Papers

The Madden-Julian oscillation (MJO) is a major source of subseasonal-to-seasonal (S2S) predictability. The MJO is commonly defined and tracked with indices such as the Real-time Multivariate MJO (RMM) index. Although the RMM provides a useful description of the MJO, its evolution can be noisy and difficult to predict. We define an MJO index using a data-driven approximation of the Koopman operator. The Koopman index captures similar tropical circulation and convection patterns to the RMM but evolves more smoothly and predictably. Skillful prediction extends to 46 days for the Koopman index compared to 11 days for the RMM under the same prediction framework. While this new approach does not recover the RMM as well as operational S2S models, which provide skillful forecasts up to 35 days, the Koopman index could complement existing MJO diagnostics in evaluating and developing extended-range forecast systems.

Let $p_n$ be the $n$th prime, and let $r,s\ge2$ be fixed multiplicatively independent integers. We count the integers up to $x$ whose prime factors all have the form $p_{r^a s^b}$ with integers $a,b\ge0$. Our asymptotic formula for this count has relative error $o(1)$ and is explicit down to the multiplicative constant. For $(r,s)=(2,3)$ these integers are the prime codes of the ordinals below $\omega^{\omega^2}$, so the formula settles that case of the counting problem of Vernaeve, Vindas and Weiermann.

We propose a novel class of anomalous nuclear matter: self-bound, neutron-rich droplets trapped in false vacuum associated with the nuclear liquid-gas phase transition in heavy-ion collisions. During the early stage of the fireball expansion, strongly correlated local clusters dynamically decouple from the bulk medium and are excited into the liquid phase. As the ambient fireball cools rapidly, these clusters are quenched into metastable anomalous droplets with isospin asymmetry from ambient neutron-enrichment. Mechanical equilibrium among nuclear pressure difference, Coulomb repulsion, and surface tension stabilizes droplets at radii of order $\mathcal{O}(10)$ fm. Isospin asymmetry induces high potential barrier that suppresses decay channels, yielding long lifetimes. These droplets are expected to exhibit characteristic charge-to-mass ratios distinct from conventional neutron-rich nuclei, providing clear experimental signatures for future heavy-ion collision searches.

It is often assumed that general stationary solutions to the wave kinetic equation are described solely by conserved fluxes and temperature. The families of solutions parameterized by these quantities are referred to as warm cascades, and are derivable from differential models of wave kinetics. These models rely on the assumption of local interactions, and we demonstrate by a time scale argument that the nonlocal effect of thermal damping on the cascade may result in dependence on an additional parameter, the UV cutoff, calling into question the validity of warm cascade solutions. This is shown for systems with both three-wave and four-wave interactions. We then consider the depletion of the cascade by this damping, and present a numerical demonstration of this nonlocal and nonuniversal behavior.

We present an efficient wideband construction of directional $\mathcal{H}^2$-matrices for the electrical field integral equation that, in contrast to existing constructions, supports not only box trees but also geometry-adaptive cluster trees. To accommodate geometry-adaptive cluster trees, we determine the number of directions from the electrical size of each cluster (instead of the level of a box tree), construct the directions using Spherical-Fibonacci points, and establish a hierarchy between the direction sets of a cluster and its children through an angular nearest-neighbor mapping. We construct the nested directional representation using the incomplete adaptive cross approximation, for which we introduce a robustified tree-mimicry pivoting strategy that prevents premature convergence for block-structured matrices arising from certain geometries and meshes. Numerical results demonstrate that the proposed approach achieves the desired accuracy, requires no more storage than the octree-based construction and substantially less when the geometry or discretization is poorly matched to octree clustering, and exhibits the expected $\mathcal{O}(N\log N)$ scaling for high-frequency problems.

We prove that the twisted endoscopic character identities between triality $\mathrm{PGSO}_8$ and the endoscopic group $\mathrm{G}_2$ imply the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G}_2$. In the course of proving the main result, we also establish some fundamental results on representation theory of $\mathrm{PGSO}_8$ with triality. A key feature of our approach is an application of the adjoint group of type $E_6$.

