Papers

This paper argues for the historical utility of general relativity textbooks written during, or shortly before, the Renaissance of general relativity. More so than research papers, textbooks offer a narrative account of the field–one that may differ substantially from the accounts of other authors addressing the same subject. Textbooks on general relativity therefore constitute a distinctive form of testimony to the intellectual forces that shaped general relativity, particularly during its reinvention period from 1955 to the mid-1970s. A second pillar of this argument is the observation that nearly all principal investigators at the research centers previously identified by Lalli et al.–centers that functioned as intellectual epicenters of the Renaissance of general relativity–eventually produced a textbook associated with their own school of thought. To situate this observation within the broader development of the field, the paper presents a concise history of general relativity textbooks from the theory's inception in 1915-16 to the 1980s. This history illustrates one way in which textbooks can serve as sources for reconstructing the intellectual dynamics of the Renaissance of general relativity.

[Bass and Burdzy 1999] introduced a stochastic flow of homeomorphisms of the real line $\mathcal R_t:x\mapsto \mathcal R_t(x)$, driven by a Brownian motion. Ray-Knight theorems for the process $\mathcal R_t^{-1}(0)$ were later obtained by [Hu and Warren 2000]. We extend their results by proving an integral representation driven by a common white noise for the local times of $\mathcal R_t^{-1}(0)$, in analogy with the case of the standard Ray-Knight theorems [Aïdékon, Hu and Shi 2024]. We generalize this representation to the setting of a Bass-Burdzy flow driven by a drifted Brownian motion perturbed at its maximum, and use this framework to answer a question of [Aïdékon, Hu and Shi 2026] concerning the description of the conditional law of a perturbed reflecting Brownian motion given its occupation measure in terms of Bass-Burdzy flows.

High-frequency (HF) single-station localization estimates an emitter location from measured directions of arrival (DOAs) and an ionospheric propagation model. When the propagation mode composition cannot be identified from conventional direction-finding (DF) measurements, the same DF observation may produce multiple physically valid ground landing points under different propagation modes, making the location inversion ambiguous. This paper proposes a multimode time-frequency information fusion localization method (MTFIF-L).Rather than assuming a propagation mode a priori, MTFIF-L retains valid landing points generated under different propagation modes and uses repeated observations across time windows and, when available, multiple operating frequencies to progressively constrain the resulting candidate locations. Experiments on four measured HF links examine the respective roles of multimode candidate retention, cross-window processing, and cross-frequency processing. All four links yield unique location decisions. Links A–C achieve relative errors of $1.40\%$, $0.78\%$, and $3.41\%$, respectively.Link D, the only single-frequency case, also yields a unique decision from repeated temporal observations, although its post- localization error is substantially larger. Propagation-path analysis further reveals link-dependent differences in reflection layer, hop count, magnetoionic mode, and elevation angle among the ray-tracing paths associated with the measured links.Overall, the results show that repeated temporal observations can support localization within an individual frequency, while multifrequency information provides additional robustness against unreliable frequency-specific outcomes, enabling HF single-station localization under unknown and potentially coexisting propagation modes while retaining interpretable propagation information for post-localization analysis.

The parabolic-elliptic Keller-Segel system \[ \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v), \\[1mm] 0 = \Delta v - \mu + u, \qquad \mu:=\frac{1}{|\Omega|} \int_\Omega u, \end{array} \right. \qquad \qquad (\star) \] is considered under homogeneous Neumann boundary conditions in the ball $\Omega=B_R(0)\subset {\mathbb R}^n$, where $n\ge 2$ and $R>0$. The main results identify a mass level $m_\star(n,R)>0$ as critical in the sense that $\bullet$ whenever $0<m<m_\star(n,R)$, the constant equilibrium of ($\star$) given by $u\equiv v\equiv \frac{m}{|B_R|}$ is locally asymptotically stable with respect to the norm in $L^\infty(B_R)$, but that $\bullet$ if $m>m_\star(n,R)$, then any solution of ($\star$) emanating from nonnegative and nonconstant continuous radial initial data $u_0$ with $\int_{B_R} u_0=m$ and $\frac{1}{|B_r|} \int_{B_r} u_0 \ge \frac{m}{|B_R|}$ for all $r\in (0,R)$ blows up in finite time. The value of $m_\star(n,R)$ can be determined in an essentially explicit manner in dependence on principal zeroes of appropriate Bessel functions of the first kind; in particular, $m_\star(2,R)\approx 14.68197 \cdot \pi$ for all $R>0$. Accordingly, as a supplement to known mass-dependent blow-up dichotomies these findings reveal a genuinely secondary critical mass phenomenon for ($\star$) especially also in its two-dimensional version in which no precedent of this form seems known.

