Papers

We prove that if a minimal ordered structure $(M, <, \ldots)$ with infinite chains in an arbitrary language extending the language of strict orders interprets (in some power $M^n$) the linear order $(\omega, <)$, then this fact can be witnessed for $n=1$ via the incomparability relation of an $<$-definable strict order $R$; that $R$ is unique up to “almost equality”, i.e., finite rearrangements of elements of $M$; and that $R$ can be defined from $<$ in a constructive way. We also show that several variants of the question whether a minimal ordered structure interprets an infinite linear order are all equivalent.

Education agencies often summarize test score distributions by counting how many students scored in 3 to 5 different bins. The HETOP model transforms bin counts into estimated means and standard deviations, assuming that scores follow a normal distribution within each school or district. Past HETOP implementations ran slowly, taking 3–60 minutes, if they finished, when given bin counts for all 1,151 districts in Texas. Our new function, \code{fast\_hetop()} in the R package \pkg{binest}, runs all Texas districts in less than a second. Users can choose between maximum likelihood, empirical Bayes, sample-based or population-based estimates. Estimates are strongly correlated with true values, but have bias when the score distribution is skewed and scores are concentrated in the lowest or highest bin.

In this work we initiate the study of competitive algorithms with arrival-time incentive compatibility for random-order online bipartite matching in settings where the users care only about receiving service (matched vs. unmatched) and not which offline resource serves them, while the platform's objective is to maximize total matching reward. This captures applications such as ride-sharing where the users primarily care about being matched to a ride while the platform internalizes the cost of dispatching a distant driver; dispatching homogeneous service requests to heterogeneous servers (cloud/edge routing); and assigning customer requests to a pool of providers with different flexibility (e.g., English-only vs. bilingual agents). Our main question is: Is constant-competitive matching possible for incentive-compatible, random-order edge-weighted matching on complete bipartite graphs? Motivated by the LP-based treatment of incentive compatibility in the classical secretary problem by Buchbinder et al., we impose a constraint that the ex ante probability of selection is equalized across all arrival positions. We answer our main question in the affirmative and propose the first constant-competitive algorithm for incentive compatible edge-weighted random-order online matching on complete bipartite graphs. The competitive ratio of our algorithm is parameterized by the imbalance factor $k := n/m$ – where $n$ and $m$ are the numbers of online and offline nodes, respectively, and $k$ is a positive integer. In particular, we obtain a competitive guarantee of the form $c_k - O(1/\sqrt{m})$ where $c_1 \approx 0.162$ and $c_k \to 0.02308\ldots$ as $k \to \infty$. We also present algorithms with strictly improved competitive ratio of $\approx 0.07 + O(1/m)$ for the binary-weighted case ($0$-$1$ rewards).

Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the dual domain, these pointwise constraints give rise to functional dual variables. In this work, we propose to learn these dual variables, motivated by the fact that their values encode useful information about the underlying constrained problem. By representing the dual variable as a parametric function of each sample, we enable the learned multiplier to be evaluated on new, unseen samples. This contrasts with standard empirical dual formulations, which assign an independent multiplier to each training sample. We characterize the error in the recovered primal solution induced by restricting the dual variable to a parametric function class and show that it is controlled by how well this class approximates the optimal statistical multiplier. Moreover, we show that the learned parametric multiplier retains the sensitivity interpretation of the optimal statistical multiplier, yielding approximate sensitivity guarantees that extend beyond the samples used for training. We empirically validate our theory across a variety of everywhere learning tasks, showing that the resulting constrained problems can be solved efficiently and that the learned dual variables provide meaningful representations of sample-level sensitivity.

This article is aimed at introducing a new procedure to define reference solutions to which the numerical approximations of anisotropic problems arising in plasma physics may be compared. In this context, the main issue is related to the construction of functions with no gradients along the vector field defining the anisotropy direction. The so-called solution manufacturing, implemented so far in the literature, only applies to frame- work where all the computations can be carried out analytically. In the present paper, we propose a new method in which this requirement is not mandatory. Indeed, via a Riemannian metric, we use a propagation of the boundary value by the flows related to the vector field defining the anisotropy direction. This permits to extend the application of the solution manufacturing to a broader range of contexts.