Construction safety reporting often relies on manual logs and static templates that provide limited feedback and leave daily activities disconnected from relevant regulations. This paper introduces CARES (Conversational AI Reporting for Enhanced Safety), a conversational AI system that integrates regulatory guidance into daily reporting to support construction safety education. CARES combines proactive multi-agent dialogue, retrieval-augmented generation (RAG), and automated report generation. The system guides users through reporting tasks, retrieves relevant regulatory passages using hybrid retrieval, and converts conversations into structured daily reports. Regulatory sources and the evolving report are displayed alongside the dialogue to support user review and correction. A preliminary evaluation involving 15 construction management students assessed retrieval quality, response faithfulness, and conversational relevance. CARES achieved an overall faithfulness score of 0.74 and an answer relevance score of 1.00, while initial retrieval ranking remained an area for improvement. These results provide preliminary evidence of the technical feasibility of regulation-grounded conversational reporting. The study highlights opportunities to integrate regulatory knowledge into routine documentation, with future work needed to evaluate effects on report quality, safety awareness, and learning outcomes.

This paper proposes a structured approach to learning linear operators for control systems from data. We address both structural and learning-theoretic aspects of the problem. To derive structural assumptions, we propose using the well-established framework of (semi)groups for evolution equations, as operators in control systems are of the same type. Further, we propose analyzing learning algorithms through the lens of the inverse problems framework. This reveals how a learned model depends on the data via error decompositions, convergence guarantees, and optimal regularization – enabling us to compare existing methods and derive provably advantageous algorithms. In order to obtain these results, we restrict our scope to bounded operators on Hilbert spaces. Although this may appear restrictive, existing approaches often make this assumption implicitly to obtain matrix-like representations. We demonstrate the power of using these frameworks by deriving a convergent estimator for time-varying systems.

Let $V$ be a complex symplectic vector space and let $\mathbb{P}(V)$ carry the induced contact structure and symplectic polarity. We study the loci of hypersurfaces containing codimension-two cones supported on hyperplanes. The starting point is the following characterization: a projective subvariety $X\subset\mathbb{P}(V)$ which is a hypersurface of degree at least two in a hyperplane $H$ is involutive if and only if it is a cone whose vertex contains the polar point $\sigma(H)$. We give a short proof, construct the corresponding incidence spaces, compute their dimensions and express the incidence degrees as Segre-class integrals. In $\mathbb{P}^3$ the incidence map is birational for every $d\ge m\ge 2$ except $(m,d)=(2,2)$, and the same holds in $\mathbb{P}^5$; the quadratic case is exceptional in every dimension, the incidence having generic degree $2n$ in $\mathbb{P}^{2n-1}$. We also give a sufficient criterion for birationality in higher dimension, closed formulas in $\mathbb{P}^3$ and coefficient formulas in $\mathbb{P}^5$. For quadric cones in $\mathbb{P}^5$ the degree is the product of shifted binomial factors and an irreducible polynomial of degree 36, and we explain where the shifted factors come from.

Given red and blue points drawn from Poisson point processes of equal intensities, we match them by locally minimizing a cost function. In our paper, we identify all possible measurable cost functions on $\mathbb{R}^d$ such that the resulting matching is scale invariant. Our cost functions can be asymmetrical, which we refer to as unbalanced cost functions. The investigation is motivated by arXiv:2012.07129 where the authors consider scale invariant cost functions with added regularity assumptions. Furthermore, we discuss how different the unbalanced matchings are compared to these more regular cost functions for points on $\mathbb{R}$.

Tool-augmented large language model (LLM) agents fail in a way no tool-selection or tool-security method addresses: they call tools that do not exist and pass arguments no schema declares. Existing defenses either pick the right tool (selection) or constrain what an agent may do with real tools (gating), both of which presuppose the emitted call refers to a real tool at all. We show this is a structural blind spot: a hallucinated call is by construction not a decision any gate made, so no gate can reject it. This paper is primarily a measurement and benchmark study. We give a five-class taxonomy of tool hallucination (H1-H5) and, as a reference point, the Resolution Rung: a training-free, closed-world resolver (registry membership plus a signature check) whose interest is where it must sit, not what it computes. We prove hallucination defense must precede any causal gate, and characterize the one irreducible residue (borrowed arguments schema-indistinguishable from a valid call). Across ten hosted models under two invocation surfaces we measure 322 genuine hallucinations; fabricated-tool calls concentrate on the unconstrained raw-JSON surface (34 vs. 3), and model scale does not help (a 675B model matches a 7-8B one). We then extend to the Model Context Protocol, where merging several servers into one namespace creates hallucination surfaces a single registry cannot express (a second taxonomy, M1-M5); on the live MCP surface we measure 154 hallucinations, including from frontier models that were clean on the single-registry surface, because collisions and shadowing are structural to the merge. We release the versioned Hallucinated-Tools Benchmark (HTB) so any resolver is comparable across submissions.

