Papers

Multi-agent LLM systems (MALS) introduce a privacy-leakage problem that conventional sensitivity-based defenses miss, since information disclosed to one authorized agent can propagate through routine coordination to an unauthorized one, without compromise or malicious behavior. This motivates topology-aware enforcement that blocks unauthorized propagation while preserving authorized disclosure. We evaluate 485 scenarios across coordinator-worker, peer-to-peer, and hierarchical topologies, instrumenting seven communication channels and measuring surface leakage and disclosure to topology-introduced recipients. We introduce RECONS, a Detect -> Decide -> Transform sanitizer conditioning intervention on recipient and execution context rather than sensitivity alone. Topology changes where protected information propagates, with disclosure to topology-introduced recipients rising from 0% to 52.2% while surface leakage stays nearly flat at 60.6-62.8%. This effect persists across four generator models and a second orchestration framework, though magnitude and relay paths differ; framework choice separately drives a 150x leakage spread, so topology alone is not sufficient. RECONS reduces residual disclosure from 96.7% without sanitization to 29.25%, preserving 94.1% of authorized disclosures versus 20.5% under blanket redaction. Detection coverage is the dominant bottleneck, accounting for 95.5% of residual disclosures. These results show that privacy enforcement in MALS must reason about the recipient and communication path realized at runtime, not sensitivity or topology assumptions alone.

E-commerce user preferences evolve dynamically within sessions, exhibiting concurrent and multi-centric interest distributions. While existing multimodal sequential recommendation methods leverage global attention to compress historical interactions, they inadequately capture the concurrent nature of multi-interest behaviors and fail to model the underlying multi-centric distribution of user intent. To tackle this issue, we propose OT-FlowRec, an optimal transport-guided multi-bridge flow matching framework that explicitly models multi-interest distributions to facilitate multimodal sequential recommendation. Unlike single-path generative models, OT-FlowRec constructs a mixture of parallel, interest-specific transport flows to model the multi-centric distribution characteristics, where each flow preserves a distinct user interest cluster via an optimal transport plan. Then, a geometric transport mechanism is designed to establish minimum-cost paths from the latent multi-interest distribution to target preference prototypes to provide multi-interest awareness. Moreover, a progressive time-sampling warmup strategy dynamically biases optimization weights toward the final states of the generation process, bridging the gap between continuous global distribution fitting and practical top-$k$ ranking metrics. This approach achieves explicit interest disentanglement, ensuring the preservation of a multi-peaked preference representation instead of collapsing it into a unimodal average. Extensive experiments on three public datasets demonstrate that OT-FlowRec outperforms existing state-of-the-art baselines.

Models of curvature-driven membrane sorting couple composition directly to membrane bending elasticity. Here we show that shape deformations can destabilize a homogeneous state without this composition-dependent mechanical coupling. We analyze the eigenspectrum of the Laplace-Beltrami operator on deformed spheres analytically, and verify it numerically. As the deformation amplitude increases, the spectral degeneracy breaks, and the lowest nonzero eigenvalue decreases substantially. Using Cahn-Hilliard dynamics, we show that this eigenvalue softening provides a purely geometric route to phase separation.

Recent diffusion- and conditional flow matching (CFM)-based emotional voice conversion (EVC) systems achieve strong conversion quality. However, they typically rely on multiple sampling steps, because the conditioning specifies which emotion to impose while its acoustic realization is left to the sampler. In this paper, we propose Prime-EVC, a one-step expressive EVC architecture based on emotion-primed flow matching. Our key idea is to reallocate the emotional conversion between the conditioning and the sampler: a FiLM-fused speaker-emotion style, an emotional variance adaptor, and direct emotion and spectro-temporal supervision assemble an emotion-rich conditioning upstream, rendering the residual conversion left to the CFM decoder attainable within one Euler step. Experiments on the ESD corpus demonstrate that single-step Prime-EVC surpasses five representative EVC systems on every quality metric and exceeds 4- and 100-step DurFlex-EVC in subjective naturalness and emotion while running 3.4–50 times faster than both.

