Papers

We investigate anisotropic domain wall and cosmological solutions in $D$-dimensional gravitational theories of arbitrary spacetime signature coupled to scalar fields with a scalar potential. We identify a class of scalar potentials for which the second-order equations of motion admit a first-order formulation. The associated bosonic flows allow non-trivial Ricci-flat worldvolumes, while their Killing-spinor realization further requires the worldvolume to admit a non-vanishing parallel spinor. Five-dimensional ${\cal N}=2$ gauged supergravity provides a concrete realization of this construction, with the worldvolume geometry determined by its signature and giving rise to pp-wave, hyper-Kähler, and hypersymplectic geometries. We further construct a general class of anisotropic solutions depending on a single variable, with the anisotropy encoded in a constant traceless matrix. A particular branch arises when a subset of scalar fields contribute through their kinetic terms but do not enter the scalar potential; these fields follow geodesics on the scalar manifold. As an explicit application, we recover the Kasner-dilaton-AdS solutions and show that, in the appropriate limit, they satisfy the first-order flow equations.

Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.

Long-horizon tasks with sparse rewards pose an exploration bottleneck for goal-conditioned reinforcement learning: a policy started from the initial state rarely reaches the goal and receives no learning signal. Reference motions, hand-designed curricula, and shaped rewards supply this signal but require demonstrations or task-specific engineering; automatic start-state and goal curricula avoid this but typically expand from one side only, so the full distance to the target must be covered from that side. We propose the Bidirectional Voronoi-biased Exploration curriculum for Reinforcement learning (BVER), which expands from both ends at once. Inspired by bidirectional RRT planning, BVER grows start states outward from the goal and goals outward from the initial state distribution, biases both toward unexplored task space, and steers them toward each other, training one goal-conditioned policy on both. On point-mass mazes, quadrupedal box climbing, and robot-arm ring-on-peg transfer, BVER learns faster than all compared reference-free curricula. On box climbing, it reaches 95% success on a 0.4 m box in roughly 65% fewer iterations than the best of them, is the only one of them to learn to climb a 0.7 m box, and yields a policy robust to start, goal, and yaw variation. Without a demonstration, it approaches the sample efficiency of reference-based curricula on the 0.4 m box and on ring-on-peg transfer. Ablations show that expanding from both ends outperforms either direction alone.

Emerging multi-agent LLMs demand privacy-preserving edge deployment, yet current inference systems struggle with these collaborative workflows. Specifically, the memory-bound decode phase causes severe bus contention on unified memory architectures (UMA), paralyzing naive CPU-GPU co-execution. Furthermore, speculative decoding in multi-agent workloads faces extreme variance in drafting difficulty, alternating between complex reasoning and predictable structured generation. Compounded by frequent tool-induced stalls, this highly fragmented execution severely underutilizes hardware and defeats traditional static batching. We present EdgeAgent, a cross-layer inference system explicitly co-designed for edge UMA and multi-agent workloads. At the micro-architectural level, it bypasses rigid graph-compiler constraints to enable zero-copy UMA-aware tensor parallelism, utilizing asymmetric memory layouts to fully saturate both CPU and GPU compute units. At the scheduling level, it dynamically allocates draft budgets based on real-time sequence predictability to bound bandwidth waste. Concurrently, an asynchronous suspend-and-yield mechanism actively evicts stalled agents, ensuring continuous hardware saturation during unpredictable tool invocations. Extensive evaluations on an Apple M4 SoC demonstrate that the UMA-aware execution alone contributes a 1.29x speedup over batched speculative decoding. Adding the agent-aware scheduling lifts the full EdgeAgent system to a 1.77x speedup under extreme tool-use latencies.

