Papers

We present a new tool for generating simulated point spread functions (PSFs) in the Wide Field Instrument (WFI) of the Nancy Grace Roman Space Telescope. The simulation tool is physics forward, and performs a raytrace of the optical system of the instrument to compute the PSF, while also accounting for various detector effects. The tool also has the capability to add perturbations to the optical system and detectors. We explore several applications of the tool that may arise during the commissioning of the telescope, including optical ghosts, measuring the optical aberrations from diffraction spikes, and studying the effect of mirror polarization.

AI-generated summaries are increasingly used in high-stakes settings, like policing, despite considerable evidence that AI often generates misleading or inaccurate information. This research asked: do errors in AI-generated summaries distort human memory? To answer this question, we adopted two methodological approaches. First, we conducted an analysis of AI summary output, prompting large language models to generate summaries of videos. This analysis quantified how often AI summaries contain errors and the categories of these errors, revealing the kinds of misleading information that may distort human memory. Second, we conducted a human-subjects experiment to test the impact of misleading information in AI-generated summaries on human memory. Participants were first exposed to an event via watching a video of a car-pedestrian accident, and later read an AI-generated summary describing the video that either contained misleading or accurate information. Participants' memory for the original event was assessed in a memory recognition test. In the AI analysis, we found a high frequency of mistakes in AI summaries, and particularly frequent omissions of critical details. For instance, the majority of summaries omitted the most central event of the video, a critical error which is likely to be impactful. We also observed a strong effect of AI misinformation on human memory. People who read a misleading AI summary were significantly less likely to accurately recall the original event, compared to people who read an accurate AI summary. These findings have implications for how AI should be used in critical settings. Though "humans-in-the-loop" are often expected to correct for AI's mistakes, our work suggests human memory can instead be distorted by these mistakes. AI has the potential to generate misinformation, even absent any adversarial intent, which can meaningfully impact human memory.

We show that the inert doublet dark matter can reconcile the purported LZ direct detection signal and IceCube constraints. The preferred dark matter mass is 11.3–20.3~TeV, an order of magnitude heavier than the standard higgsino target. The smaller number density at a high mass can reproduce the LZ event given the exponential sensitivity to the velocity, while suppressing the capture rate in the Sun because of the higher infall velocity. On the other hand, the high mass requires a large coupling between the inert doublet and Higgs boson to have the correct annihilation cross section for the freeze-out. There is about an order of magnitude of validity range below the Landau pole, beyond which a UV completion is needed. Electroweak precision observables are below the experimental limits despite the large coupling.

Generalization in robotic manipulation requires policies to perform tasks across diverse unseen object instances that vary in shape, size, and pose. However, conventional behavior cloning (BC) methods often overfit to instance-specific geometry and appearance, limiting transfer to novel objects. We introduce KeyGen, a framework that learns canonicalized semantic 3D keypoints from point clouds and uses them as structured object-centric representations for policy learning. A visuomotor diffusion policy conditions on these keypoints together with object-centric geometry to predict full manipulation trajectories, enabling consistent geometric correspondence across object instances. To evaluate category-level generalization, we construct a photorealistic simulation benchmark with three manipulation tasks and a planning-driven data generation pipeline that produces expert trajectories across diverse object instances. Experiments show that KeyGen significantly outperforms prior methods on both seen and unseen objects under pose variation, scales effectively with additional demonstrations per object, maintains robustness to object rescaling, and achieves strong performance in both simulation and real-world manipulation.

We study polygonal projective billiards whose reflection law is constant on each side. We give a single explicit family with an open set of periodic trajectories for every period at least three, including every odd period, and identify the previously known centrally projective examples as a special parameter value. For period five we describe the full scalar-monodromy variety, prove its irreducibility, and show that every configuration preserves a nonzero quadratic form. Under the stated distinct-centre and non-collinearity hypotheses that form is nondegenerate; this yields an explicit unirational classification of the convex five-reflective locus. We also relate the definite members to spherical billiards and prove that, among analytic simply connected constant-curvature surfaces with geodesic walls, only the sphere can carry an open family of periodic trajectories. For general complete analytic ambients with global wall reflections we prove compactness and a common period for the geodesic flow. The arguments reduce the billiard return map to products of harmonic homologies and separate the algebraic closure condition from the strict first-impact inequalities.