Emotional image editing aims to change the emotion a scene conveys while preserving its essential content. Because the same scene can support different emotional interpretations, achieving an emotional goal requires visual changes grounded in the source context. Motivated by the Component Process Model, which links emotional responses to event appraisal, we investigate neural representations as a reference for these editing decisions. Using TRIBE v2, an fMRI encoding model, we analyze 400 source-target pairs across eight emotion categories. Hidden states from EmoEdit, EmoEditor, and AffectDelta correspond more strongly to predicted target-image responses in visual regions than in affect-related regions. This imbalance motivates ROI-ReFT, which combines source visual responses as a content reference with a predicted affective response change as an editing direction. Two interacting branches use both conditions to guide a frozen editor throughout generation. Predicted responses of the generated image supervise affective change and constrain visual drift. On a post hoc selected subset of 400 editing requests, ROI-ReFT achieves 91.75% target-emotion accuracy and 83.25% joint success, with the same output both matching the target emotion and reaching source-output DINO-I of at least 0.80. Our code and dataset will be publicly released.

Anticipation of vessel trajectories is an essential task when navigating at sea. This applies to both human navigators and autonomous surface vessels. Trajectory forecasting enables sub-routines such as collision avoidance to assess the situation and react accordingly in time. This paper investigates Transformer and Performer models for trajectory prediction of surface vessels in confined waters. Using widely available position data from the Automatic Identification System (AIS), candidate models are trained and evaluated. Historical information on how other vessels have moved in the local area surrounding each agent is conveyed using positional heat maps. The heat maps are generated using Kernel Density Estimation (KDE) and encoded with a Convolutional Neural Network (CNN) before entering the Transformer models. The models are trained with quantile loss to efficiently obtain a model-aware prediction interval, as this is crucial for timely collision avoidance. The proposed model architectures are shown to greatly outperform previous work while the inclusion of local heat maps enables the prediction of vessel movement that is not otherwise indicated from the previous positions.

Chromatic villainy is the maximum, over rearrangements of optimal graph colorings, of the minimum Hamming distance to a proper coloring with the same color multiplicities. Weak villainy allows the repair to change these multiplicities. We give exact composition laws for disjoint unions and determine the eventual growth under repetition. Write $mG$ for the disjoint union of $m$ copies of $G$. For every graph $G$, with $k=\chi(G)$, weak villainy satisfies $B_{\mathrm w}(mG)=mF_k(G)$ whenever $k\mid m$, where $F_k(G)$ is the maximum distance to a proper $k$-coloring over all assignments of $k$ color labels to vertices. Its bounded defect from $mF_k(G)$ is eventually periodic; we give an explicit stabilization bound and identify the least period, which divides $k$. For ordinary villainy, we obtain a computable rational slope $\Lambda(G)\ge F_k(G)$ such that $B(mG)=m\Lambda(G)+O_G(1)$, where the error is bounded independently of $m$ and eventually periodic, with a computable period and threshold. Consequently the difference between the two values is bounded exactly when $\Lambda(G)=F_k(G)$, and otherwise grows linearly. The slope is determined by a finite optimization using at most $k$ source assignments. We also answer the unrestricted superadditivity questions negatively: for every $C>0$, a connected graph can lose more than $C$ in weak villainy after union with a triangle, and some connected $3$-chromatic graph $G$ satisfies $B(G\sqcup G)<2B(G)-C$. Finally, both exact values on an $n$-vertex graph can be computed in time $f(B_{\mathrm w}(G))(n+1)^{O(1)}$, without either value being supplied. Threshold recognition is fixed-parameter tractable as well.