What can and cannot be predicted by a model when only limited information is available? We answer this question by constructing a ladder of information limits that organizes prediction tasks according to their information requirements: from memoryless and memory-augmented trajectory forecasts to event prediction, stationary statistics, and generative laws. The analysis, which is independent of the model structure or architecture, identifies the minimum attainable error along with the information limitations that give rise to it. The approach distinguishes information hidden in unresolved variables from information recovered through time-delayed observations and connects these contributions to Mori–Zwanzig memory. The ladder also reveals why Lyapunov growth alone cannot characterize reduced-order prediction error, why stationary statistics may remain predictable even when individual trajectories become unpredictable, and why stochasticity can represent (but cannot recover) missing information. Numerical studies of the Kuramoto–Sivashinsky equation and the Lorenz system illustrate these results across the ladder. This unified perspective provides a principled language for understanding the fundamental limitations of ROMs for a given prediction task and for clarifying whether improved predictions require richer observations, greater precision in the input, or additional memory.

We define a quadratically enriched pushforward for proper morphisms between smooth, proper Deligne–Mumford stacks over an arbitrary field using Grothendieck–Serre duality. We apply this pushforward to define quadratically enriched Euler classes and Euler numbers of relatively oriented vector bundles on smooth, proper Deligne–Mumford stacks. Finally, we define quadratically enriched fundamental classes for smooth, proper schemes over an arbitrary field, and we use these to propose a definition of quadratically enriched quantum $K$-invariants when the moduli space of stable maps is smooth, tame, and relatively oriented.

Burnout is a chronic occupational syndrome, and open source is close to a worst case for it: maintainers absorb unbounded demand with no manager to reallocate work and no organization to notice decline. The cost is not only personal. Burnout precedes withdrawal, and in projects sustained by a handful of maintainers, one departure can break infrastructure that thousands of downstream systems depend on. Yet the field has no way to see it coming: self-report inventories, the only existing measure, miss exactly the contributors most in need of detection and cannot be applied retroactively, so the field cannot even ask how common burnout is or what helps. We present BurnRiSc, a framework that operationalizes the Oldenburg Burnout Inventory's two dimensions, exhaustion and disengagement, as 14 behavioral and linguistic signals computed from GitHub activity and scored against each contributor's own history. The signals aggregate into two weighted dimension scores, with weights learned from labeled cases, and average into a monthly Burnout Risk Score (BRS). In a preliminary evaluation across 68 contributors in ten repositories (ten disclosed burnout cases, twelve comparable-volume collapses, and 46 comparison contributors), sustained BRS elevation precedes 6 of 10 disclosures by 6-15 months, 8 of 10 when adding peak BRS as a second criterion, and 10 of 10 over any prior time frame. We thus present BurnRiSc as evidence that burnout is screenable from public data.

Gaussian Splatting has significantly improved the quality of novel view synthesis with explicit Gaussian representation. However, we observed that existing 3D Gaussian Splatting methods (3DGS) often suffer from surface collapse issues on reflective regions, and thus produce inferior geometry and low-quality specular. In this work, we propose a physically-based deferred rendering framework, named Reflection-aware Gaussian Splatting (RGS), that can accurately model specular regions and improve novel view synthesis performance. Specifically, we found that a powerful 3D foundation model can provide a strong 3D geometric prior to foster correct geometric modeling. Based on this, we propose a cross-view shape consistency regularization to regularize the geometry surface with the large model prior and cross-view constraints. In this manner, our RGS can produce smoother geometric surfaces on reflective regions while reducing geometric hollows. To further improve rendering results on reflective regions, we present a reflection-aware densification strategy that is designed to capture specular variations across various views. With this strategy, our RGS is able to render novel views of objects in higher quality. Extensive experiments demonstrate our method consistently renders high-quality reflective objects, achieving state-of-the-art performance.

