Papers

Language models frequently generate outputs in unintended languages or scripts, a phenomenon known as off-target generation. While existing research has focused on language selection, the dimension of script knowledge remains understudied: before any linguistic understanding can occur, users must recognize the graphic symbols in a model's response. We investigate whether Small and Large Language Models (SLMs and LLMs) possess script knowledge by testing them on multi-scriptic languages. Through two complementary experiments, we evaluate whether models (1) adapt their output script to match the input, and (2) follow explicit instructions to generate text in a specified script. The models we tested demonstrate substantial script knowledge: they all achieve a near-perfect Latin script fidelity (more than 98%) and follow script instructions with high frequency. Nevertheless, we notice differences between LLMs and SLMs, with higher scores for LLMs including for non-standard script combinations.

AI agents are increasingly being programmed to automate knowledge work over large collections of unstructured data. Such automation requires repeatability: when the underlying evidence is unchanged, the agent's categories, priorities, and counts should not shift materially between runs, even if each individual answer appears plausible. We introduce a repeat-run evaluation framework that aligns semantically equivalent categories and focuses on two operating metrics: theme churn, the normalized change in the returned category set, and volume disagreement, the change in counts for categories that persist. We evaluate three recurring customer-feedback tasks across eight frontier models, corpus sizes from 100 to 5,000 records, multiple prompts, and three execution designs: raw generation, taxonomy-free hierarchical decomposition, and a taxonomy-grounded agent (TGA) using persistent themes, subthemes, and record-level predictions. With Claude Opus 4.8 and the 1,000-record corpus fixed, TGA reduces theme churn by 86–88% relative to both raw generation and hierarchical decomposition, while matched-theme volumes have zero disagreement. The taxonomy-grounded agent is more stable than every raw model in the screen, remains more stable at each corpus size, and keeps this advantage when theme matching is made stricter or looser. Although evaluated on customer feedback, the framework targets repeated synthesis of unstructured corpora more broadly, including financial reports, legal documents, incident records, and scientific literature. Overall, these results show that taxonomy grounding produces more consistent and repeatable outputs for recurring knowledge work.

Ground roll suppression remains a challenge in land seismic data processing, particularly when strong surface wave energy exhibits significant overlap with effective reflection events in the low frequency band. Conventional approaches, such as frequency-wavenumber (F-K) filtering, Radon transform-based methods, and other spatial filtering techniques, often fail to achieve satisfactory results under such conditions due to limited resolution and poor amplitude preservation. To address this problem, a time-frequency domain ground roll suppression method that integrates the synchrosqueezed wavelet transform (SSWT) with local adaptive subtraction filtering is proposed. First, seismic traces are transformed from the time-space domain into the time-frequency domain using SSWT, which provides a highly concentrated time-frequency representation. Based on the distinct distribution characteristics of ground roll noise and effective reflection signals in the time-frequency domain, a ground roll model is extracted. Subsequently, a local adaptive subtraction filter is applied to adjust the amplitude and phase of the extracted ground roll model, and the corrected model is subtracted from the original seismic data to obtain the final suppressed result. Applications to both synthetic and field seismic data demonstrate that the proposed method effectively attenuates ground roll energy while maximally preserving the amplitude and waveform characteristics of reflection signals. Compared with conventional time-frequency-based ground roll suppression approaches, the proposed method exhibits superior amplitude fidelity and improved noise attenuation performance.

Collisionless shocks accelerate particles at a rate set by the diffusion coefficient of those particles in waves they themselves generate. Theory fixes that coefficient only in steady state, and no measurement has tested whether an evolving shock ever reaches that state. We report Parker Solar Probe observations of a fast, near-parallel interplanetary shock at 0.24 au, encountered four hours after eruption, with the upstream waves and the protons they scatter recorded on the same magnetic field line. From the wave spectra alone we derive the parallel mean free path of 0.05-30 MeV protons, resolved in energy and in distance from the shock. The mirror force of the measured compressive fluctuations supplies the scattering through the pitch angles that gyroresonance cannot reach. The mean free path grows with distance nearly as the steady self-generated solution requires, yet the steady balance holds at one energy only, near 1.3 MeV. The intensity profiles are a factor of two shallower than the measured coefficient predicts, because the waves are still growing. Confinement fails between 2.3 and 6 MeV, beginning a factor of two below what the age of the shock allows. The growth of the waves its own particles drive, rather than its age or its size, limits the energy an evolving shock confines.

