Papers

Among the different ways of approaching the semantics of process calculi, true-concurrency models stand out for their ability to highlight subtle interplays between events. At their heart lie three crucial relations: concurrency, causality and conflict. This paper shows that reversibility, when endowed with a notion of independence, provides a rich tooling to study and characterise these true-concurrency relations. First, we prove that systems admitting pre-reversibility (i.e., that can be extended with an independence relation satisfying some basic axioms) have a unique notion of independence, events, concurrency, causality and conflict. We then analyse the relationship between independence and the true-concurrency relations, establishing novel independence-based characterisations of causality and conflict. Our second series of contributions revolves around two concrete process calculi and two syntactic notions defined on their transition labels, namely independence and dependence; we prove that they partition connected transitions and characterise elegantly concurrency on adjacent transitions. This part of our development was machine-checked using the proof assistant Beluga. Last, we study how the key mechanism commonly used in reversible process algebra can be used as a proxy to retrieve causality and core independence on past events. We conclude by discussing how our results extend beyond reversible systems.

Negative-resistance microwave oscillators can simultaneously sustain autonomous oscillations and coherently scatter electromagnetic waves, enabling active reflection beyond conventional linear amplification. Here we demonstrate giant resonant reflection gain from synchronization-induced phase localization in a self-sustained tunnel diode oscillator operating near 2.96 GHz. Weak resonant RF injection drives a transition from a broadband free running state to a phase localized narrowband reflected carrier. The resulting reflected enhancement reaches 83.1dB relative to the injected signal and is accompanied by greater than order of magnitude linewidth collapse, nonlinear injection pulling, and a synchronization bandwidth of 15.84 kHz. Time resolved spectrograms directly resolve injection locking and frequency entrainment, while noisy Stuart Landau simulations reproduce the observed spectral concentration and detuning dependent gain roll off near the Hopf instability. Artificially increasing phase diffusion with broadband bias noise suppresses the reflected enhancement, confirming synchronization-induced quenching of phase fluctuations as the origin of the giant coherent reflection gain.

We reduce the leading redundancy coefficient for binary codes correcting any fixed number $t\ge2$ of deletions from $2t$ to $2t-1$. This is the first improvement to that coefficient since Levenshtein's 1965 bound. More generally, over every fixed alphabet of size $q\ge2$, codes of length $n$ correcting any combination of at most $t$ insertions, deletions and substitutions exist with redundancy $(2t-1)\log_q n+O_t(\log_q\log_q n)$. For two deletions, the upper-bound coefficient drops from $4$ to $3$, halving the gap to the lower-bound coefficient $2$. The leading coefficient $2t-1$ also holds for $t$ bounded substring edits, where both the removed and inserted strings have bounded length. The proof combines random binary linear hashing of substring counts with a two-colouring argument. A linear dependence among differences of substring-count vectors forces their local changes to overlap, and this overlap lowers the redundancy coefficient from $2t$ to $2t-1$. The result provides an edit-distance analogue of Varshamov's 1957 bound in the Hamming metric, both in the leading redundancy coefficient and in the role of linear independence in the proof.

We prove the existence of a McKean–Vlasov stochastic process with jumps associated to the nonlinear parabolic equation $\partial_t u = \Delta_p u + \Delta_p^s u$ in $\mathbb{R}^N\times(0,\infty)$, where $\Delta_p$ is the $p$-Laplacian and $\Delta_p^s$ is the fractional $p$-Laplacian. Our approach is the following: first, after proving the existence of a solution for the PDE presented earlier, we rewrite it as a nonlinear Fokker-Planck-Kolmogorov equation whose measure-valued solution is guaranteed when $p\ge4$. Then we solve the martingale problem associated to our FPKE via a new superposition principle for non-local Fokker-Planck-Kolmogorov equations, which only requires an integrability condition on the local coefficients. Finally, thanks to the martingale solution obtained, we derive the existence of a weak solution for the McKean-Vlasov's type SDE with jumps whose infinitesimal generator is a << hybrid version >> of the operator $\Delta_p+\Delta_p^s$.

