Papers

Since compact, interpretable classifiers correspond to simple programs, it is natural to ask if LLM-based coding agents can be used to learn interpretable models from data. In this paper we present a simple harness that repeatedly prompts a coding LLM to produce the next rule in a rule set, given a sample of labeled examples. We show that this approach is competitive with, and often superior to, state-of-the-art rule-learning methods on tabular data, especially with small training sets, and wins by large margins on text, including against another LLM-based rule learner; that this approach outperforms standard harnesses, and that the approach immediately leads to new kinds of interpretable models, since coding agents are not restricted to search a highly restricted hypothesis space. In addition to the advances made in learning interpretable models, these results are of interest because they introduce a new class of coding benchmarks - construction of interpretable classifiers - which includes quantitative measurements of output quality (i.e., test-set error) and existing mature “specialist coding algorithms” (i.e., existing learning methods).

Fix a polynomial $P(x)=\sum_{j=0}^m a_jx^j$ of degree $m$, and let $I_kP$ be its $k$-fold antiderivative with all integration constants zero. Borwein, Chen, and Dilcher proved that, after $x=ky$, the nonzero zeros of $I_kP$ converge to the nonzero zeros of $L[P](y)=\sum_j a_j j! y^j$. That convergence determines the leading linear motion but neither the constant offset nor successive differences. We compute the next two terms at a simple nonzero zero $\lambda$ of $L[P]$. Integer-order and Riemann-Liouville integration reduce, after scaling, to one rational family $c_j(h)=\prod_{\ell\le j}(1+\ell h)^{-1}$ sampled at $h=1/k$ and $h=1/\alpha$. We prove $r_k=k\lambda+C_P(\lambda)+D_P(\lambda)/k+O(k^{-2})$ with explicit $C_P$ and $D_P$. Hence $\lambda$ is at once the scaled zero, the limit of successive root differences, and the continuous-order velocity, each with an explicit correction; $C_P(\lambda)$ is the offset of an asymptotic line. For binomials the limiting spacing is a multiple of a gamma-ratio quantity, the Factorial Fraction, and the nonzero reduced zeros form an exact regular polygon at every positive order. For real quadratics the collision order of two branches takes a simple discriminant form. In every degree the collision discriminant carries a universal factor, the one familiar from Laguerre polynomials and supported at negative orders. In the coordinates $(\alpha,x)$ all trajectories lie on one plane curve of degree $m$ with leading form $L[P]$. At a nonzero zero of $L[P]$ of multiplicity $q$, the nearby zeros split on the scale $\sqrt{k}$ like the zeros of the Hermite polynomial $He_q$, and for real $P$ the nonzero zeros stay real at every positive order exactly when $L[P]$ is real-rooted.

Masked diffusion language models (MDLMs) decode by repeatedly committing tokens to masked positions, but these commitments are usually irreversible. A token chosen under sparse, partial context is kept fixed, even when later context no longer supports it. Existing samplers mainly decide when to commit a token, but rarely check whether an already committed token should still be kept, allowing early mistakes to propagate. We trace this issue to confidence drift, where the model's confidence in a committed token drops from its sparse commit-time context to the denser context available later. Based on this signal, we propose CoDR (Confidence Drift Remasking), a training-free and sampler-agnostic refinement pass. CoDR estimates drift for all committed positions in only k forward passes via k-partition probing, then remasks and regenerates only the tokens the model no longer endorses. Across two backbones, four reasoning and coding tasks, and three base samplers, CoDR improves average accuracy across all evaluated model-sampler configurations and improves most individual task settings with modest overhead. Controlled experiments show that the gains come from targeted confidence-drift remasking rather than extra compute alone, and that CoDR uses far fewer forward passes than prior remasking methods. Code is available at https://github.com/YueWu0301/CoDR.

