Papers

Global synchronization has been largely investigated in static higher-order networks and little attention has been brought to directed, temporal higher-order networks. We hereby make a step in this direction by studying the emergence of global synchronization in periodically fast switching systems with directed higher-order interactions. By working in the framework of the Master Stability Function, we show that the linearized dynamics includes two time-dependent Jacobian matrices, both evolving on the timescale of the synchronous solution, together with a generalized Laplacian evolving on a fast switching timescale, resulting from the hypergraph time evolution. To address this two-timescale structure, we establish a fast-switching stability criterion for directed balanced higher-order structures. The latter condition allows to decouple the parallel and transverse perturbations to the synchronization manifold. By relying on the average theory for dynamical systems, we are able to prove exponential stability of global synchronization in the fast switching higher-order network. The proposed theory is then illustrated by using a higher-order Stuart–Landau model, which provides a natural benchmark for the theory. Directionality can move Laplacian eigenvalues into instability regions off the real axis, hence destabilizing synchronization; our results nevertheless reveal that temporal switching can counteract this destabilizing effect and restore global synchronization when the directed structures alternate sufficiently rapidly, even though the instantaneous directed higher-order structures are individually unstable.

Temporal grounding is fundamental to audio understanding, yet large audio language models (LALMs) remain weak at it on long audio, where hallucinations compound and annotated data is scarce. Existing benchmarks cover only short clips or offer coarse, synthetic annotations. We introduce EgoSCAPE, a manually verified benchmark created from Ego4D with 700 real audios of durations up to 5 minutes, annotated with dense captions, sound sources, audio timelines, and temporal grounding queries. We further propose ATTEST, a GRPO-based reinforcement learning framework that improves temporal grounding without changing the base model's architecture or token vocabulary. ATTEST combines (i) a counterfactual grounding reward penalizing predictions that survive removal of their acoustic evidence, (ii) an attention-density reward encouraging generation to attend to its own claimed time spans, and (iii) token-wise advantages giving segment-level credit for long dense captions. ATTEST outperforms prior temporal grounding methods on existing dense captioning and grounding benchmarks, with fewer hallucinations. Together, EgoSCAPE and ATTEST establish a rigorous evaluation-training recipe that brings temporally grounded audio understanding closer to practical, long-form deployment.

Hydrogen-rich materials offer a route to high-temperature conventional superconductivity, but often require extreme pressures. Here we report a first-principles study of NaH$_6$, identified in our large-scale hydride search and independently predicted in a subsequent high-throughput study. Several phases compete, with $R\bar{3}m$ and $Pm\bar{3}m$ dominant over broad pressure ranges. The $R\bar{3}m$ phase remains dynamically stable down to 10 GPa, where its calculated $T_\mathrm{c}$ is 34 K, rising to 99 K at 50 GPa. Cubic $Pm\bar{3}m$ becomes thermodynamically competitive at higher pressures and reaches a calculated $T_\mathrm{c}$ of 230 K at 50 GPa, decreasing only weakly upon further compression. Molecular dynamics and phonon-renormalization calculations support structural persistence over the sampled timescale and indicate relatively small anharmonic effects. Despite their high $T_\mathrm{c}$, both phases contain elongated H$_2$-like units, often considered unfavorable for high-$T_\mathrm{c}$ hydrides. Mode-resolved electron-phonon coupling links Raman-active hydrogen vibrations to superconductivity. In $R\bar{3}m$, the linewidths of these modes increase with the pressure-induced tilt of H$_2$ units relative to the threefold axis, alongside the rise in $T_\mathrm{c}$. A minimal symmetry-based model of the vibration-induced second-moment tensor of the hydrogen sublattice shows that these trends are consistent with a significant contribution from response components perpendicular to the threefold axis. NaH$_6$ thus represents an unusual molecular-like hydride in which hydrogen-sublattice reorganization may enable high-$T_\mathrm{c}$ superconductivity at comparatively moderate pressures.