We investigate holographic Krylov complexity in bottom-up holographic QCD models describing the confined phase, using the recently proposed correspondence between the growth rate of Krylov complexity and the proper radial momentum of probes, such as particles and strings, falling in the bulk spacetime. As representative confining backgrounds, we consider two horizonless geometries, namely the dilaton-deformed AdS-soliton and the deformed thermal-AdS spacetime, both arising as solutions of an Einstein-dilaton gravity system. We find that the Krylov complexity associated with a massive particle exhibits qualitatively distinct behavior in these two backgrounds when analyzed in the Einstein frame. In the deformed AdS-soliton geometry, the complexity undergoes periodic oscillations, with both the oscillation period and amplitude depending on the parameters of the model. In contrast, in the deformed thermal-AdS geometry, the complexity grows exponentially at late times and does not display oscillatory behavior. We then investigate string dynamics in the string frame and find that the Krylov complexity exhibits oscillatory behavior in both confining backgrounds. This behavior is traced to the emergence of an additional turning point in the deep infrared of the string-frame geometry. Motivated by this observation, we further analyze massive-particle dynamics in the string frame, where we find qualitatively similar behavior in the two confining backgrounds. Our results demonstrate that the Krylov complexity of confined holographic systems depends sensitively on the choice of probe and frame, while also revealing a closer correspondence between the two confining geometries in the string-frame description.

This paper presents a data-driven approach to lossless and lossy source compression using polar codes. Classical polar source coding achieves fundamental limits with low complexity for binary memoryless sources. However, for unknown q-ary sources with memory, successive-cancellation (SC) decoding requires an explicit source model and can be computationally prohibitive. We present analytical SC recursions and show that exact implementations scale quadratically with alphabet size and cubically with state-space size. To overcome these limitations, we develop neural polar decoders trained directly from data to approximate conditional distributions of synthetic polar coordinates without requiring an explicit source model. These learned distributions enable estimation of entropy rates, mutual information, and rate-distortion functions, and support explicit polar compression schemes. For lossless compression, we identify high-entropy polarized coordinates and reconstruct the remaining coordinates using the learned SC recursion. For lossy compression, we combine neural polar decoders with a neural test channel to estimate and optimize the mutual information-distortion tradeoff and construct an explicit lossy polar code. We also extend the framework to Wyner-Ziv compression with decoder side information by learning conditional polarized distributions and a reconstruction mapping. Experiments on memoryless sources, sources with memory, and real genomic data show that the learned decoders closely match analytical SC decoders when available and remain applicable when conventional methods are computationally infeasible or the source model is unavailable.

Cross-view geo-localization remains challenging due to drastic appearance variations and geometric distortions caused by viewpoint changes. Existing methods primarily rely on discriminative feature learning or explicit geometric alignment, yet often overlook an important observation: humans tend to match scenes by integrating the spatial context of multiple landmarks rather than relying solely on isolated local visual cues. Inspired by this, we propose a Spatial Context Modeling (SCM) module, which traverses feature maps along four orthogonal directions and models interactions among the resulting directional representations at each spatial position. By aggregating complementary directional observations, SCM constructs richer scene layout representations. Since reliable spatial context depends on robust visual features, we introduce a High-Frequency Information Guidance (HFIG) module that extracts stable structural cues from the frequency domain. By emphasizing edges and contours that are less sensitive to appearance variations, HFIG encourages the model to learn more robust representations. Extensive experiments demonstrate that our method achieves competitive performance on standard cross-view geo-localization benchmarks while exhibiting strong robustness under more challenging scenarios with unknown orientations and limited fields of view (FoVs).

