Papers

Lumped-element networks give transparent, passive models of acoustic impedances whose low- and high-frequency limits can be read from the circuit, but a systematic, arbitrarily accurate construction for non-rational impedances is lacking. Continued fractions, one- and two-point Padé approximants and their identity with ladder networks and Cauer synthesis are introduced in tutorial form and applied to two examples: the radiation impedance of a baffled circular piston and the throat impedance of a horn with a piston mouth. The even contraction of the piston's continued fraction has positive coefficients, certified by interval arithmetic for the first 100 pairs, and yields a ladder of positive resistances, masses and compliances; with 14 elements the error is 4e-4 up to ka = 5. Beranek's four-element network is, to about 2%, the order-two two-point Padé approximant. A horn modelled as a cascade of waveguide sections is a continued fraction whose tail is the mouth impedance; the infinite exponential horn is a periodic continued fraction, an exact high-pass ladder. The piston networks are passive at every certified order (up to 202 elements) and are extended without changing existing elements; for a finite horn the error of the mouth network passes one to one to the throat impedance.

Hate speech has become increasingly prevalent on social media, raising concerns about its detection, interpretation, and moderation. Persian, a relatively low-resource language, lacks sufficient annotated data and computational resources for fine-grained hate speech analysis. In this study, we introduce a fine-grained, multi-hop benchmark for explainable Persian hate speech analysis, covering content triage, target identification, hate tactic and moral foundation analysis, textual evidence extraction, harmful narrative inference, and severity assessment. By evaluating state-of-the-art large language models (LLMs), we find that performance generally declines as tasks require more fine-grained semantic and inferential reasoning. Proprietary models generally outperform open-weight models, while reasoning-oriented models show no consistent advantage. Incorporating intermediate reasoning steps substantially improves severity prediction compared with one-shot assessment. Our analysis further reveals that Incitement to Violence or Harm is most strongly associated with higher severity, while political-affiliation targets are particularly associated with subversion-based moral framing. Overall, this work provides insights into LLM-based hate speech analysis and supports more accountable moderation of Persian-language social media. The benchmark is publicly available at https://github.com/kalhorghazal/From-Triage-to-Impact.

Neural partial differential equation (PDE) surrogates trained with mean squared error (MSE) can capture dominant dynamics but often lose high-frequency information and fine-scale structures. Generative models (e.g., Flow Matching) can capture the distribution of fine-scale details, yet stochastic errors may accumulate during autoregressive rollouts and compromise long-term stability. To address these limitations, we introduce Refine and Align(ReAl), a model-agnostic plug-in that augments pretrained PDE surrogates to improve the reconstruction of high-frequency structures associated with complex physical phenomena. In the refinement stage, a conditional flow-matching model learns the residual distribution around the deterministic base prediction, recovering missing fine-scale structures while retaining the dominant dynamics. In the alignment stage, to mitigate the generative discrepancies amplified in the autoregressive rollout, particularly in chaotic systems, we generate multiple trajectories from the same input and reinforce the refiner with trajectory-level rewards, thereby achieving long-horizon dynamical alignment. Experiments across diverse surrogate architectures and PDE tasks demonstrate that ReAl consistently improves high-frequency fidelity, forecasting accuracy, and long-horizon stability.

Kemp and Ramgoolam proposed a basis of monomials for a commutative semisimple algebra with generators \(C_1,\ldots, C_L\), constructed from a degeneracy graph which records how the eigenspaces of \( C_1\) are successively split by \( C_2,\ldots, C_L\). They showed that the basis property is equivalent to the non-vanishing of the determinant of the matrix of values of these monomials on the projector basis, and conjectured a factorised formula for this determinant, as a product of powers of eigenvalue differences. We prove this formula for any number of generators. The proof uses graph analogues of Newton polynomials. Their evaluation matrix is not triangular in general, but expanding the rows of the children of each node of the penultimate layer in a Newton basis of their eigenvalues makes it block triangular, with diagonal blocks given by smaller degeneracy graphs in which the final layer is removed. The formula then follows by induction on the number of layers. We show that the exponents in the determinant are overlap volumes of higher-dimensional Young diagrams attached to the nodes of the graph: intervals, ordinary Young diagrams, plane partitions and their higher analogues. Finally, the block triangular structure gives an explicit recursive inversion of the evaluation matrix, expressing the projectors in the monomial basis.