Localizing latent structures in the activation space of language models (LMs) is central to understanding and controlling their behavior. Yet, localized structures can differ substantially in their causal influence, raising the question of what makes a structure actionable. We tackle this question by casting causal influence as a product of three factors and showing empirically that they act as interpretable, distinct constraints: capacity, measuring the sensitivity of the model's output to movement along the structure, responsiveness, capturing how promotable the concept is given the current context, and alignment, reflecting how well the structure aligns with the context-specific representation of the concept. Across 4 LM families and 50 concepts, we observe that causal effectiveness requires all factors to be high; low capacity and responsiveness reduce it by 84% and 95%, respectively, while low alignment can reverse it, suppressing concept expression. Moreover, we find that causality is context-dependent rather than an intrinsic property of the structure, with causally effective directions forming a low-dimensional subspace that varies across contexts. By restricting the training of linear probes to this subspace, we introduce causal probes that achieve 17%-118% improvement in steering across models, with only 3% reduction in concept detection.

Frontier multimodal large language models (MLLMs) are increasingly positioned as general purpose visual reasoners as part of the quest for artificial general intelligence. A key test of this generality is whether they can perform novel visual judgments that humans can make reliably from visual evidence and task instructions, without task-specific parameter optimisation. We investigate this question through the task of medical image alignment assessment, where the goal is to establish whether there is anatomical correspondence between two images. Human visual assessment of image alignment is still the gold standard and most common approach; however, it requires trained operators and is impractical to scale for large datasets. We evaluate recent generations of MLLMs on two exemplar medical image alignment tasks, varying both prompting strategies and image-presentation methods. We compare against a locally fine-tuned MLLM and a task-specific CNN to examine the trade-off between frontier general purpose models and smaller models that require specific task optimisation but can be used locally. We show that are reaching an inflection point, where frontier MLLMs can now perform effective visual assessment of medical image alignment. Models released only a few months ago generalise poorly and, in some settings, perform barely above chance, whereas GPT-6 achieves over 85% across almost all scenarios tested. Fine-tuned local models can match or exceed frontier-model performance on the tasks on which they are trained, but transfer substantially less effectively to unseen settings. These findings identify medical image alignment as a useful test bed for generalist visual reasoning and suggest that frontier multimodal models are beginning to acquire capabilities that could support a common quality-control mechanism across heterogeneous medical-imaging pipelines.

This paper investigates analytical solutions of a continuous analogue of a class of Volterra quadratic stochastic operators of a two-sex population using the homotopy analysis method. The positive invariance of the state space of the system is established. By means of Lyapunov functions, inclusions for the $\omega$-limit sets are obtained, together with exponential decay estimates for individual components of the trajectories under the corresponding conditions on the coefficients of the system. Sufficient conditions are obtained for the coincidence of the $\omega$-limit sets of the discrete and continuous models. For the diagonal invariant subset, sufficient conditions are established for the periodicity of all interior non-equilibrium trajectories. By means of a majorant series, a sufficient condition for the absolute and uniform convergence of the homotopy series on $[0,+\infty)$ is obtained under the Hurwitz stability of the reduced Jacobian of the system. In addition, explicit analytical solutions of the Cauchy problem are found for special relations between the heredity coefficients. Computational experiments show a rapid decay of the terms of the homotopy series and good approximation accuracy already when using the first few terms of the expansion.

A central question in the prediction of stochastic processes is the extent to which past information can improve the probability of correctly predicting the next state. We introduce the Memory Prediction Excess (MPE) to address this question quantitatively. The MPE measures the average improvement in prediction accuracy obtained by using the entire observed history relative to using only the static marginal distribution, in discrete-time finite-state processes. It is defined as the difference between the expected optimal conditional prediction accuracy and the optimal static prediction accuracy. Its basic properties are examined: the MPE is always non-negative; it admits an upper bound depending on the static accuracy, attained if and only if the future is almost surely a deterministic function of the past; and degenerate cases in which the MPE vanishes are characterized. A normalized version, taking values in the unit interval, is introduced as a dimensionless measure of predictive efficiency. A lower bound is derived by comparing predictions based on histories of different lengths, showing that the expected optimal prediction accuracy is monotone with respect to the history length. The framework is extended to finite-length histories, where the finite-history MPE (FH-MPE) measures the predictive gain attainable when only the most recent observations are retained. This leads to the notion of a minimal memory length required to achieve the same predictive performance as the full history. For finite-order Markov chains, this minimal memory length is shown to be bounded by the Markov order. The MPE and its variants are formulated in terms of conditional probabilities and prediction accuracies, offering a probabilistic perspective on the predictive utility of memory that is complementary to classical information-theoretic approaches.