Polynomial transformations of data encoded in quantum operations are a building block of quantum algorithms, and their query complexity measures how often those operations are used. For multiple variables, existing methods either realize restricted polynomial families or implement monomials separately at a query cost exponential in the number of variables. We present a quantum circuit that implements every multivariate trigonometric polynomial up to an explicit normalization. The circuit processes one variable coherently over the frequency components of the remaining variables, allowing all components to share the same signal queries. Each variable is queried exactly as many times as its degree in the polynomial, and we prove that this query complexity is optimal. We further extend the construction to commuting unitaries. The resulting circuit applies the multivariate polynomial simultaneously across their shared eigenbasis, using the minimum numbers of forward and inverse queries to each unitary. We also study trainable rotations with fixed preparation and a local readout of the last input. At query depth at least two, independent uniform initialization gives every active readout gradient a variance lower bound set by its squared branch weight and the inverse square root of the depth, uniformly over data states and dimensions. For supervised squared loss, retaining sample correlations gives an initialization gradient-variance bound in terms of targets and input spectra. This also bounds the expected loss decrease after the first exact gradient step with a specified step size. These results provide a scalable and practical solution for developing multivariate quantum algorithms and quantum learning models.

We model an academic curriculum as a generator of a language of feasible study plans: prerequisites are monotone Boolean formulas in conjunctive normal form, degree requirements are credit-threshold covering constraints, and a study plan is a sequence of terms bounded by a per-term credit capacity. Within this model, we settle the complexity of the two natural planning objectives, the number of terms to a degree and the total credit load, and we isolate the structural commitment responsible for each source of hardness. Time to degree is polynomial whenever the per-term capacity is unbounded, for arbitrary disjunctive prerequisites and arbitrary electives, so disjunction never contributes to its hardness, yet it becomes strongly NP-hard as soon as capacity binds, even without any prerequisite. Load is complementary: disjunction and overlapping electives are each strongly NP-hard in isolation and their complexity does not depend on capacity, while load is polynomial on the conjunctive, mandatory fragment. The two objectives therefore have disjoint sources of hardness. We show that the delay-factor component of the standard curricular-complexity metric is a polynomially computable upper bound on time to degree, exact on the conjunctive fragment and loose elsewhere by a quantity we name the disjunctive slack, and we prove that program subsumption is coNP-complete and consensus prerequisite recovery is NP-complete. Instantiating the model on a corpus of twenty-two universities, we find that 88 percent of prerequisite-bearing courses are purely conjunctive and that capacity, not prerequisite logic, is the operative constraint on time to degree. The curriculum corpus is openly available (https://doi.org/10.5281/zenodo.22334674), and the analysis and figure-generation code accompany the paper.

World action models integrate future visual dynamics with robot action prediction, but their scalability remains limited by the need for action-annotated robot trajectories. Observation-only videos contain rich evidence about interaction dynamics, but existing approaches typically use them either to pretrain visual representations that must later be adapted for control, or to infer latent actions that are subsequently grounded to robot commands. We present NAVA-WAM, which introduces native action-prior learning by directly pretraining the action policy from observation-only videos, avoiding indirect representation-to-control transfer or a separate latent-action model. Our training consists of two stages. First, we pretrain on observation-only videos, where future-video flow-matching supervision over visual transitions is propagated through transition-structured joint attention to optimize the Action-DiT and learn action-relevant priors. Second, we use action-labeled demonstrations to post-train the Action-DiT for robot control through joint video–action flow matching, while asymmetric attention decouples the visual branch from iterative action denoising and enables efficient action-only inference. Extensive experiments show that NAVA-WAM consistently outperforms prior approaches under both in-distribution and out-of-distribution settings, while demonstrating strong action-label efficiency and effective real-robot generalization. These results establish native action-prior learning as an effective approach to directly pretrain action policies from observation-only videos, providing a scalable path beyond action-labeled robot data.

Few-step neural text-to-speech models often rely on short- ened diffusion or flow-matching schedules, or on distillation from pretrained multi-step teachers. To avoid these depen- dencies, we present DriftTTS, a few-step mel-spectrogram generator trained without a generative teacher, distillation, or adversarial discrimination. DriftTTS uses a distribution- matching drift objective in a mel-domain feature space defined by raw mels and a frozen masked-autoencoder encoder pretrained on the same LJSpeech training split. On-policy rollout trains the decoder on its own interme- diate states and supports inference up to the trained roll- out depth. On LJSpeech, DriftTTS at NFE=4 achieves 3.87 dB MCD and 3.7% WER, compared with 3.85 dB and 3.4% for Matcha-TTS. In a fully paired blind listen- ing test, DriftTTS obtains 4.18 MOS, compared with 3.96 for Matcha-TTS and 4.22 for ground truth. These results demonstrate competitive few-step synthesis without a pre- trained generative teacher. Code can be found at https: //github.com/BASHLab/driftTTS.git