Retrieving information from visually rich documents requires matching queries against pages that contain complex evidence in tables, figures, and layout-dependent structures. Current vision-language retrievers address this but incur query-time costs that grow with corpus size and are impractical to scale. We propose SCOUT, a cascaded two-track retrieval framework that separates retrieval performance from exhaustive search. The visual track first uses a lightweight parent retriever to filter the corpus to a compact candidate pool, then applies a stronger multi-vector reranker only to those candidates. In parallel, a semantic track retrieves over hierarchical page and document summaries generated offline to provide a signal complementary to visual matching. The outputs are fused through cross-modal query refinement, which uses semantic scores to adjust the visual query representation before final ranking. We evaluate SCOUT on 4 major benchmarks against 6 baselines and observe a significant query-time latency improvement up to 80.7x (28.8x on average) relative to the best baseline, while exceeding state-of-the-art retrieval performance by up to 7.8% NDCG across all benchmarks.

Regime-switching multi-factor models are widely used in quantitative finance, but filtering does not by itself determine when an agent should act on inferred regime changes. We formulate online regime detection with latent factors and hidden regimes as a Bayesian decision problem balancing false alarms, detection delay, and misclassification. Since posterior regime probabilities are generally non-Markovian, the problem is represented as a measure-valued optimal stopping problem and approximated using particle filtering with Monte Carlo dynamic programming. A single-change-point Heston model provides a benchmark. With observed variance, the problem reduces to a two-dimensional Markov free-boundary problem, while under latent variance decisions are based on the filtered posterior measure. Numerical experiments in Heston and regime-switching Vasicek models show that the latent-information procedure can outperform feasible plug-in rules.

AI agent communities sustain lexical persistence, popular terms spread, recur, and achieve broad adoption, but whether they also develop the temporal semantic structure characteristic of human linguistic communities remains open. We compare MoltBook (AI agent community, 8 weeks), PTT (Chinese human BBS, 19 years), and Reddit (English human forum, in matched 8-week windows) using Compass-Aligned Distributional Embeddings (CADE), measuring semantic drift (B1), neighborhood stability (B2), and lag-1 autocorrelation of per-word drift trajectories. Across the platforms, lag-1 autocorrelation forms a memory-horizon continuum. AI agents' result clusters at the low end, while human platforms show longer-range temporal dependence. MoltBook exhibits approximately 2$\times$ the B1 drift and 20-30% lower B2 stability than both human platforms. As a partial control for community age, r/vibecoding (founded 2025-02-08) shows significant ACF in its first 8 weeks ($0.082$, $p<.001$) and over 15 weeks ($0.220$, $p<.001$); MoltBook's ACF remains non-significant ($p = 0.41$), consistent with the gap not reducing to developmental stage alone. We interpret this pattern as evidence that lexical diffusion alone does not guarantee diachronic semantic consolidation. The findings are consistent with a contrast between communities whose semantic trajectories accumulate long-range interaction constraints and communities whose outputs are repeatedly regenerated from largely fixed pretrained distributions.

The problem of maximizing vertex-degree-based topological indices over trees with a prescribed order and maximum degree $\Delta$ has traditionally relied on ad-hoc combinatorial arguments. In this paper, we establish a unified linear programming approach that systematically resolves these extremal problems. By formulating the optimization over degree-pair multiplicities, the search for an extremal tree reduces to minimizing a discrete dual penalty. Treating vertex degrees as continuous variables yields an analytical single-variable test condition that guarantees global optimality. We apply this framework across a diverse collection of invariants. We prove that the standard basic feasible solution is optimal for the Tangent Sombor, $SO_1$, $SO_2$, Albertson, and $\sigma$-irregularity indices for all $\Delta \ge 3$. However, the dual optimality conditions establish exact analytical thresholds at which the standard basis loses optimality, necessitating a transition to alternative basic feasible solutions. For the Arithmetic-Geometric ($AG$) index, the standard basis is optimal strictly for $\Delta \ge 9$; for smaller maximum degrees ($3 \le \Delta \le 8$), optimization shifts to an alternative edge basis, allowing us to explicitly construct and characterize all extremal trees across congruence classes, including chemical trees ($\Delta \in \{3, 4\}$). Conversely, for the Triangle Volume index ($SO_{11}$), the standard basis is optimal exclusively for $\Delta \le 8$, while for $\Delta \ge 9$ we analytically derive a novel, degree-dependent optimal basis to explicitly construct its extremal configurations.

Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable architectural diversity, these methods often share a common input representation: raw coordinate-value pairs $(x, u(x))$. We ask whether inputs aligned with PDE differential structure can improve learning. Through Picard iteration on mild solutions, we show that derivatives of the input appear explicitly in the solution operator, suggesting that providing derivative features should reduce the network's implicit differentiation burden. We prove this intuition: providing derivative features improves approximation bounds from $O(W^{-(s-m)/d})$ to $O(W^{-s/d})$, where $W$ is parameter count, $s$ is input regularity, $m$ is the PDE order, and $d$ is spatial dimension. Our central finding, however, is a surprise: the optimal derivative order $\beta^*$ is strictly less than the PDE order $m$. This gap arises from a bias-variance tradeoff in spectral space that we characterize in closed form. Learning $\beta$ from data achieves automatic spectral regularization. We introduce $\partial$-NO (del-NO), for derivative-augmented neural operators, an architecture-agnostic augmentation that provides learnable fractional derivative features to any neural operator backbone. Across benchmark problems and architectures, $\partial$-NO consistently improves prediction accuracy, with learned orders that reflect a representation of known physics modulated by noise and finite-sample constraints.

We investigate excited-state effects in nucleon sigma-terms in lattice QCD using twisted-mass clover-improved fermion ensembles. We study correlation functions with nucleon and multihadron nucleon-$\sigma$-meson interpolating operators. The analysis is performed using three gauge ensembles, including one ensemble simulated with two degenerate light, a strange, and a charm quark with quark masses tuned to approximately their physical value. We solve the generalized eigenvalue problem that arises from the matrix of correlators and show that the three-point function for the light sigma-term obtained using the optimal linear combination of interpolating operators has substantially reduced time dependence without loss of statistical precision. We apply Laplace filtering and investigate residual excited-state contributions in the extraction of $\sigma_{\pi N}$. Using the same optimal linear combination of correlators as for $\sigma_{\pi N}$ for the strange sigma-term we also observe suppressed excited state contributions over an extended range of source–sink time separations. For the charm sigma-term, we observe negligible time dependence within the large statistical uncertainties, and these improvements show no significant effect.

We summarize previously published computer simulation studies of a metal electrodeposition model that considers diffusive cation flux, a fast reaction in contact with the electrode or with the growing deposit, and adsorbed atom diffusion in finite time windows. Simulations with various parameters show compact, fractal, dendritic deposits, and dynamic transitions between different morphologies during the growth of individual samples. The dendritic shapes are characterized by hierarchical organizations in which branches of a given order reproduce the shape and crystalline orientation of the branches of the previous order, in contrast to the random branching of the fractal deposits formed by DLA and related models. The simulations show dendrites with maple leaf shape in SC lattices, pine tree shape in FCC lattices, and flower-like shape in HCP lattices, with surfaces predominantly oriented in the lowest-energy configurations of each lattice. Simulations with nucleation restricted to a nanoscale seed show the initial formation of faceted particles followed by dendrite formation, in agreement with silver electrodeposition on substrates patterned with gold nanoparticles. A quantitative application to faceted and dendritic silver obtained in the same experiment provides values of the model parameters which are consistent with the characteristic widths of these structures being of the same order of magnitude of the diffusion lengths of atoms on (111) and (001) surfaces. Using an extended model for iron electrodeposition on Si(100), the simulations qualitatively reproduce the initial formation of multilayer islands, small oscillations of the roughness of a polycrystalline compact film after island coalescence, and instability development. Possible directions for applying this modeling to the electrodeposition of other materials are suggested.

