Papers

In spatial data analysis, global measures of spatial correlation provide useful insights into the general spatial patterns, but fail to capture local variations. Local Indicators of Spatial Association (LISA) address this limitation by identifying local clusters and spatial outliers, offering valuable applications in many fields of research such as public health, urban planning and environmental monitoring, to name only a few. However, the application of LISA tools in hypothesis testing is undermined by the presence of the multiple testing problem which dramatically increases the risk of committing Type I errors especially when dealing with very large datasets. Standard corrections procedure (like, e. g., Bonferroni and Benjamini-Hochberg procedures) fail to consider the spatial dependence among the various LISA tests and, furthermore, they are overly conservative. This paper proposes an adjustment that, by incorporating the notion of the "effective sample size", improves statistical inference balancing false discovery rate control and statistical power.

Metaheuristic comparisons are often reported at evaluation budgets far larger than an expensive engineering simulation can afford. This paper presents REMBGO, an evaluation-budget-aware refinement of EMBGO. Its contribution is not any single operator: it is the integration of population preservation, scale-normalized exploration and recovery mechanisms whose parent-relative benefit is concentrated under restricted function-evaluation budgets. REMBGO is evaluated on CEC2022 at a primary, application-aligned budget of 1040 function evaluations, with a surrounding budget ladder reported descriptively to characterise budget dependence rather than as a family of controlled hypotheses. A component-removal study finds no individual mechanism whose removal survives multiplicity correction, consistent with an integrated rather than a single-operator contribution. The algorithm is then applied to EAF–STATCOM controller tuning, and the resulting frozen gain vectors are transferred without retuning to twenty pre-specified unseen stochastic arc realizations ($210$ fixed-gain simulations, all feasible). The selected gain-vector main effect accounts for only $3.6$–$5.8\%$ of the crossed validation variation, against approximately $61.4\%$ for interaction plus residual, and the matched REMBGO–EMBGO paired differences are controller-dependent in sign and not statistically significant. REMBGO is therefore presented as a resource-aware refinement whose benefit must be stated together with the evaluation budget, not as a universally superior optimizer.

Video reward optimization can increase proxy rewards while reducing video dynamics, a mismatch we identify as motion collapse, including under a video-level motion-quality reward. We propose GraftOOD, which replaces part of the online rollouts in selected prompt groups with out-of-distribution video exemplars. A shared velocity-regression objective combines group-relative reward rectification with sequence-level exemplar supervision, requiring neither exemplar generation trajectories nor an additional supervised-loss coefficient. We characterize its pointwise optimal field as a source-posterior-weighted combination of the two source-specific target fields. We construct GraftSet-Video, containing 9,588 format-matched exemplars for 2,397 prompts, to supply external supervision. On Wan2.1-1.3B, GraftOOD raises Dynamic Degree from 4.86 to 44.41 relative to reward-only FlowAWR, while HPSv3 decreases from 8.10 to 7.32 and VisionReward remains close. At the main setting, GraftOOD leads nine of ten metrics among three exemplar-augmented methods. Ablations of exemplar frequency and within-group count reveal dynamics–reward trade-offs rather than uniform gains from increasing exemplar usage. These results support external exemplar supervision as a complement to scalar reward feedback, without equating higher measured dynamics with coherent, visually plausible motion in the generated videos. Code is available at \href{https://github.com/Fuzm7/FlowAWR}{GraftOOD}.

Let $R$ be a Noetherian regular local ring of mixed characteristic and dimension four, and let $r$ be a member of a regular system of parameters. We prove that every finitely generated projective module over $R[1/r]$ is free. We also prove that $\mathrm{Sp}_4(R[1/r])$ acts transitively on unimodular columns of length four and that every determinant orientation of a rank-two projective module is induced by a basis. The argument reduces freeness to two vanishing results: the degree-three Zariski cohomology of the naive degree-four Milnor–Witt sheaf and the alternating Witt group of $R[1/r]$. We establish these results using integral degree-two algebraic $K$-theory, supported hermitian $K$-theory, and local motivic cohomology. A finite-rank symplectic comparison relates the image of the completion obstruction to Milnor–Witt multiplication and yields the required symplectic frames.