Vision language models (VLMs) incur substantial inference cost because every visual token is processed by the attention and MLP projections of every decoder layer, even when token-specific visual computation is unnecessary at many depths. We introduce Patch-to-Prune (P2P), inspired by Mechanistic Interpretability, a training-free framework that converts activation patching from a diagnostic tool into an inference-time computation bypass. P2P performs validation-guided forward and backward layer sweeps to identify decoder regions whose visual-token projection outputs can be replaced by fixed neutral proxy activation vectors within a user-specified accuracy tolerance. Unlike conventional token-pruning methods, P2P preserves the sequence length, token order, positional information, attention mask, and residual pathways, thereby pruning computation without removing tokens or modifying the pretrained model weights. We evaluate P2P on four VLMs from the Qwen2.5-VL and LLaVA families across seven multi-modal benchmarks using mutually disjoint calibration, validation, and test partitions. P2P at a 3% tolerance retains around 94% of dense accuracy while reducing FLOPs by 55%. Beyond these efficiency gains, our layer-wise analysis suggests that visual processing in VLMs is non-uniformly distributed across decoder depth: early and late layers often require little token-specific visual computation, whereas intermediate layers appear to perform most task-relevant visual integration, enabling later reasoning to rely largely on visual information already embedded in shared residual and textual representations. This makes P2P both an efficient inference framework and a causal lens into visual information processing in VLMs.

Video is an abundant, inexpensive source of human motion data that is rich in extreme athletic behaviors. Making it usable for humanoid robots, however, is not a matter of simply retargeting a reconstructed trajectory: video-derived motion is physically inconsistent, devoid of actuation information, and says nothing about failure or recovery. We present KungfuAthleteBot (KAB), a framework that treats learning high-dynamic motion from video as the central problem and resolves each of these three failure modes in turn. (C1) We build the KungfuAthlete dataset from videos of national-level martial artists and introduce a physics-guided parabolic trajectory correction that removes height floating, ground penetration, and high-frequency jitter from reconstructed aerial and landing phases. (C2) Because video carries no force information, strict tracking of a reconstructed trajectory is dynamically infeasible, and error-driven initialization keeps re-launching the policy from infeasible aerial poses. We introduce physics-driven pseudo-low-kinetic-energy (LKE) sampling, our central mechanism for making such references learnable: it biases initialization towards dynamically feasible states, letting the policy discover feasible actuation patterns instead of imitating infeasible ones. (C3) Finally, we introduce a direct training paradigm in which disturbance rejection and fall recovery are learned inside the same policy that tracks the video motion, requiring no recovery reference data and no manual mode switching. On a humanoid robot, KAB learns dynamic skills from video and recovers from arbitrary falls in about 0.7 s, the fastest reported recovery for a unified policy. Ablations on the unified policy confirm the necessity of its components, supporting the view that repairing and compensating video data, rather than only collecting more of it, is what unlocks high-dynamic humanoid skills.

Rejection policies must remain useful as candidate sets and tasks change. We compare Laya, Jev and Qwen2.5-7B-Instruct using public reference labels, testing Laya/Jev policy transfer at equal calibration budgets and all three models on artificial omission, natural retrieval misses and public out-of-scope queries. Source calibration often fails to preserve the target operating point. A Jev policy calibrated on DBpedia rejects 69.3% of covered Emotion test inputs, while an Emotion policy loses detection entirely. Retrieval exposes a different tradeoff: with ten intent candidates, Laya detects 99.0% of out-of-scope queries but rejects 48.8% of covered queries. Separating missing-answer sources reveals these costs alongside retrieval coverage. The benchmark provides shared inputs, explicit decision and failure categories, and reproducible scoring to assess rejection policies under the conditions in which they are reused. Code and benchmark artifacts are available at https://github.com/luckykevvv/Decision_Model_Benchmark.