LLMs are rapidly reshaping peer review, making it important to understand how reviewers use them in practice and how different LLM-use policies affect review outcomes. We investigate these questions through a randomized experiment and an anonymous post-survey at ICML 2026, a major machine learning conference involving over 24,000 papers and 17,000 reviewers. Reviewers were assigned to either a conservative policy prohibiting all LLM use or a permissive policy allowing limited assistance, with randomization among a subset of main-track papers and reviewers. Policy assignment had near-zero effects on final paper decisions, paper scores, and reviewer confidence, although reviews under the permissive policy were 5.5-7% longer. Post-survey responses (N=1,486) revealed diverse attitudes toward LLMs and substantial noncompliance: 22.5% of conservative-policy reviewers reported using an LLM despite the prohibition, and 36.5% of permissive-policy reviewers reported at least one explicitly disallowed use. We discuss implications for future peer-review policy and tool design.

We demonstrate physics-constrained agentic development of a meta-generalized gradient approximation (meta-GGA) functional using a large language model (LLM) to assist the search and optimization of a band-gap-oriented revision of r2SCAN. No real bonded systems were fitted, preserving r2SCAN's nonempirical philosophy. Across the finalist set, band gaps and several molecular subsets improve relative to r2SCAN; the top finalist, r2SCAN+, reduces the band-gap MAE on a benchmark comprising 24 solids from 1.26 to 0.96 eV and the aggregate MAE on 329 molecular properties from 4.79 to 4.42 kcal/mol. We first curated 78 exchange and 90 correlation candidate correction terms from r2SCAN's dimensionless ingredients, spanning polynomial terms through third degree, exponentials, exponentially damped products, and ratios. Allowing each candidate to combine one to three correction terms from the exchange catalog, the correlation catalog, or both yields about 8 x 10^5 distinct forms, making exhaustive high-throughput screening impractical. We defined the search criteria for the LLM agent using r2SCAN's exact constraints, physical norms, and the targeted iso-orbital derivative response. The agent then combined these criteria with its pretrained knowledge and accumulated search feedback to propose and refine sparse forms, prioritizing terms tied to the iso-orbital response; a second LLM critic screened proposals before deterministic verification. Compared with uniform random search, the workflow learned from prior evaluations, incurred far fewer downstream rejections (0.6% versus 24.6%), and located stronger high-response candidates: 51 agentic candidates exceeded the best random-search response of 1.263, with the overall best reaching 1.331. These results show that agentic search can support density-functional development when flexible hypothesis generation is coupled to automated physical verification.

In evidence-based policymaking, typically one experimental sample is observed, then a learned policy recommendation is implemented at scale. Policies learned from the experimental data can perform well in expected welfare, yet random sampling in the experiment can produce recommendations with poor welfare outcomes. In this paper, we ask: how should policy learning algorithms balance expected welfare against sampling risk? Our main contribution is to show that algorithmic stability plays a central role in characterizing and navigating the tradeoff. Intuitively, if a policy learning algorithm's recommendation remains stable when one experimental unit is replaced, then that algorithm has limited sampling risk. We propose a method for policy learning called policy-vote bagging, which learns treatment decisions on many subsamples then averages their votes into treatment probabilities. Relative to using one subsample, averaging across subsamples preserves expected welfare and improves expected utility for a risk-averse researcher. We derive sharp bounds linking estimation accuracy, subsample size, and welfare variation, including an exact guarantee under CARA utility.

