Papers

LLM agents are deployed into infrastructure that grants them broad host authority, yet existing agent-security benchmarks and defenses operate almost exclusively at the application telemetry layer: the served tool manifest, the user prompt, and the model's messages. Some threats, however, smuggle malicious instructions and actions past the application boundary, leaving them invisible to that layer. In this work, we bridge that gap by pairing application-level agent telemetry with kernel-level syscall traces to present the first paired-evidence characterization of kernel-level versus application-layer signal for agent security. To quantify the value of the enhanced telemetry, we introduce Agent Cross-Layer Evidence (ACE), a paired-session corpus of 4,047 sessions and 17 threat models spanning six delivery-vector families and 14 of the 25 OWASP LLM and agentic threat categories, organized into 12 attack mechanics with per-mechanic characterization of where the most discriminative evidence lies. Across four distinct detector families, we find that kernel evidence is discriminative on its own and that composing it with application-layer evidence generally outperforms either single-layer view, revealing complementary signals that single-layer analyses can miss. We further demonstrate generalization to unseen attack families and transfer to an alternate agent runtime. Together, these findings establish the value of cross-layer evidence for agent security.

We propose the turning-point count-discrepancy indicator (TPCD) for diagnosing orbital chaos from a single trajectory in relativistic Hamiltonian systems with two oscillatory degrees of freedom. TPCD measures the largest cumulative departure of one turning-event count from its mean rate per reference cycle, requiring neither a neighboring orbit nor a phase-space partition and applying to both massive particles and photons. We establish its long-time behavior under explicit event–phase assumptions. Rigid phases with an exact event–phase correspondence obey a strict discrepancy bound of unity, and linearizable regular tori with bounded degree-one phase deformations obey a finite, orbit-dependent bound; both imply that the normalized indicator decays to zero as the record grows. A diffusive fluctuation mechanism instead yields a Brownian-bridge scaling and a finite statistical scale. Integrable Kerr motion validates the construction, recovering prescribed frequency ratios from event counts to within $2.6\times10^{-5}$ for six targets, including an irrational ratio. In charged-particle scans around a Kerr black hole in an external test magnetic field, TPCD and the fast Lyapunov indicator agree for all 80 sampled trajectories. In the Schwarzschild–Melvin photon model, a trajectory with elevated finite-time TPCD but low fast-Lyapunov values is identified as regular once its indicator trends downward over an extended integration, showing that finite-time values must be read together with their long-time trend.

We report the emergence of Moiré droplet in two-dimensional ultracold bosons subjected to a spin-dependent optical lattice, effctively realizing a twisted-bilayer configuration. We show that the droplet formation dramatically enhances the visibility of Moiré pattern in the density profile, even for exceptionally weak lattice potentials. The Moiré pattern can be enhanced similarly by increasing the lattice depth, which, however, also induces droplet diffusion characterized by a spreading density profile. Furthermore, we demonstrate a dynamical generation of Moiré pattern by dragging a small droplet through a moving lattice. At appropriate velocities, the droplet undergoes bifurcation and exhibits pronounced Moiré pattern within periodic time intervals. Our results establish the ultracold droplet as a compelling platform for simulating interacting Moiré physics, particularly the interplay between Moiré lattice and bound-state formation.

Maximizing the number of addressable spins within a fixed volume can improve ensemble quantum sensor sensitivity, but dense packing usually increases dipolar interactions and excited-state transport, shortening coherence and suppressing optical readout. Here we report a 2:1 cocrystal of 6,13-dihydropentacene and pentacene (DHP/Pc) containing 33.3 mol% pentacene ($3.3\times10^{5}$ ppm; $9.51\times10^{20}$ cm$^{-3}$), a volumetric spin-site density more than two orders of magnitude above previous benchmarks, NV-diamond and pentacene-doped p-terphenyl (PDP). Despite this density, DHP/Pc exhibits microsecond spin coherence, room-temperature optically detected magnetic resonance and coherent control. Time-resolved measurements indicate that the long-lived triplet population is generated predominantly by intersystem crossing and exhibits strong, non-thermal sublevel polarization. Density-functional theory calculations further suggest that the native cocrystal geometry weakens electronic coupling between neighboring pentacenes, while the higher DHP triplet energy creates a barrier to triplet migration. These results identify molecular packing and coformer triplet energetics as complementary design parameters for preserving coherence in high spin-site density systems, demonstrating cocrystallization as a promising route to dense, optically addressable spin materials for room-temperature ensemble quantum sensing.