Semantic operators allow users to filter unstructured data using conditions expressed in natural language, but existing systems typically invoke an LLM for every input tuple. Analytical workloads often contain repeated or related filters whose results could be reused. Such reuse is risky because it requires inferring whether filter conditions are equivalent, whether one implies another, or whether they are mutually exclusive. An incorrect judgment can omit qualifying tuples or include nonqualifying ones. We introduce SemReuse, a system for safely reusing previous semantic-filter results. SemReuse stores each result as a materialized view and compares new filters with existing views to identify tuples that can provisionally be accepted or skipped without another LLM call. Because these decisions rely on a fallible language reasoner, SemReuse audits every rewritten result. Its pooled stratified audit uses exact finite-population bounds to provide jointly valid per-query recall and precision guarantees. If the requested guarantees cannot be established, SemReuse evaluates additional tuples and progressively approaches full evaluation. Thus, incorrect relation judgments affect efficiency rather than the validity of the reported guarantees. Experiments on large labeled corpora and real LLM executions show reductions of up to 15.4x. They also identify cross-filter inconsistency as the main source of repair cost.

Constant-step stochastic gradient descent with momentum (SGDM) augments the parameter recursion with a momentum state that carries geometrically decaying memory of past stochastic gradients. We study this coupled recursion as a nonlinear time series and develop a framework for its stationary behavior and distributional limits. The joint parameter-momentum process forgets its initialization geometrically under a finite $p$th moment for $p > 1$, yielding a unique stationary causal solution. Under a second-moment condition, this contraction leads to an invariance principle and quenched Gaussian limit for averaged SGDM, while a small-learning-rate analysis gives a Gaussian limit for the last iterate. In a stochastic-curvature quadratic model, we further study how the rate of initialization forgetting relates to stationary variance and averaged fluctuations.

The Zak-OTFS carrier waveform is a pulse in the delay-Doppler (DD) domain, and given the input-output (I/O) relation at one DD point in a frame, we can predict the I/O relation at all other points. While it is simple to acquire the effective wireless channel with Zak-OTFS, the cost of embracing inter-carrier interference is equalization complexity. The cost of linear minimum mean-square error (LMMSE) equalization grows cubically with the frame size. We describe how to use channel knowledge to reduce equalization complexity. For any pulse shaping filter, and for fractional delays and Dopplers, we show that the DD channel matrix is unitarily similar, through the discrete Zak transform, to a time-domain (TD) matrix that is a weighted sum of cyclic delay and Doppler operators, where the weights are the taps of the effective channel. We also obtain a dual frequency-domain (FD) form through an additional Fourier transform. The TD matrix is banded with a width set by the delay spread that is independent of the Doppler spread, whereas the FD matrix is banded with a width set only by the Doppler spread. We design a receiver that reads off the two widths from the channel estimate, selects the cheaper domain, and solves the banded system exactly, using a bordered Cholesky factorization that treats the quasi-periodic wrap-around without sacrificing degrees of freedom. Filters that decay slowly need a few preconditioned conjugate gradient steps. We show that the complexity of equalization becomes linear in the frame size. Simulations match direct DD-LMMSE error rates with three to four orders of magnitude fewer multiplications. A single receiver handles channels with very different delay and Doppler characteristics.

Orbital optimization within the variational quantum eigensolver (VQE) framework is useful for improving active-space quality and accurately capturing electron correlation with shallow quantum circuits. The orbital-optimized unitary coupled cluster (OO-UCC) method [W. Mizukami et al., Phys. Rev. Res. 2, 033421 (2020)], in its original formulation, employs the orbital gradient and Hessian in a Newton–Laphson procedure. In this study, we propose sequential orbital-optimized unitary coupled cluster doubles (SOO-UCCD), extending the gradient-free sequential minimal optimization approach [K. M. Nakanishi et al., Phys. Rev. Res. 2, 043158 (2020)] to orbital rotation parameters. Based on the frequency structure implied by the algebraic properties of the orbital rotation generators, our method determines each orbital rotation angle from a nine-point energy profile. The energy landscape is evaluated by classically transforming the Hamiltonian integrals and contracting them with the reduced density matrices already measured for the VQE energy evaluation. This allows for orbital optimization without evaluating the orbital gradient or Hessian. By building on the core benefits of the OO-UCC framework, our method provides a gradient-free and hyperparameter-free orbital-optimization procedure. State-vector simulations for LiH in the STO-3G basis show that SOO-UCCD reproduces UCCSD-level accuracy along the bond-stretching curve and exhibits macro-iteration convergence comparable to that of L-BFGS-based orbital optimization.