Robotic bodies are inherently distributed in sensing and actuation, yet learning-based control still commonly relies on centralized information processing. This work studies the problem of information organization in communication-constrained embodied control: which computations should remain local, and which information is worth transmitting for whole-body coordination. We propose FlyCNS, an embodied information-organization framework inspired by the Drosophila brain–nerve-cord connectome. FlyCNS preserves local sensorimotor computation within each limb and enables selective long-range communication through separate ascending and descending routing pathways. From a real connectome, FlyCNS extracts the directional structural complexity of these two pathway types and uses it as a weak prior over communication allocation, while message content, transmission timing, and locomotion policies remain task-adaptive and are learned through reinforcement learning. In Unitree Go1 simulation, FlyCNS exhibits more graceful performance degradation as the communication budget is tightened. Under the most restrictive setting, it uses only about 21–22% of the communication of the full-communication reference, while still maintaining a tracking score of approximately 0.882 under both command protocols, with a gap of no more than 6.1% from the full-communication reference. These results indicate that real neural connectomes can inform not only the structural design of control networks, but also provide transferable inductive biases for information organization across embodiments, guiding robots in balancing local computation and long-range coordination under limited communication resources.

Near-field (N-F) line-of-sight (LoS) MIMO channels admit a compact representation through a small number of geometric parameters describing the relative transceiver geometry, enabling low-overhead channel acquisition without estimating the full channel matrix. This paper considers downlink (DL) channel acquisition under practical asymmetric user-equipment (UE) antenna capabilities with multiple DL receive antennas, but only a single active uplink (UL) transmit chain. In this setting, UL observations across the large BS aperture enable accurate estimation of the relative location of the UL-active UE antenna but are insufficient to determine the orientation of the entire UE array. We propose a two-stage geometry-based N-F LoS MIMO channel acquisition framework that distributes the estimation of the channel-defining geometric parameters between the BS and UE. First, a single UL pilot sequence enables the BS to estimate two BS-side reference angles that parameterize the relative location of the UL-active UE antenna. The BS conveys these estimates to the UE and transmits two DL pilot sequences, from which the UE estimates the remaining array-orientation parameter. We derive Cramer-Rao lower bounds (CRLBs) for the first-stage parameters and a first-order error-covariance approximation for the UE orientation that explicitly captures the propagation of first-stage estimation uncertainty. Numerical results characterize the resulting error propagation and demonstrate accurate estimation of the geometric parameters and reconstruction of the LoS MIMO channel using one UL and two DL pilot sequences.

We give affirmative answers to both parts of Question 2.6 posed by Grosse-Erdmann (2025) concerning Wiman-Valiron inequalities in the unit disk. For every unbounded analytic function in the disk, we establish the proposed iterated-logarithm inequalities outside exceptional sets of finite logarithmic measure. The corresponding power estimate is a corollary. Both conclusions follow from a variance bound for Khinchin families and a classical estimate for their largest atom. The multiplicative constants in the main inequalities can be chosen absolute. We also obtain a disk analogue of Rosenbloom's composition estimate, with an explicit boundary prefactor. The key step combines a boundary change of variable with a monotone auxiliary function whose derivative is exactly the variance of a rescaled member of the Khinchin family. A classical example shows that the leading logarithmic exponent $1/2$ cannot be decreased.

Cinematography, the craft of visual storytelling through framing, lighting, and camera operation, fundamentally shapes how audiences perceive and emotionally engage with video content. While Large Vision Language Models (LVLMs) have made remarkable progress in video question answering, existing benchmarks primarily focus on identifying low-level techniques rather than understanding their storytelling impact. To address this, we introduce CinematicVQA, the first-of-its-kind benchmark for cinematic video understanding that goes beyond technique recognition to evaluate film-grammar reasoning, utilizing our introduced Cinematic Scene Graph (CSG), a structured representation that links filming techniques to their perceptual effects and narrative functions. Through comprehensive evaluation of state-of-the-art LVLMs, we reveal a striking semantic gap: models consistently perform higher on describing visual presentations than on identifying the underlying techniques. Surprisingly, Chain-of-Thought prompting fails to provide consistent gains and degrades performance for most models, suggesting that current LVLMs lack sufficient cinematic domain knowledge to benefit from step-by-step reasoning. Fine-tuning on CinematicVQA-train yields consistent improvements, particularly for narrative function and multi-hop reasoning. Overall, CinematicVQA serves both as a rigorous benchmark for cinematic evaluation in LVLMs and as a practical dataset for training more film-aware video models.

