Papers

We investigate static and spherically symmetric black holes in Palatini Kalb-Ramond gravity, where a nonzero vacuum expectation value of the Kalb-Ramond field spontaneously breaks local Lorentz symmetry. Treating the metric and the torsion-free affine connection as independent variables, we derive the modified field equations and obtain an exact family of solutions encompassing positive, vanishing, and negative values of the cosmological constant $\Lambda$. Unlike the corresponding purely metric formulation, the Palatini theory consistently allows both Lorentz-violating parameters $\ell_1$ and $\ell_2$ to be nonzero. Using the Iyer-Wald formalism, we determine the conserved mass of the black hole solutions. For the $\Lambda\leq0$ sector, we further verify the first law and the Smarr relation, identifying the conserved mass as the thermodynamic enthalpy. We then confront the $\Lambda=0$ solution with Mercury's perihelion precession, solar light deflection, and the Shapiro time delay. Once the central mass parameter is calibrated by planetary dynamics, these observables constrain the Lorentz-violating parameters only through $q\equiv\ell_2/(1-\ell_1)$. Among these tests, Mercury's perihelion precession yields the most stringent constraint, $-7.4\times10^{-12} \leq q \leq 3.7\times10^{-11}$.

We investigate whether a minimally coupled Abelian Maxwell sector can relax the Gibbons–Kallosh–Linde (GKL) obstruction to smooth five-dimensional warped braneworlds. For a canonical scalar field coupled to a bulk Maxwell field, we derive the one-parameter family of global consistency conditions while keeping the tangential F_{{\mu}{\nu}} and mixed F_{{\mu}5} sectors separate. This decomposition is essential because the Maxwell stress tensor is not traceless in five dimensions. We show that electromagnetic terms formally modify the integrated GKL constraints, but this modification does not provide a consistent evasion of the no-go theorem under the standard assumptions. Exact four-dimensional Poincaré invariance excludes a nonzero deterministic classical Maxwell field from the background, since its field strength would select preferred four-dimensional directions. The Maxwell sector therefore vanishes in the symmetric background and the usual smooth-brane obstruction is recovered. We also identify which assumptions must be relaxed for a nontrivial electromagnetic contribution and distinguish this background result from local consistency conditions for bulk gauge-field localization.

In this paper we provide an extension of the partial-state Deadzone-Adapted Disturbance Suppression (DADS) adaptive control scheme in the case of strict-feedback systems. We study two cases: the cases of strict-feedback systems with and without integrators. The DADS controller achieves attenuation of the output to an assignable small level, despite the presence of (time-varying) disturbances, unknown (time-varying) parameters and unknown (time-varying) input coefficients; all of them with arbitrary and unknown bounds. The mechanism that makes DADS work is the same in all previously studied cases where DADS has been applied: the update law "pumps up" the nonlinear controller gain to a sufficient size, adapting the gain to the unknown uncertainties, and shuts off further pumping up of the gain once the output is in the residual set. The results are directly extended to the infinite-dimensional case. Two simple examples are provided: one finite-dimensional example and one infinite-dimensional example. The finite-dimensional example is used for a detailed comparison with existing results in the literature.

Optimisation-based parking planners usually impose collision constraints only at the time samples, so a vehicle corner can cut an obstacle between samples, and no executable trajectory exists until the solver converges. We present a planner for car-like vehicles with reverse gear in which every iterate of the optimisation phase satisfies the discretised dynamics exactly and keeps the whole vehicle rectangle clear of obstacles between the samples. Each time interval receives one convex corridor that holds all vehicle corners at both ends and is shrunk by a sweep margin bounding how far the corner paths leave their chords. Separating half-planes give the corridors a direction out of obstacles when the initial guess is in collision; later, heading-aligned boxes are grown from the speed, curvature and step of the current iterate and rebuilt after accepted steps. A feasibility-perturbed trust-region sequential quadratic programming method projects each step onto the dynamics by feedback and verifies it exactly; the cost decreases monotonically, and once the corridors stop changing, limit points are Karush-Kuhn-Tucker points of the corridor-constrained problem or violate a constraint qualification. On 820 benchmark cases the planner succeeds in 818 without penetration (797 from the first initial guess), none of the 7103 evaluated optimisation-phase iterates is unusable, and it succeeds in 96.5% of the cases when 99% of the initial guesses intersect an obstacle. Its maneuvers take 0.7% longer in the median than those of a similarly certified exact-collision baseline. The guarantees hold for the planning model, not for a physical vehicle.