We prove the non-characteristicness of the completed self-sum of the universal nilpotent cone in $T^*\mathrm{Bun}_G$ relative to the moduli of curves, for reductive groups $G$ of semi-simple rank $1$. In particular, this implies the non-characteristicness of the $\mathcal{H}om$-sheaf between Betti automorphic sheaves for groups of semi-simple rank $1$. We also construct an example of a collision of universal nilpotent Higgs fields, proving that the completed self-sum is not non-characteristic for $\mathrm{GL}_n$, $n\ge 3$, relative to the moduli of curves of genus $g\ge 4$.

Bayesian predictive regions account for parameter uncertainty but can be poorly calibrated under model misspecification, even with expensive full MCMC. Cheaper approximations such as variational inference reduce the cost but often yield less accurate predictive distributions. We propose SCOPE (Score-guided Conformal Posterior Exploration), which retains the predictive quality of full MCMC while achieving calibrated coverage at a fraction of its cost. The key observation is that a prediction region can depend on the posterior mainly through a few parameter directions that move the region's boundary, and these are generally not the directions of largest posterior variance. SCOPE gives nonconformity scores a new role in guiding posterior computation: score gradients on a held-out guide set, weighted toward the target boundary, identify the relevant directions. MCMC explores this subspace, while an inexpensive projected variational approximation carries the remaining uncertainty. The same guide set calibrates the region's final density level. We establish asymptotic coverage for SCOPE and provide a split variant with finite-sample validity. Controlled simulations show that score-guided exploration yields more accurate calibrated regions than non-targeted direction choices at low active rank. Across simulated and real benchmarks, SCOPE has a median test-NLL gap of only 0.002 nats relative to full Hamiltonian Monte Carlo (HMC), and on the real benchmarks it runs 12-15 times faster.

Can quantum advantages in computational efficiency coexist with quantum advantages in privacy? In this paper, we construct and use MasonQ, a universal brickwork transpiler, to answer this question with a resounding yes. We approach this question by bridging two seemingly disparate paradigms: universal blind quantum computation (UBQC), based on measurement-based quantum computation, and quantum machine learning (QML) algorithms such as the Harrow-Hassidim-Lloyd (HHL) algorithm and quantum recommendation systems. We provide new upper bounds on the depth of UBQC brickwork graphs, establishing that $D = \mathcal{O}(\omega n)$, where $\omega$ is the circuit width and $n$ its computational gate complexity. This is enabled by our newly developed transpiler MasonQ, which maps arbitrary quantum circuits to computational brickwork graph states. Given an optimal Qiskit circuit as input, we prove optimality (up to logarithmic corrections) of the MasonQ transpiler in terms of asymptotic scaling of the total brickwork graph width and depth after decomposition into bricks, enabling systematic cost analyses of blind implementations in near-term experiments and asymptotic regimes. Leveraging MasonQ, we derive depth bounds for several representative blind quantum machine learning (B-QML) algorithms, including the quantum Fourier transform, the HHL algorithm, recommendation systems, and quantum transformers. Lastly, we analyze concrete resource estimates for near-term demonstrations of blind quantum machine learning. We propose a minimal B-QML implementation requiring only a $12$ qubit quantum server. To the best of our knowledge, MasonQ is the first functional and optimal universal circuit-to-brickwork-graph transpiler to implement the full brickwork transpilation process from first principles.

We prove a one-sided central limit theorem for $\log |L(\tfrac 12,\chi)|$ in a thin family of $n$-th order Hecke characters, for $n \geq 3$. The proof combines the method of Radziwiłł and Soundararajan with a recent asymptotic formula of Diaconu, Ion, Paşol, and Popa for the twisted second moment with a power-saving error term. We also obtain upper bounds of the conjectured order of magnitude for the $2k$-th moments for $0< k< 1$.

