Papers

Natural language specifications let non-expert users task robot teams, and large language models (LLMs) have recently proven effective at grounding such semantic specifications into plans for heterogeneous teams. Existing approaches assume missions that terminate and environments that, while unknown, do not change, but both assumptions fail in many emerging applications. For example, a disaster-response mission does not terminate, and its environment changes continuously as hazards spread and evacuees move. We identify three ways an LLM orchestrator breaks in this setting: its prompt grows without bound, its reasoning degrades as agents and targets accumulate, and it stops actively monitoring after covering the search space once. We build on the successful framework of grounded generative intelligence, and address each issue with a classical idea. A Markovian state summary, rebuilt from the semantic map at every invocation, replaces the growing interaction history. Partial delegation lets the orchestrator assign a subset of robots to an autonomous multi-agent protocol and reserve its reasoning for generating subtasks that require detailed parameters and careful ordering. Lastly, observation staleness, surfaced explicitly in the prompt, together with task-and event-triggered re-prompting, keeps the team vigilant. In a simulated urban search-and-rescue mission with spreading fire and moving evacuees, our framework rescues 98% of civilians versus 89% for the strongest baseline while using six times fewer tokens. Additional ablations isolate the contribution of each mechanism.

Recent observations that deep learning models train at the edge of stability have renewed interest in understanding stability properties of classical optimization algorithms. For quadratic objectives, standard gradient descent has a sharp stability threshold: it converges from every initialization when $\eta<2/L$, diverges from almost every initialization when $\eta>2/L$, and diverges from every nonzero initialization when $\eta>2/\mu$. For non-Euclidean gradient descent, the corresponding known guarantees are weaker: convergence holds for every initialization when $\eta<2/S$, where $S$ is the generalized sharpness, while every nonzero initialization diverges when $\eta>2/\mu$. The behavior in the intermediate regime $2/S<\eta<2/\mu$ is not fully characterized. We show that Hilbertian norms are the only ones for which $2/S$ is an almost-everywhere sharp threshold for every positive-definite quadratic objective. Using linear conjugacy between non-Euclidean and Euclidean gradient descent, we show that for general norms the intermediate regime can contain arbitrarily many edges of stability associated with distinct attracting directions. We identify a forward-invariant region of exponentially divergent directions beyond the generalized stability threshold. When the directions of minimum curvature are finite and nondegenerate, we prove that, sufficiently close to $2/\mu$ from below, only their invariant directions remain convergent. We give smooth two-dimensional constructions with arbitrarily many distinct thresholds, arbitrarily large relative threshold separation and show these properties to be stable.

We study a natural greedy algorithm for the Airplane Refueling Problem (ARP), based on a well-known priority rule. We show that this algorithm achieves an approximation guarantee of $9/20$, noticeably improving the previously known $1/12$ guarantee for a fast algorithm. We also show that the same priority rule can be implemented in $O(n\log n)$ time and $O(n)$ space using a dynamic convex-hull data structure. These results provide a worst-case approximation guarantee for an existing greedy priority rule and establish an efficient implementation. In the real-RAM model, the running-time bound is independent of the magnitude of the processing times. The resulting method is also suitable as a fast primal routine inside more complex exact and approximation algorithms for large instances. These results narrow the gap between theoretically strong but complex approximation schemes and lightweight algorithms that can be used directly in computational pipelines. The algorithm combines a simple selection rule with a provable performance bound, making it a useful baseline for further algorithmic studies of ARP.

AI agents can evolve by using environment feedback to revise their harnesses, the software managing model inputs, tool use, memory, and execution, while keeping foundation models frozen. Existing studies focus on single agents, leaving joint harness evolution in multi-agent systems (MAS) underexplored. A single global optimizer faces growing context and workload as the system scales, while access restrictions may prevent sharing agent internals or system-wide feedback. We propose HarnessNet, a framework for hierarchical harness evolution in MAS. Its basic unit, Agentron, comprises an evolvable forward harness, a foundation model, and a local optimizer that can observe and modify only that harness. Agentrons form a layered graph through which environment feedback propagates backward, with upstream optimizers receiving node-specific feedback from the downstream layer. This decomposes joint harness evolution into smaller, coordinated tasks with separate contexts, reducing individual optimizers' context and workload while keeping access local. Optimizers need not access all agent trajectories or raw environment feedback. Experiments on AgentBench with multiple foundation models demonstrate the feasibility of training HarnessNet. Compared with a single global optimizer, HarnessNet achieves comparable performance gains while respecting local privacy and requiring fewer tokens and less time per optimizer call. A migration study shows that the evolved harnesses remain jointly effective after replacing the foundation models, suggesting transferability across models.