We consider the question which functions $f$ may appear as limiting functions of the $N$-point correlation. We obtain sharp point-wise lower and upper bounds. The explicit examples constructed to show the sharpness of the bounds are based on van der Corput sequences.

Overtourism concentrates visitor demand on few iconic sites, while other points of interest (POIs) in the same area often remain known only to a narrower public. This imbalance is especially critical in mountain environments, where limited infrastructure amplifies environmental pressures. Discovering lesser-known POIs is relevant for redistributing tourism demand spatially, valuing underrepresented heritage, and temporally, easing high seasonality pressures on popular POIs. Across the literature, definitions of lesser-known POIs or hidden gems remain scattered, and existing scoring approaches remain incomplete, relying on narrow indicators (e.g., number of photos, reviews, likes) which fail to characterize mountain POIs holistically. These approaches are further constrained by their reliance on commercial proprietary sources, or by questionnaires that are subject to memory bias. To address these gaps, we introduce a novel multi-dimensional metric, the Obscurity Score, that groups fragmented literature into four key dimensions (International Awareness, Attractiveness, Promotion, and Accessibility) to systematically detect and characterize lesser-known POIs and enable their promotion as a first step toward mitigating overtourism. To operationalize this score, we develop a generic pipeline mapping open data sources onto these four dimensions. Preliminary results from a web-based prototype demonstrate the practical relevance of the proposed approach.

CAD segmentation datasets are predominantly synthetic or automatically labelled, leaving it unclear how well existing methods transfer to real-world engineering tasks. Fastener-relevant hole detection represents one such task, requiring human annotation and exhibiting greater geometric complexity than commonly used benchmarks. We address this gap through three main contributions. First, we develop two task-specific rule-based methods, one graph-wire-search and one multi-view based, and complement them with a human-annotated benchmark dataset derived from engineering CAD data that also enables training of UV-Net and AAGNet, representative learning-based approaches for B-Rep segmentation. Second, we conduct an extensive experimental study including parameter optimisation, evaluation on our benchmark dataset, cross-domain generalisation on a synthetic dataset, and an assessment of the feasibility of the approaches at varying dataset sizes and IoU thresholds. Third, we provide evidence-based insights into the strengths and limitations of different approaches: rule-based methods generalise well without training data, with the graph-wire-search method favouring recall and the multi-view method favouring precision, whereas learning-based methods achieve strong performance with sufficient annotations but exhibit reduced robustness under domain shift. These findings highlight trade-offs between data requirements, and robustness, and provide guidance not only for hole detection, but more broadly for real-world CAD segmentation tasks.

Multimodal LLMs can fail to read text embedded in an image's coarse structure (text a human recovers by squinting) and report that no text is present. We name this class Squint Text and study it as a recognition deficiency, motivated by cases from a production moderation pipeline. We introduce SquintBench, comprising 1076 production-derived moderation images, and SquintCtrl, a controlled synthetic suite for mechanism diagnosis. Frozen-weight analysis shows that hidden text leaves a coarse signal while glyph identity is weakly represented; identity becomes substantially more accessible when the correct spatial regions are supplied, implicating spatial selection as a major bottleneck. Suppressing high-frequency content also improves reading at a fixed visual-token budget, while visual token count may also contribute. These findings motivate Squint OPSD: a frozen teacher receives a downscaled view and the ground-truth transcription as privileged context, and its token-level distributions supervise a student along on-policy trajectories. At inference, the student reads the original image alone. Squint OPSD reaches 88.61 ANLS on SquintBench, versus 26.50 for the unadapted backbone, 24.44 for the best general-purpose model on the original view, and 68.60 at best for an off-the-shelf model under a downscaled view. These results substantially narrow the gap between available visual evidence and its generated read-out without auxiliary views at inference.

The BROJA partial information decomposition provides an operationally motivated way to separate the information that two sources carry about a target into unique, redundant, and synergistic components. For continuous and high-dimensional variables, however, computing the BROJA decomposition requires solving a difficult optimization problem. Previous work showed that, when each source-target pair is jointly Gaussian, the problem can be reduced to finite-dimensional numerical optimization. Here, we derive a closed-form solution to this optimization problem, enabling direct computation of the BROJA decomposition in the general multivariate Gaussian setting. The resulting closed-form expression enables speedups exceeding two orders of magnitude for high-dimensional Gaussian BROJA PID. Code is available at https://github.com/brainsandmachines/Eigen_PID.