The environmental transport of microplastic particles has raised concerns because of their potential ecological and human-health impacts. A particular challenge for experiments on microplastic transport in soils is the fact that soil is a highly complex and non-transparent porous medium. Thus, our knowledge of transport mechanisms of microplastics in soils and related ecological implications is still limited and computational simulations offer an additional possibility to obtain important insights into the physical transport behaviour of microplastics. Yet, direct particle-resolved simulations in realistic soil structures for macroscopic sample sizes remain a computational challenge. We introduce an efficient pore-network model, minD-PNM, that predicts particle breakthrough curves in water-saturated soils using experimental X-ray micro-computed tomography ($\mu$CT) pore geometries as the only input. The model combines an approximately $t^{-3}$ pore-scale transit time distribution with a minimum-dissipation partition of multi-inlet-multi-outlet pores, and propagates these distributions through the pore network to predict breakthrough curves. We benchmark minD-PNM against lattice Boltzmann and immersed boundary simulations for small systems, and against microplastic column experiments in quartz sediments for macroscopic sample sizes. In both cases, the predicted breakthrough curves agree well with the corresponding reference data. Because it requires only geometric information, minD-PNM scales to macroscopic sample volumes offering a practical tool for contaminant-hydrology studies of particulate pollutants.

Magnon chiral damping denotes damping that is asymmetric with respect to the magnon wave vector. Such nonreciprocity has been attributed to antisymmetric Dzyaloshinskii-Moriya spin interactions. Here, we provide an alternative theoretical explanation of magnon chiral damping using linear spin-wave theory and antisymmetric Gilbert damping introduced within the Landau-Lifshitz-Gilbert equation of motion. First, employing a minimal model of a single sublattice ferromagnet on a rectangular lattice, we show that the effective magnon damping is independent of the system's energy, including contributions from Dzyaloshinskii-Moriya interactions. Considering scalar nonlocal Gilbert damping, the effective damping parameter $\alpha_{\rm eff}$ becomes wave-vector dependent. In the long-wavelength limit, $\alpha_{\rm eff}$ acquires a quadratic dependence on $\bf{k}$. Furthermore, the antisymmetric component of the Gilbert damping tensor gives rise to asymmetric (nonreciprocal) magnon damping. We find the asymmetry to be linear in $\bf{k}$ in the long-wavelength limit, consistent with recent experiments. Extending the analysis to a two-sublattice system, we consider cross-sublattice Gilbert damping. In the presence of only scalar Gilbert damping, broken reciprocity in magnon relaxation arises from Dzyaloshinskii-Moriya interactions. In contrast, the cross-sublattice antisymmetric component of the Gilbert damping tensor can generate nonreciprocal magnon damping even if the Dzyaloshinskii-Moriya interaction is parametrically set to zero, providing an alternative mechanism for asymmetric spin-wave relaxation. Notably, the nonreciprocity induced by antisymmetric Gilbert damping is roughly an order of magnitude larger than that arising from Dzyaloshinskii-Moriya interactions.

Discrete motion tokenizers encode motion as atomic units and are widely used for co-speech gesture generation. It remains unclear which motion properties, especially those relevant to gesture semantics, are recoverable from these codebooks. We probe a reconstruction-trained codebook using 19 co-speech gesture descriptors spanning from raw motion to abstract communicative function. Results show that geometry and handedness are readily decodable from token embeddings, while motion category is only weakly decoded despite showing systematic differences in discrete code usage. This gap between reconstruction quality and descriptor decodability suggests that reconstruction objectives alone do not guarantee that gesture semantics are captured, and that evaluating codebooks on such properties can guide the design of more semantic motion tokenizers.

