Papers

We study minimal sets of torus homeomorphisms admitting an irrational circle factor whose fibres are thin essential annular continua. For totally irrational pseudo-rotations and homeomorphisms in a nontrivial Dehn-twist class, we prove uniqueness of the minimal set when the fibres are Jordan curves on a residual set of base parameters. The same conclusion holds if the fibre cores are Jordan curves, or if the fibres are locally connected, on a nonmeagre set of parameters. The residual hypothesis cannot be replaced by a full-measure hypothesis, even under area preservation and topological transitivity. For every totally irrational rotation vector, we construct such a map with Jordan-curve fibres almost everywhere and uncountably many pairwise disjoint uniquely ergodic minimal Cantor sets. We also construct examples in every nontrivial Dehn-twist class, with prescribed irrational vertical rotation number and bounded deviations. In both families, the Jordan-curve parameters form a meagre set of full Lebesgue measure.

Two transformative classes of AI systems are reshaping how organizations operate: digital AI, which reasons over enterprise knowledge to power chatbots and agent workflows; and physical AI, which learns to control robots and autonomous systems from video, gameplay, and sensor telemetry. Both face the same foundational bottleneck: raw knowledge at scale, spanning heterogeneous modalities, locked in private corpora that existing AI infrastructure cannot access reliably or efficiently. We propose Universal Knowledge Perception (UniK) as a common platform for both classes, covering the full knowledge lifecycle (ingestion, enrichment, indexing, retrieval, and continuous evaluation) across modalities from rich text and video to molecular data and sensor telemetry. We present UniK, built on Polymath Retrieval (multi-index fusion over automatically enriched indices) with no task-specific fine-tuning. Across five digital AI domains (medical literature, open-domain QA, chemistry, legal video proceedings, and government open data) UniK combined with an open-source 70-billion-parameter model consistently matches or outperforms frontier proprietary LLMs that are orders of magnitude larger: 76% RAG accuracy on government data versus 47% for GPT-5; 77.9% on medical QA without fine-tuning; topping all open-source chemistry pipelines. We show that the same infrastructure directly addresses the data curation, indexing, and retrieval challenges facing physical AI world model training, where the knowledge problem is harder but structurally identical.

We develop exponential family synthetic controls (EFSC), a distributional version of synthetic controls for a panel of datasets. Each cell of the panel corresponds to a dataset drawn from an exponential family whose natural parameters factorize probabilistically across units and times. We estimate the latent factors using black-box variational inference. This replaces the usual weighted-average view of synthetic controls with a flexible probabilistic model that operates on full distributions. We propose causal estimands based on divergences between pre- and post-intervention distributions induced by the posterior of the natural parameters, together with distributional placebo tests to support causal inference and assess the significance of the estimated effects. We validate the proposed framework on synthetic and real data. Across a variety of exponential-family distributions, EFSC accurately recovers causal effects induced by exponential tilts, together with the corresponding divergences between treated and counterfactual distributions. The framework also captures effects induced by structural perturbations of the latent factors and by heavy-tailed noise contamination. Finally, we apply EFSC to study the expansion of Medicaid under the Affordable Care Act (ACA) and its impact on the distribution of health insurance coverage across U.S. states. Code is available at https://github.com/blei-lab/efsc.

The sooner we receive information, and the more accurate it is, the better planning decisions we can make. Every day, prediction markets let anyone bet on tomorrow's high temperature in cities around the world, creating a market-implied forecast built on dispersed information. We use the past five years of market data from the Kalshi exchange for seven American cities to extract, hour by hour, the market-implied forecast. We use this forecast as a measuring instrument to see how much information about the temperature the market makes public before the public forecasting system does. We race it against the leading American and European weather forecasts. In six of the seven cities we study, the market beats the most accurate single public forecast, the National Blend of Models (NBM). Aggregating every city-day, at the end of the market's first hour of trading it beats the best single public product by about 10 percent in root-mean-square error, and holds its lead through the day, overnight, and into the target day. Looking at how the forecasts move over time, we find the National Blend travels four times further toward the market between its postings than the market travels toward the NBM. The market does not react to new weather forecast updates; instead, the forecast slowly publishes information that the market had already shared publicly.