Modern LLMs and AI agents increasingly support data engineering workflows that integrate evidence from unstructured sources. Such pipelines typically do data retrieval, integration, and ranking before proceeding to more complex agentic reasoning or actions, e.g., for scientific discovery. The core retrieval problem in these workflows jointly executes multi-attribute filtering, multi-vector search, exact relational joins, and thresholded embedding-similarity joins. Given a planned query and monotone scoring function, our DASE query engine constructs and ranks candidate evidence tuples. It comprises (i) a multi-step reasoning query model over structured predicates, multiple vectors, and relational links; (ii) SemJI, a sparse materialized embedding-similarity join index for rare near-neighbor pairs; and (iii) a co-designed execution layer that combines predicate-aware ANN traversal, batched access, and threshold-based score aggregation. On scientific-discovery workloads, DASE retrieves candidate evidence for multi-step reasoning queries 6x to 46x faster than strong RDBMS, rerank, and vector-database baselines at comparable recall; and for tasks that require semantic-operator post-processing, DASE acts as a high-recall prefilter that makes downstream LLM evaluation both cheaper and more accurate – e.g., on SemBench E-Commerce it improves BigQuery quality from 0.67 to 0.80 while cutting cost from $2.42 to $0.54.

We investigate the pairing symmetry of the ground-state phase diagram of an extended two-dimensional $t$-$t'$-$t''$-$J_z$ model, in which the first-, second-, and third-nearest neighbor electron hopping terms ($t,t'$ and $t''$) and an anisotropic Ising-like antiferromagnetic interaction $J_z$ are treated on the same framework. We find that the dominant pairing symmetry depends sensitively on the sign and magnitude of the hopping parameters $t'$ and $t''$, showing pure $p$-wave, pure $d$-wave, or coexisting pairing channels, highlighting the decisive role of these terms. We further explore the role of the long-range and short-range repulsive interactions in the formation of pairs and analyze the specific case of hole-doped cuprates. Our results indicate that repulsive interactions favors hole pair escaping of the stripe domains. Furthermore, pairing correlation calculations strongly suggest that repulsive Coulomb interactions drive reentrant superconducting behavior at experimentally observed underdoped regime ($\delta\approx0.07$ to $0.15$), as in Neodymium-based cuprates.

To design many Bayesian studies, the sample size is chosen to attain sufficient power to reject a null hypothesis or a desired probability that an interval estimate is sufficiently narrow. Determining the minimum suitable sample size for studies with complex models typically requires intensive Monte Carlo simulation. One simulation-based strategy to consider the sample-size space involves estimating sampling distributions of posterior summaries, such as posterior probabilities or interval estimate lengths, at various sample sizes. Another strategy instead explores these sampling distributions via stochastic root finding over the sample-size space, where the entire sampling distribution of posterior summaries is not estimated at any given sample size. The performance of these competing approaches can be assessed using their Monte Carlo sampling distributions of sample size recommendations across repeated implementations. In this paper, we theoretically derive these Monte Carlo sampling distributions for various Bayesian sample size determination approaches. To promote best practices for Bayesian sample size determination, we conduct extensive numerical studies to estimate these Monte Carlo sampling distributions for the sampling distribution estimation and exploration approaches to assess their bias, precision, and sensitivity to tuning parameters.

Instructional materials can be passed along to new instructors, yet the instructional reasoning, such as instructional intentions, contextual information, and reflective insights behind their design, is rarely preserved. Traditional Learning Management System (LMS) tools are designed to store instructional artifacts rather than reasoning. To address this issue, we propose Teaching Memory, a design approach that treats instructional reasoning as a primary form of knowledge. We present a design-oriented framework for preserving instructional reasoning in a lightweight manner within instructors' existing workflows, enabling continuity and reuse.