Interferometric Synthetic Aperture Radar (InSAR) offers a low-cost, wide-area solution for near continuous infrastructure monitoring. However, translating InSAR observations into automated anomaly warnings remains challenging because displacements are relative, affected by uncertainty, and acquired along line of sight (LOS). We introduced a probabilistic warning framework that accounts for these factors. LOS displacements were modelled through a Gaussian distribution. A limit state function was defined to describe the displacement exceedance, and the time-dependent probability of exceedance was evaluated. Instead of a fixed threshold, warnings were identified through abrupt increases in exceedance probability. The framework was validated using three case studies of quay walls in Amsterdam, providing timely anomaly warnings and issued no warnings for the non-collapse case. Results demonstrate the potential of a probabilistic interpretation of InSAR time series for deformation anomaly warning.

We continue the systematic study initiated in arXiv:2602.05185 of the relationship between the spectral theory and descriptive combinatorics of bounded-degree Borel pmp graphs, particularly in the non-regular setting. We first adapt a classical result of Nikiforov to give a new spectral lower bound on the approximate measurable chromatic number. For certain non-regular graphs, this bound improves on the approximate measurable version of Hoffman's classical bound established in arXiv:2602.05185. Next, we strengthen a characterization in arXiv:2602.05185 of approximate measurable bipartiteness in terms of the spectrum of the adjacency operator by generalizing to the case of non-regular graphs. Finally, we introduce the measurable domination number and adapt several classical results of Lu, Liu, and Tian to give a bound on the spectral gap of the Laplacian operator in terms of the measurable domination number.

Recent speech LLMs can leverage rich paralinguistic cues, enabling more complex and personalized interactions. However, little work investigates how this sensitivity can lead to stereotyping, and existing evaluations largely measure demographic disparities without distinguishing beneficial personalization from stereotypical behavior. We introduce BASIS-Bench, a benchmark designed to disentangle these two aspects through three axes: (1) demographic robustness, measuring disparities in content-based tasks across speakers and demographic classification capabilities; (2) stereotypical bias, measuring whether perceived demographic cues trigger unprompted stereotypical behavior; and (3) personalization, measuring whether models can tailor responses to demographic characteristics when explicitly requested. We evaluate eight recent speech LLMs and find that, despite often recognizing demographic cues, most fail to translate them into appropriate personalization. Explicit demographic labels improve personalization but also amplify stereotypical associations already present in the textual backbones. These findings highlight the need to train speech LLMs not only to perceive demographic cues, but to learn when they should shape their responses.

Text-guided long-term human motion generation is essential for applications such as continuously operating digital avatars. Despite recent progress on short clips, existing models struggle with multi-segment instructions that involve anaphora, where constraints established in earlier segments must be preserved over time. In this paper, we introduce a novel task of long-term motion generation from such anaphoric compositions. To mitigate this, we present ELMA, an episodic long-term motion dataset with dense segment-level annotations that preserve cross-segment dependencies. Built via a fully automated collection and filtering pipeline, ELMA extracts high-quality, continuous 30-second clips from in-the-wild videos, capturing the episodic narratives necessary for long-range state modeling. Leveraging this dataset, we fine-tune state-of-the-art motion generation models to incorporate long-range context. Extensive experiments reveal fundamental shortcomings in current models when handling context-dependent instructions. We demonstrate that ELMA enables significant improvements in both global physical realism and semantic alignment, setting a robust new baseline for long-term motion synthesis.