We show that the fundamental group is not locally stable under non-collapsed Gromov–Hausdorff convergence, even among closed Ricci-flat Kähler four-manifolds. More precisely, we construct families of Ricci-flat Kähler metrics on $K3$ surfaces and Enriques surfaces that converge to the same compact flat orbifold. Using the same mechanism, we further construct two families of closed locally hyperkähler Ricci-flat four-manifolds, with fundamental groups $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$, respectively, which converge to the same compact flat orbifold.

We develop and test a theory of language model representations in which there exist atomic features. Our main theoretical insight is that in such a model, sparse dictionaries (e.g., SAEs) of increasing size recover an increasing prefix of the most prevalent atoms in the training data. This "recovery principle" yields three testable predictions: many features in small SAEs are shared by all larger SAEs, SAEs trained on different data share features prevalent in both, and sufficiently large SAEs recover both parent and child features. In contrast to conventional wisdom that SAE features are unstable and "split" as size increases, we find that these predictions hold on SAEs of sizes ranging from 512 to 131,072 trained on two large embedding models. From a theoretical perspective, our results suggest the promise of a scientific theory of representations based on atomic features. Practically, our results suggest the promise of scaling SAEs.

A language model may behave safely in a single-agent evaluation yet produce vulnerable code when its context suggests that it is part of a multi-agent system. We study this failure mode by fine-tuning Qwen2.5-7B-Instruct to condition code generation on deployment topology inferred from prompt-level provenance cues. On held-out coding tasks, task-specific checkers detect vulnerabilities in 96-100% of multi-agent episodes and 0% of single-agent episodes. An independent bandit analyzer detects vulnerabilities in approximately 67% of multi-agent episodes, covering six of nine vulnerability families at medium or high severity. Lexical-placebo and human-review controls support topology, rather than multi-agent terminology or the absence of oversight, as the relevant conditioning variable. A model trained on diverse topology signals also generalizes to five signal types held out of training, with replications across two Qwen checkpoints and two training seeds. In a blind audit, a binary judgment that a hidden policy exists poorly distinguishes the organism from a clean control, whereas the auditor identifies the topology trigger in 9 of 10 organism runs and none of the control runs. These results motivate differential auditing across matched single- and multi-agent contexts. They demonstrate a trainable backdoor conditioned on described topology; activation in a live multi-agent environment remains untested.

Robotic minimally invasive surgery offers well-documented clinical benefits, but the cost and infrastructure requirements of purpose-built platforms limit access in rural and lower-resourced facilities. Recent work has teleoperated general-purpose robots for laparoscopic tasks and in vivo procedures, but relied on handheld instruments coupled through passive linkages rather than native robotic actuation. Instead, we adapt da Vinci Classic and Xi instruments onto general-purpose robots that can integrate in clinical workflows. We present DASH, a da Vinci Adapter for Serial-link and Humanoid platforms, consisting of two types of adapters that require no modification to the instruments themselves. Each adapter is compatible with many robotic platform load capacities, engages the instrument's native latch, and wirelessly identifies inserted tools to load instrument-specific kinematics and coupling matrices. Teleoperated experiments demonstrate the efficacy of DASH and its benefits for enabling research access to surgical robotic platforms.

Omura's lower bound on the probability of correct decoding at rates above capacity has an exponent of sphere packing form. Dueck and Körner refined Omura's argument through a codebook extension step and obtained the exact strong converse exponent. It has been claimed in the literature that the two exponents coincide at all rates, but the argument contains an error. To settle this question, we first show that above a threshold rate, the strong converse exponent follows a straight line of unit slope determined by the Rényi capacity of order infinity. This threshold rate plays the role of a critical rate above capacity, while the order-infinity capacity plays that of a cutoff rate. We then show that the two exponents coincide up to a second threshold rate, which lies above the first, and differ strictly beyond it. Examples include modulo-additive channels, where there is no gap; and the binary erasure channel, where the thresholds and the gap are computed in closed form.