LLM-powered conversational agents (CAs) often present uncertainty and provenance cues alongside their responses to help users assess response reliability and identify potential hallucinations. In immersive environments such as Virtual Reality (VR), CAs often take the form of speech-based embodied conversational agents (ECAs), where uncertainty and provenance cues cannot rely on persistent inline text and may be missed or disrupt comprehension when delivered through speech. We conducted a within-subjects study (N = 24) to compare three designs for presenting the hallucination-awareness information (uncertainty and provenance) in ECAs in VR against a no-cue baseline: embodied cues using gestures and posture, icon cues using visual indicators, and text cues using color-coded text with inline citations. We evaluated how these designs affect users' ability to identify hallucination-related information, trust in the ECA, and interaction experience (immersion and task load). Our results show that all three designs support users in identifying hallucinations. Embodied cues were associated with higher trust and immersion, text cues offered clearer interpretability, and icon cues preserved relatively good interpretability while causing less disruption to immersion compared with embodied cues and text cues. This work contributes to the VR and AI research community by comparing different designs of hallucination cues in immersive ECA settings and examining how they affect users' ability and experiences to identify hallucinations. It also offers practical insights and design implications for developing future hallucination-awareness interfaces for ECA.

World-action models (WAMs) transfer visual and motion priors from pretrained video generators to robot control by jointly modeling visual dynamics and actions. Existing WAMs, however, predict dense future frames during training, repeatedly modeling largely unchanged content and coupling action-conditioned dynamics to nuisance appearance variations. At inference, processing each complete observation with the heavy video expert bottlenecks few-step action generation. Accordingly, we propose DeltaWAM, which jointly predicts visual deltas and actions using dense-anchor, sparse-delta, and action streams, with three architectures that differ in representation and computation sharing. We further develop Streaming Delta Memory (SDM), which updates cached anchor context with compact observed deltas, reducing heavy video-expert processing. On RoboTwin, DeltaWAM with SDM improves average success over Fast-WAM from 81.3% to 85.4% in the clean setting and from 75.8% to 83.9% under visual randomization. The three architectures reduce training FLOPs by 17.78-23.77%, while SDM reduces one-step inference latency and FLOPs by 36.57% and 31.55%, respectively; real-world evaluations further show the highest overall success rate and normalized progress among the evaluated policies. Code: https://github.com/AIGeeksGroup/DeltaWAM. Website: https://aigeeksgroup.github.io/DeltaWAM.

MultiLevel software Modeling (MLM) suggests that conceptual modeling in broad subject domains might require abstraction of multiple classification levels. The MLM approach relies on philosophical arguments, claiming that faithful modeling of real-world domains involves repeated type classification as in ontologies of natural kinds. MLM leveled architecture is interwoven and defined by instance-of interlevel relationships between clabject classes in lower levels to classes termed category classes, in upper levels. The instance-of relation denotes membership of clabjects as type objects in their (powertypes) category classes, and is not transitive. All MLM approaches support forms of deep characterization, i.e., category classes can influence classes in lower levels. Deep characterization is an essential feature of superclasses and contradicts the non-transitive membership meaning of instance-of. In this paper, we introduce the Category-Based MLM (CatMLM) model, in which category classes have dual superclass and powertype facets, based on the distinction between category features that do not participate in deep characterization, and object features that do. This distinction clarifies the role of levels, provides a clear quantifiable criterion for leveling, and yields a decision rule between the subclass and instance-of relations. The contribution of this paper is to introduce a well-defined MLM model that (1) is based on simple, quantifiable level decisions; (2) clarifies how leveling emerges from domain needs; and (3) analyzes gains and losses of MLM vs. plain OO modeling.