Graph-based retrieval-augmented generation (RAG) is widely used for multimodal, cross-document question answering. However, building corpus-level graphs is expensive, slow to query, and difficult to maintain. We present TrioRAG, a graph-free multimodal framework that integrates evidence from three complementary signals: the question, the anchor image, and a VLM-enhanced query generated from both. Each signal retrieves independently over a shared multi-vector index of page text and page images, and the results are combined through late fusion. Further, we introduce AutoQA, a multimodal automotive benchmark whose questions are grounded in noisy, web-sourced images rather than clean document-sourced figures. Its questions require reasoning across manuals. We position it as a model-curated testbed rather than a human-validated gold standard. Across three benchmarks, TrioRAG matches or outperforms graph-based systems while reducing total cost and accelerating per-query inference by 1.6-2.3 times. By construction, AutoQA grounds its questions in out-of-corpus web images. In this setting image retrieval reaches only 19.3% document-level recall, while text-derived signals, especially the VLM-enhanced query, keep retrieval robust.

We study machine-learning detection of controlled beyond-General-Relativity (beyond-GR) deviations in gravitational-wave signals, using both synthetic aLIGO-PSD noise and real LIGO H1 detector strain. Three deviation families are applied to General-Relativistic inspiral-merger-ringdown waveforms: amplitude modulation, phase modulation, and frequency modulation, each parameterized by a dimensionless strength coefficient $\beta$. A hybrid classifier combining a one-dimensional convolutional neural network with ten hand-crafted waveform statistics is trained on GR and modified waveforms and tested on a deviation type excluded from training. The central result is a quantitative detectability curve as a function of $\beta$. Using the real GW150914 strain as a template and real H1 detector noise, we find a detection threshold at $\beta \approx 0.25$, with accuracy rising smoothly from chance at $\beta \leq 0.2$ to perfect classification at $\beta \geq 0.5$. The threshold value is specific to the quadratic-in-time modulation form adopted here and should not be interpreted as a generic constraint on beyond-GR parameters. We nevertheless argue that the negative result at small $\beta$ is informative: it establishes a quantitative limit on machine-learning-only beyond-GR searches in real detector noise, in the absence of matched-filter signal extraction.

Consider an increasing number of consistent estimators to be averaged when only estimated weights are available. The underlying parameter of interest can be identical across estimators (homogeneity) or not (heterogeneity). The contribution of the paper is threefold. First, it is shown that the interaction of the estimated weights with the estimators can generate specific bias terms. This constrains the number of estimators that can be aggregated when weight estimation is ignored in inference. Second, the paper proposes estimated adaptive weights, which allow for standard Gaussian inference in a uniform manner and are asymptotically optimal both under homogeneity and heterogeneity. Third, conditions ensuring the validity of the Cochran (1937) Q test of homogeneity with estimated variance are given.

Goal-conditioned reinforcement learning aims to learn policies that reach specified goals, but remains challenging in offline settings with sparse rewards and long-horizon dependencies. In such settings, goal-completion information can be temporally distant from the early decisions that enable success, while offline value estimation introduces additional error. We study this issue from a reward-propagation perspective and show, in a stylized delayed-goal setting, how goal-directed value separation can become small relative to local estimation error. Motivated by this analysis, we propose Reward Stimulation Implicit Q-Learning (RSIQL), a simple non-hierarchical method that introduces additional reward signals at progress-making intermediate states in offline trajectories. RSIQL uses an auxiliary goal-conditioned value function to identify intermediate states estimated to make progress toward the goal and applies reward stimulation to provide less-delayed training supervision. Unlike hierarchical methods, RSIQL does not learn a separate high-level subgoal policy. Experiments on D4RL goal-reaching benchmarks and OGBench show that RSIQL improves over goal-conditioned IQL on average and achieves performance competitive with hierarchical offline goal-conditioned methods, while retaining a simple flat policy structure.

Robot manipulation policies are improving quickly, and real-robot evaluation remains the standard evidence for that progress. It still relies on a human to reset the scene between rollouts, which consumes operator time and leaves the initial state distribution unspecified, so results reproduce poorly. A recent system, AutoEval, automates both reset and scoring, but only for single-step tasks, because a long-horizon rollout can terminate in combinatorially many configurations that no single learned reset policy covers. We present HALTER, a Harness for Autonomous Long-horizon Task Evaluation and Reset, which restores the scene by planning over a library of learned atomic reset skills, so demonstration cost scales with the size of that library rather than with the number of terminal states. HALTER builds a spatial scene graph online from point clouds and vision foundation models, and an LLM reasons over this graph to score the rollout, plan the reset, and verify that the reset succeeded, without collecting labeled success images for any task. On four long-horizon tasks on a Franka arm, HALTER restores the scene in 76% of episodes, against 52% for AutoEval and 65% for a motion-planning reset, and it estimates the completed-skill fraction correctly in 90% of episodes, against 76%. Its reset-verification verdict is correct in 91% of episodes, compared with 78% for AutoEval. It also cuts the operator time of an evaluation campaign by 72% relative to manual reset. We further measure compositional generalization on three held-out tasks, where HALTER resets 74.7% of episodes against 1.3% for a per-task reset policy, and we ablate the scene representation and the graph update rate.