Large language model (LLM)-based multi-agent systems are increasingly applied across diverse domains, yet different applications require different forms of agent organization. Existing studies typically adopt predefined organizations, such as Star, Chain, and Tree, or learn communication graphs to improve performance on specific tasks. However, these methods are largely designed and evaluated within a limited set of application domains, providing little understanding of whether an organization effective in one domain remains suitable for others with different collaboration requirements. We present OpenDGO, a controlled benchmark and analysis framework covering six real-world domains and three collaboration settings: Sequential Dependency, Parallel Decomposition, and Information Integration. Under matched tasks, agents, tools, and resource limits, OpenDGO compares fixed and learned organizations while separately examining communication graphs, role assignments, input assignments, resource budgets, and component failures. Our results show that there is no “one-organization-for-all” solution: preferred organizations vary across applications, and even the same communication graph can yield different outcomes under different role and input assignments. These findings highlight the need for application-dependent organization design, aiming to understand which organization is suitable for a given application, under what conditions, and why.

We study periodic homogenization of fully-nonlinear second-order Hamilton–Jacobi–Bellman and Isaacs equations subject to a homogeneous Dirichlet boundary condition and the numerical approximation of the effective Hamiltonian, where the diffusion matrix is assumed to satisfy the Cordes condition. In the first part, assuming the Cordes parameter is sufficiently large, we show existence and uniqueness of $W^{2,p}$ solutions to the true cell problem, prove homogenization under minimal regularity assumptions, and establish a quantitative homogenization result. In the second part, we propose and rigorously analyze $W^{2,p}$-conforming and mixed finite element methods for the approximation of the corrector, which are then used in the approximation of the effective Hamiltonian. The key tool used throughout this work is Campanato's concept of near operators.

World Action Models (WAMs) have emerged as a promising alternative for embodied intelligence by jointly predicting future world states and robot actions. However, their heavy visual encoding and iterative generative inference incur substantial latency, limiting their applicability to high-frequency closed-loop control. Existing training-free acceleration methods typically optimize a single stage, yielding limited speedups or degraded control under aggressive reuse. In this work, we systematically profile the inference overhead of WAMs and observe abundant redundancy across Transformer computation, diffusion denoising, and consecutive policy queries. However, the safe removal of such redundancy depends strongly on its impact on action prediction and control sensitivity. Based on these observations, we introduce MARS, a training-free and plug-and-play framework for multi-level WAM acceleration. MARS selectively removes low-impact attention computation, adaptively accelerates diffusion inference according to motion granularity, and speculatively reuses predicted future visual representations across consecutive queries with online verification. Together, these complementary mechanisms provide remarkable acceleration while limiting approximation error. Extensive experiments across LIBERO, LIBERO-PRO, and RoboCasa show that MARS achieves up to $4.00\times$, $3.94\times$, and $2.10\times$ end-to-end speedups, respectively, while maintaining task success rate close to the original policy. Moreover, MARS generalizes across different model backbones and across simulation and real-robot experiments, substantially improving the efficiency–performance trade-off of WAM inference. Our code is available at https://github.com/PKU-VaLuE-Lab/MARS.

The Type II SN 2024ggi is one of the nearest core-collapse SNe to have exploded in recent decades. Its proximity has enabled extensive multiwavelength monitoring from early times through the nebular phase. Signatures of late-time interaction between the SN ejecta and hydrogen-rich circumstellar material (CSM) have recently been reported. Here we extend its study using late-time optical photometry and spectroscopy from 570 to 820 d after explosion. We investigate the emergence and evolution of late-time ejecta-CSM interaction and constrain the geometry of the interaction region and the properties of newly formed dust. Comparisons with other interacting SNe II and with synthetic spectra are presented. We model the H$\alpha$ profile with the Monte Carlo radiative-transfer code Damocles, including both gas and dust components. Spectroscopic signatures of interaction precede the photometric flattening. The spectra evolve from ejecta-dominated to interaction-dominated as H$\alpha$ develops a broad, boxy profile. The optical light curves subsequently flatten relative to the $^{56}$Co decay rate at approximately 650-670 d. The emission lines show a systematic blue-to-red asymmetry that requires a dust component newly formed within the ejecta. The inferred dust mass formed in the ejecta is $10^{-6}-10^{-5}$ M$_\odot$ if the grains are amorphous carbon or a carbon-silicate mixture, but can reach up to $10^{-3}$ M$_\odot$ for pure silicates.

