtual reality (VR)-based rehabilitation studies often emphasize performance improvements without considering the cognitive and physical effort required to achieve them. This study introduces a threshold-anchored efficiency framework that jointly evaluates gait performance and overall effort. A normative walking-velocity target of \(T=1.29\) m/s was derived from the mean walking speed of non-fallers in an independent MS gait dataset and used as a clinically motivated reference point. Thirty-four adults with MS were evaluated across eight VR feedback conditions spanning unimodal, bimodal, and multimodal feedback. For each condition, we quantified the proportion of the velocity gap to the target that was closed and the associated cognitive and physical burden. Pareto efficiency analysis identified five non-dominated conditions: Static Visual, Spatial Auditory, Auditory+Visual, Auditory+Vibrotactile, and Multimodal, whereas Spatial Vibrotactile and Vibrotactile+Visual were dominated. Spatial Auditory showed a favorable performance-effort trade-off, closing 72.7% of the velocity gap while maintaining below-average burden. Multimodal feedback achieved the greatest gap closure (95.6%) but also imposed the highest burden. These findings demonstrate that greater gait improvement does not necessarily correspond to greater rehabilitation efficiency and provide a quantitative framework for comparing VR feedback strategies according to both performance gains and participant burden.

Replacing a visible advertisement in a broadcast frame is geometrically straightforward but photometrically delicate. A pasted graphic can have the correct perspective and still appear detached when its brightness, shading, or shadow disagrees with the surface beneath it. This paper presents Ad-Relight, an inference-only procedure for transferring scene illumination to a supplied advertising graphic without collecting a banner-specific training set. The procedure first separates slowly varying shade from graphic structure, then probes a pretrained diffusion relighter with two nearly identical backgrounds to isolate the contribution of the target region. A final pass combines this residual with a smoothed luminance field and a soft attenuation mask. Across 560 generated placements, the approach improves structural similarity, perceptual distance, and illumination agreement over geometric compositing and direct relighting baselines. Human judgments and an automated preference study show the clearest gains on floor-mounted graphics with nonuniform lighting. The current study is image based; temporal stabilization remains an open extension.

Video understanding agents acquire evidence through an executable harness that controls what they observe and how they use those observations. However, execution traces contain only the evidence acquired by the current harness, leaving competing explanations for failure unresolved and limiting the basis for self-improvement. We introduce Video-RSI, a framework for recursive self-improvement in which a video understanding agent uses its own language model to revise its harness. Through active video investigation, the model revisits the original training videos to test competing failure explanations with additional observations, grounding proposed changes in evidence beyond the existing trace. Cost-aware harness evolution turns these diagnoses into reusable revisions and determines which revisions to retain by considering both answer accuracy and visual cost. Across our evaluation settings on video understanding benchmarks, the evolved agent improves accuracy while processing fewer frames and achieves competitive accuracy-efficiency trade-offs against existing video understanding agents. These results demonstrate the potential for video understanding agents to improve their own evidence acquisition and use through harness evolution. Code is available at https://github.com/bingjunluo/Video-RSI .

We formulate a class of systems of Euclidean correlation functions for compact $d$-dimensional conformal field theories which are not necessarily unitary. We also introduce conformal $d$-vertex algebras, $d$-dimensional analogues of full vertex algebras, and prove that such an algebra is obtained from every system of conformally covariant correlation functions. Finally, for each $d\geq 2$, we construct a family of examples satisfying these axioms, corresponding to generalized free scalar fields. For $d>2$, this family contains both unitary and non-unitary examples.

We show that a closed spin four-manifold with nonzero signature, even after being punctured along a finite graph, does not admit a complete metric with uniformly positive scalar curvature. We also show that this implies Schoen's conjecture on $L^{\infty}$-metrics with non-negative scalar curvature for these manifolds. This is in contrast to higher dimensions. A key new observation, which could be of independent interest, is that Gromov's $\mu$-bubbles are a convenient class of boundaries for the APS boundary value problem for the Dirac operator.