Gossip, defined as evaluative talk about absent third parties, is widely seen as a uniquely human social practice. This study examines whether comparable discourse emerges spontaneously in a community of autonomous AI agents. We compare Moltbook, a Reddit-style platform populated by AI agents, with PTT, a large human-operated bulletin board in Taiwan. To reduce differences attributable to communicative setting, we analyze two public, asynchronous forums using the same operational definition of gossip. Gossip occurs on Moltbook, but its prevalence is 2.6 to 6 times lower than on PTT, depending on the denominator used. On both platforms, gossip frequently targets locally prominent figures, tends to elicit agreement from the first respondent, and is rarely presented as unsupported rumor. The clearest difference concerns how subsequent responses develop. Among threads containing at least one codable reply, challenges occur in 65.1% of human threads but only 21.3% of agent threads. Moreover, following an early aligning response, consensus remains unchallenged in 83.6% of agent threads, compared with 44.7% of human threads. This thread-level contrast remains after controlling for thread depth and board composition and under recalibration against two human annotators. Estimates based on individual reply turns are less robust and are therefore reported as bounds. These findings suggest that AI-agent communities reproduce the informational dimension of gossip, while the extent to which gossip performs comparable relational functions remains unresolved.

Analog in-memory computing performs the matrix-vector multiplications of neural networks directly inside the memory array, which saves time and energy. But each memory cell stores only a few levels and is noisy, so one cell cannot hold a weight precisely. The standard fix is to split each weight across several cells, like digits of a number. The base of this split decides the trade-off: a large base gives fine resolution but amplifies the noise, and a base near one averages the noise but wastes resolution. The best-known prior analysis considers only the noise, and so it always picks a base of one. We propose a principled method that also accounts for the limited number of levels per cell. It gives the optimal base in closed form, from a single measurement of the device noise. On a device-physics simulator, the optimal split is 3.3 dB more accurate than the common base-16 split, and it beats equal splitting in end-application accuracy.

We address a question of Canary–Taylor and Canary–Minsky–Taylor for sufficiently symmetric compact hyperbolic $3$-orbifolds with totally geodesic boundary. We give sufficient conditions on the symmetries of such an orbifold to show that, among the complete convex cocompact structures on the interior, the structure with Fuchsian ends is a critical point (respectively, a strict local minimum) for the critical exponent. We also provide an infinite family of non-rigid examples fulfilling these conditions.

We investigate the global dynamics and cosmological viability of non-singular solutions in an anisotropic Bianchi type I universe featuring an interacting vacuum energy component $V$ and a perfect fluid $\rho$, extending previous work based on a Robertson-Walker geometry. By modeling the energy-momentum transfer via a phenomenological four-vector $Q_\mu$, we reduce the field equations to a four-dimensional autonomous dynamical system for the expansion rate $\Theta$, total shear $\sigma$, energy density $\rho$, and vacuum component $V$. We examine two distinct forms for how the interaction depends on $\rho$ and $V$: a linear coupling $Q_1 \propto \Theta[\xi(V_\Lambda - V) + \chi \rho]$ and a non-linear coupling $Q_2 \propto \Theta \rho (1 - V/V_\Lambda)$. Using a potential-energy analogy and phase-space analysis, we show that the linear model $Q_1$ naturally admits non-singular bouncing trajectories. In contrast, unlike the Robertson-Walker case, for the non-linear interaction $Q_2$, invariant boundary surfaces in phase space strictly constrain the domain of expansion ruling out cosmological bounce scenarios for physical matter configurations.

System $F_{<:}^{\top}$ has decidable subtyping but lacks minimum types. We prove that typechecking is decidable for arbitrary explicitly annotated terms with unrestricted subsumption. The difficulty is that type abstraction uses a variable's declared bound to type its body, while quantified subtyping forgets that bound. We construct finite covers that preserve all required subtype comparisons across this change of context. These covers yield a compositional finite typing basis and a decision procedure. We then derive a backward checker that propagates acceptable targets without constructing the complete typing basis. Rectangularity of typing families gives a uniform elimination domain while retaining every result type, even when the canonical type is not least. Finite inverse families transport targets through type substitution. The same inverse specification recovers bound forgetting and yields finite type-avoidance families. Both typechecking procedures are total Rocq functions proved equivalent to the original typing judgment. For a separate symbolic word-RAM realization, we prove a quartic worst-case work bound. We measure family representation sizes and comparison storage in independent OCaml prototypes on synthetic checking judgments.