We develop an adaptive Galerkin neural-network method for computing minimum-$L^2$-norm interior controls for wave equations with spatially varying coefficients. Within the Hilbert Uniqueness Method, adjoint waves are approximated directly in space-time by least-squares Galerkin projections onto trial spaces enriched by neural-network basis functions selected through residual-based training. Linear Galerkin solves determine the adjoint approximations, and a separate linear system reconstructs the control. The least-squares objective provides an indicator for adaptive enrichment and stopping; the experiments use a Ritz-based terminal-data version whose continuous-error interpretation additionally requires an eigenpair consistency estimate. The main difficulty is that adjoint errors perturb this reconstruction system. Assuming observability of the continuous equation, we derive sufficient stability conditions involving a worst-case factor $\sqrt{n}$ multiplying the maximal adjoint error, where $n$ is the number of retained terminal modes. A fully discrete error estimate separates terminal-space truncation, adjoint approximation, and assembly errors, yielding convergence to the minimum-norm control when the truncation error, the $\sqrt{n}$-weighted adjoint error, and the assembly errors tend to zero as $n$ grows. For spectral terminal bases, additional regularity and uniform contraction assumptions yield quantitative convergence rates and show that $O(\log n)$ accepted enrichment steps per mode suffice to balance the neural and truncation errors. Numerical experiments on a nonconvex Cassini oval, a square containing a low-speed lens, and a three-dimensional ball with a graded coefficient illustrate the method.

Non-intrusive reduced-order modeling is essential for systems simulated with black- or gray-box solvers, yet computing accurate data-driven models remains challenging when the dynamics exhibit large-amplitude transient energy growth. This is because state-of-the-art non-intrusive methods typically rely on orthogonal projection onto high-energy linear or nonlinear manifolds identified by minimizing static reconstruction losses, which truncates low-energy, yet dynamically important, states. Intrusive methods such as Balanced Truncation and its extensions address this issue by using adjoint information to define dynamics-aware oblique projections. Here, we show that balancing-based oblique projections for nonlinear systems can instead be computed non-intrusively from forward simulation data. Specifically, we develop a framework to compute the nonlinear empirical reachability Gramian and balance it against its observability counterpart, projected onto a suitable restriction subspace. This procedure provably recovers the oblique projection of Balanced Truncation when the dynamics are linear and the range of either Gramian is contained in the restriction subspace. Moreover, in the linear case and in the absence of adjoint information, we show that the minimax-optimal restriction subspace spans the dominant eigenspaces of the reachability Gramian, which informs an efficient balancing algorithm with cost comparable to a standard SVD. Once the oblique projection is computed, we use Operator Inference to learn the latent-space dynamics on its range. The method is demonstrated on several examples of increasing complexity, including the three-dimensional incompressible flow past a wing with $8\times 10^7$ degrees of freedom. In all examples, the Balanced Operator Inference models significantly outperform their POD-based counterparts, reducing forecasting error by up to two orders of magnitude.

