Papers

We prove that the Benjamin-Bona-Mahony equation is almost surely globally well-posed with respect to random Gaussian initial data of negative Sobolev regularity in $H^{s}(\mathbb{T})$ for any $s>-\frac 14$. This result is sharp in view of the mild probabilistic ill-posedness due to Oh-Tzvetkov (2026). This also improves on a previous result of the author which established this only in a logarithmically negative regularity. To break through this logarithmic regularity barrier, we combine the $I$-method with the low-high argument from Bona-Tzvetkov (2007), which motivates a refined first-order expansion for solutions.

The intrinsic carrier concentration of superconducting materials may not be optimal, and different superconducting properties may have distinct optimal doping levels. Here, we show that Ca substitution increases the hole concentration in intrinsically underdoped epitaxial (Y$_{1-x}$Ca$_x$)Ba$_2$Cu$_4$O$_8$ (YCa124) films with $x \leq 0.10$, driving YCa124 toward optimal doping, increasing $T_c$ and $J_c$. At 40 K, 10% Ca doping increases $J_c$ by factors of 2.4 and 10 at 0.03 and 6 T, respectively, compared with the undoped film. The field dependence of $J_c$ follows $J_c \propto B^{-0.5}$, independent of Ca content, indicating that Ca substitution does not alter the dominant pinning mechanism. This field dependence is consistent with pinning by planar Y-125 stacking-fault intergrowths observed by electron microscopy. In addition, Ca substitution slows thermally activated vortex motion (creep) at $T \gtrsim 15$ K, while at lower temperatures the creep rate $S$ shows an unusual decrease with increasing field. Finally, we consider how doping tunes the upper bound on $J_c$, set by the depairing current density $J_d$, and the lower bound on creep, set by the Ginzburg parameter $G_i$. We find positive correlations between $J_c$ and $J_d$, and between $S$ and $G_i$, and compare them with trends across a broad range of superconductors.

We present a traceable instructional module that maps documented learner difficulties in quantum superposition and measurement to explicit learning goals, classroom activities, and assessment evidence. Using the general two-level Hamiltonian as the organizing physics framework, the module implements this mapping through a five-activity classroom sequence and grading rubric targeting four recurrent difficulties: interpreting superposition as physical splitting, confusing a quantum state with its representation or measurement context, mixing theoretical probabilities with finite-sample frequencies, and using inconsistent notation across states, amplitudes, probabilities, and measurement outcomes. The instructional design is organized through a reversible mapping from documented barriers to learning goals, activity responses, and assessment evidence, allowing each assessment item to be traced back to the specific difficulty it is intended to address. The module uses the standard general two-level Hermitian Hamiltonian, represented by a \(2\times2\) matrix, as the physical framework connecting its eigenstates, computational-basis amplitudes, Born probabilities, and sampled outcomes. The contribution is a challenge-targeted instructional design that organizes standard quantum mechanics into a traceable classroom sequence linking documented learner difficulties to learning goals, activities, assessment criteria, and implementation guidance. The mathematical structure uses standard Hamiltonian and measurement conventions, supporting direct incorporation into an undergraduate quantum-mechanics course.

Deep learning classifiers for dermoscopic skin lesions often reach high in-distribution accuracy while quietly relying on spurious background cues such as skin tone, device vignetting, and embedded rulers, rather than on lesion morphology. This undermines robustness and fairness across skin tones. This work asks whether Explainable AI (XAI), typically used only to audit a finished model, can instead be repurposed as an active training signal that corrects this shortcut without sacrificing diagnostic accuracy. We introduce CAMEO (Class Activation Mapped Equitable Overlay), a framework that improves skin-lesion classification by selecting stable model explanations and using them to separate lesions from their backgrounds. It then replaces the background with realistic synthetic skin while keeping the lesion unchanged. On HAM10000 and dark-skin ISIC images, CAMEO maintained accuracy while reducing background-driven errors by nearly four times. It also made the model's attention more consistent when backgrounds changed. Results across multiple tests show that reducing reliance on background information improves robustness, with Fitzpatrick-based backgrounds providing a realistic and interpretable approach. Results show that XAI-guided augmentation can make dermoscopic classifiers measurably more robust and fair at no cost to accuracy. They also clarify that it is the mechanism and not the specific tone palette that matters, and that the lasting contribution of XAI here lies in stability-screened, annotation-free lesion localisation rather than in the robustness number itself.