Humanoid robots are expected to perform diverse human-level tasks in daily environments, many of which require precise regulation of interaction forces. While recent vision-language-action (VLA) models have shown promise for semantic planning and visuomotor control, existing humanoid systems primarily represent actions through geometric motion goals and rely on whole-body controllers focused on motion tracking, with limited explicit reasoning or control of interaction forces. This limitation is particularly relevant in contact-rich tasks, where geometrically similar motions may require different force regimes depending on the task context and where visual observations may become unreliable after contact. In this work, we present Opt2VLA, a force-aware VLA framework that introduces explicit force commands at the VLA-to-control interface for humanoid whole-body manipulation. A single multi-task VLA policy jointly predicts both geometric motion goals and continuous contact-force references, which are tracked by task-specific reinforcement learning (RL)-based whole-body controllers. To provide scalable and physically grounded supervision, we generate dynamically feasible and contact-consistent training data via whole-body trajectory optimization (TO) with explicit force references. We evaluate Opt2VLA on three contact-rich humanoid tasks and show that explicit force conditioning enables more accurate and consistent force regulation than motion-only control, while physically grounded torque supervision from TO further improves force tracking accuracy and stability. Closed-loop evaluations further demonstrate language-conditioned force modulation with Opt2VLA in simulation and on humanoid hardware.

Diffusion models are increasingly adapted from generation to conditional prediction, where a conditioning signal is combined with an evolving noisy representation of the target. In fully supervised segmentation, however, the conditioning image can already support direct target prediction, so endpoint performance alone establishes neither reliance on the added diffusion state nor a deterministic advantage over image-only prediction. For state reliance, we disrupt target-derived state content or correct image-state pairing during retraining of twelve published methods across three datasets, with ten matched seeds per setting. All 40 original-method comparisons whose evaluated-mask routes remained downstream of noised-quantity reconstruction exhibited state reliance, whereas all 30 comparisons with a segmentation-supervised bypass preserved reference performance. Rerouting five originally bypass-capable methods by forcing segmentation supervision through noise-to-mask reconstruction converted all 30 corresponding comparisons from preserved performance to state reliance. For deterministic utility, matched image-only counterparts achieved similar or better performance in 28 of 35 settings overall, including 16 of 20 whose native methods relied on both audited state properties. These results identify supervision path as a determinant of state reliance in the audited methods. Separately, matched image-only counterparts show that diffusion-specific computation often provides no deterministic endpoint advantage, including in methods that rely on the audited state properties. More generally, when conditioning already supports strong target prediction, diffusion-specific claims require additional evidence that the added state is used and that diffusion-specific computation improves the claimed capability beyond a matched condition-only counterpart.

LLMs can generate fluent descriptions from tables, but their outputs may remain logically unsupported by the structured data. We introduce STAT-TO-TEXT, a controlled task in which LLMs generate quantified natural language inferences from statistical tables using quantified constructions such as all, some, no, and most. To evaluate these inferences, we use an LLM generated Python checker code which when executed verifies the corresponding truth conditions against the table. We compare four open-weight LLMs across model families and scales, evaluating faithfulness, logical accuracy, table coverage, and diversity. Our results show that model scale and family matter, with the largest model (GPT-OSS-120B) consistently producing the most faithful inferences without sacrificing greater table coverage and quantifier diversity, as opposed to smaller models. These findings are supported by human annotation, which shows that the automated checker closely aligns with human judgments.

We investigate satellite survival through gas redistribution in a dense circumplanetary disk with a low dimensionless viscosity parameter $\alpha \sim 10^{-6}$. The model combines modal Lindblad excitation, launch-dependent shock deposition, 3D effects, and an instantaneous Rayleigh adjustment that conserves angular momentum and suppresses sharp density gradients. An isolated Ganymede-mass satellite depletes the disk outside its orbit and stalls under a calibrated three-dimensional Lindblad torque. This behavior is consistent with the non-feedback branch of Rafikov's stalling criterion. The inward migration stalls near 15 Jupiter radii ($R_J$) when the gas depletion exterior to the satellite's orbit reduces the outer torque by the amount required to balance the torque of the undepleted inner disk, even when we adopt a transport prescription that begins smoothing density gradients halfway to Rayleigh marginality. Likewise, two Callisto masses form an extended depleted region and stall in nearly steady orbits before a late close encounter; however, a self-consistent disk response to satellite eccentricity remains to be modeled. A simulation of a Ganymede-mass satellite adds a specified source of unsaturated local angular momentum deposition by buoyancy torques, reducing the late radial oscillations indirectly caused by non-local shock deposition. Lastly, we redistribute gas while conserving angular momentum to proactively inhibit Rossby-wave unstable pressure bumps at the gap edges. We find that this approach preserves gap clearing and strong migration suppression for Ganymede and the two Callisto masses. In the pressure-adjusted run, the two Callisto masses are captured in a 7:5 resonance and retain eccentricities below 0.06.

