Papers

The $\textit{Colored Knapsack Problem}$ (ColKP) generalizes the classical Knapsack Problem by partitioning the items into color classes and requiring the selected items to admit an ordering in which consecutive items have different colors. The problem is weakly $\mathcal{NP}$-hard and admits two pseudo-polynomial dynamic programming (DP) algorithms proposed in the literature. These two DP algorithms have worst-case running times $O(b \, n^4)$ and $O(b^2 \, n^3)$, respectively, where $b$ is the knapsack capacity and $n$ is the number of items. We develop the first approximation algorithm for the ColKP. By rounding an optimal basic solution of the linear programming relaxation of its natural integer programming formulation and repairing color feasibility, we obtain a linear-time approximation-algorithm whose worst-case performance ratio is $1/3$. We then reformulate both DP algorithms so that profit, rather than knapsack capacity, indexes their pseudo-polynomial dimension, and combine them with profit scaling to obtain two fully polynomial-time approximation schemes (FPTASs). The first FPTAS runs in $O(n^5/\varepsilon)$ time for nonnegative profits and in $O(n^6/\varepsilon)$ time for arbitrary integer profits. The second FPTAS runs instead in $O(n^5/\varepsilon^2)$ and $O(n^7/\varepsilon^2)$ time, respectively. The approximation guarantee, along with new structural insights, provides the bounds needed to control the scaled profit range and establish these running times.

We introduce several notions of resonance for systems exhibiting weak or partial dissipation: $\dot u=Au+f(t)$, with $A$ the generator of a strongly stable semigroup $S(t)$ on a Hilbert space $H$. We refer to resonance as the phenomenon where a time-periodic $f$ may yield an unbounded $u$, classically occurring when $A$ has imaginary eigenvalues. In infinite dimensions, however, unbounded growth may depend on topological choices, and several “resonances" may occur. Classically, existence of $T$-periodic $u$ under $T$-periodic $f$ is equivalent to a range condition: $\mathcal{R}(I-S(T))=H$. Consequently, its failure permits unbounded solution growth and we elucidate that connection through properties of $S(t)$. We describe a hierarchy of range failures, and provide an associated resonance taxonomy. The growth rate of ~$||(A-\lambda I)^{-1}||_H$ on ~$i\R$ dictates a regularity gap between $u$ and $f$, and, for rapid growth in $\lambda$, that gap can be infinite. In this case, we demonstrate implications for periodic solvability, and a mechanism for constructing smooth resonant forces. The theory developed here is motivated by (and demonstrated for) a hyperbolic-parabolic system, where the latter component provides the only system dissipation. Such dynamics are a simplification of fluid-structure phenomena, which demonstrate strong stability but do not provide unconditional periodic well-posedness. Though point-spectral resonance is ruled out, we note that $\mathcal R(I-S(T))\neq H$. Our main result here shows that, for a carefully constructed geometry, a classical heat-wave system possesses periods $T$ which yield infinite derivative loss and, via supporting results, yield resonance with smooth forcing.

We present psi4-cbo, an open-source extension of the Psi4 program for simulations within the cavity Born-Oppenheimer Approximation (CBOA). By treating the cavity photon mode on the same footing as the nuclear coordinates, psi4-cbo incorporates light-matter coupling into standard electronic structure workflows. These workflows include self-consistent field calculations, response theory, analytic gradients, joint Hessians, and geometry optimization. The package is designed for reproducibility and is documented with working examples for its main workflows. To evaluate the approximations inherent to the CBOA framework, we use an exact \gls{qedfci} reference. Resolving the correlation energy into electron-electron and electron-photon channels enables us to precisely determine the point at which the CBOA becomes quantitatively sufficient. Additionally, we highlight that, since self-consistent treatments dress the cavity modes, satisfying experimental resonance conditions is method-dependent. As a practical application, we investigate the chromophore acrolein under vibrational strong coupling and detail how to locate resonances on the dressed photon modes rather than the bare molecular bands.