Concurrent long-range (LoRa) transmissions over the same time-frequency and spreading factor (SF) resources generally result in packet collisions, as the gateway cannot distinguish the overlapping signals from different end devices (EDs). This paper advocates a new fluid antenna multiple access (FAMA) framework for LoRa, referred to as lora-FAMA, to provide spatial opportunities for LoRa multiuser communications. In lora-FAMA, a gateway employs a single fluid antenna connected to only one radio-frequency (RF) chain, whose radiating element traverses the antenna aperture by sequentially visiting all candidate positions, i.e., fluid antenna `ports', within each symbol interval. The signal segments collected along the trajectory are compensated using the channel state information for the target ED. As a result, the desired signal is coherently accumulated, whereas the signals from other EDs experience unmatched channel variations and thus cannot be coherently combined. Applying the compensation separately to each active ED enables simultaneous multiuser transmission. We analyze the statistical performance of lora-FAMA under asynchronous transmissions and spatially correlated fading, as well as the large-aperture limiting case with independent and identically distributed fading. Numerical results show close agreement between the analytical and Monte Carlo results. It is revealed that, with a normalized aperture of $4\times4$ and $\mathrm{SF}=9$, a gateway can simultaneously serve more than $10$ EDs over the same frequency and SF resources while maintaining a symbol error rate below $10^{-4}$. These results demonstrate the potential of fluid antennas to enable LoRa multiple access without multiple RF chains.

Effective robot assistance beyond narrow roles and repetitive tasks requires robots to be proactive - to decide what needs to be done rather than waiting to be told. While proactivity is increasingly explored, it lacks a unified formulation, and work in the domain is typically evaluated offline against static human models that cannot capture the effect of a robot's actions on the environment and the user's own behavior. We introduce a unified formalism for proactive robot assistance, organize it into three levels, and provide a framework to address the highest level of unprompted proactive assistance. We then show that offline evaluation overstates performance in this setting, and contribute a closed-loop evaluation with a human model that adapts to the robot. Finally, we present a method, GAP, that instantiates our framework, learning from passive observation to anticipate user goals and act. Under closed-loop evaluation, prior state-of-the-art methods collapse, in some cases adding more work than they save, while GAP remains robust and substantially outperforms them.

To solve an overdetermined polynomial system numerically, one first makes it square, usually by replacing the given equations with as many random linear combinations as there are unknowns. This is a provably safe step, but it can substantially enlarge the supports. The alternative is to keep that many of the given equations themselves. Selection preserves sparsity but risks geometry: a genuine solution can cease to be an isolated point of the subsystem's zero set. We show that deciding whether a safe choice exists is NP-complete, already for an explicit family of systems of degree three with radical ideal and exactly three simple rational solutions. For strong selection with the nondegenerate rational solutions supplied explicitly, three is the exact threshold when degrees are polynomially bounded: one or two solutions reduce to matroid intersection, three already give NP-completeness. Even without a degree bound, an arbitrarily long list never takes the decision problem beyond NP. On the hard family, five natural notions of a faithful subsystem coincide, and every failing choice fails visibly: its zero set contains an affine subspace through one of the three solutions. A degree-four variant shows that cost information does not help: every candidate that could possibly succeed has mixed volume exactly three, and the problem is NP-complete still. The construction realizes Karp's three-dimensional matching problem as the selection of a square subsystem from the given equations.