Every evaluation run of a vision-language model (VLM) already produces per-question artifacts (predictions, judged correctness, metadata) that leaderboards reduce to a single score and then discard. We reuse those artifacts to audit the benchmark itself, and add an audit layer to VLMEvalKit: six detectors that run as post-processing over saved outputs, plus one additional text-only rerun with visual inputs removed, emitting a per-question report. The layer reports per-question findings together with aggregate audit statistics; for the headline quantities, it attaches permutation-null excess where applicable, interval estimates for proportions, and sensitivity to the model pool. Auditing MMStar, a benchmark curated specifically so that the image is indispensable, with three models, we find zero aggregate accuracy gain from the image on 20.2% of its questions. An item-matched permutation null accounts for 17.0%, leaving a +3.2 pp excess (corrected permutation p = 0.001). This excess is concentrated in the mathematics and science categories and is absent from coarse perception, a localization consistent with knowledge substituting for visual evidence; confirming that mechanism would require item-level review. A second detector flags 134 questions on which every model that answered in parseable form picked the same non-gold option, and these candidates peak in the perception categories, whereas the zero-gain excess is largest in mathematics and science & technology. Replacing the LLM judge with exact string matching changes no conclusion, and every scoring discrepancy between the two traces to one model whose free-form answers a parser cannot read. On a binary yes/no benchmark the detectors measurably fall out of calibration, a scope boundary that we measure and report. The audit layer, the prediction artifacts and the generated reports accompany this submission.

Pretrained diffusion Transformers provide powerful generative priors for image restoration, yet adapting them to structure-sensitive tasks remains challenging. Existing methods mainly rely on dense low-resolution features as conditions, which often entangle salient objects with dominant backgrounds and provide limited abstraction for recurring structures across scales and samples. We propose MOSAIC, an object-centric representation learning framework that learns compact structural conditions for generative model adaptation. MOSAIC organizes degraded observations into structural slots that capture complementary object-level and layout-level evidence, integrates them across resolutions, and retrieves recurring priors from a shared prototype memory to complement incomplete image-specific information. The resulting representations are injected into selected layers of a frozen diffusion Transformer through lightweight residual modulation, preserving its pretrained generative prior. We instantiate MOSAIC for remote sensing image super-resolution, where small objects, repetitive structures, and large-scale variation provide a challenging testbed. Experiments on UCMerced, AID, and RSSCN7 show consistent PSNR improvements across $\times 2$ and $\times 4$ settings and favorable LPIPS results at $\times 4$. Qualitative results further demonstrate improved preservation of small objects, structural boundaries, and repetitive spatial patterns.

These are notes to accompany my public lecture at the International Congress of Mathematicians, in Philadelphia in July, 2026. The goal is to discuss some developments at the interface of AI and mathematics in the context of the long conversation of mathematics.

Proteinoid microspheres are electrically active assemblies of thermally polymerised amino acids that exhibit spontaneous oscillations, spike-like events, stimulus-dependent responses, adaptation and collective dynamics. We formulate these observations as an applied-mathematical problem and develop a unified dynamical framework for information processing in proteinoid networks. Individual microspheres are represented by nonlinear excitable or oscillatory systems, whereas interactions are described by weighted adaptive graphs and, in the spatial limit, reaction–diffusion dynamics. The framework combines signal propagation, attenuation, fading memory, adaptive coupling, synchronisation, information transfer, reservoir readout, robustness and energetic constraints. We define a task-relative proteinoid intelligence functional from normalised measures of stimulus information, memory, adaptation, directed information transfer, task performance and robustness, penalised by energetic and structural costs. Analytical results establish a joint-response information bound, an upper bound on linear memory for stable linear networks, and existence of an optimal admissible coupling matrix under compact constraints. Dimensionless groups identify the relative time scales and coupling regimes governing the problem in nonlinear and adaptive network dynamics.

We study a stationary ergodic mean-field game of scalar type where the representative player controls a diffusion through two-sided singular controls exerted only at the jump times of an independent Poisson process. For each mean-field parameter, we solve the novel constrained ergodic singular control problem, proving that the optimal policy is of threshold type: the diffusion is reset at Poisson arrival times to the nearest boundary point of an interval. Our explicit probabilistic derivation of the stationary distributions induced by Poissonian threshold singular controls is a key contribution of independent interest. This distribution is used to construct the mean-field fixed-point map. We prove existence and uniqueness of the stationary mean-field equilibrium by combining the stationary density with the monotonicity and continuity of the optimal thresholds in the mean-field parameter. The model provides a tractable framework for a case study of partially reversible investment with singular adjustments under exogenous intervention constraints.

