Papers

We investigate construction-dependent Floquet topology in a two-dimensional lattice formed by stacking Su-Schrieffer-Heeger (SSH) chains with co-located sublattice orbitals. We present two constructions in the decoupled-chain limit. Construction-I: the constituent SSH chains are topologically trivial with winding number $w=0$. Construction-II: the constituent SSH chains are topologically nontrivial with $w=1$. Although these constructions are unitarily equivalent in the static limit, circular driving distinguishes them because the hopping processes related by the transformation correspond to different physical bond vectors and therefore acquire different Peierls phases. Using the Floquet-Sambe formalism, we determine the quasienergy spectra and phase diagrams in terms of the lower-band Chern number $C_L$ and directional Zak phases $(Z_x,\, Z_y)$. We find distinct Floquet phase structures, including low-frequency phases with $C_L = -3$ and $C_L = -4$ in the two constructions. Since the Chern number does not resolve the topology of the two quasienergy gaps separately, we further calculate the dynamical winding numbers $W_0$ and $W_\pi$, and verify the corresponding chiral edge states. In particular, at identical driving parameters, both constructions can have the same Chern numbers $C_L=-2$, while their gap-resolved winding numbers are $(W_0,\, W_\pi)=(0,\,+2)$ and $(-2,\,0)$, respectively. We also calculate the time-averaged optical Hall conductivity and show that $ C_Le^2/h$ determines its dc value for ideal full-band occupation. At the same time, its finite-frequency response contains photon-assisted contributions. Our results demonstrate that the physical construction of the constituent chains, although irrelevant to the static bulk spectrum, can play a decisive role in the Floquet topological structure. We discuss possible experimental realizations of the driven model.

We build and apply an $\textit{ab initio}$ stochastic Bethe-Salpeter Equation (sBSE) approach to planar cyanine dye aggregate clusters containing up to 2,856 valence electrons. Using a transferable, parameterized screened exchange kernel, we resolve dielectric response, exciton delocalization, and optical spectra within a unified many-body framework. Remarkably, the sBSE transition densities validate the Frenkel exciton picture in real space and provide a practical first-principles route to its screened couplings. The calculations reproduce $\textit{H}$-, $\textit{I}$-, and $\textit{J}$-like spectral evolution and reveal that spatially dependent screening does not merely shift excitonic bands, but reshapes their dispersion, leading to changes in the relative energies of bright and dark exciton states. These results establish sBSE as a predictive framework for large molecular aggregates.

Let $E$ and $F$ be separable symmetric Banach sequence spaces, and let $C_E$ and $C_F$ be the corresponding ideals of compact operators on a separable Hilbert space. We prove that if $C_F$ is isomorphic to a complemented subspace of $S_E$, then $F=\ell_2$. As a consequence, if $C_E$ is isomorphic to $C_F$, then $E=F$ with equivalent norms. This answers Pełczyński's 1979 question concerning the uniqueness of symmetric structure. We also strengthen Arazy's result by showing that if $E$ has finite cotype and $C_F$ embeds isomorphically into $S_E$, then $F=\ell_2$. For reflexive $F\ne\ell_2$ with non-trivial Boyd indices, the embedding theorems of Lindenstrauss and Szankowski yield a separable reflexive symmetric sequence space $E$ with trivial cotype such that $C_F$ embeds isomorphically into $S_E$. This gives negative answers to several questions raised by Arazy in 1981.

We give algebraic proofs of two conjectural relations between quantum $A$-periods and thermodynamic Bethe ansatz (TBA)-like equations for quantum mirror curves. The quadratic relation follows from constant terms of shifted product expansions. For higher-degree relations, a cyclic quantum-torus trace and a finite matrix determinant identify the period with the free energy of nonoverlapping rods. Their density equation yields the TBA-like equation, with normalization fixed by the rod length. Both proofs hold as formal power series in the complex structure parameter, with exact dependence on $q=e^{i\hbar}$.

