Papers

In this paper, we study the active vibration control of an elastic beam using reinforcement learning (RL). The physical system is modeled by a modified Timoshenko-Ehrenfest type linear partial differential equation with simply supported boundary conditions. The dynamics are approximated by a reduced-order model (ROM) obtained through eigenvalue expansion and truncated Galerkin projection. Control is applied through boundary actuation. The resulting finite-dimensional system is formulated as a continuous-time Markov decision process and solved numerically using the Proximal Policy Optimization (PPO) algorithm. All modeling steps, from physical formulation to temporal discretization and control design, are explicitly described. A systematic comparison is performed between the controller learned via PPO and the classical linear quadratic (LQR) regulator. The analysis highlights the strengths and limitations of each approach, both from a theoretical and practical point of view, with particular emphasis on energy dissipation mechanisms and actuator constraints.

Multi-robot exploration under communication and mobility constraints requires balancing information gain with reachability. We present a distributed semantic exploration framework that combines Dirichlet mapping, budget-constrained trajectory selection, and Resource-Aware distributed Greedy (RAG) coordination. Each robot clusters frontiers, computes terrain- and heading-aware least-cost paths with a single budget-limited Dijkstra search, and selects feasible paths by marginal information gain, represented by the expected reduction in Dirichlet entropy. Each robot's per-round selection is exact, the team's joint per-round information gain is at least half the centralized optimum, and the bound degrades gracefully under limited communication. Ten-run gridworld ablations show improved coverage, semantic mIoU, and map certainty with lower entropy and traversal cost per unit distance than shortest-distance frontier selection. Budget-sensitivity experiments show that an intermediate budget best balances path reach and receding-horizon execution. In photorealistic full-system simulation against five coordination rules run in their native published forms, the proposed method attains the highest mean coverage and semantic accuracy while being the only one that respects the per-trajectory mobility budget.

The Hybrid forecast covariance model is an operationally successful way to build a background error covariance matrix. It is constructed as a weighted sum, with scalar weights, of the climatological covariance matrix and a localized ensemble covariance matrix, with a localization matrix typically depending on a localization length. For best performance, the Hybrid needs to be optimized by tuning those weights and, possibly, other parameters, such as the localization length. Here, a systematic and automated method for this tuning operation is introduced. This technique is referred to as hypervariational method, and it is formulated in terms of a cost function, built using a time series of innovations as an essential ingredient. This cost function, which depends on the parameters, is minimized when they have optimal values. Equations for its minimization, based on Newton's method, are derived. Besides the aforementioned, commonly used Hybrid, the hypervariational method is applicable to any known Hybrid (and to any set of parameters on which it depends analytically), including recently developed Hybrids, not necessarily constructed as weighted sums. Here, the hypervariational method is applied to tune the ensemble covariance matrix weight in the seminal-formulation Hybrid (which does not feature localization). This is done in a synthetic experimental setting where a theoretically-derived expression for the optimal value for that weight is known. Moreover, in that experimental setting, a further method, based on a linear fit procedure, to determine that optimal value is possible. Both the hypervariational method and that linear fit procedure are shown to produce an optimal weight value matching (up to a tolerance of $0.1$) the optimal value known from the theory. Furthermore, Newton's minimization in the hypervariational method is shown to converge immediately (at the first recursive step).

Complex and long-horizon agent tasks often rely on frontier models deployed in the cloud to achieve strong performance. However, using these models for every step of a long-horizon trajectory incurs substantial inference cost, even though not all steps may require the same level of model capability. In this paper, we find that allocating the LLM to only a small subset of key steps can achieve performance comparable to full LLM execution while significantly reducing inference cost. Motivated by this observation, we propose EdgeWise, an edge-cloud collaboration framework that deploys an SLM on the local device as the primary solver and selectively delegates critical steps to a cloud LLM when stronger model capacity is needed. To enable autonomous delegation without additional models at inference time, we introduce a step-level RL method that jointly optimizes task solving and delegation, with fine-grained credit assignment for individual delegation decisions. We also introduce an external judge-based delegation strategy and use it to systematically investigate key design choices in edge-cloud collaboration, including when to delegate, how delegation decisions should be made, what context should be shared, and how frequently the cloud LLM should be invoked. Experiments show that EdgeWise matches or outperforms pure-LLM execution while reducing inference cost up to 62% on SWE-Rebench and 34% on Terminal-Bench 2.1. We further deploy EdgeWise on a local workstation, demonstrating comparable cost savings in a practical edge-cloud setting.