Decision-only language models return a probability for every answer option instead of generating text, which makes them attractive as survey respondents and as judges. We audit the cultural values of one such model, TypeSafe's JEV, with the Values Survey Module 2013. We asked it the 24 items as 12 matched Saudi and 12 matched American personas and without a persona, in English and Arabic, under eight ways of formulating the request (288,000 answers). JEV's answers were highly repeatable (ICC 0.997), and without a persona they resembled those of its own American personas. When the persona was Saudi rather than American, the answers moved in the direction of the human Saudi-US difference, reproducing 87% of its size in English but 62% in Arabic, with long-term orientation reversed. A language cross shows that the smaller difference in Arabic comes from the language of the items, not from the language of the persona description. Age shifted the profiles about as much as nationality, gender shifted them more for Saudi than for American personas, and JEV was less confident in Arabic and for Saudi personas. These patterns held in every request design, although the model never generates text.

Generative models make molecular crystal structure prediction fast, but their samples still exhibit geometric and packing violations. Physics can be introduced during training, post-training, or inference, yet these choices are rarely compared with the generator and physical signal held fixed. We introduce CrystAF, an all-atom crystal flow-map generation model, and use it with the UMA interatomic potential to systematically study where physics should enter. Post-training learns physical preferences directly into CrystAF, improving molecular validity and crystal packing while leaving sampling unchanged: physics is paid for once during training rather than repeatedly at deployment. In contrast, UMA relaxation is effective at repairing local clashes but makes generation 6–26$\times$ slower, while learning from relaxed targets provides little benefit. These routes are complementary rather than competing. Physics-informed post-training first shifts the generated distribution toward more physically reasonable structures, after which inexpensive inference-time corrections further remove clashes and restore stereochemistry that the generator cannot represent. Importantly, the same post-training strategy also improves the multi-step all-atom Clari-M and rigid-body MolCrystalFlow generators, demonstrating transfer across architectures and representations. Together, our results suggest a simple principle: learn reusable physical alignment into the generator, and reserve inference-time physics for residual constraints that are better corrected than learned.

Let $G$ be a group acting continuously on a compact metric space $X$. This naturally induces an action of $G$ on the space $\mathcal{K}(X)$ of nonempty compact subsets of $X$. In [KS26], Kra and Schmieding define a system $(X,G)$ to be IC-rigid if the union of the supports of the $G$-invariant Borel probability measures on $\mathcal{K}(X)$ is as small as possible. They leave open the question of existence of IC-rigid abelian systems. We show the existence of IC-rigid actions for three classes of abelian groups: mixing rank-one $\mathbb{Z}$-actions, horocycle flows, and certain mixing actions on a Cantor space of $G=\bigoplus_{n=1}^{\infty}G_n$, where $(G_n)_n$ is any sequence of nontrivial finite abelian groups. In the course of proving these results, we introduce the notion of weakly asymptotic pairs and establish its close connection to topological minimal self-joinings.

As black-box machine learning models become increasingly common, extracting interpretations with uncertainty quantification has become a critical challenge. One popular type of interpretation is leave-one-covariate-out (LOCO) feature importance, while prior LOCO inference methods often require data-splitting or model-refitting. A recent ensemble framework, LOCO-MP, addresses these challenges using minipatches that subsample both observations and features, but massive feature subsampling can hurt prediction in high-dimensional sparse settings. Motivated by this limitation, we consider minipatch ensembles with adaptive feature sampling guided by LOCO importance, and propose LOCO-AdaMP, which enables free LOCO inference for the resulting adaptive minipatch ensemble. We show that LOCO-AdaMP yields substantially improved predictive models while retaining asymptotically valid feature importance inference without data-splitting, despite the complex dependence between the adaptive sampling distribution and the LOCO importance statistics. Our analysis relies on a careful leave-two-out perturbation bound for the iteratively updated sampling probabilities together with the stability of LOCO scores induced by observation subsampling. Empirical results on synthetic and real datasets demonstrate advantages of LOCO-AdaMP over existing methods in predictive performance, inferential power, and stability. Overall, LOCO-AdaMP provides a flexible ensemble framework (agnostic to base models) that delivers both strong predictive performance and asymptotically valid, powerful feature importance inference for regression.

