Papers

For every integer $d\geq 3$ and real number $Q\in \left(d,\frac{d(d-1)+2}{2}\right]$, we construct a $Q$-Ahlfors regular metric measure manifold $(M,\mathbf{d},\mu)$ of topological dimension $d$ and analytic dimension $2$ that satisfies a Poincaré inequality. For every $Q>\frac{d(d-1)+2}{2}$, the construction yields a metric measure manifold $(M,\mathbf{d},\mu)$ that is doubling, satisfies a Poincaré inequality, and for which $M$ has $\mu$-essential Hausdorff dimension $Q$. The manifold is $\mathbb{R}^d$ equipped with Lebesgue measure and a sub-Riemannian distance given by vector fields that are locally Hölder continuous but not Lipschitz continuous. These metrics give an uncountable family of new models that are genuinely distinct from the only known families of metric manifolds satisfying a Poincaré inequality: weighted and deformed Carnot groups and smooth sub-Riemannian spaces. The construction is modeled on a singular variant of a filiform Carnot group.

Optical isolation suppresses back-reflections that destabilize lasers, produce parasitic interference, and increase crosstalk in photonic systems. Although free-space and fibre-optic isolators are mature, no broadly adopted on-chip technology yet combines strong isolation, low insertion loss, broad bandwidth, compact footprint, and scalable fabrication. The difficulty is twofold: Lorentz reciprocity must be broken, and every relevant backward spatial, spectral, and polarization channel must be suppressed. This Review develops a common framework for assessing proposed solutions. We first distinguish pairwise nonreciprocity from intensity-asymmetric transmission and from true isolation using the constitutive relations and scattering matrix. We then compare three physical routes to an integrated nonreciprocal response: magneto-optical bias, externally driven space-time modulation, and nonlinear optical processes. Topological and non-Hermitian systems are treated as cross-cutting design frameworks that can route, protect, or enhance an underlying nonreciprocal response, but do not by themselves break reciprocity. Finally, we examine fundamental constraints and practical trade-offs among isolation, insertion loss, bandwidth, footprint, modal coverage, drive requirements, and fabrication compatibility. The resulting mechanism-based perspective connects reciprocity-breaking physics to the requirements of scalable photonic integrated circuits.

Generating deployable websites from visual prototypes and textual requirements is increasingly feasible with multimodal models, yet keeping generated projects consistent with their prototypes remains challenging. Prototypes specify layouts and visual elements, while requirements describe interaction workflows and deployment constraints. Existing UI-to-code methods and coding agents often treat layout reconstruction, interaction implementation, and project editing separately, allowing visual elements, files, workflows, dependencies, and render evidence to lose their correspondence across generation, verification, and update. We call this problem prototype-to-project state drift. We propose VisStateCoder, a state-aware framework that maintains these correspondences in a Project State Graph. The graph connects four types of state nodes through typed links and supports prototype grounding, graph-guided generation, and render-evidence-guided scoped updates that map failed checks to affected files while preserving files outside the update scope. We evaluate VisStateCoder on Vision2Web using five foundation models across Static Webpage, Interactive Frontend, and Full-Stack Website tasks. Averaged across models, VisStateCoder improves overall scores over the strongest baseline for each model by 26.1 and 22.6 points on Interactive Frontend and Full-Stack Website tasks, respectively. It also reduces verified-state drift, measured by checks that pass in one update round but fail later, compared with alternative state representations. An annotation study of 50 tasks finds that the constructed graphs achieve 95.6% edge-level F1.

Agent Skills improve LLM agents by making task knowledge reusable across sessions. Learning transferable Skills requires evidence about a procedure and its conditions of use, which a successful task attempt can leave untested. We introduce Socratic Skill Learning (SSL), which interleaves expert teaching with Student practice. An Educator guides investigation while the Student remains the sole environment operator and Skill author, able to question, test, and adapt advice. To test reuse beyond the learning task, we construct SkillTransferBench, with 35 task families and 408 executable cases, pairing public variation specifications with held-out evaluation in fresh solver sessions. On the main 22-family, 155-case cohort, Fixed-Window SSL reaches 0.801 utility, versus 0.723 without a Skill, 0.761 for adapted Trace2Skill (trajectory distillation), and 0.751 for adapted SKILL-KD (contrastive distillation). Across three model pairs on shared families, interleaved guidance outperforms expert authoring and post-hoc teaching. Process analysis links guidance to Student writing and package revision; a case study shows the Student testing and refining a proposed procedure for later reuse. As demand for new lessons falls, the cost of fixed-window review grows. Issue-Guided SSL tracks unresolved questions across Skill revisions to select and focus review, reaching 0.805 utility with 61.7% fewer Educator tokens and 16.9% fewer total acquisition tokens than Fixed-Window SSL on the main cohort.