Reinforcement learning has helped AI agents solve increasingly difficult tasks, but high rewards do not always reflect the work users intended. In recent incidents and controlled evaluations across the AI industry, agents trained to maximize reward have accessed unauthorized information, attempted to evade monitoring systems, and even breached sandbox protections to attack external systems. As agents become more capable, this behavior could pose increasingly serious risks. To measure this problem, we introduce CheatBench, a benchmark of cheating in AI agents across mathematical research, knowledge work, coding, visual tasks, and other domains. Its environments combine challenging assignments with opportunities to cheat, allowing researchers to study how agents pursue a goal when honest work is difficult. CheatBench supports comparisons across models and task categories, providing a testbed for measuring and reducing cheating as agents take on more consequential responsibilities. We publicly release CheatBench at https://cheatbench.ai

Partial Least Squares (PLS) regression extracts a few outcome-aligned directions in a high-dimensional X and is widely used across applied science, but inference on the resulting fit is either expensive, biased and discouraged, or absent. We reduce inference to held-out OLS refits of the supervised subspace, a primitive shared by PLS, supervised PCA, and linear probes, and supply two tests using held-out correlations: a Nadeau-Bengio corrected asymptotic t-test as a fast approximation, and a permutation test with comparable power, finite-sample valid under outcome-predictor independence and iid rows. Held-out predictions are unchanged under any orthogonal rebasing of the supervised span, so an interpretable basis such as varimax inherits the joint claim but not a per-axis p-value; per-component claims come from a fixed-sequence test on the PLS extraction order. We validate on synthetic geometries, two NIR chemometric datasets, and cross-lingual word-embedding regressions; the exact test also transfers to supervised PCA and a ridge probe. The proposed tests have more power than CV-permutation-Q^2, at a fraction of its cost. A pre-run check on n and the spectrum of X says when the approximation is safe. We release a Rust library with Python, R, and Julia bindings, plus a Python text pipeline.

We extend Rainwater's theorem that, for Baire measures on a compact Hausdorff space,a measure singular with respect to any measure from a $w^*$-compact convex set $M$ of probability measures sits on a Baire set which is $\mu$-null for every $\mu\in M$. Our main result shows that this statement holds under the weaker assumption of convex analyticity of $M$. In the standard way, this extends the Glicksberg–König–Seever decomposition theorem. We also give conditions for our results to hold for sets of signed measures.

World models jointly learn latent representations and dynamics that predict how high-dimensional observations evolve under actions. In this work, we propose a JEPA-style world model in which, rather than learning arbitrary latent dynamics, we restrict them to follow a bilinear parameterization. This structure enables efficient planning and control while shifting the modeling burden onto the encoder, encouraging richer representations that expose the controllable geometry of the system. In particular, this structured parameterization allows us to structurally enforce action recoverability, thereby preventing representation collapse by construction. Although prescribing a bilinear parametrization may appear restrictive, we show that a broad class of nonlinear dynamical systems admits a transformation under which the dynamics become bilinear. Empirically, we show across standard 2D and 3D control tasks that representations with bilinear-parameterized dynamics can be learned directly from high-dimensional observations, reducing planning time by nearly three orders of magnitude while retaining or even improving control accuracy. We also propose more demanding regimes of longer-horizon planning and real-time control, and demonstrate that our method succeeds in both, moving JEPA-style world models beyond short-horizon offline planning.