Adapting a construction of Kurihara in the setting of Drinfeld modular forms, we define Poincaré series on the Drinfeld half-plane $\Omega$. These series are built from products of meromorphic $1$-forms that are naturally associated to geodesics on the Bruhat-Tits tree. We establish convergence under a finiteness condition on the geodesics, verify this condition in several cases, and give sufficient conditions for the resulting cusp forms to be nonzero. For the principal congruence subgroup $\Gamma(\mathfrak{n})$ of $GL_2(\mathbb{F}_q[T])$, we construct explicit linearly independent families of Poincaré series by lifting certain $k$-forms from the components of the analytic reduction of $\Gamma(\mathfrak{n})\backslash\Omega$. We formulate conjectures on the vanishing orders at cusps, and we prove the first of them for an explicit family of Poincaré series by computing the corresponding expansions at the cusps; as an application, we obtain the Drinfeld modular forms $h$ and $\Delta$ as Poincaré series (up to a sign). Finally, for cocompact groups attached to quaternion algebras over $\mathbb{F}_q(T)$ that split at $\infty$, we show that the Poincaré series span the whole space of modular forms of given weight and type.

Whether an initially crack-free heterostructure fails at its interface or within an adjoining phase is controlled by the relative cohesion of competing atomic planes, but how interfacial chemistry, crystallographic orientation, and intermixing reshape this competition remains unclear. Here, we combine density functional theory (DFT) with a fine-tuned atomistic foundation model to resolve tensile fracture in coherent diamond/cubic boron nitride (cBN) heterostructures. The resulting potential reproduces independent DFT tensile responses, including an unseen (001) interface orientation. Interfacial termination, orientation, and diffusion-induced intermixing jointly determine fracture resistance and fracture-plane selection. C-N-bonded (111) and C-B-bonded (001) remain interface-controlled throughout the investigated intermixing range, whereas pristine C-B-bonded (111) fractures at a neighboring B-N plane inside cBN because the interface is more strongly bound. Increasing the diffusion fraction from 0 to 50.0% causes a nonlinear decrease in fracture strength from 50.3 to 15.8 GPa and drives a bulk-to-interface transition through three regimes: cBN fracture up to 4.86%, configuration-dependent competition between 7.6 and 10.1%, and interfacial fracture at 12.5% and above. Atom-resolved stress fields and DFT separation energetics show that this transition is associated with stress relocation and a reversal in the relative cohesion of competing planes, while electron localization analysis connects the cohesion hierarchy to termination- and orientation-dependent bonding. These results establish an atomistic framework for controlling fracture resistance and fracture pathways in strongly bonded heterostructures.

Let $C$ be a pointed closed convex cone in $\mathbb{R}^n$ with nonempty interior, and let $S^{n-1}$ denote the unit sphere in $\mathbb{R}^n$. The $L_p$ Minkowski problem for $C$-close sets is to determine, for a real number $p$ and a nonzero finite Borel measure $\mu$ defined on $\Omega_{C^\circ}=S^{n-1}\cap \mathrm{int} C^{\circ}$, whether there exists a $C$-close set $\mathds{A}$ such that $\mu$ is the $L_p$ surface area measure of $\mathds{A}$. In this paper, we will solve the problem for $p\in (0,1)$ and for $\mu$ being a nonzero finite Borel measure on $\Omega_{C^\circ}$. Moreover, we establish the continuity of solutions to the $L_p$ Minkowski problem for $p\in [0, 1]$ in several settings.