Thermal-to-visible (T2V) face translation has important applications in nighttime biometric recognition, low-light surveillance, and human interpretation of thermal observations. The task remains challenging because thermal images do not directly record visible appearance, while the cross-spectral cues useful for reconstruction vary across frequency components and semantic roles. Existing spatially conditioned models tend to process these cues through a homogeneous adaptation path and do not explicitly separate local structure from global identity. We propose FreqID-Control, a parameter-efficient framework that organizes thermal guidance according to spectral reliability and semantic role while preserving the pretrained generative prior. It combines frequency-routed low-rank adaptation, which allocates separate transformation subspaces to low-frequency structure and high-frequency detail, with shared cross-spectral identity conditioning, which supplies compact global identity tokens independently of spatial thermal tokens. A controlled analysis on MCXFace and SpeakingFaces provides the empirical basis for this design, revealing stable low-frequency correspondence and edge-localized detail correspondence. Experiments on both datasets demonstrate strong image fidelity and biometric identity preservation, while controlled ablations on MCXFace confirm the complementary contributions of frequency routing and shared identity conditioning.

In this paper, we prove that every Hermitian conformal class on a connected noncompact complex manifold of dimension at least two contains a Gauduchon metric. We give a sufficient condition for uniqueness of such Gauduchon metrics up to scaling in terms of functions bounded from above and their Levi forms. This condition is necessary when the manifold has at least two ends. In that case, uniqueness in a fixed conformal class is equivalent to the assertion that every positive solution of the complex Laplace equation for a metric in that class is constant. For a connected noncompact complex Lie group of dimension $n$, uniqueness in every conformal class is equivalent to the assertion that, for every Hermitian metric, every positive solution of the complex Laplace equation is constant. These properties hold exactly when the complex tangent space of a maximal compact subgroup has dimension $n-1$; such a group is abelian. In a conformal class containing a balanced metric, the same equivalence holds without a restriction on the number of ends. We also prove uniqueness for manifolds with a suitable potential on a compactification with compact fibers over a point, the real line, or a parabolic Riemann surface. The examples include compact pluripolar deletions, partially deleted compact fibers, and semipositive line bundles. We construct conformal Gauduchon metrics which are not related by scaling on Stein manifolds and on the total space of $\mathcal O_{\PP^1}(1)^{\oplus2}$.

Weak gravitational lensing offers a direct probe of the projected dark matter distribution in cluster-scale structures and the surrounding cosmic web. We investigate the capability of the China Space Station Telescope (CSST) to recover non-spherical dark matter morphologies using mock reduced-shear maps generated from cosmological N-body simulations. We apply the deep-learning-based MIU2Net mass-reconstruction framework to CSST-like wide- and deep-field source densities, focusing on two representative systems: filament-connected halo pairs and elongated halos. MIU2Net accurately recovers halo centers, elongated mass distributions, and the filamentary structures connecting halo pairs in both survey configurations. Halo centers are localized within about 0.1 h^(-1) Mpc, and elongated-halo shapes and orientations are reliably recovered. Filament paths are stable against shape noise, with mean normalized instability parameters I_F, defined as the mean deviation from the true filament locus in units of R_200, decreasing from 0.041 to 0.037 in the low-redshift bin and from 0.051 to 0.045 in the high-redshift bin from the wide to deep field. The recovered filament shapes remain consistent with the true maps at the percent level. Compared with conventional Kaiser-Squires reconstruction, MIU2Net better preserves low-contrast anisotropic structures while suppressing small-scale noise. These results demonstrate that CSST weak-lensing data, combined with machine-learning-based mass reconstruction, will enable statistical studies of cluster assembly, anisotropic matter accretion, and the connection between massive halos and the filamentary cosmic web.