Teams of unmanned aerial vehicles (UAVs) deployed for search and monitoring missions frequently operate as partially connected networks, forcing each robot to trade off exploring the environment against relaying information to teammates. This tradeoff is especially acute when robots are semantically heterogeneous: an observation that appears uninformative to the robot that made it may be critical to a teammate with complementary detection capabilities. In this work, we formalize this setting as the heterogeneous mission-aware coverage (HMAC) problem, which couples complete multi-robot coverage of an area with capability-constrained mission-relevant target (MRT) discovery under intermittent communication. We then present DORA, a divergence-oriented data-relay algorithm that drives communication by the value of information to the team rather than by discovery alone. DORA quantifies the mission-relevant divergence between a robot's current information state and its estimate of each teammate's knowledge, capturing mission relevance, discovery novelty, sensor uncertainty, and the age of information. We evaluate DORA in simulation across four environments with differing object densities and spatial structure, and validate it on a physical UAV platform. Our results show that DORA improves MRT resolution delay by up to 74.8% over traditional time-based communication scheduling methods.

We define a class of classes of complete first-order theories, denoted by $\mathfrak{D}_{n\text{-var}}$, using positive consistency-inconsistency configurations and generalized indiscernibles. It contains the classes of stable, simple, NIP, NTP$_1$, NTP$_2$, NATP, NCTP, NBTP, NWP, NGP, and NPM$^{(k)}$ theories. For any dividing line $D\in\mathfrak{D}_{n\text{-var}}$ and any complete first-order theory $T\notin D$, we can always find a formula $\varphi(x,y)$ witnessing $T\notin D$ with an indexed set of parameters such that the set of its instances required to be consistent has a realization whose algebraic dimension over the whole set of parameters is $|x|$. We call statements of this form $n$-variable theorems, as they may be regarded as weak versions of one-variable theorems. Under the appropriate hypotheses on $T$, we prove that $T\in D$ if and only if the corresponding theory belongs to $D$ for (i) $T^{gt}$, (ii) $T_P$, (iii) $T^{ind}$, (iv) $T^G_K$, (v) ACF$_T$, and (vi) any completion of $T^{\bar\delta,nc}_g$. These are, respectively, the theories of generic trivializations, lovely pair expansions, $H$-structure expansions, vector spaces with a dense-codense generic $K$-subspace, algebraically closed fields with a distinguished subfield, and generic non-commutative derivations of algebraically bounded fields. The $n$-variable theorem is essential in proving (i)–(v). We also prove preservation for a special case of Mordell-Lang theories. We extend the framework to a larger class $\mathfrak{D}^h_{n\text{-var}}\supseteq\mathfrak{D}_{n\text{-var}}$, capturing higher-arity dividing lines such as NOP$_k$, NFOP$_k$, and NIP$_k$ for $1<k<\omega$. The $n$-variable theorem and preservation results (ii), (iii), (iv), and (vi) also hold for this larger class, while (i) holds assuming ${\rm acl=dcl}$.

Traditional reinforcement learning (RL) techniques focus on maximizing expected cumulative reward, where each action assumes to take a constant unit of time. However, this assumption does not hold for agentic RL tasks such as machine learning engineering (MLE) agents, where actions involve data loading, feature engineering, and model training that take variable durations. Efficiency matters in modern agentic RL where actions are costly. To address this limitation, we adapt from continuous-time RL and Semi-Markov Decision Process (SMDP) formulation and propose Reward-rate Policy Gradient (RPG), where we focus on optimizing the reward rate – the long-term reward per unit of time. RPG estimates the reward rate from off-policy samples, then charges each action for the time it consumes at that rate. We first conduct theoretical analysis in the bandit setting to establish that RPG approximates the optimal reward rate and empirically demonstrate it outperforms baselines while avoiding enumeration over the policy space, a known issue for an existing method. We then further apply RPG on a small language model (Qwen3.5-4B) with self-improvement loops and empirically show it obtains higher rewards within a fixed time budget than vanilla RL on MLE-Bench and NanoGPT, with a 19.2% and 85.7% margin, respectively. Our method provides a practical solution for optimizing performance under wait time considerations in modern agentic RL tasks, where actions interact with external environments and cost time.

In diseases where clinical guidelines are incomplete, contested, or mutually contradictory, knowledge completeness and dynamic conflict-aware synthesis are two safety-critical properties that standard Retrieval-Augmented Generation systems do not provide. Therefore, we present \sysname, an adaptive retrieval calibration clinical question-answering agent for ME/CFS, a disease where diagnostic frameworks coexist and major guidelines actively contradict each other on treatment. ARCagent contributes three components. First, a 1,706-chunk, 10-source knowledge base with a structured inter-guideline conflict registry spanning all active ME/CFS diagnostic frameworks. Second, a conflict-aware retrieval calibration pipeline that re-ranks retrieved evidence using query-specific focus and conflict signals. Third, a benchmark scored by LLM-as-Judge, avoiding systematic underestimation averaging 10.1 percentage points caused by keyword matching. ARCagent achieves 95.3%, outperforming all base LLMs. Code is available at https://github.com/Yukyin/ARCagent.