Little red dots (LRDs) are compact red sources at z>~4. Broad lines suggest accreting black holes, yet radio and X-ray measurements are usually weak. Local LRDs allow multi-frequency, multi-epoch radio studies that are inaccessible at high redshift. We search archival radio images for a counterpart to the local LRD J092359+415736 at z~0.323, quantify its long-term radio variability, and identify the plausible origin of the radio emission. Flux densities at the optical position are measured in FIRST, LoTSS, RACS, VAST, and VLASS products spanning 0.144-3.0 GHz and 1994-2024. A compact 144 MHz counterpart is detected at 42sigma in LoTSS, coincident with the Gaia position, and is recovered in FIRST, RACS, VAST, and VLASS. LoTSS and ASKAP give a spectral index alpha ~ -0.30 +/- 0.11. The source varies on multiple timescales: FIRST at 1.4 GHz (1994) is a factor of ~2.6 below ASKAP (2021-2024) and below the extrapolated LoTSS-ASKAP spectrum, indicating long-term brightening over 26 yr; the 3 GHz flux density rises by 2.3sigma between VLASS epochs 2.2 and 3.2. A star-formation-only origin would require ~200 Msun/yr, against an unobscured H-alpha upper limit of 3.3 Msun/yr, implying an extreme obscured starburst. Ordinary radio supernovae and tidal disruption events are strongly disfavoured by the luminosity and 30-yr recovery, while refractive scintillation would itself require an ultracompact nuclear emitter. The persistent radio counterpart is best explained by accretion onto the central black hole. Among the three radio-detected local LRDs, this source is intermediate in luminosity and the only one with reported multi-year variability, adding a temporal dimension to the radio diversity of the class.

Let $k>\ell\ge 1$ be integers. For a family $\mathcal{F}$ of $k$-uniform hypergraphs ($k$-graphs), its $\ell$-degree Turán density $\gamma^{(k)}_\ell(\mathcal{F})$ is the asymptotic maximum of the normalized minimum $\ell$-degree over all $\mathcal{F}$-free $k$-graphs. In this paper, we prove that for all integers $k>\ell>2$ and every $\alpha\in[0,1)$, there exists an infinite family $\mathcal{F}$ of $k$-graphs such that $\gamma^{(k)}_\ell(\mathcal{F})=\alpha$, while every finite subfamily $\mathcal{F}'\subset \mathcal{F}$ satisfies $\gamma^{(k)}_\ell(\mathcal{F}')>\alpha$. This confirms the conjecture of Mubayi and Zhao on codegree Turán densities for every $k > 3$. As an immediate consequence, the set $\Gamma^{k,\ell}_{\infty}$ of $\ell$-degree Turán densities of nonempty $k$-graph families is $[0,1)$ whenever $k>\ell>2$, which answers a question of Lo and Markström from 2014.

A key challenge in the design of next-generation colliders is predicting the effects of beam-beam interactions and using these predictions to optimize machine performance. Beam-beam interactions are characterized by strong focusing forces, radiative effects, and the generation of background particles. While analytical formulas provide insight into the dynamics of beam-beam interactions, these nonlinear, coupled effects are most accurately described with numerical methods. In this paper, we introduce the open-source particle-in-cell code WarpX as a modern tool for modeling the interaction point in future lepton colliders. WarpX provides high-performance execution on distributed GPU architectures within an open-source and actively maintained code base. We present convergence scans and benchmarks against the established beam-beam codes GUINEA-PIG (v1.2.2) and CAIN (v2.42) for luminosity spectra, photon emission, and secondary-particle production under a wide range of beam parameters corresponding to different collider concepts. Our results show that WarpX (v26.09) reproduces the benchmark beam-beam observables while enabling GPU-portable, extensible simulations. These results establish WarpX as a scalable platform for high-fidelity beam-beam modeling in future collider studies.