Time-series analysis is increasingly studied in multimodal settings, yet most benchmarks pair temporal signals with text or with visualizations derived from the same signal. This leaves open whether multimodal large language models (MLLMs) can integrate time series with real-world visual evidence. We introduce MMTA (multimodal temporal analysis), a benchmark of tri-modal tasks with diverse cross-modal complementarity patterns among time series, text, and vision. MMTA spans nine domains – robotics, autonomous driving, human action, manufacturing, AR assistance, healthcare, recommendation, finance, and climate – under video+TS and image+TS layouts, with a 3,524-sample test split covering classification and forecasting. The benchmark standardizes heterogeneous real-world sources into a shared schema with domain-specific prompts, provenance documentation, and success-weighted metrics that penalize both wrong answers and failed generations. Evaluating eight open-source and proprietary MLLMs reveals a shared bottleneck: representing time series as text creates very long token sequences and weakens fine-grained alignment with visual evidence, especially in long-video settings. We then introduce TimeOmni-v, a multimodal LLM extension with a dedicated time-series encoder, temporal positional alignment, modality-aware token layout, and a forecasting head. TimeOmni-v improves long-video classification and time-series inference efficiency, showing that MMTA not only exposes representation and grounding failures but also motivates targeted model design.

Non-Hermitian dynamics possesses distinct left and right eigenstates, but their normalization freedom obscures a direct probabilistic interpretation. Starting from a globally Hermitian system governed by the standard Born rule, we generalize dynamical quantum phase transitions (DQPTs) from a reference state to a physical subspace. This generalization provides a clear probabilistic interpretation of left and right states: when each state is normalized to itself, their mutual overlap determines a directly accessible dynamical transition rate. We discuss the new phenomena governed by this emergent non-biorthogonal Born rule and further identify a class of exceptional-point DQPTs (EP-DQPTs), at which the eigenstates of the critical propagator coalesce. Our theory places the probabilistic interpretation of non-Hermitian quantum mechanics on the firm footing of Hermitian quantum mechanics.

ARES (Ab initio atomic mateRial modEling Software at JLU) is a plane-wave density-functional-theory (DFT) code written entirely in Rust as a layered 22-crate workspace. It supports norm-conserving pseudopotentials and the projector augmented-wave (PAW) method with the local-density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) functionals, {\Gamma}-only and explicit k-point sampling, smearing and mixing, forces, stress, relaxation, band structures, densities of states (DOS) and dispersion corrections; execution is serial or MPI-distributed over k-point pools, band groups and plane-wave rows. The code's distinguishing engineering choice is its validation apparatus. Every numerical component is checked against Quantum ESPRESSO driven from the same physical and numerical inputs, and the comparison is organized as numbered fixtures kept in the repository whose reference data is regenerated by a script instead of being captured once. On six materials spanning a semiconductor, three metals and two two-dimensional systems, band energies within one electronvolt of the Fermi level agree with the reference to a median below 0.4 meV. The pseudopotentials the code reads are validated against all-electron reference data as well: the median delta factor is 0.696 meV/atom over all 65 paired elements. Restrictions are stated with the capabilities: two functionals, no spin-polarized or spin-orbit path, a stress implementation with an explicit scope, and no accelerator execution.

Multimodal large language models (MLLMs) have achieved strong performance on diverse vision-language tasks, but their computational demands limit deployment under constrained budgets, particularly on edge devices. Many works focus on Knowledge Distillation (KD) and try to transfer knowledge from powerful teacher models to students. In addition to reducing model size, visual token compression provides a complementary route to efficiency, but introduces mismatched visual token counts that complicate direct token-wise knowledge transfer. To mitigate this, we propose DVTR-KD, a knowledge distillation framework based on Dense Visual Token Reconstruction, which reconstructs the teacher's dense visual tokens from the student's compressed tokens. We reconstruct visual states after the final LLM layer and at the input to an intermediate layer identified as important for visual-information readout. At the intermediate layer, reconstruction is supervised through the teacher's response predictions rather than by direct token-wise KL or MSE matching. An auxiliary attention-readout loss complements this response-level supervision by aligning how the student and the original teacher integrate contextual information when predicting responses. Evaluations on diverse benchmarks demonstrate that DVTR-KD improves the performance of token-compressed students while retaining the inference efficiency afforded by visual token compression.