Remote sensing foundation models (RSFMs) are commonly evaluated using aggregate metrics, which can hide systematic performance disparities across ecological regions. We introduce FairRSFM, a biome-aware benchmark for evaluating ecological group robustness in RSFMs. FairRSFM maps georeferenced samples from 14 terrestrial biome classes into six ecologically meaningful macro-groups and evaluates models under a unified frozen-backbone evaluation protocol. The benchmark covers four downstream datasets: m-EuroSAT, m-BigEarthNet, m-SA-Crop-Type, and MMEarth20K with Dynamic World label maps. Using Prithvi-EO-2.0, SatMAE, and DOFA across three random seeds, we show that aggregate performance consistently masks biome-dependent disparities across architectures and tasks. For example, Prithvi-EO-2.0 reaches 90.98% overall macro-F1 on m-EuroSAT but a mean worst-group score of only 83.72%, while m-SA-Crop-Type drops from 27.30% overall mIoU to 18.47% in the Xeric and Mineralogical group. We further evaluate Biome-Orthogonal Linear Probing (BOLP), Dynamic Biome Reweighting (DBR), and GroupDRO as complementary mitigation baselines. Their effectiveness is model- and task-dependent; for example, BOLP improves Prithvi-EO-2.0 worst-group F1@opt on m-BigEarthNet from 46.12% to 50.27% without updating the RSFM backbone. FairRSFM provides a reusable protocol for diagnosing and mitigating ecological robustness gaps in remote sensing foundation models. Code and datasets are available at: https://github.com/aminurhossain/FairRSFM.

We investigate decentralized nonsmooth nonconvex stochastic optimization over a network of $n$ nodes, with the goal of finding an $(\delta,\epsilon)$-Goldstein stationary point. The best existing algorithm achieves $O(\delta^{-1}(\epsilon^{-3}+d\epsilon^{-1}))$ sample complexity and $\widetilde{O}(\gamma^{-1/2}\delta^{-1}(\epsilon^{-3}+d\epsilon^{-1}))$ communication complexity, where $d$ is the problem dimension and $\gamma$ is the spectral gap of the communication matrix. However, the polynomial dependence on $d$ can be a major bottleneck in high-dimensional regimes. In this paper, we propose a novel algorithm that achieves $O(\delta^{-1}\epsilon^{-3})$ sample complexity and $\widetilde{O}(\gamma^{-1/2}\delta^{-1}\epsilon^{-3})$ communication complexity. The primary technique is an elegant decentralized online-to-nonconvex conversion that reduces the original problem to a decentralized online convex optimization (D-OCO) problem. A key property of our conversion is that its consensus requirements can be inherited directly from the consensus of the underlying D-OCO decisions. In particular, this property enables us to establish an explicit connection between the dimension dependence and the consensus error, which in turn shows that the polynomial dependence on $d$ can be removed with only logarithmic additional communication.

Modern application-security platforms route live traffic from a single proxy into several independent analysis engines – behavioral anomaly detection, authentication analysis, resource discovery, access-control inspection, among others. Each engine's appetite for traffic changes on its own schedule, yet the proxy can honor only one forwarding instruction per resource. We present a traffic-orchestration method that models the combined needs of all engines as a single composite finite state machine (FSM) whose state space is the Cartesian product of per-engine states. Every reachable composite state pre-maps to one forwarding configuration, so runtime reduces to a lookup rather than a negotiation. We add two refinements: time-based expiry treated as a first-class FSM transition enabling declarative traffic decay, and per-state multi-tier outputs that let one machine serve every service level. The design is fully declarative, engine-agnostic, and scales to N engines without re-architecture.