A droplet breaks up in tens of microseconds, and a recording captures perhaps a dozen frames. The states in between cannot be recovered without repeating the experiment, and simulating them is too costly to sweep an operating envelope. Yet they are present in the corpus as a whole: a campaign spanning a device's actuation range produces morphologies resembling those any single recording missed. Exploiting that requires a representation that is low-dimensional, invertible, and faithful to shape rather than to sampling. Proper orthogonal decomposition supplies the first two but measures distance in sampled coordinates; manifold learning supplies the third but no map back to a shape; elastic shape analysis supplies a shape metric but no reduced coordinates. SHROM composes all three. Interfaces are represented by their square-root velocity functions, a neighbour graph is built over that shape space, and an autoencoder is trained to reconstruct while penalising latents in which graph neighbours are not latent neighbours. The demonstration uses 301,539 inkjet droplet contours and four filmed break-up sequences. The graph term does not improve reconstruction. It determines whether position in the latent carries meaning: clustering the latent of an otherwise identical model recovers the shape-space partition at chance level (ARI = 0.063 +/- 0.059), and at 0.781 +/- 0.049 with the term active. Waveform parameters predict the full contour at R^2 = 0.878 +/- 0.026. Negative results are reported in the same terms. The graph metric proved immaterial across five choices, and interpolation error saturates at the reconstruction limit, so a plain autoencoder leads that task. The main limitation is interpolation across a topology change: no component of the regularised latent holds both a single-component and a post-break-up shape, whereas an unregularised autoencoder mixes them freely.

Pairs of spheres sharing an acoustic trap sometimes spin intermittently despite having no self-propulsion, no obvious power source, and no symmetry-breaking mechanism, switching between rocking and spinning within a single trajectory. Nonreciprocal wave scattering powers this emergent activity, and drag shapes their dynamics by coupling rotations to translations. Mismatched pairs can pass through a supercritical Hopf bifurcation into a quasiperiodic torus on which the pair's orbit reverses regularly and, farther from equilibrium, into deterministic chaos. Experiments motivate this mechanism and share its qualitative signatures; simulations reveal a full noise-free route from passivity to chaos, and suggest how analogous dynamics can emerge in other active-matter systems.

Let $u:\mathbb{S}^{2n+1}\to\mathbb{CP}^n$ be a smooth nonconstant harmonic map. We prove that its Morse index is equal to $ 2n+2$ if and only if \begin{equation*} u = h \circ \pi \circ \Xi, \end{equation*} where $\Xi:\mathbb{S}^{2n+1}\to\mathbb{S}^{2n+1}$ is an isometric transformation, $\pi:\mathbb{S}^{2n+1}\to\mathbb{CP}^n$ is the Hopf map and $h:\mathbb{CP}^n\to\mathbb{CP}^n$ is a holomorphic map with degree one. When $n=1$, it refines a classical result of Urakawa and a recent result of Rivière. Moreover, we prove that $h\circ\pi\circ \Xi$ has nullity $3n^2+5n$.

A wide range of methods have been proposed, including physics-informed neural networks, which are powerful but do not guarantee identifiability of the dynamics, symbolic regression, which requires a set of precomputed operations, and causal discovery, which is more principled but usually relies on strong assumptions that physical systems may violate. In this work, we develop a theory-grounded method and prove that under a set of permissive assumptions, the structural drivers and drift of stochastic delayed differential equations are identifiable. Our method outperforms others on a benchmark for driver identifiability, and on a second benchmark to evaluate physical consistency of the learned dynamics.

We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those commonly used in practice to model relaxation. The atomic-scale model consists of two periodic chains containing $N$ and $N+1$ atoms per common cell and is exactly moiré-periodic at the atomic scale. Its energy combines harmonic nearest-neighbor intralayer interactions with nonlocal interlayer interactions generated by an even $C^2$ pair potential with polynomial decay. The associated continuum energy couples linear elasticity to a periodic misfit potential, obtained by periodizing the pair potential, which penalizes unfavorable local stackings.