Let $\ell$ and $p$ be distinct prime numbers, $K$ a local field with residue characteristic $p$, $C$ a complete algebraically closed extension of $K$, and $X$ a quasi-compact quasi-separated rigid space over $K$. When $\mathop{\mathrm{char}} K = 0$, we prove that the alternating sum of traces of elements in the positive part of the Weil group acting on $R\Gamma(X_C,\mathbb{Q}_{\ell})$ is independent of $\ell$ and is an integer, extending a result of Mieda to the singular case. We also give optimal bounds for the $p$-adic valuations of the eigenvalues of geometric Frobenius liftings acting on $H^i(X_C,\mathbb{Q}_{\ell})$, proving a conjecture of Lu–Zheng. In the general case, we give optimal bounds for the $p$-adic valuations of the eigenvalues of geometric Frobenius liftings acting on $H^i_c(X_C,\mathbb{Q}_{\ell})$, and we show that these eigenvalues are algebraic integers and Weil numbers, thereby extending results of Lu–Zheng and Mieda to the positive characteristic case.

In remote regions lacking terrestrial infrastructure, aviation users increasingly demand Internet services comparable to ground cellular networks. This paper proposes a space-air-ground integrated network (SAGIN) architecture that combines ground networks, civil aviation networks, and low Earth orbit (LEO) satellites. Based on real North Atlantic flight data, a heterogeneous aviation Internet is constructed to support diverse aircraft service requirements. A composite Quality of Experience (QoE) metric, characterized by transmission delay, jitter, and content similarity, guides efficient resource utilization. The dynamic connectivity of SAGIN is modeled using a reconfigurable time-expanded graph (RTEG). With Network Function Virtualization (NFV), data delivery is formulated as a Service Function Chain (SFC) deployment across ground stations, relay aircraft, and satellites, resulting in a long-term QoE maximization problem. A tailored Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm incorporating LCSS-based path filtering and softmax-based action selection is developed. Simulation results demonstrate that the proposed approach enables seamless connectivity for heterogeneous aircraft and consistently outperforms game-theoretic and MATD3 methods in terms of QoE.

The formation of the evaporation residues in the $^{30}$Si$+^{186}$W reaction leading to the compound nucleus $^{216}$Ra$^*$ has been studied in the framework of the dinuclear system (DNS) model. The capture, complete fusion, quasifission, and incomplete fusion cross sections have been calculated at the collision energies $E_{c.m.}=107.6-172.2$MeV by averaging over the orientation angles of the axial symmetry axes of the deformed $^{30}$Si and $^{186}$W nuclei. The incomplete fusion is considered as the breakup of the DNS with the emission of the $\alpha$ particle from its very mass-asymmetric configuration, which is populated by the nucleon transfer in collisions with large orbital angular momentum. The survival probabilities of the excited $^{216}$Ra and of the conjugate nucleus $^{212}$Rn formed after the $\alpha$-particle emission have been calculated using the statistical model. It is shown that the complete fusion is the main source of the evaporation residues at the lower collision energies, while above $E_{c.m.}=128$MeV the Rn isotopes formed in the incomplete fusion give more than half of the calculated evaporation residue cross section. The sum of both contributions describes the slow decrease of the measured total evaporation residue cross section at these energies, where the yield of the Ra isotopes decreases by an order of magnitude. The calculation of the de-excitation of $^{216}$Ra$^*$ with the emission of protons and $\alpha$ particles shows that the contribution of the complete fusion to the cross sections of the isotopes $^{212}$Rn and $^{211}$Rn is negligible, and these isotopes are formed in the incomplete fusion. The fusion probability calculated for the partial waves $\ell\leq30\hbar$ is about 0.75 in comparison with the value $0.57\pm0.08$ extracted from the experimental data at the same collision energies.