Normal-mode splitting reveals coherent cavity–magnon hybridization but does not certify finite-time quantum-state transfer. We describe quantum transfer in a passive, linear cavity–magnon system coupled to thermal reservoirs as a thermal-loss channel specified by its coherent transmissivity $\eta$ and output-referred thermal population $\nu$. For single-rail qubits, we calculate the phase-corrected average fidelity and compare it with the deterministic measure-and-prepare benchmark of $2/3$. A Bell pair shared by the cavity and an isolated reference retains reference–magnon entanglement if and only if $\eta>\nu$. An input squeezed vacuum of strength $r$ yields sub-vacuum magnon fluctuations if and only if $\nu<\eta(1-e^{-2r})/2$. When the initial magnon and both reservoirs have the same occupation, an analytically determined peak-transmissivity time optimizes all three tasks. These task-dependent benchmarks show that a conventional linewidth-based strong-coupling criterion does not guarantee quantum-transfer performance. Conversely, entanglement or squeezing can survive below that spectroscopic reference when the added noise is sufficiently low. These benchmarks provide quantitative targets for transfer timing and thermal-noise control in intracavity-to-magnon quantum interfaces.

Prevailing multi-vector visual document retrievers store each page as about a thousand patch vectors, often in vector databases run by a third party. Since no one can read a page from its vectors, this index is easily treated as less sensitive than the page. However, because the index keeps one vector per patch in raster order, and each vector is computed by a vision-language model pre-trained to read documents, we hypothesize that whoever runs or breaches the store can reproduce a page from its index alone. We frame inversion as conditional document image generation and infer from the vectors what the attack needs: the encoder, the page shape and, for shuffled vectors, their order. On the ViDoRe v3 benchmark, pages inverted from raw indices recover 47% of the words and 45% of the sensitive tokens. Used as queries against the stored indices, they rank their source page first 98.4% of the time. We test two cheap protections, token pooling and shuffling, which both cut word recall to about 8%. A model that restores the order of a shuffled index raises the share of source pages ranked first from 3.8% to 93.5%, while inverting a pooled index remains open. To test generalisation, we apply the same attack unchanged to another multi-vector retriever: its inverted pages still rank their source page first 70.2% of the time, though its word recall stays below a nearest-neighbour baseline. Multi-vector visual document retrievers are therefore vulnerable to inversion through their stored index, which should be protected like the documents it encodes.

Hessian spectra at trained models in deep learning exhibit a persistent pattern: eigenvalues organize into distinct clusters, including a large bulk near zero and a few isolated outliers. This paper shows that a natural account of these spectral phenomena emerges when the original setting is understood as a departure from a nearby, otherwise hidden, highly symmetric reference. Modifications, including changes to the architecture, data distribution, or parameter metric, expose a nearby reference configuration whose Hessian exhibits rich invariances-ones not accounted for by weight symmetries. There, symmetry enables a precise description of the spectra, forcing high-dimensional kernels and eigenvalues of large multiplicity. Returning to the original configuration breaks the Hessian symmetry and thereby produces the observed hierarchy of clusters and outliers. The framework is developed in some generality, with a detailed analysis of three-layer ReLU networks and applications to convolutional, graph, and transformer models, as well as to the NTK. The same mechanism is further shown to yield analogous spectral structures in layerwise Hessians and the Gauss-Newton matrix.

