Papers

Let $\mathbf{G}=\{G_1,\dots,G_{2n}\}$ be a collection of not necessarily distinct balanced bipartite graphs of order $2n$ with a common bipartition $V=(X,Y)$. A cycle $C$ with $V(C)\subseteq V$ and $|E(C)|\leq 2n$ is called rainbow in $\mathbf{G}$, if there exists an injection $\phi\colon E(C)\to [2n]$ such that $e\in E(G_{\phi(e)})$ for each $e\in E(C)$. The graph collection $\mathbf{G}$ is said to be rainbow bipancyclic if it contains a rainbow cycle of every even length from 4 to $2n$. In this paper, we show that if $e(G_i)\ge n^2-n+1$ for each $i\in[2n]$, then $\mathbf{G}$ is rainbow bipancyclic unless $G_1=G_2=\dots=G_{2n}\cong B_{n}^1$, where $B_{n}^1$ is the graph obtained from $K_{n,n}$ by deleting all edges in its one subgraph $K_{n-1,1}$. As a corollary, we obtain that if $\rho(G_i)\ge \rho(B_{n}^1)>\sqrt{n(n-1)}$ for each $i\in[2n]$, then $\mathbf{G}$ is rainbow bipancyclic unless $G_1=G_2=\dots=G_{2n}\cong B_{n}^1$, which strengthens Theorem $5$ of [Electron. J. Combin., 33(3)(2026), \#P3.29] and Theorem $1.6$ of [Linear Algebra Appl., 743(2026), 250–270] from rainbow Hamiltonicity to rainbow bipancyclicity. We also characterize all bipartite graph collections that are not rainbow bipancyclic under the condition $\rho(G_i)\ge \sqrt{n(n-1)}$ for each $i\in[2n]$

Preference alignment enables language models to better reflect human values, but the preference data contains sensitive information, especially when derived from surveys about political beliefs, social norms, religion, gender attitudes, and cultural values. This paper studies privacy-preserving alignment on questionnaire-derived data from the World Values Survey, where supervision takes the form of ordinal labels rather than standard pairwise rankings. Existing efforts mainly focus on general privacy protections upon model training, while data-specific methods for survey data remain unexplored. We first show the vulnerability of aligned models, then formulate the task as rating prediction and introduce label differential privacy. Building on this formulation, we construct a differential private pipeline utilizing three privacy mechanisms: randomized response, exponential mechanism, and DP-SGD. Experiments show that simple label-level mechanisms outperform gradient-level methods, and proper aggregation function for preprocessing also make large contribution. The new fine-grained private comparison motivates explorations toward language model alignment with formal privacy guarantees.

Humans expand their locomotion capability by wearing appropriate footwear, such as hiking boots for mountains or skates for ice. Footwear changes the ground-contact interface and enables traversal of otherwise difficult terrain. In contrast, locomotion controllers are typically trained for a fixed morphology, and their performance can degrade when shoes alter foot geometry, mass, and friction. We propose SHOES, a sample-efficient framework for adapting locomotion policies to footwear-induced morphology changes. SHOES freezes a simulation-trained nominal policy and fine-tunes only lightweight, identity-initialized modulation modules on the robot, preserving the initial behavior while enabling efficient hardware adaptation. We also introduce SafeBox, a workspace-aware waypoint sampler that constrains online adaptation within a user-defined workspace. The simulation results with a shoe-equipped Unitree Go2 show that SHOES substantially recovers locomotion performance after footwear-induced morphology changes using limited additional adaptation. Under the same adaptation budget, SHOES outperforms FiLM-only, Linear Adapter-only, and residual-RL baselines. Real-world experiments on a Unitree Go2 fitted with human shoes further evaluate the effectiveness of SHOES for hardware deployment.