A recurrent-depth language model reuses one block of weights several times in a row. The number of repetitions, which we call loops, is chosen when the model runs, not when it is trained, and running fewer is cheaper and faster, so a deployment may choose to do it. Running fewer loops also makes these models less safe, and the loss of safety is larger than the loss of anything else we measured. We study four released Ouro checkpoints and Huginn-0125. At half of its trained depth, Ouro-1.4B-Thinking still solves 0.692 of the GSM8K maths problems, against 0.775 at full depth, keeping 89% of its accuracy. Over the same reduction, the rate at which it helps with harmful requests rises from 0.038 to 0.205, 5.3 times higher. The information is not lost: a linear classifier reads whether a request is harmful from the model's internal state after a single loop, with an ROC AUC of 0.967 against 0.986 at full depth. What the missing loops remove is the refusal that should follow. We measure the effect with four instruments, one generating no text at all, and reproduce it on a second model family. Removing a single direction from Ouro-1.4B's internal state at full depth drops its refusal rate on harmful prompts from 0.950 to 0.130, identifying what the shallow model is missing. Two run-time repairs do not help: the models' early-exit rules do not spend more loops on harmful requests, and choosing a depth per request does not recover the loss. Changing the training does. Standard safety training makes the shallow model safe only by refusing 0.865 of harmless requests, while training at randomly chosen depths reaches a separation of +0.399 between harmful and harmless refusal at one loop, against +0.118. On Huginn-0125 it keeps harmful help at or below 0.040 at every depth from 1 to 32 loops, where standard training reaches 0.194, and it costs no accuracy at full depth.

We construct a sentence of $L_{\omega_1,\omega}$ having exactly $\aleph_1$ many countable models up to isomorphism, but no perfect set of non-isomorphic models. This disproves Vaught's conjecture for infinitary logic. The construction follows a framework devised by Robin Knight, and the proof has been formally verified in Lean.

We study the long-time behavior of the infinite-energy solutions to the white-forced Navier–Stokes equation in an infinite pipe $\mathbb{R}\times (-1,1)$ with no-slip boundary conditions. The equation is globally well-posed in uniformly local spaces satisfying the divergence-free condition. Under suitable degeneracy and spatial decay assumptions on the noise, we prove the uniqueness of the invariant measure and establish polynomial mixing in the dual-Lipschitz metric. This provides an affirmative answer to Open Problem 1 posed by Kuksin and Shirikyan \cite{KS17} in the case of zero cross-sectional flux.

Nearest-neighbor (NN) search underlies countless robotics algorithms, but many state spaces are not Euclidean: orientations live on $SO(2)$ or $SO(3)$ and poses on $SE(2)$ or $SE(3)$, and a Euclidean KD-tree on their raw coordinates returns wrong neighbors. We present a header-only, dependency-free C++ KD-tree library for exact NN search on user-defined product manifolds declared at compile time: the space is composed from base manifolds ($\mathbb{R}^n$, $SO(2)$, $SO(3)$, $S^n$; products $SE(2)$, $SE(3)$, tori) with a single type alias, and the library synthesizes a metric whose pruning is provably admissible, wrap-aware for circular coordinates and double-cover-aware for unit quaternions. Experiments confirm exactness (recall $1.0$ vs an exhaustive scan under the same product metric), where the Euclidean-on-raw shortcut collapses to recall $\approx 0.5^{m}$ for $m$ rotation blocks, with up to three orders of magnitude speedup over brute force. We further contribute an incremental, self-balancing single-tree index for points under heavy churn (e.g. sliding-window LiDAR maps) or $SE(3)$ trajectories: bounded memory and faster updates than prior work, with an optional asynchronous tail-latency-bounding mode. The implementation is open source: https://github.com/jlblancoc/nanoflann

Subnanometer transition-metal chalcogenide nanowires provide a one-dimensional platform in which electronic functionality and mechanical response can be tuned through chemical composition. Here, density functional theory calculations are combined with machine-learning force-field (MLFF) molecular dynamics to investigate MoS, MoSe, MoTe, WS, WSe, and WTe nanowires. The optimized structures are dynamically stable within the harmonic approximation, and their electronic character evolves systematically across the chalcogen series: MoS, MoSe, WS, and WSe are metallic, whereas MoTe and WTe are semiconducting, with HSE06 band gaps of 0.52 and 0.20 eV, respectively. The effective axial stiffness decreases from sulfides to selenides and tellurides, consistent with the increase in metal–chalcogen bond length; using a circular effective cross section, the corresponding Young moduli range from 392 to 718 GPa. All six nanowires have negative formation energies relative to the selected elemental reference phases. MLFF trajectories extending to 2.5 ns at 300 K preserve the one-dimensional morphology and local atomic order, providing evidence of finite-temperature dynamical stability on the simulated time scale. The corresponding MLFF molecular-dynamics energy traces are shown in. We further examine the response of the nanowires to axial strain and curvature, including strain-induced band-gap modulation in the tellurides. These results establish composition and mechanical deformation as complementary routes for tuning the electronic and mechanical properties of ultrathin transition-metal chalcogenide nanowires and support their further investigation as components of flexible nanoelectronic systems.