Monocular colonoscopic 3D reconstruction is important for surgical robotic colonoscopy, but remains challenging due to weak texture, specular reflections, limited view overlap, and non-rigid tissue motion. Conventional multi-view 3D reconstruction methods rely on stable correspondences and approximate rigidity, which are often violated in colonoscopy. Existing endoscopic methods often rely on domain-specific supervision, whereas there are not enough in-vivo labeled data available to adapt geometry foundation models to clinical colonoscopy. We present Colon3R, a cross-domain semi-supervised framework built on pretrained VGGT that transfers coupled camera, depth, and pointmap geometry from labeled phantom and simulated data to unlabeled in-vivo colonoscopy without requiring target-domain geometric annotations. Unlike source-only fine-tuning, which learns only from phantom and simulated data, Colon3R directly exploits unlabeled in-vivo video through teacher-derived cross-view supervision. Our proposed hierarchical quasi-rigid reliability selects reliable supervision at the sequence, directed-pair, and pixel levels, while source-preserving adaptation retains the learned coupled geometry during target-domain adaptation. Extensive experiments demonstrate that our method achieves superior overall performance over state-of-the-art approaches in depth, pointmap, and camera pose estimation. Qualitative comparisons on real in-vivo colonoscopy further show substantially more complete and geometrically consistent reconstructions than competing methods under clinical domain shift. The code is publicly available at https://github.com/vglx/Colon3R.

Preparing interacting quantum systems in low-energy or ground states is a fundamental task in quantum simulation and quantum information processing. In realistic settings, dissipation and active cooling can typically be engineered only on a limited subset of the system. We study the dissipative dynamics of excitation-number conserving quantum systems governed by a GKLS master equation with local jump operators acting on a subset of qubits. We establish sufficient conditions under which such localized dissipation drives the full system to a unique globally attractive zero-excitation state. In particular, we prove that if the Hamiltonian generates excitation transfer described by a graph for which the dissipative subsystem forms a zero forcing set, then the zero-excitation state is the unique globally attractive stationary state. When this state coincides with a ground state of the Hamiltonian, the same mechanism realizes ground-state cooling. Our results provide a graph-theoretic criterion for global state preparation from localized dissipation, which we illustrate using a nearest-neighbor Heisenberg spin chain. For this model, a reduction to the single-excitation sector further yields a scaling estimate with the length of the chain which indicates efficient cooling.

Screening a phone call for fraud needs a trustworthy probability after every caller turn, in milliseconds. Jev-style typed decisions promise exactly that: declared options go in, one calibrated probability per option comes out of a single forward pass, with no generated text. We test an open implementation of this readout, JevLite, on scam-call screening: Qwen3-4B is LoRA-tuned so that the temperature-scaled softmax over two answer-label logits is P(scam). On 41 held-out CallScreenBench scenarios (577 per-turn decisions) a three-seed ensemble reaches AUROC .974 with calibration error .052, non-inferior to an LLM judge (MiniMax-M3) at a pre-registered .02 margin, with no false alarms on legitimate calls, decisions 1.14 turns earlier under the same hang-up rule, and 64.5 ms per decision on one consumer GPU, 4.9x lower than the same backbone fine-tuned to generate its answer. The gain is in the readout and calibration, not accuracy: a fine-tuned ModernBERT encoder is not significantly worse, the recipe was selected with test-set exposure, and all callers are synthetic. We claim no architectural novelty; the contribution is the application and an evaluation reporting calibration, false alarms and decision timing alongside AUROC.

Students increasingly study alongside generative artificial intelligence (AI), yet unguided access to fluent answers invites cognitive offloading, and there is little evidence on which configurations of AI tutoring produce learning. Two design margins are usually bundled together: pedagogical structure (how the tutor teaches) and interaction modality (how students talk to it). We separate them. In a preregistered randomized field experiment in a graduate corporate-finance course of an online MBA, we randomized 86 students between a structured tutor grounded in the course materials and a holdout in which consumer AI remained freely available. Within the tutored arm, each student's channel alternated weekly between voice and text, so the modality effect is identified within student. Structure mattered: tutored students gained 6.63 points more than ability-matched peers (p=.007), and the gain was concentrated in written reasoning, where the share of answers reaching relational quality rose from 8% to 49% in the tutored arm against 8% to 27% in the holdout. Modality did not matter for learning. The instructor's own final, on file for all 86 randomized students, shows the same direction (2.6 points of 100, with no difference on a pre-treatment midterm). Voice nearly doubled conversational interaction and cost 2.8 times as much to deliver, yet it produced weekly mastery statistically equivalent to text, even as students came to prefer it. Pedagogical structure shapes what students practice, and modality shapes how they interact with the tutor. Making an AI more humanlike does not by itself make it more educational.