We prove that the cyclic sum $\sum_{i=0}^{10}(x_i-x_{i+1})/(x_{i+1}+x_{i+2})$ is nonnegative for every strictly positive real eleven-tuple, with indices taken modulo eleven. Clearing denominators reduces the problem to a homogeneous polynomial. Subtracting the smallest coordinate then separates the proof into nonnegativity of a common-translation derivative and nonnegativity on a full boundary face. We supply exact rational polynomial certificates in Gram-matrix form for both statements. The derivative certificate uses a linear multiplier, centered monomials and cyclic averaging; the boundary certificate uses a strictly positive quadratic multiplier and uncentered monomials. Their verification requires 6,069 cyclic coefficient comparisons and 34,304 literal coefficient comparisons. All 606 certificate matrices are certified by integer congruences with strictly diagonally dominant images. A Lean 4 development formally verifies the certificate checks and their connection to the original inequality. The exact certificate data, replay programs, and formal sources are publicly available.

Author Name Disambiguation benchmarks are predominantly derived from closed infrastructures that may not reflect conditions in open bibliographic environments. We present OC-AND, an open citation-enriched benchmark for AND constructed by remapping the WhoIsWho dataset with bibliographic and citation metadata from OpenCitations. The dataset is produced through a reproducible five-stage pipeline involving DOI verification, metadata validation, OpenCitations enrichment, and author-centric transformation. OC-AND retains the WhoIsWho ground-truth files and partition structure unchanged, while its publication files are restricted to publications that could be matched to a validated DOI and an OpenCitations record. It introduces realistic characteristics of open environments: heterogeneous metadata completeness, absent abstracts and affiliations, asymmetric citation coverage, and sparse graph connectivity. The dataset contains author records with associated citations, enabling evaluation of AND methods in settings closer to real-world open scholarly infrastructure scenarios. OC-AND is released as open data with complete provenance documentation and pipeline code, supporting reproducible research and the development of citation-aware disambiguation approaches.

AI systems are making rapid progress in mathematics, but this progress is hard to measure. Benchmarks of solved problems saturate, and in benchmarks of open problems each problem can be resolved for the first time only once. We present SqueezeBench, a benchmark that is resilient to saturation: a success raises the bar instead of removing the problem. Each problem fixes an integer function $f(n)$ whose values are known only for small $n$, and the benchmark keeps a lower and an upper record on it. A record is a computable Lean function with a machine-checked proof that it bounds $f$. A submission proposes a new function and proves that it bounds $f$, that it is no worse than the current record at any $n$, and that it is strictly better at some $n$. Once accepted, it becomes the record that the next submission has to beat. The system thus chooses the bound as well as its proof, and it may improve the record at a single $n$ or its growth rate. At every $n$, the gap between the two records shows how far the certified bounds are from determining $f(n)$. Every proof is checked by two independent Lean kernels, so no referee needs to check the mathematics. The checks also reject a function that computes $f$ by exhaustive search at small $n$, and a maintainer only reads the submitter's report and looks for such a search at larger $n$. We release ten problems from extremal combinatorics with twenty proved initial records and the admission tools. As a baseline, agents based on a frontier language model, with at most one hour per record, had 82 submissions accepted and improved every record, without going beyond the published literature. Agents based on two newer models then started from these records, had 60 more submissions accepted and improved 19 of the 20 records again. For eight of the ten problems, at least one record is still asymptotically behind the best published bound.

This paper deals with the problems of decision theoretic estimation of the scale parameter, $\sigma$, and the entropy (Shannon or Renyi) in general scale mixture models with unknown location. Employing Kubokawa's approach, under convexity of the loss $L(t)$ either in $t$ or in $lnt$, improved estimators of $\sigma$ are derived. If $L(t)$ satisfies an additional condition, the problem reduces to estimating $\sigma$ in the degenerate (scale mixture) model. As the entropy is a linear translation of $ln\sigma$, its estimation under a loss $L_0(u)$ amounts to estimating $\sigma$ under $L(t)=L_0(lnt)$, with the quadratic loss $L_0(u)=u^2$ and Brown's loss $L(t)=(lnt)^2$ being a typical case. Thus, in the case that $L_0(u)$ is convex improved estimators of the entropy are directly obtained from respective estimators of $\sigma$. The results are applied to scale mixtures of normal and exponential distributions, including the multivariate $t$ and multivariate Lomax distributions.