This paper, we introduce and study biatomic systems in Hilbert spaces, a natural generalization of classical atomic systems; this new concept allows us to represent bounded linear operators using two Bessel sequences simultaneously. In addition, we establish equivalent characterizations of these systems, study their relationship with Bessel biframes and demonstrate the stability of the class under natural operations: duality with respect to the adjunct, orthogonal projections, unit operators and concatenation.

Expectiles are tail-sensitive distributional summaries with important applications in financial risk measurement and forecasting, yet statistical theory for their online estimation from dependent data remains limited. We study a one-pass, stochastic-gradient algorithm with constant learning rate $\gamma$ for estimating the marginal expectile of a stationary causal process. The recursion admits a unique stationary causal solution and geometrically forgets its initialization. Under short-range dependence, its last iterate is asymptotically Gaussian at the $\sqrt{\gamma}$ scale, with variance governed by the population curvature and the long-run variance of the expectile score. For long-memory linear processes the scale changes to $\gamma^{\beta-1/2}\ell(1/\gamma)$, with a Gaussian limit arising from a fractional Brownian motion integral. We further derive the joint long-memory limit for multiple expectile levels and characterize its limiting covariance structure. Various numerical experiments corroborate the predicted Gaussian approximations and regime-specific fluctuation scales.

We study the two-dimensional non-rotating primitive equations with positive horizontal and vertical viscosity and without thermal diffusion. Our main results are fourfold. First, for every integer \(s\ge4\), we prove that sufficiently small, compatible, doubly periodic \(H^s\) perturbations of a stably stratified rest state with an affine temperature profile generate unique global strong solutions; the horizontal velocity and temperature remain uniformly small at the initial Sobolev order despite the derivative loss in the full diagnostic vertical velocity, and strict stratification persists. Second, we establish an inverse-map conservation law that determines the terminal temperature solely from the initial temperature: the terminal label is identified as the normalized increasing rearrangement of the initial label modulo the vertical period, and the terminal perturbation admits a quadratic expansion with cubic remainder. Third, the limiting equilibrium uniquely minimizes the quadratic perturbation energy among compatible, strictly stratified states with the same periodic label distribution. Finally, we establish sharp algebraic decay in suitable lower-order Sobolev norms for both velocity components and for the temperature and pressure differences from equilibrium. Exact nonlinear solutions provide matching lower bounds, establishing optimality for uniform estimates over the small-data class. The proofs combine weighted energy methods, spectral analysis, and inverse-map identities.

We develop explicit second-order particle-in-cell (PIC) methods for the Vlasov–Ampère and Vlasov–Maxwell systems using the scalar auxiliary variable (SAV) approach. Two schemes are proposed for each system: a predictor-based scheme and a symmetric splitting scheme using a scaled electric field. The methods exactly preserve the discrete Gauss law and a modified total energy. Numerical experiments for electrostatic and electromagnetic problems demonstrate the expected dynamics as well as the conservation properties of both invariants.

Reinforcement learning improves tool-use agents, yet fine-grained credit assignment remains challenging even with step-level feedback. An observed error may be inherited from an earlier decision, while multiple responsible decisions may share the same downstream consequence or participate in later recovery. We introduce Error-Chain-Aware Optimization (ECHO), a responsibility-aware credit assignment framework that separates responsibility identification from credit allocation. A frozen judge combines retrospective trajectory analysis with decision-time assessment from the policy-visible prefix to distinguish newly introduced errors, inherited consequences, missed corrections, and successful corrections. ECHO then counts shared downstream consequences once across responsible decisions and constrains rewards for repairing self-induced errors through source-funded recovery, producing bounded action-level supervision alongside terminal supervision. Experiments on six diverse tool-use benchmarks at both 4B and 8B scales show strong and consistent improvements over the compared baselines, with ECHO achieving the highest score on five of six benchmarks at each scale. These results support decision responsibility as a useful basis for fine-grained credit assignment in tool-use agents. Our code is available at https://github.com/xid32/ECHO.