Comparing temporal networks is a challenging problem in network analysis. Commonly adopted methods compare structural properties of temporal graphs and can be highly sensitive to the pre-selected features. However, temporal networks are the support of dynamical processes, and a process may take place in statistically indistinguishable ways on structurally different temporal graphs. In particular, a dissimilarity measure that compares temporal graphs based on how spreading processes unfold on them is highly desirable. In this work, we first define the Time-Shift DTW, a dissimilarity between epidemic curves that accounts for both differences in their shape and temporal shifts. We then introduce Epidemic-Aware Temporal Graph Dissimilarity (EATGD), a deterministic and differentiable dissimilarity between temporal graphs that combines an embedding-based temporal graph distance with a set of topological and temporal features. Its parameters are calibrated using stochastic SIR simulations to maximize the correlation with the Time-Shift DTW, after which graph comparisons require no further epidemic simulations. Using empirical human proximity networks from the SocioPatterns collaboration and synthetic temporal graphs, we show that EATGD captures epidemic-based graph dissimilarity and generalizes across heterogeneous network settings. Its differentiability and computational efficiency make EATGD suitable for integration into machine-learning pipelines and provide a potential loss function for training generative models to reproduce epidemic dynamics without requiring an exact reconstruction of fine-grained network structure.

3D scene graph generation requires understanding both object semantics and metric spatial relations. However, existing open-vocabulary methods often struggle with spatial predicates because language similarity reflects semantic co-occurrence rather than explicit geometry. We propose GHOST, a Geometry-constrained Hybrid diffusion framework for Open-vocabulary 3D Scene graph generaTion. GHOST jointly models continuous node geometry and discrete edge predicates, following a geometry-to-constraint-to-predicate denoising process to ensure geometrically consistent relation prediction. It introduces language-grounded constraint induction, which maps predicate embeddings to differentiable geometric constraints that guide both layout refinement and predicate reweighting. A Geometry-Topology Collaborative Denoiser further couples node and edge reasoning through noise-adaptive interaction and orientation-aware modeling. Experiments on 3DSSG demonstrate state-of-the-art performance in both closed-set and open-vocabulary settings, including over 17-point gains over RelationField on spatial predicates.

Spectral duality structures (SDS) explain why a distinguished family of initial distributions makes the absorption probabilities of resetting processes insensitive to the resetting mechanism. Here we study their axioms. We prove that the six defining conditions are mutually independent and determine what each one contributes. The key tool is a structure theorem valid for an arbitrary permutation and an arbitrary positive weight: every insensitive distribution is supported on a union of cycles balanced at a common level, and the level of a cycle is fixed by the geometric mean of the weight on it. From it, positivity selects the admissible root, the constant orbit product is equivalent to the existence of an insensitive distribution of full support, and the involution is equivalent to the response rank being equal to the number of free weight parameters. Without the duality relation, insensitivity of a single distribution is cheap and generically isolated; duality turns it into structural neutrality of the separatrix. The full-rank condition splits into two layers: a weaker condition is equivalent to maximal response rank, while full rank also excludes insensitivity at any other level. We then show that a single SDS is internally rigid: compatible semigroup structures force a constant weight, compatible abelian group structures obey a precise arithmetic condition, congruences form a simple lattice, and the automorphism group is computed explicitly. Finally, the axioms do not determine the orientation of the response; in the two-site case we give the exact condition under which the geometric and analytic sign criteria agree.

We investigate whether SiO maser line profiles can distinguish asymptotic giant branch (AGB) stars from red supergiants (RSGs) and identify unusual AGB-classified sources near the RSG regime. We compiled 2,956 detected SiO maser spectra for 1,551 objects and constructed reference samples of 1,068 O-rich AGB stars and 36 RSGs. The full width at zero intensity (FWZI) was reliably measured for 1,020 AGB stars and 32 RSGs. AGB stars are concentrated at narrow line widths: 81.5% have FWZI <10 km s^-1, whereas 81.2% of RSGs have FWZI >15 km s^-1 and none has FWZI <10 km s^-1. Infrared two-color diagrams provide only partial separation. Combining FWZI with luminosities based primarily on quality-filtered Gaia/Bailer-Jones distances, with independent literature distances for several RSGs, reveals a weak tendency for wider SiO maser lines at higher luminosities but no clean boundary. We therefore define an empirical RSG-adjacent region in the FWZI-luminosity plane, 15 <= FWZI <= 26.6 km s^-1 and 3.9 <= log(L/L_sun) <= 4.9, to characterize the high-luminosity, broad-line tail of the AGB-classified sample. Ten sources fall within this region. Using infrared SEDs, DUSTY fits, OH/H2O maser information, and variability, we find that six are most naturally interpreted as luminous AGB-like objects, two warrant follow-up to assess possible high-initial-mass AGB, RSG-like, or SAGB-related interpretations, and two are less securely constrained because of poor DUSTY fits. The RSG-adjacent region is therefore a physically mixed screening space, not a definitive classification box, for selecting high-priority follow-up targets.

