Papers

LLM agents can produce harmful effects through sequences of ordinary operations. Judging such actions requires establishing both the authority that permits them and the origin of the data they carry. We present AGATE, an authorization and data-provenance gate at instrumented agent-harness boundaries. Operator declarations and host approval events ground authorization; delegated actions are constrained by grants that bind to exact parameters, expire, and permit a limited number of uses. Source registration connects observed inputs to subsequent transfers, while an effect ledger tracks repeated requests. Deterministic checks make decisions without an LLM in the decision path and retain their grounds with execution evidence for forensic replay. Adapters integrate three production harnesses – DeepSeek Harness, OpenCode, and OpenClaw – without modifying host code, translating each host's native observation and veto points into a single shared gate interface; the judgment core is identical in all three, and only enforcement depth differs. Our evaluation combines 153 exercised attack-chain records with deployment, utility, and reconstruction experiments. The deployment observations expose how tool declarations and data checks govern business actions, including a bypass through parameter rewriting. Six of eleven benign file-processing scenarios contain denial events, revealing the utility cost of content-based provenance policies. Across 252 runs on 63 sanitized scenarios, replay agrees with live graph projections for all 63 scenarios on each of two platforms. These results establish the feasibility of provenance-based runtime judgment and identify content transformation, legitimate reuse, and observation coverage as concrete limits.

Packing and covering problems for geometric regions have been studied under many notions of complexity, including VC-dimension, union complexity, shallow-cell complexity, and fatness. Although these restrictions often yield constant-factor approximation algorithms, they do not by themselves generally lead to PTASs. A recurring feature of known hardness constructions is that one region may be pierced by many others: a region $B$ pierces $A$ when $A\setminus B$ is disconnected. We study geometric instances through the piercing degree. Since piercing is symmetric for Jordan regions, this is the maximum degree of the corresponding piercing graph. Our main result is that, for every fixed piercing degree, the standard local-search algorithms give PTASs for the unweighted Discrete Independent Set and Set Cover problems. The proof constructs a sublinear balanced separator for an appropriate locality graph and applies it adaptively throughout the recursive local-search analysis. This guarantee depends only on the piercing degree; in particular, it places no bound on the number of components created by an individual piercing pair. We also prove a polynomial shallow-trace bound depending only on the piercing degree. As consequences, for every fixed piercing degree, weighted Set Cover admits a deterministic $C_r$-approximation and weighted Discrete Independent Set admits a deterministic $O(r+1)$-approximation. These results extend the known guarantees for non-piercing families and apply, for example, to axis-parallel rectangles when every rectangle is pierced by only a bounded number of other rectangles.

Precision manipulation with contact-critical interactions is often history-dependent: visually similar observations can correspond to different latent interaction states and therefore require different actions, while small execution errors can alter task outcomes. Policies relying on the current visual observation alone cannot resolve such ambiguity; force-aware and memory-augmented methods enrich physical or temporal context, while reactive high-rate policies improve local contact response, yet long-horizon temporal reasoning and precision execution remain largely decoupled in existing methods, limiting reliable progression in visually aliased precision manipulation. To bridge this gap, we introduce History-Conditioned Interaction Reasoning and Execution (HIRE), a cross-rate framework comprising a history-conditioned Interaction-State Reasoner (ISR) and a high-rate Interaction-Manifold Executor (IME). ISR encodes ordered wrench history with a temporal wrench encoder and Force Perceiver as persistent physical evidence for state-consistent action generation, while IME structures contact-critical motion into intrinsic progress and transverse correction for precise execution; their cross-rate loop allows the resulting physical traces to inform subsequent reasoning. In real-robot experiments across surface, insertion, and rotational interactions, HIRE achieves at least 90% completion across all evaluated task stages while improving interaction-state disambiguation, execution precision, and generalization. More broadly, HIRE provides a unified reasoning–execution perspective on precision manipulation under history-dependent partial observability, where physical interaction both realizes task intent and reveals latent-state evidence for future decisions. Code will be released upon publication.