The EU Cyber Resilience Act (CRA) turns product cybersecurity into a lifecycle compliance obligation for manufacturers, importers, distributors, and integrators of products with digital elements on the EU market, a load that falls largely on small and medium-sized enterprises (SMEs) that rarely have dedicated governance, risk, and compliance (GRC) capacity. We present CYBERFORT, an open-source CRA-first compliance platform developed under the EU Digital Europe Programme and one of twelve projects in the EU CRA cluster. CYBERFORT operationalises the CRA through a guided scope self-assessment, a question bank tied to Annex I and the vulnerability-handling obligations, and a compliance-checking engine that links every answer to controls, policies, and machine-attested evidence, reusing ISO/IEC 27001, NIS2, and GDPR controls only where they coincide with CRA obligations. Its central contribution is the compliance chain, a traceable structure linking each product risk through its controls and policies to the CRA obligations it satisfies, and onward through evidence to the technical-documentation file and EU declaration of conformity, so that every operational gap is traceable and can be closed before market placement. Deployed at https://access.cyber-fort.eu/ for a first cohort of 43 organisations, the platform is presented with the engineering behind the chain, measured results from a completed end-to-end case study on a SIEM/XDR product with AI-driven remediation spanning the CRA obligation chapters, and the controlled effort study that remains in progress.

The ability to control magnetic systems without external magnetic fields has attracted attention recently, with all-optical magnetic switching showing increasing promise. Gaining fine control over light-matter interactions in magnetic nanostructures is essential for advancing opto-magnetic technologies, but remains challenging because strong optical coupling must be achieved within ultrathin magnetic structures at the target wavelength. Here, we show that coherent optical interference can increase this interaction in patterned magnetic metasurfaces. Arrays of permalloy nanomagnets are placed on a thin dielectric spacer above a reflective back-plane, forming a magnetic metasurface whose reflected wavefront is defined by the nanomagnet geometry, fill factor, and spacer thickness. Destructive interference between the metasurface and back-plane reflections yields near-perfect absorption, exceeding 95% for circular nanomagnet arrays in both simulation and experiment. The absorbed power is dissipated almost entirely within the nanomagnets, with only a few percent lost in the metallic back-plane. Enhanced absorption is also accompanied by a stronger magneto-optical Kerr effect, driven by both increased light-nanomagnet interaction and reduced reflected background. These results provide a general approach for achieving high optical absorption and strong magneto-optical response in nanoscale magnetic systems, supporting advances in optically addressable spintronics, magnetic sensing, and all-optical magnetic control.

Lossless compression can reduce the storage and movement of model weights without changing their floating-point values, but repeated statistical analysis and code construction add computational overhead. We study whether the statistical structure of exponents can be prepared once and reused. For this, we introduce NeuralZip, which groups chunks with similar exponent distributions, shares Huffman codes, and selectively represents recurring exponent tuples using packed exponents, thereby achieving additional moderate compression ratios. A setup chooses these representations before subsequent encodings, while every encoding still processes the current tensor values. In floating-point model checkpoints, post-setup compression is 1.81-21.33$\times$ faster than the baselines and achieves exact bit-to-bit reconstruction. We show that this setup can be precomputed and transferred from another compatible architecture, preserving similar compression ratios and avoiding the need to amortize setup costs. Therefore, compression adaptation is transferable and reusable. Training checkpoints demonstrate continued reuse as the weights evolve. Finally, GPU experiments reduce active memory usage by up to 27.5$\%$ while reproducing the logits exactly.

We investigate helicity effects in electron-positron pair production in circularly polarized electric fields with frequency chirping using the quantum-kinetic formalism for fermions. In particular, we calculate helicity-resolved momentum distributions and characterize the helicity imbalance through the helicity-asymmetry parameter for various electric-field configurations, including temporally asymmetric fields and dynamically assisted two-color fields with different frequency-chirping configurations. We find that right- and left-helicity electrons preferentially populate opposite momentum half-spaces along the out-of-plane momentum direction, leading to a pronounced helicity asymmetry in the produced electron distributions. For temporally asymmetric fields, frequency chirping substantially modifies the momentum distributions and can strongly enhance the helicity asymmetry, with the response depending sensitively on the pulse asymmetry parameter. For symmetric and elongated pulses, the helicity asymmetry approaches 100% at sufficiently large chirp strengths, whereas the compressed-pulse case exhibits a qualitatively different response with suppressed asymmetry at large chirp. For dynamically assisted fields, chirping the weak high-frequency component produces the strongest helicity response, reaching a maximum asymmetry of nearly 87% in the combined field, while chirping the strong field alone results in only a moderate asymmetry of about 12%-14%. Simultaneous chirping produces a large helicity imbalance together with substantial restructuring of the momentum spectrum, although its helicity response is weaker than that obtained by chirping the weak field alone. These results demonstrate that helicity-resolved momentum distributions provide additional information on the spin-dependent dynamics of Schwinger pair production beyond that contained in helicity-summed spectra.