We establish finite-dimensional von Neumann type inequalities for commuting matrix tuples in noncommutative operator balls. Let $\Omega=\mathbb{D}_Q$ be the NC operator ball of a linear pencil $Q$ with linearly independent coefficients. If $\Omega(1)$ admits a transitive subgroup of automorphisms with NC lifts and $\Omega(1)$ has the bounded $H^\infty$-Gleason property at the origin, then $\|f(T)\|\leq C_{\Omega,n}\|f\|_{H^\infty(\Omega(1))}$ for every commuting tuple $T\in\Omega(n)$, with $C_{\Omega,n}=(2\rho_{\Omega}K_{\Omega})^{n-1}$; here $K_{\Omega}$ is the Gleason constant and $\rho_{\Omega}$ is the sum of the suprema of the coordinate functions on $\Omega(1)$. The scalar coordinate bounds persist at every matrix level. The hypotheses hold for products of row and column balls, where $\rho_{\Omega}=d$, yielding an unconditional estimate $(2dK_{\Omega})^{n-1}$. For a general type I Cartan domain $R_{p,q}$, we obtain only a conditional result: the same bound holds provided the scalar domain has the bounded $H^\infty$-Gleason property at the origin, which we do not establish when $\min(p,q)\geq 2$.

NVIDIA Grace–Blackwell systems make CPU–GPU memory increasingly unified at the programming level, but unified addressability does not make the memory system uniform. A CUDA managed allocation on GB200 may be served from GPU-local HBM, accessed through host/system memory, demand-migrated, prefetched, reused after GPU access, or evicted and reloaded under capacity pressure. The problem is that these states share a programming interface while exercising different hardware paths and runtime mechanisms, making a single “Unified Memory bandwidth” number misleading. This paper presents a placement-controlled microbenchmark study of CUDA Unified Memory on NVIDIA GB200, using GH200 as a Grace–Hopper baseline and GB10/DGX Spark as a validation platform. Our methodology separates local HBM access, host/system-memory access, explicit movement, managed first touch, prefetch, reuse, access-pattern sensitivity, oversubscription, and CPU–GPU handoff, then summarizes the observations with a measurement-calibrated model of compute, access, migration, eviction, synchronization, and handoff costs. On GB200, a 1~GB STREAM-style triad reaches 3963~GB/s from local HBM but 304~GB/s through host-mapped CPU/system memory; for a 256~MB streaming kernel, cold CPU-initialized managed memory reaches 14.1~GB/s, while managed prefetch and reuse reach 4606~GB/s and 4504~GB/s. Below the capacity boundary, prefetched and reused managed memory remain above 4.6~TB/s, but at 125% of CUDA-visible memory they fall to 968~GB/s and 1214~GB/s, showing that Grace–Blackwell unified memory must be understood through placement, access history, locality, reuse, and capacity pressure.

Mixture-of-experts (MoE) language models activate only a few experts per token, yet all expert weights must be stored. Mixed-precision quantization reduces this storage cost by assigning higher bit-widths to sensitive experts and lower bit-widths to resilient ones, but expert rankings alone do not determine how strongly to weight their errors. To address this gap, we propose NatScale, a contrast-calibrated allocation framework for mixed-precision MoE quantization. It uses a model-specific power transformation to calibrate gradient-based expert weights to an information-theoretic contrast target while preserving rankings. We jointly evaluate each expert's gate, up and down configurations to estimate its output error. We then combine these errors and calibrated weights with an existing prior based on weight spectra, variance and precision decay to select configurations under a storage budget. Across three models, NatScale achieves the lowest native-to-quantized KL divergence and the highest top-token agreement in all nine settings against five allocation baselines. It also yields the lowest perplexity in seven settings. These findings highlight the importance of objective-aware precision allocation.