We validate Leonid Space's space weather forecasts through comprehensive cross-validation of retroforecasts scored against the entire F10.7 and Ap historical record. We built a unified forecast model that jointly forecasts F10.7 and Ap on all timescales from 3 hours up to multi-decade chains of future solar cycles. This was used to generate an archive of historical 15-year retroforecasts, after performing a leave-one-out fit of the model on held-out data and conditioning only on historical data available at the time. The accuracy of this archive was scored against measured space weather indices at all lookahead horizons from 1 day to 15 years, using the continuous ranked probability score (CRPS) as the primary quality metric. All other publicly available F10.7 and Ap forecast archives were scored using the same approach, including NASA's MSAFE and Schatten forecasts, SWPC's 27-day, 45-day, and Solar Cycle predictions, SWPC/USAF's RSGA, SIDC's Ursigram, CLS, Athens, KSO, BGS, SEPC's 3-day and 27-day forecasts, AFRL/NSO's SIFT, and BoM. Taken together, these 15 flux forecasts and 12 Ap forecasts compared on common lookahead metrics make up the most comprehensive cross-comparison of space weather forecasts we are aware of. Over a common forecast interval since 2000, Leonid had the lowest CRPS prediction error of any F10.7 or Ap prediction model: strictly lowest for Ap at all lookaheads and for F10.7 up to 5 years, and parity with MSAFE after 5 years. Much of this performance comes from our well-calibrated uncertainty bands, and we urge space weather forecasters to include calibrated uncertainties with their predictions and to issue retroforecast archives that can be used to rigorously evaluate their generating models.

In observational studies, the overlap assumption, also called positivity, is frequently strained in practice. Limited overlap destabilizes widely used estimators such as inverse propensity weighting (IPW), whose variance depends on density ratios that explode as propensity scores approach zero or one. To address this challenge, we propose the Stable Transport Estimator (STE), an optimal transport-based approach for estimating average causal effects when overlap holds but strict overlap fails. Unlike IPW, the variance of STE contains no density-ratio factor; it is governed by the transport map itself and stays finite under bounded moments, even when density ratios diverge. By replacing reweighting with a geometry-aware transport map, STE constructs stable counterfactual comparisons without requiring density estimation or propensity score modeling. STE further extends to settings where the overlap condition is violated: when covariate supports overlap only partially, a linear interpolation transport map enables principled extrapolation with explicit bias-variance trade-offs. We establish consistency, asymptotic normality, and a variance characterization that makes explicit the contribution of the estimated transport map to the asymptotic variance. Across synthetic and real datasets, STE demonstrates improved robustness, reduced bias, and markedly more stable variance compared to existing estimators.

Response-supervision timers in the 5G Non-Access Stratum (NAS) bound the time allowed for signaling exchanges before retransmission or abnormal-case handling begins. In non-terrestrial networks, that interval can include satellite propagation, terrestrial transport, and processing by multiple core-network functions. Under current 3GPP specifications, the applicable timer value for satellite access is selected according to the satellite NG-RAN radio access technology (RAT) type. However, control paths within the same low Earth orbit (LEO) network can differ in propagation delay and processing load. This article reviews the relevant 3GPP timer semantics and traces the delay components covered by different timers through 5G registration. It organizes candidate refinements along two dimensions: configuration granularity and information scope. A registration case study illustrates the trade-off between avoiding premature timer expiry and recovering promptly from message loss. The article identifies the information and coordination that future specifications would need to address to support interoperable timer configuration.

