Papers

We report on hyperfine structure measurements of the $1s2s\,{}^{3\!}S_1 \rightarrow 1s2p\,{}^{3\!}P_{0,2}$ fine-structure transitions in the spectrum of $^{11}$B$^{3+}$ ions. The helium-like ions were created in an electron beam ion trap (EBIT) and ejected after a short production period of 15 ms. A challenge of the experiment was the treatment of the complex energy-time-profile of the created ion bunches and the sensitivity of the collinear laser spectroscopy to the starting potential inside the EBIT. Despite these complications and the low statistics of the experiment, we were able to confirm and improve the results of a previous measurement of these transitions. While we find moderate tension in the results for the hyperfine parameters of the $^{3\!}P_{0,2}$ levels, their fine-structure level energies are in reasonable agreement between experiments and with theory.

Research using large language models (LLMs) to generate synthetic populations shows that model outputs compress human variation. We ask whether this compression also distorts where dispersion is concentrated across social groups. Using 93,901 respondents from 66 countries and territories in Wave 7 of the World Values Survey, we compare observed life satisfaction with predictions from six LLMs. All six substantially understate overall dispersion. Yet after normalizing for these scale differences, they largely reproduce the human income gradient in well-being inequality: lower-income groups remain relatively more heterogeneous than higher-income groups. The pattern is robust to country fixed effects and alternative weighting schemes, and extends directionally to employment, education, and perceived control. In a separately preregistered mechanism experiment using Claude Sonnet 5, counterfactually increasing income strongly raises predicted mean life satisfaction but produces essentially no linear change in predicted dispersion. Removing income from the respondent profile leaves the negative dispersion gradient almost unchanged; the same pattern appears with Gemini and DeepSeek, although somewhat attenuated. These findings show that LLMs can substantially compress well-being dispersion while preserving much of its socioeconomic structure, and that this structure does not depend on the explicit income cue alone.

We report a pre-registered test of five hypotheses about the synapse-flow random walk on the connectome of the male Drosophila central nervous system (166,700 neurons, 124 million synapses), in which a walker moves to a postsynaptic partner in proportion to synapse number. The hypotheses concern the spectral gap and its dependence on the neck connective, the localisation of the leading modes of an input-normalised signed map, the certified mixing depth measured by the Dobrushin coefficient, its robustness to per-synapse detection confidence, and the dependence of the signed spectrum on the neurotransmitter sign convention. After public registration and a code freeze, each was tested once. Two held: the two-neuron photoreceptor modes that lead the signed spectrum are an artefact of normalising by very small inputs, removed by an input floor at the median, and they do not depend on the sign convention. Three failed: at a threshold of five synapses per connection the spectral gap is an order of magnitude smaller than predicted ($|\lambda_2| = 0.9965$) and the chain is certifiably far from mixed after 128 steps, and at no confidence level tested was the mixing depth certifiably robust. Exploratory analyses trace the slow mode to eleven neurons of the cord, seven of them mesothoracic efferent neurons, that become nearly closed once weak connections are dropped, find a similar boundary set in the lamina of the FlyWire female brain, show that null models preserving cell-type wiring reproduce the slow modes, and show that exact chains built from the confidence data change the depth profile after 32 steps by at most 0.017 at the pre-registered confidence level, far less than the worst-case certificate allows. Random-walk summaries of connectomes are dominated by nearly closed sets at the edges of the reconstruction unless these are treated explicitly.

Cable-suspended hoisting is widely used to move heavy or bulky payloads that cannot be handled conveniently by rigid pick-and-place systems, for example in crane-assisted construction. Robotic hoisting using flexible cables is challenging because payload motion is underactuated, external disturbances vary, and delayed or lost visual observations can make the perceived payload state stale at control execution. These effects are particularly critical during precise insertion of a suspended payload's sockets onto rebar pins, which is a very common task in construction environments. We present SwingRL, a residual reinforcement-learning (RL) framework that combines an age-aware world model, a classical anti-swing prior, and a recurrent residual policy to address two coupled problems: stale feedback and uncertain dynamics. The world model propagates the newest received payload observation to the current control step using the executed commands, providing a time-aligned state estimate under delayed and lossy sensing. The prior supplies nominal tracking and swing damping. The residual policy learns bounded corrections to the prior rather than the complete control law, compensating for system-parameter variation, external disturbances, and remaining state-estimation errors. We evaluate SwingRL against classical and learning-based baselines across a cumulative difficulty ladder covering system-parameter variation, wind disturbance, degraded sensing, and strong gusts. Under the most difficult setting, SwingRL achieves 69.5% strict and 77.3% broad success, exceeding all baselines by at least 60 percentage points, respectively. World-model ablations support the role of time-aligned state estimation in maintaining insertion success as observation loss increases. Finally, without real-robot fine-tuning, SwingRL achieves 90% success on the physical rig.