This article is devoted to the mathematical analysis of a new Navier–Stokes-$\alpha$ model involving a nonlinear filter equation. The resulting model is governed by a doubly nonlinear parabolic–elliptic coupled system. In our previous work [M.~F.~Cortez and O.~Jarrín, Mathematical study of a new Navier–Stokes-alpha model with nonlinear filter equation – Part I, J. Math. Fluid Mech. 28, no.~12 (2026)], we established the global well-posedness of weak Leray-type solutions and the existence of a global attractor. In the present work, under natural assumptions on $A(\cdot)$, we investigate several additional properties of this model, with particular emphasis on higher-order regularity and its consequences for the long-time dynamics. The regularity analysis constitutes a central and delicate issue, since the nonlinear structure of the elliptic filter and its coupling with the evolution equation preclude a direct application of the standard regularity arguments available for linearly filtered Navier–Stokes-$\alpha$ models. Overcoming this difficulty requires new higher-order estimates for the nonlinear elliptic filter equation, which may also be of independent interest. Among the results obtained, two constitute the main contributions of the article. First, we establish uniform higher-order regularity for the global attractor. This result is then used as a fundamental ingredient in proving an exact determining-modes property for complete trajectories on the attractor: if the projections of two complete trajectories onto a sufficiently large finite-dimensional space of Stokes modes coincide at every time, then the two trajectories coincide identically.

Integrated photonic technologies require active materials capable of providing large optical modulation within compact footprints and low losses. The large optical nonlinearities of exciton-polaritons offer a promising route to meet these requirements, yet their integration into photonic circuits remains challenging because strong light-matter interactions must be combined with low-loss transport and spatially localized control. Here, we demonstrate active phase and amplitude modulation in halide perovskite polaritonic waveguides integrated with electrical microheaters. Local electrothermal actuation drives a structural phase transition in the perovskite, modifying the complex refractive index dispersion near the excitonic resonance. By tuning the excitonic fraction of the propagating mode, the waveguides can therefore operate either as a phase shifter with a tuning efficiency of 0.2 mW mm, approximately one order of magnitude lower than silicon modulators with similar geometries, or as an intensity switch , providing 1 dB/um modulation depth at 20 mW. Our work establishes phase-change excitonic reconfiguration as a route towards compact polariton circuits for nonlinear photonic applications.

To an oriented quiver with boundary $\Gamma$ and a compact connected Lie group $G$ we associate a Nahm-Kirchhoff moduli space $\mathcal{M}_{\mathbb{H}}(\Gamma)$: solutions of Nahm's equations on the edges with Kirchhoff matching at interior vertices, modulo boundary-trivial gauge transformations. For connected $\Gamma$, $\mathcal{M}_{\mathbb{H}}(\Gamma)$ is a smooth manifold of dimension $4(|E|-|\Gamma_{\mathrm{int}}|)\dim G$ with a hyperkähler structure arising as an infinite-dimensional hyperkähler quotient. Via a Kempf-Ness argument on the Cartan-Hadamard manifold $G_{\mathbb{C}}/G$, we prove a quiver analogue of Donaldson's theorem identifying it with the complex-symplectic quotient $\mathcal{M}_{\mathbb{C}}(\Gamma)$ of the complex Nahm equations by the complexified gauge group. This quotient is independent of edge lengths and isomorphic to a finite-dimensional complex-symplectic quotient of $(T^*G_{\mathbb{C}})^E$, while the hyperkähler metric depends on them: uniform rescaling acts by a homothety, and the transported metrics genuinely vary. By cutting and gluing, $\Gamma\mapsto\mathcal{M}_{\mathbb{C}}(\Gamma)$ is a 2D TQFT valued in complex Hamiltonian manifolds, à la Moore-Tachikawa, whereas the hyperkähler refinement is not functorial on $\mathbf{Cob}_2$: spines of a cylinder with different lengths give non-isomorphic spaces. Retaining lengths, these spaces form a metric field theory, a functor of non-unital monoidal categories from metric cobordisms to hyperkähler manifolds composed by hyperkähler reduction; over each cone of $M_{g,n}^{\mathrm{trop}}$ they give a family with fixed complex-symplectic fibre and varying metric. Finally, harmonic gauge representatives converge as an internal edge collapses, and on a long edge with regular semisimple Higgs field the Kempf-Ness minimizer is exponentially confined near its centralizer; the limiting metrics are left open.