We quantize the exterior region of an odd-dimensional Kerr-AdS black hole, in which all rotational parameters are equal, using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions $w_i$, whose corresponding eigenvalues all have multiplicity one, and spatial eigendistributions $v_{ij}$ corresponding to the same eigenvalues but having multiplicities $m_i\ge 1$. In principle, the $m_i$ may be arbitrarily large. When only the exterior region is considered, there is no criterion for determining the values of the $m_i$. However, when the quantization of the interior region is also considered, the same ambiguity does not arise, because the multiplicities can be chosen to be maximal. It is therefore natural to use the same values in the exterior region. Because the temporal Hamiltonian is the same in both regions, the interior and exterior eigenvalues coincide, and this choice defines a unitary equivalence between the respective Hilbert spaces and Hamiltonians. The unitary equivalence between the Hilbert spaces and their respective Hamiltonians preserves the complete quantum-statistical information carried by all normal states in the interior and exterior regions of the black hole. Hence, there is no information paradox at the quantum level.

GPU lossless compression requires both compact complete frames and fast checked recovery. We evaluate fixed-capacity causal byte-bank representations under a shared 512-row probability budget, select a single representation via a pre-payload complete-cost proxy charging both empirical cross-entropy and compressed model tables, and align two rANS states per 8\,KiB chunk with the causal byte banks. Independent byte banks decode concurrently, whereas intra-word conditional banks decode in two ordered phases. On ten structured imaging and electrophysiology inputs, split-bank execution lowers aggregate median encode-plus-recovery time by 13.10% for 0.18% additional frame bytes, and reduces complete encoding cost by 44.16% relative to a matched native-CPU model control while supporting a standalone CUDA-free CPU receiver. In a twelve-configuration GPU comparison, Split GPX produces 5.75% and 7.11% smaller complete frames than Zigshuffle + nvCOMP Zstd at 35.14% and 19.03% lower paired cost for 64\,KiB and 8\,KiB requests. For multi-channel sample-interleaved waveforms, extending causal differencing with zero-oracle GPU stride screening (strided-residual) reduces holdout 12-lead PTB Diagnostic ECG frames by 49.89% (from 71.47% to 35.81% of raw bytes, 37.20% smaller than Zigshuffle + Zstd-1 and 46.67% smaller than OpenZL-9) while preserving byte parity across all single-stream benchmarks.

Long-context decoding is increasingly constrained by key–value (KV) cache memory and bandwidth. Existing fixed-budget compression methods typically separate retention from compensation, while a retention ranking specifies neither discarded attention mass nor the direction of induced output error. We start from an exact factorization: eviction error equals evicted attention mass times the directional gap between the evicted centroid and retained output, highlighting the importance of set-level coverage in retention and mass-preserving memory writing. We introduce CORE COverage Calibration and Evicted-Mass REdistribution for KV Cache, which distills an offline allocation combining query utility and log-determinant coverage into a lightweight cache-aware indexer. At inference, one calibrated distribution drives both channels: its Top-$B$ ordering retains complementary KV states, while its excluded allocation mass and conditional weights parameterize latent-memory writes without a separate write-weight predictor or online log-determinant evaluation. Our analysis provides a four-term pre-compensation error certificate, characterizes non-additive coverage interactions, and establishes mass-independent write stability with hierarchical bounds through recurrent and query-adaptive normalization. Across three backbones, CORE exceeds the strongest RULER baseline by up to 3.78 points at 90% compression; LongBench and repeated-eviction evaluations further demonstrate strong effectiveness and decoding efficiency.

We prove a Denjoy-Wolff theorem for uniformly quasiregular self-maps of the unit ball in $\mathbb{R}^n$, $n\geq 2$: either all orbits are relatively compact, or the iterates converge locally uniformly to a single point of the sphere. No properness, surjectivity, or boundary extension is assumed. The key tool is a Schwarz-Pick lemma valid in all dimensions: every quasiregular map preserving a bounded measurable conformal structure is non-expanding for a modulus metric built from that structure, and uniformly quasiregular maps preserve such a structure by a theorem of Iwaniec and Martin. Since this metric is not geodesic, we pass to an associated chain metric, which we show is Gromov hyperbolic with boundary the sphere, and apply a theorem of Karlsson. As an application, a stable Fatou component of a uniformly quasiregular map of $\overline{\mathbb{R}^n}$ that is a uniform domain with uniformly perfect boundary is an attracting basin, a rotation domain, or a parabolic basin with a unique boundary fixed point. Non-injective examples of both escaping types are constructed in every dimension.