Quantitative genetics is the study of continuous traits and the statistical analysis of phenotypic variation, that is, the observable differences in physical traits among individuals within a population. If family relationships between individuals are known, phenotypic variation can be partitioned into genetic and environmental components. Some traits, such as growth trajectories, can be described as a function of a continuous index and are known as function-valued traits. However, function-valued traits from different individuals often vary not only in their shape (amplitude) but also in the speed at which the biological process develops (phase). In this work, we present and compare two approaches to account for amplitude and phase variations in estimating the additive genetic and environmental components. The first one follows from a conventional framework where warping functions remove phase variations, and then the aligned curves are analysed. The second approach adopts the perspective of looking at the aligned curve and the warping function as a joint functional object. In both cases, we propose a functional mixed-effects framework that uses functional principal components as the data-driven basis for genetically correlated data. The proposed procedure is applied to simulations and a real-case study of Tribolium castaneum growth trajectories.

The DP color function $P_{DP}(\mathcal{H}, k)$ of a hypergraph $\mathcal{H}$ is defined as the minimum possible value of $P_{DP}(\mathcal{H}, \mathcal{F})$ taken over all $k$-fold covers $\mathcal{F}$ of $\mathcal{H}$. It serves as an extension of the classical chromatic polynomial. In this paper, we investigate the DP color function for two constructions: the join of a hypergraph with a complete graph and vertex-gluings of certain hypergraphs. Both constructions extend some results of Becker et al.

These notes summarize the content of a one-week course given by Luis Vega on the binormal flow model applied to describe the dynamics of three-dimensional vortex filaments in incompressible fluids following the Euler equations. This topic touches connections between the binormal flow, the Schrödinger map and the 1d cubic nonlinear Schrödinger equation, providing a rich casuistry linked to the physical and numerical phenomenology. This course was part of the $2^{\text{nd}}$ Advanced Summer School held at the Institut d'Etudes Scientifiques de Cargèse (IESC), at Cargèse (Corsica), from $20^{\text{th}}$ to $30^{\text{th}}$ June 2023. These notes have been written and completed by two of its attendees, Elena Danesi and Pablo Merino.

Cyber-Physical Systems are developed through multiple model based activities, comprising several stages of development. As the development progresses through simulation, experimentation, and operation, observations of system execution may reveal missing, uncertain, or invalid design knowledge. The path from execution results to persistent design-time enrichment, however, is often implicit. This paper addresses this challenge by proposing an evidence driven workflow for systematically transferring knowledge produced during simulation and operation back into design-time models. We demonstrate the workflow using an Influence Model, a design-time artefact used to represent how design artefacts and environmental factors jointly affect system response properties, using a sign-following robot use case. We show how simulation evidence can enrich Influence Models by supporting participant pruning decisions, interaction characterisation, influence-function abstraction, and validity-scope information. The application demonstrates the feasibility of the workflow for simulation-based evidence and its potential benefits to improve design-time reasoning and feedback in subsequent development iterations.

Large language models (LLMs) have taken the world by storm. Their ability to communicate with us in our own language, and to reason about our world, has made them a favorite tool for writing, answering questions, and much more. Their answers already influence our decisions and our actions. What would happen if LLMs themselves could act in the world directly? What would happen if LLMs could interact with each other? Agentic LLMs combine the power of large language models with the ability to act in the real world. In this book we will discuss how agentic LLMs work, how they act, how they interact, and what this means for us, as users.