An ongoing challenge in sensory neuroscience is to characterize the feature dimensions encoded by cortical populations. Recent approaches probe feature selectivity in a data-driven way, by synthesizing a most-exciting-input (MEI) for a target neural population. While this approach has been successfully applied to human higher visual cortex using fMRI data, generating MEIs for early- and mid-level retinotopic visual areas requires additional modeling constraints due to small receptive field sizes. To address this challenge, we introduce two novel MEI generation frameworks, Receptive Field Diffusion for Visual Exploration (RF-DiVE) and Receptive Field Gradient Optimization (RF-GO). Both methods use a population receptive field (pRF)-constrained voxelwise encoding model; RF-DiVE combines this with a pretrained latent diffusion model, while RF-GO uses regularized gradient ascent. When applied to single voxels in retinotopically defined areas V1-hV4, using data from the Natural Scenes Dataset, we obtain MEIs that exhibit consistent structure within the pRF, suggesting selectivity for local features like contour, color, and texture. We systematically compare MEIs generated by RF-DiVE and RF-GO using two encoding backbones, performing in-silico validation of predicted responses to MEIs using independent encoding models. Across all methods and all visual areas, MEIs elicit higher model-predicted responses than the most activating natural images. We further find that the choice of generation framework and encoding backbone differentially affects MEI properties, including their visual appearance, structural interpretability, and cross-model generalizability. These results offer a new approach for performing data-driven characterization of spatial and feature selectivity across human visual cortex.

Offline reinforcement learning seeks optimal decision rules from previously collected data. In some applications, a decision can be an entire function, such as a fluence map in radiation therapy or a smooth movement trajectory in robotics. In this paper, we study the finite-sample theory for fitted Q-iteration (FQI) with functional actions in a discounted infinite-horizon setting. Three major difficulties arise in this setting: first, the absence of a Lebesgue probability density for functional actions complicates coverage descriptions; second, conventional coverage requirements can be restrictive; and third, the large functional action space makes greedy optimization in FQI challenging. To address these difficulties, we study smoothness-regularized policy search under a critic-relative coverage condition. This condition measures how well logged data distinguish relevant action-value differences without requiring an action density. Our main theorem gives finite-sample guarantees for learned-policy regret relative to the best value within a fixed smooth class of functional-action policies. The results allow trajectory lengths to be either bounded or growing and Q-functions to be fitted by either functional-input kernel ridge regression or adaptive functional neural networks. For a few examples, we can obtain polynomially decaying regret bounds in the number of logged transitions, up to logarithmic factors, with logarithmically many FQI iterations. Numerical experiments show gains of learned functional-action policies over constant-action policies and support our adoption of a critic-relative coverage condition.

Binomial coefficients for multidimensional arrays count occurrences of particular configurations. For the sake of presentation, the emphasis is put on column-binomial coefficients for two-dimensional finite arrays. In this article, we first show that these coefficients can be computed through some Magnus transform. To get structural and combinatorial information on arrays, we then define \((k,\ell)\)-binomial equivalence for finite arrays and, from it, the \((k,\ell)\)-binomial complexity function of an infinite array. Roughly, two finite arrays are \((k,\ell)\)-binomially equivalent when they share the same number of subarrays of size at most $k\times \ell$. We obtain general results on the \((k,\ell)\)-binomial complexity of infinite arrays coding direct products of infinite words. Our main theorem gives an exact formula for the \((k,\ell)\)-binomial complexity of the two-dimensional Thue–Morse array. To that end, we closely examine the action of the bit-wise complement on the \(k\)-binomial equivalence classes of the factors of the Thue–Morse word.