Physical AI models such as Vision-Language-Action (VLA) architectures enable generalist robotic policies through large-scale transformer backbones and diffusion-based action decoders. While edge GPU platforms excel at parallelizing the compute-intensive vision-transformer workloads, they exhibit fundamental limitations for the Diffusion Action Expert (DAE) module: the iterative denoising process requires repeated parameter loading from DRAM across multiple steps, resulting in memory-bound performance where the GPU's massive computational throughput remains underutilized. This mismatch between DAE's I/O-intensive characteristics and GPU's compute-centric architecture motivates a heterogeneous acceleration approach. This paper presents EdgeDAE, a heterogeneous FPGA-GPU system that strategically partitions workloads based on computational characteristics. We offload the perception-heavy vision-transformer to GPU while accelerating DAE inference on FPGA through complete on-chip parameter storage in BRAM/URAM. This architecture eliminates the memory bottleneck by co-designing quantization strategies, fixed-point arithmetic, and hardware-efficient random number generation for the FPGA fabric. Compared to an edge GPU baseline, EdgeDAE reduces end-to-end inference latency by 52.5% for Octo-Small and 38.7% for Octo-Base, with up to $2.10\times$ higher throughput; compared to a consumer GPU (RTX~4090), it achieves ${\sim}17\times$ higher energy efficiency.

In the designer-port routing-labeling problem, every vertex of a rooted tree receives a binary label and the child edges receive distinct port numbers. Given only the labels of a source and a destination, a decoder must return the first port on their path. Gawrychowski, Janczewski, and Lopuszanski gave labels of length $\log_2 n+O((\log_2\log_2 n)^2)$, whereas the previous lower bound was $\log_2 n+\Omega(\log_2\log_2 n)$. We prove that every scheme for all $n$-vertex trees needs a label of length $\log_2 n+\Omega((\log_2\log_2 n)^2)$ for every sufficiently large $n$. The result allows arbitrary port assignments and imposes no computational restriction on either the encoder or the decoder. Thus the second-order term in the optimal worst-case label length is determined up to constant factors.

Large language models (LLMs) are increasingly deployed in privacy-critical domains (e.g., healthcare, finance, and government), but their propensity to memorize and disclose personally identifiable information (PII) poses serious security and compliance risks. Existing defenses typically force a trade-off between model utility, privacy protection, and access to fine-tuned private knowledge. We propose LoRA-Oriented Control via Keyed Entry Tokens (Locket), a practical framework that embeds fine-grained, policy-driven access control directly into LLM generation. Locket trains a set of lightweight LoRA (Low-Rank Adaptation) adapters, each encoding a distinct access policy (e.g., full reveal, partial redaction via PII masking, or reveal under a specified differential privacy level). A compact gating module is trained to associate a learned keyed entry token with exactly one LoRA adapter via sequence-level hard routing; the presence of a valid token acts as an authorization key that unlocks corresponding private knowledge, while an invalid or absent token triggers a privacy-preserving adapter that redacts or sanitizes sensitive content. This design ensures Locket remains fully compatible with off-the-shelf LLMs, supporting scalable deployment while satisfying regulatory and privacy requirements. We evaluate Locket across multiple datasets (Enron, ECHR, Yelp) and a diverse set of state-of-the-art LLMs, including Qwen3 (1.7B and 8B), Meta's Llama-3.2 (1B and 3B), and Google's Gemma-2-2B. Our extensive experiments demonstrate that, when the correct token is provided, Locket preserves perplexity comparable to fine-tuning on raw data (without any defense). Conversely, when the token is missing or invalid, it substantially reduces PII leakage while maintaining utility and perplexity on par with strong baseline defenses.