The exact capacity of the binary deletion channel remains unknown despite decades of work on achievable rates and converse bounds. We establish a computer-assisted approximation whose error is below $0.0095$ bits per transmitted bit, uniformly over all deletion probabilities. The mean certified error bound, with uniform weighting of deletion probability, is below $0.006522$. The estimate is the midpoint of explicit lower and upper bounds. For the converse, a stationary-source reduction is combined with finite inequalities covering every allowed input configuration. Two constructions control the unobserved input beyond a finite window: one uses a common outside survivor sequence and bounds omitted deletion patterns, while the other cancels an entropy term to make outside probabilities enter linearly. For the lower bound, finite-state inputs combine output-entropy estimates with selected disjoint counts of compatible deletion masks; independent-run inputs retain additional uncertainty about output-run boundaries. Directed numerical checks establish the finite inequalities. An analytic comparison between deletion probabilities then extends the pointwise bounds over the entire parameter range. The lower endpoint supplies rates within $0.019$ bits of capacity in the asymptotic coding sense. We give the derivations, recorded computational costs, and complete numerical inputs and programs needed to verify the result.

This paper studies axially symmetric Abrikosov-Nielsen-Olesen vortices in the quartic Abelian Higgs model as the magnetic flux becomes arbitrarily large. The emphasis is on developing the rigorous asymptotic analysis behind the formal large-flux expansions of Hakim, Lemaitre, and Mallick '01 and Dumitrescu, Gaikwad '25. For every coupling constant less than 4 we prove that the radius of the magnetic core is of the size predicted by the physics literature. We identify the interface between then normal and super-conducting regimes with the classical normal-to-superconducting transition layer in Ginzburg-Landau theory. The theorem of Chapman-Howison-McLeod-Ockendon '91 proves its existence, uniqueness and monotonicity. The connection of the Gaussian tail of the scalar field on the left with the interface is made directly with the Weber equation. The core Higgs equation is treated as a semiclassical Sturm-Liouville problem in the left overlap region, where the Higgs field decays like a Gaussian. The exterior region is described perturbatively around modified Bessel functions. A key step is to show that the matching map between the admissible Cauchy data at the two ends of the linearized interface equations has maximal rank.

Sparse tensor contractions are bottlenecked by sparse-sparse coiteration loops that resist standard loop vectorization. We present Splyce, an auto-vectorization framework in MLIR that overcomes this through a dual-path execution model. By decoupling coordinate intersection from pointer management via selective predication, Splyce inherently eliminates data-dependent branches as a side effect, allowing modern superscalar engines to maximize instruction-level parallelism and hide memory latency. Beyond simple branch elimination, our transformation exposes independent computation that can be executed concurrently, increasing functional-unit utilization that would otherwise be constrained by sequential dependencies. Evaluation across foundational sparse tensor kernels demonstrates performance ranging from 1.96X to 2.86X on synthetic inputs, with consistent speedups sustained across a vast majority of irregular real-world datasets from the SuiteSparse collection. Ultimately, Splyce demonstrates that by converting unpredictable control-flow into a predictable data stream, compiler-driven speculation can effectively reconcile the memory efficiency of compressed storage with the execution-unit throughput of modern superscalar architectures.

Consider a sequence of i.i.d.~trials $X=\{X_1, X_2, \ldots, X_n\}$ where $p(X_i=j)={1}/{d}; j=1,2,\ldots, d$, or more generally $p(X_i=j)=p_j; \sum_{1\le j\le d}p_j=1$. We consider the variable $D$ that counts the number of distinct substrings of all lengths,$1\le k\le n$ in $X$ and prove results concerning $E(D)$.