World models are usually judged from the inside: by prediction loss, by the return a policy earns in imagination, or by how convincing their frames look. We judge one from the outside. We learn a structured, multi-agent world model of a complete ten-hero MOBA (206 units, every hero acting every tick, games of up to 6,000 ticks), train a policy only inside it with 1,400-tick free-running imagined episodes, and measure that policy in the real game against the opponent the game ships with. The real game never provides a gradient; it provides the policy's own games as training data for the world model, and an online evaluation that selects and anchors the policy. Run as a continuous asynchronous Dyna loop, the policy wins 70.2% of real games as radiant (421 of 600; 95% CI 66.4-73.7) on seeds never used for any decision, up from 0% for dream training alone and 33.7% before the loop. It wins none as dire, and neither does the shipped opponent when it plays itself. Four findings explain the result. Model exploitation is invisible from inside the dream: every unanchored run collapsed within a few updates while no in-dream metric tracked the collapse. A world model that is accurate on its training corpus is badly wrong on the policy's own games, and Dyna repairs it there, which is worth +9.2 points of real win rate with the policy recipe held fixed. Finally, the policy inherits its world model's fidelity profile mechanic by mechanic: the model represents the macro game but not crowd control, cast timing or lethality, and the policy wins by map-wide pressure with almost no coordinated fighting. We release the world model, the dream-PPO harness, a world-model debugger, the evaluation protocol, and every policy and log.

We extend the generalised Calderon Transfer Principle as presented in \cite{dBL} to the setting of trace preserving group actions of $\sigma$-compact locally compact Hausdorff groups on semifinite von Neumann algebras $\M$. At its essence the transfer principle consists of showing that a large class of regular operators in the group context may be translated to operators in the algebra context by means of this group action. The end result is a protocol for proving ergodic convergence results for group actions on noncommutative Orlicz space of semifinite von Neumann algebras. We start with proving the existence of the transferred operator in the noncommutative context. Two tools are developed for the purpose of actually proving convergence results: (1) a theory of what may be called 2-variable decreasing rearrangements for the algebra $L^\infty \overline{\otimes} \M$ (where ($\Gamma,\nu$) is a Radon measure space) and (2) a concepts of maximal operators suited to the present context. These tools are then used to lift the ergodic convergence results presented in \cite{dBL} to the noncommutative setting. In closing we present examples illustrating the application of the tools

We investigate an all-optical scheme for high-sensitivity measurements of the Earth's scale magnetic field ($B$). The scheme is based on the Bell-Bloom technique with frequency-modulated light. A single elliptically polarized light beam is used both for pumping the alkali-metal atoms and probing Larmor precession of their spins under the external magnetic field. In contrast to many other high-sensitivity magnetometry schemes based on nonlinear polarization rotation of the light, the proposed approach enables the observation of magnetic resonance via changes in the light-beam ellipticity parameter. The approach has been validated in experiments with a vertical-cavity surface-emitting laser, irradiating a $0.125$ cm$^3$ cesium vapor cell filled with a buffer gas. In the current experimental conditions, the achieved sensitivity is estimated at $220$ fT/$\surd$Hz under $B$$\,\approx\,$$50$ $\mu$T, while the shot-noise floor corresponds to $\approx\,$$20$ fT/$\surd$Hz. The bandwidth is estimated at $\approx\,$$1$ kHz. The proposed simple and robust single-beam scheme is well suited for miniaturization and is therefore particularly promising for the development of compact, highly sensitive, low-power-consumption atomic magnetometers for a wide range of applications in the geomagnetic field.