Explainable face forgery detection requires not only correct judgments but also forensic evidence supported by the input image. However, training cues are typically derived from the forgery generation pipeline. Since images available to the model are of limited quality and resolution, it is difficult to observe the fine-grained traces these cues refer to. Training methods that further supply such cues as privileged supervision exacerbate the problem, as the student is taught to articulate evidence it cannot perceive. The student consequently resorts to templated or over-generalized expressions, giving rise to the correct-answer, wrong-evidence (CAWE) failure. We propose a dual supportability audit that filters privileged cues before distillation. Each candidate cue must be predictable from the remaining privileged context and causally tied to high-attribution visual regions in the current image. Only cues satisfying both conditions receive substantial distillation weight, preventing unsupported details from leaking into the student. Experiments across eight benchmarks show that our method maintains or improves detection accuracy while significantly raising explanation faithfulness compared to existing paradigms.

Fine-tuning large language models at scale is increasingly limited by the memory cost of backpropagation. Zeroth-Order (ZO) optimizers reduce this burden by relying only on forward function evaluations, but they still exhibit a substantial performance gap to first-order (FO) optimizers such as Adam. We argue that this gap does not arise solely from the absence of explicit gradients: FO fine-tuning also benefits from informative low-rank optimization geometry, large-scale signal aggregation, and well-conditioned update directions. Motivated by this, we introduce StructZO, a structured Zeroth-Order optimization framework for memory-efficient LLM fine-tuning. StructZO performs large-query ZO estimation within an activation-induced informative subspace and applies spectral control to the resulting reduced-space update before mapping it back to the original parameters. This lets ZO aggregate useful directional signals in a compact, geometry-aware space while avoiding the activation and optimizer-state memory costs of backpropagation. We show theoretically that, when the induced subspace captures concentrated optimization-relevant directions, StructZO reduces the effective ZO estimation dimension from $mn$ to $mr$, with the remaining projection error governed by the spectral tail of the activation Gram matrix. Empirically, across OPT-series and Llama3.1-8B on diverse downstreamtasks, StructZO improves over the strongest existing ZO baselines by up to $8.7%$ relative on average and up to $26.9%$ relative on individual tasks, while remaining within $1.5%$ of FO-Adam on average. These results suggest that structured and spectrally controlled ZO updates can substantially narrow the gap between ZO and FO optimization.

The growing use of language models for forecasting motivates a broader evaluation of their world-model capabilities. Such evaluation must go beyond predictive accuracy to assess hidden-state inference and intervention prediction. Real-world forecasting benchmarks offer limited access to hidden-state ground truth and controlled experiments. We introduce CivWorldBench, a benchmark built on a multi-agent strategy game engine with recorded internal states, controlled observations, and paired intervention rollouts. Its 1,900 decision points from 475 worlds support three task levels: association forecasting, belief inference, and intervention prediction. Reference predictors support attributable evaluation of capability gaps, with an expert harness and empirical ceiling estimates contextualizing scores. Stored trajectories make intermediate predictions verifiable, while agent-play experiments test whether world-model capabilities support decision-making. The main panel comprises eleven frontier language models. Composite benchmark scores correlate with real-world forecasting leaderboards on matched model panels, more closely than with a general-capability index, supporting its use as a proxy for real-world forecasting capability. Strong association forecasts do not consistently extend to belief inference or intervention prediction, and effect magnitudes remain poorly calibrated despite informative direction predictions. Process verification reveals errors missed by final-answer evaluation, and structured reasoning improves intervention prediction for the strongest model in the process study. Agent-play experiments identify useful assisted plans and motivate evaluating decision-relevant capabilities beyond association forecasting. These findings identify hidden-state inference, intermediate-state prediction, and effect calibration as priorities for world-model training.