Financial question answering often requires precise numerical extraction, unit handling, and arithmetic over tables and text, but applying expensive verification uniformly wastes test-time compute. We propose BudgetVerify, a budget-tiered generator-verifier framework that routes each generated answer to one of three verification tiers: no verification, lightweight check-and-revise, or higher-cost solve-first-then-compare verification. The router is trained from offline correctness and token-cost outcomes and, at test time, selects a verification tier using information available before verification, including the question, context statistics, the generated answer, and associated generator metadata. The selected tier either returns the generated answer directly or invokes the corresponding verifier. Across six commercial and open-weight base models, BudgetVerify consistently produces more efficient accuracy-cost Pareto frontiers than fixed verification policies by selectively allocating stronger verification only when it is useful. Although absolute performance varies across models, these efficiency gains and the resulting qualitative frontier shape are consistent across generator models.

Hybrid-attention models replace most softmax attention layers with linear attention, reducing KV-cache growth and enabling larger decode batches where recurrent-state access becomes a major bottleneck. ReplaySSM amortizes state updates by buffering keys and values, but each new query still requires a full-state read even though the state remains unchanged between state updates. We observe that low-rank state-weighted query approximation accurately preserves state-read outputs. Although future queries are unknown, the basis vectors used to approximate them can be fixed offline. Based on this observation, we introduce SketchSSM, which preserves full-state updates while approximating reads. At each state update, SketchSSM reads the full state once to precompute outputs for these basis vectors, storing them in a compact sketch. Each subsequent decode step combines the sketch vectors with query-dependent coefficients to reconstruct the output without a full-state read. Across four Mamba-2-, GDN-, and KDA-based models, SketchSSM at a mean sketch rank of 8 reduces state-access traffic by approximately 10$\times$ while matching the average accuracy of the FP32 full-state baseline across four decode benchmarks, and preserves recall on four RULER retrieval tasks. At this rank on one NVIDIA B300, linear-attention kernel speedups over the Standard vLLM baseline reach 7.30$\times$, 5.02$\times$, and 5.24$\times$ for Mamba-2, GDN, and KDA, respectively, with up to 2.77$\times$ higher decode throughput on Nemotron 3 Super.

The Berger-Charpin conjecture predicts that the permutation automorphism group of a cyclic code is generally the $q$-affine group, which is generated by the shift and the Frobenius multiplier on the index set. The word generally is not made precise in the literature, and the goal of this series of papers is to study when the Berger-Charpin conjecture or its variants hold. In this first part, we establish a natural connection between the theory of cyclic codes and the theory of cyclotomic association schemes (equivalently, Schur rings over cyclic groups). Using it, we show that the $q$-affine group is not the correct group to expect for certain code lengths. We characterize these lengths by an arithmetic condition, and show that they have density zero.

Behavior cloning (BC) is vulnerable to covariate shift during closed-loop execution, where small prediction or execution errors can drive the robot toward states poorly covered by the demonstration data. We focus on action-sequence planning, where a policy predicts a finite-horizon sequence of actions as a reference trajectory for robot execution. Existing approaches to covariate shift often rely on collecting additional corrective demonstrations, requiring further environment interaction and access to an expert or reference policy. We propose Perturbation-Augmented Recovery Supervision (PARS), a simple training approach for improving recovery using only existing demonstrations. PARS perturbs the robot's proprioceptive state and anchors only the later portion of the predicted trajectory to the original demonstration, leaving the earlier portion free to generate corrective motion and recover toward the demonstrated behavior within the planning horizon. Unlike conventional input-noise augmentation, which preserves the original supervision target over the entire prediction horizon, PARS explicitly provides trajectory-level supervision for recovery from perturbed states. PARS requires neither additional environment interaction nor expert queries and can be instantiated across different action-sequence policy classes with only minor modifications to their BC objectives. Experiments on 51 RLBench manipulation tasks with flow-based, transformer-based, and diffusion-based policies demonstrate that PARS improves robustness to covariate shift during closed-loop execution.