Attack Path (AP) modeling is fundamental to cybersecurity analysis, where the Planning Domain Definition Language (PDDL) has been widely adopted to encode APs into formal and machine-verifiable representations for automated reasoning about vulnerability exploitation, attack progression, and their potential impacts. However, existing AP modeling approaches largely rely on expert-driven manual construction, limiting their scalability and ability to keep pace with rapidly evolving cyber threats. Large language models (LLMs) are promising candidates, as their extensive pre-trained knowledge and reasoning capabilities enable them to interpret and transform threat intelligence into formal representations. In this paper, we propose CVE2AP, an LLM-based approach for automatically generating PDDL-encoded attack paths from natural language CVE (Common Vulnerability Exposure) descriptions. CVE2AP leverages structured prompting and incorporates an error-feedback mechanism that iteratively refines the generated paths using planner-reported syntactic and solvability errors. We conduct a systematic empirical evaluation across multiple LLMs and generation configurations, assessing generation quality across syntactic, solvability and semantic dimensions, together with token consumption and generation time. The results demonstrate that CVE2AP effectively generates high-quality PDDL-encoded attack paths, achieving up to 86.9% syntax correctness, 78.6% solvability, and 93.1% semantic correctness under LLM-as-expert evaluation, while GPT-5.5 offers the best quality-cost trade-off and error feedback yields the most consistent quality improvement.

Continuous-variable quantum key distribution (CV-QKD) networks require routing strategies that account simultaneously for secret key generation, relay trust and finite network resources. We introduce Quantum Utility Routing (QUR), a weighted routing framework for networks combining trusted point-to-point links with untrusted CV Bell measurement relays. Transition level composable finite size secret key rates (SKRs) are incorporated directly into the route search, allowing QUR to balance bottleneck SKR against route geometry and resource use. We consider graph optimized QUR (QUR$_{\mathrm{go}}$) and a fixed weight implementation (QUR$_{\mathrm{fw}}$) that uses machine learning to avoid repeated graph specific weight optimization, and benchmark both against A* and Max–Min routing. At the default network configuration, QUR$_{\mathrm{go}}$ and QUR$_{\mathrm{fw}}$ improve the mean path SKR relative to A* while requiring substantially fewer network resources than Max–Min. The framework also maintains secure connectivity over a broad range of trusted node availability by exploiting untrusted infrastructure as measurement relays. These results demonstrate that routing in CV-QKD networks can be treated as a configurable trade off between cryptographic performance and network resource consumption.

We investigate noise disparity in multi-class speech classification tasks and develop a strategy to prevent classifiers from exploiting class-dependent noise characteristics. Building on our previous work for binary classification, we introduce a multi-class cross-augmentation scheme that exposes each class to the noise characteristics of the other classes, thereby removing the association between individual noise conditions and class labels. We compare this training-based approach with speech enhancement (SE) as a preprocessing strategy, which aims to suppress noise-related cues directly from the input. Experiments on multi-class emotion recognition show that cross-augmentation effectively mitigates the effect of noise disparity across a range of signal-to-noise-ratios, while SE has a detrimental effect on model performance.

Deepfake detection in videos remains challenging, as manipulated content may appear visually consistent at the frame level while exhibiting subtle temporal inconsistencies. This paper introduces an interpretable deepfake detection framework that models spatially and temporally coherent facial features in video sequences. Unlike end-to-end deep models relying on implicit representations, the proposed approach explicitly encodes physically grounded forensic cues, enabling transparent analysis and improved multi-dataset generalization. The pipeline transforms videos into identity-consistent facial trajectories, segments them into fixed-length temporal windows, and represents each frame using 68 structured descriptors spanning four complementary domains: photometric, textural, geometric, and compression-based features. These descriptors provide a compact multi-domain representation of manipulation artifacts and are processed by a Long Short-Term Memory (LSTM) network to capture temporal dependencies and subtle irregularities. Evaluation on four benchmark datasets, FaceForensics++, Celeb-DF v2, a curated subset of the DeepFake Detection Challenge (DFDC), and DeeperForensics, yields strong and consistent F1-scores of 98.0%, 91.0%, 97.6%, and 96.2%, respectively. The approach also demonstrated a good cross-dataset generalization, providing a robust and interpretable solution for video deepfake detection.