Hematite ($\alpha$-Fe$_2$O$_3$) is a prototypical antiferromagnetic platform for high-speed spintronics and magnonics, yet its finite-momentum magnon dynamics and spin-reorientation mechanism remain incompletely understood. Here we use low-wavenumber magneto-Raman spectroscopy to resolve both $k=0$ and finite-$k$ sub-terahertz magnons in $\alpha$-Fe$_2$O$_3$ across the Morin transition. We find that the limiting group velocity $v_0$ remains nearly field independent, whereas the finite-$k$ group velocity $v_{\mathrm g}$ is strongly modified near the Morin and spin-flop transitions. By combining parallel- and transverse-field measurements with spin-wave modeling, we further extract the temperature-dependent Dzyaloshinskii–Moriya field $H_{\mathrm D}$ and uniaxial anisotropy fields $H_{\mathrm{K1}}$ and $H_{\mathrm{K2}}$. We find that $H_{\mathrm D}$ is weakly temperature dependent at approximately 2.0–2.3~T, while $H_{\mathrm{K1}}$ decreases rapidly and $H_{\mathrm{K2}}$ changes only weakly. This contrast drives the sign reversal of the effective anisotropy field and quantitatively accounts for the Morin transition. Our results establish low-wavenumber Raman spectroscopy as a quantitative probe of finite-momentum antiferromagnetic magnons and provide key material parameters for hematite-based magnonics.

We study the dynamics of a run and tumble particle (RTP) in a bistable potential, in contact with a heat bath. We find the exact form of the steady state position distribution as well as its time-dependent form in Laplace space. We use this result to study relaxation properties of the spatial probability density and find that it converges to the steady state from the center outwards, with the relaxation front moving ballistically in time. Physically this ballistic behavior arises when observing relaxation properties at the tails of the density, where the distance of the particle from the origin is larger than the length-scale describing the steady state of the RTP. We also find the exact form of the mean first passage time, and the long-time behavior of the first passage time distribution. This allows us to coarse-grain the dynamics as a dichotomous Markov process, a paradigm for a wide class of bistable processes. Coarse-graining, however, comes at the cost of a loss of information: while the RTP possesses a finite entropy production even at steady state, it identically vanishes for its coarse-grained description.

We study bounded, simply connected, convex, and C2-smooth domains in the space R^n for finite n greater than 1. For such domains we use the diameter to find balls with the property that they are included in this ball, while the diameter of the ball is chosen to be minimal. With a simple transformation we are able to map our domain onto a domain inside the open unit ball. We derive estimates for the Poincare constants of scalar and vector functions on those domains. The main ingredient is the first eigenvalue of the Laplacian or the Stokes operator with vanishing Dirichlet traces, respectively (we use results of [21]). Additionally we apply the relation of the first eigenvalues and one eigenfunction of the (scalar) Laplace and the Stokes operator cf. [21]. Our estimates for the Poincare constants are new. The dimension n of the space has significant effect on the quality of our estimates. This is illustrated with the help of an example.

We study the complementary version of Hedetniemi's problem for infinite graphs. We prove that if a graph $G$ and its complement $\overline{G}$ are both uncountably chromatic while their categorical product is countably chromatic, then $|V(G)|=\omega_1$. Assuming $\diamondsuit$, we construct a graph $G$ on $\omega_1$ such that $\chi(G)=\chi(\overline{G})=\omega_1$ and $\chi(G\times\overline{G})=\omega$; the construction uses two suitably chosen minimal Countryman lines. We also define a c.c.c. forcing of cardinality $\omega_1$ that adds a graph with the same properties. It remains open whether ZFC alone proves the existence of such a graph.

In recent years, several methods for detecting when large language models (LLMs) hallucinate have been developed. These methods are often benchmarked with open-domain question answering (QA) datasets containing questions and corresponding short reference answers. First, an LLM is used to generate answers to questions within the QA dataset. Then, some automated labeling strategy is used to label these answers as hallucinated or not by comparing them with the reference answers in the dataset. This evaluation setting creates a methodological ambiguity between two criteria: reference faithfulness (whether the answer is fully supported by the reference) and factual correctness (whether the answer is free from contradictions and factually false specific claims). In practice, automated labelers may apply the former criterion even when the intended target is the latter. We study this potential criterion mismatch using 900 human-labeled question-answer pairs spanning three commonly used QA datasets and three generator models, with labels targeting answer-level factual correctness. We evaluate lexical similarity metrics, a reference-entailment NLI baseline, and seven LLM judges under controlled prompt variants as automated labelers. Our experiments reveal substantial disagreement both among automated labeling strategies and between these labels and human annotations. Many strategies also exhibit strong directional error biases, and for most judge-generator pairs, replacing a faithfulness-oriented prompt with a factual-correctness prompt improves agreement with human annotations and reduces false-positive dominance, indicating that automated hallucination labels depend strongly on how the target criterion is specified. Label-source choice should therefore be considered a fundamental part of benchmark design and made explicit, validated, and matched with the benchmark goal.