A printed tapered-slot coupling probe with a partially inserted 12-mm wire element is characterized for short-range microwave coupling through a brain-mimicking agar–gelatin–saline phantom and ex vivo brain. Simulated and measured free-space $S_{11}$ responses agree over a measured $-10$-dB band spanning 5.78 to 6.86~GHz, corresponding to a 1.08-GHz bandwidth and approximately 17.1~percent fractional bandwidth. In a controlled two-probe experiment, the phantom was introduced and removed while the probe arrangement and measurement conditions were retained. This comparison was repeated under the same retained arrangement, with the same general $S_{21}$ differential behavior observed across repetitions. Near 6.3~GHz, measured $S_{21}$ was approximately $-25$~dB with the phantom present and approximately $-40$~dB in air, corresponding to an $\approx 16~\mathrm dB$. Ex vivo goat brain measurements repeated more than five times showed reproducible behavior. Across 5.78–6.86~GHz, the ex vivo goat-brain $S_{21}$ response closely followed that of the phantom, with an approximately figure-derived maximum operating-band difference of about 1.5~dB. The observed increase in $|S_{21}|$ is interpreted as a property of the complete probe–medium–probe system, including loading, mutual coupling, interfaces, geometry, propagation, and material loss. The measurement does not uniquely identify a tissue-intrinsic mechanism.

A hereditary graph class has strongly edge-sublinear separators if, for some constant $0 \leqslant b < 1$, every graph in the class with $m$ edges admits a balanced separator of size $\mathcal O(m^b)$. We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding particular induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].

Let $\NT(m,n)$ be the total number of parts in the partitions of $n$ with rank $m$, and let $\MW(m,n)$ be the total number of ones in the partitions of $n$ with crank $m$. Using the uniform generalized-rank estimate of Liu and Zhou, we establish asymptotic formulas for $NT(m,n)$ and $\MW(m,n)$. Put $\beta_n=\pi/\sqrt{6n}$ and $L_n=\log(1/\beta_n)$. For every fixed $A>0$, uniformly for $|m|\le A\sqrt n$, we prove \begin{align*} \NT(m,n)&=\frac{p(n)L_n}{4}\sech^2\!\left(\frac{\beta_nm}{2}\right) +O_A\!\bigl(p(n)\log L_n\bigr) \intertext{ and} \MW(m,n)&=\frac{p(n)}4\log(1+e^{-\beta_nm}) \sech^2\!\left(\frac{\beta_nm}{2}\right) +O_A\!\bigl(p(n)\sqrt{\beta_nL_n}\bigr). \end{align*}

Planet formation requires growth over 12 orders of magnitude in size, from micron-sized dust grains to fully formed planets. The formation of km sized planetesimals is the most challenging stage, where radial drift and fragmentation rapidly remove meter- sized solids from the protoplanetary disc. Overcoming this barrier requires favourable conditions for streaming instability to concentrate solids. These problems are exacerbated in binary star systems, where gravitational perturbations and disc truncation reduce the efficiency of planetesimal formation pathways. Planetesimal capture provides an alternative mechanism where unbound planetesimals are captured by the protoplanetary disc through gas-drag, potentially bypassing the most restrictive growth stages. We investigate this process in circumstellar and circumbinary discs using over 30 million numerical experiments across a range of binary separations. For circumstellar discs, capture of large planetesimals is suppressed below 50 au, with the strongest reduction at around 10 au, broadly consistent with the observed decrease in planet occurrence in binaries. Tight binaries can still capture O(1) km-sized planetesimals, increasing to O(10) km-sized in wider systems during the birth cluster's lifetime. Circumbinary discs are much less efficient, with capture rates dropping to around 1 percent of the single-star case for binaries above 1 au and becoming negligible for large planetesimals at wider separations. Overall, planetesimal capture provides a supplementary channel for delivering solids to binary systems and mitigating inefficiencies in in-situ planetesimal formation.

Neuromorphic sensing and computing promise low latency and high energy efficiency for robotics, yet most event-based visual place recognition (VPR) pipelines reintroduce dense, frame-like computation downstream of an inherently sparse sensor, forfeiting the sensor's latency advantage. In this paper, we address the problem of resolving an event-based VPR query in tens of microseconds on a commodity CPU. We train a two-layer spiking neural network (SNN) with additive spike-timing-dependent plasticity (STDP), which drives the learned weight matrix towards a strongly bimodal distribution, amenable to aggressive magnitude pruning. At inference, our pipeline exploits this sparsity by reading only the pruned weights corresponding to the query's active pixels. As surviving weights share a near-uniform magnitude, each neuron's score reduces to an integer count of matching synapses instead of a weighted sum, lowering per-query latency. This computation is small enough to remain resident in a CPU's fast on-chip cache. On three event-based VPR benchmarks, our sparse SNN exceeds the recall of LENS, an existing event-based SNN, while reducing per-query latency by 5.5-6.2x to tens of microseconds. It matches the recall of a dense variant of our network and of the sum-of-absolute-differences (SAD) baseline, while reading 10x fewer weights than the dense variant. We further characterise how recall and latency scale with the number of active pixels and reference places. These results suggest that the sparsity of both event-based input and learned weights can already be exploited for low-latency inference on conventional processors.