Sulphur is drastically depleted from the gas phase in dense starless and prestellar cores, creating the long-standing "missing sulphur problem". Observations of sulphur-bearing molecules are crucial to understanding sulphur chemistry, core-environment relationships, and the physical evolution of star-forming regions. We present a survey of four sulphur-bearing molecules, HCS+, OCS, H2CS, and SO, towards 15 starless and prestellar cores in the Perseus molecular cloud using the Yebes 40m telescope. The HCS+ 1-0, OCS 3-2 and 4-3, H2CS 1_{0,1}-0_{0,0}, and SO 3_2-2_2 transitions were observed, fitted with Gaussian profiles, and column densities were calculated assuming local thermodynamic equilibrium (LTE). We also compare these with observations of CS, CCS, and CCCS from a previous study. HCS+, OCS, H2CS, and SO are detected in 100%, 93%, 100%, and 73% of the sample, respectively. Derived column densities are (2.2-17.0)x10^11 cm^-2 for HCS+, (1.9-25.0)x10^12 cm^-2 for OCS, (1.0-15.0)x10^12 cm^-2 for H2CS, and (0.3-17.0)x10^13 cm^-2 for SO, spanning over an order of magnitude. HCS+ and SO abundances strongly correlate (inversely and directly, respectively) with core volume density, reinforcing their early- and late-type status. Correlations indicate a differentiation between carbon and oxygen chemistry for sulphur-bearing molecules, with CS showing the strongest correlations as expected. Cores in protostellar outflow paths do not show consistently higher abundances. The chemical age (SO/CS) correlates with physical age (volume density), except for Per752, an outlier likely linked to an enhanced cosmic ray ionization rate. These results provide a robust observational baseline constraining chemical models of sulphur chemistry in early star formation.

We propose ATOM (Abstract Transition and Option Modeling), a hierarchical navigation framework that combines higher-level graph planning with reusable lower-level option policies for efficient repeated navigation in large-scale 3D environments represented by hierarchical structures such as 3D scene graphs (3DSGs). ATOM operates on a hierarchical graph representation, implemented using, for instance, the Rooms and Places layers of a 3DSG, where each directed abstract transition is associated with a navigation option. For each transition, ATOM computes and stores a reusable option policy along with its state-dependent cost-to-go. Across repeated navigation tasks, ATOM maintains a smoothed empirical distribution over option initiation states and uses it to progressively refine the corresponding abstract transition cost. Ablation studies show that ATOM reduces cumulative repeated-planning time by 97.5% relative to a monolithic MDP baseline while maintaining trajectories within approximately 7% of a Global Places A* shortest-path reference. Experience-informed refinement further reduces abstract transition-cost estimation error by 10.3%. Physical experiments validate ATOM on an F1Tenth vehicle, successfully completing all five navigation queries with 43% of inter-region option executions reusing previously generated solutions.

The shift towards 6G wireless networks calls for advanced waveforms to support emerging applications such as ultra-reliable and massive machine-type communications. Among the proposed candidates, OTFS, ODDM, OTSM, and OCDM share the common feature of exploiting the delay domain for data transmission. While these waveforms offer significant advantages in high-mobility and sensing scenarios, their integration into multi-user uplink systems reveals a critical challenge: timing misalignment (TM). Unlike OFDM, where residual timing offsets translate into phase rotations, delay-based waveforms experience actual shifts of resources, whose impact we investigate in this work. We show that the aforementioned waveforms can be unified under a time-invariant setup through a common input–output relation, which enables a unified analysis of TM in uplink resource allocation. The results reveal a fundamental trade-off between interference mitigation and guard overhead in the presence of TM. We further benchmark the observed behavior against OFDM under Doppler spread as a reference impairment and highlight the analogy between TM in delay-based allocation and Doppler spread in frequency-based allocation. The results show that delay-based waveforms can maintain a net performance advantage over OFDM in the considered setup. Beyond this unified Doppler-free analysis, we evaluate the joint impact of Doppler spread and TM on each waveform individually. We also investigate BER performance and show how coding can mitigate the resulting interference. This study therefore establishes a problem framework that motivates the development of future compensation and scheduling strategies for practical multi-user operation of delay-based waveforms.