Community health workers (CHWs) in the Global South increasingly encounter AI-powered tools, yet the counseling work central to their role remains largely unsupported. We study communication practices among Accredited Social Health Activists (ASHAs) in rural Rajasthan, India, through simulated family-planning calls, semi-structured interviews, and an LLM chatbot roleplay design-probe with 20 participants. In calls, ASHAs often responded to social or material concerns by shifting to health-risk information, denying concerns, promising unspecified help, or listing medical solutions with limited explanation. A smaller set of responses instead engaged concerns, sought permission before involving family members, or left decisions with beneficiaries. We interpret these patterns through Motivational Interviewing, emphasizing restraint from correcting, persuading, or over-solving. Drawing across observed calls, interviews, and probe reactions, we derive design considerations for AI roleplay training: keep AI in a rehearsal role, provide descriptive rather than prescriptive feedback, and evaluate counseling process rather than agreement with prescribed responses.

Retrieval-Augmented Generation (RAG) systems typically employ fixed retriever and generator configurations across queries, despite substantial differences in query complexity and information needs, leading to inefficient allocation of computational resources. While retrieval and generation adaptivity have been studied independently, their joint effect on end-to-end RAG performance remains underexplored. We systematically analyze how retriever and generator complexity interacts across factoid and multi-hop question answering (QA), including bridge and composition reasoning tasks. Our analysis shows that stronger retrieval generally yields larger gains than increased generation effort, but both exhibit diminishing and non-monotonic returns, indicating that higher-complexity configurations are not uniformly better across queries. Motivated by these findings, we introduce DRAG, a query-adaptive framework for selecting retriever-generator configurations. We first propose DRAG$_\text{QPP}$, a training-free routing approach that uses Query Performance Prediction (QPP) signals to guide retriever selection and perplexity-based measures over retrieved context to guide generator selection. We further introduce DRAG$_\text{SFT}$, a supervised routing approach that fine-tunes an LLM to jointly predict retriever-generator configurations. Across three LLM families and four QA benchmarks, \qpprag~achieves performance comparable to strong static RAG baselines while substantially reducing inference latency, whereas DRAG$_\text{SFT}$ consistently improves effectiveness over static and training-free adaptive baselines. Overall, DRAG demonstrates that jointly adapting retrieval and generation achieves a more favorable effectiveness-efficiency trade-off than static RAG pipelines.

Reliable confidence estimation is increasingly central to the trustworthy deployment of language models: a calibrated estimate of the probability that an output is correct decides what to ship, what to escalate, and what to retry. Existing confidence estimators, however, share one design premise: they only read the current inference process, either by introspecting on it, scoring its token probabilities, or resampling it. We argue that the current inference is not a sufficient basis for confidence. We propose XConf (eXperiential Confidence): estimating confidence together with the model's accumulated experience. The experience is stored as a record of the model's own graded past episodes, each holding the task, the model's reflection, its stated confidence, the outcome, and a lesson written once the grade arrived. Given a new task, XConf's Recall stage retrieves past episodes on similar tasks met with a similar stated confidence, and reads off their historical success rate; its Reflect stage shows the model this record, has it name its recurring failure mode, and restate a confidence now informed by its own track records. Our estimator is format-general, requiring no logit access or weight updates, and costs only one answer generation. Across nine benchmarks spanning reasoning, coding, multimodal QA, and interactive agents, and four models from three families, XConf beats or matches ten-sample self-consistency in discrimination (AUROC) on 23 of 24 comparisons, with much lower calibration error (ECE), at a tenth of the generation cost. Used for selective prediction, abstaining on the 10% least-confident episodes raises the delivered success rate by up to 8.7 points on agent tasks. We therefore see experiential confidence estimation as a new paradigm for future general-purpose confidence estimation.