The increasing event complexity and data rates foreseen for future LHC coinditions motivate a transition from selecting proton-proton ($pp$) collision events by reconstructing predefined signal candidates to constructing a reduced data stream by interpreting the relevant event features in a signal-agnostic way. We explore the capabilities of deep-learning-based architectures on heavy-flavour physics using LHCb as a case study. Graph-based full-event interpretation techniques address the problem by representing visible products of $pp$ collisions as nodes of a graph, and reconstructing heavy-hadron decay chains hierarchically. A new neutral-particle-aware architecture extends the input data from charged tracks to calorimeter clusters, and uses metric learning to clusterize particles from the same decay chain in a common latent space. Tests on inclusive simulated $pp\to b\bar b$ events show that this approach retains its ability to reconstruct decay chains across a broad range of topologies and multiplicities. We discuss the resulting physics opportunities, with a focus on inclusive $b\to s\ell\ell$ measurements and on searches for exotic hadrons.

Layer-wise post-training quantization methods let each layer compensate for the quantization error inherited from earlier layers. We ask under what assumptions such compensation guarantees a network output error no larger than without it. For linear networks of any depth, with the required calibration Gram matrices invertible, if the rounding error of each layer has zero conditional mean and a deterministic second-moment map common to both schemes, as under subtractive dither on an unbounded grid, then compensation with strengths in $[0,1]$ fixed in advance gives a mean-square output error no larger than no compensation, each scheme being followed along its own trajectory. The exact gain separates error removed directly from reduced excitation of later rounding noise. Outside this setting the comparison can fail. With rectified linear activations it fails for two independent reasons: noise changes activation states, and, even when no state changes, the correction moves error from samples on which a unit is inactive to samples on which it is active. With stable activations, commutators between the calibration projection and the activation patterns bound the excess. With a bounded codebook, even unique exact layer-wise minimizers with no overload can give a larger output error. For fixed rounding errors it already fails for two scalar linear layers, refuting a published universal guarantee. An exact residual identity gives the necessary and sufficient condition on a common layer input. All these comparisons hold the calibration input fixed. On two 8B models at 4 bits, fixed half-strength compensation beat uncompensated rounding in every model, text and draw tested, yet no rule for choosing the strength beat a layer-wise rule consistently, and lowering the full-network loss on the data used to choose did not reliably lower it on new text.

Households compare their living standard with others' and dislike changing it. We study consumption and investment when felicity depends on consumption relative to a benchmark, the population's geometric average consumption, and cuts in felicity weigh more than increases. Asset returns are exogenous. For finitely many types and arbitrary initial wealth and inherited standards, a mean field equilibrium exists under a weak interaction condition, and for fixed budget multipliers the benchmark is the fixed point of a contraction. In a complete market with common risk, a mean field equilibrium at empirical type frequencies is an exact Nash equilibrium of the finite game, for any preferences over relative consumption. We bound the gain from deviating when plans computed at another composition are used. We compute equilibria in which groups with different wealth, inherited standards, and loss aversion revise spending at different dates. With identical households and common risk, the unique symmetric equilibrium is the policy of a single loss averse household with modified curvature. In a baseline example, ignoring the inherited standard costs up to 17% of wealth, while small errors about the composition of the reference group cost less than 0.5%.

Entanglement witnesses are a key instrument in determining the entanglement of unknown bipartite qubit systems without requiring a full tomography. Riccardi et al. (2020) proposed a set of two-qubit witnesses, denoted $\{W^3\}$, which require a set of local measurements in three bases. In this work we propose an additional set of witnesses, denoted $\{W^5\}$, that build on $\{W^3\}$ and require measurements in two additional bases. We present an adaptive two-step method that uses the measurement results obtained for $\{W^3\}$ to select which $W^5$ to evaluate. We computationally demonstrate that our adaptive two-step protocol can identify 72% of entangled states generated according to the methods of Roik et al. (2021) while requiring measurements in only five of the nine bases needed for full quantum tomography. Additionally, we experimentally verify the behavior of both sets of witnesses using polarization-entangled photon pairs.