Graph neural networks are central to materials property prediction and machine-learning interatomic potentials, yet their reliance on specialized graph libraries hampers portability and reproducibility, and property and force-field models have historically required separate graph pipelines. We present ALIGNN 2.0, a dependency-free, pure-PyTorch reimplementation of the Atomistic Line Graph Neural Network, with the line graph and its batching built from scratch, running on current-generation accelerators and unifying scalar, spectral, tensorial, per-atom, and force-field prediction behind a single graph, a combination that to our knowledge no existing framework provides. Comparing radius and k-nearest-neighbor (kNN) graphs, the wider kNN graph is more accurate for properties while the smoothly varying radius graph is required for energy-conserving molecular dynamics. On the JARVIS-Leaderboard, ALIGNN 2.0 leads on 26 of 30 single-property benchmarks against the original ALIGNN, with large gains for piezoelectric and dielectric maxima, exfoliation energy, moduli, and superconducting Tc. The LAMMPS- and OpenMM-compatible ALIGNN-FF matches leading universal potentials on the Matbench-Discovery and CHIPS-FF benchmarks at a small fraction of their parameters while scaling to hundred-thousand-atom cells. We further use ALIGNN 2.0 as the denoiser in a conditional crystal-diffusion model, where explicit line-graph message passing consistently lowers structural denoising loss. We also show, as work in progress, that an independently diffused, redundant bond-angle state is learnable but does not uniformly improve reconstruction or combine additively with the line graph. Finally, from a single relaxed structure the same framework reconstructs infrared, Raman, optical-dielectric, and neutron spectra in agreement with experiment and DFT, and drives frozen-phonon electron-microscopy image simulation.

Open clusters are fundamental tracers of the chemical and dynamical evolution of the Galactic disc. This study presents a systematic characterisation of 14 understudied open clusters from the Pismis catalogue, selected for a well-defined stellar sequence in Gaia DR3 and spanning a wide range of ages and distances. Using high-precision Gaia DR3 astrometry, we provide a high-fidelity modernisation of these historical discoveries while testing our analytical framework across diverse stellar populations. Membership probabilities were determined via the unsupervised UPMASK algorithm using Gaia DR3 positions, proper motions, and parallaxes. To ensure high sample purity, the member samples entering the isochrone fits were restricted to P >= 0.90, with astrophysical parameters calculated through membership-weighted likelihoods. Fundamental properties – age, distance, reddening, and metallicity – were derived using a Bayesian Nested Sampling approach to isochrone fitting, chosen for its robustness against the parameter degeneracies typical of dense Galactic fields. The 14 systems exhibit a broad range of properties, with ages from approximately 11 Myr to 1.5 Gyr and distances spanning approximately 690 to 5445 pc. These refined, uniform parameters reconcile historical observations with the precision era of modern astrophysics, providing a homogeneous baseline for systems that large-scale automated surveys recover only partially. A direct cross-match against widely used automated catalogues shows that they typically contain only about a third of the members identified here, and substantially less in the most crowded fields, underscoriecific analysis. This workcontributes to a more complete census of the Galactic disc and sets out a reproducible, per-cluster licable to the manycomparable low-latitude systems still to be characterised.

Useful quantum computation requires the fault-tolerant implementations of a universal gate set which are generically not efficiently simulable. We devise an algebraic framework that allows for efficient sampling from the measurement distribution of fault-tolerant circuits that implement diagonal logic gates in the third level of the Clifford hierarchy. Upon successful sampling we also provide sufficient conditions for decoding success. The resulting estimate for the logical failure rate is an overestimate, which becomes more accurate for blocks that are fault tolerant against arbitrary local errors. The non-Clifford simulation overhead is independent of the number of logical qubits, making the method particularly attractive for large-scale simulations. The framework is based on viewing the non-Clifford gates in the circuit as a cohomology invariant of an underlying spacetime fault complex. The method can also be interfaced with Clifford simulators to simulate larger fault-tolerant circuits and algorithmic subroutines.

Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.