Academic access programs distribute frontier artificial intelligence as research infrastructure, but awards and institutional authorization are distinct stages. We examine the handoff through structured coding of 15 publicly documented access pathways captured on 19 September 2026, of which ten met prespecified inclusion criteria, and a process trace at one US university. Two isolated model-assisted coding passes found explicit eligibility criteria in nine programs and three implied institutional prerequisites across the corpus. Downstream specification was weaker: access duration was unstated in six programs, seven reported no use or outcome metric, and liability assignment was unstated in five to seven. Public terms did not establish an unambiguous institution-independent path from award to intended use in eight to nine programs, a composite that includes possible and unclear cases. In the institutional trace, policy required review even for free tools. A bounded request generated a ticket but no substantive response or decision pathway during the observation window. We define the authorization gap as the distance between an access award and authorized research use. Tracking first use, clearance, time to first use, and persistence would help programs distinguish allocated resources from usable scientific infrastructure.

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan–code–component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

While foundation models have revolutionized natural language processing and computer vision by leveraging universal vocabularies, Graph Machine Learning (GML) remains fractured due to the absence of a unified feature and structural representation across diverse domains. Existing works claiming to be Graph Foundation Models (GFMs) are typically restricted to node-level predictions or require fixed feature dimensions, failing to provide a truly task-agnostic backbone for the full spectrum of graph learning applications. In this paper, we introduce the Universal Classifier (UC), which supports arbitrary feature and class cardinalities, unifying node-, edge-, and graph-level objectives under a single similarity-based classification objective. The UC reformulates all node-, edge-, and graph-level prediction tasks as maximizing similarity in the latent space: by lifting heterogeneous features and labels into 3D latent tensors, the model learns transferable features independent of specific input schemas. This architecture allows a single pre-trained model to generalize to node classification, node regression, and link prediction across unseen graphs with varying feature semantics. Experiments show strong zero-shot transfer performance across node-, link-, and graph-level tasks.

Mixture-of-Experts (MoE) layers are central to frontier language models, and recent architectures push toward more and smaller experts. In this regime, the standard linear router becomes a bottleneck: with $M$ experts and hidden dimension $h$, its per-token cost $\Theta(Mh)$ dominates the MoE layer once $M$ is large. We introduce MoRE (Mixture of Rank-reduced-routed Experts), which factorizes the router weight matrix at rank $r$ and reduces the routing cost to $O((h + M)r)$. We prove that rank logarithmic in $M$ suffices for routing expressivity when the number of active experts is fixed, and is necessary up to precision factors. We also prove that logarithmic rank preserves load balance in a Gaussian memorization model, and training on a synthetic phonebook task shows that low rank does not hurt memorization. At matched active FLOPs, the factorization allows a factor of $\Theta(h/r)$ more experts. To realize this gain in wall-clock time, we design a fused Triton kernel at inference that avoids expensive memory operations on HBM. Empirically, MoRE improves memorization on the phonebook task and performance on knowledge-intensive Q&A benchmarks after pretraining, while matching reasoning ability. Code available at https://github.com/Matheart/MoRE_code.

We expand on the concept of admissible pairs from \cite{Levin:GCD} and explore its relation with the main Diophantine arithmetic inequalities, with discriminant term and for points of bounded degree, that have been predicted by Vojta \cite{Vojta:1998}. In this context, among other new results, we prove a harder implication which is in the spirit of Vojta's approach to the abc Conjecture (from \cite{Vojta:1998}). As our main result, and application of our viewpoint here, we deduce for the case of certain general type nonsingular Deligne-Mumford stacks, with projective course moduli space, a form of the Bombieri-Lang Conjecture for $(D_0,S)$-integral points of bounded degree. A key input for this is a slicing theorem, for Deligne-Mumford stacks, that was obtained by Abramovich and Várilly-Alvarado, \cite{Abramovich:VarillyAlvarado:Pera:2017}, and building on earlier work of Kresch and Vistoli \cite{Kresch:Vistoli:2004}. Another important ingredient is an inequality of Silverman, from \cite{Silverman:1984}, which bounds the discriminant of points in projective space in terms of their heights. As an illustration of our results, we discuss them within the context of the interesting work of Abramovich and Harris \cite{Abramovich:Harris:1991} and others.