As physical samples of distant planetary systems, the compositions of interstellar objects (ISOs) should correlate with the properties of their diverse parent stars. We combine a chemical partition model with a sample of stellar elemental abundances from APOGEE DR17 to predict the abundances of commonly-observed cometary volatiles in ISOs. We find that the compositions of ISOs vary significantly between different stars. In particular, we predict a strong correlation between an ISO's ammonia abundance and its parent star's metallicity: high-metallicity stars will create ISOs rich in ammonia. This suggests the production rates of NH$_3$'s photolytic daughter products are an ideal observational tracer for the origins of ISOs. We infer that 2I/Borisov formed around a star of near-solar metallicity ($-0.4\lesssim[\mathrm{Fe}/\mathrm{H}]\lesssim0.3$), and corroborate the velocity- and isotope-based inferences that 3I/ATLAS formed around a lower-metallicity star ($-0.8\lesssim[\mathrm{Fe}/\mathrm{H}]\lesssim0.0$). The production rates of 2I and 3I imply both only contain hypervolatiles such as CO and N$_2$ that are trapped in other less-volatile ices, similar to typical Solar System comets. Despite this, we argue that true hypervolatile-ice-rich ISOs may exist; they would exhibit high CO and N$_2$ production rate ratios, possibly similar to those of C/2016 R2 (PanSTARRS). Our predictions provide context for future ISO discoveries, opening a path to link the properties of their origin systems to observable production rates.

Graph transfer learning (GTL) provides a promising paradigm for adapting knowledge from source graphs with sufficient labels to label-scarce target graphs. However, existing approaches often assume that transferred knowledge is uniformly reliable, ignoring the different transferability of samples caused by structural and distribution shifts across graphs. This limitation leads to negative transfer and unnecessary computational overhead. In this work, we propose SUCRe, a selective uncertainty-aware contrastive representation method for GTL. The key idea is to selectively adapt and transfer graph knowledge according to its estimated reliability. Specifically, we introduce structure-aware entropy-based matching discrepancy, which jointly models feature uncertainty and structural coherence to ensure accurate feature adaptation between graphs. Moreover, we develop a domain-aware semi-hard negative sampling strategy that constructs informative contrastive sets by filtering unreliable cross-domain relationships, reducing computational redundancy while enhancing representation discrimination. Extensive experiments on graph transfer benchmarks demonstrate that SUCRe achieves competitive performance with improved efficiency.

Coded diffraction patterns (CDPs) provide a structured and physically relevant model for phase retrieval, but the dependence among Fourier measurements generated by a common mask makes sharp stability analysis challenging. For a fixed unit-norm signal $\boldsymbol{x}_\star \in \mathbb{C}^n$, let $\boldsymbol{X}_\star=\boldsymbol{x}_\star\boldsymbol{x}_\star^*$, and let $\mathcal A$ be the lifted CDP measurement operator. We prove that, with $L=O(\log n)$ random masks, the following uniform lower isometry holds with high probability: $\|\boldsymbol{X}-\boldsymbol{X}_\star\|_F \lesssim \log^2(2n) \frac{\|\mathcal A(\boldsymbol{X}-\boldsymbol{X}_\star)\|_2}{\sqrt{nL}}, \boldsymbol{X}\succeq\boldsymbol{0},$ from which we derive two consequences. First, for $\boldsymbol{y}=\mathcal A(\boldsymbol{X}_\star)+\boldsymbol{e}$, PhaseLift-type convex programs achieve the Gaussian-type stable recovery bound $\|\widehat{\boldsymbol{X}}-\boldsymbol{X}_\star\|_F \lesssim \frac{\log^2(2n)}{\sqrt{nL}}\|\boldsymbol{e}\|_2.$ Second, in the noiseless case, the nonconvex factorized loss has a benign landscape when the factor width satisfies $r = O(\log^5(2n))$: every second-order critical point $\boldsymbol{V}\in\mathbb C^{n\times r}$ satisfies $\boldsymbol{V}\boldsymbol{V}^*=\boldsymbol{X}_\star$. The key ingredient is a uniform operator-norm bound over row subsets of the dependent CDP measurement matrix, which permits the removal of a controlled set of adaptively selected rows while preserving tangent injectivity.

The prospect of fully autonomous transactional agents did not appear on the horizon until the advent of high capability language models. With such models, the operational benefits of adaptive task orchestration and independent (but constrained) decision making are tantalizing for enterprises and individuals alike. However, each such agent carries with it a serious attack surface in the form of prompt injection which can compromise any soft "guard rails" that may have been placed in context. The consequences of these attacks include credential ex-filtration which, if left unmitigated, renders the whole category of such agents unusable due to breach of trust. Furthermore, expecting a growth of autonomous agents, a security framework for them would require a form of decentralization to scale. Drawing on the proposed OAuth Agent Authorization Profile and the W3C DID and VC standards, we propose a framework based on the principles of capability based security with decentralized agent identity whereby agents access services based on tokens that are cryptographically bound to the agent's and issuer's identities and specify their scope. Services can validate that the delegation chain only involves scope attenuation before acting on any given token. We show that such a layer that lives outside the language model's context window in a secure module can enable agents to act within enforceable security boundaries.