We study the massive scalar quasinormal-mode spectral problem on a Schwarzschild background using an extended Chebyshev spectral method. The massive dispersion relation has a two-sheeted analytic structure, which we uniformise before discretisation. This converts the radial problem into a seventh-degree polynomial eigenvalue problem while incorporating the quasinormal-mode boundary conditions at the horizon and spatial infinity. The method yields stable spectra for low multipoles, high overtones, and frequencies on both sides of the nominal mass threshold, including regimes in which WKB and continued-fraction approaches become difficult to apply. For complex frequencies, the far-field behaviour cannot be classified from the real part of the frequency alone, but depends on the complex wavenumber and its Riemann sheet. We also identify stable families of purely imaginary roots with approximately uniform spacing in their damping rates, whose physical interpretation remains open. The Schwarzschild scalar problem is intended as a controlled benchmark for massive-field quasinormal-mode calculations rather than as a direct model of tensorial Kerr ringdown.

This study provides a data-driven analysis of a novel dataset of single-cell Anion Exchange Membrane water electrolyzers (AEMWE), operated under constant current load across multiple heterogeneous experimental campaigns. We train and evaluate a range of machine learning models with different complexity, including linear baselines, LSTMs and CNNs, to perform medium-term forecasting of the cell voltage degradation curve. The models are assessed within a rigorous training and evaluation framework specifically designed for heterogeneous industrial data.

Thermodynamic uncertainty relations bound the fluctuations of time-antisymmetric currents. Stochastic efficiency is not one: a ratio of two odd quantities, it is even under path reversal, and for the conventional ratio $-W/Q_h$ no moment exists. We work with the exergetic ratio $\eta=W/(W+T_0S)$, whose moments exist, and ask how much of its variance a finite perturbation of the dynamics can certify when linear response cannot. The question is specific to nonlinear observables: for every current, and every observable linear in transition counts and residence times, the multiparameter Cramér-Rao bound over rate and site perturbations already equals the variance. For $\eta$ it does not. The Cramér-Rao bound vanishes on a hyperplane of perturbation directions, while the Barankin multi-point bound, applied to tilted path measures, stays positive there and recovers 75% of the variance of $\eta$ in a three-state motor model where every linear-response bound is zero. The Gram matrix of tilted Markov-jump path measures is a Feynman-Kac matrix exponential whose potential is the Hellinger integrand of the jump intensities, and the cost of a perturbation is its $\chi^2$ divergence, which no dissipation bound controls. The bound captures 1.25-1.57 times the best linear-response bound, and the gain persists on networks of up to sixteen states. For an Ornstein-Uhlenbeck process the construction is exactly solvable: the optimal tilt scales as $T^{-1/2}$ and three test points nearly reach the supremum. Two limits are established. The gain is a short-window effect that disappears as the counts become Gaussian, and the bound cannot be turned into inference: coarse measurements bound $\chi^2$ only from below. The construction is a computational instrument for a model in hand, not an uncertainty relation.

We introduce a novel proof strategy for semiparametric Bernstein-von Mises theorems based on Stein's method combined with an information-geometric framework. Rather than controlling the effect of the prior on the asymptotic marginal posterior distribution of the functional of interest through the stability of an integrated likelihood under a suitable perturbation, we characterise its influence through the prior-weighted divergence of suitable vector fields over the statistical model. Applying Stein's method in this setting instead of the usual Laplace-transform approach yields explicit non-asymptotic upper bounds on the bounded-Lipschitz distance between marginal posterior distributions and the corresponding Gaussian limits predicted by semiparametric efficiency theory. These bounds consist entirely of local scalar differential quantities associated with the functional, the prior and a chosen vector field-typically related to the efficient influence function-evaluated over posterior contraction sets. We apply the theory to quadratic functionals in Gaussian white-noise models and to linear, quadratic and general integral functionals in histogram density models, with both conjugate and non-conjugate priors. For linear and quadratic functionals, the same theory identifies the differential term responsible for posterior bias and allows us to remove it through a natural functional correction, yielding Bernstein-von Mises-type theorems in regimes where they may fail for the original uncorrected functional.