Text-based person retrieval under a sim-to-real gap (synthetic training data, a real-image gallery) is usually tackled with costly fine-tuned cross-encoders. We ask whether a frozen-encoder system can compete. We present SCOUT, which casts cross-modal retrieval as prediction in embedding space. A trainable predictor maps the patch tokens of a frozen video encoder into the embedding space of a frozen text encoder under a bidirectional InfoNCE objective, and no encoder is fine-tuned in the base model. The video encoder is V-JEPA, the text encoder is EmbeddingGemma, and the predictor is initialized from a Qwen3.5-0.8B decoder. We make three findings. First, the best frozen text encoder is simply the one whose geometry best matches the video features. A training-free alignment score ranks three candidate text encoders in the same order as their retrieval accuracy on our held-out split (Spearman $\rho = 1.0$); a fourth, LLM-based encoder shows the rule is metric-dependent, holding for a neighborhood-overlap score ($\rho = 0.8$) but not for a linear probe ($\rho = -0.2$). Second, two precision-targeted levers, parameter-efficient ExPLoRA adaptation of the video encoder and a training-free attribute-decomposed reranker built on a vision-language model, improve the top-rank precision that otherwise limits the frozen system, adding 2.2 points of leaderboard R@1. Third, a local-versus-public calibration study explains which interventions transfer to the real domain. On AI City Challenge 2026 Track 4 the full retrieve-fuse-rerank system reaches 84.25 mAP@10 on the final leaderboard, while a single frozen model submitted alone reaches 60.63. Our trained components cost about 95 GPU-hours. CMP, the dataset authors' fine-tuned cross-encoder that trains for sixteen GPU-days, is one fusion member of the full system, not an alternative. Code and annotations: https://github.com/abtraore/SCOUT-ECCV

Algebraic Retrieval lets AI agents compose search strategies at query time. Relevance criteria, eligibility constraints, and ranking preferences can be expressed together in a mathematical query. The query surface exposes available operations, so an agent can combine them for the question at hand and revise a program after inspecting results. We evaluate execution parity, not agent behavior or retrieval quality. Building on Programmatic Embedding Modulation (PEM), which exposes vector and score arithmetic during retrieval, we demonstrate contrastive scoring, candidate-pool reranking, and weighted ranking as composable queries, alongside executable SQL and PyTerrier counterparts. On the public 11,429-document Vaswani fixture, each program's implementations select the same document set with score differences below 1e-6; one tied pair orders differently across scoring paths.

This work focuses on range characterization of spherical mean transform (SMT) in odd-dimension Euclidean space. In a recent work, a simpler description characterizing the range of SMT in odd dimensions was derived. This involved symmetry relations involving certain linear ordinary differential operators acting on the coefficients of the spherical harmonics expansion of the function in the range. The sufficiency part of this characterization was shown using an existing range characterization result due to Agranovsky-Kuchment-Quinto. In the current work, we provide a direct and constructive proof showing the sufficiency of the aforementioned symmetry conditions and we obtain this without invoking any of the existing range characterization results. As an added advantage, given a function $g$ satisfying the range conditions, our approach provides an explicit construction of a function $f$ such that the SMT of $f$ is $g$.

The muscles that power insect flight fall into one of two categories: 1) synchronous muscles that contract under direct control from the nervous system, and 2) asynchronous muscles which have an intrinsic stretch activation response that spontaneously generates wingbeats without the need for signaling from the brain. It is thought that the emergent nature of asynchronous wingbeats provides both adaptive and responsive capabilities for flight control. To date, most flying robots use synchronous actuation. In this paper we develop the first flight-capable flapping wing robot that uses asynchronous actuation. We demonstrate that asynchronous actuation allows wings to respond to changes in the resonant mechanics of the body without control input, and wings can react instantaneously to collisions with obstacles with no extrinsic sensing needed. Flight tests within cluttered environments demonstrate that asynchronous actuation significantly improves stability and performance when compared to synchronous actuation. In total this work demonstrates that a flapping wing robot actuation strategy that emulates the asynchronous muscles of flying insects can provide fast, reactive actuation responses before a control system would need to intervene. This partitioning of embodied control to both the low-level actuation dynamics and and high-level sensorimotor system provides a compelling blueprint for new flying robots.

We present a typed two-dimensional $\lambda$-calculus whose equality evidence is computational: a path between two terms is an explicit finite sequence of one-step conversions (the $\beta$- and $\eta$-contractions, the congruences, and the structural rules), and every property of paths is proved by recursion over that sequence, with any step as a base case — in deliberate contrast with Martin-Löf type theory, where identity is generated by reflexivity alone and all properties go through the non-computational $J$-eliminator. The higher structure is imported from the $2\beta$- and $2\eta$-conversions of the theory of an arbitrary higher $\lambda$-model: we obtain 2-dimensional coherence laws, computable naturality of homotopies (via inductive homotopies and their explicit evaluations), a 2-dimensional path type with transport, and a parity invariant that proves the system consistent and really intensional: the $\beta$- and $\eta$-contractions are provably distinct evidence, while in the native syntax of Idris (core MLTT) they are identified by definitional equality. Commutative diagrams accompany the main constructions, and the theory is fully formalized in Idris 2. A parallel Lean formalization is published in the Palomar registry \cite{palomar2026lean}. A philosophical reading closes the paper: constructivism in the BHK sense, proof-relevant intensionality, and the boundary between syntax and semantics, drawn relative to MLTT and HoTT.}