The future Electron-Ion Collider (EIC) will offer new opportunities to search for physics beyond the Standard Model. We study resonant anomaly detection using machine learning and the full particle content of an event. We consider a new neutral gauge boson and a heavy neutral lepton as illustrative signals with different electron-jet topologies. Weakly supervised learning uses this event information to enhance the sensitivity of an invariant-mass search without identifying individual signal events during training. Comparisons with high-level observables show that the electron kinematics account for an important part of the separation, while correlations among the particles provide further sensitivity. We also construct a conditional full-event generator by adapting a model pretrained on LHC jets to produce EIC background events. A scan over signal fractions demonstrates substantial signal enhancement using the learned background reference, providing a proof of concept for this approach at the EIC. Finally, we consider a fully unsupervised graph autoencoder that provides modest signal enhancement but retains sensitivity at signal fractions too small for effective weak supervision. Our results motivate full-event anomaly detection as part of the EIC physics program and identify directions for developing methods suited to its distinct kinematics.

We prove every term of Svinin's even-order recurrences is a Laurent polynomial in the initial values.

Efficient and accurate estimation of the detection probability of a gravitational wave event given its source parameters remains a challenging problem because it conventionally requires expensive Monte Carlo injection campaigns. We present a machine learning-based approach using Normalizing Flows (NFs) to estimate the detection probability of gravitational wave events for a LIGO/Virgo/KAGRA O4-like detector network configuration. We utilize the publicly available injection dataset as training and test data. We test our method and implementation by evaluating the raw NF performance as a generative model based on its ability to recover the correct parameter distributions of detected events. In addition, we compare the detection efficiencies predicted by the NF emulator with those from Monte Carlo importance sampling and find good agreement. Furthermore, estimating the detection efficiency for a wide variety of population models, including those with sharp features, can be more precise than estimates obtained via Monte Carlo importance sampling. We show that the NF emulator can be used in population analysis of gravitational wave sources, similar to previous neural network approaches. The training code and trained models from this work are publicly available.

Malicious coordination has long been regarded as a principal source of information ecosystem pollution. Here, we focus on crude, text-repetition-based coordination. As the demand for mitigating its dissemination has grown, scholars have studied such coordination, focusing especially on bot detection. Few studies, however, have characterized malicious coordination per se or examined how it elicits reactions from general users. Leveraging a dataset of 734,173 Chinese-language coordinated accounts and around 495 million coordinated posts published between May 2024 and March 2026, this study analyzes the characteristics of coordinated behavior and how general users react to coordinated posts. We report three findings: (1) most coordinated accounts are crude and retain the classic marks of automation, and the same criterion applied to Japanese-language accounts over the same month yields a share six times lower; (2) their content is overwhelmingly non-political; (3) regarding their reach, most reactions within large observable cascades originate from coordinated accounts themselves, while posts classified as potentially harmful or illegal material receive a comparatively high proportion of reactions from outside the Chinese-dominant population. We provide a longitudinal quantitative map of crude Chinese-language coordination appearing in X's Japanese-classified stream.

Synthetic gauge fields provide a powerful route to engineer photonic wave dynamics, especially in synthetic frequency dimensions formed by modulated resonator modes. While most previous realizations have focused on Abelian or lower-rank non-Abelian structures, a photonic implementation of SU(3) gauge fields in the synthetic frequency dimension has remained lacking. Here we propose a route to realize SU(3) gauge structure using three coupled ring resonators with modulation- and interference-engineered mode conversion. We formulate a tight-binding Hamiltonian with matrix-valued hopping generated by the Gell-Mann matrices and show how its evolution can be decomposed into experimentally implementable optical elements. The resulting platform supports SU(3)-structured band dispersions with color-resolved texture and wave-packet dynamics shaped by SU(3) gauge fields. Full-wave-inspired numerical modeling further confirms the expected spectral response and Zitterbewegung-like motion in SU(3) subspaces. Our results introduce SU(3) gauge fields into synthetic frequency photonics and establish a route toward higher-rank non-Abelian control of light in modulated resonator systems.