Reinforcement learning is crucial for improving large language models' reasoning and generalization. It relies on massive rollouts whose lengths become increasingly long-tailed as context windows grow. In on-policy training, these long-tail rollouts can result in GPU bubbles, reducing system utilization and limiting RL scalability. Asynchronous or partial-rollout methods improve throughput by relaxing synchronization, but inevitably introduce stale off-policy samples (trajectories) that may hurt final accuracy. Existing approaches mainly mitigate this off-policy issue by reweighting off-policy samples during training, yet they can still leave a performance gap compared to fully on-policy training. In this work, rather than passively reweighting samples during training, we propose RollVerify, a lightweight RL framework built on partial rollout that actively verifies and repairs samples before they enter training. Specifically, it introduces an off-policy shift metric OPS, to quantify the off-policy deviation of partially generated trajectories. Guided by the OPS constraint, RollVerify performs both sequence-level and token-level verification to identify and truncate invalid suffixes of trajectories. This yields high-quality samples that protect the models' accuracy while preserving the efficiency gains of partial rollout. Experiments on mathematical and tool-assisted mathematical reasoning show that RollVerify achieves accuracy comparable to on-policy training while reducing training cost. Additional code-generation results provide preliminary evidence beyond mathematics.

Compression is a fundamental tool in data management. Today's compression schemes are generally designed by hand to apply to many different types of data (e.g., run length encoding or arithmetic encoding), leading to a zoo of general-purpose algorithms which work well for many datasets, but may not be optimal for any specific dataset. Inspired by recent advancements in agentic coding, we propose synthesizing custom-tailored data compression algorithms on a per-dataset basis. Unlike prior work using agents to synthesize database components, a data-specific compression algorithm can be fully verified at construction time, alleviating most correctness concerns. Modern file formats, like AnyBlox and F3, allow including the synthesized code alongside the data itself. Experimentally, we show that our synthesis agent can expand the compression-factor/decompression-speed Pareto front, outperforming general-purpose methods by nearly $2\times$ in compression factor.

We determine the worst-case behavior of the heavy-ball method on smooth strongly convex functions, first for Polyak's quadratic-optimal parameters and then for arbitrary constant parameters. For Polyak's tuning, the exact dimension-uniform exponential rate is the largest growth factor of an interpolable mixture of rotating geometric sequences. Four algebraic families determine this rate at every condition number. Two frequencies suffice, and one function in dimension five attains the rate at every horizon up to constant factors. We recover the sharp convergence threshold $9+4\sqrt5$ of Badithela and Seiler. For general tunings, an exact linear feasibility criterion characterizes dimension-uniform linear convergence through the angle between the characteristic polynomials of the two extreme quadratics. This gives a continuous condition-number threshold and resolves the second heavy-ball riddle of Goujaud, Taylor and Dieuleveut. The regions between consecutive cycle tongues are Farey gaps, each containing convergent and divergent tunings. Regular portions of the threshold surface are analytic plateaus with fixed periodic frequency support. Every rational rotation number in a gap anchors a single-harmonic plateau; mixed-harmonic plateaus and an exact two-lag threshold point also occur. Along tongue edges, explicit multiplier inequalities and second-order expansions of competing Farey fans bound the transition from single-harmonic to mixed-harmonic extremals. The rate bounds and the extremal constructions follow from a common interpolation and separation argument that preserves initialization with zero momentum.