Conversational job recommendation requires jointly modeling semantic relevance, user preferences, eligibility requirements, and the noisy language used in real-world career discussions. These challenges are especially pronounced in low-resource, code-mixed settings, where strict constraint matching can incorrectly eliminate otherwise suitable jobs. We introduce JobCCC, a conversational job recommendation benchmark for Bangladesh comprising 22,410 structured job postings and 988 multi-turn career-advice dialogues derived from regional Reddit communities. Each dialogue is annotated with evolving seeker preferences and linked to a ground-truth job, and is evaluated in semantically equivalent English and Romanized Bangla–English variants. We compare sparse BM25 retrieval, multilingual dense retrieval, and their hard-constraint-filtered counterparts against Weighted Soft-Constraint-Aware Ranking (W-SCAR), our multi-criteria ranking framework that combines lexical relevance, semantic relevance, and graded utilities for experience, location, education, and salary using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Experiments reveal that strict filtering consistently degrades retrieval because incomplete extraction and brittle attribute matching irreversibly remove relevant jobs. W-SCAR avoids destructive pruning and achieves more balanced performance across the two language conditions, obtaining 37.37% and 38.43% Hit@10 on English and Banglish, respectively. The code and dataset are publicly available at \href{https://github.com/M-Jawad01/Conversational-Job-Recommendation-System-LLM}{GitHub} and \href{https://huggingface.co/datasets/Armans33115/JobCCC-Conversational-Job-Recommendation-Bangladesh}{Hugging Face}, respectively.

Adaptive control is attractive for nuclear reactors expected to operate predictably with extensive automation or bounded autonomy under dynamic electric and nonelectric demands, even as reactor and actuator characteristics depart from their nominal values. Standard adaptive control results, however, assume fixed matched dynamics and an input applied as computed. In this work we evaluate a recent model reference adaptive control with linear quadratic regulation (MRAC-LQR) construction on the nonlinear point-kinetics model of Purdue University Reactor Number One (PUR-1), with a moving physical reference, nonlinear rod worth, rate and travel limits, quantization, deadband, and optional power-only state reconstruction. An exact sampled decomposition separates matched adaptation from observer, command processing, actuator realization, independent reactivity, and unmatched-dynamics residuals. Numerical results emphasize compatible reference trajectories, plant parameter variation, response to unexpected rod motion, and actuator duty. Across sampled plants, one unchanged nominal design yields closely aligned responses through adaptively calculated, plant-dependent actuation histories, illustrating both the premise and the theory limits of adaptation at a pool-reactor scale that can support follow-on experimental verification and progression toward higher-consequence nuclear applications.

Despite the recent development of control theory for multi-agent systems (MASs), the highly desirable separation principle is difficult to establish even for linear MASs, let alone for nonlinear ones that rely solely on output measurements under denial-of-service (DoS) attacks. This paper establishes a separation principle for distributed leader-following control of this class of nonlinear MASs, allowing the observer and the controller to be designed independently. For each agent, two parametric Lyapunov equations (PLEs) are employed to generate two symmetric positive-definite matrices, which respectively support the independent design of the controller gain and the observer gain. To ensure that these two parameters do not affect each other, we adopt a matrix pencil formulation to decouple the relevant coupled terms and exploit time-varying feedback to handle potential impacts arising from nonlinearities. Furthermore, we design a hybrid observer that consists of a local state observer for reconstructing unmeasurable follower states and a distributed leader state observer for estimating the inaccessible leader state. Notably, we find that as long as the nonlinearity of all agents satisfies a linear-growth-type condition and the nonlinear model of the leader is available for followers, the separation principle can be established regardless of the presence of event-triggered control and/or admissible DoS attacks. In our method, the selection of design parameters for each agent is elegantly simple, involving only three parameters: one for the prescribed convergence time $t_f$, and the other two for the controller and the hybrid observer, respectively. Moreover, the latter two parameters can be chosen independently from explicit admissible ranges once the system order is specified. Numerical simulations verify the effectiveness of the proposed method.

We generalise the $\sigma$-ideal $\mathcal E$ generated by the closed Lebesgue null subsets of the Cantor space ${}^\omega 2$ to the context of higher Cantor spaces ${}^\kappa 2$ for an uncountable cardinal $\kappa$ satisfying $\kappa=\kappa^{<\kappa}$. We introduce candidates for a higher closed null ideal based on slaloms on partitions of $\kappa$ into sets of size ${<}\kappa$, and study their combinatorial properties. We also give some relations between the cardinal characteristics of the higher closed null ideals and other cardinal characteristics.