Scientific agents are mostly evaluated on whether they complete tasks or recover known results; we instead study variation across repeated open-ended campaigns. Sixteen separately initialized sessions of one model-harness configuration received a frozen database of 12,499 metal-organic frameworks, a methane-storage objective, a pinned protocol and a one-week budget. Strategies diverged into four approaches spanning 100–5,000 screened structures, and eight built 2,253 hypothetical structures. Yet the agents recovered the same materials frontier near 200 cm^3/cm^3, and an independent calculation of the database's porous region found its nine best structures all among their reports. Enforced checks on half the agents raised fresh-run reproduction from one of eight to eight of eight but could not detectably improve conclusion validity, because fifteen of sixteen agents selected the same audit-excluded entry, an incomplete structure whose missing anions created artificial pore volume. Replicated agents thus reveal both robust conclusions and common-mode errors from shared inputs.

Long-term cooling of planetary interiors is expected to progressively establish thermally stable stratification in the liquid outer core, yet its influence on dynamo action remains incompletely understood. Here we present three-dimensional numerical simulations of fingering double-diffusive convection-driven dynamos to investigate how progressively strengthening thermally stable stratification, modifies compositional convection driven flows and dynamos. Our results show that dynamo evolution is governed by a competition between Lorentz-force regulation and stratification-induced flow reorganisation. When stratification is weak, the system remains in a strong-field regime characterised by a relatively stable, dipole-dominated magnetic field, despite reduced flow intensity. As thermally stable stratification strengthens, systematic changes in flow morphology emerge, including the development of prograde equatorial zonal flows. Once a critical stratification strength is exceeded, flow reorganisation becomes dominant, leading to an abrupt transition to a weak-field dynamo accompanied by a sharp decline in magnetic energy. In the weak-field regime, magnetic field intensity exhibits enhanced temporal variability and continues to decay as stratification further strengthens, eventually resulting in dynamo cessation even when compositional buoyancy persists. These results indicate that thermally stable stratification may play an important role in regulating planetary dynamos and provide new insight into the long-term magnetic evolution of terrestrial planets.

Previous work on Egyptian Arabic in NLP has focused largely on the prestigious Cairene Egyptian Arabic (CEA) dialect, resulting in a lack of representation for the less prestigious Sa'idi Egyptian Arabic (SEA) dialect both in LLM and resource development. Does this lack of representation influence an LLM's view of the acceptability of SEA (upstream), and does an upstream bias against SEA lead to worse performance (downstream)? We investigate the upstream effect of SEA dialectal features on LLM preferences in a Targeted Syntactic Evaluation (TSE) task which reveals a significant bias against SEA across multiple LLMs. We then analyze the effect of these same features on downstream model performance on MMLU benchmarks and show that models experience a degradation in performance when presented with SEA. This work highlights the need for further exploration on how sub-dialectal variation impacts language technologies.

Programmers write formal specifications, and LLMs implement them, proving that each implementation matches its spec. Taken to its extreme, this makes specification languages the new programming languages. We argue that an unambiguity constraint is key: in addition to proving that its implementation satisfies the specification, the LLM must also prove that any other implementation satisfying it must produce the same outputs on the same inputs, i.e. that the relation formed by the constraints is deterministic. This leaves the LLM no leeway on program semantics: as with a conventional compiler, the generated code never needs to be read and can be regenerated from the spec at any time. Under this constraint and with a powerful LLM, the difference between a specification language and a programming language becomes essentially meaningless, and the LLM essentially becomes a part of the compiler toolchain. The arrangement doubles as a strong form of AI control: an untrusted model writes the code, yet its work is tightly checked by a verifier. To demonstrate that our LLM-in-the-compiler paradigm is feasible when supported by our unambiguity constraint, we present Djinnlang, a high-level specification language built for this future. A Djinnlang program consists only of specifications — the programmer never writes executable code. In place of a traditional compiler, a symbolic translator lowers each spec to Dafny stubs and proof obligations, and a driver harness orchestrates an LLM that fills in implementations and proofs, all checked by the Dafny verifier. We evaluate our language and implementation on multiple examples and we show that it is self-hosting: an LLM can implement the Djinnlang translator from its specification and the reimplementation can verify itself.