Value alignment is a central objective in AI and HCI research, yet no validated instrument measures how users perceive it. This gap hampers the comparison and accumulation of findings and limits the effectiveness of applications, where understanding users' viewpoints is critical. We construct and evaluate a 13-item psychometric scale that measures perceived value alignment across two components: value understanding and value manifestation. It is based on a large item pool drawn from prior empirical studies, filtered by experts, and finally assessed by users (N=607) across diverse AI scenarios. Confirmatory factor analysis on an independent sample (N=259) confirmed the two-factor structure and high internal consistency for both subscales. Using optimization, we also derived a 6-item short form for quick administration. The scale is a reliable measure, providing HCI researchers with a common evaluation metric across contexts.

The Linux kernel is one of the largest and longest-maintained open source projects in existence. With more than 40 million lines of code, understanding the kernel's internal structure and assessing its software evolution is a great challenge. In this paper, we present an approach to visualize the Linux kernel using our software visualization tool ExplorViz. We analyze commits from the Linux Git repository using a custom analysis service. The web-based frontend utilizes the 3D city metaphor for visualization of the software structure. Metrics such as the number of lines are collected for each file and are accumulated for directories and commits. Calculated metrics can be mapped to the building's dimensions or be displayed via a heat map. A wide range of visualization, search, and filter options enable the interactive exploration of the visualized data. We present both a visualization of all files in the kernel repository and a visual analysis of the code evolution of Rust files in the Linux kernel. Demo video: https://youtu.be/3ODnERqD8g0

We propose a novel unfitted finite element method based on polynomial splines over hierarchical T-meshes (PHT-splines) for elliptic partial differential equations (PDEs) posed on domains whose boundaries are described implicitly by a level-set function. Exploiting the enhanced smoothness of the spline space, we formulate the method by minimizing the $L^2$ residual of the PDE over an extended neighborhood of the physical domain. This formulation allows the method to be implemented entirely on the background mesh using standard element-wise quadrature. It yields a symmetric positive-definite linear system and avoids the geometric construction of curved cut subregions in boundary elements, as well as the associated nontrivial numerical integration. We establish well-posedness of the numerical scheme and derive optimal a priori error estimates in the $H^1$ norm. In addition, we employ a residual-based a posteriori error indicator to guide local adaptive refinement of the hierarchical T-meshes. Numerical experiments corroborate the theoretical results and demonstrate the accuracy and efficiency of the proposed approach.

We study normalized ground states for the nonlinear Schrödinger energy on two-dimensional square grids with unbounded defects. We first show that unbounded defects do not necessarily destroy the dimensional crossover, proving its persistence on the half-grid and the quarter-grid. We then consider a prototypical defected grid where a macroscopically two-dimensional region coexists with an unbounded one-dimensional channel. On this graph, normalized ground states do not exist for sufficiently small or sufficiently large masses, showing that the one-dimensional component can dominate the variational problem and induce loss of compactness. Finally, we show that this mechanism is sensitive to the local geometry of the graph: suitable additional defects preserve small-mass nonexistence but restore the existence of ground states for large masses. Our analysis combines small-mass energy asymptotics with a large-mass blow-up argument.

Vision-Language Models (VLMs) have shown strong performance across a wide range of downstream vision tasks, thanks to the complementary information contained in the respective domains. Despite the performance gains, most of these approaches rely on aligning these domains using the cosine similarity metric, which fails to capture token-level structure and cross-modal interactions prior to the classification stage. This is especially critical in biomedical applications under federated constraints, where data sharing is restricted, labeled data is scarce at each site, and it differs widely across institutions, leading to substantial statistical heterogeneity. To overcome this issue, we propose FedSSMCoOp, a federated few-shot image classification framework that enables multimodal learning while preserving data privacy. With the help of the SSM-based Vision Mamba and Cross Mamba blocks, and by optimizing only the soft-prompt and communication-prompt updates in the federated setting, the framework prioritizes both computation and performance. Importantly, this eliminates the need to use an external Large Language Model (LLM) for feature alignment. The framework is further trained and evaluated on various biomedical image datasets, and its performance is assessed. The proposed framework delivers stable performance relative to the baselines and is, on average, 1.96 times lighter. The corresponding script will be made available soon.