Quantum annealers can sample degenerate optima unevenly, so the composition of finite-read output matters when multiple solutions are sought. We investigate whether problem structure can steer this output through node-dependent anneal offsets for Minimum Vertex Cover (MVC). In MVC, vertex degree equals the number of incident edge-cover constraints and therefore measures local constraint participation. We use this relation to define degree-conditioned offset-scheduled quantum annealing (DC-OSQA), a static rule assigning more negative offsets to vertices with larger max-normalized degree. Experiments used a D-Wave Advantage2 system1 quantum processing unit (QPU). For each graph, DC-OSQA was compared with a zero-offset baseline using the same MVC encoding, fixed physical embedding, majority-vote chain decoding, and 1000-read budget. A sampled bitstring was counted as a certified candidate only if it represented a feasible vertex cover and its cardinality matched the minimum independently certified by integer linear programming. Across 120 paired comparisons on sparse Barabasi-Albert graphs with two attachments per added vertex and graph sizes N = 70-150, DC-OSQA increased the mean number of distinct certified candidates from 171.7 to 455.8 and the mean number of complete-linkage Hamming-distance families from 22.5 to 80.0; paired gains were positive at every tested size. These shifts, together with lower empirical concentration, indicate a change in the composition of the observed certified support. At N = 150, the degree-aligned assignment exceeded the within-instance mean over 20 random reassignments of the same offset values in 19 of 20 graphs for certified-support size and all 20 graphs for Hamming families. Within the tested ensemble, these results show that an MVC-specific degree rule changes the certified optima observed within a fixed QPU read budget.

Physics-Informed Neural Networks (PINNs) typically exhibit spectral bias, where some frequencies of the target function converge more slowly than others. In this work, we analyze the training dynamics of Fourier Feature PINNs in the Neural Tangent Kernel regime to address this limitation. We derive an explicit evolution equation to estimate the residual error in the frequency domain, demonstrating that the convergence rate of specific frequencies is primarily governed by the product of the differential operator's symbol and the spectral density of the initialization weights. Leveraging this theoretical insight, we propose an informative initialization strategy that tailors the initial weight distribution to the specific PDE being solved. With this method, we can diminish the operator-induced spectral bias, balancing the convergence rates across the frequency spectrum and achieving better prediction accuracy. Numerical experiments on linear and nonlinear partial differential equations confirm that this initialization strategy improves learning dynamics and approximation accuracy across frequencies compared to standard initialization methods, with no additional training cost.

Marriott and Watrous showed that quantum Merlin–Arthur games admit generic error reduction without increasing witness size [Computational Complexity, 2005]. In this work, we show that this state-size-preserving amplification property does not hold for polynomial-time quantum computation with quantum advice. In particular, we present decision problems for which even a vanishing additive error reduction requires longer advice. More precisely, for every polynomially bounded advice length $m(n)=\omega(1)$ and every error bound $\varepsilon(n)$ that stays below $1/2$ by at least an inverse polynomial, there is a positive function $\delta$ with $\delta(n)=O\bigl(\min\{(\log m/m)^{1/4},\ \sqrt{\log m/m}\,/(1/2-\varepsilon(n))\}\bigr)$ such that $\mathsf{BQP}_{\varepsilon}/\mathsf{q}m \subsetneq \mathsf{BQP}_{\varepsilon + \delta}/\mathsf{q}m$; for constant $\varepsilon$ the gap is $O(\sqrt{\log m/m})$. Here, $\mathsf{BQP}_\varepsilon/\mathsf{q}m$ is the class of languages recognizable with error at most $\varepsilon(n)$ by a polynomial-time quantum algorithm with an $m(n)$-qubit advice state that only depends on the input length $n$. We show this by proving a stronger separation $\mathsf{P}_{\varepsilon+\delta}/\mathsf{r} m \not\subset \mathsf{BQP}_{\varepsilon}/\mathsf{q} m$, where $\mathsf{P}_{\varepsilon}/\mathsf{r}m$ is the class of languages recognizable with error at most $\varepsilon(n)$ by a deterministic polynomial-time algorithm with an $m(n)$-bit advice string sampled from a distribution that depends only on $n$.