An efficient shallow Ritz method was developed in [8, 9] for one-dimensional linear diffusion and diffusion-reaction problems. In this paper, the method is extended to a nonlinear diffusion-reaction equation with a cubic reaction term: (1) a basic error estimate of the shallow Ritz discretization is established and (2) a reduced block Newton (rBN) method for solving the resulting non-convex optimization problem is developed. Again, the computational cost of the rBN method is $\mathcal{O}(n)$ for one-dimensional problems, where $n$ is the number of neurons. Combining a convex splitting scheme for time discretization with the efficient shallow Ritz method, we develop a time-stepping neural network method for solving the Allen-Cahn equation. The unconditional energy stability of the time discretization and an error estimate in the $L^2$ norm are established. Numerical experiments demonstrate that the neural network approach yields accurate solutions for singularly perturbed nonlinear diffusion-reaction equations and the Allen-Cahn equation. The method effectively resolves interior and boundary layers without oscillations and significantly outperforms the finite element method on fixed uniform meshes.

Recent video super-resolution (VSR) models achieve efficient one-step generation through diffusion distillation. However, high-resolution inference remains costly, and distilled models are difficult to align with human preferences. These challenges call for improvements in both model architecture and training strategy. We present FlashVSR+ to address both limitations. On the architecture side, we introduce hybrid attention based on the strong locality observed in pretrained VSR models, while retaining sparse global interaction for long-range consistency. It achieves up to $2\times$ DiT speedup and 45% lower peak memory, enabling spatially untiled 4K VSR on a single 24GB RTX 4090. On the training side, we propose Reward-Yield Distribution Matching Distillation (Ry-DMD) for preference-aligned one-step generation. Ry-DMD uses reward-weighted teacher rollouts to incorporate black-box rewards into distribution matching, without backpropagating through the reward model. We further show that Ry-DMD generalizes beyond VSR to T2I generation. Together, FlashVSR+ delivers stronger restoration quality and substantially improves high-resolution efficiency, with consistent gains in user preference. We release our code, models, and training data at \href{https://www.flashvsr.tech}{\textcolor{FlashBlue}{www.flashvsr.tech}}.

The dominant barrier to running large clinical language models at the point of care is not arithmetic throughput but graphics memory: consumer GPUs cap at 4-16 GB, while the working set of a 27-billion-parameter model in 4-bit precision is 17-25 GB. We argue that the edge node should be treated as capacity-enabled (system RAM) rather than compute-limited (GPU VRAM), and we test this on commodity hardware. Using an INT4 build of a 27B open model as an architecture-faithful stand-in for a 27B medical model, we measure the memory footprint, inference latency, energy, and federated communication cost of a fully CPU-based pipeline driven by synthetic Fast Healthcare Interoperability Resources (FHIR) prompts. On two independent consumer machines (a desktop-class machine with 67 GB of RAM and a 6 GB GPU, and a mobile workstation with 34 GB of RAM and a 4 GB GPU) the model loads entirely into system RAM (37% and 60% utilization, respectively) while both GPUs are out-of-memory before the first step. Inference runs at overnight-batch speed (0.6-2.4 tokens/s for the 27B model), and federated fine-tuning would transmit only a 22.6 MB low-rank adapter, a 99.96% reduction over full weights. The capacity result is independent of CPU microarchitecture, RAM size, operating system, and GPU. We further identify an open, CPU- and NPU-optimized inference runtime as the natural production path for this approach, indicating a privacy-preserving and broadly deployable route for on-premises clinical AI. All data is synthetic; this is a research artifact and not a medical device.