This paper studies semi-static variance-optimal hedging of variance swaps in the rough Heston model under a risk-neutral measure. We combine dynamic trading in the underlying asset with static positions in a finite basket of European options, with the aim of minimizing the variance of the residual hedging error. Exploiting the Markovian lift provided by the forward variance curve, the Fourier representations of the claims and the Laplace transform characterization of the log-price, we derive semi-explicit formulas for the optimal strategies and the hedging error. We then study the optimal claim selection problem, investigating numerically how the choice of static instruments depends on the Hurst index. Under standard parametrization, we discover that "three options are roughly enough", i.e. adding three static vanilla options reduces the hedging error by more than 95% relative to the purely dynamic hedge for all considered roughness regimes H= 0.1, 0.3, 0.5.

Electrical transport in non-centrosymmetric materials exhibits a nonlinear conductivity tensor component that generates second-harmonic voltages in response to applied electric fields. Harnessing this effect is essential for developing zero-threshold electromagnetic energy harvesters and broadband frequency upconverters, both of which require maximizing the nonlinear responsivity. Here, we demonstrate that inhomogeneously strained macroscopic slabs of the topological insulator Bi$_2$Se$_3$ achieve a record-high nonlinear responsivity of $10^4\,\mu$m/V: a six orders of magnitude boost compared to its thin-film counterparts. We attribute this giant enhancement to a classical geometric nonlinear transport effect, which is driven by complex strain gradients within the bulk material. Notably, a similar geometric mechanism known as geometric nonlinear Hall was previously observed only in microscale-patterned structures. Our findings establish macroscopic strain engineering as a powerful route to enhance nonlinear transport, with immediate relevance to a broad class of layered systems, including transition metal dichalcogenides and moiré heterostructures.

3DGS-MCMC has replaced the gradient-driven density control of 3D Gaussian Splatting with opacity-based sampling and relocation, and is now the de facto standard for prior-free densification under a fixed primitive budget. Because opacity stays high where the scene is already well reconstructed, this sampling sends most new primitives to the foreground and leaves the background under-reconstructed. At low budgets, prior-based methods such as ConeGS and EDGS outperform it, at the cost of a pre-trained radiance field or dense image matches and a separate initialization stage. We argue for a comeback of error-driven densification within the fixed-budget MCMC framework. Our confidence-aware densification keeps the fixed budget and gradual growth of 3DGS-MCMC, but places primitives by the image error instead of the opacity. New primitives are drawn mostly where screen-space gradients are large. We favor primitives with a low learned confidence, which marks regions the reconstruction still explains poorly, and relocate the primitives that contribute least to the rendered images to these places. Averaged over 24 scenes, our method outperforms 3DGS-MCMC in PSNR, SSIM and LPIPS at every budget from 100k to 2M primitives. At 100k, without a prior or an initialization stage, it recovers 0.84dB of the 1.05dB PSNR by which ConeGS leads 3DGS-MCMC, and from 500k on, it has the highest PSNR and SSIM of all fixed-budget methods we compare with, including ConeGS and EDGS. While inherently prior-free, our densification can also exploit priors: from the ConeGS or EDGS initialization, it matches ConeGS in PSNR and SSIM at 100k and is best in all three metrics at 500k.