Noncollinear ferrimagnets combine a net magnetic moment with internal spin degrees of freedom, creating opportunities to couple magnetic, mechanical, thermal, and electronic responses. Using first-principles calculations, symmetry analysis, atomistic spin simulations, and transport modeling, we identify stable NbMnX$_2$ ($X$ = S, Se, Te) monolayers with noncollinear ferrimagnetic ground states and Curie temperatures up to 313 K. Competing exchange, Dzyaloshinskii–Moriya interactions, and magnetic anisotropy produce field-responsive canted states that couple strongly to the lattice and charge carriers. Magnetization rotation changes the elastic modulus of NbMnTe$_2$ by up to 36%, while lattice entropy substantially enhances the near-room-temperature magnetocaloric response of NbMnS$_2$ and NbMnSe$_2$. In NbMnSe$_2$, rotation restores a mirror-protected crossing, continuously closes an approximately 0.13 eV gap, and produces a conductivity-based anisotropic magnetoresistance ratio up to 10,000% at 100 K. The combined results establish noncollinear NbMnX$_2$ monolayers as a multifunctional platform for two-dimensional spintronics, nanomechanics, and thermal control.

Persistence diagrams (PDs) represent multiscale topological information as multisets of birth-death pairs $(b,d)$. How best to use them with Transformers, however, remains unclear. Connecting PDs to Transformers requires choosing how topological information is tokenized and exposed to self-attention. Prior methods use specialized designs for tokenization, aggregation, Transformer blocks, or attention, but are hard to compare since reported results rarely share PD inputs, splits, or model-selection rules. We instead confine the diagram-specific design to point representation, mapping each birth-death pair through fixed random Fourier features while leaving the Transformer backbone unchanged, and call this recipe Persistence Positional Encoding (PPE). In matched controls on eight TU graph benchmarks (TU8), changing only point representation shifts macro accuracy by 5.49 to 6.47 percentage points (pp), against 0.47 to 1.45 pp from changing the downstream module, identifying point representation as the dominant design variable tested. We further reevaluate vectorizations, kernels, learned representations, and Transformer-based models under one protocol with shared PD inputs, outer folds, and validation-only selection. Among all evaluated PD methods and downstream configurations, PPE achieves the highest mean on most benchmarks, including TU8, ORBIT5K, and MCB-C. Finally, we prove that grid averaging leaves a reconstruction error at any resolution, whereas a Transformer with fixed random Fourier frequencies is almost surely universal. PPE thus offers a minimal, Transformer-native baseline for persistence diagrams, and a common protocol for future comparison.

We develop a theory of ionization-assisted instability that governs the reflection of intense electromagnetic pulses from a semiconductor surface. Local overheating of the material increases the free-carrier density and conductivity, which in turn enhances the absorption of the incident radiation and further amplifies local heating and avalanche ionization. At high pump repetition rates, the overheating accumulates from pulse to pulse, leading to a gradual rise of the local material temperature and free carrier density - a positive feedback loop that drives thermal runaway. However, this effect competes with diffraction of the pump field on the emerging perturbation of the dielectric permittivity or on the surface relief, which reduces the local electric field amplitude in the overheated regions, thus providing negative feedback. We show that the competition between heat diffusion and diffraction near-field weakening creates conditions for the exponential growth of temperature perturbations with a certain wavenumber determined by the pulse repetition rate, pump field, thermal conductivity and other material parameters. The derived analytical expressions accurately describe the spatial period of deeply subwavelength structures observed in recent experiments on silicon structuring by intense terahertz radiation, and reproduce qualitatively dependencies of their period on the pump intensity, the incident wavelength and the number of pump pulses.

We prove that, under suitable assumptions, the space of order continuous orthogonally additive operators between Riesz spaces is a Riesz space. As a consequence, we give a negative answer to an open problem posed by Mykhaylyuk and Popov concerning the order continuity of the modulus of an order continuous orthogonally additive operator. We also show that, under an appropriate condition on the domain, every order continuous orthogonally additive operator is order bounded, obtaining an orthogonally additive analogue of the corresponding result for linear operators. Moreover, we establish the order boundedness result in ZF for atomic Riesz spaces and in ZF with dependent choice (DC) for Dedekind complete Riesz spaces. Finally, we characterize when every orthogonally additive operator is an abstract Uryson operator.