Wafer-scale accelerators promise ultra-low-latency AI inference, but current system stacks still carry an unsustainably high cost premium. The reason is that many current and emerging inference techniques, such as batching and MoE, introduce runtime dynamism that existing wafer-scale systems cannot support efficiently. As a result, they must choose between two unsatisfactory options: accept suboptimal latency, or preserve low latency by restricting dynamic techniques, thereby limiting the models they can support and reducing aggregate throughput. This tradeoff significantly increases the cost of low-latency serving. We present MeshRT, the first wafer-scale system to achieve both ultra-low latency and high throughput for LLM inference. MeshRT achieves this via a novel system architecture, which we call compile-time governance of runtime dynamism. This architecture features new system abstractions and mechanisms that enable MeshRT to compile dynamic events arising from LLM inference directly into per-core schedules, enabling asynchronous and decentralized execution with low runtime overhead. Implemented on a commodity wafer-scale accelerator, MeshRT preserves ultra-low latency while improving throughput by up to 56$\times$ over the state-of-the-art system for wafer-scale accelerators. Against measured single-instance SGLang results on H200, MeshRT achieves 4.5-7.0$\times$ lower latency. Under ideal linear scaling of those GPU measurements to an approximately power-matched H200 cluster, MeshRT achieves 1.7-13.0$\times$ higher decode system throughput in the low-latency regime.

The rapid deployment of generative AI raises the question of whether pervasive cognitive offloading drives a measurable, potentially irreversible decline in unassisted human reasoning. We examine this question with a phenomenological dynamical model based on the Cattell-Horn-Carroll distinction between fluid intelligence ($G_f$) and crystallized intelligence ($G_c$). Starting from the discrete-time Bivariate Latent Change Score formalism used in cognitive-aging research, we derive its continuous-time linear counterpart and introduce a fast third variable representing composite machine-intelligence capability. The machine variable enters the human subsystem through Hill-function modifications of the self-feedback and cross-coupling coefficients. We emphasize that our phenomenological model captures both the positive and negative effects of AI on human cognition. By formalizing the qualitative concepts of positive and negative impacts, we introduce definitions for AI-induced cognitive decline and AI-induced cognitive augmentation. A singular-perturbation reduction, justified via Tikhonov's theorem, collapses the resulting three-dimensional system onto a two-dimensional slow manifold. On this manifold we locate two bifurcations of the equilibrium. In one parameter regime, weakening the contribution of fluid reasoning to crystallized knowledge produces a saddle-node bifurcation that eliminates the stable positive equilibrium. In another, reversing the contribution of crystallized knowledge to fluid reasoning creates opposing feedback; increasing fluid self-feedback then reduces damping and produces a supercritical Hopf bifurcation with a stable periodic orbit. We discuss limitations and future directions, interpret our results as a phenomenological account of a coupled socio-technical system, and state the conditions under which each dynamical regime applies.

We prove the Kung–Traub conjecture: a deterministic stationary root-finding method without memory, using at most $n$ real scalar function or derivative evaluations per iteration, cannot have local order greater than $2^{n-1}$ on every real analytic function with a simple zero. For $n\geq2$, the bound is attained by the methods of Kung and Traub. The local estimate is required at every sufficiently close starting point, with constants that may depend on the function. Evaluation points and derivative orders may be chosen adaptively, and the rules for choosing them and processing the data are unrestricted. The proof uses a localisation property of polynomial Wronskians to obtain a lower bound at each fixed scale. A diagonal construction then gives one entire function, with derivative bounded above and below on the real line, for which every larger order fails. We also obtain a sharper bound when evaluations are made in prescribed groups, and prove the corresponding result for complex scalar evaluations. The results of this paper are also formally verified in Lean.

We study how discrete normal-segment levels control equilibrium Josephson transport between two Kitaev-ladder superconductors. Away from resonance, detuning opens a selective-clamping window: inter-leg hybridization removes the phase dependence of a $0$-favoring low-energy ground-state contribution while retaining a competing $\pi$-favoring contribution, allowing a smooth negative first harmonic even for bulk-topologically trivial leads. At resonance and $\phi=\pi$, an exact collective-clamping identity makes both low-energy ground-state contributions phase independent above a threshold, although individual quasiparticle levels can remain dispersive. Finite-energy quasiparticles then produce a positive residual first harmonic in a controlled sweet-point regime. For fixed $0<\phi<\pi$, helicity mixing instead yields a positive resonant low-energy harmonic in the weak-coupling limit. Exact identities, fourth-order sign rules, and recursive Green-function calculations establish how resonant alignment changes the spectral contributions governing Josephson phase selection.