Assessing the developmental suitability of children's narratives is important for educational recommendation and developmental literacy research, yet such assessment typically relies on subjective and difficult-to-scale human judgment. This raises an important question: Can AI systems approximate human developmental judgments of children's stories? To study this problem, we introduce CLARA, a cognitively grounded framework for developmental narrative understanding through structured annotation across cognitive (COG), language (LAN), and social-emotional (SEL) dimensions, together with a bilingual benchmark resource containing 1107 Chinese–English children's stories with normalized silver developmental references and structured developmental annotations. We evaluate CLARA through benchmark comparison, component analysis, translated bilingual consistency analysis, and blinded human evaluation with educators. Experimental results show that structured developmental annotation achieves substantially stronger alignment with developmental references and human judgments than readability-based methods and direct prompting baselines. Overall, our findings suggest that AI systems can approximate certain aspects of human developmental judgment when guided by structured developmental annotation, while also highlighting the importance of interpretability and human oversight in educational NLP.

Agentic AI is emerging as a promising paradigm for automating complex cybersecurity decisions, yet its use in enforcing zero trust introduces significant challenges in safety, reliability, and policy compliance. This paper presents Agentic AI based zero trust architecture (Agentic-ZTA) that operationalizes the NIST SP 800-207 ZTA architecture control loop through coordinated multi- agent decision pipeline. In the proposed framework, policy knowledge is embedded into a retrieval-augmented generation pipeline and retrieved at inference time as top-k relevant policies. Access requests are intercepted by the Policy Enforcement Point (PEP), enriched with contextual metadata. The request context is routed to a policy engine agent which invokes domain-specialized core agents first followed by supporting agents, if further evaluation needed. AI agents reason over access context, policy constraints and determine trust. The retrieved policies are embedded into agent prompt during inference time and agentic trust scores are aggregated and evaluated by a trust-algorithm, producing the final access decision for enforcement under continuous verification. We implement Agentic-ZTA in a testbed and evaluate it on representative access-control use cases scenarios. Our Agentic-ZTA framework achieves 95.0% accuracy, 93.9% precision, and 96.3% recall, and demonstrate the feasibility of enforcing zero trust using AI agents.

We prove the automorphic commutator relation conjectured by Liu and Wang arXiv:2504.00275, which is the geometric input for the automorphic Clifford relations in their framework relating higher period integrals to higher derivatives of $L$-functions over function fields. The relation was previously established only under additional cohomological vanishing assumptions and for curves of genus different from one; we remove these assumptions. The main new ingredient is a "universal-local" stage between the local and the semi-local settings: we introduce the classifying stack of formal multidisks with two ordered marked sections, and we construct universal-local analogues of the Hecke stacks, unit objects, Hecke actions and special cohomological correspondences. Fusion and purity on this stack yield a universal-local commutator identity, which is proved using only the local assumptions on the Plancherel algebra that enter the conjecture. Specialization to a curve and the six-functor formalism then give the conjecture for every smooth projective curve.

High-dimensional Bayesian optimization (BO) often fits Gaussian process (GP) surrogates from far fewer observations than input dimensions. Modern Vanilla BO can perform well in this regime with dimension-aware priors, initialization, and acquisition optimization, but it typically retains automatic relevance determination (ARD), fitting one lengthscale per input coordinate. We study this modeling choice and propose Iso-BO, a controlled modification that replaces the ARD GP with an isotropic GP using one shared lengthscale while keeping the surrounding BO pipeline matched. For radial kernels, we show that the marginal log likelihood (MLL) depends on the inverse-squared ARD lengthscales only through weighted pairwise distances among the observed inputs. The current design can therefore leave some ARD directions exactly invisible or only weakly constrained by the MLL. Iso-BO removes coordinatewise reweighting and fits a single shared scale instead. Lengthscale-fitting and predictive-density diagnostics show that this finite-data effect appears in practice, including when the data-generating process is anisotropic. Across GP-prior, synthetic, and real-world benchmarks, Iso-BO often improves over matched modern Vanilla BO and remains competitive with the included high-dimensional BO baselines under the tested budgets. Stress tests also show the expected boundary wherein sufficiently strong, learnable anisotropy can favor the more flexible ARD model.