Phononic frequency combs have been demonstrated experimentally and theoretically in the kHz-MHz regime under nonlinear driving; however, their spontaneous formation in the GHz-THz regime remains rare. We investigate the spontaneous formation of frequency combs in van der Waals solid CrGeTe$_3$, where combs of spacing $\sim$2 cm$^{-1}$ were experimentally proposed to occur in a flat phonon mode but are now reported to originate from isotopic distribution. Our spectral energy density calculations using machine-learning-augmented molecular dynamics simulations show comb-like features with reduced spacings of $\sim$0.1 and 0.6 cm$^{-1}$ in the same mode at 50 and 200 K. However, the spacings of the comb-like features are comparable to the phonon linewidth, making precise identification of the frequency comb challenging. From a comprehensive analysis of different modes of CrGeTe$_3$, we identified two conditions to distinctively observe the combs beyond the experimental resolution: (i) an intramolecular or isolated mode with reasonably large third- or higher-order anharmonicity from phonon self-interaction and (ii) limited phonon scattering channels. Our analysis of other van der Waals solids highlighted that these conditions are met for the nearly flat intramolecular $E_{2g}$ and $A_{2u}$ phonon modes of WSe$_2$. The detailed calculations showed the formation of a spontaneous frequency comb with spacings of 1.7 and 0.67 cm$^{-1}$ from coherent superposition of four and five-phonon eigenstates in the $E_{2g}$ and $A_{2u}$ phonon modes, respectively. Available Raman scattering data of the $E_{2g}$ mode in the literature provide preliminary, if not conclusive, evidence of comb formation. Our findings offer a deeper understanding and open avenues for engineering long-lived phononic frequency combs for various practical applications.

T-state cultivation is a resource-efficient protocol producing logical T states but recent benchmarks show that its logical error rate is considerably higher than intended i.e. than S-state cultivation, which is the analogous protocol for producing logical S states. In this paper, we explain this T-S discrepancy by analytically showing, under circuit-level depolarising noise, that distance-3 (-5) T-state cultivation has fault distance 2 (3) due to Pauli hook errors that propagate to coherent Clifford errors after its final double-check circuit; such errors remain Pauli in S-state cultivation, which consequently retains fault distance 3 (5). As part of our analysis we derive a general formula, and an $\mathcal O(n^3)$-time algorithm for fixed logical-qubit count, for the acceptance probability of a logical mixed state afflicted with a Clifford error, where $n$ is the physical qubit count. We then design flags that detect the malignant hook errors in cultivation, improving the pre-escape logical error rate from $\Theta(p^3)$ to $\Theta(p^5)$. At noise level $p =10^{-3}$, this is a 4.9$\times$ improvement, costing a 1.36$\times$ increase in attempts per accepted shot.

The detection of the Diffuse Supernova Neutrino Background (DSNB) is one of the main goals of the current and the next generation of neutrino experiments. Based on results published by the Super-Kamiokande (SK) collaboration, we study the sensitivity of current and future water Cherenkov detectors to the DSNB. We reproduce current constraints and estimate the sensitivity to the DSNB of ten years of SK data and of a next-generation water-Cherenkov detector like Hyper-Kamiokande (HK). We find that, even with increased exposure, SK's sensitivity is relatively modest, while HK has the potential to deliver a statistically significant discovery of the DSNB in ten years. Along the way, we perform a detailed study of the relevant atmospheric neutrino backgrounds and argue that an accurate treatment of neutrino oscillations and propagation is essential when it comes to properly inferring the sensitivity to the DSNB and measuring its flux.

The recently introduced concept of quantum-state texture (QST) has found applications ranging from the identification of unknown quantum gates to the study of quantum phase transitions and criticality, and has already been experimentally investigated. Here, we advance its resource-theoretic formulation in several directions. Our approach centers on the experimentally accessible grand sum–the sum of all matrix elements of a density operator in a given basis. We clarify several points raised in the recent literature, including the relation between texture distillation and a simple grand-sum-based QST monotone. We completely characterize free operations for a single qubit and study the resulting state-conversion order; classify relevant families of free operations in arbitrary dimensions; derive bounds relating the texture of composite systems to that of their subsystems; and introduce the basis-independent concept of set texture. Together, these results strengthen and broaden the resource theory of QST, providing a foundation for its further development and applications.

In the moduli space of abelian varieties, Prym loci parametrise Prym varieties associated to covers of curves with fixed degree and monodromy data. We derive and implement an algorithm computing the tautological projections of classes of Prym loci. The key input is a comparison formula relating three different Hodge bundles on moduli spaces of admissible covers. We present computer and hand calculations for double and triple covers, with the locus of hyperelliptic Jacobians as a special case. Two applications follow. First, we calculate the degrees of the Prym maps in the codimension-zero cases, unifying a series of previously ad hoc results. Second, we prove in low genera the non-divisibility of the Jacobian class by the Prym class.