The Any Light Particle Search II employs a highly sensitive heterodyne detection system to measure an ultra-weak electromagnetic field that is reconverted from axions inside a regeneration cavity (RC). The initial design of the heterodyne system utilized a local oscillator laser (LO) that was resonant with the RC to form an interference beatnote with the weak signal field exiting the cavity. A weakness of this design is that it is possible for the out-of-mode field component of the LO to be larger than the in-mode component, allowing its noise to dominate the optical component of the noise budget and reducing the SNR of the experiment. This problem can be addressed by introducing a second, non-resonant laser as the LO. Since the in-mode light of this laser does not couple to the cavity, significantly more of its power is reflected than when the LO is resonant. We present a model for the measurement noise that predicts these design changes increase the SNR by a factor of roughly 35. This model was then confirmed experimentally by injecting a weak signal to the RC and examining the difference in the sensitivity of the detection system in each of these configurations.

We develop a differential-geometric approach to contractive projections on complex Banach spaces based on Levi forms of plurisubharmonic functions. We show that if a projection $P$ contracts a $\mathrm{C}^2$ plurisubharmonic function $\Phi$, then, at any point of its range, the Levi form of $\Phi$ defines a tangent Hilbertian geometry for which $P$ becomes an orthogonal projection. When the range is finite-dimensional and the relevant Levi forms are nondegenerate, comparing the Levi geometries associated with different points leads naturally to positive relative operators and associated one-parameter groups. We apply this framework to tracial noncommutative $\mathrm{L}^4$-spaces. Exploiting the cubic form of the duality mapping, we characterize contractive projections by a Jordan triple orthogonality property and prove that a projection on $\mathrm{L}^4(\mathcal{M})$ is $2$-contractive if and only if it is completely contractive. When the ambient von Neumann algebra is finite-dimensional, we identify the relative operator associated with the left and right tangent forms on the range with a restriction of an inverse square root of a modular operator on a linking von Neumann algebra. This entails that the range of any $2$-contractive projection is completely isometric to a rectangular noncommutative $\mathrm{L}^4$-space associated with a $\mathrm{W}^*$-ternary ring of operators. As a consequence, every such projection is contractively decomposable. Finally, for every $1 < p < \infty$ with $p \neq 2$, we prove that every finite-rank $2$-contractive projection on a tracial noncommutative $\mathrm{L}^p$-space is completely contractive. For $p > 2$, we obtain a weighted ternary description of its range in terms of a finite-dimensional $\mathrm{W}^*$-$\mathrm{TRO}$.

Embodied world models enable scalable simulation of embodied interactions for robot learning. However, existing models are prone to Model Laziness, as they focus on visual fidelity at the expense of physical reasoning and lack process-level supervision over the temporal dynamics of manipulated objects. In this work, we propose EVEWorld, a physical evolution-supervision framework for physically consistent target evolution. EVEWorld consists of two components: Instance-Guided Restoration (IGR) and Temporal Instance Alignment (TIA). First, IGR promotes instance consistency through restoration supervision. Second, TIA promotes cross-frame consistency by aligning target instances across adjacent frames. We further introduce the Model Laziness Rate (MLR), a metric that measures persistent violations of instance consistency in generated trajectories. Extensive experiments on DreamGenBench, EWMBench, and PBench demonstrate the effectiveness of EVEWorld, notably achieving an 87.5% reduction in MLR compared with GigaWorld-0. On the WorldArena 2.0 Track 1 leaderboard, our model ranks 6th in JEPA Similarity and 17th overall, which further validates the performance of our evolution supervision strategy.

We prove that metric measure spaces arising from $2$-manifolds equipped with Riemannian metrics $g$ such that $g, g^{-1} \in L^\infty_{\rm loc} \cap W^{1,p}_{\rm loc}$ are infinitesimally Hilbertian. Along the way, we establish uniform lower $1$-capacity bounds of several $1$-dimensional subsets of $\R^2$.

Training long-horizon agents to solve complex tasks requires effective supervision over extended interaction sequences. However, sparse terminal rewards obscure intermediate contributions, while on-policy distillation can lose informative teacher guidance as student-generated histories grow. To address this problem, we introduce SCAD, which organizes interactions into planning and bounded subtask execution, distills execution in local contexts, and refines planning credit through cross-rollout subtask prefix trees, with planning receiving full terminal credit and execution receiving positive terminal credit and teacher guidance. Across all evaluated benchmarks, SCAD improves macro-average accuracy over the strongest training baseline by 4.48 percentage points for text tasks and 4.19 points for multimodal tasks. SCAD effectively combines outcome-based credit assignment with teacher-guided distillation to improve planning and execution in long-horizon agents.