We study multiple zeta values in positive characteristic. We construct, using $\infty$-adic multiple zeta values, a coaction of the $\infty$-adic multiple zeta value algebra modulo $\zeta_A(q-1)$ on the $\infty$-adic multiple zeta value algebra itself, and prove that it agrees with Mishiba's coaction constructed via special values of Carlitz multiple polylogarithms. We also determine the coaction on the $\star$-inverse values and show that the antipode on the $\infty$-adic multiple zeta value algebra modulo $\zeta_A(q-1)$ is given by the $\star$-inverse operation. In particular, these results prove Mishiba's conjecture concerning the coaction and the antipode for $\infty$-adic multiple zeta values.

Learned particle simulators based on graph neural networks achieve strong one-step accuracy, but errors compound over long horizons. An underexplored variable is the interaction graph: existing methods fix its topology via k-nearest neighbors or a static radius rule, regardless of local model confidence. We propose making this graph adaptive: a per-particle variance head, trained jointly with the acceleration head under a heteroscedastic Gaussian NLL loss, drives a trajectory in which high-uncertainty particles receive an expanded neighborhood. This is done at little extra inference cost by using the previous step's uncertainty estimate. A key discovery is that the variance head learns a meaningful notion of uncertainty: high-variance particles concentrate near complex regions, such as splash zones or free surfaces. When this signal drives graph topology, the resulting AdaptGNS simulator achieves a strict Pareto improvement on WaterDrop and a modest gain on Sand. Given the model's stronger performance on WaterDrop, we hypothesize that adaptive graphs are most useful when complexity is concentrated in space. Our code can be found at https://github.com/aidenzhou8/AdaptGNS.

This work addresses the computation of extreme values of observables along trajectories of dynamical systems over an \ks{infinite time horizon}. The setting is intrinsically global: trajectories may exhibit large transient excursions, approach their largest values only asymptotically as time tends to infinity, or escape to infinity in finite time. The proposed framework treats these \mk{ scenarios} in a unified way, so that the resulting extreme values reflect both the transient and the asymptotic behavior of the dynamics. The main difficulty is that neither the time interval nor the state space is assumed to be compact. We address this by combining a radial compactification of the state space with a compactified clock variable and discounted occupation measures. This yields a description of trajectory ensembles on compact sets via occupation measures and the associated Liouville's equation. Extreme values are then characterized through a family of reachability problems for level sets of the observable, which can be solved by a bisection procedure. On the theoretical side, we prove a superposition principle for an infinite-horizon Liouville's equation with a time-distributed terminal measure. This result shows that the measure formulation represents ensembles of stopped admissible trajectories, including trajectories \ks{that never stop}, and establishes equivalence between the trajectory-level and measure-level descriptions.

Looped transformers reuse weights across recurrence steps, making low-bit quantization especially attractive. We identify two distinct failure modes of standard post-training quantization. On Huginn-3.5B, per-channel INT4 fails primarily at the non-residual loop-entry adapter, while quantizing the residual core is much less damaging. We call this feedback exposure: a quantized layer perturbs the recurrent state without an identity path, and the resulting error is fed back at later steps. Controlled experiments on linear filters and Mamba state-space models show that feedback exposure also occurs outside transformers. Grouped INT4 reveals a separate failure, calibration blindness: our one-step GPTQ baseline builds its Hessian from step-0 activations, leaving input directions used later in the recurrence nearly unweighted. Across nine checkpoints from seven looped architectures, one-step GPTQ is worse than round-to-nearest (RTN) on the primary task metric for five checkpoints. Accumulating the GPTQ Hessian across recurrence steps outperforms both one-step GPTQ and RTN on all nine checkpoints and recovers bf16-level accuracy on Huginn. These results separate two questions for PTQ on looped models: where quantization error enters the recurrence, and which states calibration sees.