Recent modeling of the JWST spectra of the Y-dwarf CWISEPJ193518.59-154620.3 (Faherty et al. 2024; Suárez et al. 2025) and the T-dwarf SIMPJ013656.5+093347.3 (Nasedkin et al. 2025) indicates the presence of a thermal inversion in their atmospheres, implying an additional source of heating. Auroral energy deposition has been proposed as a potential mechanism. In this work, we model auroral energy deposition processes and the resulting atmospheric response to assess whether physically motivated auroral electron beam energy spectra can reproduce the inferred thermal inversions. We simulate the effects of several auroral electron beam energy spectra consistent with observations of the Jovian population of auroral electrons and scale them to the total electron flux expected for brown dwarfs. We find that auroral energy deposition alone cannot reproduce both the magnitude and pressure level of the inferred inversion in either object. While inversions are produced in our models, they occur at pressures that are too low compared to those required by the observations. These results suggest that the actual population of auroral electrons includes a stronger high-energy component than considered here, that additional heating mechanisms contribute to the observed thermal inversions, and/or that heterogeneous heating of the atmosphere is important for determining the observed emission.

Shared-control arbitration mechanisms can fail structurally when they are driven by quantities that evolve on the same automation-assisted trajectory that unsafe automation can corrupt. Under unsafe assistance, arising from faults or flawed design, the arbitration logic can adapt to the corrupted trajectory instead of resisting it. Focusing on workload regulation, this paper proposes a framework that prevents this problem by anchoring the safety constraints to an unassisted pilot trajectory. A baseline model evolving without automation assistance generates the acceptable workload envelope, while an assistance-induced deviation barrier and a closed-form mismatch bound relate actual and baseline workload evolution. The resulting control barrier function based quadratic program is always feasible and guarantees forward invariance of an augmented safe set. Simulations on an F-16 pitch-tracking problem show that the proposed method prevents workload-constraint drift under unsafe assistance.

We present an integer-coordinate realization of a genus-3 polyhedral surface with eight planar simple nonagonal faces. It has 24 vertices and 36 edges, and each vertex is incident with three faces. Every pair of faces shares an edge: 20 pairs share one edge and 8 pairs share two. Vertex coordinates, face walks, and plane equations are given. Exact verification confirms that all faces are planar, the surface is closed and orientable, no unintended intersections occur, and the realization has $C_4$ symmetry. The construction is based on an earlier construction and preserves its incidence structure.

We present NeMo Data Designer (NDD), an open-source, general-purpose framework for multi-modal synthetic data generation (SDG). Designed to be intuitive to use, NDD provides a declarative configuration format in which human and/or agent users define each dataset column, with column types spanning text, code, structured outputs, images, embeddings, and statistical samplers that are explicitly configured to steer dataset diversity. Additional column types and functionality can be introduced using the framework's flexible plugin system. NDD's configuration is an inspectable artifact, supporting workflow sharing and reproducibility. SDG is an inherently iterative process. NDD therefore builds a preview-and-revision loop into its core workflow, allowing users to generate and inspect a small number of records, refine the specification, and rerun generation at full scale. At runtime, NDD resolves dependencies, schedules calls to user-provided model endpoints, and retries failed requests. We describe NDD's architecture and programming model and present case studies spanning structured, agentic, multimodal, and domain-specialized tasks, including datasets used in Nemotron model development and in production enterprise deployments.

Large language model (LLM)-based agents are increasingly used across software engineering, web automation, research, and productivity applications. Their integration of planning, memory, tool use, code execution, and external interactions enables greater autonomy but also introduces new reliability, safety, and security risks. We present a large-scale empirical study of quality assurance (QA) practices in 157 open-source LLM-based agent projects with at least 100 GitHub stars. We analyze documentation, source code, configurations, and tests to characterize QA practices across execution surfaces, safeguards, testing artifacts, risk scenarios, and recurring gaps. We find that current QA primarily focuses on basic functionality and high-risk actions, while coverage remains fragmented. Safeguards are inconsistently applied across equivalent execution routes, tests rarely examine boundary, adversarial, or multi-step tool-use failures, and identified risks are seldom translated into end-to-end QA checks. These findings highlight the need to move beyond feature-level testing toward systematic end-to-end validation that ensures agent workflows remain within intended boundaries when interacting with untrusted inputs, tools, persistent state, and external APIs.