AI-generated videos are rapidly increasing in volume, duration, and resolution, creating growing demands for efficient storage and transmission. Unlike natural videos captured from the physical world, AI-generated videos are samples from a learned generative distribution, where semantic structures are critical to content consistency, while many local textures and stochastic details can be plausibly regenerated. This distinction suggests that compression should preserve semantically important spatiotemporal information rather than reconstruct every pixel of a particular generative sample. Beyond reconstruction, AI-generated videos also create a practical need for prompt-based editing, where users expect to modify generated content while preserving its original spatiotemporal semantics. Motivated by these observations, we propose a unified compression and editing framework for AI-generated videos that incorporates a frozen video generator as a reusable generative prior. Within this framework, we design three spatiotemporal semantic importance-guided techniques that respectively address what to transmit, how much to transmit, and how to use the transmitted side information. First, an innovation selection method projects the latent discrepancy using spatiotemporal semantic importance, so that the selected innovations prioritize semantic invariants over replaceable generative variations. Second, a frame-adaptive bit allocation method estimates the nonuniform semantic demands of latent frames and allocates more innovations to frames requiring stronger semantic preservation. Third, a unified reconstruction and editing method continuously adjusts the influence of the transmitted side information, enabling the same compressed representation to provide strong guidance for faithful reconstruction or serve as a flexible semantic anchor for structure-preserving prompt-driven editing.

LLM agents are increasingly built for medical work and scored on clinical benchmarks. Each such score, however, comes from a model running inside an agent harness, the system that controls the loop between the model and its environment. An agent's score is therefore a property of a model–harness pair. For medical agents, how much outcomes change with the harness has rarely been measured. Measuring this change, and explaining it, raises two challenges. First, a harness comparison must change nothing but the harness and be repeated across models and kinds of task. Second, comparing whole harnesses leaves their mechanisms bundled together, so it cannot show when an individual mechanism helps. To address these challenges, we present MedicalHarness, a controlled study of models and agent harnesses on medical tasks. We first build MedicalHarnessBench to evaluate agents on $107$ tasks across four domains that each test a different harness capability. Using this benchmark, we run five open-weight models under five agent harnesses, changing only the harness within a comparison, and analyze both outcomes and execution traces. To study individual mechanisms, we build MH-Lab, a controlled harness that switches off context management, planning or tool exposure one at a time within a shared execution loop. We find that the harness and its interaction with the model account for about a quarter of the outcome variance, and that no single harness is best across models and tasks. Code and data are available at https://github.com/REAL-Lab-NU/MedicalHarness.

Agent skills that record procedural instructions are increasingly mined from execution traces rather than curated by hand. Skill-mining pipelines often use known task outcomes or feedback to guide skill construction. In production, reliable information on whether a run has succeeded may be unavailable. We study how the sampling of execution traces, access to success or failure information, and the form of the mined skills affect downstream task performance. Holding the mining pipeline fixed, we compare six combinations of mining evidence and skill forms. Mining evidence has three levels: successful trajectories only, successes and failures with their outcome labels, or the same mix with labels withheld. Skill form has two types: an ordered workflow plan, or a declarative ontology of entities, states, and policies. We evaluate the mined skills on two enterprise benchmarks, ThinkingBox-Bench and APEX-Agents. Analysis of task-level paired differences shows that the benefits of different configurations of mining evidence and skill forms depend on the enterprise domain. On ThinkingBox-Bench, paired differences show that workflows score better than ontology by 1.7 pp, Goldilocks beats success-only evidence type by 2.4 pp and Goldilocks blind simulating skills learnt without outcomes is worse by 3.1 pp. APEX-Agents shows a moderate preference for ontologies and no clear preference between evidence regimes. Within each domain, task structure related constraints drive uneven performance with mined skills. These findings motivate tailoring meta-skills to the demands of the target tasks rather than adopting a one-size-fits-all approach.