In many safety-critical applications, control of uncertain dynamical systems relies on observers that estimate states and external disturbances. Neural network observers can improve estimation accuracy, but certifying their Lyapunov stability via Linear Matrix Inequality (LMI) constraints leads to large-scale semidefinite programs (SDPs) that are difficult to solve for large networks. To overcome this scalability bottleneck, we propose a novel two-stage training framework for provably stable neural network observers. Our approach decouples the optimization into a point-guided Lyapunov pre-training phase, which rapidly achieves high estimation accuracy and local stability over sampled states, followed by an LMI fine-tuning phase that efficiently satisfies a strict global Lyapunov stability certificate. We provide formal theoretical guarantees for local stability radii and probabilistic coverage over a prescribed compact error-state domain under specified regularity and sampling assumptions. Experiments on nonlinear control benchmarks and X-29 aircraft ablations show that our LMI-certified neural network observers train significantly faster than direct LMI-based methods and generalize robustly across diverse systems, achieving improved tracking accuracy over a range of observer baselines. The code is available at https://github.com/Berry-Myon/LearningNeuralNetworkObserver.

Multi-modal planning is promising for autonomous driving by representing multiple plausible behaviors in ambiguous and long-tail scenarios. Existing methods mainly focus on improving trajectory multi-modality, enhancing trajectory representations, or reshaping the candidate distribution. Nevertheless, we identify a pronounced generation-evaluation asymmetry in multi-modal planning: despite strong oracle performance, existing planners often fail to reliably select the best available candidate, leaving substantial planning potential unrealized. To address this challenge, we propose iDriveVLA, a multi-modal planning framework that improves the candidate trajectory space while enabling more reliable and context-aware trajectory evaluation. Specifically, iDriveVLA introduces a unified trajectory evaluator comprising a Safety-aware Scorer for quality and risk estimation, together with a VLM-guided Modulator for scene-adaptive criterion weighting. We further develop an oracle-aligned progressive training strategy consisting of candidate imitation pretraining, candidate space refinement, and semantic ranking alignment. On the public NAVSIM v1 leaderboard, iDriveVLA achieves a new state-of-the-art performance of 94.95 PDMS, surpassing the human-expert reference.

Every finite nonempty incomplete uniquely decipherable code with maximum word length $k$ has an uncompletable word of length at most $4k^2-3k$. The bound is independent of the number of codewords and their total length. Deleting a complete codeword cycle gives a finite path-counting identity; Kraft equality then supplies a short word of deficient compressed mass. Cyclic averaging and padding turn it into an uncompletable word. Conditional expectation makes the construction polynomial-time and also decides completeness. First-return words extend the bound to mortal families of nonnegative integer $n\times n$ matrices with joint spectral radius at most one, provided every strongly connected component has a vertex meeting every cycle. Such a family has a zero product of length at most $4n^2-3n$. A binary partial deterministic family with $2k-1$ states has shortest zero product of length $k^2+k-1$, establishing the optimal quadratic order. The bounds and the explicit-code algorithm, including its polynomial work bound, are proved in Lean.

Translation of the genetic code into proteins is universal across life, with ribosomes serving as the ancient molecular machines enabling this information transformation. We propose that early replication and protein biosynthesis were inseparable functions performed by a single ancient RNA molecule: the riboreplisome. This hypothesis addresses fundamental challenges facing RNA world, protein world, and RNA-protein co-evolution theories – particularly the problem of non-Darwinian starting points and the interdependence of replication and translation machineries. We present a 12-step evolutionary pathway from simple RNA replicase to proto-ribosome, supported by quantitative modelling demonstrating that only two steps require non-Darwinian transitions while the remaining ten proceed through standard selection. The single-molecule riboreplisome architecture provides an approximately 6-fold evolutionary advantage over multi-component "RNA soup" scenarios, principally by maintaining genetic linkage and retaining catalytic products close to the replicating genome (resisting diffusion loss); structural resistance to parasitic "cheater" molecules follows as a corollary. The riboreplisome framework explains the origins of ribosomal, transfer, and messenger RNA as derivatives of a single ancestral molecule, while providing a driving force for cellular compartmentalisation. Although the original riboreplisome is likely lost to deep time, molecular remnants may persist in extant biological RNA. Identification or reconstruction of riboreplisome-like molecules could advance both origin-of-life research and synthetic biology applications.