Pinching-antenna systems (PASS) offer flexible radiation points for integrated sensing and communication (ISAC), but existing designs largely assume continuous antenna placement, which may be impractical with pre-installed hardware. We investigate a discrete-activation multi-waveguide PASS-ISAC system that selects sparse transmit and receive pinching antennas (TPAs/RPAs) from predefined locations. We formulate a communication-rate maximization problem by jointly optimizing beamforming and TPA/RPA activation under transmit-power, activation, and sensing signal-to-noise ratio (SNR) constraints. To solve this nonconvex problem, we develop a low-complexity joint discrete pinching-antenna activation and beamforming optimization (JDPABO) algorithm based on alternating optimization, successive convex approximation, and reweighted $\ell_1$ minimization. Simulations show that JDPABO approaches continuous-placement performance at low sensing SNR requirements and outperforms fixed activation schemes with sparse PA activation.

CLIP's visual encoder produces only global image representations, limiting its use in region-level tasks. Existing adaptations rely on visual prompting, input masking, or encoder fine-tuning, each compromising pre-trained representations. We propose LAS-CLIP, a Lightweight Adapter Steering approach that keeps every CLIP parameter frozen. A compact MaskAdapter generates per-head, per-layer attention biases from an input mask and injects them into the frozen self-attention layers, steering attention toward the target region. Crucially, because the backbone remains strictly untouched, LAS-CLIP seamlessly reverts to vanilla CLIP when no mask is provided, preserving its foundational zero-shot capabilities. With approximately 116K to 145K trainable parameters and 100K training samples on two T4 GPUs, LAS-CLIP achieves competitive or superior results compared to Alpha-CLIP on ImageNet-S zero-shot classification and RefCOCO referring expression comprehension, despite the latter fine-tuning its entire encoder on millions of samples. Qualitative analysis further confirms stronger representational fidelity under incorrect masks and in downstream generation.

Deep reinforcement-learning policies for order execution can vary substantially across training seeds, so apparent architectural gains may reflect favourable training realisations rather than reproducible properties of the architecture. We evaluate vanilla Double Deep Q-Learning (DDQL), K-means-partitioned mixtures of DDQL experts at $K \in \{2, 4, 8\}$, and dense networks parameter-matched to the $K{=}4$ and $K{=}8$ expert budgets on 5-minute mean-aggregated BTC/USDT limit order book data from Binance. No learned configuration significantly improves mean implementation shortfall over DDQL. Under the reported specification, all have higher mean shortfall than TWAP (0.39 bps) and immediate liquidation (0.21 bps) in an environment whose frictionless replay and terminal-urgency penalty make early liquidation nearly costless; 11/100 vanilla-DDQL runs, versus none in either MoE $K{\geq}4$ arm, converge to a policy that waits until forced liquidation. We then decompose this specification on a device-matched baseline. Annealed exploration alone eliminates observed collapses (12/100 to 0/100; exact McNemar $p{=}4.9{\times}10^{-4}$), matching the elimination under expert partitioning. Combining annealed exploration with the aligned reward restores collapse in 19/30 runs; with all three specification changes, it rises to 48/100. In this environment, expert partitioning is unnecessary to suppress collapse and appears to mask a training-specification failure rather than confer an intrinsic performance benefit. No MoE $K{=}8$ run collapses under any of the six specifications tested. Across-seed dispersion is lowest at $K{=}8$ but non-monotone and not robust to family-wise adjustment, while within-policy tail risk worsens monotonically with $K$. The apparent attribution of the failure mode reverses between 30 and 100 seeds, illustrating the importance of repeated-seed evaluation.

The Eisenbud-Goto conjecture stated that for a homogeneous prime ideal in a polynomial ring over an algebraically closed field, the Castelnuovo-Mumford regularity is bounded above by the multiplicity minus height plus one. In 2017, McCullough and Peeva showed that the regularity of an arbitrary homogeneous prime cannot be bounded by any polynomial function of the multiplicity. For ideals generated by polynomials with at most $c$ terms, we present a bound on the regularity which is less than triple exponential in $c$ and the multiplicity. Furthermore, for toric ideals we get a bound that is smaller than double exponential in terms of multiplicity.