Pseudonymous accounts and complex smart-contract ecosystems substantially hinder the tracing of illicit cryptocurrency fund flows. Existing Graph Neural Networks (GNNs) have achieved promising performance in blockchain fraud detection, yet their static node- or edge-level predictions do not naturally generalize to multi-hop fund tracing. Meanwhile, existing tracing methods mainly rely on predefined heuristics to capture multi-hop relationships, limiting their adaptive reasoning capabilities. To bridge this gap, we introduce CryptoFlowBench, a benchmark constructed from authoritative reports on cryptocurrency-related illicit incidents, with four tasks spanning local to multi-hop fund tracing. These tasks pose substantial challenges to existing learning- and heuristic-based methods, particularly in complex multi-hop scenarios. We therefore propose ChainSleuth, a graph-tool-augmented agent that iteratively reasons, invokes graph tools, and updates its tracing trajectory, enabling adaptive information acquisition and recovery from erroneous paths. Experiments show that no baseline consistently dominates all four tasks, revealing substantial gaps between local fraud detection and multi-hop fund tracing. ChainSleuth achieves notable improvements on multi-hop tasks, demonstrating the potential of agentic graph reasoning for cryptocurrency fund investigation.

Diffusion models, particularly Diffusion Transformers, achieve strong image and video generation quality but remain expensive at inference time due to repeated denoiser evaluations. Feature caching offers a deployment-friendly acceleration strategy by reusing or predicting intermediate representations without retraining the generator or modifying the sampler. However, existing cache-then-forecast methods often rely on Taylor-style finite-difference extrapolation, which can become unstable over longer cache intervals, and typically predict local module outputs whose errors may accumulate through subsequent denoiser blocks. We propose BeziCast, a training-free diffusion acceleration framework that forecasts output-proximal denoising representations using low-order B'ezier trajectories. BeziCast estimates B'ezier control points via Tikhonov-stabilized fitting, providing a smooth, capacity-controlled temporal parameterization that avoids explicit high-order derivative estimation and decouples trajectory capacity from cache-query density. To moderate aggressive extrapolation, we further derive equivalent forecasting weights and introduce a convex-hull-inspired guardrail that detects high-risk predictions and softly pulls them toward a conservative simplex-projected estimate. Extensive evaluations across advanced image and video diffusion models demonstrate the effectiveness of BeziCast. In particular, BeziCast accelerates FLUX.1 by up to (4.79\times) and HunyuanVideo by up to (4.11\times), while preserving substantially better generation quality than competing acceleration baselines.

The estimation of heterogeneous treatment effects is a central objective of causal inference. However, state-of-the-art algorithms to solve this task are based on machine learning principles, and thus behave as black boxes. Consequently, the identification of covariates driving heterogeneity remains a challenging and open problem. To address this limitation, we introduce CausalTreeHFD, an interpretable extension of causal forests, based on the Hoeffding functional decomposition adapted to tree ensembles. Our approach decomposes predictions of conditional average treatment effects (CATE) into contributions from individual covariates and pairwise interactions, providing a direct characterization of the factors driving treatment effect heterogeneity. We establish the consistency of CausalTreeHFD, which converges towards the Hoeffding decomposition of the underlying CATE function, under standard assumptions for the analysis of causal forests. Experiments on simulated and real datasets show that CausalTreeHFD accurately identifies relevant covariates and interactions, and precisely recovers their contributions to heterogeneous treatment effects.

An edge of a multigraph is rich with respect to a proper edge-coloring if all the edges adjacent to it receive mutually distinct colors, and a proper edge-coloring is a rich-neighbor coloring if every non-isolated edge has a rich edge adjacent to it. The least number of colors in such a coloring is the rich-neighbor chromatic index chi'_rn(G). So far it was studied for subcubic graphs only, and multigraphs of larger maximum degree are considered here for the first time. The only upper bound valid in general was the quadratic one inherited from the strong chromatic index, while a single rich edge already requires 2D-1 colors in a D-regular graph, where D denotes the maximum degree. We give an upper linear bound chi'_rn(G) <= 6D-8 which holds for every loopless multigraph G with D >= 3, and we show that a coloring realizing this bound can be found in polynomial time. Consequently chi'_rn(G) = Theta(D). For D-regular graphs with D >= 3 the lower bound is 2D-1, and the upper bound is 5D-8. The bound 5D-8 holds more generally for every multigraph with D >= 3 which has a dominating P_{>=3}-system, and we characterize these multigraphs: such a system exists if and only if k_2(G-T) <= 2|T| holds for every set T of vertices, where k_2 counts the components on two vertices. In particular the bound holds for every graph with 3 <= D <= 4d-4, where d denotes the minimum degree. The paper is concluded with a conjecture on the tight upper bound on chi'_rn(G).