Analytical studies of zonal-flow (ZF) excitation by fluctuating fields, such as drift-wave turbulence and Alfvén eigenmodes (AEs) driven by energetic particles (EPs) in tokamaks, are usually carried out via intricate gyrokinetic calculations and simulations whose results are notoriously difficult to interpret. Here, we report a transparent result that is also not limited to any particular modes or frequency range. Using oscillation-center theory that captures both ponderomotive forces and quasilinear diffusion, we derive a compact formula for the ZF drive produced by any fluctuating field in terms of the field's canonical momentum and the dissipation power density. For ZFs generated by drift waves, our model subsumes the local relation between the zonal velocity and the drift-wave energy density that was previously derived ad hoc. The simplicity and generality of our result also opens a path toward optimization of ZF excitation with external waves and bridges the physics of AE-EP interactions with that of poloidal flows driven by radiofrequency waves in fusion plasmas.

Stellar-mass compact objects spiraling into massive black holes in galactic nuclei (referred to as "extreme-mass-ratio inspirals", or EMRIs) will be an important class of sources for the Laser Interferometer Space Antenna (LISA). A stellar-mass compact object can radiate in the millihertz band for years to decades before it plunges into its massive black hole, so a substantial fraction of the EMRIs that LISA can detect will still be inspiraling when the mission ends. We calculate what fraction of detectable EMRIs will plunge after the mission ends, and for those we calculate how they are distributed as a function of various parameters, such as their post-mission lifetime. To do this, we draw from astrophysically motivated populations, backward-integrate fully relativistic Kerr FastEMRIWaveforms trajectories for a given time to plunge, and compute the full LISA response over both the four-year nominal and ten-year extended observing windows. We calculate the detectable fraction as an explicit function of time to plunge at signal-to-noise ratio (SNR) thresholds of $\rho=10$, 20, and 30. We find that post-mission EMRIs are roughly one in four of the LISA-detectable population at $\rho>20$ over the four-year mission, and roughly one in six over the ten-year extended mission. The in-window detectable fraction varies by nearly a factor of six at $\rho>20$ across the massive black hole spins and secondary masses we ran, while the share stays between 25% and 33% for the four-year mission and between 13% and 20% for the ten-year one across all of them. The search for EMRIs that plunge more than $\sim 1$ year after the mission ends may require a different algorithm than the one used for EMRIs that plunge during the mission, and the fact that post-mission detections are a substantial fraction of all detections gives some urgency to developing a detection pipeline suitable for them.

We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in $(3+1)$ dimensions. Building upon our recent formulation of the interpolating conformal algebra in $(1+1)$ dimensions, we propose an interpolation method for the conformal group $SO(4,2)$. A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle ($0 \leq \delta \leq \frac{\pi}{4}$). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit ($\delta = \frac{\pi}{4}$), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in $(1+1)$ but dynamical in $(3+1)$. This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a $6 \times 6$ interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.

This paper incorporates uniform planar arrays into a cooperative dynamic spectrum access (DSA) mechanism based on the IEEE 1900.5.2 spectrum consumption model (SCM). Unlike prior work on SCM-based DSA that assume a fixed radiation pattern, the proposed DSA mechanism treats the radiation pattern as a design variable and jointly designs the precoder and spectrum allocation. The system model is a cell-free downlink, multiuser, multiple-input single-output network, an architecture that suits the dense indoor deployments of large-scale networks such as online retailers' fulfillment centers. The main objective is to reduce spectrum use while meeting a target signal-to-interference-plus-noise ratio at every receiver. To this end, this paper proposes a leakage-aware iterative water-filling precoder using uplink-downlink reciprocity, a power-control method that further encourages spectrum sharing, and a sequential admission algorithm that allocates spectrum to base stations based on the SCM compatibility test. Simulations in an indoor warehouse setting show that the proposed DSA mechanism better utilizes the spatial dimension for spectrum sharing.