Recovery risk measures incorporate explicit liability-recovery requirements into asset-liability risk assessment. We study their specialization to optimized certainty equivalents (OCEs), allowing the underlying utility specification to vary across recovery levels and encompassing Recovery Average Value at Risk (RecAV@R) as a special case. For finite recovery specifications, we use the dual penalty representation to characterize redundant recovery regimes and derive position-independent screening conditions. For a subfamily of the Cressie-Read power-divergence family, including entropic and truncated-quadratic specifications, we obtain an exact characterization on atomless probability spaces: universal redundancy is equivalent to a two-dimensional convex-hull condition involving recovery levels and divergence-scale parameters. On such spaces, universal redundancy for RecAV@R reduces to pairwise dominance, whereas for power-divergence OCEs it can arise from the joint effect of several recovery regimes. For nonlinear OCE utilities, we develop a certified piecewise-linear approximation framework for portfolio optimization. In finite-scenario models, the approximating problems are finite-dimensional linear programs, while utility approximation errors transfer directly to the Recovery OCE, yielding explicit error bounds and convergence rates. Uniform approximation over the portfolio domain further implies convergence of optimal values and stability of optimal solutions. A numerical asset-liability study illustrates the effects of recovery-dependent risk preferences and the accuracy and convergence of the approximation.

Reinforcement Learning (RL) substantially improves planning performance in autonomous-driving Vision-Language-Action (VLA) models. However, existing RL methods rely on scalar trajectory rewards that measure overall quality but fail to identify specific planning errors or provide actionable correction signals. In long-tail scenarios, errors in scene understanding, behavior selection, and trajectory execution are compressed into a single score. We observe that Reflective Guidance turns trajectory evaluation into explicit diagnoses and corrective instructions, substantially improving planning accuracy. Yet such guidance requires an initial prediction and its evaluation results, making it unavailable for direct single-pass inference. We propose Reflect-VLA, which treats Reflective Guidance as training-time privileged information and internalizes its planning benefits through Dual-Path On-Policy Self-Distillation (Dual-OPSD). Unlike scalar-reward optimization, Dual-OPSD uses the driving score only to route student-generated trajectories. It distills dense token-level corrective distributions from the teacher for risky trajectories while applying self-imitation to preserve reliable ones. To provide reliable corrective distributions on student rollouts, the teacher is progressively constructed through Driving-Knowledge Pretraining, Planning-and-Refinement SFT, and Self-Refinement Rejection Sampling. At inference time, Reflect-VLA generates trajectories in a single pass without explicit guidance or iterative refinement. Experiments on NAVSIM v1/v2 and Bench2Drive demonstrate competitive planning performance while reducing training time by over 90% compared with RL.

We give deterministic algorithms for approximating the girth~$g$ of an undirected graph with $n$ vertices, $m$ edges, and nonnegative real edge lengths. For every integer $k\geq2$, our algorithm returns a cycle of length at most $\frac{2k}{3}g$ in $O((m+n^{1+2/k})k\log n)$ worst-case time. For every constant~$k$, this matches the stretch and the expected running time of the randomized algorithms of Kadria, Roditty, Sidford, Vassilevska Williams, and Zwick [SODA'23, SICOMP'26] and Kadria, Roditty, and Vassilevska Williams [ESA'26]. In general, it loses only a factor of $O(\min\{k,\log n\})$ in the term that depends on~$m$. The best previous deterministic trade-off, of Kadria, Roditty, Sidford, Vassilevska Williams, and Zwick [SODA'22], has stretch~$k$ instead of $\frac{2k}{3}$ at the same exponent (for even~$k$) and requires integer edge lengths. In particular, for $k=3$ we obtain a deterministic $2$-approximation in $O((m+n^{5/3})\log n)$ time for real edge lengths, whereas the deterministic algorithm of Ducoffe [SIDMA'21] for real lengths has stretch $2+\varepsilon$. Our main technical idea is that a deterministic construction of the Thorup–Zwick hierarchy used by these algorithms may stop exploring as soon as it finds a cycle: the approximation analysis only needs clusters truncated at half the best cycle certificate found, so balls stopped in this way need not be hit. Together with a degree-weighted selection rule, this bounds the work of each level by its number of edges and stored ball entries. More generally, a ball need not be hit whenever the analysis only uses clusters up to a radius bounded by a certificate that the algorithm has already found.

This paper presents a finite-time stabilization method for the integrator chain via optimal control techniques by introducing a tailored cost function. We analyze key properties of the resulting value function to derive the corresponding Hamilton-Jacobi-Bellman equation. Numerical simulations illustrate the effectiveness of the approach.

We reprove and generalize a result of Derksen describing the Hilbert polynomial of the vanishing ideal of a transversal subspace arrangement in projective space. When the subspaces have all codimension 2, we describe explicitly the local cohomology modules of the corresponding defining ideal. This is achieved via a complex naturally associated to the subspace arrangement, whose basic properties are also investigated.