We prove sharp arithmetic localization for one-dimensional quasiperiodic potentials with jump discontinuities, beyond uniform transversality. Our results include every non-constant $C^1$ monotone sampling function, even with arbitrarily large flat regions, and also certain non-monotone potentials. A key new mechanism is a symbolic unique-continuation principle: first-return words to the region where $f'>0$ have no common Dirichlet resonance, forcing eigenfunction mass to transfer away from flat or negatively sloped regions and recovering quantitative monotonicity of finite-volume eigenvalue branches.

Probability generating functions (PGFs) are a fundamental tool in mathematical epidemiology to characterize the stochastic evolution of epidemics via branching process theory. However, they are rarely used as operational tools in real-time during an outbreak, the main barrier being a lack of a systematic, computational methodology to describe epidemiological time series, such as cases or hospital admissions over time. Here, we introduce a general and computationally efficient framework for outbreak analytics based on PGFs. We first develop a method to encode joint distributions of incidences and their noisy measurements by realistic surveillance systems. Then, by transforming PGFs to cumulant generating functions (CGFs), we enable efficient evaluation of these joint distributions. We demonstrate the practicality of our approach for Bayesian inference and short-term forecasts, offering a significant computational advantage over simulation-based methods. Altogether, our framework operationalizes generating functions and paves the way for their broader adoption in computational epidemiology.

Periodically driven quantum systems exhibit a wide range of complex dynamics, including chaos. Yet, at special parameter values, their evolution can recur exactly. Several quantum protocols have recently been proposed that exploit exact Floquet recurrences to demonstrate genuine quantum advantage. Such recurrences can be studied through the arithmetic structure of the Floquet unitary. In this work, we establish a necessary and sufficient arithmetic criterion for exact recurrence and determine the minimal recurrence period when one exists. Because recurrence is a global property of the unitary, it holds for every initial state. Applying our framework requires only knowledge of the number field associated with the Hamiltonian parameters. We demonstrate the method using the kicked Ising chain, establishing exact recurrences in both Clifford and non-Clifford regimes. We further show that, in the recurrent non-Clifford regime, magic–a resource for quantum computation–is generated at intermediate times and undergoes exact periodic revivals enforced by the recurrence of the full Floquet unitary. By connecting number theory, quantum many-body dynamics, and quantum information, our work shows that exact recurrence extends beyond Clifford circuits and opens new avenues for magic generation and quantum hardware benchmarking.

We present near- and mid-infrared broadband imaging observations of the edge-on protoplanetary disk 2MASS J16281370-2431391, a.k.a. the 'Flying Saucer', obtained with NIRCam and MIRI on board JWST. These data are combined with archival optical and near-IR broadband imaging from HST, millimeter dust continuum emission from ALMA, and optical lightcurves from the K2 and TESS for a comprehensive multi-wavelength study. The JWST observations reveal a reversal of the flux ratio between the two reflection nebulae at near-infrared wavelengths (2-3 $\mu m$), which can be explained by a misaligned inner disk. For the first time, JWST reveals the bright lining along the disk edge at 2 and 3 $\mu m$, arising from forward scattering of background photons by dust grains near the $\tau\approx 1$ layer. By combining the dust lane thickness measured with HST and JWST, we find the dust grains up to at least $\sim$3$\mu$m are vertically mixed throughout the disk and have undergone significant growth. In addition, comparison of earlier HST/NICMOS J and K band images with those from JWST/NIRCam reveals variability in the scattered-light morphology, as well as measurable proper motion of the system with respect to the background stars, confirming that the Flying Saucer is co-moving with the young star population of $\rho$ Ophiuchi.