Integrated deep reinforcement learning (DRL) and model predictive control (MPC) methods are increasingly used to control autonomous systems by combining their complementary capabilities. DRL learns control policies through interaction with the environment. MPC uses a system model to optimize control inputs while accounting for constraints. In DRL-MPC frameworks with shared control authority, both the DRL agent and the MPC controller each determine part of the control inputs. However, common learning formulations treat MPC as part of the environment and therefore do not explicitly account for MPC's contribution to control or its interaction with the DRL agent. This paper proposes a novel composite-gradient learning (CGL) method that integrates the MPC controller into the learning process by representing the DRL and MPC control inputs as a joint action and accounting for their interaction when updating the DRL agent during training. CGL is evaluated on two multi-class freeway traffic networks with different strengths of interaction between the DRL and MPC control inputs and it is compared with alternative methods that treat MPC as part of the environment or that only partially incorporate MPC into learning. The results show that CGL offers limited benefit under weak interaction, but learns higher-performing control policies than the alternative methods in a subset of training runs under strong interaction, although the average control-performance gains remain modest.

Document repositories evolve continuously. Guidelines and policies are revised, superseded, and re-uploaded, so the same content recurs in different wording and newer versions refine or contradict earlier ones. These inconsistencies belong to the growing collection rather than to any single document, yet existing work treats versioning, duplicate detection, and contradiction detection as isolated pairwise tasks and stops once a pair is labeled. We present GVD (Governed Versioning and Deduplication), a framework that unifies cross-document version linking with rule-level conflict resolution under an auditable update policy. Incoming documents are assigned to version families through bidirectional rule alignment, and their rules are compared against the family memory to identify duplicates, contradictions, asymmetric refinements, and new knowledge, with Counterfactual Span Probing (CSP) resolving related pairs that inference misclassifies as neutral. Relation-specific policies suppress duplicates and escalate only consequential changes for review, retaining version lineage as an audit trail. The pipeline runs fully locally, with no large language model. On 120 enterprise documents processed as 140 ingestions across 59 version families, GVD reaches an F1 of 0.97 for version-family construction and 0.94 for rule-level consistency, with CSP raising rule consistency from 0.90 to 0.94.

A large language model (LLM) agent can follow more graph paths without acquiring more independent evidence. GraphEcho tests whether agents mistake these repeated encounters for additional corroboration. The benchmark varies path counts and evidential origins while holding evidence content fixed, and evaluates both judgments and active exploration. Controlled synthetic experiments reveal model-dependent judgment shifts, but redundant supporting paths increase the share of repeated walks across all evaluated frozen agents. Provenance-aware post-training (PAPT) reduces revisits and improves synthetic accuracy, yet covers fewer distinct sources. On scientific claims, it continues to reduce repetition while accuracy declines. These findings expose a gap between efficient exploration and effective evidence use: an agent can learn to stop repeating itself while overlooking information it needs. GraphEcho provides a controlled way to evaluate both what graph agents conclude and whether their exploration reaches distinct evidential sources.

Detection efficiency in gated-mode single-photon avalanche detectors recovers gradually after each gate edge, limiting attainable count rates, yet quantitative recovery models exist only for free-running operation. We extract the gated recovery time constant of a free-running InGaAs/InP detector at 1550 nm by sweeping the gate frequency from 100 kHz to 1 MHz and globally fitting count rates across four dead times, requiring neither a pulsed laser nor a time-to-digital converter. The recovery time decreases linearly with detection efficiency, from 301 to 161 ns between 10 % and 25 %, at 9.3 ns per percentage point. We further resolve a periodic count-rate modulation consistent with bias-dependent capacitive gate feedthrough.

We leverage the high resolution and spectral stability of the Keck Planet Finder (KPF) spectrograph to investigate macroturbulence broadening via the stellar cross-correlation function (CCF). As our calibration sample, we use main sequence benchmark slow-rotators v$\sin$i < 4 km/s where rotation rates were derived from the most robust asteroseismic mode splitting measurements, independent from spectral line broadening. We fit a linear relationship for macroturbulence as a function of derived $\nu_{max}$, the frequency of maximum power due to stellar oscillations, with an RMS scatter of 90 m/s. Previous studies have calibrated macroturbulence against T$_{eff}$, but we find $\nu_{max}$ to be a lower dispersion predictor by a factor of 4 indicating a deeper relationship between $\nu_{max}$and convective motions.