In single-field inflation, linear perturbations originate as quantum fluctuations and undergo a quantum-to-classical transition on super-horizon scales as the decaying mode of the comoving curvature perturbation $\mathcal{R}$ is suppressed. This transition provides a condition for the validity of a classical stochastic description of $\mathcal{R}$. We characterize classicality through the suppression of the quantum commutator relative to phase-space variances and the evolution of the squeezing parameters. In the Starobinsky model, we show that this transition becomes mode-dependent at linear order due to the transient ultra-slow-roll (USR) phase. This is because the decaying mode transiently grows during the USR phase modifying the squeezing dynamics, and shifting the classicalization time depending on when modes exit the horizon relative to the USR phase. We then study the implications of this mode-dependent transition for the stochastic description of perturbations. Using the Green's function method, we show that the stochastic spectrum reproduces the power spectrum of the quantum state initialized in the Bunch-Davies vacuum, independently of the mode-dependent transition when the gradient term is retained in the Langevin equation, for both white and colored noise coarse-graining. In contrast, ignoring the gradient term in the Langevin equation introduces an explicit dependence on the coarse-graining parameter $\sigma$. Homogeneous matching procedure can be used to set mode-dependent $\sigma(k)$ that reproduces the power spectrum of the quantum state at the end of inflation. Crucially, however, we show that the matching times precede the classicalization times for modes near the USR transition. Therefore, the transient USR phase in this model leads to a mode-dependent condition for when linear curvature perturbations can be described as classical stochastic noise.

The association of active galactic nuclei (AGN) with high-energy neutrinos has been studied through population and individual source analyzes, but whether these associations reflect physical processes or chance coincidences remains open. Blazars, AGN with relativistic jets aligned with the line of sight, spatially consistent with IceCube high-energy events, offer a natural framework to address this question. Combining multifrequency observations with physically motivated emission models allows us to assess whether these sources can plausibly account for the detected neutrinos. We study six blazars with single gamma-ray counterparts to well-reconstructed IceCAT-1 high-energy events, accounting for the improved localization expected from IceCAT-2, and compile their multifrequency spectral energy distributions (SEDs). We model these sources within a lepto-hadronic framework, exploring their parameter space to reproduce the observed emission while favoring solutions that maximize neutrino production. The SEDs can be reproduced with compact emission regions close to the broad-line region with moderate Doppler factors. The emission is generally leptonic-dominated, with subdominant contributions from hadronic cascades, except for one source where the gamma-rays are hadronic-dominated. For four, the energy density of the relativistic particles is close to equipartition with the magnetic field. The predicted neutrino detection rates reach up to $~5x10^{-2}$ per year, mostly compatible with one observed IceCube event under Poisson statistics. While these blazars are unlikely to significantly contribute to the diffuse neutrino flux, their properties are consistent with being possible counterparts to individual neutrino events, driven by contributions of external photon fields to the hadronic interaction rate, even for sources where these fields have previously been considered as non-significant.

Generative models are increasingly central to many de novo discovery pipelines, in which designs are generated at scale and filtered through virtual screens to determine a set of candidates to experimentally validate. While Bayesian optimization (BO) is a natural fit for this setting, as it uses past evaluations to guide future proposals, the computational overhead required for its sequential decision-making becomes a bottleneck when virtual screens are relatively cheap. We make BO practical in this regime by exploiting the unique combination of a linear model constrained to a spherical domain where high-dimensional latents concentrate. We build off recent work justifying the use of linear surrogates, while deriving nearly closed-form solutions to the surrogate modelling and acquisition problems that exploit spherical symmetry. The result is at least a 100x speedup over state-of-the art baselines, with matching or improved performance across molecular and image generation benchmarks. Altogether, our method makes BO a practical drop-in for de novo pipelines where it was previously too slow to consider.