Spintronics drives the search for functional materials, pursuing room-temperature dilute magnetic semiconductors to realize practical, energy-efficient devices. This paper presents a theoretical investigation into the magnetic properties of w-AlN doped with Cr, Ru, and Rh atoms, using spin-polarized density functional theory calculations with supercell models. Calculations of point-defect formation energies as a function of the Fermi level predict that Cr4+, Ru4+, and Rh3+ are the most favorable charge states substituting Al in w-AlN. With these preferred charge states, Cr-doped AlN is stable in the ferromagnetic state, preferable for spintronic devices, across a wide concentration range (1.85 to 16.67% of Al). Conversely, Ru- and Rh-doped AlN are unstable in the ferromagnetic state relative to the antiferromagnetic state. Further investigation into the electronic density of states reveals a fascinating evolution: for Cr concentrations below 5.56%, the Fermi level resides within the band gap directly above the valence band maximum, keeping the system insulating. It transitions to a high-spin half-metallic state between 7.40% and 12.96%, and finally transforms into a normal metal at 16.67% Cr. This behavior is absent in the DOS of the antiferromagnetic model of Ru- and Rh-doped systems, where insulating and metallic behaviors instead appear non-sequentially with varying concentrations.

Reliable absolute pose estimation in urban environments is undermined by outlier measurements and incorrect temporal associations that can persist in tightly coupled estimators. Global Navigation Satellite System (GNSS) observations provide globally referenced measurements but are prone to multipath effects. Visual-inertial sensing supplies local motion constraints, but false visual associations can corrupt the estimator. We present SeA-RVINS, a fixed-lag factor-graph Real-Time Kinematic (RTK) visual-inertial system for robust urban pose estimation. A semantic-aware learned stereo frontend rejects unreliable tracks before persistent landmarks enter the graph. For double-differenced GNSS measurements, SeA-RVINS applies Dynamic Covariance Scaling through configurable batch, scalar, and latent-pivot robust formulations while retaining the shared-pivot correlation structure. We propose a hybrid ambiguity-continuation strategy that shares one ambiguity state over short arcs with verified continuity and softly links successive arcs through random-walk factors. On an approximately 20-km route from the public TEX-CUP dataset, including about 50% deep-urban driving, the latent-pivot configuration achieves 100% availability and a 1.6-m maximum horizontal error, with 96.16% and 99.90% of epochs below 1.0 and 1.5 m, respectively. The implementation is released as open-source software

Evaluating claim admission in shared agent memory is challenging because repeated claims may be mistaken for independent evidence. An agent may copy or paraphrase a retrieved belief, while admitting a false claim exposes subsequent agents to it. To study this problem, we introduce the Correlated Promotion Benchmark (CPB), which evaluates whether candidate claims should be admitted to shared memory.CPB-Static constructs a frozen test split from publicly annotated sources with fixed gold actions. CPB-Live runs multi-agent teams over a shared store, records all writes and retrievals, and tracks source lineage defined by each scenario. A separate consumer answers from the store alone. We evaluate eight admission policies across four agent families. Our results show that policies which deduplicate sources reject many true claims alongside false ones, whereas policies preserving answer coverage admit nearly as many false claims as unrestricted sharing. Gating on declared source type reduces false adoption to 0.06–0.09, compared with 0.22–0.47 for other answering policies. Once an uncontested false belief enters memory, the consumer asserts it in 0.97–0.99 of probes across all families. No non-oracle policy consistently rejects false claims across verbatim copies, paraphrases, and paraphrases declared authoritative. These findings reveal the limitations of admission policies without access to source lineage.

Modern service platforms often provide customers with real-time congestion information, such as anticipated waiting times, before they decide whether to use a service. This creates an intertemporal tradeoff in service recommendation: directing a customer to a service may generate immediate value, but the resulting congestion can make that service less attractive to future customers. We study this tradeoff through a finite-horizon stochastic optimization problem in which a platform dynamically recommends among multiple services, each represented by a queue, with customers' joining probabilities decreasing with congestion. We first formulate the problem as a Markov decision process and show that optimal decisions generally depend on the joint congestion state, giving rise to a prohibitively large state space. We develop two complementary approximation algorithms that overcome this curse of dimensionality. First, we provide a quasi-polynomial-time approximation scheme that uses truncation and rounding of the model primitives to compress the joint congestion state, while carefully accounting for how these approximations affect the stochastic evolution of the system to establish near-optimality. Second, we develop a polynomial-time LP-guided algorithm that replaces the joint-state representation with service-level marginal information and achieves a (1-1/e) approximation guarantee under substantially more general service and joining dynamics. Finally, we show that monotone joining behavior, whereby customers become less likely to join as a service becomes more congested, marks a fundamental tractability boundary: without monotonicity, the problem is NP-hard to approximate within any constant factor. This establishes monotonicity as a key behavioral property that enables tractable dynamic service recommendation despite the complexity introduced by congestion-dependent joining.