The Hilbert–Poincaré series of the Chow rings of the toric varieties of matroids, often called the Chow polynomials, and the $f$-polynomial of their boundary complexes, called the chain polynomials, have been conjectured to only have real zeros. We construct several explicit infinite families of matroids from finite geometries, whose multichain counts fail to be log-concave. They share a common geometric construction called hyperplane coalescence, together with several classical operations in projective geometry and combinatorial designs. This induces failures of log-concavity for Chow, augmented Chow, chain, and $h$-polynomials of several explicit infinite families of matroids, disproving the real-rootedness conjectures of Ferroni–Schröter, Huh–Stevens, and Athanasiadis–Kalampogia-Evangelinou from the lowest possible ranks. As an application of the same mechanism, we also give counterexamples to the log-concavity of $h$-polynomials of graph associahedra, answering in the negative a question of Sack.

We present a theory-oriented overview of the significance of charged-lepton flavor violation – one of the cleanest windows onto physics beyond the Standard Model. We also summarize the current experimental landscape and illustrate how different measurements can diagnose the underlying new physics.

We provide a $\operatorname{poly}(\log\log n)$-round randomized LOCAL algorithm for the constructive Lovász Local Lemma with polynomial criterion $pd^{c} < 1$, for a sufficiently large constant $c$. The best previous general round complexity was $\widetilde O(\log n)$. The key ingredient is a local reduction that amplifies the LLL probability exponent quadratically, while increasing the dependency radius only by a constant factor.

Attention-based multiple instance learning (MIL) pools a variable-size bag of instance embeddings into one vector. In batched training, bags are padded to a common length, and the pooled output is expected not to depend on how much padding was added or on the order in which instances are stored. This expectation holds only if padded rows are removed from both the numerator and the softmax normalizer. Common implementation idioms meet it only under side conditions. Zeroing padded features alone does not work. Masking logits with $-\infty$ fails on empty bags and on nonfinite padding. Masking with a large negative constant is exact only after floating-point underflow. We define masked attention pooling with a guarded normalizer and prove in Lean 4 with mathlib that it is invariant under any bijective reindexing of rows and under appending any finite number of masked rows with arbitrary real features and logits. We also prove that values at masked positions are irrelevant and that an all-masked bag maps to zero. The theorems hold for arbitrary finite index types and feature dimensions. Using the jax-lean certificate pipeline, we connect these theorems to the Jaxpr traced from the JAX kernel itself. Lean checks translation certificates for two concrete shapes, identifies the generated functions with the generic specification, and transfers both invariances to the imported Jaxpr's real-arithmetic semantics. All audited theorems depend only on Lean's three standard axioms. The results concern ideal real arithmetic. Floating-point execution, XLA, and the JAX tracer and importer remain outside the proof.

Dynamic spatial audio reasoning requires a model to associate changing acoustic observations with the correct source and recover its spatial state at a queried time or interval, a challenge intensified by overlapping speech and source motion. To study this problem, we introduce Sonic-Bench, comprising 2.8K first-order Ambisonics clips and 28.8K target-specific question-answer pairs across 480 simulated indoor scenes. The benchmark covers localization, distance estimation, and motion reasoning in single- and dual-source settings. We further propose SonicWorld, which integrates physical, learned acoustic, and semantic features into persistent source states through learned transitions and recurrent updates, and projects them into an Omni LLM for spatial reasoning. Compared with Spatial-Omni on the Sonic-Bench test split, SonicWorld improves direction accuracy from 31.98% to 34.69% and reduces azimuth error from 57.22{\deg} to 48.01{\deg}. In zero-shot transfer to Spatial LibriSpeech, SonicWorld retains strong localization performance, achieving 73.98% direction accuracy and 19.29{\deg} azimuth error, compared with 27.14% and 70.74{\deg} for Spatial-Omni.