An activation-steering coefficient sets intervention strength, but requesting a particular degree of persona expression requires a behavioral scale. We study persona dosing: controlling a language model through a trait description and a requested mean intensity. PersonaDose specializes a shared, description-conditioned FLAS controller on persona responses, then calibrates its flow time against measured trait expression. Training responses are not paired with requested target intensities. Across Llama-3.1-8B, Qwen3-8B, and Gemma-3-4B, PersonaDose raises core-trait expression at the Persona Vectors coherence floor of 75 by 33.2, 18.3, and 17.8 points over contrastive activation addition. Calibration-selected settings retain an expression advantage on held-out questions, although the coherence floor does not hold for every trait there. Across seven trained traits, calibrated requests yield mean targeting errors of 4.7-6.2 points over 14-22 calibration-reachable targets out of 28 per model. These results separate the behavioral range learned by a controller from the accuracy of requests within that range.

In some randomized trials the primary outcome is costly or slow to measure, while auxiliary variables that predict it are available for everyone. The outcome can then be measured in a probability sample. We study an adaptive design in which the statistician who selects outcomes to measure is blinded to treatment assignment. Outcomes from an initial random sample are used to fit pooled models for the outcome and its residual variance. These set the sampling probabilities for the remaining participants and may be refitted as outcomes accumulate. After unblinding, arm means are estimated by augmented inverse probability weighting. The estimator is unbiased for the complete-data treatment difference for any working models, and a martingale central limit theorem gives Wald intervals under repeated updating. We bound the variance lost by estimating the sampling rule. The bound is linear in the error of the fitted residual variance, quadratic when the optimal probabilities are not truncated, and relates the initial sample size to the learning rate of the models. Relative to designs using treatment assignment, the blinded design loses a term due to unequal residual variances in the two arms and a term due to the conditional treatment effect, which is second order near the null. In simulations, coverage was near nominal. Adaptive sampling was 12% to 34% more efficient than simple random sampling and needed 10% to 26% fewer measured outcomes for the same precision. In a resampling study of an antifungal trial, adaptive sampling reduced the sampling variance by 39%.

An event camera produces an asynchronous stream, but what is visible in that stream depends on how a downstream consumer, such as a model or detector, processes time. The same timestamp change may leave a coarse temporal representation unchanged while changing the response of a model that preserves finer timing. We characterize this dependence as observer-relative stealth. For recorded event streams, retiming an event within its protected accumulation window leaves the accumulated integer tensor exactly unchanged. We use this exact blind space to construct Null, a gradient-guided timestamp-retiming attack, and define SC-ASR_A(tau) to measure attack success while bounding the change visible to observer A. On DVS Gesture at a 10% event budget, Null reaches 81.56 +/- 5.81% ASR on ConvSNN and 98.67 +/- 0.45% on a GRU while preserving the protected tensor exactly. On DailyDVS-200, a protocol-scale Multi-View Fusion Network variant reaches 99.28 +/- 0.11% exact-null ASR, compared with 9.70 +/- 1.06% for its matched control. In a five-attack comparison, Null is the only method with nonzero attack success at exact observer equality, reaching 81.4% on DVS Gesture and 87.35% on DailyDVS-200. We also search the same exact blind space with an independently implemented constrained projected-gradient optimizer, C-PGD. At matched victim-gradient evaluations, C-PGD reaches 84.50 +/- 2.89% ASR on DVS Gesture and 89.55 +/- 4.39% on DailyDVS-200, again with exact protected equality. Perturbations that are exactly hidden from the protected observer become visible under shifted, finer, overlapping, and randomized temporal views. Adding observer constraints reduces the real-valued blind-space fraction from 87.5% to 75.0% to 62.5%, while DVS ConvSNN ASR falls from 74.9% to 61.9% to 37.2%. These results show that stealth is not a property of the perturbation alone.

Wireless time-series generation is useful for emerging applications that will drive the adoption and integration of machine learning tasks within next-generation networks, such as waveform classification in shared spectrum bands and interpretation of the physical world through integrated sensing and communications. Unlike a generic time series, wireless signals have time-frequency duality, where a frequency domain bandwidth constraint implicitly imposes latent structural constraints on the evolution of the time-domain sequence. In this paper, we develop Anchored Latent Flow (ALF), a latent space flow model for label-conditioned signal generation that exploits this duality. Our flow model "reasons'" through a spectrogram, which is a 2-D representation of the signal constructed by applying a windowed Fast Fourier Transform to successive, overlapping signal segments and mapping their frequency-domain power components across time. Specifically, we shape the latent space of the flow model through a training-time auxiliary objective that is supervised by the (latent) spectrogram (i.e., anchoring through the spectrogram). By guiding the flow field to reason through a spectrogram, the generated sequence maintains long-range coherence across time and greatly improves the signal quality at inference. Empirically, ALF exhibits state-of-the-art generation quality and reconstruction error across various signal lengths, waveform classes, signal-to-noise ratio (SNR), and channel conditions, reaching a train on synthetic, test on real (TSTR) accuracy of 84.5%, a 1.9X average memory reduction, and 100X average compute speedup over existing models. Our design further enables downstream tasks, including style transfer and data augmentation, and has broad utility for the wireless community.