Agent behavior depends on the harness surrounding a language model, but it remains unclear whether language models can reliably improve such harnesses for hardware-design tasks. We study automatic harness evolution around a fixed subject model on 12 proprietary design-verification root-cause localization tasks. Across five trials per task, automatically evolved harnesses increased completed attempts by 71-76% and any-hit task coverage by 80-100%, while total correct attempts improved by only 18-24%. The strongest success reproducible at least twice result improved by one task, and later candidates exchanged gains across tasks rather than preserving them. An auxiliary candidate improved on a four-task validation set excluded from search but tied its baseline on a subsequent 12-task replay containing both search and validation tasks, so the selected gain did not persist across the full pool. Across the tested lineage, useful search, evidence, and finalization behaviors appeared in different candidates but did not consistently consolidate into a single harness that dominated across tasks and metrics. In a separate CVDP cross-benchmark case study, an automatically evolved defined-width repair harness produced 35.6% more functional passes than its 142-task reference baseline; the final functional verifier scored completed outputs but was not shown to the subject agent during repair. These results support archive-aware selection when evolution yields complementary specializations without consistent consolidation.

For a surface with an odd number of punctures, the moduli space of flat $SU(2)$ connections with traceless holonomy around each puncture is a symplectic manifold. When the moduli space is nonempty, there is a natural homomorphism from the mapping class group of the punctured surface to the symplectic mapping class group of this moduli space. It is shown that this homomorphism is injective if and only if the dimension of the moduli space is greater than $2$. This generalizes work of Seidel and Wehrheim–Woodward. Also given is a complete classification of Lagrangian spheres in the projective plane blown up at $5$ points with its monotone symplectic structure, which is the moduli space for the 5-punctured sphere. Furthermore, it is determined when two such Lagrangian spheres can be displaced by a symplectic isotopy. Results are also obtained regarding Lagrangian spheres in the intersection of two quadrics in $\mathbb{C}\mathbb{P}^5$. The proofs involve instanton Floer theory and results on Heegaard splittings. A main technical result establishes the approximation of any Hamiltonian isotopy of the $SU(2)$ moduli space by holonomy perturbations which are used in instanton homology.

In flow-matching text-to-speech (TTS), different speech realizations can induce different target velocities under the same generation conditions. A deterministic velocity field trained with squared error predicts their conditional mean, thereby marginalizing realization-dependent variation. Meanwhile, modeling such variation does not inherently provide a semantically interpretable interface for attribute manipulation. We propose ReaFlow-TTS, a realization-conditioned flow-matching framework that introduces an utterance-level stochastic realization latent and uses it to condition velocity prediction throughout the generation trajectory. We further impose valence-arousal-dominance (VAD) semantics on the realization space, enabling direct and graded attribute manipulation without target speech at inference. Experiments demonstrate improved synthesis quality over a matched full-mask baseline and reproducible latent-induced pitch, energy, and timing tendencies across initial-noise samples, providing behavioral evidence that the latent is used as a reusable realization condition. Subjective evaluation further demonstrates graded VAD manipulation across generation contexts with only modest changes in naturalness.

This paper is concerned with the Weyl problem, i.e., the existence of isometric immersions or embeddings of two-spheres into the three-dimensional Euclidean space or general ambient three-manifolds. We establish two results on the degenerate Weyl problem, namely when the Gaussian curvature $K_g$ is only nonnegative rather than strictly positive. First, for a smooth metric $g$ on the two-sphere, if $K_g$ is strictly positive except at finitely many points where the Hessian of $K_g$ is positive definite, then $g$ admits a global $C^{2,1}$-isometric embedding into $\mathbb{R}^3$. It appears to be the first result on the degenerate Weyl problem with purely intrinsic conditions on $g$. Second, for a general simply-connected ambient three-manifold $(\mathcal{M},{\overline{g}})$, if $K_g \geq K_0 \geq {\rm sec}_{\overline{g}}$ for some constant $K_0$, $(K_g-K_0)^{-1/2} \in L^p$ with $p \geq 2$, and a certain uniform pinching condition holds for approximate nondegenerate isometric immersions, then there exists a $W^{3,p}$-isometric immersion. Alongside we also resolve the nondegenerate Weyl problem (i.e., when $K_g>0$) into general simply-connected ambient three-manifolds for $g$, ${\overline{g}} \in C^{2,1}$.