Automated alpha factor discovery is critical for modern quantitative research. While large language models (LLMs) have increasingly been integrated into quantitative workflows, existing agent-based approaches remain highly susceptible to severe backtest overfitting. To address this challenge, we propose EvoQuantLab, a training-free, dual-loop self-evolving framework for robust factor discovery. Instead of relying entirely on LLM generation, EvoQuantLab deploys an inner genetic-programming (GP) loop that dramatically improves token efficiency while evolving typed factor expressions under structural and diversity constraints. An outer diagnosis loop then systematically audits evidence across cycles to drive protocol-level improvements. Furthermore, our evaluation pipeline applies multi-metric validation to rigorously filter out spurious factors before deployment. Extensive out-of-sample experiments across both daily and hourly frequencies – covering equities and cryptocurrency – demonstrate the robustness of EvoQuantLab. Specifically, on daily CSI 500 and S&P 500 tasks, EvoQuantLab achieves leading annualized returns of 18.34% and 21.30%, consistently outperforming existing agent baselines. On high-turnover hourly cryptocurrency data, EvoQuantLab delivers a 37.91% annualized return while effectively avoiding execution collapse.

In this paper we deal with the theory of Regular Lagrangian Flows, as initiated in [29] and axiomatized in [2]. In the first part of the paper we show in Theorem 4.3 (see also Corollary 4.5) that the decomposition of $\mathcal{L}^{1+d}$-almost all the space time in a family of (essentially) disjoint characteristics, the technique at the basis of the well posedness in [1] (for planar, divergence-free and autonomous vector fields), and in [13] (for vector fields having a suitable regularity in space, including BV vector fields) is not only sufficient for well posedness, but also necessary. This shows that in many cases the typical uniqueness statement of the DiPerna-Lions theory, namely that the path $\mathbb{X}(\cdot,x)$ is (essentially) unique given the initial position $x$, can, as in the classical theory, be strengthened by saying that the paths $\mathbb{X}(\cdot,x)$ (essentially) do not branch. As the simple Example 1.1 shows, when we consider vector fields with singular divergence well posedness results may hold only for solutions that do not change sign. In the second part of the paper we revisit [8,9] obtaining a well posedness result for special vector fields of bounded deformation and nonnegative solutions, under a mild regularity assumption (5.3) with respect to the time variable, weaker than the space-time $SBD$ regularity assumption made in [9] for nearly incompressible vector fields. Finally, we revisit carefully the constructions of Section 9 of [13], to see how they provide existence and uniqueness for (1.2) assuming $BV$ regularity in space, in the class of nonnegative bounded solutions.

Egocentric video provides a continuous first-person record of everyday activities, making it a natural foundation for wearable AI assistants. Unlike offline video understanding, streaming systems must process observations as they arrive, while queries may refer to experiences from the distant past. Recent work has begun to explore whether information can be recalled across long temporal gaps. Yet remembering how far is only part of the challenge: recurring objects, actions, and locations also require models to remember exactly which detail belongs to which event. We introduce EgoProbe, a benchmark that evaluates streaming egocentric memory along these two complementary dimensions: long-range retention, i.e., how far, and event-specific recall under interference, i.e., how exact. Built on long-form egocentric videos, EgoProbe uses an event-grounded data engine to extend recall intervals, identify related events, and construct event-grounded distractors, followed by human verification. It contains two subsets: EgoProbe-Base, which evaluates long-range recall without intervening related events, and EgoProbe-Echo, which challenges models with similar intervening events and event-grounded distractors. EgoProbe-Echo adopts coarse-to-fine multi-turn probing: the first turn evaluates coarse-grained event recall, while the second tests whether the model can retrieve the target-specific detail associated with the designated event. Extensive evaluation across diverse models reveals substantial limitations in long-range recall, with further challenges in recovering target-event details among related experiences. Even when models correctly answer coarse-grained questions, they often fail to recall the specific details of the designated event. EgoProbe exposes this underexplored failure mode and provides a testbed for advancing long-range and exact memory in streaming egocentric video understanding.