Assuming a smoothness property for mixed-characteristic shtuka spaces and hyperbolic localization for twisted sheaves, we determine the inertial restriction of the Fargues-Scholze $L$-parameter for irreducible depth-zero representations. Let $E$ be a non-archimedean local field of residue characteristic $p$, let $G$ be an unramified connected reductive group over $E$, and let $\pi$ be an irreducible smooth depth-zero representation of $G(E)$ over $\overline{\mathbb{F}}_{\ell}$ where $\ell$ is a prime number which does not divide $p|\pi_0Z(G)|$. Let $\varphi_{\pi}^{\operatorname{FS}}$ be the Fargues-Scholze $L$-parameter associated to $\pi$. We describe the restriction of $\varphi_{\pi}^{\operatorname{FS}}$ to the inertia subgroup in terms of Deligne-Lusztig theory. We prove this by computing the inertia action on the cohomology of shtuka spaces with depth-zero level structure. As an application, we prove that the Fargues–Scholze $L$-parameters agree with DeBacker–Reeder $L$-parameters over $\overline{\mathbb{Q}}_{\ell}$.

Visual artifacts such as charts, technical diagrams, webpages, and document pages underpin scientific, commercial, and engineering workflows. Editing these artifacts requires direct modification, dependency-aware updates, preservation of unaffected content, and compliance with domain constraints. We define this capability as Visual Artifact Operation (VAO). Prior benchmarks test parts of this problem, including cascading updates in charts. We study direct edits, dependent updates, and preservation across visual domains and pixel, code, and agent paradigms under one image-only protocol. We introduce Visual Artifact Operation Bench (VAO-Bench), comprising 1,573 manually screened tasks across nine artifact categories and three difficulty levels. VAO-Bench uses executable artifacts and deterministic rendering to trace reference transformations and annotate direct edits, dependent updates, and preservation constraints. All systems receive the same source image and instruction; we evaluate pixel-space editors, code-generating multimodal systems, and tool-using agents on direct-edit accuracy, dependency-aware update, content preservation, domain validity, and visual quality. Experiments show that executable-code systems better support dependent updates, while pixel-space editors offer faster execution and strong visual quality. Explicitly stating dependencies improves both paradigms, identifying implicit-update inference as a central bottleneck. VAO-Bench provides a reproducible foundation for dependable visual artifact editing across generation paradigms.

Recent world action models draw on video generation priors to jointly predict future observations and robot actions. Adapting these priors to control requires determining how future predictions should guide policy learning. RAP-WAM combines predictive Rehearsal and Action Perturbations (RAP) with future-supervised queries and Coupled Action Projection for policy learning. Predictive rehearsal trains on model-generated inputs while retaining recorded targets, and accumulates recurring errors into a spatial prior. We perturb actions and measure changes in video predictions. Action-response-based spatiotemporal credit assignment combines these responses, prediction error, and the rehearsal prior to allocate visual supervision; spatially aggregating the responses determines supervision intensity across future action steps. No separate scoring network or deployment-time probe is required. The base learns from a video-pretrained backbone without intermediate pretraining on external embodied data. We evaluate the fixed base and its agent-refined, task-conditioned system. On 42 RoboDojo tasks, their average success rates are 12.85% and 15.62%, with Scores of 17.86 and 20.59. Across 15 real-robot tasks, the complete system achieves 89.00% task-macro-average success, exceeding the strongest of five baselines by 37.67 percentage points. Across 315 fixed-output simulation windows, 45.21% of response-top20 positions fall outside error-top20, revealing information beyond prediction error. Videos and further details are available on the project website: https://rapwam.github.io/.