Spherical harmonics have been studied extensively and are used in many fields of application. We consider the probably earliest application of spherical harmonics, namely for a representation of the solution of the Laplace equation on the $d$-dimensional unit sphere where the boundary data are represented in a spherical harmonics basis. We consider general $d \geq 2$. For the solution $u$ of the Laplace equation the fundamental maximum principle holds. If one approximates the boundary data in the finite dimensional space spanned by all spherical harmonics of degree at most $N$, the resulting discrete solution, denoted by $u_N$, does in general not satisfy the maximum principle. In this paper we derive sharp estimates for $r_N^{\rm max}$ such that the maximum principle holds for $u_N(x)$ for all $x \in \Bbb{R}^d$ with $\|x\| \leq r_N^{\rm max}$. We show that for $d=3$ one has $r_N^{\rm max} \gtrsim 1- 3 N^{-1} \ln\big( 2^\frac13 N \big) $. Similar estimates are derived for $d \neq 3$. We also study the sharpness of these estimates.

In this paper, we study Hölder regularity of local weak super-solutions to the parabolic equation associated with fractional $p$-Laplacian type operators $$ \partial_t u(t,x)-\text{p.v.}\int_{\R^d}|u(t,y)-u(t,x)|^{p-2}(u(t,y)-u(t,x))J(t;x,y)\,dy=0,\quad (t,x)\in \R\times \R^d, $$ where $\text{p.v.}$ denotes the principal value, $p\in(1,\infty)$ and the kernel $J(t;x,y)$ is comparable (uniformly with respect to $(t;x,y)\in\R\times\R^d\times\R^d$) to the fractional $p$-Laplacian kernel $|x-y|^{-d-sp}$ with $s\in(0,1)$. Our contribution extends the fundamental work of Kassmann and Weidner to the nonlinear case $p\ne 2$. In particular, we provide an explicit nonlocal parabolic tail condition in terms of an $L^{1+\varepsilon}$-norm in the time variable (for a suitable $\varepsilon>0$) for all $p\in(1,\infty)$, under which Hölder regularity holds. Our proof is based on the method of expansion of positivity, which is the key ingredient in the reduction-of-oscillation argument.

In one dimension, Anderson localization by a disordered potential sets in at any strength, whereas localization by a quasiperiodic potential in the Aubry-André model occurs through a transition at a critical strength. Disordered photonic time crystals exhibit a temporal counterpart of this Anderson localization, in which light, instead of decaying in space, stops propagating and grows in time. Whether a counterpart of the Aubry-André transition exists in photonic time quasicrystals remains an open question. Here we show that it does, and that the transition occurs at mobility edges in momentum rather than in energy. These edges arise even under impulsive modulation, where the field obeys the self-dual almost-Mathieu equation exactly, and for general analytic modulations Avila's global theory reveals the condition under which they form. The Aubry-André transition thus extends from spatial lattices to the time domain, where it sorts light by wave number into components that propagate and components that stop and grow.

This paper presents the first experimental validation of InteRFeX, a non-uniform receive only (passive) array located at the Nova Systems Space Precinct in Peterborough, Australia, designed for space domain awareness applications. It operates over a frequency range of 70 to 300 MHz and is capable of functioning in a range of observational modes, including as a coherent passive bistatic radar for space surveillance, which is the focus of this work. InteRFeX exploits commercial broadcast transmissions as illuminators of opportunity, combining cross-ambiguity function processing for bistatic range and range-rate retrieval with MUSIC-based direction-of-arrival (DoA) estimation for angular localization. The International Space Station (ISS) serves as the experimental target, with measurements evaluated against Two-Line Element (TLE) orbit predictions. Taking advantage of the dual-polarized array, all four reference–surveillance polarization combinations are evaluated, revealing differences in detection rate and mean signal-to-noise ratio (SNR) over the observation pass, with bistatic-range RMSEs of approximately 1 km relative to the TLE-derived reference. Independently, the MUSIC-based DoA estimates exhibit a mean angular separation of approximately $0.45^\circ$ from the TLE-derived reference directions. The angular deviations are further decomposed into along-track and cross-track components, enabling a more detailed characterization of the DoA offsets relative to the TLE-derived reference trajectory. The processing framework also includes a first-order bistatic link-budget analysis to estimate the expected SNR over the observation geometry. These results demonstrate the feasibility of passive-radar space domain awareness using radio-interferometric array technology and establish the proposed signal-processing pipeline as a basis for a dedicated coherent passive-radar mode within InteRFeX.