Multimodal Large Language Models have made significant progress in referring expression comprehension (REC), yet most REC benchmarks still focus on final-target localization. Complex queries often involve intermediate visual references with different dependencies on prior grounding, but final-only evaluation leaves this process unexamined. To address this gap, we formulate trajectory-level REC, in which models receive an ordered sequence of grounding steps constructed from a single complex query and localize the target regions associated with each step. We instantiate this setting in ReferFlow-Bench, which characterizes structured region transitions through four trajectory types, namely Refinement, Shift, Reset, and Mixture. Experiments show that current models struggle to consistently ground intermediate visual references across successive steps. We further propose ReferFlow, which decouples interleaved text-latent trajectory generation from coordinate decoding. Specifically, Stateful Region Latent Reasoning represents each target region as an object-indexed state composed of continuous latents, with explicit visual and spatial supervision to preserve region information for subsequent grounding. Trajectory-Aware Parallel Decoding then recovers all coordinate blocks in parallel through four geometry-constrained refinement rounds, with each block conditioned on its corresponding trajectory prefix, thereby reducing within-box sequential dependencies and eliminating cross-box autoregression. We further apply Grounding-Aware GRPO to promote consistent grounding across steps and learn adaptive trajectory generation from complex REC queries. ReferFlow achieves leading performance on general REC benchmarks and ReferFlow-Bench.

Human demonstrations are today used largely for pretraining vision-language-action models, with little ability to use the same data for target-embodiment or task-oriented training, which scalable deployment of robots in industrial and general environments depends on. A human demonstration recorded on a simple and scalable device such as a mobile phone can serve as post-training data for a robot whose body differs in structure and capability from the human who recorded it. This is made possible not by retargeting the hand's motion but the object's. A capture yields a body-free record: the object's pose over time, its contact intervals, and a reconstructed 3D object with provenance. Any robot, given as a URDF and a short descriptor, is solved against that record and scored in simulation against the demonstrated object motion as ground truth: the human-to-simulation leg of human-to-simulation-to-robot transfer, measured per robot. Each (robot, episode) pair gets one outcome: pass, failure with a named mode, or refusal, with its reason, before any motion. The method runs as a working system over a growing collection; the set analysed here is a sample of it: 42 captures solved on 8 robots, 157 pairs, of which 31.2% pass, 52.2% fail, 14.0% are refused and 2.5% are unauditable (kinematic feasibility, +/-50 mm / +/-15 deg, in simulation). Refusals held up: every pair the checks refuse on stored evidence yet ran anyway failed (13 of 13; 5 on a body whose public model welds its hand). A description file could not be shown to screen a robot: its outcomes were barely more predictable than guessing. No policy has yet been trained on the record. The record decides what a robot may post-train on; whether the policy then works on the real robot is the simulation-to-robot question, answered downstream.

Preference optimization ranks final answers and trajectory RL maximizes aggregate returns, yet neither credits the local change that turns a flawed reasoning state into a better one. We introduce Lifted State Policy Optimization (LSPO), which establishes this finite, cost-adjusted transition as the primary unit of learning. Each textual answer is augmented with a learned continuous coordinate, forming a lifted state that an energy function evaluates and orders. A shaped reward drives energy descent net of edit and step costs, and an internalization loss absorbs selected low-energy answers into the direct generator. On Qwen3.5-27B, the resulting single-pass policy reaches 71.8% aggregate accuracy across mathematics, science, code, and logic benchmarks, matching test-time reflection at 71.9% with 28% lower latency and 25.8% fewer tokens. The pattern holds across dense and mixture-of-experts backbones, and matched controls confirm that transition credit and the lifted coordinate each contribute, as does answer internalization. Our code is available at https://github.com/Venomrko/lspo.