FIPS 203 standardizes ML-KEM for post-quantum key establishment. Its polynomial multiplication relies on NTT butterflies with exact modular arithmetic over q = 3329. Dedicated NTT accelerators minimize latency with fixed modular arithmetic and stage schedules. A CPU-Grounded Linear Array (CGLA) reuses one programmable linear datapath across several workloads. Mapping the transform to this datapath requires exact FP32 reconstruction and explicit stage transitions across the ARM-to-CGLA interface. We implement an eight-stage cyclic radix-2 driver over the ML-KEM modulus by splitting each twiddle into 8-bit and 4-bit parts before modular reduction. This driver differs from the standardized seven-layer incomplete negacyclic NTT and does not implement the full ML-KEM polynomial multiplication path. The arithmetic sequence keeps every integer below 2^24. One 41-PE call fuses the first two radix-2 stages, and six 47-PE calls execute the remaining stages while scattering outputs into next-stage records. Across four cohorts, 105 FPGA runs match all 817152 output coefficients. At batch size 64, measured FPGA end-to-end latency is 27.5 us per NTT, and the ASIC projection is 6.74 us. With PE gating, projected ASIC system energy is 10.1 uJ per NTT at batch size 8 and 58.9 uJ at batch size 64.

We investigate coherent quantum transport through silicon nanotube (SiNT) junctions in high magnetic fields up to 60 T using a tight-binding model combined with the non-equilibrium Green's function formalism, and magnetic field included via Peierls substitution. We consider junctions of metallic nanotubes (6,0)+(6,0) and semiconducting ones (9,9)+(9,9), and examine the effects of the overlap length, inter-tube distance, magnetic-field direction, and field strength on the electronic transmission. In contrast to carbon nanotube junctions, the SiNT systems exhibit irregular transmission oscillations and do not show the emergence of highly conductive gateway states. The transmission is substantially more sensitive to a magnetic field perpendicular to the nanotube axis than to a parallel field, while increasing the field strength progressively modifies the transmission spectrum. Increasing the overlap length results in more frequent transmission oscillations, whereas increasing the inter-tube distance modifies their positions and amplitudes without changing their overall character. Generally, similar trends are observed for both types of junctions, involving metallic and semiconducting nanotubes. However, in the junction of semiconducting nanotubes, one observes peculiar additional field-dependent in-gap transmission features. These results demonstrate that the magnetic-field response of SiNT junctions is strongly governed by their geometry and differs qualitatively from that of pristine carbon nanotube junctions.

We establish an averaging principle for a class of multiscale mean-field forward-backward stochastic differential equations and identify several novel phenomena that are absent from classical fast-slow systems. In contrast with classical fast-slow systems, the effective dynamics cannot in general be obtained by simply freezing deterministic slow parameters and averaging against the invariant measure of the resulting fast equation. The appropriate averaging object is instead provided by a frozen fast dynamics in a random environment and its associated conditional invariant measures, which retain the coupling between the slow state and its distribution. The forward-backward structure creates a further obstruction: local averaging estimates need not remain stable when propagated over an arbitrary time horizon. We identify a uniform restart stability condition for the averaged system under which this obstruction can be overcome. Using a joint lifted semigroup for the state-law dynamics, together with a two-scale discretization and a Gordin-type decomposition, we prove strong averaging for both the forward and backward components with optimal convergence rate $O(\varepsilon^{1/2})$. As an application, we apply the general theory to a class of mean-field stochastic control problems and develop an efficient algorithm for solving such mean-field control problems.

A quantum circuit for Gaussian elimination is developed in this work. While previous quantum implementations of Gaussian elimination were restricted to $\mathrm{GF}(2)$, the proposed design is generalized to any finite field. Compared with previous works in $\mathrm{GF}(2)$, the developed circuit achieves garbage-free construction while retaining the best known asymptotic Toffoli depth up to logarithmic factors.