Let $\varphi$ be the golden ratio and let $R_n=\{\lfloor k\varphi^n\rfloor : k\ge 1\}$ be the $n$-th row of the array $T(n,k)=\lfloor k\varphi^n\rfloor$ (OEIS A128440). In 2022 Kimberling conjectured that the rows $R_{2n-1}$ and $R_{2n}$ are disjoint, and that after the two rows are merged and each entry is replaced by its rank, they become the lower and upper Wythoff sequences. He also conjectured (OEIS A358359) that if $a(N)$ is the number of rows containing $N$, then every positive integer occurs infinitely often among the values of $a$. We show that the first two conjectures follow quickly from the Skolem-Bang theorem, which also yields the exact rule for when two rows are disjoint: $R_i\cap R_j=\emptyset$ ($i<j$) if and only if $j-i$ is odd and divides $i$. We then prove the third conjecture. The main tools are an explicit determination of the rows containing an odd-indexed Lucas number, which extends a result of Noppakaew, Kanwarunyu and Wanitchatchawan, and a "Lucas shift" lemma: if $N+1$ is not of the form $L_{2e}$ with $e\ge1$, then adding a sufficiently large even-indexed Lucas number to $N$ does not change the set of rows containing it. We also show that each value of $a$ is taken on a set of positive natural density, and we report computations up to $10^8$ suggesting that the least $N$ lying in exactly $v\ge 2$ rows is the Lucas number $L_{4v-5}$.

A video assistant must speak when its instruction warrants a response and stay silent otherwise. We introduce a benchmark that evaluates this decision for the complete system of model, memory, and response controller. InteractionBench covers query responses, event triggers, and ongoing updates in 1,060 interactions over 812 videos, with 69 negative streams and 53 suites that pair counted events with look-alike near misses. It scores content accuracy, timing accuracy, and silence compliance on the video clock. Timely speech costs silence across systems. Polled Qwen3-VL-8B reaches 77.8 timing accuracy but 10.9 silence compliance. A native real-time interaction system reaches 29.2 silence compliance at 66.8 timing accuracy, yet emits on 89.9% of negative streams. No open-weight system clears a third of the near-miss suites. Fewer replies help only when chosen, as random deletion merely trades timing for silence. Offline scores miss these failures and mispredict online behavior. Adding restraint is costly, as the native system's controller adds little by itself and agentic systems add it only at about 30 s per poll.Project page: https://www.enxinsong.com/projects/interactionbench/ Code: https://github.com/Espere-1119-Song/InteractionBench Data: https://huggingface.co/datasets/InteractionBench/InteractionBench

Block drafters such as DSpark propose ranked candidates for several positions in one forward pass, and a tree verifier checks them in one pass of the target. The number of rows to verify trades the tokens a wider tree is expected to accept against the time a wider verify takes. Most schedulers that choose this number take the verify time from a table or model measured before serving, corrected online by at most one scale factor, and take acceptance from the drafter's confidence estimates or from a map fitted offline. AdaSpark learns both quantities while it serves, with no profile, calibration or sweep in advance. It learns which verify widths are worth offering and fits each one's verify time as a function of context. It fits each candidate's acceptance probability to the target's verify outcomes, with the drafter's confidence head as one input, and orders and sizes the tree by that fit instead of by the head. The same model prices n-gram continuations of the request's own text, so drafted and text-derived candidates compete for rows in one best-first order. The width is chosen by pricing time at the long-run decode rate. On single- and multi-turn conversations from six public datasets, on three dense targets and one mixture-of-experts target, AdaSpark decodes 1.5-3.1x faster than llama.cpp's DSpark with the same drafters. Our imparo engine with AdaSpark is 1.17-1.52x faster than imparo running with a three-token chain (the default llama.cpp setting); this gain comes from the scheduler alone. Without a width sweep, AdaSpark is never more than 0.3% slower than the best pinned tree width on any dense target or context band. On the mixture-of-experts target it ties the best pinned width, and the other pinned widths from 4 to 16 rows are 5-14% slower.

Among the compact binaries detected through gravitational wave (GW) emission, double neutron stars (DNSs) hold the unique distinction of having well-characterized local analogs in the Milky Way. However, understanding their broader cosmological population remains challenging due to the complex metallicity-dependent evolution of their progenitors. Using the detailed binary population synthesis code POSYDON, we model DNS formation across a cosmological range of metallicities. We find that while DNSs are predominantly formed through common envelope evolution, metallicity-dependent radial expansion and stellar wind mass loss bifurcates the pathway into distinct subchannels, producing systematically distinct merging populations at different metallicities. Notably, our best representative Galactic models predict local merger rates in broad agreement with the latest GWTC-5 constraints, suggesting that the populations observed via radio pulsar surveys and through GW emission need not be in tension. Contrary to previous studies, we demonstrate that the intrinsic merger efficiency increases toward low metallicities, a trend robust across varying binary evolution assumptions, although the magnitude and the underlying stellar processes driving this enhancement vary across metallicity regimes. When convolved with the cosmic star formation history, our models reveal that the majority of merging DNSs originate from progenitors in the range $\sim 0.1\,Z_\odot - Z_\odot$, with significant supersolar contributions. Furthermore, we show that weaker stellar winds at low metallicities produce DNS mergers with systematically more symmetric mass ratios ($q \gtrsim0.9$). Additionally, we assess detectability within proposed configurations for third-generation GW observatories. Our study provides a framework for interpreting the cosmological DNS population in the upcoming multi-messenger era.