Many deformed nuclei exhibit low-lying rotational bands with negative parity. In mean-field calculations, such bands follow from symmetry restoration when the variational solution spontaneously breaks parity. However, they can also be computed in cases where the breaking of parity is not spontaneous but rather enforced by an octupole constraint. In this paper, we extend these techniques to coupled-cluster computations. We introduce octupole-constrained coupled-cluster theory, which explicitly breaks the parity of the correlated intrinsic state and restores parity and angular momentum as good quantum numbers by projection after variation. We perform coupled-cluster singles-and-doubles (CCSD) computations for $^{20}$Ne using two- and three-nucleon forces from chiral effective field theory. The energies of the positive-parity ground-state rotational band are close to data and depend only weakly on the constrained octupole moment and the Hartree–Fock reference. In contrast, the energies of the negative-parity rotational band are more sensitive to these auxiliary quantities.

Incentives can align private interests with collective goals, but their design becomes intertwined with learning when agents' preferences are unknown. This paper develops an adaptive incentive-design framework for multi-agent linear-quadratic dynamic games, where a system planner can simultaneously learn agents' private preferences and steer their strategic behavior towards the social optimum. To this end, we first characterize the complete family of affine incentives that implement the social optimum as the unique open-loop Nash equilibrium while ensuring exact budget balance. When agents' preferences are unknown, we develop an online algorithm to estimate their preference parameters and establish strong consistency of the estimates under a weak trajectory-dependent excitation condition, without requiring persistent excitation or i.i.d. trajectories. We then integrate this estimator into an active-learning incentive mechanism that combines certainty-equivalent coordination with decaying random probing. We prove that the probing generates sufficient information through the agents' equilibrium responses and the system dynamics, ensuring consistent preference learning from the resulting closed-loop trajectories. We show that the induced trajectories converge almost surely to their socially optimal counterparts, while cumulative social-cost regret relative to the full-information oracle and cumulative net-budget imbalance grow sublinearly. Simulations of a transboundary pollution game demonstrate the effectiveness of the proposed framework.

Speech recognition on low-cost microcontrollers is, in practice, limited to keyword spotting or a fixed list of commands. We present Oído, an inference engine that runs open-vocabulary English speech recognition entirely on an ESP32-S3 (240 MHz dual-core Xtensa LX7, 512 KB of SRAM, 8 MB of PSRAM, 16 MB of flash, no neural accelerator). Oído executes a 13M-parameter Conformer-CTC model with int8 weights, per-frame dynamic int8 activations and int8 attention on the chip's SIMD instructions, with a schedule designed around flash and PSRAM bandwidth. On LibriSpeech test-clean/test-other the on-device arithmetic reaches 3.70%/8.23% word error rate (WER), within 0.12 points of full precision, and 3.33%/7.15% with an on-chip 1.3M-parameter language model; a transducer head gives 2.99%/6.67% and an int4 variant fits in 8.3 MB. This is 2.3-2.8x fewer errors than the vendor's recognizer on the same chip, and fewer than Whisper tiny.en and Moonshine tiny in full precision on a laptop, including in real noise and reverberation. Measured on a physical board, the firmware runs at 1.97x the duration of the audio on one core, with transcripts identical to an instruction-exact emulator: accurate, but not yet real time (a 4 s command is transcribed about 8.7 s after it ends). The two-core schedule gives wrong results on silicon and is disabled. A streaming variant shows partial text while the speaker talks and delivers the final text 4.1-11.1 s after clips of 3.6-10.6 s (7.2-22.4 s in utterance mode) at 4.86%/11.03% WER; a Spanish model makes 34-60% fewer errors than multilingual Whisper tiny. Code and models are released.

A realized tail-risk conditional autoregressive expectile (RTCARE) model is proposed for joint forecasting of value-at-risk (VaR) and expected shortfall (ES). Realized tail measures such as the realized quantile and the realized ES, constructed from intraday high-frequency returns, are incorporated into the dynamics and measurement equations of the conditional expectile, allowing information about lower-tail risk to enter the forecasts. The parameters are estimated by Markov chain Monte Carlo, and we evaluate the resulting VaR-ES forecasts in numerical examples and in an empirical application using U.S. stock-return data. Across the considered tail levels, the RTCARE models deliver competitive and often superior forecasting performance relative to existing alternatives, with stable results across Monte Carlo replications and rolling forecast evaluations.