Fast Tendermint reduces Tendermint's good-case latency to two communication steps for n>=5f+1. We show that its published round-change rule violates Agreement: one Byzantine process suffices for every f>=1, and for f>=2 two Byzantine processes suffice without double signing. The failure occurs when a process advances past a round without recording the value that may have been decided there. The Quint specification that accompanies the protocol does not allow this kind of round skipping and is not affected; the violation lies in the published pseudocode. We present two repairs. Walk requires a process to leave each round on a quorum of that round's precommits and to precommit before leaving. It keeps the recorded valid state and removes the wait after a precommit quorum. Justify carries the evidence needed to accept a proposal in the proposal itself, removing both the recorded valid state and the proposer's synchronization wait. Both satisfy Agreement and Validity under asynchrony and Termination under the partially synchronous gossip model of Tendermint and Fast Tendermint. Both retain proposal timeouts. The main text presents the executions that violate Agreement and explains the two repairs. The appendices provide proofs, a brief comparison with other round-change designs, and an extension to chains.

Current image-text evaluation often relies on a global score, which gives limited insight into which semantic details are supported by the image. Explainable metrics provide rationales, but the visual evidence supporting those rationales can still be difficult to verify. We introduce VisExMEM, a reference-free evaluator that decomposes captions into atomic claims, localizes visual evidence, verifies each claim, and averages claim-level support into a global score. Explanations use the same evidence and decisions. We train Qwen3.5-based 4B and 9B models on 100K samples with multi-task SFT, counterfactual refinement, and evidence-aware GDPO. Across eight benchmarks, VisExMEM-9B achieves the highest descriptive composite among open-source evaluators in our comparison, exceeding VQAScore by 11.7 points while remaining competitive with GPT-5.6 Sol. We also introduce AGITA-Bench, containing 600 human-annotated image-text pairs and 8.7K atomic claims for global and claim-level evaluation. For untuned Qwen3.5 and GPT-5.6 Sol controls, decomposed prompting raises the same composite by 3.6-5.1 points relative to holistic prompting. Human evaluation shows that VisExMEM explanations outperform prior explainable metrics and approach GPT-5.6 Sol.

Medication recommendation requires jointly considering diagnoses, comorbidities, longitudinal patient history, and treatment interactions. Although recent retrieval-augmented generation approaches using language models have shown promise for clinical recommendation, most existing systems rely on fixed retrieval pipelines that cannot adapt to diverse clinical retrieval scenarios and may introduce noisy or irrelevant evidence. We propose ARMED, an adaptive clinical RAG framework that dynamically expands retrieval according to retrieval sufficiency and current-admission relevance. ARMED first observes the initial retrieval outcome and selectively performs supplementary or fallback multi-query retrieval when additional evidence is needed. The framework also incorporates a relevance gate that activates only clinically relevant same-patient history and organizes retrieved evidence into structured query-level clinical evidence. Experiments on MIMIC-IV demonstrate that ARMED consistently outperforms previous static retrieval baselines and improves overall medication recommendation quality. By combining locally runnable small language models with adaptive retrieval, ARMED supports medication recommendation without relying on external language model APIs or task-specific fine-tuning.

In magnetically ordered systems, the spin gap in the magnon spectrum is normally expected to decrease on warming and close at the transition out of the long-range order. The presence of a pseudo-Goldstone gap is commonly associated with nonlinear terms in spin-wave theory. However, its precise origin and detailed properties can vary and remain under debate. Here we show by means of inelastic neutron scattering that the pseudo-Goldstone gap in the Heisenberg helimagnet ZnCr$_2$Se$_4$ exhibits an atypical, nonmonotonic temperature dependence: the gap increases over much of the ordered phase before closing near $T_\mathrm{N}$. These results align with recent spin-dynamic simulations based on an effective quartic potential in an isotropic system~[Phys. Rev. B 113, L220411 (2026)]. As the pseudo-Goldstone spin gap in ZnCr$_2$Se$_4$ is dominated by quantum effects at subkelvin temperatures, its characteristic growth on warming is caused by thermal fluctuations.

We propose a novel amorphous oxide semiconductor (AOS)-based conductive-semiconducting-conductive (CSC) MOS test structure to effectively sense, discriminate, and analyze distinct trap-induced conductance losses in AOS transistors. In conventional test structures, non-ideal metal-AOS contacts convolute the conductance loss generated by various trap states. The CSC architecture mitigates these contact-related artifacts, enabling the decoupling of interface states and shallow states. Furthermore, the contributions from leakage, series resistance, and device-geometry effects are identified and calibrated. Our results yield bias-resolved trap profiles and reveal three distinct regimes: (1) In the depletion region, interface states dominate the conductance loss. These states exhibit sub-microsecond time constants and their density increases slightly with deeper depletion, which is associated with donor-like states. (2) From weak to moderate accumulation, shallow states become the primary contributor, displaying a Gaussian-like volumetric density-of-states distribution with response times spanning from microseconds to nanoseconds. (3) In the strong accumulation regime, interface states regain dominance with an increased state quantity, while their time constants remain invariant. These bias-resolved profiles clarify how different trap populations impact AOS transistors under distinct operating conditions, providing intuitive metrics for understanding reliability degradation. Consequently, the CSC structure offers a simple, scalable, and robust platform for trap characterization in AOS transistors.