We prove the rectangular cyclotomic expansion conjecture of Kameyama, Nawata, Tao, and Zhang for reduced colored HOMFLY-PT polynomials of arbitrary zero-framed knots. We also prove their explicit double-twist formula for every rectangular color and all pairs of nonzero integer twist parameters. For each knot, we construct a double Newton expansion with coefficients in $\mathbb Z[A^{\pm1},q^{\pm1}]$. These coefficients are uniquely determined and independent of the width and height of the rectangular color. The construction uses finite-rank representation symmetries and integral interpolation. The double-twist formula follows from a simultaneous exterior-power comparison of the two four-point Casimir operators and the known one-row formula. Finite transition formulas express the double Newton coefficients of double-twist knots in terms of the prescribed twist coefficients.

Crowdsourced imagery provides timely, fine-grained, street-level observations for disaster mapping, complementing conventional remote sensing imagery (RSI) during emergency response. However, such imagery is often unstructured, spatially ambiguous, and lacks reliable geographic metadata, making manual geolocalization and interpretation labor-intensive and difficult to scale. This work proposes a multi-task Geospatial Reasoning Disaster mapping framework, namely GRDisaster, to examine the potential of vision-language models (VLMs) in understanding, geolocalizing, and reasoning over crowdsourced disaster imagery. GRDisaster is built on a newly curated benchmark dataset derived from PhotoMappers, comprising 26,340 images organized into human-validated volunteered geographic information (VGI), street-view imagery (SVI), RSI cross-view triplets covering multiple disaster events from 2018 to 2024. The framework combines deterministic and probabilistic cross-view geolocalization with multi-view fusion to associate VGI images with georeferenced SVI and RSI. It introduces two sets of spatial reasoning indicators for cross-view geolocalization validation and disaster damage assessment. These indicators use structural, environmental, and global-scene cues to validate cross-view correspondences and visually observable damage evidence with expert-verified annotations to assess disaster severity, improving the interpretability of VLM outputs. To our knowledge, this study provides the first systematic investigation and unified evaluation framework for examining how VLM-based spatial reasoning can transform crowdsourced disaster imagery into actionable geospatial artificial intelligence (GeoAI) through cross-view geolocalization validation, interpretable spatial reasoning, and damage-aware severity assessment.

In this paper, we construct the matrix nth root of a multivariate polynomial with coefficients in a field K which possesses an nth root of unity. Moreover, we explain why this concept is interesting. Finally, we give several examples to illustrate our construction.

Verifying large C codebases requires translating them into formally checkable semantics, but most autoformalization work reports a single aggregate success rate that conflates two different failure modes: code the translator declined to handle and code the translator translated incorrectly. We present a deterministic code-property-graph (CPG)-based exporter that translates C source into a small Lean~4 core semantics under a three-tier correctness discipline: hole-free, call-closed, and dynamic-hole-risk, that keeps these modes distinct. Applied to a re-export of the SQLite source tree (8{,}602 functions, over 1.5~million AST nodes), the exporter translates 5{,}222 functions (60.7%) hole-free, of which only 2{,}134 (24.8%) are call-closed, a $2.4\times$ gap a single rate would hide. Both figures are reported in a full per-construct trust ledger rather than a single score. Our main contribution is methodological: a protocol for separating constructs that are fundamentally unresolvable by whole-program static analysis (such as public API boundaries) from constructs that only look that way. For example, we retracted our own “impossible” classification of function-pointer/vtable dispatch after tracing a concrete counterexample in the target codebase. Separately, a search for “more holes closed” surfaced a latent silent-wrong-answer bug: a translation that succeeded with an incorrect result rather than declining, a failure mode we argue is more dangerous than any hole, and one a hole-count-only evaluation would never surface.