We demonstrate a compact, practical all-fiber source of non-degenerate telecom-band polarization-entangled photon pairs assembled from off-the-shelf components. The compact fiber-integrated architecture is designed to be affordable, straightforward to assemble and align, and compatible with existing optical-fiber infrastructure. Photon pairs are generated through type-0 spontaneous parametric down-conversion in a pigtailed periodically poled lithium-niobate waveguide embedded in a Sagnac interferometer. At 0.5 mW pump power, quantum-state tomography yields a Bell-state fidelity $F_{\Phi^-}=0.850$, purity $P=0.836$, and concurrence $C=0.782$. A separate CHSH measurement gives $S=2.3301\pm0.0075$. The measured Bell-state fidelity is sufficient for the reconstructed polarization state to support qubit teleportation above the classical fidelity limit under ideal protocol operations. Analysis of the density matrix shows that approximately 96.7% of the population remains in the desired $|HH\rangle$-$|VV\rangle$ subspace, with a normalized coherence of approximately 0.86. A residual relative-phase offset indicates that local phase compensation could increase the Bell-state fidelity to approximately 0.8865. We further characterize the brightness–quality trade-off and obtain a corrected pair-rate slope of $(0.918\pm0.040)$ Mcps mW$^{-1}$. The broadband emission and fiber interfaces offer a route to multiuser entanglement distribution through off-the-shelf multichannel wavelength-division multiplexers with passbands matched to the signal and idler wavelengths.

Convective instabilities are studied from a Lagrangian perspective in order to gain new insights into how the resulting global, long-lived coherent flow structures organize themselves. We consider a 2D annular fluid layer uniformly heated from the inside and subject to radial gravity and propose several new Lagrangian diagnostics for characterizing its convective instabilities. In particular, we perform a comprehensive Lagrangian analysis of the flow field across a wide range of dimensionless parameters, establishing a heuristic correspondence between convective plumes and curves of local maxima of Finite-Time Lyapunov Exponent (FTLE) fields. Moreover, we characterize coherent swirling motions inside convective rolls, which are associated to the non-zero curvature of the flow. By introducing a sliding window method for our finite-time kinematic measures, we demonstrate a direct relationship with radial heat flux quantified by means of the Nusselt number and identify relevant dynamical transitions that leave a trace on both. Finally, we propose a formal criterion for determining viscous boundary layer (UBL) thickness by virtue of radial FTLE profiles and validated against a classical Eulerian method.

This paper presents a JAX-Python implementation of the galaxy power spectrum up to one-loop order in the effective field theory of large-scale structure, based on both the Eulerian and Lagrangian perturbation theories. The code uses JAX to enable automatic differentiation with respect to parameters such as cosmology, galaxy bias, or counterterm coefficients. This facilitates applications such as parameter inference using the gradient of the posterior, e.g., Hamiltonian Monte Carlo sampling. The code can compute both the EPT and LPT power spectra in a few milliseconds on a GPU, after just-in-time compilation. We also identify the various sources of numerical errors associated with discretization, and design the numerical implementation to minimize them, achieving relative errors of order $0.01\%$ at scales $k \lesssim 1\, h\, \mathrm{Mpc}^{-1}$, compared with brute-force numerical integration. Notably, this is the first auto-differentiable implementation of the one-loop galaxy power spectrum based on LPT. The natural resummation of the long-wavelength displacements in LPT further makes the code well suited for applications involving features in the power spectrum beyond the standard BAO feature, including primordial features. Our code, elf, is publicly available.

We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.