We study the boundary regularity of solutions for the tempered fractional Laplacian \[ (-\Delta)^s_\lambda u=f \quad \text{in }\Omega, \qquad u=0 \quad \text{in }\mathbb{R}^n\setminus\Omega, \] where \(0<s<1\), \(\lambda>0\), and \(\Omega\subset\mathbb{R}^n\) is a bounded Lipschitz domain satisfying the exterior ball condition. The tempered operator is defined by \[ (-\Delta)^s_\lambda u(x) = c_{n,s}\operatorname{P.V.} \int_{\mathbb{R}^n} \frac{u(x)-u(y)}{|x-y|^{n+2s}} e^{-\lambda|x-y|}\,dy, \] which was originally proposed in [Koponen, Phys. Rev. E (1995), 1197-1199]. % Exponential tempering preserves the leading singularity of % the kernel but destroys its homogeneity, preventing a direct % application of classical boundary regularity estimates. % Extending these estimates [Ros-Oton and Serra, J. Math. Pures Appl. (2014), 275–302] to the tempered setting therefore % requires overcoming the difficulties caused by the loss % of scale invariance. By decomposing the operator into the classical fractional Laplacian and the correction operator \(\mathcal Q_\lambda^s\), and combining approximation, localization, and iterative arguments with interpolation inequalities, we establish the global estimate \[ \|u\|_{C^s(\mathbb{R}^n)} \le C\|f\|_{L^\infty(\Omega)}. \] For more regular data, we derive interior and boundary-weighted Schauder estimates. In particular, under suitable regularity assumptions on \(f\), these estimates yield \[ |D^\nu u(x)| \le C\,\delta(x)^{s-|\nu|}, \quad |\nu| > 0, \] where \(\nu\) is a multi-index and \(\delta(x)=\operatorname{dist}(x,\partial\Omega)\). These bounds quantify the possible growth of higher-order derivatives near the boundary and provide a regularity foundation for numerical error analysis of the tempered problem.

We study absorption at the origin in radial pressureless Euler flow in $\mathbb{R}^n$, $n\geq2$. For rotation-invariant nonnegative locally finite initial mass and bounded radial initial velocity vanishing at the origin, we prove global existence and uniqueness in a full-space radial entropy class with a one-sided Lipschitz bound and an initial kinetic-energy trace. Absorption is permanent, including retention of any initial origin atom. For finite positive mass with finite second moment, a Lagrangian projection representation characterizes the absorbed mass and its left limits at positive times through extreme minimizers of a free-position primitive. We derive a radial scalar momentum balance with a nonnegative Stieltjes boundary impulse measure. The minimum value of the same primitive yields a weighted Stieltjes identity equating accumulated time-weighted impulse with the integral of initial radii over absorbed labels, valid also for jumps and singular continuous absorption; the boundary impulse measure and the absorption measure are mutually absolutely continuous on $(0,\infty)$. For such finite-mass data with common total mass, strong $L^2$ convergence of initial quantiles and Lagrangian velocities, together with convergence of initial origin masses, yields convergence of absorbed mass at continuity times of the limiting absorption and local weak convergence of absorption measures on $(0,\infty)$. Finally, even with a fixed smooth initial radial probability density, every probability measure compactly supported in $(0,\infty)$ can be realized as the absorption measure by choosing a bounded radial initial velocity; in particular, purely singular continuous absorption occurs.