Functional near-infrared spectroscopy (fNIRS) provides portable and spatially localized measurements of cortical hemodynamics, but differences in channel count, probe layout, signal distribution, and task type hinder joint pretraining across datasets. We introduce GeoNIRS, a geometry-aware framework that uses source-detector locations as a shared spatial reference across heterogeneous probe layouts. GeoNIRS compresses variable-size channel sets into a fixed-size latent representation and employs bidirectional HbO/HbR cross-reconstruction with contiguous temporal masking. GeoNIRS-base is pretrained on eight heterogeneous datasets, while GeoNIRS-large scales to 22 datasets. Neither downstream data nor labels are used during pretraining, enabling evaluation under a strict cross-task setting. To our knowledge, GeoNIRS is the first fNIRS framework to explicitly model physical channel geometry during joint pretraining across heterogeneous channel configurations, and the first to provide complete source code and downloadable pretrained checkpoints. We evaluate GeoNIRS on eight held-out tasks spanning clinical and auditory assessment, pain and affective processing, semantic decoding, and motor function. GeoNIRS achieves the highest task-averaged balanced accuracy among the evaluated conventional machine-learning, fNIRS-specific, general time-series, and fNIRS pretraining baselines. Compared with random initialization, pretraining improves average balanced accuracy by 4.12 percentage points under linear probing and 3.30 points under full fine-tuning, with larger benefits when labels are scarce. GeoNIRS also remains robust to missing input channels. Geometry perturbations and pretraining ablations further show that both channel geometry and cross-chromophore reconstruction contribute to the learned representations.

Spatial understanding is a necessary step in moving multimodal large language models (MLLMs) toward reasoning about the 3D physical world. Their visual pretraining data, however, is almost entirely 2D, so the visual tokens processed by MLLMs often lack inherent 3D structural information. A growing number of methods inject such structure by transferring representations from external vision or geometry models, and collectively establish that such transfer helps. Behind these methods lies a largely underexplored question: what makes a visual representation good for spatial understanding? To answer it, we first separate what is transferred from how it is transferred, and then trace the resulting differences back to properties of the representations themselves. What we transfer comes from 3D geometry models, self-supervised image and video models, vision-language models, and generative models, in the form of latent features or explicit depth and point maps. We transfer it either by distillation, using it as a supervision target, or by fusion, feeding it as an additional input. We find that a representation's 3D structure correlates strongly with how much it helps, measured by cross-view consistency for latent features and by depth and reconstruction accuracy for explicit geometry. We further show that the form of a representation dictates the mechanism it needs. Latent features gain as much from fusion as from distillation; explicit geometry gains little from fusion, and most of its distillation gain depends on a geometry decoding head. Guided by these findings, we distill both latent features and explicit geometry into a single MLLM. Taking only RGB video as input, it consistently improves over its base model on both static 3D and dynamic 4D spatial reasoning benchmarks.

Proactive dynamic grasping requires robots to predict the future state at which physical contact will occur, rather than reacting to the currently observed object pose. But what future must the robot predict, and at what level of abstraction? We argue that contact-relevant rigid-body state in SE(3) is a compact task-sufficient abstraction for this problem: it directly determines where and when the robot should establish contact, without requiring visually complete future scenes. This insight leads to a lightweight object-centric forecast-then-select framework that predicts future rigid-body trajectories from short pose histories and uses a reachability-aware interception selector to choose feasible contact states under kinematic and timing constraints. Trained with randomized physics simulation over primitive shapes, the forecaster transfers to real objects once their metric geometry and SE(3) state histories are recovered. Experiments across simulation and real-world dynamic grasping tasks show that our framework improves the average success rate from \(24.5\%\) to \(62.0\%\) in simulation, and from \(15.3\%\) to \(67.3\%\) in real-world catching, conveyor, and turntable interception. The SE(3) forecaster runs in \(15\,\mathrm{ms}\), orders of magnitude faster than dense visual future prediction, enabling real-time contact decision making. Our results suggest that effective proactive grasping does not require imagining the entire future scene. Instead, predicting the compact physical future that determines contact provides an effective and practical abstraction for real-time dynamic grasping.