Most videos capture only a narrow field of view and provide no spatial audio, limiting the sense of immersion they can provide. Recent video generation models can expand perspective videos into panoramic ones, but do not provide the corresponding spatial soundscape. Without spatially consistent audio, these expanded visual worlds remain incomplete. This paper presents OmniDream, a training-free framework that transforms a silent monocular video into an immersive audiovisual experience, where viewers can freely look around while sounds remain spatially aligned with the visual scene. At the core of OmniDream is an object-centric audio representation that disentangles each sound source's intrinsic audio content from its scene-dependent acoustic effects, enabling independent audio generation, physics-based simulation of propagation effects, and flexible spatial audio rendering. Experiments show improved audio-visual alignment, spatial correctness, and perceptual immersiveness over baselines. Examples are available on https://huggingface.co/spaces/CuriousAlien000/spatial-audio-360-demo

Sparse autoencoders (SAEs) expose interpretable features in large language model activations, yet existing structured SAEs impose single-parent trees or forests, while post-hoc graphs permit multiple parents but neither guide feature learning nor ensure reliable relation recovery. We introduce the Adaptive Graph Sparse Autoencoder (AG-SAE), a structure-guided training paradigm that treats each feature's complete parent set as an atomic structural hypothesis and lets evidence select zero, one, or multiple parents. By competing complete parent sets against null, subset, and alternative explanations, AG-SAE identifies jointly necessary multi-parent relations while rejecting redundant or spurious alternatives and verifying that each child contributes beyond its parents. The induced topology over SAE features then defines a differentiable structural loss that guides SAE training, while topology-guided refinement mitigates feature absorption and uses persistent reconstruction gaps exposed by the learned structure to initialize new features. The entire graph is then induced again from the revised dictionary by reassessing every feature's complete parent set, closing the dictionary-graph self-consistency cycle. Experiments demonstrate exact mixed-topology recovery in a controlled toy model, greater relational reliability and semantic validity than structured and post-hoc baselines on real LLM activations, and stronger feature-level causal interventions than conventional SAE features. AG-SAE thereby turns recovered mixed-topology feature structure into an unsupervised training signal that improves the dictionary, enables reliable feature organization beyond the topological limitations of trees, and exhibits stronger causal control beyond reconstruction.

We study the delayed one-dimensional swarmalator model when all units share a common intrinsic frequency {\omega}. Unlike the zero-frequency case, {\omega} cannot be removed by a rotating-frame transformation because delayed interactions retain the phase accumulated over the lag. The result is a two-order-parameter analogue of the delayed Kuramoto model: the asynchronous state acquires incoherence lobes, the synchronized state becomes a rotating branch stable even when both the spatial and phase couplings are repulsive, and the phase wave develops narrow resonant stability bands. These delay-selected windows overlap to produce broad branch coexistence, including a narrow window near K=-J where all three canonical states-asynchronous, phase wave, and synchronized-are simultaneously stable. In regions where no canonical branch is stable, the order parameters oscillate persistently.

This paper develops a safe and fully decentralized multi-agent reinforcement learning (MARL) algorithm to solve a class of discrete-time control problems on networks, including the persistent monitoring problem. Fully decentralized control of agents, while offering numerous benefits, faces issues such as exponentially increasing sample complexity, lack of global information about the system, and challenges in coordinating between agents. To address these issues, this paper introduces a fully decentralized multi-agent reinforcement learning algorithm that integrates deep reinforcement learning with safety considerations. This method feeds a history of local observations of the network's state into two parallel neural-network branches: the graph encoder, which adds structural information and correlations among nodes, and a state estimator, which predicts the uncertainty at each node in the graph. Additionally, the result of feeding that input into an actor-critic network is passed through a discrete-time control barrier heuristic to reduce the likelihood that any node will be neglected. This approach enables teams of fully decentralized agents to solve challenging problems by increasing system awareness and incorporating built-in safety measures to prevent the adoption of potentially harmful control policies. Numerical results from a custom simulation environment demonstrate that the proposed algorithm achieves 26.3 percent lower average uncertainty than a centralized control policy and is within 1 percent of the uncertainty performance of a more computationally complex algorithm with added attention layers.