A recently developed relativistic quantum optics approach for a fast electron beam-optical modes interaction problem (Optica 6, 1524–1534 (2019)) contains suggestion about a smallness of the error induced by replacement $\Psi_{\vec k}\approx\Psi_{\vec k_0}$ for noninteracting free electron Dirac spinors at such wave vector $\vec k$ that $\left|\vec k-\vec k_0 \right| \ll\left|\vec k_0\right|$ with $\vec k_0$ as a peaked wave vector of a focused electron beam. Here, based on quantum information approach we strictly investigated a degree of coincidence of spinors $\Psi_{\vec k}$ and $\Psi_{\vec k_0}$ by calculating fidelity for them. The analytical expression is obtained. It is shown that the fidelity inevitably depends on not only wave vectors $\vec k$ and $\vec k_0$ but also on mutual orientation of $[\vec k_0,\vec k]$ and $\hat{\vec{s}}^{\dagger}\vec{\sigma}\hat{\vec{s}}$ with $\vec{s}$ is a two-component spin unit vector and $\vec{\sigma}$ is a vector of Pauli matrices. This result can be conceived as a chirality-like effect in the fidelity and constraints spin arbitrariness when applying the developed relativistic quantum optics approach to the problems of interest. A geometrical configuration of $\vec k_0$, $\vec k-\vec k_0$, and $\hat{\vec{s}}^{\dag}\vec\sigma\hat{\vec{s}}$ that is optimal in terms of fidelity is established.

In this paper, we study the metric properties of pluriharmonic $\alpha$-Bloch-type mappings $f=h+\overline{g}\in\mathcal{H}(\mathbb{B}^{n},\mathbb{C}^{n})$ on the unit ball $\mathbb{B}^{n}\subset\mathbb{C}^{n}$. By synthesizing local real-part estimates with the subharmonicity of $\log(\vert{} \det Dh(z) \vert{} + \vert{} \det Dg(z) \vert{})$ along hyperbolic geodesics, we establish a globalized non-trivial lower bound across the entire unit ball $\mathbb{B}^{n}$. Using this structural decay estimate, we prove that the invariant weight quantity $D_{f}^{n,\alpha}(z)$ satisfies a global Hölder continuity estimate of order $1/n$ with respect to the Bergman metric $\beta$. Furthermore, we investigate composition operators $C_{\varphi}(f)=f\circ\varphi$ induced by holomorphic self-mappings $\varphi\in\mathcal{A}(\mathbb{B}^{n},\mathbb{B}^{n})$. We establish both sharp sufficient and necessary sampling conditions for $C_{\varphi}$ to be bounded from below on the pluriharmonic $\alpha$-Bloch space $\mathcal{B}_{P(n,\alpha)}$.

Fine-tuned geospatial foundation models (GeoFMs) pretrained on large satellite archives have been shown to improve crop classification accuracy and geographic transferability. However, their operational performance beyond the training distribution remains poorly characterized. We evaluated the out-of-distribution performance of a widely adopted GeoFM [Prithvi-EO-2.0] across 37 events in 12 countries on three continents and validated against regional reference products. Results indicated that the mean overall accuracy (OA) declined from 0.65 in the United States to 0.40 in Europe. Beyond accuracy metrics, we assessed five key aspects of model performance: whether model confidence indicates signal failure, sensitivity to observation windows, the effect of coarsening class schemes, and robustness to both band loss and cloud- and shadow-contamination. Accuracy collapsed when the observation window misaligned with local crop phenology, while deterministic confidence remained high. Expected calibration error increased for seven of eight paired events, and 12-51% of each affected scene was confidently mislabeled at near-zero precision. Monte Carlo dropout entropy registered the shift in all eight, indicating that much of the apparent cross-continent decline reflected phenological misalignment rather than spatial transfer. Two adjustments recovered accuracy without retraining. Consolidating 13 classes into 10, based on the model's dominant confusions, raised the mean OA by 8.4 percentage points. Compressing the window toward near-real-time use preserved accuracy across a 45- to 90-day plateau, peaking near 75 days, though arms tighter than 30 days fell about 0.11 below that plateau. Fine-tuned crop GeoFMs therefore transfer usefully only where observation windows match local growing seasons. We translate these findings into operational guidance for the reliable deployment of the released model.