Asynchronous EEG event detection supports practical brain-computer interfaces by identifying event classes and temporal boundaries directly from continuous recordings without predefined event boundaries at inference time. The primary challenge lies in extracting event-related patterns embedded in ongoing background activity. To address this, we propose NeuroDETR, a discrete spatiotemporal multiscale framework that combines structured tokenization with event-aware feature refinement. Multiscale temporal codebooks capture brief responses and sustained dynamics, while Spatial-Pyramid VQ hierarchically encodes spatial structure across EEG channels. These complementary representations form a compact event memory for jointly classifying events and estimating their onsets and offsets. Before tokenization, we apply FOCAL, an event-aware sparse attention module that uses predicted event presence to guide temporal feature refinement and spatial aggregation, emphasizing likely event periods while preserving context across the recording. Experiments on eight EEG datasets that span diverse paradigms demonstrate state-of-the-art performance. These findings provide a basis for the development of BCI systems that recognize meaningful neural activity during continuous interaction and monitoring.

The thermal properties of the \(\rho\) meson are revisited within the soft-wall AdS/QCD framework. The dilaton background is calibrated against lattice QCD screening-mass data through a neural-network-assisted inverse procedure. Using this calibrated background, we compute the temporal vector spectral function and the lowest vector quasi-normal modes. The pole mass \(m_{\mathrm{pole}}(T)\) and thermal width \(\Gamma(T)\) are then extracted from the corresponding complex quasi-normal mode frequencies. Adopting the vanishing real part of the quasi-normal mode frequency, \(\omega_{\mathrm{Re}}(T_d)=0\), as a criterion for meson dissociation, we estimate \(T_d\approx168\,\mathrm{MeV}\). As the temperature increases, the thermal width grows, and the spectral function evolves from a narrow Breit-Wigner-like resonance peak into a transport peak, confirming the QNM prediction that the vanishing of the pole mass is accompanied by the emergence of a transport peak and making it difficult to identify a quasiparticle peak. A numerical extraction of the dispersion relation shows that the propagator can be described by a finite-temperature simple-pole form with momentum-dependent thermal width, characterized by a diffusion coefficient \(D(T)\) and an effective propagation speed \(u(T)\), whose temperature dependences are also extracted. This form modifies the usual relation between the screening and pole masses. These results may provide a useful reference for effective studies of the hot hadronic medium.

We study the finite-sample convergence of Q-learning algorithms for the average-reward formulation of Reinforcement Learning (RL) with options. While options allow temporarily extended and hierarchical actions, the average-reward formulation incorporates continual tasks beyond discounted and episodic RL. We establish the first $\tilde{O}(1/\text{iterations})$ convergence guarantees, in the mean-square sense, for average-reward option Q-learning algorithms in both the inter- and intra-option settings. First, we prove that both inter- and intra-option Bellman operators satisfy multi-step span contractions under unichain assumptions. Then, we propose synchronous estimators of these multi-step option Bellman operators leading to two variants of option Q-learning. Finally, we extend the stochastic approximation framework to prove convergence rates of these two algorithms under the minimal assumptions used in the literature.

Partially optimal assignments (also called persistencies) allow combinatorial optimization problems to be reduced by fixing a subset of variables to values consistent with at least one optimal solution. For the quadratic unconstrained binary optimization (QUBO) problem, such assignments can be computed efficiently via autarkies of quadratic posiforms. However, the largest autarky domain and thus the number of fixed variables can depend on the specific posiform representation. We show that every quadratic posiform with the greatest possible constant term (the roof-dual bound) yields the largest autarky domain obtainable from any quadratic posiform. By computing such a roof-dual-optimal quadratic posiform and a corresponding autarky with largest domain in polynomial time, one can therefore attain the maximum partial optimality obtainable by quadratic posiform autarkies in polynomial time. This justifies the computation of roof-dual-optimal quadratic posiforms and corresponding autarkies in popular polynomial-time algorithms and establishes that finding additional partial optimality in QUBO requires going beyond autarkies of quadratic posiforms.