Quantum computation offers a promising alternative to classical Monte Carlo methods by naturally avoiding sign problems through unitary evolution. A common misconception follows from this: because quantum simulation sidesteps the sign problem, it is often assumed to be an essentially perfect substitute for classical sampling. This is false—quantum measurements are intrinsically stochastic, and estimating observables often requires a number of samples that grows exponentially with system size, time separation, or inverse temperature, exactly as in the classical signal-to-noise problem. In this work, we analyze the origin and structure of signal-to-noise problems in quantum computation, drawing parallels with classical Monte Carlo, and demonstrate that such noise persists even in sign-problem-free regimes. We discuss strategies to mitigate it, in particular a quantum generalization of Stein control variates construction, in which unbiased estimators are built from operator commutators $[X,A]$ and their discrete diagonal counterparts, and validate the approach with exactly solvable numerical examples that quantify the achievable variance reduction. Our results underscore that variance reduction, not merely sign-problem avoidance, is required to make quantum algorithms practically viable for many-body physics.

Recently, the possibility of having sterile Majorana neutrinos charged under $B-L$ gauge symmetry in the bulk of the dark dimension has been explored. We point out a cosmological restriction on the Majorana mass of bulk neutrinos leading to mass $\gtrsim 100~{\rm GeV}$. This avoids the over-production of Kaluza-Klein neutrino towers in the early universe thus resolving the cosmological neutrino catastrophe of extra dimension scenarios. If the mass of the bulk neutrino is at the lower end of this bound, it can potentially also explain the recently observed Fermi halo excess on gamma rays through the evaporation of long-lived 5d (i.e. dark) black holes through Hawking radiation to bulk neutrinos, which promptly decay into standard model particles.

Deep research requires connecting multiple steps of search, reasoning, and computation, with intermediate findings guiding what to investigate next. As investigations grow, agents must maintain research state across model calls and check findings before errors propagate into subsequent work. We introduce PANINI-DR, a multi-agent harness that separates coordination of the overall investigation from the research and verification of individual subquestions. A shared workspace, built on the Generative Semantic Workspace representation, records subquestions, their dependencies, findings, and supporting evidence. Researchers investigate individual subquestions, while a separate verification agent checks proposed answers against those subquestions and their evidence. Verification feedback guides further investigation, and recorded findings inform subsequent assignments. We evaluate PANINI-DR on BrowseComp-Plus, FRAMES, and MoNaCo against seven state-of-the-art deep-research harnesses, all using a shared language-model backbone and frozen corpora. PANINI-DR achieves the strongest average performance across the three benchmarks. On BrowseComp-Plus, it achieves 73.3% accuracy, outperforming the next-best harness by 16.0 points. Its advantage is strongest on hard questions, where it answers nearly twice as many as the next-best harness. Ablations further show that structured planning and persistent state improve performance, as does checking each finding against its cited evidence before it is reused. Because a model can answer correctly from memory alone, we also analyze the evidence retained by each harness. PANINI-DR achieves the highest answer recoverability from saved evidence on all three benchmarks, while complementary claim-support audits show stronger evidence-backed answers. Accounting for this evidence changes how harnesses compare and further strengthens PANINI-DR's advantage.

Large Language Models (LLMs) have been shown to be computationally expensive and vulnerable to jailbreak attacks, in which adversarial prompts bypass safety alignment and induce harmful responses. To address this inefficiency, a range of techniques have been proposed to enable efficient LLM inference. Depth-based dynamic inference has demonstrated promising results by enabling outputs to be generated from intermediate layers. It offers the flexibility to adjust model behavior based on the available resource budget. However, how this flexibility affects the robustness of LLMs against jailbreak attacks remains unexplored. In this paper, we address this gap via a comprehensive investigation into the impact of depth-based dynamic inference on the robustness of LLMs against jailbreak attacks. Specifically, we make the following key observations: 1) Shallow exits are consistently more robust to jailbreak attacks than deeper ones; 2) Exit depth affects how easily the adversarial suffix can be optimized, with deeper exits reaching lower attack loss; and 3) Adversarial suffixes affect utility uniformly across exit depths. These insights can help design dynamic inference methodologies that are more robust to jailbreak attacks. Code is available at https://github.com/LassNajmuldeen/balcony-jailbreaking

We prove Krzyż's conjecture for the sixth coefficient. Every holomorphic function $f(z)=\sum a_kz^k$ from the unit disk to the punctured disk satisfies $|a_6| \le 2/e$. Equality holds precisely for rotations of $\exp(-(1-z^6)/(1+z^6))$. Every extremal has a Herglotz representation with at most six atoms. By the reduction of Agler and McCarthy and the entropy theorem of Lei and Zhang, it suffices to exclude extremals with fewer than six atoms. We do this by a rigorous computer-assisted branch-and-bound, leaving the equality case entirely to the analytic argument. The main ingredients are explicit first-order conditions for extremals with fewer than the maximal number of atoms, which reduce to Chebyshev relations when one atom is missing, and a bound for the total mass obtained by convexity of the Poisson integral. The same method independently establishes the full-degree property for the known cases $n=3,4,5$.