This paper develops theoretical and numerical extensions of Birkhoff pseudospectral transcription for aerospace optimal control problems. Building on the recently proposed body of knowledge, a Birkhoff integration operator is derived for flipped Legendre Gauss Radau (fLGR) grids, drawing connections to regular LGR grids and to the favorable conditioning properties that make Birkhoff interpolants particularly appealing. We also propose the enforcement of differential constraints via pseudospectral operators, and the primal and dual equivalence of this approach to state augmentation is established for control-rate limits. The numerical developments include the formulation and solution of heterogeneous multiphase optimal control problems, parameterized non-affine time mappings, composition of affine scaling and equilibration methods, and a hybrid derivative strategy to combine linear pseudospectral operators with numerical derivatives for nonlinear functions. These methods are implemented in the RAPTOR (Rapid Algorithm for Pseudospectral Trajectory Optimization and Robustification) transcription framework and assessed through feature-oriented benchmarks: a one-dimensional landing problem, a planar orbit-raising scenario, an atmospheric entry problem, and a multiphase reusable launch vehicle problem with simultaneous booster-recovery and upper-stage-insertion trajectories.

Evaluating fashion retrieval systems remains challenging due to the limited availability of benchmarks that capture the fine-grained, open-ended queries encountered in real-world search and recommendation. Existing benchmarks often rely on manual curation, predefined taxonomies, or synthetic prompts, limiting scalability and semantic coverage. We introduce FASHION-RQ: Mining Hierarchical Semantic Structure for Automated Evaluation of Fashion Retrieval, an automated framework that derives user-type queries and relevance sets directly from catalog structure. Our key insight is that hierarchical discrete representations learned by Residual Quantized Variational Autoencoders (RQ-VAE) organize products into semantically coherent clusters at progressively finer granularities. We leverage this structure to construct FASHION-RQBENCH, a scalable benchmark without manual query annotation or predefined taxonomies. We propose four complementary tasks for evaluating ranking, relevance classification, fine-grained sibling discrimination, and paraphrase robustness, alongside query- and attribute-level relevance metrics. Experiments across recent retrieval models demonstrate that FASHION-RQBENCH differentiates model capabilities across query types and attributes. A human study further shows that benchmark queries achieve comparable naturalness and higher intent clarity than real user queries, supporting their validity for real-world evaluation. The code and FASHION-RQBENCH dataset will be publicly released upon acceptance.

Multi-agent deliberation can improve recognition by criticizing and revising candidate answers, but fixed controls cannot respond to changes in disagreement or reasoning quality. We present an adaptive multi-agent controller (ADMA) that learns continuous policies for proposal, challenge, arbitration, and coordination while keeping the task model frozen. Shared trace features describe quality, agreement, and progress, while role-specific features support decentralized control during inference. One controller trained on legal and financial reasoning is transferred without policy updates to four textual and multimodal benchmarks and two successive task-model versions. With Qwen3.5 held fixed, ADMA-Full improves accuracy by 6.2-14.2 percentage points over Direct and by 2.8-3.0 points over ADMA-Fixed. Paired bootstrap ranges for the Full-Fixed comparison are positive on three tasks. Outcome decompositions show that recoveries exceed introduced errors, while process assessment records fewer false-consensus events and more supported correct outcomes. Transfer to Qwen3.6 remains task dependent, which bounds the generality of the learned policy. Median token and latency ratios are 14.3-18.7 and 7.8-16.5 relative to Direct. These results show that adaptive deliberation can improve fixed-model recognition when its task-dependent gains justify the additional computation.

For a graph $H$, the suspension $\widehat H$ of $H$ is a graph obtained from $H$ by joining a new vertex to every vertex of $H$. The generalized Turán number $\textrm{ex}(n,K_3,\widehat H)$ is the maximum number of triangles in an $n$-vertex $\widehat H$-free graph. For fixed $k \ge 4$, Mubayi and Mukherjee conjectured that \[ \textrm{ex}(n,K_3,\widehat P_k) =\left\lfloor\frac{k-2}{2}\right\rfloor\frac{n^2}{8}+o(n^2), \] as $n \to \infty$, where $P_k$ is the path on $k$ vertices. They verified the conjecture for $k=4,5,6$. In this paper, we determine the asymptotic value of $\textrm{ex}(n,K_3,\widehat P_k)$ for every $k\ge 4$ via a unified approach and thus prove the conjecture of Mubayi and Mukherjee.