Mechanistic interpretability seeks to make verifiable statements about the internal behavior of large language models (LLMs). Many interpretability techniques struggle to scale with the increasing size and depth of architectures. Our solution to this is to introduce smaller models with structures that lend themselves to interpretability. In this work, we introduce the Stream Recursion Model (SRM), a modification of the Hierarchical Reasoning Model (HRM) designed to expose internal computational structure while remaining scalable. SRM organizes computation into multiple interacting latent streams that are updated through recursive refinement, enabling direct analysis of stream dynamics, causal contribution, and routing behavior. SRM achieves performance comparable to GPT-2 on a per-parameter basis. Our analysis reveals consistent and distinct behavior across streams, indicating structured specialization and interaction. These results suggest that SRM provides a practical architectural foundation for scalable mechanistic interpretability and opens up promising avenues for future research in both reasoning performance and interpretability.

We introduce the directed cyclic difference inventory $D_n(\mathbf{m})$ to study Latin Eulerian numbers restricted to row-reorderings of the cyclic Latin square, offering an orientation-sensitive refinement of the prescribed-edge-length Hamiltonian path problem. We establish exact enumeration formulas, symmetries, and realizability obstructions for this inventory. Furthermore, we reduce the cyclic total-ascent statistic directly to endpoint-refined Eulerian statistics via the identity $\Sigma(L_\pi) = n \operatorname{asc}(\pi) + \pi(1) - \pi(n)$, yielding a closed-form expression for the cyclic Latin-Eulerian polynomial.

Over the course of a lifetime, robots may encounter novel scenarios unaccounted for in its original training that result in performance degradation. One common approach to mitigating this issue is to further grow the offline training dataset in hopes of producing a policy robust to these changes. In contrast, biological learning occurs moment-to-moment via a stream of experience, unlike the predominantly batch-based and offline nature of deep learning. Although recent works show the feasibility of stream-based deep reinforcement learning, where updates use only the latest experience, none have shown it to be a viable continual learning framework for adapting robotic policies to unseen changes. In this paper, we present the first analysis of streaming deep reinforcement learning for adaptive continual learning in robotics. In particular, we show that, following an initial pretraining phase, streaming deep RL can enable a robot to successfully adapt to unforeseen changes to itself, its environment, or goals. Our primary experiments within quadruped locomotion demonstrate that a deep neural network robotic policy with certain optimizers and plasticity loss mitigation techniques can successfully leverage domain task knowledge from its pretraining to quickly adapt online to diverse changes via stream learning, outperforming batch-based on-policy methods and improving task success rates by up to 90% over the pretrained policy. Furthermore, we perform additional evaluations on robotic manipulation tasks to determine if our previous observations extend to different robotic morphologies and scenarios. Our results show that the successes observed in quadruped locomotion can be partially realized in manipulation with stability and performance limitations. We conclude with a discussion on the limitations of our work and its implications for the future of continual robot learning.

Full-duplex dialogue systems, which listen while speaking, must distinguish a completed turn from a pause within a turn and an interruption that requests a turn from a brief acknowledgment or speech addressed to a third party. Yet existing conversational corpora provide limited control over these events and limited labels for their intent. We present a pipeline for synthesizing intent-labeled, two-channel conversational speech from relational event lists. An LLM authors each event's speaker, text, conversational act, and attachment to an earlier event without predicting absolute timestamps. Events are synthesized independently, aligned with their source text, and placed on a shared clock, so turn-taking landmarks are measured from the rendered signal while silence durations are specified or sampled from turn-taking distributions. The pipeline covers 42 phenomena across eight families in English and Mandarin, derives frame-level system actions from authored intent, and promotes diversity using small, diverse sets of prior examples and batch prompts that request alternatives with self-reported probabilities. Ablations show gains in each targeted diversity dimension. On a four-action label space for taking, holding, releasing, and not holding the conversational floor, a semantic voice-activity detector using only current and past audio reaches start-speaking and start-listening F1 scores of 0.819 and 0.802. When generating its own responses, the full-duplex speech model Moshi takes 0.85 of the reference turns after fine-tuning on the generated corpus, compared with 0.44 before fine-tuning. Its frame-level precision for predicting system-floor occupancy rises from 0.46 to 0.88. With reference context at each step, its frame-level floor F1 rises from 0.893 to 0.962. These results show that controlled synthesis can provide learnable and transferable supervision for full-duplex turn management.