Climate-intensified hurricanes disrupt urban mobility, yet whether recovery is equitable across the rural-urban gradient is unclear. Analyzing device-based mobility for Hurricanes Helene and Milton, we find local activity restarted within approximately 4.5 days in both storms, whereas reconnection to the outside world took 5 days in coastal-urban Florida but 11 in inland-rural Appalachia. The gap lies in external reconnection, not local restart, implying planners should target rural isolation.

Identifying a robot task from a short instruction is sensitive to which descriptions are available for retrieval. We investigate this effect in the natural-language instructions included with the RLBench manipulation benchmark. We extract 296 fixed descriptions from 62 publicly available task files and compare five training-free lexical rankers over 80 random choices of one indexed description per task. Exact strings assigned to conflicting task labels are excluded from the primary score. Character n-gram TF-IDF achieves 61.3% mean top-1 accuracy on the resulting held-out instructions, compared with 55.6% for BM25 and 54.9% for word TF-IDF. Across gallery choices, character TF-IDF ranges from 55.2% to 66.8%; its 5th-95th percentile range is 56.9%-64.8%. Adding a second indexed description improves character TF-IDF by 7.0 percentage points on matched queries. These results quantify the influence of reference wording and representation choice on instruction-to-task retrieval under a consistent evaluation protocol.

A graph is called a chain graph if it is bipartite and the neighborhoods of the vertices in each color class are linearly ordered by inclusion. We study the generalized spectral determination of chain graphs of adjacency rank $4$. We first show that generalized cospectral chain graphs have the same number of isolated vertices, reducing the problem to the connected case. For connected rank-$4$ chain graphs, we derive four explicit equations in the cell parameters that are necessary and sufficient for generalized cospectrality. These equations reduce to a quadratic equation in a single parameter. As a consequence, every connected rank-$4$ chain graph has at most one generalized cospectral mate, and the possible mate can be reconstructed explicitly. We further obtain a simple sufficient condition for a rank-$4$ chain graph to be determined by its generalized spectrum (DGS) and, in particular, prove that every double star graph is DGS. Finally, we construct an explicit infinite family of non-double-star rank-$4$ chain graphs that are DGS but not determined by their adjacency spectra, with both the graphs and their complements being connected.

We investigate the relationships between fragments of SRP and diagonal reflection principles. It turns out that the subcomplete fragment of SRP, augmented with CH, implies that the nonstationary ideal on $\omega_1$ is not saturated, but that Larson's diagonal reflection principle $OSR_{\omega_2}$ holds. In contrast, it was known that the full principle SRP implies the saturation of the nonstationary ideal on $\omega_1$, but it does not imply $OSR_{\omega_2}$. We find several instances of this phenomenon: pairing (variations of) the subcomplete fragment of SRP with stronger failures of the nonstationary ideal on $\omega_1$ to be saturated allows us to conclude more instances of diagonal reflection principles, while boosting (the corresponding variations of) the full principle SRP with strong forms of the saturation of the nonstationary ideal allows us to produce models where these principles still hold, yet weaker versions of diagonal reflection fail.

Federated learning (FL) enables collaborative model training without data centralization but struggles with incentive alignment, accountability, and robustness under heterogeneous non-IID data. Existing decentralized FL (DeFL) systems leverage blockchains for coordination yet face high on-chain overhead, unverifiable self-reports, and weak fairness guarantees. We present the FLAI Protocol, a trusted execution environment (TEE)-backed DeFL framework that integrates enclave-validated aggregation, sparse Peer Evaluation Graph (sPEG) scoring, and on-chain settlement. sPEG incorporates peer-based quality, class coverage, promptness, effort, and reputation into composite contribution scores. The protocol formalizes contribution evaluation and tokenized incentive distribution, ensuring verifiable fairness and resilience against free-riding and collusion. We evaluate FLAI on image, text, and healthcare datasets and demonstrate parity with FedAvg in utility while improving fairness and accountability. A case study in consumer eHealth (aggregating wearable and electronic health record data for real-world evidence generation) illustrates the protocol's applicability to privacy-critical domains where equitable rewards, auditability, and data sovereignty are essential.