Multi-agent systems built on large language models (LLMs) are increasingly deployed in high-stakes settings such as finance, healthcare, and software engineering, where agents coordinate through natural-language messages. The same channels, however, let colluding agents exfiltrate confidential information or coordinate unauthorized actions, and steganography can hide such communication inside outputs that look ordinary to an auditor reading the transcript. Existing provably undetectable LLM steganography protocols are not suited to realistic deployments. High-capacity schemes assume a symmetric setting where the receiver can reproduce the sender's output distribution, the state-of-the-art protocol for asymmetric agents has very low capacity, and most approaches rely on a pre-shared secret key. We make the threat of undetectable agent collusion concrete with Codetta, a high-capacity steganographic protocol for independently deployed agents in realistic asymmetric settings. Codetta combines a shared public model that estimates the communication channel, a sampling mechanism that preserves the sender's output distribution, and an adaptive error-correcting code. It further removes the pre-shared key through a steganographic key exchange that lets independently deployed agents establish a shared key while keeping the transcript computationally indistinguishable from ordinary model outputs. Across three agent workloads and three sender models, Codetta achieves up to $94\times$ the capacity of the state-of-the-art asymmetric protocol, and its key exchange establishes a shared key with about 80k visible tokens at an empirically certified failure probability of at most $4.1\times 10^{-3}$. These results show that effectively undetectable collusion is becoming feasible between independently deployed agents, so auditing must go beyond inspecting communication transcripts.

We study the differential privacy (DP) of a graph shift operator (GSO) when an analyst observes the output of a graph filter. In particular, we study the setting in which the input signals to the graph filter are drawn from a differentially private distribution. Unlike approaches that perturb the GSO or the filter output, we use the randomness already present in the inputs to protect the GSO. This yields an equivalent level of privacy protection to that of the perturbation methods without adding noise, and thus a better privacy-utility trade-off. We provide an explicit characterization of the privacy loss and its certificate in terms of the zeros of the graph filter. In doing so, we show that the log-likelihood ratio between the releases of two adjacent topologies is governed by the distances from each zero to the graph frequencies of the two GSOs. Then, by uniformly bounding the log-likelihood ratio over the adjacent topologies, we obtain an explicit $(\varepsilon,\delta)$-DP guarantee for Gaussian inputs. We further show, via a Cramér–Rao bound, that the zero placement that limits the privacy loss also raises the floor on the adversary's reconstruction error. Finally, empirical validation is performed on a synthetic network of financial exposures, where the largest position a pair can conceal and the accuracy with which it can be sized are collinear across pairs. Both are set by the graph-frequency content of the pair, and the full network becomes recoverable only as the certified budget grows.

We develop a Ramsey theory for leaf-generated subsets of finite products of trees. Our starting point is a Theorem of Furstenberg and Weiss which states that for every $k\geq 1$ and $\alpha>0$, if $A$ is a subset of the leaves of $T_n$, where $T_n$ is the complete binary tree of height $n$, with size $|A|\geq 2^{\alpha n}$, then for $n$ sufficiently large the ancestor closed sub-tree $T_A\subset T_n$ generated by $A$ must contain a copy of $T_k$ such that (1) all vertices in the same level of $T_k$ are mapped into vertices at the same level of $T_A$, (2) if a non-leaf vertex $x\in T_k$ is mapped into a vertex $y \in T_A$, then the two children of $x$ are mapped into descendants of the two children of $y$, and (3) the levels of $T_A$ occupied by the copy of $T_k$ form an arithmetic progression. For the product $T_n \times T_n$ of two binary trees, we show that for every $k\geq 1$ and $\alpha > 1$, for $n$ sufficiently large, every subset $A$ of the leaves of $T_n\times T_n$ of size at least $2^{\alpha n}$ has that its ancestor closure $\Gamma_A\subset T_n \times T_n$ contains similarly structured arithmetic copies of the height $k$ four-ary tree, where the four children of every non-leaf vertex in the source tree are required to map below the four distinct diagonal children of the image vertex, where a diagonal child of a vertex $(x,y) \in T_n \times T_n$ is obtained by moving one level down each in each component. Our results generalise to product of $d$-many finite $b$-ary trees with a sharp critical exponent of \[ \alpha_{\text{crit}}(d,b) =d-1 + \log_b(b-1).\] Geometrically, our results imply that any set $E\subset [0,1)^d$ of upper Minkowski dimension greater than $\alpha_{\text{crit}}(d,b)$ contains arithmetic $b$-adic branching patterns of arbitrary finite order.