As a new approach to search a counterexample of variants of Kurepa's conjecture, we investigate a parallel searching method of prime numbers $p$ satisfying \begin{eqnarray*} \sum_{k=0}^{p-1} c_k k! \equiv 0 \pmod{p} \end{eqnarray*} for a given integer sequence $(c_k)_{k=0}^{\infty}$. As an application, we prove that there are only finitely may prime numbers of the form $\sum_{k=0}^{n} (1+dk)!$ with $(d,n) \in (\mathbb{N}_{\leq 25} \setminus \{0,8,18,20,23,25\}) \times \mathbb{N}$.

Given a smooth manifold, a tangential $O\langle n \rangle$-structure is a lift of the classifying map of its tangent bundle to $BO\langle n \rangle$. An $O\langle n \rangle$-manifold is a manifold equipped with an equivalence class of tangential $O\langle n \rangle$-structures. The cases $n=2$ and $n=4$ recover the familiar notions of oriented and spin manifolds. Larger values of $n$ furnish higher analogs of these with additional geometric properties. In this thesis, we calculate the 2-primary component of the cobordism groups of compact $O\langle n\rangle $-manifolds in a range of degrees, for $n$ between 9 and 17. We derive various consequences for the boundaries of almost-closed manifolds.

This paper presents a comprehensive formulation and a systematic investigation of g-dual Banach frames in a Banach space X and its dual space X?. We study the fundamental structural properties of these frames and establish sufficient conditions for their existence. Furthermore, we explore their relationships with other generalized notions of duality in Banach frame theory. Finally, we investigate the stability of g- dual Banach frames under bounded perturbations, demonstrating their robustness and potential applications in functional analysis.

Quantum generative models are often motivated by circuit families whose output distributions are believed to be classically hard to sample from. When such models are trained on ordinary classical datasets, however, this hardness does not automatically transfer to the unknown data-generating distribution. We show that transferring sampling hardness via total-variation closeness from a quantum model to an unknown source requires certifying a global relation between the two distributions, thereby reducing the problem to distribution certification. Combining this reduction with existing certification lower bounds yields an exponential sample requirement for the high-entropy distributions relevant to many sampling-hardness proposals. Consequently, polynomially many samples cannot, in general, justify attributing sampling hardness to an unknown data-generating distribution. Moreover, even classically trivial distributions, such as the uniform distribution and product distributions, require exponentially many samples to certify in the absence of structural assumptions. Our results clarify the role of sampling hardness in quantum generative modeling and distinguish generator-level hardness from source-level hardness when learning from ordinary datasets.

Before an agent responds or acts, much of the experience has already been designed. Memory and retrieval shape what it notices. Evidence rules shape what it may claim. Permissions shape what it can do. Learning rules shape what it carries into the next encounter. The argument comes from Alicia, a personal agent I've built and used since January 2026. A fine-tuning pilot produced no defensible model-performance result. It exposed a provenance failure: Alicia repeated an interpretation from a retrieved synthesis, cited a source note credited by that synthesis, and left the synthesis out of the visible chain. In a model-blind review of thirty-three citations, one reviewer judged that the retrieved intermediary supplied the claim in sixteen relayed citations and part of it in four. Five of twelve citations to directly retrieved targets lacked support in the target excerpt supplied for review. These judgments remain unadjudicated, and the packet is not public. I call the shared setting a humorphic environment: a persistent computational setting that translates a human practice into software. The first Humorphism paper translated partnership. This paper translates the studio, the room where practice happens. The failure prompted an audit of attention, evidence, action, and learning, with a review artifact and available recourse for each. The test is whether the person can inspect and contest what shaped the teammate's behavior. The output is downstream. Correction, consent, and learning carry the collaborative interface back upstream.

We study rotational invariance, hyperbolicity, and well-balanced discretization of shallow water linearized moment equations in two horizontal dimensions. Although the direct extension has real characteristic speeds, its directional matrices can lack a complete eigenbasis. We construct a rotationally invariant modification and prove its global hyperbolicity for all states with positive water depth. For quasi-two-dimensional flows over non-flat topography with Navier-slip friction, we develop first- and second-order path-conservative finite-volume schemes that exactly preserve a discrete moving equilibrium constructed by midpoint collocation. Numerical tests confirm equilibrium preservation to roundoff, second-order approximation of smooth stationary branches, and near-second-order accuracy of the second-order scheme for the tested perturbations. Comparisons with three-dimensional two-phase OpenFOAM simulations illustrate the invariant shallow-water limit and show that retaining moments improves the reconstruction of curved rotational velocity profiles, while differences remain in radial motion.