Security Operations Centers (SOCs) for information technology and operational technology share one incident-response problem: a flood of correlated alerts and too few analysts. Large Language Models (LLMs) are increasingly proposed as reasoning engines that triage alerts and, in autonomous deployments, issue commands that block IPs, kill processes, or quarantine files on production hosts. This coupling introduces a new risk: a single adversarial alert can become a remote code path through the LLM's reasoning, leading it to recommend an action the SOC then executes. We present a constrained-action architecture with two coordinated layers: (i) a SIEM/XDR control plane that grounds remediation in correlated host events and confines the LLM's output to a closed intent vocabulary whose templated commands are executed by thin endpoint agents, backstopped by an argument validator; and (ii) a NeMo-Guardrails proxy that wraps the SOC-analyst LLM with input- and output-rail policies, evaluated out-of-the-box against a SOC-specific adversarial corpus we release. The stock proxy lifts injection recall from 25.0% to 94.5% at a 0.1% false-positive rate, and a live red-team exercise confirms that the closed intent vocabulary and argument validator contain the observed LLM failure modes before any command crosses the trust boundary. As an architectural fit (not yet a measured operational-technology deployment), the constrained-action property suits critical-infrastructure settings where a wrong remediation has physical, not merely operational, consequences. The loop is best run human-in-the-loop or delayed: the measured rail latency keeps inline control out of scope.

We study the relation between viscosity solutions and weak solutions of the equation $$\partial_t\left(|u|^{p-2}u\right)\,=\, \operatorname{div}(|\nabla u|^{p-2}\nabla u).$$ We prove that at least for non-negative functions these are equivalent concepts.

Multipartite interactions provide a unique route to generate hybrid quantum states, yet their intrinsically weak nonlinear coupling limits the controllable manipulation of the resulting correlations. Here we show that cooperative double squeezing and cavity Kerr nonlinearity together enable controllable engineering of Kerr-filtered hybrid states in a tripartite spin-photon-phonon system. Double squeezing exponentially enhances the spin-mediated photon-phonon pair-generation channel, whereas the Kerr interaction selectively reshapes the photonic component while maintaining the underlying tripartite conversion process. This mechanism reconstructs the composition of the hybrid excitation and gives rise to a fourfold phase-space manifold associated with spontaneous $Z_{2}^{(a)}\times Z_{2}^{(b)}$ parity breaking. Our results reveal a strategy for engineering hybrid quantum states by combining interaction amplification with mode-selective nonlinear filtering.

Enterprise resource planning (ERP) systems record operations as transactions spread across hundreds of normalized relational tables. Extracting an operational key performance indicator (KPI) from this schema requires a separate, bespoke join for almost every metric. We show that an event log, a canonical (case, activity, timestamp) representation derived from the same tables, collapses this heterogeneity into one flat structure, from which KPI families reduce to reusable operations after a one-time mapping. Using standardized event logs built from hundreds of SAP S/4HANA customers under a shared activity ontology, we define three families of process-derived KPIs (volumes, durations, and rates) and extract them uniformly across customer systems for two common end-to-end organizational processes, order-to-cash and procure-to-pay. We normalize rates and screen series for minimum coverage to support comparison across customers of very different sizes. We then characterize heterogeneity across industries and tenants using descriptors derived directly from the canonical form, before analyzing the resulting KPI time series. The same process executes heterogeneously across customers and industries, yet this shared representation enables direct comparison of sales- and procurement-side signals, including lead times and order arrivals. Using this shared representation, we characterize which KPI families are forecastable and find a recurring ordering from volumes through durations to rates across both processes and a highly heterogeneous customer base; a pretrained time-series foundation model (Chronos) is competitive with classical baselines such as ARIMA and ETS on rate and duration series, while classical models retain an edge on volumes.