We consider the Frank–Wolfe algorithm for solving variational inequalities over compact polytopes under a monotone $C^1$ operator $\Phi$. The linear minimization oracle returns vertices, and we assume a coercivity condition on the Jacobian of $\Phi$ at a solution. We prove last-iterate convergence to the unique solution at rate $O(k^{-\min\{\alpha,1\}})$ for step sizes $\gamma_k=\alpha/(k+\beta)$ with $\beta\geq\alpha>0$. The bound holds uniformly over starting points and vertex tie-breaking. In particular, both $1/(k+1)$ and $2/(k+2)$ give $O(k^{-1})$ distance. A matching lower bound shows that this distance guarantee is worst-case order-optimal among prescribed admissible step-size schedules. We also obtain rates $O(k^{-\min\{\alpha,1\}})$ for the Frank–Wolfe gap and $O(k^{-\min\{\alpha,2\}})$ for the dual gap. These yield $O(\varepsilon^{-1})$ and $O(\varepsilon^{-1/2})$ calls to each oracle for sustained gap accuracy $\varepsilon$ when $\alpha\geq1$ and $\alpha\geq2$, respectively, with instance-dependent constants. We also treat more general prescribed step-size schedules.

The rapid proliferation of autonomous AI agents in decentralized ecosystems challenges existing identity paradigms. While human identity is traditionally anchored in biological and/or self-asserted attributes and government credentials, AI agents lack a standardized definition of selfhood, creating critical gaps in trust and accountability. This paper introduces a novel framework for establishing Decentralized AI Identity rooted in Self-sovereign identity (SSI) principles. We propose a formal model that clearly distinguishes human users and AI agents, enabling distinct verification logic for each class while maintaining a unified identity calculus. The central to our contribution is the ABCD Framework, a multi-layered approach to agent identification and verification: (A) Algorithmic Fingerprint, which binds the identity to static model architectures and provenance; (B) Behavioural Fingerprint, which verifies dynamic performance metrics over time; (C) Cryptographic Identity, which anchors the agent via Decentralized Identifiers (DIDs) and (D) Delegation, which cryptographically binds agent actions to respective human accountability. By orthogonalizing these dimensions, we model how systems can enforce granular trust policies ranging from simple authentication to complex liability assignment, thereby solving the black box identity problem in the autonomous economic activities of AI agents.

Tool-augmented language models ground their responses in external tool outputs, improving reliability beyond parametric knowledge alone. However, even when the correct tool is called and returns accurate information, models may still contradict such outputs, omit critical details, or generate unsupported claims. Existing hallucination benchmarks for tool-augmented dialogue primarily focus on the tool-calling stage, evaluating whether the correct tool and arguments are selected, while overlooking errors that arise during post-tool response generation. To address this gap, we introduce ToolHACE, a span-level benchmark for hallucination detection in tool-augmented LLM responses, covering five fine-grained hallucination categories. Through extensive experiments with modern hallucination detectors, we show that post-tool-call hallucinations are widespread and remain challenging to detect. Our results further demonstrate that effective detection requires training on specialized tool-augmented corpora, while transfer from tool-agnostic hallucination datasets performs poorly in this setting. These findings highlight the need for dedicated benchmarks and models for reliable hallucination detection in tool-augmented language systems.

Full-duplex spoken language models (FD-SLMs) support simultaneous listening and speaking, but often lag behind half-duplex spoken language models (HD-SLMs) in general capabilities. We propose Dialogue-to-Duplex (D2), a framework that converts pretrained HD-SLMs into high-capability FD-SLMs at fine temporal granularity. D2 adapts the original audio encoder to streaming through decoder-free representation distillation and learns full-duplex interaction through supervised fine-tuning. We systematically study the effects of chunk size on full-duplex interaction, general capabilities, and inference computation. We apply D2 to two distinct HD-SLM architectures, Qwen3-Omni and LLaMA-Omni 2. At a 12.5Hz update rate, Qwen3-Omni-D2 achieves 99.2% turn-taking success with 521-ms latency, 99.5% interruption success, and a state-of-the-art VoiceBench score of 70.1.