Indoor climbing creates access barriers for blind and low-vision (BLV) climbers because route understanding and in-climb next-hold localization are typically visually mediated and socially dependent. We present HoldLight, a workflow-centered accessibility system combining layered pre-climb route preview, concise real-time next-hold cueing, and explicit fallback under uncertainty. We grounded the design through formative inquiry with BLV climbers, refined the interaction via pilot testing, and conducted a controlled within-subjects evaluation comparing HoldLight with a controlled on-demand human-support condition derived from current support practices. Findings provide initial evidence that structured support can improve pre-climb route understanding, support recovery from next-hold uncertainty, and reduce immediate human re-entry for routine route-information clarification under controlled conditions. HoldLight contributes a bounded accessibility workflow, demonstrating where structured route-information is helpful, where explicit fallback is necessary, and how technical assistance can integrate with retained human safety oversight.

Altermagnets combine compensated magnetic order with momentum-dependent spin splitting, which makes them promising for future spintronic and magnonic applications, but their macroscopic responses can be strongly reduced by domain averaging. In hexagonal $\alpha$-MnTe, three symmetry-related in-plane Néel-vector orientations and their time-reversal counterparts form six magnetic domain states, complicating both magnetic structure determination and measurements of the chiral magnon response. Using single-crystal neutron diffraction, we show that an in-plane field applied along the $[-1,1,0]$ direction produces a common magnetic domain orientation that saturates near $\mu_0H=2$ T. A constrained refinement of 61 nuclear and magnetic reflections collected at 2 K and 2 T yields $\mathbf{M}\parallel[1,1,0]$, an ordered moment of $4.62(8)~\mu_\mathrm{B}$ per Mn, and an orientational domain population at $r_A:r_B:r_C=0.97:0.03(5):0$ that is compatible with a nearly complete alignment of orientational domains. Furthermore, an abnormal behaviour in the temperature dependence of the selected reflections is observed in 60-88 K, its microscopic origin is discussed within the context of possible intrinsic piezomagnetic or magnetoelastic effects. Because unpolarized diffraction neither distinguishes domain repopulation from continuous Néel-vector rotation nor resolves time-reversal antiphase domains, the field-prepared state is a near-single-orientation state rather than a truly single-domain state. This non-contact domain control provides a practical complement to strain and field-cooling approaches for preparing well-defined magnetic states in bulk $\alpha$-MnTe.

Adaptive notch filters (ANFs) based on the normalized least mean squares (NLMS) algorithm are an established technique for suppressing narrowband interference in GNSS receivers. The traditional solution for multiple interferers is simply cascading the NLMS-ANF into multiple stages but this solution degrades performance when multiple chirp jammers of similar power are present. We propose a low-complexity modification to the cascaded NLMS-ANF update rule to resolve this: a local gradient (LG) formulation: LG-ANF. The LG-ANF forms a locally bandlimited gradient signal by translating the input to baseband around the current frequency estimate, low-pass filtering it, and translating it back, thereby attenuating competing interferers before adaptation. The modification generalizes the traditional NLMS-ANF to handle the similar-power multiple interferer problem, using just one additional parameter. We characterize the gradient-averaging failure analytically and visually, demonstrate independent chirp tracking in the worst-case two-chirp scenarios, and evaluate statistical suppression performance by sweeping amplitude ratio against a standard NLMS-ANF, a frequency-locked-loop (FLL)-based ANF and a per-sample oracle upper bound. We further characterize the LG advantage over various ANF parameters and chirp conditions. Simulations show that the LG-ANF reduces to the standard NLMS-ANF outside the pathological multi-chirp regime, while recovering up to 4dB of in-band suppression around pathological amplitude ratios under per-condition optimization of the local bandwidth, and up to 13dB for selected edge-case parameter combinations. These optimized results represent an upper bound on the achievable LG gain. In a hardware experiment using a fixed alpha_lp=0.5, the LG-ANF extends position-lock survival by 24s relative to the standard ANF.