Efficient task scheduling in heterogeneous computing systems remains a fundamental challenge in embedded and high-level synthesis flows. This paper presents MoSAIC (Motif-aware Scheduling with AI-driven Cognition), a learning-based framework that bridges the gap between exact and heuristic scheduling approaches for DAG-based applications. The system uses the reasoning capabilities of large language models (LLMs) to learn the relationships between DAG structures and scheduling priority functions. The framework first leverages the OR-Tools CP-SAT solver [4] to generate optimal schedules, which are then used to supervise the learning of compact priority-based scheduling functions through Bayesian Optimization. These learned heuristics capture relationships between scheduling decisions and structural graph features such as rank, depth, and fanout, enabling the construction of a reusable knowledge base across diverse DAG instances. Experimental results across synthetic graph families and real-world benchmarks, including PolyBench and MachSuite, show that the learned heuristics consistently improve over classical approaches such as HEFT [2], while maintaining low runtime overhead. The results indicate that combining optimal supervision with learning-based generalization provides a practical approach for scalable and adaptive task scheduling.

Large language models are increasingly used in computer science education. However, the teaching abilities of even the most powerful LLMs are limited: they tend to reveal the solution prematurely and may lose focus on the learner's current debugging objective. To address this, we introduce SocraticRepair, a planning-guided Socratic tutoring framework for program debugging and miscon- ception repair that adapts prior planning-guided tutoring work (Li et al., 2026b). The framework is instantiated in the Python programming domain by fine-tuning Qwen2.5-Coder-7B-Instruct on synthetic multi-turn tutoring dialogues constructed from four preprocessed programming datasets. The system is evaluated using a predefined set of independent metrics and benchmarked against a general-purpose LLM. The experiments show that SocraticRepair achieves higher scores on stepwise scaffolding and question quality while also substantially reducing premature solution disclosure. The results also identify reliable pedagogical plan generation as an important remaining challenge.

Large language models often produce judgments that resemble human responses, but it remains unclear whether they internally capture linguistic nuances such as conventional versus idiomatic meaning. A layer-wise representational analysis was conducted on two equal-sized pre-trained models, Llama-3.2-1B and Gemma-3-1B-PT, to examine whether and where these models differentiate linguistic traits from input. The analysis combined layer-wise probing with geometric distance measures, using the top embedding dimensions ranked by principal component loadings for each layer. The results show that even with equal capacity, models organize linguistic information in fundamentally different ways, suggesting the need to analyze internal representational geometry, examining not just behavioral outputs but semantic space alignment when evaluating how closely human and model language interpretation correspond.

We study stochastic convex optimization, where each sampled function can be evaluated at two arbitrary points. Our accelerated method chooses step sizes, batch sizes and smoothing radii from function values. A forward difference between smoothing scales controls the radius; we account for changes in the smoothed objective. Under the stated regularity and second-moment assumptions, exact function evaluations give \begin{multline*} \mathbb{E}\bigl[f(x_N)-f(x^\star)\bigr] \le \widetilde{O}\biggl( \frac{\sqrt{d}\,M_2 D}{\sqrt{T}} +\min\biggl( \frac{L D^2}{N^2},\; \frac{d^{1/4} M D}{N}+\frac{\sqrt{d}\,M D^2}{\gamma_{\max} N^2} \biggr)\biggr). \end{multline*} Here $N,T,d,D$ denote the numbers of optimization steps and paired evaluations, the dimension and a feasible-set diameter bound, respectively. Evaluations are available within Euclidean distance $\gamma_{\max}$ of the feasible set. For the population objective $f(x)=\mathbb{E}_{\xi} F(x,\xi)$, $M$ satisfies $|f(x)-f(y)|\le M\|x-y\|_2$, and $M_2$ satisfies $\mathbb{E}_{\xi}\|\nabla F(x,\xi)\|_2^2\le M_2^2$ for sample weak gradients in the interior of the evaluation domain. The method requires no $L,M,M_2$, where $L$ is a Lipschitz constant of $\nabla f$; set $L=+\infty$ without smoothness. The method uses exactly $2T$ values in $3N$ sequential sampling rounds with predetermined batches, or $5N$ with batches chosen from observations. An extension selects a search radius without a supplied distance bound. Fixed radius parameters can leave nonvanishing error; suitable choices depending on the budgets yield convergence.