Superconducting strip single-photon detectors (SSPDs) have emerged as scalable, wide-strip variants of traditional nanowire counterparts. Despite practical advantages including improved optical fill factors and enhanced signal-to-noise ratios the fundamental detection physics governing these micro-scale geometries remains largely unexplored. Here, we investigate the underlying photoresponse of a 20 um-wide tungsten silicide SSPD, demonstrating a slew-rate-corrected timing jitter of 13.2 ps at 532 nm and 20.5 ps at 1550 nm, alongside saturated internal detection efficiency up to 1550 nm. Using focused free-space optical scanning, we reveal that detector timing jitter is strongly influenced by a spatially dependent slew rate between edge and center absorption events. To mitigate this impact, we utilize a parallel superconducting rail architecture to actively redistribute supercurrent. This in-situ tuning minimizes the latency mismatch and mitigates thermally activated intrinsic dark counts, extending the device's ability to operate at higher temperatures. Finally, comparing these dynamics with time-dependent Ginzburg-Landau (TDGL) modeling elucidates the physical origins of the position-dependent photoresponse, highlighting how superconducting rails or specialized readout electronics can mitigate negative impacts on timing jitter.

Automated Program Repair (APR) benchmarks have traditionally been constructed as static datasets whose characteristics are inherited from the defects they contain. While this paradigm has enabled decades of progress, finite corpora provide limited experimental control, become increasingly susceptible to contamination as they are reused, and cannot be systematically regenerated or adapted as evaluation requirements evolve. We propose specification-driven benchmarking, a paradigm in which benchmarks are defined by executable specifications and realized through benchmark generation. The specification explicitly declares the intended properties of the benchmark (including program context, fault taxonomy, difficulty, validation strategy, and corpus constraints) while a generation pipeline realizes those requirements through independent generation, validation, and corpus management components. We develop the conceptual foundations of this approach by introducing a taxonomy of benchmark specification dimensions, establishing how each specification dimension maps to deterministic architectural responsibilities, and arguing that independent validation is a structural requirement for trustworthy benchmark generation. An end-to-end example illustrates how specification choices propagate through the pipeline to produce benchmark instances whose properties are independently verifiable. By treating the benchmark as an executable specification rather than a static dataset, the proposed paradigm shifts benchmark construction from artifact curation to declarative experimental design.

Reliable intervention-oriented uncertainty quantification from Earth observation (EO) remains challenging when continuous treatment shifts, spatial dependence, limited support, and satellite-outcome uncertainty must be addressed simultaneously. Existing causal, conformal, and spatial approaches address parts of this problem, but their direct combination does not generally recover the appropriate interventional reference law because candidate reassignment jointly alters treatment likelihood, standardized residuals, and graph-dependent residual likelihood. This study presents GeoDose-CP, a support-aware conformal framework for localized stochastic potential outcomes under continuous or mixed continuous-atomic treatment. Its central methodological contribution is a graph-local target-orbit law that jointly represents intervention-induced treatment shift, the inverse outcome-scale Jacobian, and spatial residual dependence. The framework further provides exact weighted candidate inversion, a scalable sparse approximation with explicit discrepancy accounting, and refusal under inadequate support. Evaluation used controlled known-truth experiments, MineDoseBench, treatment-density sensitivity analysis, external conformal comparators, and a multi-mine New South Wales (NSW) study. In MineDoseBench, GeoDose-CP achieved mean selective coverage of 0.9692 across 27 configurations and a minimum local q0.05 of 0.8951; exact-sparse auditing produced nine inclusion disagreements over 2,700 targets. In the NSW study, the absence of an auditable longitudinal rehabilitation treatment rendered treatment-dependent inference nonoperational rather than forcing inference through a proxy exposure.

Speech and voice are multidimensional signals that capture both communicative intent and underlying physiological processes, providing a unique, non-invasive window into health. Analyzing these signals has the potential to yield digital biomarkers that (i) provide scalable, objective measurement tools for research and clinical care and (ii) reflect the presence or progression of diverse conditions, including neurological, psychiatric, respiratory, and cardiovascular disorders. Realizing this promise, however, requires the field to overcome pervasive reproducibility and generalizability issues due to heterogeneous data collection, processing, and analysis practices. A major source of this heterogeneity is how underlying acoustic measures themselves are defined and computed. In this paper, we outline key considerations across the speech biomarker discovery lifecycle, from data collection through machine learning modeling to clinical interpretation, needed to achieve reliable, reproducible, and clinically translatable results. Chief among these is the need for harmonization efforts to start from common, precisely specified measure definitions. As a first step, we therefore provide definitions, physiological correlates, and computational implementations for a minimal, clinically interpretable set of core speech measures spanning respiration, phonation, articulation, and fluency. We close by discussing ongoing standardization efforts and the open challenges that remain in advancing the adoption of speech- and voice-based digital biomarkers.