The randomized primal-dual framework of Devanur, Jain, and Kleinberg (SODA 2013) splits each unit matching gain between endpoint dual variables according to the matched offline rank. The gain-sharing function affects the certificate but not Ranking's decisions. Keeping the splitting rule and expected edgewise feasibility criterion fixed, we define certifying capacity as the strongest uniform guarantee obtainable by functional optimization over a prescribed function class. Its shortfall from Ranking's actual competitiveness is the certifying gap. We study unweighted online bipartite matching under adversarial arrivals on graphs with online degree at most $d$ and on $d$-regular graphs. The optimized protocol is tight on both degree-one classes and in the unrestricted setting, but has a strictly positive gap on both degree-two classes, even over all measurable nonnegative complementary splits. In both degree-two settings, we determine Ranking's exact competitiveness and the exact certifying capacity over nondecreasing gain-sharing functions. For general $d$, we optimize over nondecreasing, right-continuous functions $f:[0,1]\to[0,1]$ with $f(1)=1$, using their probability-measure representation. Both the certifying capacity and actual competitiveness converge to $1-1/e$ in both instance families as $d\to\infty$. The resulting gap is at most $1/(2ed)+O(d^{-2})$ for online degree at most $d$; on $d$-regular graphs, it vanishes but is at least $(1/(2e)-o(1))/d$. These results distinguish function-class restrictions from limitations of the fixed protocol and motivate tighter randomized primal-dual frameworks.

Thought templates, skill libraries, agent memories and caches turn many reasoning steps into one. We call this reasoning contraction. A contracted memory saves reasoning steps and errors until its facts change, then quietly answers wrong. Most systems trust memories by counting successes and failures. We prove that such counters are badly tuned change detectors: a symmetric counter notices a partial change only after a power of its false-alarm horizon, and an unclipped one may never notice it. On five LLMs answering multi-hop questions over edited facts, ExpeL- and ACE-style counters serve 7.0-13.5x more stale answers than certified memories given the same information, and on code tasks with an exact verifier 35-73x more. Safety also has a price. When facts change and each memory is judged only by its own verified outcomes, one number, the certification load, sets how much reasoning any safe memory can skip, and under Zipf demand it yields a scaling law. Our recipe weighs each memory's failures by its own likelihood ratio, certifies its utility against live reasoning, and restarts the certificate when facts change, with the likelihood-ratio detector as the safety net for unannounced changes; for large edits it also invalidates the memory.

We completely classify aperiodic automorphisms of the Razak–Jacelon algebra $\mathcal{W}$ up to outer conjugacy. As a technical ingredient, based on the works of Connes, Herman–Ocneanu, Kishimoto, and Sato, we introduce a notion of weak stability for automorphisms of simple separable monotracial C$^*$-algebras. We also consider automorphisms of UHF algebras of infinite type and the Jiang–Su algebra. In particular, we classify aperiodic “UHF-absorbing” automorphisms of UHF algebras of infinite type up to outer conjugacy.