Let $\mathbf A$ be a totally nonnegative matrix over a real closed non-Archimedean valued field, and suppose that its valuation $A$ is tropically totally nonnegative. Although the valuations of the classical eigenvalues are weakly majorized by the tropical eigenvalues of $A$, equality can fail through cancellation. We give a necessary and sufficient condition for equality. The only obstruction is dominant cancellation in the principal minors that give the essential coefficients of the tropical characteristic polynomial. In other words, equality holds exactly when the classical and tropical Newton polygons agree at the breakpoints determined by the diagonal entries. We describe the exceptional lifts by explicit polynomial equations in the leading coefficients. We also study these equations on each irreducible component of the admissible parameter space. Finally, we give a complete $3\times 3$ criterion and a family that contains both ordinary lifts with spectral equality and exceptional totally nonnegative lifts without it.

Let $\mathbb H^n$ be the $n$-dimensional hyperbolic space, and $\Delta_{\mathbb H^n}$ be the Laplace–Beltrami operator on $\mathbb H^n$. Let $u=u(t,\cdot)$ be the solution to the wave equation $\partial^2_{t}u-\big(\Delta_{\mathbb H^n}+\frac{1}{4}(n-1)^2\operatorname{Id}\big)u=0$ with initial conditions $u(0,x)=f(x)$ and $\partial_tu(0,x)=0$. In this article we show that for a radial function $f$, $2n/(n-1)\leq p<\infty$, $\gamma<1/p$ and $T\geq 0$, there exists a constant $C_p$ independent of $f$ and $T$ such that $$ \left(\int_T^{T+1}\|u(t,\cdot)\|^p_p\mathrm d t\right)^{\frac1p}\leq C_{p,\gamma}\,\mathrm e^{(n-1)\left(\frac12-\frac1p\right)T}\left\|(-\Delta_{\mathbb H^n})^{\frac{n-1}2\left(\frac12-\frac1p\right)-\frac\gamma2}f\right\|_p. $$ We also show that the exponential part $\mathrm e^{(n-1)(1/2-1/p)T}$ of the bound is optimal.

Moving target defense (MTD) against advanced persistent threats (APTs) in industrial control systems (ICS) has well-established game-theoretic formulations, but their practical value hinges on equilibrium computation, which faces two gaps: full-rank value iteration is prohibitively expensive at industrial scale, and the resulting defense strategies admit no certified robustness against adversarial perturbations. We first reveal that the attack and defense influence matrices of ICS dynamics are intrinsically low-rank: APTs infiltrate through a handful of entry points and MTD reconfigures only a few components per cycle. Our theory makes four contributions. First, an augmented gradient matrix certifies that the low-rank structure propagates through the non-smooth Bellman operator of the zero-sum stochastic game, so that every Bellman target lies near a low-dimensional subspace and low-rank truncation incurs an explicit error bound (Lemma 1, Theorem 1). Second, we propose the Dynamical Low-Rank Nash Equilibrium algorithm, named DLR-NE, which augments the rank-r search space each iteration, regularizes the core matrix spectrum, and retracts via truncated SVD, and prove that it converges geometrically to a neighborhood whose error decomposes into five physically interpretable sources (Theorem 2). Third, its per-step cost is O(nr^2), a Theta(n/r^2) speedup over full-rank value iteration (Theorem 3). Fourth, a single weight trades accuracy against a certified sensitivity bound of the induced defense strategy under core-matrix perturbations (Corollary 1). Six experiments on a nonlinear power-system testbed confirm each prediction, with 94% parameter compression at 2.3% utility loss. All experimental data and code are publicly available.

This paper studies decentralized safe path following for multiple quadrotors on intersecting paths, where safety requires both collision avoidance and strict adherence to pre-assigned routes. The proposed controller reformulates transverse feedback linearization as a constrained quadratic program with four equality constraints: two enforce convergence to and strict adherence to the path, and two prescribe the desired speed and heading. Safety is achieved by relaxing only the along-path speed constraint, while the path and heading constraints remain hard. Under the stated assumptions, and for admissible initial conditions, the controller guarantees that all agents converge to and thereafter follow their assigned paths, avoid collisions, and avoid attitude singularities. We evaluate the controller in the Drake physics engine on non-planar intersecting paths and compare it against two nominal-plus-safety-filter cascades. Code and additional results are available at https://gradslab.github.io/safe_multiquad_pf/.