Relational in-context learning (ICL) conditions predictions on the labeled support examples and their linked tables, creating a failure mode when the support set contains target-derived features that are unavailable for the query. We formulate this problem as support-set target leakage, distinct from leakage during dataset construction, temporal splitting, or representation learning. Here, the target-derived (leaker) columns are present only in the labeled support set during relational in-context inference, while queries remain clean. We construct 14 synthetic leaker types, corresponding to 20 columns, spanning proxies with different noise levels, coverage, modalities, semantic transparency, and relational distances. We evaluate a frozen relational encoder with an ICL head on held-out RelBench databases and use Integrated Gradients (IG) to rank and remove suspicious columns. Our results show that the effect of support-set leakage varies across tasks and relational distances. Target-table leakers cause the clearest degradation, while one- and two-hop leakers are not consistently used by the model. IG ranks target-table leakers highly across datasets and partially recovers performance in settings where leakage has the largest effect.

We develop a fully relativistic extension of the energy-conserving, unstaggered electromagnetic-potential particle-in-cell method introduced in our earlier nonrelativistic work. As in the nonrelativistic generalized-momentum formulation, the fields are advanced by a Crank–Nicolson discretization of the Lorenz-gauge potential equations, the current is deposited from particle orbits, and charge is advanced through the discrete continuity equation. The new ingredient is a generalized-momentum adaptation of the Higuera–Cary relativistic particle pusher. The vector-potential force is decomposed into an orbit-discrete-gradient part, which enforces the same finite-difference chain rule used in our earlier nonrelativistic formulation, and a skew part, which generates a Higuera–Cary magnetic rotation in mechanical momentum. For prescribed fields and frozen orbit data, this generalized-momentum Higuera–Cary map is a unit-Jacobian conjugacy of the mechanical Higuera–Cary map and preserves particle phase volume in $(\xx,\PP)$. For the fully coupled implicit step, the same orbit data define the current deposit, mesh-to-particle gather, vector-potential chain rule, and relativistic kinetic-energy secant velocity. The resulting particle work cancels the Crank–Nicolson field-energy balance, yielding exact relativistic total-energy conservation up to nonlinear solver tolerance, orbit-quadrature error, and roundoff. A self-adjoint Fourier projection removes modes on even-grid Nyquist planes while preserving the particle–grid work identity. Numerical tests are organized around cold relativistic two-stream and Weibel/filamentation instabilities, with diagnostics for energy drift, Gauss's law, the Lorenz gauge, particle–grid work, and the orbit chain rule.

Circumfacular regions are dark chromospheric structures surrounding magnetic regions whose properties and contribution to solar activity diagnostics remain poorly understood. We investigate their photometric and geometric properties using full-disk H$\alpha$ and Ca II K observations acquired by the Chromospheric Telescope (ChroTel) from 2012 to 2020, spanning the maximum and declining phases of solar cycle 24 and the beginning of cycle 25. We develop an automated segmentation algorithm to identify circumfacular regions and define a photometric index analogous to existing excess and deficit indices. We compare their temporal evolution with those of plages, dark features, and filaments on solar-cycle and Carrington-rotation timescales. Circumfacular regions develop after the H$\alpha$ plage brightening become visible and persist into the decay phase of active regions. At activity maximum, they are the most extended chromospheric structures, covering more than half of the visible solar disk. Their mean intensity varies only weakly throughout the solar cycle; consequently, their index variability, as well as that of the other photometric indices, is driven primarily by changes in area coverage. H$\alpha$ and Ca II~K indices are strongly correlated, although their correlations weaken toward solar minimum. This activity-dependent relationship is primarily driven by the decline of the area of H$\alpha$ excess regions during periods of low activity, and the increasing relative contributions of deficit and circumfacular regions. Our results therefore suggest that circumfacular regions should be considered when interpreting disk-integrated chromospheric observations of the Sun and solar-type stars.