The rapid advancement of cybersecurity agents in vulnerability discovery has increased the need for benchmarks that evaluate their capabilities accurately. However, synthetic benchmarks lack realism, real-life benchmarks are prone to contamination, and many existing benchmarks have already been saturated by current models. We therefore set out to develop a benchmark that is realistic, reproducible, resistant to contamination, and challenging. Our key insight is that real-life business-logic vulnerabilities are subtle and exercise complex application interactions, making them naturally demanding. The difficulty lies in specifying evaluation criteria precise enough to faithfully measure model capabilities while keeping the tasks free of data-leakage. We introduce AnonVul, a cross-language benchmark of 132 application-level business-logic vulnerabilities, built by a semi-automated pipeline that anonymizes each task, injects oracles from expert-written specifications, and differentially verifies proof-of-concept exploits. The benchmark spans nine languages, with two evaluation tracks on black-box and grey-box settings, where each task runs in a sandbox with specialized oracles embedded in key exploitation steps. We evaluate six state-of-the-art vulnerability-discovery agents on the AnonVul benchmark, measuring discovery success, cost-effectiveness, anonymization sensitivity, oracle validity, and failure modes. Our results show that AnonVul remains challenging, with the best agent succeeding in only 23.11% of attempts. On a matched cohort of 20 vulnerabilities, restoring software identity increases discovery from 21.25% to 40.83%, highlighting the importance of controlling recognizable software knowledge when evaluating vulnerability discovery.

Safety verification of a Markov decision process (MDP) asks whether the probabilities of reaching several failure states jointly lie in a convex safe region under every scheduler. Watanabe and Unno (2026) prove safety by refining an outer approximation of the failure probabilities, where each query bounds a nonnegative weighted sum of the probabilities. Their rule selects weights by the largest Euclidean violation. We present a unified framework to measure violation in an explicitly chosen error unit: directions are scored by the support-function gap between the outer approximation and the safe region, normalized by the support function of the unit. We show that the maximal score, when positive, equals the smallest enlargement of the safe region in multiples of that unit that contains the outer approximation. The Euclidean unit recovers the earlier rule; two new rules are generated by the unit cube and the safe region itself. We experimentally evaluate how the choice of measurement rule affects the performance of safety verification for MDPs.

Textual reasoning before acting has improved vision-language-action (VLA) models, but at the cost of latency: every action conditioned on the reasoning text must wait for autoregressive decoding. We show that actions do not need to wait for or condition on the generated reasoning to benefit from it, because the reasoning supervision already improves the backbone representation. We introduce TacitVLA, a reasoning VLA whose action expert never attends to the reasoning it generates for the current call. On long-horizon tasks where the reasoning text also serves as episodic memory, it can generate each entry during action execution rather than before acting. We evaluate it in a controlled study on four benchmarks spanning manipulation and autonomous driving, memory and non-memory tasks: RoboMME, RMBench, LIBERO, and PhysicalAI-AV. On all four, TacitVLA matches the performance of its explicit-reasoning counterpart at up to 3.4x lower latency, and matches the latency of the same architecture trained without reasoning at up to +17.1% success. In absolute terms, it surpasses the best previously published results on the RoboMME Counting suite (82.7% vs. 66.8%) and RMBench (77.5% vs. 56.5%), and reaches 72.9% on LIBERO-Plus and a 52.5% scene score on the public split of the PhysicalAI-AV closed-loop driving challenge. Project page: https://tacitvla.github.io.

We study the stability of the variable coefficient wave equation $u_{tt}-u_{xx}-(1+x^{2})u_{yy}+\chi_{\mathbb G}u_{t}=0$ on the rectangle $(-1,1)\times(0,\pi)$ with Dirichlet boundary conditions, where the viscous damping acts on a vertical strip $\mathbb G=(\eta-\delta,\eta+\delta)\times(0,\pi)$. We establish a precise relationship between the location of the damping region and the rate of energy decay. We prove that the associated semigroup is exponentially stable whenever the closure of the damping strip meets the line $x=0$, i.e., $|\eta|\leq\delta$, despite the existence of rays that never enter the damped region. When the damping region is strictly bounded away from $x=0$, the semigroup decays at the sharp rate $(\log(2+t))^{-1}$. The proofs combine separation of variables, one-dimensional resolvent estimates, a reflection identity for the harmonic oscillator, and Gaussian quasimodes. We then consider the spectral Galerkin approximation based on the Dirichlet eigenfunctions of the constant coefficient Laplacian and show that, although the sequence of semigroups resulting from the approximation converges to the continuous one, it fails to be uniformly exponentially stable.