We study the effect of boundary conditions on the selection of wavenumbers in pattern-forming systems. Prior work established that, for a large class of boundary conditions, equilibria only within a narrow band of wavenumbers are compatible with the boundary. We demonstrate here that for a large class of initial conditions, solutions evolve towards an extremal member of this narrow band of equilibria. In fact, this extremal member is neutrally stable, nonlinearly unstable, and the convergence is realized through a series of snapping events at the boundary. We observe this behavior in simulations of the Swift-Hohenberg equation when the pattern forming region is confined to a large spatial interval through a parameter quench. We prove the convergence in a phase-diffusion approximation using comparison principles and astutely chosen subsolutions that mimic the snapping behavior.

Magnetic flux trapped in a superconducting circuit shifts the critical currents of nearby Josephson junctions and disturbs the operation of the circuit. The usual remedy is a moat etched through the ground plane to hold the flux away from the logic. We report direct write silicon ion implantation with a focused ion beam as a way to make moats without etching the film, by locally suppressing superconductivity in niobium (Nb). Single implanted lines were written across Nb electrodes in films of three thicknesses over two orders of magnitude in ion fluence, and the transition temperature, resistance, and critical current density of each line were measured. The transition temperature of the line falls with fluence while the surrounding Nb is unchanged, and the critical current density falls by about two orders of magnitude before the line becomes resistive at 4.2 K. The product of the critical current and the resistance of the lines follows a single power law in reduced temperature. This gives an estimate of the critical current of a line at any temperature from its transition temperature and resistance. A time dependent Ginzburg-Landau simulation indicates that an implanted region can capture and hold a vortex. From these results we suggest a starting ion energy and fluence for implanted moats in a 100 nm Nb ground plane at 4.2 K and estimate the equivalent broad beam fluence.

Area laws express the expectation that entanglement in gapped quantum ground states scales with a boundary rather than a volume. In one dimension this holds for every Rényi entropy, and the Rényi area-law conjecture asserts the same in higher dimensions for each fixed $0<\alpha<1$. Here we disprove this conjecture in every spatial dimension two and higher. We construct finite-range Hamiltonians with fixed local dimension, bounded interaction strength, unique ground states and a uniform spectral gap, whose ground states exhibit volume-law Rényi entanglement while obeying a von Neumann area law and remaining connected to product states through uniformly gapped local paths. The mechanism is error-space complexity: locally identifiable components of arbitrarily small weight can encode states with high entanglement complexity. We also establish the worst-case rank-error trade-off for approximate ground-state projectors, a key tool in one-dimensional area-law proofs. At fixed gap, the optimal Schmidt rank at projection error $\epsilon$ across a planar cut of cross-section $A$ scales as $\exp[\tilde{\Theta}((A\log\epsilon^{-1})^{2/3})]$ when $\log\epsilon^{-1}\gtrsim A$. Thus $\alpha=1$ is the sharp threshold for a universal Rényi area law within this adiabatically connected class.

In the context of Tor, deanonymization attacks via traffic correlation have long been studied for both clients and onion services. Complementing prior investigations that utilize fine-grained flow metadata such as packet sizes and timings, we study a relatively less explored yet easier-to-obtain adversarial capability: deanonymization using only coarse NetFlow-style telemetry, such as one-minute, 1-out-of-1,000 sampled packet counts. We first revisit active NetFlow-based traffic analysis attacks against Tor onion services and show, through large-scale experiments with live Tor data, that coarse telemetry is sufficient to deanonymize a targeted onion service when the adversary can induce discernible traffic patterns through controlled downloads. We then introduce a stronger active attack based on controlled introduction requests, which removes application-specific assumptions and gives adversaries more flexibility while achieving comparable success rates. Finally, we present a passive deanonymization attack that sends zero traffic to target onion services. The attack exploits Tor's puzzle-based DoS defense as a side channel: public puzzle difficulty reveals service-load changes that can be semantically matched against NetFlow traces. Our findings show that coarse network telemetry poses a practical deanonymization threat to onion services today and call for proactive mitigations and a redesign of the globally visible defense signals that may leak service-load information.