We present Suêtes, a fully differentiable, non-hydrostatic, limited-area atmospheric dynamical core implemented in JAX. Suêtes includes both a semi-implicit semi-Lagrangian scheme and a Split-Explicit Runge-Kutta scheme with acoustic substepping, enabling applications from coarse regional simulations to convection-permitting dynamics. Its terrain-following geometry, spatial discretization, time integration, initial conditions, lateral boundary treatment, and included physical parameterizations are all compatible with reverse-mode automatic differentiation. A single reverse-mode pass can therefore compute sensitivities of forecast diagnostics to selected initial and boundary fields, physical parameters, topography, and computational geometry. We provide a series of numerical experiments—including a tracer-source inverse problem, a sensitivity analysis of a three-dimensional squall-line, adversarial perturbation construction an ERA5-driven downslope hurricane force wind event, topography optimization, and terrain-following coordinate optimization—demonstrating the versatility of Suêtes as a framework for gradient-based diagnosis and model development at regional and convection-permitting scale.

A 3D scene reconstructed from a single image is most useful when represented not as a rendering or a fixed 3D output, but as an explicit scene program whose execution yields a scene that can be inspected, edited, and queried. We present LEGO-Anything, an Image-to-Code framework in which a coding agent iteratively writes and executes Blender code, inspects scenes and renderings, and revises the program. To evaluate end-to-end scene recovery, we introduce LEGO-Bench, a simulator-grounded benchmark with 208 images from 104 diverse indoor and outdoor scenes. LEGO-Bench separately scores artifact validity, visible-surface geometry, and rendered appearance. Its simulator-grounded design enables extensibility and precise automatic evaluation. Among evaluated agents, GPT-6-astra achieves the strongest overall results, with 53.4% indoor and 39.6% outdoor scores, yet substantial gaps remain between delivering valid scene artifacts and faithfully recovering scene geometry and appearance. Analysis of agent construction trajectories reveals three recurring issues: weak scene initialization, regressive edits during iteration, and unreliable self-evaluation. These findings motivate LEGO-Plugin, a training-free harness plugin for more controlled iterative scene construction, which improves all six evaluated models, with relative gains of up to 62.7% in overall score. Finally, we test whether reconstructed scenes can represent natural images and support vision tasks. In LEGO-World, we derive object detections, instance masks, and relative depth as deterministic queries on scenes reconstructed by GPT-6-astra. These readouts show non-trivial performance across all three tasks but fall well short of specialized vision models, suggesting that program-constructed scenes from current coding agents are a promising but not yet sufficiently precise representation of natural images.

Bandwidth extension (BWE) is fundamentally localized: the most perceptual distortions are not average-case distortions, but rare high-frequency (HF) transients that standard, risk-neutral objectives tend to smooth away. To close this gap, we seek solutions in the risk-sensitive and uncertainty-aware decision science rules and present UDSS-BWE, which introduces five decision-science and uncertainty-aware discriminators: CVaRD (does tail pooling to amplify HF artifacts), CCD (a primal-dual augmented Lagrangian to prevent HF overboost), MCUD (a learnable utility over spectral flatness/ centroid/ rolloff), EDD (captures epistemic uncertainty), and DROD (captures entropic KL-DRO aggregation). UDSS-BWE is also designed as a complex valued adversarial BWE framework that uses Swin-based generators, a lightweight dual-stream shifted-window backbone, to capture local and long-range structure efficiently, while learnable lattice coupling provides controlled cross-stream exchange. UDSS-BWE is optimized extensively and achieves better perceptual quality with 3.89x fewer parameters (72M vs.18.5M) over two English and French datasets under clean and noisy conditions. To the best of our knowledge, this work shows how multi disciplinary decision-science-inspired and uncertainty theories can be successfully used to design efficient discriminators for producing more nuanced audios, establishing a new baseline in the BWE task.

In a previous paper, the authors introduced, by analogy with Stein manifolds, a class of complex manifolds called $\mathscr{M}$-manifolds. This class contains all complex projective manifolds. Moreover, every compact $\mathscr{M}$-manifold is Moishezon. In this note, we construct examples showing that the class of compact $\mathscr{M}$-manifolds sits properly between the classes of projective and Moishezon manifolds.