In this paper, we focus on the examples constructed by Kanenobu and provide new family knots with the same HOMFLYPT polynomial invariants, which are distinguished by the Kauffman polynomial.

Certified robustness is critical for deploying neural networks in safety-sensitive settings, but computing exact certificates typically requires solving nonconvex optimization problems. Practical verifiers use convex relaxations: linear programming (LP) relaxations are scalable but often too conservative, whereas semidefinite programming (SDP) relaxations can be substantially tighter but are computationally expensive. We introduce a hierarchy of second-order cone programming (SOCP) relaxations that provide stronger certificates than LP while avoiding the cost of global positive-semidefinite constraints. Our construction combines convex-hull relaxations of ReLU activations, selective McCormick lifting over certified variable bounds, and second-order cone constraints induced by 2-by-2 principal minors. Adding these constraints progressively yields a monotone hierarchy of increasingly tight bounds with a controllable computation-tightness trade-off. On fully connected and convolutional networks on MNIST and CIFAR-10, SOCP-based verification improves certified robust accuracy over LP-based verification and is competitive with alpha,beta-CROWN, while remaining orders of magnitude faster than SDP-based verification. These results position selective second-order constraints as a practical middle ground between scalable LP-based and tight SDP-based certification. Finally, we introduce class-optimized robust evaluation (CORE), which applies tighter relaxations only to target classes not certified by cheaper ones. On the fully connected MNIST benchmark, CORE variants match SDP-cert's certified robust accuracy while reducing average verification time by up to 86.30%.

The rapid deployment of agentic AI has introduced complex challenges for the ethics and governance of AI systems. Agents built on large language models act through tools on behalf of people, and each deployment case brings its own instructions, policies, evidence, and stakeholders, so alignment must be formed case by case. To this end, this work proposes agentic reflective equilibrium (ARE), a computational reflective equilibrium framework that serves as an ethical alignment scaffold in the agent harness. Drawing inspiration from the reflective equilibrium of John Rawls, the scaffold links principles from the system prompt and operator policy, considered judgments, tool evidence, and candidate actions through typed support and attack relations, with provenance encoding the instruction hierarchy. The agent acts on an equilibrium of this state and calls tools or asks questions only while doing so is worth its cost, unless a due-diligence mandate requires them. Governance enters through value priorities, source authority, prohibitions, human-in-the-loop triggers, and mandates, and certificates attribute each action to the sources whose commitments drove it. We show that equilibria are Nash equilibria of a mutual-adjustment game and establish monotonicity, lexical priority, stability certificates, and a quarantine theorem for prompt injection. Two case studies illustrate the framework: a computer-use assistant told to win a refund "whatever it takes" files an honest warranty claim, refuses a fake review, and ignores an injected request for personal data; a hiring agent showcases how authority, oversight triggers, audit mandates, and hard prohibitions shape discrimination, privacy violations, and escalation. The framework offers traceability, coherence, and adaptivity, facilitating safe, secure, and trustworthy agentic AI.

The results from [Fluid Dyn 61, 20 (2026)], concerning the generalized Chapman-Enskog method and a nonlocal (i.e., non-diffusive, spatially integral) viscous stress tensor in the Navier-Stokes equation, are extended to the case of arbitrary gradients of not only hydrodynamic velocity but also temperature. The resulting equations simplify the description of tangential discontinuities and separated flows. For the specific case of an incompressible medium, a nonlocal vorticity transport equation is derived that is structurally identical to the Biberman-Holstein equation for resonant radiation transport in plasmas and gases. A power-law form has been determined for the velocity distribution function of long-free-path vorticity carriers that satisfies empirical Richardson t^3 law for the mean square of relative separation of a pair of particles in a turbulent liquid or gaseous medium.