When a language model is distilled from a teacher that shares its base parameters, the student can inherit behavioural traits of the teacher—including misalignment—even from data that is semantically unrelated to the trait (Cloud et al., 2026). All existing defences require knowing the trait. We remove this requirement and prove that a subliminally transferred trait can be recovered from the parameter updates alone, without supervision, by exploiting a single asymmetry: the trait is expressed consistently across diverse datasets generated by the teacher, whereas task-specific and shared capabilities vary. The resulting estimator returns a weight-space direction that can be amplified to discover and interpret the trait or projected out to suppress it. Applied to the subliminal-learning benchmarks of (Cloud et al., 2026), our method recovers the transmitted animal-preference traits without any trait labels and suppresses their expression with almost no impact to task performance.

Open-set visual grounding in remote sensing requires models to determine not only where a queried object is located, but also whether the image provides sufficient evidence for the query at all. Existing closed-set grounding models, however, tend to return plausible boxes even for absent objects, blurring localization confidence with genuine Visual Support. We introduce AnchorProbe-Distill (APD), a teacher-student framework that recasts open-set grounding as Visual Support learning. APD builds on the insight that supported queries should induce coherent spatial anchors, whereas unsupported or mismatched queries tend to produce unstable or misleading localization patterns. APD-T therefore uses the Original Query as a Reference Anchor to interpret query perturbations: Semantic-Preserving Queries retain the annotated target, Near-Category Ambiguous Queries are resolved according to whether they form a reliable alternative anchor or collapse onto the Reference Anchor, and Far-Category Counterfactual Queries provide rejection supervision. This reference-aware reasoning is distilled into APD-S, enabling unified localization and rejection from a single image–query pair. Experiments show that APD enables the resulting model to reject absent targets while also improving its localization of present targets.

Long-horizon embodied agents must maintain task-relevant information, coordinate heterogeneous robots, and adapt their decisions as execution unfolds. Existing benchmarks investigate dynamic task execution and embodied multi-agent coordination, but provide limited evaluation of their intersection. We introduce MAGMA-Bench, an architecture-agnostic benchmark for persistent task reasoning in dynamic multi-robot environments. MAGMA-Bench evaluates agents across increasing task horizons and controlled online perturbations, including execution failures, task interruptions, and mission updates, with scenarios requiring coordination across robots with heterogeneous capabilities. It uses a structured skill-level interface to separate task-level reasoning from perception and low-level control. We evaluate locally deployable open-weight planners, multi-agent state-tracking strategies, and frontier models. Even the strongest evaluated models fail on a substantial fraction of clean episodes, and their success rates decrease further under online perturbations. Supervised adaptation greatly improves a small model, but performance remains substantially lower on longer and multi-robot missions. We release the benchmark, 261,646 task-level training examples, and an architecture-agnostic expert-trace generation pipeline.

Solidification is expected to suppress fingering by removing mobile liquid. Here we report an unexpected re-emergence of fingering in impacting molten-tin drops: cooling first weakens peripheral fingers, but stronger undercooling restores them. At weak undercooling, fingers originate from a decelerating liquid rim and solidification reduces the effective acceleration that drives Rayleigh–Taylor-like amplification. At strong undercooling, solidification structures develop while liquid is still spreading, creating lateral mobility contrasts that redirect the residual flow. Comparison between the kinematically estimated solidification time and the experimentally measured fingering-onset and growth-termination times reveals a reversal in temporal ordering across the temperature range. A physics-based reduced-order model combines solidification-modified rim deceleration with mobility-gradient growth, captures the characteristic onset dynamics and accounts for the final finger length within the same physical framework.These findings establish solidification as an active means of regulating interfacial flow and morphology, with broad implications spanning metal-based additive manufacturing and debris mitigation in semiconducting industry.