We introduce bicomplex fiber bundles and develop a framework for bicomplex characteristic classes and almost bicomplex structures on smooth manifolds. In the first part, we present the basic definitions and properties of these bundles, including their fundamental idempotent decomposition and the correspondence between their isomorphism classes and homotopy classes of maps into the bicomplex infinite Grassmannian. We then define bicomplex characteristic classes and show that, in general, they are not determined by the Chern classes of the underlying complex bundle. We also construct the bicomplex Chern character and discuss its algebraic properties. Finally, we apply the resulting theory to almost bicomplex manifolds, providing examples and obstructions to the existence of such structures.

Speculative sampling accelerates diffusion model generation by drafting inexpensive candidate states and correcting them under a coupling that preserves the target distribution exactly, reducing the number of expensive target evaluations. Existing diffusion samplers, notably those based on reflection maximal coupling, are topologically constrained: their lookahead drafts form a chain graph, a single linear sequence, which inherently limits the acceptance rate per target evaluation. We connect speculative sampling in diffusion models to relative entropy coding (REC). This perspective shows the lookahead need not be linear and motivates our central contribution, draft trees, which enrich the candidates considered per round and lower the target function evaluations. We further adopt greedy rejection sampling, an REC algorithm, as the draft-target coupling, improving acceptance while guaranteeing exact target samples. Experiments across diverse target and draft models demonstrate up to 8.3% acceleration over the reflection coupling baseline in practical settings.

We study the complexity of quantum decomposable randomized encodings (QDRE). We establish a bi-directional connection between the QDRE model and the communication complexity model of quantum private simultaneous message protocols (QPSM), where classical communication is free, and quantum communication is the primary complexity measure. We show the following upper and lower bounds. (1) For every quantum channel mapping $n$ to $m$ qubits, we give a QPSM protocol with quantum communication $m$, using exponential pre-shared entanglement. In particular, constant-output channels have $O(1)$ quantum communication, and classical-output channels require no quantum communication. (2) With $O(n)$ pre-shared entanglement, every one-qubit-output channel has an $O(n)$-quantum-communication QPSM protocol. Conversely, there exists a channel and a constant $c>0$ for which any protocol with at most $cn$ pre-shared entanglement requires $\Omega(n)$ quantum communication. (3) In contrast, we identify a structured class of quantum channels, Clifford-induced channels, for which there exist QPSM protocols with $O(n)$ pre-shared entangled qubits and only $O(1)$ quantum communication complexity. Through our connection, we obtain analogous upper and lower bounds on the quantum encoding size of QDRE. Our results show that the amount of pre-shared entanglement plays a central role in quantum encoding size and quantum communication complexity.

Graphic designs nowadays predominantly contain human images, where people are posed and framed in a delicate way to guide viewers' visual exploration and evoke desired feelings. Despite recent progress in automatic graphic design generation, there has been no work on investigating the role of the human representations in design creation. In this paper, we seek to emphasize the importance of visual human representations in graphic design generation, by studying a novel task, dubbed as design-conditioned 3D human adding. To solve this task, we propose a model that adds 3D human representations into an existing partial design, by predicting their 3D poses, their 2D composition in the image containing them, as well as the spatial arrangement of the image in the input design, to generate a complete design. Our experiments show that our model outperforms baselines by predicting the 3D human poses, 2D framing and human image layout that better harmonize with the other existing design elements, and generating higher-quality holistic designs. Our work is the first to explore connections between 3D human generation and 2D graphic design generation, which would inspire future research in leveraging 3D information to build more powerful generative models for graphic designs in the 2D domain. The code is available at https://github.com/GreyNails/Human-aware-Design-Generation-Adding-3D-Humans-into-Graphic-Designs.

Wearable assistants require episodic memory over egocentric video, yet current vision-language models face bounded frame budgets, growing visual-token costs, and long-context retrieval failures. Under these practical constraints, we study whether textual captions can serve as reusable episodic memory. We define the Episodic Memory Video Caption QA task and introduce CapMem, a human-annotated benchmark with 75 videos totaling 33.7 hours, and 1,000 multiple-choice questions across 16 scenarios. On long videos (>20 min), full-coverage CaptionQA with 30s and 60s caption windows outperforms direct VideoQA for 10/12 and 8/12 models, respectively. On the same video subset, a matched-frame control across six Qwen models retains mean accuracy gains of 3.22 and 2.55 points, respectively. Our caption-guided retrieve-and-verify harness further improves accuracy by up to 5.3 points. These results support the effectiveness of caption memory for episodic reasoning over long egocentric video.