Modern inference systems rely on batching to exploit parallel execution and amortize serial execution overheads, but batching creates a fundamental online scheduling tradeoff: serving requests immediately reduces request queuing delay, while waiting can form larger batches that better utilize parallel hardware and improve serving efficiency. We study this tradeoff in a single-server online batching model with bounded batch capacity, fixed batch processing time, and the objective of minimizing total flow time. Our focus is on the value of finite lookahead into future arrivals over a purely online setting for scheduling. We show that the benefits of lookahead depend on the arrival model. In the adversarial setting, finite perfect lookahead has inherent limitations: for any bounded lookahead window, every online algorithm remains separated from the offline optimum by a constant factor. Thus, worst-case arrival sequences can prevent perfect knowledge of future events from fully overcoming online uncertainty. In contrast, under Poisson arrivals in the stable regime, finite lookahead is much more powerful. Although the best distribution-aware online algorithm has a nonzero asymptotic gap from the offline optimum, lookahead closes this gap exponentially fast in the window length. We prove matching upper and lower bounds up to constants in the exponent. Together, these results give a tight characterization of when lookahead can close the online–offline gap, incorporating insights from the competitive analysis of online algorithms into queueing-theoretic steady-state bounds. We also study imperfect predictions, showing that the benefit of lookahead degrades gracefully with prediction error. Simulations on synthetic arrivals and experiments on real request traces support the theory: modest lookahead substantially reduces flow time and brings online batching close to the offline benchmark.

Autonomous driving (AD) relies on multi-sensor perception to interpret the surrounding environment. However, the robustness of camera–radar fusion under adversarial conditions remains largely unexplored. This paper presents a systematic measurement study of the robustness of camera–radar sensor fusion in AD. We construct a unified evaluation pipeline on the nuScenes dataset that simulates attacks on both sensing modalities, including eight camera-image perturbations and three radar point-cloud perturbations. We evaluate five camera–radar fusion algorithms across two perception tasks, 3D object detection and depth estimation, and quantify their performance under clean and attacked inputs using standard metrics. Our evaluation reveals a clear asymmetry in the robustness of fusion systems. Camera perturbations substantially degrade both object detection and depth estimation, and moderate attack strengths are already sufficient to cause severe performance degradation. In contrast, the evaluated radar perturbations produce smaller and task-dependent effects, with object-detection models showing particularly limited degradation. Our analysis attributes this difference to the strong dependence of existing fusion architectures on dense camera features, together with the filtering, association, and confidence-weighting mechanisms commonly applied to sparse radar measurements. These results demonstrate that sensor fusion does not inherently guarantee robustness and that the contribution and reliability of each sensing modality must be explicitly considered under adversarial conditions. Based on four empirical findings, we derive measurement-guided design implications for future robust camera–radar fusion, including modality-specific reliability estimation, cross-modal consistency checking, adaptive fusion, and graceful failover under severe sensor degradation.

We present two and three dimensional direct numerical simulations of planar intrusions injected from a continuously supplied, narrow source into a linearly stratified ambient at the level of neutral buoyancy. The evolution passes through three phases. A laminar leading vortex dipole first advances at constant speed with a varicose wave train behind it; the trailing jet then undergoes a sinuous instability whose initial growth rate and wavelength agree with inviscid unstratified planar-jet theory evaluated on the local jet; the flow finally relaxes into a buoyancy-controlled wedge whose area grows linearly in time. Three-dimensional simulations show that the transition remains organized by the planar instability, while three-dimensionality reshapes the near-source region into a slowly evolving, actively mixing zone that entrains an additional twenty to one hundred percent of the source flux depending on source width. Rescaled with this measured effective flux, the downstream intrusion collapses reasonably well onto the similarity solution for a wide-source intrusion.

Let $K$ be a number field of degree $n_K$, and let $h(K)$ denote the smallest absolute value of the imaginary part of a non-trivial zero of its Dedekind zeta function. In 1979, Hoffstein proved the unconditional bound $h(K)\leq 0.87+o(1)$ as $n_K\to\infty$. In a 1990 survey article, Odlyzko stated without proof that a different kernel in Weil's explicit formula could produce $h(K)\leq 0.54+o(1)$. No further improvement on Hoffstein's $0.87$ threshold accompanied by a published proof has since appeared. We choose a linear kernel and first show that Hoffstein's original parameters already yield the improved constant $0.825$. We then generalise his linear kernel method using Stechkin's trick and prove the unconditional bound $h(K)\leq 0.6+o(1)$ as $n_K\to\infty$, giving the best proved asymptotic bound to date.