For every quartic Salem number $\beta\in(1,2)$, we prove that the Bernoulli convolution $\nu_{\beta^{-1}}$ with equal weights has correlation dimension strictly less than one. In particular, neither of the two corresponding measures has an $L^2$ density. We relate correlation dimension to exact collision probabilities and express these probabilities as positive integrals over a four-dimensional torus associated with the defining polynomial. The unit-circle conjugates produce a persistent oscillatory term; using carefully chosen return times of the corresponding rotation, we take differences that make this term small while controlling the length and cost of the resulting configurations. Many well-separated placements of these configurations then give a collision probability above the critical scale, which yields the strict dimension drop. The qualitative argument is independent of the computer-assisted estimates. Separate computer-assisted arguments give \[ 0.99999<D_2(\nu_{\beta_1^{-1}})<1-10^{-65}, \qquad 0.99999<D_2(\nu_{\beta_2^{-1}})<1-10^{-75}, \] where $\beta_1<\beta_2$ are the two quartic Salem numbers in $(1,2)$.

We present a chat assistant for interactive software exploration, embedded in the 3D software visualization tool ExplorViz. The assistant builds upon current Large Language Models (LLMs) and enables users to ask questions about the currently visualized software system and trigger actions that change the visualization through natural language. We integrate the chat assistant in our ExplorViz frontend using the CopilotKit libraries such that probabilistic LLMs are combined with deterministic and tool-based actions similar to implementations using the Model Context Protocol (MCP). The chat assistant is also enabled to restructure the software system by adding, removing, or modifying parts of the software system in the visualization. An empirical experiment with eleven participants evaluated both perceived comprehension support and the tool calls that were triggered by the chat assistant. Participants rated the assistant's generated summaries and explanations as largely correct. They also reported high usability for actions like highlighting entities in the visualization and the creation of new color themes. In contrast, open-ended chat-assisted software restructuring in the visualization showed mixed results. This suggests a need for stronger guardrails for the employed LLM and better incorporation of user feedback. Overall, the assistant was perceived as usable and promising for reducing interaction overhead during exploratory program comprehension tasks. We provide a video presenting the chat assistant's use and a reproduction package of the software system that was used in our evaluation.

We develop Delsarte theory for quantum association schemes, allowing both composition and the quantum Schur product to be noncommutative. A MacWilliams identity and positivity of the inner and dual distributions yield conic upper bounds for codes and lower bounds for designs in terms of effective size, which extends subset cardinality. These bounds recover classical linear programs for symmetric association schemes and semidefinite programs for homogeneous coherent configurations. We also quantize Schurian schemes using finite-group representations and characterize quantum block designs in quantum Johnson schemes arising from irreducible stabilizer representations by averaging over subgroups fixing prescribed points individually. In a quantum Johnson scheme on $M_2(\mathbb{C})^{\oplus10}$, we prove that the minimum effective size of a nonzero positive element satisfying the strength-two design condition is $20$, attained by complementary projections outside the center of the underlying algebra. Every such element in the center has effective size $40$, while the conic lower bound is $40/3$, strictly below the actual minimum.