Digital cultural heritage collections encode rich relations among objects, places, periods, providers, images, and source institutions, yet users typically access them through keyword search and faceted browsing. We present CULTUREBOT, an interactive framework for natural-language exploration of cultural heritage collections that combines knowledge-graph-guided retrieval, lexical-semantic retrieval, and source-linked generation. CULTUREBOT maps user queries to structured catalogue relations, enriches retrieved records with textual evidence, and generates answers that link back to the underlying repository records. We instantiate the framework on 81,852 SearchCulture records and release an online demonstration. In an expert evaluation involving six cultural-heritage specialists, 55 persona-grounded queries, and 250 evaluations, the graph-guided system was rated significantly higher than two general-purpose assistants and a non-graph ablation, with the largest gains in evidence grounding, diversity, reasoning, and completeness. These results support graph-guided retrieval as a practical way to expose the relational structure of cultural collections through conversational access while preserving links to catalogue evidence.

An isometric immersion $X: \Sigma^n \longrightarrow \mathbb{E}^{n+1}$ is biharmonic (BHH) if $\Delta^2 X = 0$, i.e., if $\Delta H =0$, where $\Delta$ and $H$ are the metric Laplacian and the mean curvature vector field of $\Sigma^n$ respectively. More generally, biconservative hypersurfaces (BCHs) are isometric immersions for which only the tangential part of the biharmonic equation vanishes. BCHs are first described and then constructed.

Time Series Foundation Models (TSFMs) provide general-purpose forecasting capabilities, yet their forecasts can remain misaligned with the temporal characteristics of a target domain. This motivates lightweight forecast correction even when only black-box access to the TSFM is available. Our key observation is that two forms of historical information provide complementary correction signals: historical analogues reveal how similar contexts evolved, while past forecast errors reveal a TSFM's characteristic deviations in the target domain. Based on this observation, we propose ECHO, a black-box forecast correction framework that learns from both sources. ECHO uses AnalogE to assess retrieved historical analogues together with the current context and base forecast, learning transferable corrections through cross-domain pretraining. In parallel, RecentE learns target-specific residual corrections from past forecast errors and refines them as causally available feedback accumulates. ECHO dynamically combines the two corrections according to their observed forecasting performance. Across 5 representative TSFMs and 9 real-world datasets, ECHO reduces MSE in all 45 backbone–dataset settings, yielding an average relative reduction of 9.26% in macro-average MSE. Its gains also extend to long-horizon forecasting.

Silicon microring resonators are promising components for photonic reservoir computing because their nonlinear optical response can transform signals and retain information about recent inputs. Under constant optical excitation, their coupled free-carrier and thermal dynamics can generate self-pulsing: a periodic output response. However, constant-input behavior does not reveal how these dynamics respond to randomly modulated signals or whether their memory is useful for temporal processing. Here, we characterize a single silicon microring resonator and a passive network of microring resonators under random input modulation. The temporal component associated with self-pulsing remains observable under random modulation, but the largest fading memory occurs near the self-pulsing boundary, where no resolved self-pulsing-like oscillation is present. reservoir computing metrics, such as memory capacity, map this accessible memory, and its decay provides effective timescales associated mainly with free-carrier and thermal relaxation. Finally, we use NARMA reconstruction to test whether the measured memory profile supports nonlinear temporal processing. Responses with a resolved self-pulsing-like component perform worse on this task, and the intrinsic memory profile is not matched to the required input history. These results show that reservoir computing metrics can characterize nonlinear microring resonator dynamics even when the physical system is not an effective standalone reservoir for the selected task.

In this article, we demonstrate that there exists an infinite family of lens spaces L(p,q) that cannot be obtained from the 3-sphere by two integral surgeries. The first such lens space in our family is L(177,29).

Speech enhancement with wearable and edge devices requires architectures that balance enhancement quality against power and memory resources. Spiking Neural Networks (SNNs) offer a promising path towards this goal through sparse, event-driven computation, but existing SNN-based speech enhancement methods are largely restricted to single-channel processing and therefore cannot exploit the spatial diversity available from microphone arrays. In this work, we propose a fully SNN framework for multichannel speech enhancement based on a fully connected architecture (FC-SNN) with sequential spike encoding, derived from a compact artificial neural network (ANN) baseline via leaky integrate-and-fire neurons. We characterize how enhancement performance scales with model size and spike-train length relative to ANN and classical beamforming baselines, and report the resulting parameter counts and computational complexity. We further compare direct and rate spike encoding, revealing a clear trade-off between event-driven computation and enhancement performance, and use these results to identify favorable configurations for edge devices.