We prove that every $(2K_2,K_4)$-free graph is recolorable. Equivalently, for every such graph $G$ and every $\ell\geq \chi(G)+1$, the reconfiguration graph of proper $\ell$-colorings of $G$, in which two colorings are adjacent if they differ on exactly one vertex, is connected. This resolves the final remaining open case in the classification of recolorable $(F_1,F_2)$-free graphs when $F_1$ and $F_2$ have at most four vertices.

Motivated by a word encoding of tree-child networks, we introduce trident tableaux, which are Young tableaux with a unique three-cell column satisfying certain conditions on successors. We construct a bijection between trident tableaux with $n+1$ columns and two-wall tableaux with $n$ columns, that is, two-row fillings with two designated columns in which vertical order is not imposed. The bijection matches the three-part decompositions of the two classes and shows that each class has cardinality $n(n+1)C_n/2$, where $C_n$ is the $n$-th Catalan number. In particular, it gives a trident-tableau interpretation of a shifted form of OEIS A002457. As a consequence, we obtain an exact enumeration of tree-child networks with one reticulation node that contain a trident, and show that their proportion among all tree-child networks with one reticulation node tends to $1/8$ as the number of leaves tends to infinity.

In experimental studies, increasing the ratio of source gases (C3H8/SiH4; C/Si ratio) for chemical vapor deposition (CVD) causes the growth rate to increase monotonically, and nitrogen incorporation tends to decrease accordingly; however, a unique phenomenon has been observed in which nitrogen incorporation increases discontinuously in the range of C/Si ratio between 1.0 and 1.5. This phenomenon is specific to the vicinal 4H-SiC(000-1) C-face and is not observed on the vicinal 4H-SiC(0001) Si-face. In this study, N incorporation behavior on a vicinal C-face during CVD is investigated using an ab initio-based approach. The calculation results suggest that when C/Si ratio is less than 1.0, the Si-terminated step edge is stable, whereas when C/Si ratio exceeds 1.0, the existence probability of the C-H-terminated step edge, where the N substitution energy is lower than in the former case, increases sharply. This change in the step-edge state across C/Si = 1.0 is thought to be the cause of the discontinuous increase in N incorporation.

Global-scale solar surface flows, including differential rotation and meridional circulation, provide key observational constraints on the solar dynamo. We investigate these flows using local correlation tracking (LCT) of chromospheric intensity structures in digitized \ion{Ca}{2}~K observations from the Kodaikanal Solar Observatory covering Solar Cycles (SC) 14 to 23 (1907 – 2007). The most valuable data coverage are from cycles 14 to 19 for two reasons: (1) it provided record for early cycles that are not commonly available; (2) it had much better duty cycle than the data of cycles 20-23, therefore the measurements had much less errors. On the other hand, the information loss in cycles 20-23 are compensated by other modern space observations. The recovered differential rotation shows relatively small cycle-to-cycle variations and remains close to the Howard reference profile. Recurring zonal-flow residual bands at low and middle latitudes are broadly associated with the activity belts during the well-sampled SC~15–19. The meridional flow is predominantly poleward in the earlier record and exhibits larger relative cycle-to-cycle variations and uncertainties. Incomplete coverage of SC~14 and sparse sampling during SC~21–23 limit detailed comparisons to the better-covered SC~15–20. Compared with its immediate successor SC~19, the strongest cycle in the record, SC~18 exhibits a stronger and continuous northern poleward meridional branch, peaking two to three years before its sunspot maximum. SC~19 shows a minor enhancement that peaks earlier prior to its own maximum. An independent comparison using PSPT observations yields a full-period correlation of $r=0.91$ between the LCT and SDO/HMI meridional-flow profiles. These results extend the observational context for solar-cycle-related flows over a century and motivate further refinement through data-driven reconstruction.