We present a framework for the modeling and analysis of geometric hybrid dynamical systems as hybrid inclusions on $C^1$-manifolds. Using tools from nonsmooth and set-valued analysis on manifolds, we derive coordinate-independent sufficient conditions for the existence of nontrivial solutions to this type of systems. We present geometric notions of uniform stability and attractivity of compact sets, and establish their equivalence to metric-based stability notions when the manifold is endowed with a Riemannian structure. We also introduce nonsmooth Lyapunov functions and a hybrid Lyapunov theorem providing sufficient conditions for uniform global asymptotic stability of compact sets. Finally, by characterizing $\omega$-limit sets of precompact solutions, we derive a hybrid invariance principle for geometric hybrid dynamical systems. The results are demonstrated through several running examples.

Three recent results describe what look like unrelated LLM reliability problems. Yin et al. (2026) show reasoning RL collapses tool-reliability representations. Suleymanov et al. (2026) show that under safety-constrained generation, large models rewrite flagged spans while small models truncate. Bastounis et al. (2024) prove any consistent-reasoning system without an implicit "I don't know" function must hallucinate infinitely often on broad problem classes. We argue these findings converge on a single intervention: calibrated abstention is what each independently identifies as the missing capability, even though the unavailability they document, a capability gap, a policy gap, and a recursion-theoretic gap, has a different source in each case. Honesty post-training has narrowed the gap in deployed models, but principled closure of the class Bastounis identifies requires a calibrated abstention function whose training signal at the leaderboard level is absent: dominant benchmarks assign zero reward to decline, so the leaderboard gradient that would select for the function does not exist. We propose four changes to evaluation: triple-scoring, abstention-rate reporting, capability-stratified evaluation, and mandatory calibration metrics. Benchmark reform is necessary, not sufficient, for closing the gap the theorem identifies.

Theoretical analysis and Monte Carlo simulation separate local-epoch effects from averaging and tuning effects in federated Lasso. How much local work should precede averaging when fitting a sparse regression? An orthogonal calculation shows that extra epochs can have no effect while averaging still enlarges the selected set. A correlated two-site construction gives an exact, nonmonotone limiting objective gap and its minimizing epoch count. We then compare coordinate-descent averaging, two thresholding modifications, and adapted FedDualAvg across twelve scenarios and 600 replicates. Methods share a penalty, independent validation samples, selection rules, and resource limits. FedDualAvg generally achieves smaller objective gaps but does not always recover variables better. Thresholding gains depend strongly on selection rules. Epoch effects vary with correlation, signal strength, site allocation, and the outcome measured. These results distinguish faster iteration from better optimization, prediction, and variable selection.

The Hubble tension motivates careful scrutiny of the redshift-independent distances underpinning the local distance ladder. Water megamasers afford a purely geometric distance from orbital dynamics in an accretion disc. For five of the six Megamaser Cosmology Project (MCP) galaxies, we present a Bayesian forward model that infers the angular-diameter distance and warped Keplerian disc parameters jointly from the very long baseline interferometry quasi-observables: maser spot positions, velocities, and accelerations. We then constrain $H_0$ from these distances and the host redshifts, including a physical distance prior, modelling the galaxy sample selection and testing a linear and a non-linear peculiar-velocity reconstruction. Accounting for peculiar velocities with the non-linear Manticore reconstruction, we infer $H_0 = 71.6 \pm 3.7$ km/s/Mpc, where the uncertainty is statistical. Relative to ignoring peculiar velocities, the linear and non-linear reconstructions lower $H_0$ by $0.8$–$1.4$ and $1.6$–$2.1$ km/s/Mpc, respectively, whereas changing the selection variable alters it by less than $1$ km/s/Mpc. We analyse the sixth galaxy, NGC 4258, separately. Modelling its disc as eccentric and quadratically warped, we infer an angular-diameter distance of $7.558 \pm 0.073$ (stat.) Mpc, within $0.13\sigma$ of the published maser distance.