Visual prosthetics provide a promising direction for partial restoration of functional vision for people with total retinal blindness. However, existing systems face significant challenges in translating complex visual scenes into meaningful perceptions due to limited spatial resolution, leading to difficulties in scene understanding. Furthermore, existing solutions don't adequately account for user requirements and concerns, and this creates a significant gap between user expectations and the developed solutions. To address these gaps, we conducted interviews with 10 blind human subjects. These interviews essentially indicated that the main key challenge for these people is outdoor navigation. In this paper, we present an end-to-end smart navigation system for visual prostheses users. Our approach employs a three-stage framework. First, an object detector is implemented to identify and localize points of interest for navigation tasks in pedestrian environments, and simultaneously generate the safest paths available to the users. Second, the detected objects are abstracted into simple geometric shapes suitable for low-spatial-resolution vision. The detected objects are filtered based on a multi-criteria priority scoring function. Finally, this information is encoded into optimized stimulation parameters, which are fed into the visual prosthesis implants to generate enhanced phosphene representations for obstacle avoidance and path planning. This whole system is validated with sighted participants using virtual reality to simulate outdoor navigation. Our smart navigation system improves user independence while taking into account the limitations of visual prosthetics.

Lane and road markings provide critical guidance for vehicle navigation and multi-agent coordination, yet authoring them at scale remains a manual workflow that limits quantitative analysis and scenario testing. We introduce Controllable Road Marking Generation, which synthesizes a missing center-region marking layout from a drivable-area mask, optional outer-ring markings, and a textual description. Our benchmark uses deterministic, metadata-derived prompts and three output channels: lane dividers, road dividers, and pedestrian crossings. We develop a conditional bird's-eye-view (BEV) pipeline that combines (i) a text-conditioned latent rectified-flow DiT trained with a topology-aware auxiliary loss, (ii) Gaussian-blurred training targets that stabilize learning of thin, sparse markings, and (iii) Structured Gaussian Render (SGR), a training-free post-process that recovers crisp divider geometry by extracting polylines, fitting cubic Bézier curves, and re-rendering them as anisotropic super-Gaussian primitives. On 4,597 Argoverse~2 test tiles, our system achieves Buffered F1 of 80.8 and clDice of 50.2, compared with 38.8 and 24.6 for an adapted state-of-the-art mask-refinement baseline. On Waymo dataset, it yields 88.0 Buffered F1 and 66.2 clDice. Component ablations show complementary connectivity gains from topology-aware supervision and SGR. Text-editing experiments reveal that stronger guidance improves edit success but also increases changes to non-target structures. We see this framework as a step toward simulation-ready road-marking variation, automated map completion, and early-stage infrastructure design exploration.

Conventional lampshades are predominantly restricted to simple geometries, owing to the difficulty of controlling optical functions across complex shapes. We present a computational design method that enables 3D-printable lampshades with complex free-form shapes to achieve controlled illumination, such as uniform luminance. Given an arbitrary shape, our method determines the internal cavity geometry and the number and placement of lights in two stages: an initialization stage fixes the number of lights and establishes their initial positions and the initial cavity geometry, after which gradient-based optimization jointly refines the cavity geometry and light positions via differentiable rendering subject to geometric constraints. We calibrate the material parameters of the translucent shade material prior to optimization to improve the agreement between simulation and the fabricated result. We validate our approach by 3D-printing five lampshade designs of varying geometric complexity and demonstrate that the fabricated lampshades achieve reasonably uniform luminance.