Online conformal prediction can fail when predictions shape actions and actions determine which outcomes enter calibration. Standard adaptive methods may retain marginal coverage while systematically miscovering the counterfactual outcomes of rarely selected actions. This paper formalizes the failure through counterfactual coverage and introduces Propensity-Weighted Online Conformal Prediction, an inverse-propensity-weighted recursion that debiases calibration. A doubly robust variant further reduces nuisance bias to the product of outcome-model and propensity errors. Under positivity and known logging probabilities, both methods attain the minimax expected coverage rate for nondegenerate calibration. Experiments on synthetic decision tasks, Open Bandit data, and financial rebalancing demonstrate counterfactual coverage gains under selection-biased logging, with prediction-set widths close to those of the oracle in the reported sharpness study.

We formulate the thermal conductance $g_e$ of a particle pair as three branch types – contact, near-contact and bond – within a single construction, and we introduce the filtration that takes this $g_e$ as its axis (the conductance filtration) together with persistence taken relative to the sink boundary. We then show that the dissipation share is exactly the logarithmic sensitivity of the effective conductance, and that a finite change of a single edge is predicted exactly in closed form. The allocation of the dissipation among branch types, and the idealisation ratio of each mechanism (interface, matrix and particle), are thereby obtained as diagnostic quantities on one and the same graph representation.

We investigate the use of neural network solvers for infinity and $p$-Laplace problems, which are fundamental in nonlinear analysis and have practical applications. Our approach employs Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) to address computational challenges associated with large $p$ values, ranging from $2$ to $1000$, on various 2D and 3D domains. Our method offers advantages over traditional physics-based solvers, especially in three dimensions where mesh-based solvers become very costly for these problems. We also establish conditional convergence results for PINN approximations of both problems and a universal approximation result for DeepONet on the parametric $p$-Poisson problem. We demonstrate the effectiveness of these neural network solvers through numerical experiments and compare their performance with conventional methods.

We determine the optimal sample exponent for direct discrete Gaussian SVP search on Haar random unimodular lattices, counting zero outputs. The output is one sampled vector, optionally divided by the greatest common divisor of its lattice coordinates. For every fixed approximation factor $1\leq\gamma<\sqrt e$, the exponent is $\gamma^2/(2e)-\log\gamma$ in natural logarithmic units; it is zero for $\gamma\geq\sqrt e$. For exact SVP this gives $0.2653689\ldots$ in base two. The converse permits arbitrary positive widths chosen from the lattice and all previous outputs, and a fixed width attains every exponent above the threshold. Aggarwal, Dadush, Regev, and Stephens-Davidowitz already give a width within a factor two of optimal for exact SVP on each lattice. We determine the explicit Haar typical rate and show that primitive reduction preserves it. An explicit finite dimensional converse controls all widths simultaneously, including recovery from long multiples; together with finite attainment bounds, it yields query guarantees in both directions. The proof uses random lattice moments and a pointwise Gaussian bound optimized over the width. We account for sampling error and separate sample requirements from generation costs in comparisons with the random lattice search of Pouly and Shen and later algorithms.

We study nonlinear holes, bubbles, kink fronts, and quantum-droplet-like states in an elongated Bose mixture governed by an extended Gross-Pitaevskii equation with attractive cubic mean-field interactions and repulsive quartic Lee-Huang-Yang contribution. We classify the constant-amplitude backgrounds: the Bogoliubov-de Gennes spectrum shows that the upper branch is modulationally stable, whereas the lower branch is unstable to long-wavelength perturbations. Grand-potential and pressure determine the vacuum-finite-density coexistence point and the unique background supporting stationary kink and antikink fronts. Symmetric holes on the stable background have a density deficit and integral width that diverge near coexistence as the hole separates into two nonlinear fronts. A multiplicative kink-antikink construction connects bell-shaped states to broad flat-top droplets and approaches the stationary quantum-droplet family as the front separation increases. An antikink-kink sum with equal signs generates bubble-like density depletions without a phase jump, whereas their difference produces dark-hole-like profiles with a $\pi$ phase difference between the asymptotic backgrounds. Bubble depth increases with front separation, distinguishing gray-like and dark-like profiles. Real-time simulations show that deep bubbles persist under weak random perturbations, demonstrating finite-time robustness without establishing spectral stability. In the asymmetric two-component model, localized relative-density modes can induce spinor-driven breakup on a modulationally stable background, while robust holes persist near the kink limit. Collisions of kink-antikink droplet-like states display phase-dependent merging, asymmetric particle transfer, and effective reflection. These results connect nonlinear fronts with bubbles, phase-jump holes, and self-bound droplets in beyond-mean-field Bose mixtures.