The Boltzmann equation is the fundamental kinetic bridge between molecular mechanics and fluid behaviour. It converts binary encounters into the evolution of a velocity distribution, underlies rigorous routes from hard-sphere dynamics to Euler and Navier–Stokes–Fourier equations, and remains indispensable when continuum descriptions fail, from hypersonic shock layers and atmospheric re-entry to rarefied multiscale flows. Yet its nonlinear collision term is conventionally represented by an infinite three-index tensor of collisional brackets, with apparently new coefficients at every polynomial order. Here we prove that this entire hard-sphere tensor contains only one primitive collision law: the exact rank-two stress-production vertex $S$. Every polynomial collision vertex is obtained from $S$ by a finite sequence of universal differential and tensor operations, and every conventional bracket follows by differentiation. Thus the interaction physics and its representation separate exactly: all hard-sphere-specific information is concentrated in $S$, whereas the hierarchy above it is universal algebra. A blind eighth-order test in a Mach-5 shock agrees with independent collision sampling and strongly amplifies a weak kinetic precursor. The hard-sphere hierarchy is infinite in dimension, but its primitive collision content consists of a single scalar law.

Distribution networks rely on conservation voltage reduction (CVR) and network topology reconfiguration (NTR) to manage demand, distributed energy resources (DERs), and tighter operating margins. Yet these strategies are typically deployed independently, despite coupled effects on feeder voltages, losses, and loading. This paper addresses that gap by developing a day-ahead mixed-integer second order cone programming (MISOCP) framework that jointly optimizes feeder head voltage control and network reconfiguration. The formulation incorporates AC branch flow constraints, ZIP load models, DERs, battery energy storage systems, and multi substation radiality. Using modified IEEE 33 bus and 123 bus systems, four configurations isolate the individual and coordinated effects of CVR and NTR. On the 33-bus system under mixed ZIP loading, NTR reduces active energy loss by 2.50%, while coordinated operation reduces it by 2.91% relative to SDN and produces a 2.46% CVR induced active load reduction relative to SDNTR. Under constant impedance loading, coordinated operation reduces active energy loss by 17.65% relative to SDN, while CVR reduces active load by 14.61% relative to SDNTR. DER portfolio scaling shows a nonmonotonic coordinated load reduction response, strongest at 20% penetration and decreasing at higher levels. On the 123 bus system, NTR reduces losses by 19.3%, while CVR reduces voltage dependent load energy by 2.3 to 2.4%. Under loading stress, SDN becomes infeasible at 120% loading, whereas CEDNTR remains feasible. Overall, the results demonstrate complementary, operating condition dependent benefits shaped by load composition, DER portfolio scaling, feeder topology, voltage margins, and source constraints, highlighting the value of joint optimization.

We consider the existence and uniqueness of positive, bounded stationary solutions of the Fisher-KPP equation with Dirichlet boundary conditions. We establish that stationary solutions are unique, and exist if and only if the generalised principal eigenvalue is strictly positive (supercriticality), in dimension at most $6$. This is sharp: we exhibit examples both of non-uniqueness and of existence at criticality in dimension $7$ or higher, including for the classical reaction $f(u)=u-u^2$. This proves a conjecture of Berestycki and Graham in the affirmative for dimension at most $6$, and in the negative for dimension at least $7$. We thereby show that branching Brownian motion cannot survive globally without surviving locally in dimension $6$ or lower, but can do so in dimension $7$ or higher, mirroring the classical transition of Brownian motion from recurrence to transience from dimension $2$ to $3$. We further show that relaxing the strong-KPP condition results in a more general sharp dimension threshold for the uniqueness/non-existence result. These results are valid without any regularity assumptions on the domain boundary. As a corollary, we show that solutions of the evolution reaction-diffusion equation are always convergent in the long run in dimension at most $6$, whilst we exhibit non-convergent solutions in dimension larger than $6$.