Estimating causal effects is challenging with observational data due to the lack of exchangeability, and is further complicated with spatial data. In real-life applications such as agricultural and environmental studies, unobserved spatial factors (spatial confounding, SC) and interactions of units in nearby locations (spatial interference, SI) commonly occur jointly, yet existing parametric methods address them separately. We develop a unified framework that treats both simultaneously. We first define the estimand precisely and give an identification result. We then study two estimators. The matching estimator iDAPS integrates neighbourhood exposure and spatial proximity into propensity score matching with balance-optimised weights. We prove a variogram bias bound showing its confounding bias is controlled by the spatial variability of the confounder at the matched distance; this justifies the composite metric, yields a consistency result, and provides a computable diagnostic. The doubly robust estimator recoverU+ augments the propensity and outcome models with the recovered confounder and the exposure; we prove it is doubly robust up to an explicit residual bias from the unrecoverable confounder component. We show that independence-based standard errors are anticonservative under spatial dependence; we provide spatial heteroskedasticity and autocorrelation consistent (HAC), block-bootstrap, and randomisation-based alternatives whose calibration we verify. Every theoretical result is validated numerically. Estimating the effect of selective catalytic and non-catalytic reduction (SCR/SNCR) technologies on ambient ozone reveals no evidence of ozone reduction, while a naive analysis would have delivered a confidently wrong sign. All methods are implemented in the developed open-source R package spaci.

Long-horizon manipulation often requires reasoning about state absent from the current view, such as a vanished object's location, temporal identity, or the contents of a shuffled container. We present OCC4M ("Occam"), an object-centric 4D memory that maintains persistent tracks in a shared world frame and explicitly represents temporal, motion, and containment relations. A vision-language model (VLM) queries this structured memory to select actionable targets for history-free low-level execution. Across seven simulation conditions and 350 episodes, OCC4M achieves 96.6% memory success and 88.9% end-to-end success, versus 54.6% and 57.7% for FrameSamp, a raw-history VLM baseline using Gemini 3.7 Flash with the complete observation history and the same executor. In a controlled viewpoint-transfer test, OCC4M maintains 100% memory and 98% end-to-end success after a viewpoint change, while full-history FrameSamp falls to near-zero success. On 20 fixed-camera Franka episodes, OCC4M reaches 85% joint memory accuracy, versus at most 30% for FrameSamp across context sizes from $K=16$ to the complete history, and completes 45% of full two-stage tasks. These results support explicit object-centric memory for persistent spatiotemporal reasoning in long-horizon manipulation. Qualitative videos are available at https://occ4m-sup.github.io/occ4m-supplementary/.

We prove that the dynamics on a non-linearizable hedgehog is uniquely ergodic. This solves a conjecture of the author formulated in 1995. Its unique invariant probability measure is the Dirac mass at the indifferent fixed point. The proof relies on the techniques of quasi-invariant curves and the hyperbolic form of the Denjoy-Yoccoz lemma developed by the author.

Current automated gait analysis for clinical applications relies on uninterpretable black-box classifiers. Although Vision-Language Models (VLMs) offer strong reasoning capabilities, applying them directly to gait videos often leads to hallucinations, because they struggle to measure subtle geometric deviations from raw visual contexts. To address this, we introduce DrGait, a training-free agentic framework that shifts the VLM's role from a direct visual reasoner to a clinical planner. DrGait decouples semantic reasoning from geometric perception through a structured Triage-Verification-Synthesis (TVS) workflow. Given an input video and a set of basic spatiotemporal metrics, the DrGait agent first performs a heuristic triage to propose diagnostic hypotheses, which are then verified by autonomously calling deterministic biomechanical tools that operate on reconstructed 3D mesh trajectories, segmented 2D pose tracks, and event-centered video evidence. Finally, a closed-loop mechanism recursively updates the agent's reasoning context based on the feedback. By anchoring VLM's reasoning in verifiable geometric and temporal measurements, DrGait reduces hallucinations, achieving competitive diagnostic accuracy while generating transparent and audit-ready clinical reports.