The presence of a nebula around massive hot stars often works as an indicator that the object is either in an advanced evolutionary stage or a rare product of close binary interaction. Here, we focus on two Be stars - PY Gem and HD253659 - whose nebulae were detected with the Wide-field Infrared Survey Explorer. We estimated their basic physical parameters from modelling the spectral energy distribution and examined their variability. We combined archival photometric data from several ground-based survey telescopes and from the Transiting Exoplanet Survey Satellite (TESS) with our own data from dedicated multi-colour photometric and spectroscopic monitoring, and concluded that, despite having similar stellar properties, the photometric variability of the two objects is strikingly different. For HD253659 we detected continuous eruptive variability and a major outburst that took place between 2016 and 2022 along with numerous flicker events seen in the TESS data. HD253659 also exhibits loop-like behaviour in the colour-magnitude diagram, consistent with build-up and dissipation phases of a circumstellar disk seen close to pole-on. In contrast, during the past ~20 years PY Gem has lost its eruptive variability and shows only small-amplitude p and g-mode pulsations classifying PY Gem as \beta Cephei hybrid pulsator. An incoherent low-frequency signal is identified as a Štefl frequency, which seems to be supported by the cyclic variation of the emission-line profiles. Detailed analysis of these stars indicates that both objects are inconsistent with evolved massive stars, and that the origin of their nebulae is more likely linked to the physics of the Be phenomenon.

Many optimization problems reveal inexpensive structural information before requiring costly final evaluation, whereas the conventional quantum approximate optimization algorithm (QAOA) applies a single aggregate objective throughout. We introduce the learned-projector quantum alternating operator ansatz (LP-QAOA), a multistage protocol that freezes optimized circuits and uses their output states to define later projector mixers. We prove a stability theorem for LP-QAOA that bounds the propagation of approximation errors through successive frozen stages. Our analysis also shows how learned-projector mixing avoids the high-order tunnelling suppression of local mixers. We conduct state-vector simulations on block-constrained spin tiling (BCST) instances, where LP-QAOA achieves higher probabilities of sampling the optimum, lower estimated logical-resource requirements, and better trainability than the tested baselines. A supporting stochastic block model experiment extends LP-QAOA to optimization problems with soft hierarchical structure. Our results highlight the potential of LP-QAOA to improve variational quantum optimization by exploiting hierarchical problem structure.

Heterogeneous robot teams distribute complementary capabilities across specialized agents, but their physical roles and capacities typically remain fixed throughout a mission. We present HARP, a Heterogeneous Aerial Robotic modules Platform in which independently deployable aerial robots physically reconfigure to compose their capabilities for field operations. HARP comprises sensor-equipped scouts, flydrive rover modules, and task-specific payload modules. Scouts map the environment and inform an energy-aware planner that jointly selects routes and air-ground mobility modes. Rover and payload modules fly independently across terrain that constrains ground travel, then autonomously assemble into a cooperative ground vehicle for energy-efficient payload transport. Motivated by environmental sampling in remote and difficult-to-traverse regions, we evaluate HARP through field experiments spanning sensing, planning, reconfiguration, airground mobility, payload transport, and task execution. We further conduct module-level deployment tests on the Greenland Ice Sheet toward future autonomous missions. HARP demonstrates how heterogeneous robot teams can adapt not only their actions, but also how their physical capabilities are composed during a mission.

Large language models (LLMs) are increasingly involved in family education, yet HCI has not systematically explained the educational interactions that emerge around them. This scoping review analyzes 53 HCI studies from 6,540 records across 19 venues. Using activity theory and AODM, it relates participants and educational objects to mediation, labour, and rules. We find that the literature centers on child–parent interaction and on language, AI literacy, and relational learning. The introduction of LLMs enabled conversational, embodied, and spatial systems to generate support from the context of an unfolding interaction. LLMs redistributed educational labour, while family and institutional rules left parents and professionals responsible for interpreting outputs and deciding how they entered practice. Evidence across families and educational purposes remains limited, especially on sustained personalization, repair labour, and how families negotiate authority and rules. The review offers a framework explaining how LLM capabilities become organized through family participation.