The discovery of integer and fractional Chern insulators in rhombohedral graphene, following their discovery in the isolated topological flat band in twisted MoTe$_2$, motivates a search for the conditions under which an electronic band can host a topological correlated state. In this Letter we introduce a “Berry basin" model which captures the essential features of rhombohedral graphene: a dispersive band with a flat bottom, momentum-space winding of a “layer" degree of freedom, and Coulomb interactions, while also including periodic potentials, enabling controlled studies of the interplay of quantum geometry, superlattice modulation, and electron-electron interactions in producing correlated topological states beyond the isolated topological band paradigm. While integer Chern insulators emerge at strong coupling without a superlattice potential, stabilizing the fractional state requires nonzero potential for all interaction strengths we access. We provide insight into the greater robustness of integer and fractional Chern insulators in rhombohedral graphene when electrons are polarized away from the moiré interface. Our results establish a new class of systems that host robust fractional Chern insulators and provide a controlled numerical platform to test competing theories of interacting topological phases.

Where crystal nuclei form in amorphous phase-change materials decides how they switch. We study six successive 4D-STEM scans, with simultaneous HAADF and EDS data, of a magnetron-sputtered Ge-Sb-Te (GST) film, restricted to the GST layer and its interface with the oxide beneath it. Nucleation sites do not differ in composition or number density: the nuclei lie on the same robust HAADF-EDS relation as the matrix, and at fixed HAADF the spread of the summed EDS signal equals its Poisson counting noise (ratio 1.03 +- 0.05). The nuclei are nevertheless crystalline and stand out in the 4D-STEM max-intensity virtual image (median z = 11.0) but not in HAADF (z = 1.3) or EDS (z = 0.3). We classify the film in four ways (HAADF intensity, I(q) phase mapping, PCA of the whole diffraction patterns and a self-supervised SimCLR encoder) and compare the electron pair distribution functions (PDFs) of all classes after calibrating reciprocal space on the Au cap. All bulk classes share one short-range structure (first shell 2.70-2.74 Å); towards the interface the first sharp diffraction peak (FSDP) moves to lower q, and every method isolates a thin interface-edge environment with a shorter or missing first shell. The I(q) classification isolates, in every scan, an interface environment that holds 62-100% of the nucleus pixels (1.2-2.5-fold above depth) and persists when the nucleus pixels are removed before classification. The interface, rather than a distinct composition or density of the nucleating volume, therefore marks where nuclei form. Over 4.7e3 e/Å^2 the HAADF signal falls by 17%, the first shell shortens by 0.03 Å and the FSDP narrows by 9%, apparently ordering the film as it damages it. All analyses used PySTEMLab, an interactive 4D-STEM analysis environment developed for this work.

The $N$-dimensional Euclidean Onofri inequality was proved by Del Pino and Dolbeault for smooth compactly supported functions in $\mathbb{R}^N$ with $N \ge 2$. In this paper, we consider the singular version introduced by Lam and Lu, and extend it to a natural weighted Sobolev space. Next, we establish a sharp singular Carleson-Chang type inequality and prove its equivalence with the singular $N$-dimensional Euclidean Onofri inequality. Furthermore, we prove the existence of nontrivial, non-constant optimizers for the functional associated with the singular Euclidean Onofri inequality, answering open questions left by Del Pino and Dolbeault in the non-singular case, and by Lam and Lu in the case with singularities. To this end, we exploit the classification result obtained for a singular Liouville-type equation involving the $N$-Laplacian. We also prove the conformal invariance of the functional, establish the sharpness of the singular $N$-dimensional Euclidean Onofri inequality in terms of optimal constants, and state several consequences, including a sharp Poincaré inequality.