We study an inverse problem for a nonlinear Schrödinger equation with a harmonic potential in some spatial directions and free propagation in the remaining directions. The nonlinearity has an unknown power and a real, spatially dependent coefficient. For small incoming data in a weighted energy space, we construct the wave operator and show that it determines both the power and the coefficient when the latter depends either on the confined variables or on the free variables. The proof uses the first nonlinear term of the wave operator and concentrated product data. We explain why dependence on the free variables requires a stronger lower bound on the power. We also discuss the outgoing wave operator, the small-data scattering operator, and coefficients depending on all spatial variables.

Industrial control system attacks are usually documented in terms of the plant where they occurred: its sensors, actuators, process stages, and control logic. Yet many attacks express a more general physical pattern–such as suppressing flow, corrupting chemical dosing, or driving a vessel toward overflow–that may also matter in a different plant. The challenge is deciding when such a threat remains meaningful on a new system rather than relying on similar component names or broad semantic labels. We present XPhysICS, a methodology for grounding documented cyber-physical threats onto a specific target system. XPhysICS converts source evidence into a provenance-linked description of what is manipulated, what physical consequence is expected, and what observations the evidence calls for. Once this analyst-guided abstraction, its vocabulary and schema version, and a target contract are fixed, XPhysICS applies deterministic grounding checks. An accepted result can be represented as a validation slice that records the mapped roles, signals, dependencies, and context intended to support later evaluation. We study 83 threat abstractions across continuous-process and manufacturing sources using separate evaluation denominators. The continuous-process study evaluates 78 abstractions against target contracts spanning water treatment, water distribution, hydropower, and chemical processes. Selected cases are exercised through controlled perturbations of simulator-role signals. We also test compatibility with several analysis styles, including the released upstream GeCo implementation, and conduct a three-objective, one-target realizability study using a paper-derived search reproduction. Across these evaluated settings, the results support treating explicit target checks and traceable evidence as separate from semantic similarity alone.

We give explicit algorithms that factor elements of the standard diagram monoids into their usual generators. These algorithms generalize sorting from permutations to partial matchings and set partitions. In every case the worst-case complexity is $n^2$, which is optimal for algorithms that explicitly list the factors. We also determine the average complexity of our algorithms.

We prove that closed Einstein four-manifolds $(M,g)$ with positive sectional curvature and Euler characteristic and signature satisfying $2\chi(M)-3|\tau(M)|\le4$ must be homothetically isometric to the round $S^4$ or to $\mathbb{CP}^2$ with the Fubini-Study metric. The proof relies on an upper bound on the ADM mass of conformal blow-ups of $(M,g)$, combined with a lower one from \cite{GM}.

Prior research has demonstrated that the choice of prompt template during Supervised Fine-Tuning (SFT) significantly impacts the robustness of safety alignment afterwards. However, the influence of template selection during Knowledge Distillation (KD) from teacher to student remains largely unexplored. Thus, we fill this gap by analyzing how different template configurations influence the pre-existing safety alignment of the student. We observe a significant degradation of safety alignment present in the aligned base instruct-tuned model. Specifically, we find that utilizing chat templates renders the model more compliant with harmful queries compared to a non-chat template. These findings are consistent across three models: LLaMA, Gemma and Qwen model families and are evaluated across multiple safety benchmarks. We further show that using a non-chat template during distillation better preserves the base student's internal representations, while chat template distillation induces a larger representational shift. Code: https://github.com/anjilab/role-of-prompt-template-in-kd

In this article, we first give a characterization of hyponormal Toeplitz operators with operator valued normal symbols. Latter, we examine when the class of hyponormal Toeplitz operators with operator valued symbols are analytic or normal.