The phase curve on a planetary object can reveal key details about its atmosphere and surface, including the presence of surface liquid oceans. Phase curves for Earth can inform the search for habitable surface environments on terrestrial exoplanets, but such phase curves are quite rare. The Clementine lunar orbiter made 3,744 observations of the Earth between February and May of 1994. These observations spanned phase angles between 3.4 and 139.1 degrees. From these data, we produce phase curves of Earth in 5 distinct bands with wavelengths between 400 nm and 1000 nm. We extrapolate fits to the phase curves to derive the geometric albedo of Earth in each filter. We examine the Earth's color as a function of phase angle and find the observed values are best fitted by models that include contributions from ocean glint. We also find a number of observations where contributions from glint are minimal but the disk-integrated color is in line with the glinting model predictions; we propose that this can be explained by the presence of optically clouds on the disk. These findings stress the importance of high-phase Earth observations for high-fidelity Earth models and for future efforts to characterize terrestrial exoplanets via direct imaging.

We investigate the extent to which the Hamas attacks on Israel of October 7, 2023, have affected German social media debates about Judaism and Israel. For this, we develop an approach to detect 26 anti-Semitic categories in user postings via large language models (LLMs). The approach is applied to Facebook and Telegram posts (N=125,718) from three months before and after the event. Methodically, we test different open-weight models in two setups—with and without user information as additional context to the post text. The best setup achieves up to 83 % F1-score for binary anti-Semitism detection on our manually coded validation set. User context provides valuable information for most LLMs and drastically reduces false positives, for example, when (critically) reporting on anti-Semitic incidents. Concerning our topic, we find that anti-Semitism is surging significantly on both platforms, while being about ten times more prevalent on Telegram compared to Facebook. Facebook users express anti-Semitic views most likely in posts about an alleged genocide in Gaza carried out by the Israeli army, whereas classic anti-Semitic stereotypes related to power and conspiracy theories are dominant on Telegram. After the attack, the discourse patterns on both platforms show signs of convergence, as classic anti-Semitism increases on Facebook, whereas Israel-related categories surge on Telegram.

Prompts are the primary mechanism for directing the behavior of large language models (LLMs). Yet the internal structure and causal hierarchy of prompts remain poorly understood: which parts are causally necessary and which are redundant is an open question. This opacity can have severe consequences. Subtle prompt variations can silently shift model outputs in critical software systems, and engineers lack techniques to reason about prompt reliability. We present \framework, a blackbox prompt-minimization framework that reduces few-shot prompts to their necessary minimal subset. We use a case study to apply \framework to a few-shot learning system and demonstrate the insights that this framework can provide. Our experiments show that few-shot exemplars can be reduced by a mean of 65.3%~$\pm$~15.8% in character count while fully preserving propositional output fidelity. The models preferentially retain logical identifiers and constraint declarations while discarding natural language prose and cross-prompt relational annotations. Our analysis also shows that some models are universal encoders, able to produce highly legible yet minimized prompts, while others are universal decoders, able to interpret minimized prompts from most other models. By identifying which components are indispensable, \framework provides a principled basis for prompt compression and structural analysis of few-shot exemplars.