One-shot personalization of autoregressive (AR) text-to-speech (TTS) models remains challenging because supervised fine-tuning (SFT) on a single reference pair rapidly degrades generation quality. We identify fixed, off-policy supervision as a key cause of failure in one-shot SFT for AR TTS, leading to blank or near-empty outputs at inference. Diversifying the training data with zero-shot pseudo-pairs eliminates this failure but yields little improvement in speaker similarity and increases word error rate because the targets remain fixed and teacher-forced. We therefore propose two on-policy approaches for one-shot speaker personalization: Group Relative Policy Optimization (GRPO) with a speaker-similarity reward and On-Policy Self-Distillation (OPSD) with soft supervision from a reference-conditioned teacher. Both on-policy methods improve speaker similarity while preserving intelligibility, with different trade-offs: GRPO achieves the strongest overall performance, whereas OPSD enables substantially faster adaptation without external reward evaluation. Further analysis confirms that these gains stem from on-policy supervision rather than target diversity, establishing on-policy training as an effective framework for one-shot AR TTS personalization.

Large language model (LLM) agents are increasingly used for vulnerability analysis, yet existing benchmarks provide limited coverage of exploitation that depends on interactions among network protocol components. Such vulnerabilities arise from inconsistencies in message interpretation, timing, state, or trust assumptions across participants. We introduce ProtoArena, a black-box, multi-component, dynamic benchmark with 80 cross-component vulnerability-exploitation environments spanning 11 protocol and application domains and 7 attack categories. Tasks are primarily informed by published protocol-attack mechanisms. Agents interact with running systems through scoped interfaces to achieve security-effect objectives without target source code. Three information levels assess guided reproduction, exploitation with mechanism and topology context, and effect-directed black-box exploration. A hybrid verifier combines rule-based checks with LLM review of independently collected traffic and logs. We evaluate five LLMs. Claude Opus 4.8 achieves the highest observed success rates: 48.8% under L1 guidance and 12.5% under effect-directed black-box L3. In a separate DNSBomb optimization experiment, it achieves a peak downstream-response to average query-input byte-rate ratio exceeding 171,000 times. The results show that agents can achieve verifiable exploitation effects in some cross-component environments, but success with limited black-box information remains low and varies across domains and attack categories. All experiments use controlled, explicitly authorized targets; they do not test production systems or disclose previously unknown vulnerabilities.

Amplitude embedding lets a variational quantum model read many classical features with few qubits, but the model output is then only a quadratic form in the normalized input. Data re-uploading, which encodes the input repeatedly between trainable blocks, can be used to enrich such a model. Because every additional upload of an amplitude embedding repeats a costly state preparation, the gain that an upload buys has to be known before the gates are spent. This tutorial thus addresses the problem of explaining what data re-uploading adds to an amplitude-embedded model and how large the gain is. We express sequential re-uploading and parallel re-uploading with two copies in one notation and show that each upload raises the reachable polynomial order by two. Under one trainable circuit family and one budget of trainable parameters, simulation results show that re-uploading raises the test coefficient of determination from 0.689 to between 0.883 and 0.975 on targets of order four and from 0.337 to between 0.642 and 0.783 on targets of order six, on all ten seeds. On a quadratic target and on handwritten digits, one upload remains the best choice, and every additional upload lowers the gate error that the classifier tolerates. These results help designers match the number of uploads to the polynomial order of the task at hand.

We study the recovery of a Hamiltonian from discrete trajectory observations using structure-preserving kernel methods. When exact-flow data are fitted through a symplectic one-step scheme, the fixed-step learning target is generally not the physical Hamiltonian itself, but a scheme-dependent inverse modified Hamiltonian. For the implicit midpoint and $p$-implicit symplectic Euler methods, we establish the existence of analytic inverse targets and show that their discrepancies from the physical Hamiltonian are second and first order in the observation step, respectively. Within an RKHS framework, we derive finite-sample reconstruction bounds for random trajectories, allowing dependence among observations from the same trajectory, and separate the error into estimation, approximation, and integrator-induced components. We further establish stability under noisy trajectory observations and develop a multistride Richardson correction that systematically raises the order of the integrator-induced error without requiring additional trajectories. Numerical experiments confirm the predicted scheme-dependent orders, the effect of Richardson correction, and the applicability of the method across several Hamiltonian systems.

We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.