It is well-known that Douady and Hubbard proved that the Mandelbrot set is connected by constructing a uniformizing holomorphic map for its complement from the Böttcher coordinates. This strategy has a clear analogue in the setting of quasiregular Mandelbrot sets. In this paper, we show that the natural generalization of the Douady-Hubbard uniformizing map is quasiconformal in a neighbourhood of infinity, as well as, in fact, outside a certain neighbourhood of the quasiregular Mandelbrot set. On the other hand, we also show that this uniformizing map can reverse orientation at some parameters, which forces it to have folds and, in particular, prevents it from being injective. This feature cannot happen in the holomorphic setting. The connectivity of the quasiregular Mandelbrot sets therefore cannot be established along the Douady-Hubbard route, and remains open.

Dense retrieval, the key component of Retrieval Augmented Generation (RAG), retrieves the most relevant documents by comparing dense vector representations of queries and passages from a large corpus. In privacy-sensitive applications, the server observes the query and controls which evidence is returned, creating both confidentiality and integrity risks. We formulate private dense retrieval as providing query privacy and retrieval integrity against a malicious server, and develop a two-round cryptographic protocol that provides both guarantees. Our protocol reduces private and verifiable retrieval to multiplication of a committed matrix by an encrypted vector and uses low-bit quantization to make this computation practical. We evaluate the resulting trade-off between cryptographic cost, retrieval quality, and downstream RAG accuracy across six embedding models, four language models, and corpora of up to 2.68 million passages. Our results show that, with a clipped quantizer, three-bit quantization largely preserves retrieval quality and downstream accuracy, while a private query over a corpus the size of a clinical reference requires one to three minutes of server time. These results suggest that private dense retrieval is already practical for moderately sized, privacy-sensitive corpora when minute-scale latency is acceptable.

Continual learning is usually studied through mechanisms that preserve old knowledge. We develop Successional Learning Theory (SLT), a mesoscopic account in which the current representation is a resident community, the incoming task is an invader, forgetting is resident displacement, joint retention is coexistence, replay is resident reinforcement, and training moves from establishment toward stabilization. Its empirical coordinate is directional pre-invasion compatibility, measured on the resident model before the incoming task is learned. Across eight experiments, compatibility orders later forgetting on the 20 directed Split-CIFAR-10 transitions (three-repeat r=-0.789, incoming-task cluster 95% CI [-0.90,-0.72], every repeat alone r<=-0.67), forecasts held-out forgetting with 24% lower error than a no-information baseline, and reproduces under controlled MNIST permutations and CIFAR-10 rotations (r=-0.804, -0.718). On an 84-transition suite, compatibility separates coexistence from exclusion at every retention threshold (AUC 0.93-0.97). Replay repairs every transition with at most 325 stored examples and is most efficient where displacement is largest. Compatibility reaches |r|=0.720, while activation, representation, Jacobian, and fixed-coefficient Lotka-Volterra specializations do not. Plasticity and feature turnover fall reliably from early to late training (15/15 and 14/15 runs). We formalize a minimum habitat-modification bound, a displacement floor, a sufficient coexistence condition, an identifiability law with a range-restriction corollary, successional stabilization, and local reinforcement. The identifiability law also predicts where the coordinate loses leverage, and the prediction matches three CIFAR-100 partitions and five optimizer regimes. SLT is a pre-adaptation diagnostic that complements replay, regularization, and projection methods.

Feed-forward 3D reconstruction models have achieved impressive performance by scaling model and dataset size, but their cost excludes most research groups and precludes edge deployment. Additionally, generating 3D supervision without sensors still relies on slow, unreliable Structure-from-Motion, as the community lacks a COLMAP-like system for neural 3D pseudo-label generation. We present OTT3R (RGB-Only Tiny Transformer for 3D Reconstruction), a knowledge distillation framework that addresses both problems on a single workstation equipped with 2 GPUs. Distilling $\pi^3$ (959M parameters) into a 102M-parameter student yields 9.4$\times$ compression and up to 7$\times$ faster inference, trained at 1.6% of VGGT's training compute. An integrated pseudo-label pipeline offers a reliable, high-throughput alternative to COLMAP, generating dense per-pixel point maps and SE(3) camera poses for a 667K-image corpus in 3.5 hours on two commodity GPUs and succeeding on every sequence we tested, including those where COLMAP fails. The general student tracks the teacher on in-distribution monocular depth and, zero-shot, outperforms COLMAP on 7-Scenes and on DTU completion, but it does not replace the teacher on out-of-distribution multi-view geometry. The deployable artifact is the domain-specialized student: after specialization at 0.2% compute, it is 4$\times$ more accurate than COLMAP on 7-Scenes at 980$\times$ throughput, with near-teacher completion. Code is available at https://github.com/TheFourthKaramazov/OTT3R