Lexical representations can encode both abstract information and information specific to particular contexts. We investigate how these forms of information are organized in language models by decomposing contextual word representations into item, class, and word-class interaction components. Across six pretrained transformers and two linguistic categories, we find that the interaction is consistently present, grows across layers, and contains information associated with both item and class. Unlike the nearly orthogonal item and class effects, the interaction overlaps with both and encodes class information beyond the shared class effect. An interaction also emerges in artificial-language learners even when the input contains only additive structure. Together, these findings show that lexical representations combine abstract information with structure specific to particular word-class combinations.

We provide a complete characterization of a finite group in which every non-supersolvable maximal subgroup is a TI-subgroup, which generalizes some known related results.

We study hyperelliptic curves on $K3$ surfaces. We show that any number of general points on a $K3$ surface of Picard rank one can be connected by a hyperelliptic curve. As a by-product we recover the Beauville–Voisin decomposition of the small diagonal, together with some new bounds on its torsion order in the integral Chow group. On the arithmetic side, given a $K3$ surface $X$ of geometric Picard rank one defined over a number field $k$, we show that there exists a finite extension $k\subset k'$ such that quadratic points are dense in $X_{k'}$, extending a theorem of Corvaja–Zucconi to $K3$ surfaces of arbitrary degree.

We propose the electric Edelstein effect (EEE) in two-dimensional (2D) systems, where crossed out-of-plane and in-plane electric fields generate a spin polarization. The gate field converts the Edelstein response from a material-fixed spin polarization into a gate-tunable one. A symmetry analysis over all magnetic layer point groups shows that the EEE is allowed in a wide range of magnetic and nonmagnetic systems, including ferromagnets, antiferromagnets, and altermagnets. The EEE plays two distinct roles: it generates spin polarization where the linear Edelstein effect (EE) is symmetry-forbidden, as in centrosymmetric materials; and it adds a new gate-tunable component, generally non-collinear with the conventional one, where the EE is already present. The two fields then act as independent knobs and raise the control dimension of the spin polarization from one to two. Our microscopic theory traces the EEE to band-geometric quantities, which are strongly enhanced near small band gaps. First-principles calculations predict pronounced effects in the centrosymmetric ferromagnet MnSe2, where the linear EE is symmetry-forbidden. In the nonmagnet SnSe where the EE and EEE coexist, the two knobs cover an extended region of the spin sphere. Our findings establish the EEE as a symmetry-guided, gate-tunable route to electrical spin manipulation and open avenues for multistate spintronics in 2D quantum materials.

Actuator sizing is an early and consequential decision: joint torque and velocity specifications fix the motors, gearboxes and brakes before any CAD model exists. Sim4RAD is a MATLAB toolkit for that phase and for the verification that follows it. It builds a rigid-body model from a handful of parameters, and four analyses supply the specification: a static analysis combining lever-arm sampling with a posture search, giving a rated torque at a chosen payload envelope and a reproducible peak torque; a dynamics pipeline that reshapes a trajectory under one of four constraints, including the actuator torque-speed envelope; a stochastic analysis over many random motions, so a specification rests on a class of motions, not one trajectory; and a workspace and dexterity analysis that separates where the arm can reach from how it can reach there. Replacing the synthesized model by a URDF file turns the same analyses to verification. A 7-DOF anthropomorphic arm is compared in three layouts differing in the shoulder axis order and in whether the last wrist joint is coaxial with the payload. The static demand at half arm length is nearly the same in all three, and it sizes the joints rather than the sampled motion; reordering the shoulder axes leaves the worst-case torque unchanged at 55 N m and the reachable volume within 8 percent. A last wrist joint coaxial with the payload removes its gravity torque, reduces the adjacent wrist joint by almost a third and cuts the last joint demand tenfold in a 5 m/s scan, at the price of dexterity (mean 0.570 to 0.348). The same arm needs 20 to 37 times more torque for a 5 m/s target than for a 2 s motion: the scenario, not the trajectory, must be fixed first. Verification should use the URDF model of the detailed design; the toolkit is available at https://github.com/LasterLi/Sim4RAD.