Weighted Shapley values represent asymmetry through positive weights and ordered priority classes. We give these parameters a preference interpretation in Roth's framework of lotteries over positions in transferable-utility games. Under common calibration, nullity, ordinary risk neutrality, unanimity efficiency, and unanimity positivity, position values in unanimity games are probability equivalents. Luce conditioning of these probabilities characterizes the Kalai-Samet family and is equivalent to partnership consistency. We separate conditioning into transitivity of revealed priority, pairwise determination of support, and invariance of positive odds. Two-player observations admit a weighted Shapley extension exactly when revealed priority is transitive and within-class odds satisfy a product rule. The extension is unique: pairwise comparisons identify the priority classes and weight ratios within each class. Larger unanimity games provide additional restrictions on supports and shares. We give constructive proofs, establish independence of the five axioms, and explain the scope and limits of the elicitation interpretation.

Assessing compound weather risks requires forecasts representing dependence between variables. CLARA (Calibrated Advection-Routing Attention) learns joint Gaussian predictive distributions of five surface variables from station observations alone, without numerical weather prediction or reanalysis; the approximately 28,000-parameter model supports CPU training and prediction. Across six multi-year folds on 96 stations, its lead-mean energy score is 4.9% lower than that of a learned comparator with matched temporal inputs (4.7% with a similar parameter count) and 11-65% lower than those of statistical baselines. Holding marginal variances fixed, removing learned correlations worsens joint negative log-likelihood by 1.0-2.8 nats per station. A covariance-scale estimator, proved consistent under stated assumptions, improves short-lead calibration but over-corrects at long leads. Synthetic interventions show an attention-bias coefficient alone does not measure forecast influence. Retrained in ten regions on six continents, CLARA outperforms persistence in all 60 multi-year region-lead comparisons and a similarly sized learned model in 57 of 60.

We present a scalable method for computing persistence pairing graphs from large cubical filtrations and use it to test whether graph organization among persistent classes contains information beyond persistence intervals alone. The method cancels equal-value pairs before global reduction, constructs the compressed complex in streaming form, and recovers graph transitions from one persistence reduction through projected relations and triangular event solves. We apply the method to 119 signed distance volumes from the DRP-372 porous media collection for permeability prediction. Each 256-cubed volume induces more than 135 million cubical cells before contraction, whereas the median compressed complex contains 37,471 generators. In validation grouped by material family, adding persistence pairing graph descriptors improves prediction over persistence summaries under both Ridge regression and partial least squares regression. In the stricter experiment that holds out one source project at a time, Ridge retains a modest improvement over persistence alone, although additional benefit beyond geometry and persistence is not consistent across projects. Two null models show that the observed persistence and graph coupling and edge target organization are strongly nonrandom, but neither uniquely explains the predictive improvement; the useful signal appears to reside mainly in coarser graph and event organization. Spatial analyses likewise distinguish persistence magnitude from graph prominence and reveal nonlocal organization among algebraically related persistence events. These results show that persistence pairing graphs provide structurally informative summaries beyond the barcode while exposing domain dependence and representative sensitivity that motivate more invariant relational descriptors.

Ship-form design combines smooth geometric representation, local shape editing, and constraints on the resulting hull. We present the Natural-Language-to-Hull Framework (NL2Hull Framework), which formulates ship-form editing as a typed discrete decision problem and connects language decisions to numerical geometry. Its Constrained Free-Form Deformation Engine (CFFD Engine) represents hull waterlines with non-uniform rational B-splines (NURBS), applies free-form deformation (FFD) to their control points, reconstructs the hull, and checks geometric constraints. We construct the Ship Design Decision Dataset (SDD Dataset) with 134,558 cleaned records and evaluate compared models on its subset Ship Design Decision Benchmark (SDDBench), containing 5,000 records and 43,496 typed questions. We propose Chip, a constrained ship-design decision model for processing natural-language requests. Chip reaches 95.90% question accuracy and 99.32% FFD exact match, with a negative log-likelihood of 0.0951, an expected calibration error of 0.0032, and a Brier score of 0.0551. The NL2Hull Framework provides a reproducible interface for evaluating language-based ship-form decisions while identifying the geometry and continuous-control components that require further development. Our code and dataset is available at https://github.com/wenhuahuo/NL2Hull.