Diffusion-based Vision-Language-Action (VLA) models achieve strong performance in embodied tasks, but their iterative sampling imposes heavy computational and memory-access cost, blocking real-time deployment on edge platforms. Existing acceleration methods either require expensive training (e.g., distillation, flow matching) or degrade perception via statically scheduled pruning and caching, ignoring the dynamic workload variance of robotic interactions. This paper presents FASA (Feedback-Aware Sampling Adaptation), a training-free runtime framework that treats real-time multimodal feedback as a control signal for the denoising pipeline: an interaction-driven range adaptor modulates the global sampling-step budget based on visual and gripper-force feedback, and a proprioception-aware step adaptor pinpoints the optimized step within the adapted range. This co-designed framework allows the underlying hardware architecture to adaptively match the workload demands of different execution phases. Comparative evaluations across several benchmarks show that the inference speed can be increased by up to 1.45$\times$ while maintaining competitive success rates, providing a novel dynamic runtime architecture paradigm for deploying heavy generative embodied AI workloads onto resource-constrained computing platforms.

We study the maximal multiplicative persistence of $k$-cycles in random Čech complexes. Let $f:\mathbb{R}^d\to\mathbb{R}$ be a probability density function, let ${P}_n$ be a Poisson process with intensity $nf$, and let $\Pi_{k,n}$ denote the largest death-to-birth ratio among all non-essential $k$-cycles ($1\le k \le d-1$). For the uniform distribution in the unit hypercube, it was proved in [9] that $\Pi_{k,n} = \Theta\left( \left(\frac{\log n}{\log\log n}\right)^{1/k}\right)$. In this paper we sharpen and extend this result to a law of large numbers, for a broad class of distributions. Most significantly, we show that the limiting constant depends only on $d$ and $k$, and not on the probability density $f$. Thus the extreme value of multiplicative persistence exhibits a universality phenomenon. We show that the limiting constant is determined by the asymptotic covering density of the $k$-dimensional sphere. Our proof identifies the geometric mechanism underlying maximal cycles, a persistent isoperimetric inequality, which gives sharp bounds on the number of points needed to generate a highly persistent cycle. By combining covering-density estimates with isoperimetric inequalities, we show that this minimum is asymptotically attained by efficient coverings of a $k$-sphere. A key ingredient is a geometric measure theory argument that uses compactness to relate discrete covering counts to the volume of a limiting cycle.

We establish product-profile anti-concentration, density, and Remez estimates for multi-affine polynomials on the cube. Let $X$ be uniformly distributed on $[0,1]^n$, and let $P:[0,1]^n\to\R$ be a nonconstant multi-affine polynomial of exact degree $d$, with all variables active. For a partition $\cB$ of the variables such that no monomial contains two variables from the same block, define $$ w_d(\cB) = \sum_{\cI\subseteq\cB, \abs{\cI} = d-1} \left(\prod_{B\in\cI}\sqrt{\abs B}\right) \sqrt{\sum_{C\in\cB\setminus\cI}\abs C}. $$ We prove the all-center small-ball estimate $$ \sup_{u\in\R} \Prob\{\abs{P(X)-u}\le\rho\} \le \Phi_d\left( C_dw_d(\cB)\frac{\rho}{\osc(P)} \right), $$ where $\osc(P)$ is the length of the range of $P$ and $\Phi_d(t) = t\sum_{j = 0}^{d-1}\log^j(1/t)/j!$ on $(0,1]$, capped at one. Every multi-affine polynomial admits the singleton partition, which yields the universal scale $n^{d-1/2}$; an admissible partition into at most $q$ blocks yields the improved scale $q^{(d-1)/2}n^{d/2}$. If $\cB$ has exactly $d$ blocks, then $$ w_d(\cB) = d\prod_{B\in\cB}\sqrt{\abs B}, $$ and products of centered block averages show that both the small-ball profile and the dependence on the full block-size vector are optimal, up to constants depending only on $d$. We also prove that $P(X)$ has a density $f_P$ satisfying $$ \norm{f_P}_{L^p(\R)} \le C_dp^{d-1} \left( \frac{w_d(\cB)}{\osc(P)} \right)^{1-1/p}, \quad 1<p<\infty, $$ with matching $p$- and block-scale growth for $p\ge2$ on the block-product models. As an application, we derive translation-invariant quotient Remez inequalities with the same structural scale. The proof combines weighted block selection, affine cube slicing, degree-lowering contractions, and the exact recursion underlying the product profile.