We study nonconvex-strongly-concave minimax problem $\min_{\mathbf{x}\in\mathbb{R}^{d_x}}\max_{\mathbf{y}\in\mathbb{R}^{d_y}}f(\mathbf{x},\mathbf{y})$ in which the objective has $\rho$-Lipschitz Hessian and condition number $\kappa$. We propose envelope cubic regularized Newton method (ECRN) which applies a refined inexact cubic regularized Newton method to the envelope of the primal function $\Phi(\cdot) : = \max_{\mathbf{y}\in\mathbb{R}^{d_y}}f(\cdot,\mathbf{y})$. We show that ECRN finds approximate second-order stationary points of $\Phi(\cdot)$ with $\widetilde{\mathcal{O}}(\sqrt\rho\,\kappa^{3/4}\varepsilon^{-3/2})$ second-order oracles, improving the condition number dependence $\mathcal{O}(\kappa^{2})$ achieved by the best known second-order methods. Our improvement comes from the key observation that the Hessian Lipschitz parameter of the envelope is $\mathcal{O}(\rho\kappa^{3/2})$, which is sharper than the order of $\mathcal{O}(\rho\kappa^{3})$ for the function $\Phi(\cdot)$. We also conduct a lower bound on second-order methods to show that our complexity is optimal up to a logarithmic factor.

Agents driven by large language models are increasingly deployed on long-horizon tasks, where they use tools and modify real workspaces. How well they perform depends as much on the harness around the model as on the model itself. Existing benchmarks measure downstream task success under a fixed harness, leaving harness engineering itself unexplored. We propose Doc2Harness, a two-stage benchmark that evaluates long-horizon harness engineering directly. In Stage 1, a build model operating inside a fixed builder harness receives an interface-only contract skeleton and a development document that consolidates behavior across twelve frontier harnesses, and then constructs a complete candidate harness in an isolated container. In Stage 2, the frozen candidate harness runs in containers separate from the construction environment, one per test case, and is driven end to end by a scripted mock model. We score each test case using four observable channels, namely the requests sent to the model, the files on disk, the process exit code, and the command output; positive controls rule out vacuous passes. Across nineteen frontier models, each evaluated with three independent builds on 328 test cases, GPT-6 Astra achieves the highest pass rate at 53.05%, while the weakest model reaches 27.44%, a gap of roughly twenty-six percentage points. Even the strongest model fails nearly half of the test cases, and failures cluster around how cross-cutting functionality is split across modules. To our knowledge, Doc2Harness provides the first deterministic benchmark for measuring long-horizon harness engineering.

Topological edge states are a hallmark of topological phases, with their existence tied to bulk band topology through bulk-edge correspondence. In photonic pseudospin-Hall systems, these states exhibit pseudospin-momentum locking, with lattice interactions and interface geometry determining each pseudospin's propagation direction. Reversing the pseudospin-dependent propagation direction without altering the lattice configuration or excitation handedness remains a fundamental challenge in controlling topological edge transport. Here, we theoretically and experimentally demonstrate cavity-tunable topological edge transport in a microwave metasurface embedded within a metallic cavity. Varying the cavity height reshapes resonator interactions, driving band inversion and topological phase transition while preserving the lattice geometry. For a fixed domain-wall configuration, this transition reverses the propagation direction associated with each pseudospin while preserving pseudospin-momentum locking. Excitations with the same handedness are observed to launch edge waves propagating in opposite directions at their respective edge-band frequencies determined by the cavity height. These results establish cavity electrodynamics as an external means of controlling the bulk topology and reconfiguring the directional response of topological interfaces, creating new opportunities for topological wave routing in fixed photonic lattice structures.

Missing data is a pervasive challenge in machine learning, often degrading predictive performance and complicating model deployment. Most existing approaches treat imputation as a preprocessing step independent of the downstream task, a separation that becomes problematic under train-test mismatches in missingness mechanisms or rates. We introduce a unified framework that treats missing entries as variables in a task-conditioned optimization problem. We instantiate this framework in two settings: an amortized approach for scenarios with missing data at both training and test time, and a latent optimization approach for settings where only training data is incomplete. The evaluation is conducted on 98 tabular datasets, and robustness under train-test mismatches is assessed on 36 datasets. Results reveal that reconstruction error constitutes a poor proxy for predictive utility (Spearman rho approximately 0.16 to 0.32), and that task-aware imputation becomes critical in scenarios where classical methods fail to recover complete-data performance, achieving win rates of up to 80% in challenging train-test mismatch scenarios.