EEG foundation models (EEG-FMs) are intended to generalize across different datasets by learning representations that, ideally, are invariant to dataset-specific EEG configurations such as electrode montages. However, EEG-FMs that accept different montages as input do not guarantee that representations and predictions remain stable across different electrode configurations, especially outside the training setting. In this work, we investigate the effects of different electrode montages through a joint functional and representational analysis of four EEG foundation models selected to span distinct montage-handling designs. We evaluate embeddings on cross-subject resting-state eyes-open/closed and within-subject motor-imagery classification under spatially informed channel reduction. Functional robustness is tested through the generalizability of linear probes across channel counts, while representational robustness is assessed through within-subject similarity and preservation of between-subject geometry. The four models show distinct robustness profiles, and the two axes dissociate: large changes in embedding similarity need not come with comparable probe degradation, and stable embeddings can still lose downstream performance. Comparing two readouts of the same encoder further shows that aggregation, not the encoder alone, determines functional robustness: pooling into anatomically aligned regions degrades less than a learned global readout, despite being montage-invariant by construction. Montage robustness is therefore a joint property of the encoder and its aggregation, and characterizing it requires both a representational and a functional axis. Input compatibility alone is evidence for neither.

Instruction-based text-to-speech (ITTS) systems enable natural-language control of expressive speech generation, but often offer limited transparency and fine-grained control over individual text units. Character-level controllable TTS systems provide explicit acoustic control, yet typically rely on user-specified acoustic attributes. To bridge this gap, we propose InstCharVoice, a unified framework that grounds natural-language instructions in character-level acoustic control. We first construct grounded instruction annotations on the WordVoice-5A-zh corpus using Qwen3-Omni. With this supervision, we train an autoregressive model to identify instruction-relevant characters and predict their acoustic attributes before generating the corresponding speech tokens. Keyword prediction and grounding-aware loss weighting help the model focus on instruction-relevant characters and attributes. Experiments show improved instruction following and keyword-level acoustic control over representative ITTS systems, with competitive speech naturalness and explicit character-level controllability. Audio samples are available at https://xxh333.github.io/instcharvoice-demo/.

Motivated by networked systems in which equilibrium conditions apply to a regulated state rather than directly to the decision variable, we study transformed-state general variational inequalities. Using a projection-residual reformulation, we develop residual feedback methods that operate in the decision space without inverting the state mapping $H$. For a one-step method, we establish an $\mathcal{O}(T^{-1/2})$ best-iterate residual rate under solution-restricted cocoercivity and linear convergence under solution-restricted strong monotonicity and residual Lipschitz continuity. We also obtain an $\mathcal{O}(T^{-1/2})$ best-iterate residual rate for a predictor-corrector method applied to the induced GVI residual under monotonicity and Lipschitz continuity. The assumptions are imposed directly on the computable residual and are illustrated by affine network and rank-deficient examples. Finally, we extend the residual framework to generalized quasi-variational inequalities with decision-dependent feasible sets.

We report the design and experimental realization of a low-loss dielectric metasurface mirror operating at 1064 nm, the primary wavelength of interferometric gravitational-wave detectors. The mirror consists of a single layer of titanium dioxide nanopillars on a glass substrate, achieving high reflectivity via guided-mode resonance. The fabricated mirror has a peak reflectance of 99.10% with a total optical loss of 0.26%, representing, to our knowledge, the highest reflectance and lowest optical loss experimentally demonstrated in a substrate-supported purely amorphous dielectric metasurface mirror operating in the visible to near-infrared. This single-layer metasurface is projected to reduce coating Brownian noise by a factor of 3-5 relative to conventional dielectric Bragg mirrors at comparable reflectivity, which would improve the performance of precision optical cavities currently limited by this noise. These results indicate the potential of dielectric metasurfaces as a platform for next-generation precision measurement systems.

We have developed a computer code that models the three dimensional nature of a sodium plasma created by laser resonance saturation. This was accomplished by taking account of the temporal and spatial distortion suffered by the laser pulse as it propagates through a nonuniform sodium atom distribution. We have also undertaken the first measurements of the radial and axial electron density and temperature profiles arising in such a plasma and have been able to demonstrate that our computer code predictions are in reasonable agreement with these results. Absorption of the laser pulse is found to be quite significant for even a few centimeters of $10^{16}$~cm$^{-3}$ sodium atom density and that as a result quite low temperature plasmas can be produced for modest energy laser pulses.