Autonomous systems increasingly rely on Large Language Models (LLMs) yet the safety infrastructure surrounding these models introduces latency and compute overhead. This limits utility in resource-constrained, time-critical deployments. Existing external guardrail models remain blind to the model's internal workings, creating a fundamental assurance gap. We ask: does the model already know when the content is harmful? We extract activations from LLaMA-3.1-8B and train lightweight MLP classifier probes (12.6M parameters) to detect harmful prompts. Evaluated on WildJailbreak, Beavertails, and AEGIS 2.0, our probes achieve F1 scores of 99%, 83%, and 84%, respectively competitive with 1000x larger guard models while cutting latency and compute costs.

Chiral $p$-wave superconductors and superfluids are central model systems in the search for topological quantum matter, but in reduced dimensions their properties are inseparable from the boundary conditions imposed by surrounding surfaces. Superfluid $^3$He provides a uniquely clean, well-established spin-triplet $p$-wave condensate in which these boundary conditions can be engineered directly. Here, we use a fourth-sound Helmholtz resonator to study the A–B phase transition of $^3$He confined to a $1.8\,\mu$m cavity after preplating the internal surfaces with $\sim4$ atomic layers of $^4$He. In contrast to our previous fourth-sound measurements, which showed no resolvable hysteresis in the transition temperature, the preplated device exhibits a clear separation between cooling and warming transition temperatures together with stochastic run-to-run variations. The hysteresis decreases toward the highest pressures studied, consistent with previous observations of the pressure dependence of $^4$He-mediated quasiparticle boundary scattering. These results demonstrate that surface preparation can qualitatively modify first-order transition kinetics in confined $^3$He, making boundary conditions an experimentally accessible control parameter for metastability and for future studies of reduced-dimension topological superfluid states.

Let $\Bbbk$ be an algebraically closed field of characteristic zero. A recent theorem of I. Pan characterizes the nonzero locally nilpotent derivations of $\Bbbk[x,y]$ in terms of their isotropy groups: such a derivation is locally nilpotent if and only if its isotropy group contains automorphisms of arbitrarily large degree. We study analogues of this characterization for several noncommutative algebras related to the affine plane. Our main result shows that Pan's characterization extends to the differential Ore extensions $A_h=\Bbbk[x][t;h(x)\partial_x]$, where $h\in\Bbbk[x]\setminus\Bbbk$. For the first Weyl algebra $A_1$, we establish the same equivalence for every nonzero locally finite derivation. For the quantum plane and the first quantum Weyl algebra, known results imply that the corresponding equivalence holds vacuously for nonzero derivations. In contrast, the converse fails for the free associative algebra $\Bbbk\langle x,y\rangle$: we construct a non-locally-nilpotent inner derivation whose isotropy group has unbounded degree. We further analyze this failure through the behavior of automorphisms and derivations under abelianization.

We present in this article data on the computed potential energy surface, permanent moment surface (from dipole to hexadecapole) and polarizability surface (from dipole-dipole to quadrupole-quadrupole) for the H$_2$O molecule, calculated at the level of the generalized gradient approximation (GGA) in Kohn-Sham density functional theory (KS-DFT) in the grid-based projector augmented wave code GPAW, using the charge perturbation code C-pol. The GGA-based functionals are PBE, RPBE and BLYP. The monomer surfaces are composed of systematic, symmetry-reduced deformations of the H$_2$O monomer and comprise 10,000 configurations per functional, with traceless Cartesian tensor moment values reported as data strings in the xyz file format. In addition, we provide cluster datasets for n-H$_2$O aggregates (n = 2-6), sampled from liquid-like configurations and computed with the same KS-DFT settings, where each extended xyz file encodes the total interaction energy of the cluster in the comment line. Finally, ab initio molecular dynamics (AIMD) trajectories of periodic liquid water boxes, containing between 25 to 150 H$_2$O molecules at ambient conditions, are included, furnishing time series of atomic configurations and energies that are consistent with the monomer and cluster data and suitable for validating classical and machine-learned water models.