Gaussian process (GP) based predictive periodic error correction, introduced by Klenske et al., learns a telescope mount's periodic tracking error online and applies the correction before the error is observed, removing the reaction lag inherent in purely reactive autoguiders. The published model uses a single periodic kernel and therefore represents the error of one gear stage: any repeating shape at one period, harmonics included, but only one period. Mounts with more than one reduction stage – strain-wave drives with a separate input stage, belt-and-worm combinations, transfer gears – produce errors at periods that are mutually incommensurate, which beat against each other and never repeat on a common cycle. We extend the model to a sum over an arbitrary number of quasi-periodic kernels, one per gear stage, each discovered from the residual spectrum, gated on the strength of its own spectral line, and refused if it is commensurate with a period already modelled. We show that a strictly periodic second kernel is unusable in practice because it demands the second period to within 0.2%, and that a squared-exponential envelope of about twenty periods removes that sensitivity at a cost of 0.02 px. On synthetic two-stage errors at realistic periods and amplitudes the extension reduces the residual by 1-40% against the single-kernel model, while leaving single-stage cases numerically unchanged. On a recorded, de-noised session with no second, incommensurate gear frequency, it still improves on the single-kernel model by 6% and on a reactive hysteresis controller by 45%, by absorbing amplitude modulation of the primary that the single kernel cannot. The implementation is dependency-free, multiplatform code in the C programming language and is released as part of the INDIGO project.

Kubernetes deployments increasingly span multiple clusters for reasons of scale, fault isolation, regulatory boundaries, and heterogeneous hardware placement, including GPU-dense clusters dedicated to AI and HPC workloads. Cilium Cluster Mesh, built on extended Berkeley Packet Filter (eBPF) technology, has emerged as a widely deployed mechanism for connecting such clusters into a single logical network without a dedicated multi-cluster gateway. Despite its adoption, the academic literature contains no systematic, reproducible evaluation of the eBPF-based multi-cluster data plane itself: existing work either benchmarks eBPF against iptables within a single cluster, or applies eBPF to cross-cluster monitoring rather than forwarding and identity propagation. The most detailed scale data available - a report of a clustermesh-apiserver failing under load at approximately 45,000 nodes across 256 clusters - comes from an industry engineering blog rather than a peer-reviewed source. This paper proposes a methodology to close that gap. We define five research questions covering latency, throughput, control-plane limits, churn, and GPU/RDMA sensitivity, and describe a testbed and eBPF-level instrumentation design. Lacking a live multi-cluster testbed for this submission, we report results from a calibrated analytical simulation of control-plane architectures fit to the production data point. These results are presented as falsifiable predictions intended for validation once the testbed is complete. This paper provides the motivation, experimental design, and preliminary simulation results to serve as a template for a full empirical study.

I prove that all Mellin residues are determined exactly by integer samples known up to errors smaller than every algebraic order, for an explicit class of functions consisting of a slow component with a complete inverse-power expansion and countably many carriers $\exp(2\pi i\sigma 2^k a^x)$ with admissible envelopes. A single exceptional null set of parameters $a>1$ works for the entire function class. The key estimate is an eventual uniform lower bound for a polynomially weighted sampling Gram matrix on windows of length $N^{1/2}$, with $O(N^{1/4})$ active modes. I derive this bound from parameter-averaged oscillatory integrals and a finite trace-moment comparison with product Haar measure, retaining the exact resonances among dyadic frequencies. Summed Taylor estimates then identify every coefficient of the slow asymptotic expansion, and a Mellin continuation argument identifies these coefficients with the actual residues. I also give an alternative derivation from existing higher-correlation estimates, an infinite-mode example, and exact counterexamples at integer parameters. The result supplies an interpolation-invariance statement for a model class motivated by Mellin averaging in quantum gravity.

XENONnT has measured a low-energy solar-neutrino signal dominated by $pp$ neutrinos. At these energies, an ultra-small pseudo-Dirac mass-squared splitting induces detectable active-sterile oscillations over the Sun–Earth baseline. We study pseudo-Dirac oscillations of the first mass eigenstate, compute the resulting modification of the $pp+{}^7$Be electron-recoil spectrum, and construct a likelihood from the published XENONnT energy spectra. We find that the XENONnT data exclude $5.9\times10^{-13}\,\mathrm{eV}^2\lesssim \delta m_1^2 \leq 10^{-11}\,\mathrm{eV}^2$ at the $2\sigma$ level, extending current solar-neutrino sensitivity to smaller mass splittings and approaching a regime previously discussed for future $pp$-sensitive detectors.