Simulation-based inference (SBI) has become a powerful approach to Bayesian inference in complex scientific models whose likelihoods are difficult or impossible to evaluate. Amortized SBI learns reusable inference models from simulated data, enabling rapid posterior inference for new observations, and modern generative models have made these models increasingly expressive. However, this reuse is limited to the prior distribution chosen during training, whereas scientific analyses often need revised priors as knowledge accumulates or alternative assumptions are tested. We introduce Spectra, a test-time adaptation method for diffusion-based SBI. Spectra uses an exact score-transport identity to obtain the adapted score from a frozen diffusion model in closed form for structured prior changes, without additional simulation or training. Across six SBI benchmarks, Spectra achieves accurate adaptation under strong prior shifts at low online sampling cost. This enables pretrained SBI models to incorporate updated prior information at test time.

Classical force fields (FFs) remain the workhorse for large-scale simulations even as machine-learned interatomic potentials (MLIPs) approach ab initio accuracy. They decompose total configuration energies into simple effective interactions whose parameters are traditionally assigned based on atom or bond types, enabling efficient simulations but also limiting their ability to adapt across configurations. Recent machine learning approaches have improved the accuracy and transferability of bonded parameters in these FFs by inferring them as functions of local atomic environments, but still rely on empirical nonbonded parameters for practical simulations. In this work, we introduce a unified approach, grappa-fullFF, which learns both bonded and nonbonded parameters consistently and simultaneously from ab initio reference data. By incorporating physically inspired regularization via supervision of the electrostatic potential and an architecture that facilitates charge equilibration, our model recovers accurate electric response properties, achieves state-of-the-art accuracy on geometry optimization benchmarks, and reproduces the conformational sampling of both classical and existing machine-learned FFs, without relying on externally assigned nonbonded parameters.

We propose a one-step implicit-explicit (IMEX) Runge-Kutta framework for high-order time integration of geometric flows. Starting from the Dziuk and Deckelnick-Dziuk parametric finite element formulations of curve shortening flow, we recast the spatially semidiscrete equations as systems of ordinary differential equations and construct second- and third-order schemes. Each stage requires only a linear solve. The key ingredient is a reduced-coefficient structure that allows the variational problem at each stage to be posed on the geometry generated by the preceding stage. The Runge-Kutta stages thus supply the required prediction geometry without a separate prediction procedure. The resulting schemes require no additional starting values. The framework also extends directly to the Barrett-Garcke-Nürnberg formulations of mean curvature flow and surface diffusion for curves and surfaces. Numerical experiments support the designed orders of temporal convergence and indicate that suitable coefficient choices yield mesh quality comparable to that of the corresponding first-order methods.

Reliable tool use requires more than triggering a mechanism or matching a query to an API description. Before selecting a specific tool, an agent must first infer the capability requirements implied by the user query. In this paper, we investigate whether these query-side capability requirements are linearly decodable from LLM hidden representations prior to generation, and how this hidden-state accessibility compares with explicit verbal classification. We introduce TACIT, a framework that decomposes external requirements along three fundamental axes: Source, Transformation, and World Effect, defining eight structurally distinct capability classes. Using 1,600 balanced training queries from benchmarks, synthetic examples, and new domain scenarios, we train linear probes on pre-generation hidden states from four open-weight LLM families. Our empirical results demonstrate that fine-grained capability structures are linearly decodable with high accuracy across all models. Crucially, however, we expose a representation-to-verbalization gap: these same models are significantly less reliable when asked to explicitly classify the same queries in natural language. This disconnect indicates that information about required external capabilities is linearly accessible in LLM hidden representations but not reliably expressed, a phenomenon we define as "structured but silent."

Interventional counterfactuals evaluate statements such as "had $A$ been $a$" by replacing the assignment for $A$ while keeping the unit's exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.