This paper presents the design, characterization, and large-signal measurement methodology of a high-order whip-mode flexural microresonator on a lithium tantalate-on-insulator (LTOI) unimorph platform. A tapered cantilever concentrates kinetic energy at the free tip through a structural velocity amplification effect, with a targeted whip mode at 9.175 MHz exhibiting a measured Q of 691 in air. The results indicate a substantially reduced susceptibility to viscous damping at high modal frequencies. In-air large-signal testing on a separate device confirms tip velocities up to 20 m/s before the reliable measurement range of the laser Doppler vibrometer (LDV) at the tapered tip is exceeded, while the device itself sustains drive levels up to 240 Vpp before failure. Transitioning to vacuum reveals photothermal-induced static bending of the LTOI cantilever under LDV laser illumination, an effect that prohibits direct velocity measurement for these resonators. Hence, it motivates an indirect extraction methodology to be implemented. In this work, a 3.85 times base-to-tip geometric amplification factor, independently calibrated at low drive, is applied to base velocity measurements to infer tip velocity under large-signal conditions. Using this approach with narrowband chirp excitation, a maximum extracted tip velocity of 58.9 m/s is obtained at 192 Vpp, with spectral analysis of the base velocity placing a conservative lower bound of 36.2 m/s on this estimate. Large-signal failure-mode analysis identifies Pt/Au electrode melting at 210 Vpp as the current velocity ceiling. These results suggest that geometric amplification in high-order flexural modes offers a viable pathway toward the high proof-mass velocities targeted for next-generation MEMS inertial sensors.

The Raman spectrum of the room-temperature altermagnet $\alpha$-MnTe is reported to contain unassigned peaks at 120(3) cm$^{-1}$ and 140(3) cm$^{-1}$, absent from the predicted phonon spectrum of the material. This has generated considerable debate within the altermagnet community and necessitates urgent resolution. This work establishes that these peaks, together with the 90(5) cm$^{-1}$ peak that matches a theoretically predicted mode, are all extrinsic, originating from elemental tellurium formed during air exposure of the surface. Raman spectra of MBE-grown thin films show that these peaks closely match those of elemental tellurium, emerge soon after air exposure, and are absent in AlO$_x$-capped films. X-ray photoelectron spectroscopy shows that air exposure breaks Mn–Te bonds and oxidizes Mn within a minute. Cross-sectional scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy reveals that the oxidation leads to Mn out-diffusion, forming a few-nanometer-thick oxide layer above a buried, Te-enriched region, likely responsible for the anomalous Raman peaks. Additionally, no sample exhibited the 175 cm$^{-1}$ Raman peak which is commonly attributed to MnTe$_2$. The aggressive surface oxidation and associated elemental Te formation in MnTe have important implications for any surface-sensitive and optical characterization of MnTe (and other similar Te-containing materials) involving even the briefest air exposure.

Accurate prediction of nitrous oxide (N2O) emissions from agriculture is important for assessing environmental impacts and supporting sustainable farming. However, prediction remains difficult because N2O emissions result from complex interactions among soil properties, climate, biochemical processes, and management practices, while high-quality observations are limited. Deep learning models can capture nonlinear relationships but often lack physical interpretability and may generalize poorly across environmental conditions. We propose the Knowledge-enhanced Agriculture-informed Neural Network (KAINN), a hybrid neural-mechanistic framework that extends the Agriculture-informed Neural Network by incorporating domain knowledge about fertilizer diffusion, soil respiration, and water-filled porosity. We evaluate KAINN using CNN, LSTM, and Transformer architectures across multiple growing seasons and input-feature configurations. The results show that KAINN generally provides lower root mean square error and mean absolute error and higher R-squared values than purely data-driven models and the original AINN. Analysis of the learned interfaces also shows smoother and more physically consistent parameter trajectories with reduced uncertainty. These findings demonstrate that incorporating environmental knowledge into neural networks can improve the reliability, interpretability, and generalization of agricultural N2O-emission predictions.