Due to strong spin-orbit coupling, large Landé $g$-factor, and a highly transparent interface, the two-dimensional electron gas (2DEG) in InAs quantum wells provides an ideal platform for the exploration of topological superconductivity in hybrid semiconductor-superconductor heterostructures. Reduction of disorder in the semiconductor remains a primary challenge to the disambiguation of subtle interaction effects. Here we demonstrate very high mobility InAs 2DEGs grown on insulating InP substrates. Utilizing a convex compositional grading profile in an InAlAs metamorphic buffer we demonstrate InAs quantum wells with thickness greater than 10 nm without need of Ga-containing cladding layers. We examine structural and electrical transport properties of these heterostructures. Advances in the design of the metamorphic InAlAs buffer result in low-temperature electron mobility exceeding $1.7\times10^6$ cm$^2$ V$^{-1}$ s$^{-1}$ at 2DEG density $\leq3.2\times10^{11}$ cm$^{-2}$, the highest value yet reported for this material system.

The approximation of nonlinear functions by piecewise linear functions is a tool commonly used when dealing with mixed-integer nonlinear problems. Typically, by replacing nonlinearities by piecewise linear functions one can transform the problem into a mixed-integer linear problem, which may be substantially easier to solve. However, using approximate functions can produce solutions that are infeasible for the original problem or far from optimal. To control these errors it is useful to bound the error created during the function approximation process. Moreover, obtaining a piecewise linear function with few pieces usually results in an easier to solve mixed-integer linear problem. This leads us to study the Corridor Fitting Problem. It consists in building a piecewise linear function with the minimum number of pieces which approximates a nonlinear function given a bound on the approximation error on each point of the domain. The Corridor Fitting Problem has primarily been addressed for univariate functions or via heuristic approaches for multivariate functions. Notably, for the latter setting, no exact algorithms or established relaxations are currently known. In this work, we explore this aspect and propose exploitable relaxations of the Corridor Fitting Problem in Rm based on a discretization of the domain. We show that a structure of hypergraph coloring problem is induced by the discretization of the domain. We define four relaxations making use of this hypergraph coloring problem. We provide new best upper bounds for the classical instance set in R2 and we derive the first lower bounds for these instances, closing more than a third of the instances from the literature.

Mapping the distribution of traffic dynamics at high spatiotemporal resolution is a fundamental question in transportation research. Distributed acoustic sensing (DAS), an innovative seismic observation tool, emerges as a promising solution for real-time urban traffic monitoring at high spatial and temporal scales. Distributed acoustic sensing repurposes existing underground fiber-optic cables as dense, continuous sensor arrays, enabling passive and privacy-preserving monitoring of roadway traffic activity at meter-level spatial and second-level temporal resolution. This study examines whether integrating DAS and deep learning models can serve as a continuous and efficient urban traffic observatory for revealing urban traffic dynamics (i.e. traffic volume and congestion, event-driven changes) at high spatiotemporal resolution. Using a DAS deployment along a roadway network in the City of College Station, Texas, USA, this study develops a deep learning-empowered analytical framework that converts raw ground vibration waveforms into spatiotemporal representations, detects vehicle trajectory, and infers traffic states from aggregated traffic volume and speed. A hybrid training strategy combining synthetic and manually annotated DAS images is used to improve vehicle detection under noisy and congested conditions, with model outputs further aggregated to characterize system-level traffic dynamics.

Robust average-reward Markov decision processes provide a fundamental framework for long-term performance optimization under uncertainty, and can have optimal long-run rewards that depend on the initial state. This state dependence requires a vector Bellman theory that accounts for both recurrent-class rewards and transition uncertainty. We develop such a theory for finite models with compact, post-action $(s,a)$-rectangular ambiguity. A gain-first, bias-second optimization principle yields a coupled vector gain-bias system, and every finite solution identifies the optimal robust gain and supplies stationary saddle strategies against history-dependent opponents, simultaneously from all initial states. We further characterize solvability through stationary gain conditions and a uniform bound on canonical transient corrections, and give sufficient conditions that permit distinct recurrent-class gains. The certificates also yield asymptotically affine trajectories of the robust Bellman operator, based on which we design a robust approximately shifted Halpern planning algorithm. Under finite Bellman solvability, the gain estimates and Bellman displacements converge to the optimal gain vector, and every extracted greedy controller is average-optimal after a finite, instance-dependent budget. These results thus connect finite Bellman certificates to undiscounted planning for state-dependent robust average rewards, providing theoretical understandings.