We construct neural approximation classes native to the graph spaces H(div) and H(curl), in two and three dimensions and, for H(div), in any dimension. Every realization lies in the space for all parameter values, and with kinked potentials, such as ReLU networks, the admissible jumps appear at finite width. The classes are images of scalar and componentwise networks under fixed operators of the de Rham complex, and do not involve a mesh or finite element emulation. For H(div) in R^n two native classes are given on an equal footing, with a skew-symmetric potential $A$: $\mathrm{Div}\,A+R_nq+\mathbf{h}$, with the divergence $q$ as an explicit unknown, and $\mathrm{Div}\,A+\mathbf{z}$ with an $H^1$ field $\mathbf{z}$; for H(curl) the analogous classes are $\mathrm{grad}\,\phi+Sr+\mathbf{h}$ in two dimensions and $\mathrm{grad}\,\phi+\mathbf{z}$ in two and three dimensions. In all of them every interface jump of the field is carried by the potential term, $\mathrm{Div}\,A$ or $\mathrm{grad}\,\phi$, while the remaining part has no interface jump (it is an $H^1$ field in the regular-decomposition classes); the classes with $\mathbf{z}$ are the componentwise approach enriched by this term. Known or learned interface geometry enters the potential through factors with trainable amplitudes, and the remaining part if the divergence jumps. The classes lead to the FOSLS-deRhaNN method, first-order system least squares with de Rham neural networks, whose loss is the least-squares functional posed in the natural spaces of the weak formulation; for elliptic equations this includes $H^{-1}$ right-hand sides and $H^{1/2}$ Dirichlet data. Elliptic equations with discontinuous coefficients and curl-curl problems are treated as instances, with the functional equivalent to the error; linear transport with discontinuous solutions and conservation laws with shocks use the same flux classes.

The 150 years old Sylvester's conjecture asserts that every prime $p\equiv 4,7,8\mod 9$ is the sum of two rational cubes. Recently, a proof of this old problem is obtained by the work of mine for the case 4,7 \cite{Yin} and the work of Burungale-Tian for the case 8 \cite{BT}. In this paper we give a shorter proof by deep mining my result in \cite{Yin} combining with the ideas of my previous work on case 8 in \cite{Yin8}. In particular, we use the ordinary trace and the Kronecker congruence of modular functions, but do not use the $\sqrt{-3}$-division boundary and Fermat isogeny as in \cite{BT}.

In this paper we develop a parabolic version of the method of moving planes on systems with a mixed local and nonlocal diffusion operator, that being $\mathcal{L} = -(-\Delta)^s + \Delta$, where $(-\Delta)^s$ is the integral fractional laplacian. We then use this result to study the quenching phenomena occurring in said systems with a singular absorption term of the type $(1-u)^{-p}$. We prove that there exists a range of multiplicative parameters for which every solution presents quenching, and that for any initial datum $u_0$, there exists a small enough multiplicative parameter such as the solution is globally defined. We also prove that the quenching phenomena cannot happen arbitrarily close to the boundary, but they are contained in a compact subset of the domain.

Aluminum nitride (AlN) is an important thermal management material whose high lattice thermal conductivity is strongly suppressed by oxygen impurities. We investigate phonon scattering by oxygen-related defects using pretrained universal machine-learning interatomic potentials (MLIPs), molecular dynamics (MD), and phonon Boltzmann transport calculations. Several pretrained MLIPs are benchmarked against density functional theory for phonon dispersions and pristine thermal conductivity. To balance accuracy and computational speed, we use a fine-tuned version of the compact SevenNet-Nano model for MD simulations. Monte Carlo annealing supports the formation of bound $V_{\mathrm{Al}}(\mathrm{O_N})_3$ complexes, whose scattering differs from that of their isolated constituents. Defect scattering rates extracted from excess spectral energy density (SED) linewidths agree reasonably with harmonic $T$-matrix predictions at low oxygen contents, supporting the independent-scatterer approximation. Incorporating these rates into an iterative Boltzmann transport equation with Bose–Einstein statistics yields thermal conductivities comparable to experimental values and captures their observed decrease with oxygen content. At high concentrations, however, the scattering rate deviates from linear scaling with oxygen content, suggesting limitations of independent-defect and pristine-phonon descriptions. These results demonstrate an efficient approach using pretrained MLIPs to quantify defect-limited thermal transport and provide insights into impurity effects beyond the dilute-defect approximation.

We study cyclic triorthogonal codes in prime dimension $p$, on which a transversal third-level diagonal gate acts as a logical non-Clifford gate. For odd $p$, we use a definition of triorthogonality that does not require self-orthogonality. For cyclic codes of length coprime to $p$, triorthogonality reduces to a sumset condition on the spectral support, which makes exhaustive search feasible: for two natural constructions, we enumerate all maximal codes of this kind for $p=3$ up to length $121$ and $p=5,7$ up to length $96$. For qubits, we prove that a cyclic code of odd length is triply even if and only if it is classically triorthogonal, giving a complete description of triply-even cyclic codes, and we determine all such codes up to length $763$. For qudits, we find codes such as $[[19,1,3]]_3$ and $[[7,1,3]]_7$, which improve on the shortest Reed-Muller and Reed-Solomon codes in both overhead exponent and distillation threshold. The latter is the first member of an infinite family of $[[p,1,2\lfloor p/6\rfloor+1]]_p$ codes.