Quantum dots (QDs) provide a versatile platform for engineering quantum-confined electronic states with functionalities relevant for optoelectronics, spintronics, and quantum technologies. While substantial progress has been achieved in coupling confined states to spin, valley, topological, or ferroelectric degrees of freedom, the realization of a multiferroic QD in which quantum confinement simultaneously intertwines with magnetism and ferroelectricity remains elusive. Here, we engineer a multiferroic QD in an artificial van der Waals heterostructure grown by molecular beam epitaxy under ultra-high-vacuum conditions. The heterostructure consists of ferroelectric SnTe nanoislands deposited on the layered magnet CrBr$_2$ supported on highly oriented pyrolytic graphite. Combining scanning tunneling microscopy and spectroscopy with ab initio calculations and low-energy tight-binding models, we demonstrate the emergence of spin-polarized discretized electronic states confined within the SnTe islands. Remarkably, the spectroscopic response of the QD strongly depends on the ferroelectric domain configuration of the SnTe nanoislands, demonstrating an interplay between quantum confinement, magnetic exchange, and ferroelectric order at the atomic scale. Our results establish engineered van der Waals heterostructures as a platform for multiferroic quantum confinement and open new routes toward electrically tunable quantum spintronic devices.

Ultra-faint dwarf galaxies (UFDs) in the Milky Way are ideal probes of low-mass galaxy formation and dark matter because they are highly dark-matter dominated. In the lowest-mass systems, however, unresolved binary orbital motion complicates dynamical mass estimates by inflating measured velocity dispersions and biasing the interpretation of the inferred masses. We develop a flexible forward-modeling pipeline, the Binary Observation Simulator, to generate mock multi-epoch radial-velocity observations of binary populations in dwarf galaxies and to quantify how binary-induced biases depend on both galaxy properties and observing strategy. We generate mock samples spanning true velocity dispersion of $\sigma_{\rm true}\sim0.75$-$3.5$ km/sec, binary fractions of $0.1$-$0.9$, and multi-epoch baselines of up to $10$ yr. We find that, while multi-epoch monitoring reduces the binary-induced bias, residual contamination remains significant for low-mass halos: even a $10$-yr baseline can leave $\sim10$-$120\%$ relative bias for systems with $\sigma_{\rm true}\lesssim1$ km/sec. We also note that small sample sizes ($\lesssim20$) introduce substantial stochastic scatter in the recovered dispersions, sometimes masking the expected improvement from longer observational baselines. Applying the framework to the real $\sim17$-yr Bootes I observing record reproduces the literature velocity dispersions, yields an empirical correction conditioned on that cadence, and shows that redistributing the same observations onto half the number of stars would have removed roughly half of the residual binary bias. These results emphasize that robust dispersion estimates for the faintest dwarfs require forward modeling of both binary populations and survey cadence.

Digital competence frameworks define the knowledge, skills, attitudes and values required for participation in digital society. The European Digital Competence Framework for Citizens (DigComp) and UNESCO digital literacy and artificial intelligence competency frameworks provide reference structures for policy, curriculum and competency development. The growth of generative and agentic AI raises a further question: does knowing what constitutes competent digital behaviour provide sufficient evidence that an individual can act competently in an authentic digital situation? This conceptual paper addresses that question through a comparative analysis of DigComp, UNESCO Digital Literacy Global Framework, UNESCO AI Competency Framework for Students, and the International Digital Driving License (IDDL). Rather than treating these frameworks as competing models, the paper distinguishes their functions. DigComp and UNESCO primarily define what individuals should know, understand, value and be able to do. IDDL addresses the subsequent evidentiary problem by assessing digital capability through behaviour observed during authentic digital tasks. Its Knowledge-Capability-Reflection model distinguishes knowing what should be done, demonstrating the required behaviour, and explaining the judgement behind it. IDDL integrates Digital Skills, Cybersecurity Awareness and AI Competency, and extends assessment to human agency under AI delegation. The paper distinguishes defined competence from demonstrated capability and positions IDDL as an interoperable behavioural assessment and certification layer that can operate downstream of international competency frameworks.