We study an interior inverse scattering problem for the two-dimensional Helmholtz equation with backscattering data, where the source and receiver coincide. Such data are common in applications, yet existing uniqueness results are almost exclusively established for full multistatic data with separated sources and receivers. We consider two main measurement regimes. In the first regime, data are collected on a closed curve inside the unknown domain. Exploiting the meromorphic dependence of the backscattering field on the wavenumber, we show that the residues at the poles determine the diagonal of the spectral projection kernel on the curve, and hence the visible part of the Dirichlet spectrum. This yields an unconditional spectral comparison: the symmetric difference of the two Dirichlet spectra is contained in the spectrum of the interior domain enclosed by the curve. If, in addition, the common visible eigenvalues have either matching multiplicities or matching restriction ranks, we obtain an area estimate bounding the discrepancy of the two domain areas by the area of this interior domain. In the second regime, data are given on a nonempty open subset of the domain, and a single non-resonant frequency already uniquely determines a bounded connected Lipschitz domain. The proof combines interior real-analyticity of the regular part of the Helmholtz Green function with its boundary blow-up.

Kubo-Ando means are a rich class of important binary operations on the set of positive elements of an operator algebra. The aim of this article is to understand the algebraic structure of these operations. We generalize a recent result of L. Molnár for $C^*$-algebras to the class of split $C^*$-by-nilpotent algebras by using the method of analytic local expansion of binary operations. Eventually, we prove that in any $C^*$-algebra $\mathcal{A}$, the identity $[x,[y,z]]=0$ implies commutativity.

We investigate the parameterized reachability problem for concurrent register machines over infinite data domains. In this framework, each machine is a program equipped with a set of local registers, the communication across machines is mediated through a set of shared registers. Both local and shared registers can take values from an infinite data domain. The program's primitive operations include copying values between registers, assigning constants, comparing registers for (dis-)equality, and nondeterministic assignments that store an arbitrary domain value into a local register. The parameterized reachability problem considers a program and a target location, asking whether there exists some n in Naturals such that an execution of n identical machines (referred to as instances) results in at least one instance reaching the specified location. We show that this problem is Pspace-complete in the general case and it becomes undecidable if a freshness assumption (i.e., each assignment must produce a unique value distinct from all constants) is applied to nondeterministic assignments. This undecidability persists even for systems restricted to two shared and two local registers. Finally, we establish optimal decidability results for two restricted settings: when each thread is limited to a single local register, or when the system utilizes only one shared register.

Movable antenna (MA) has emerged as a promising technology to unlock spatial degrees of freedom for wireless sensing systems. However, optimizing MA positions for multi-target sensing remains challenging due to the complicated coupling between the array geometry and unknown target directions, as well as severe sidelobe interference. In this paper, we propose an MA-enabled multi-target wireless sensing scheme to achieve both high-precision and robust target parameter estimation. To characterize the sensing performance while maintaining tractability, we introduce two complementary metrics, namely a lower bound (LB) of the Cramér-Rao bound (CRB) and the steering vector correlation (SVC). Specifically, by investigating the partial order relationship of the Fisher information matrix, we derive a closed-form LB of the multi-target CRB, which decouples the unknown target directions. Meanwhile, the SVC is employed to characterize the spatial correlation and sidelobe-induced interference among sensing signals over different directions. Based on these two metrics, we formulate an MA position optimization problem that minimizes the SVC while constraining the LB below a predefined threshold. To render the resulting non-convex problem tractable, we exploit the spatial symmetry of the continuous SVC function and discretize the sidelobe region, thereby transforming the spatial minimax objective into a finite set of constraints. Meanwhile, the LB constraint is equivalently reformulated as a spatial variance constraint on the MA positions. Building on these transformations, we develop a successive convex approximation (SCA) algorithm within an alternating optimization (AO) framework to iteratively optimize the horizontal and vertical MA coordinates.