Understanding how individual brain development unfolds over childhood requires modeling developmental trajectories from sparse longitudinal observations. Long-term neurodevelopmental forecasting is challenging because each child is typically observed at only a few irregularly spaced visits, while developmental dynamics vary across individuals and age. Generic continuous-time models accommodate irregular timing but often absorb these factors into a single flexible transition function, providing little structure for how population progression, individual variability, and developmental age shape the dynamics. We propose DevelopmentODE, a structured continuous-time framework that organizes population- and subject-specific variation within a shared developmental geometry while allowing the governing dynamics to evolve with age. The model builds this geometry around a developmental canal representing the population trajectory, whose local direction provides a reference for organizing subject-specific variation. Subject deviation velocities are constrained relative to this direction, while a shared nonlinear deviation field captures individual developmental motion without disrupting population-level progression. DevelopmentODE further models developmental non-stationarity through ordered age-dependent deformations of the shared vector field, progressively adapting a common dynamical structure as age changes, while elapsed time determines the integration horizon. This formulation uses population-level developmental structure to guide learning from sparse individual trajectories while allowing dynamics to evolve smoothly with age. We evaluate DevelopmentODE on longitudinal fMRI by predicting future functional connectivity of the same child from earlier observations. DevelopmentODE consistently outperforms competing baselines across short- and long-horizon predictions.

Matrix optimizers such as Muon transform each momentum matrix through an approximate orthogonalization, typically implemented by a small number of Newton-Schulz matrix multiplications. The quality and cost of this approximation depend strongly on the singular-value spectrum of its input, yet existing implementations use the same fixed polynomial routine for every layer and throughout training. We show that this uniform treatment is unnecessary: the computations in the Newton-Schulz method already reveal enough information to make the method adaptive. The Gram matrices formed inside Newton-Schulz iterations yield spectral moments through inexpensive scalar reductions, requiring no additional matrix multiplications. From these moments, we recover an estimate of the empirical singular-value distribution and use it to select a polynomial routine specialized to the current matrix. This turns Newton–Schulz orthogonalization into a spectrum-adaptive procedure that responds to differences across both layers and training time. On saved momentum matrices, spectral estimation substantially reduces orthogonalization error at a fixed iteration budget or reaches the same accuracy with fewer iterations, and in GPT pretraining up to 1B parameters it lowers the validation loss of two matrix optimizers. Our results suggest that matrix-function operations inside optimizers need not be designed for a conservative worst-case spectrum: they can cheaply measure the spectrum they are already processing and specialize computations accordingly.

Non-collinear antiferromagnets offer unconventional routes for controlling magnetic, electrical, and thermoelectric responses through their complex spin configurations and interfacial symmetry. Here, we detect exceptional interfacial properties arising from a non-collinear antiferromagnet by demonstrating a robust and quantitatively consistent exchange-bias response in an IrMn$_3$/Py heterostructure. The system consists of a 10 nm IrMn$_3$ layer coupled to a 5 nm permalloy (Py) film. Longitudinal magneto-optical Kerr effect (MOKE), anisotropic magnetoresistance (AMR), and anomalous Nernst effect (ANE) measurements independently reveal the same unidirectional field shift of approximately 50 Oe, together with a consistent cosine angular dependence. The simultaneous observation of these signatures establishes a direct correspondence between the interfacial magnetic symmetry imposed by the non-collinear antiferromagnet and the responses of the adjacent ferromagnet. This symmetry is manifested consistently in magnetization reversal, charge transport, and thermally driven voltage generation, demonstrating that the exchange-bias imprint is not restricted to a single experimental observable. Our results reveal a coherent multifunctional response of IrMn$_3$/Py and extend the conventional understanding of exchange bias beyond collinear antiferromagnetic systems. More broadly, they demonstrate the potential of non-collinear antiferromagnets as platforms for coupling magnetic, electrical, and thermoelectric functionalities in spintronic and spin-caloritronic devices.

The RecSys Challenge 2026 studies conversational music recommendation as a joint item recommendation and response generation problem: given a multi-turn dialogue, systems must retrieve relevant tracks from a large catalog and produce a grounded natural-language response. This paper presents the challenge task, dataset, evaluation protocol, and official results. Beyond the leaderboard, we analyze the 16 accepted systems through a common retrieve–rerank–generate framework and examine how recommendation performance varies across users, requests, and dialogue contexts. Strong systems commonly combine heterogeneous candidate sources and preserve source-specific evidence for learned reranking. Across the system papers and our organizer-side analysis, robust design also means 1) grounding cold-start retrieval in multi-turn conversation and item signals, 2) using intent detectors, and 3) modeling the full multi-turn context rather than the current query alone. We further identify limitations of the benchmark and evaluation protocol, including single-ground-truth relevance and teacher-forced evaluation of synthetic dialogues. Together, these findings provide practical guidance for future conversational recommender systems and shared evaluation efforts.

Modern LLM evaluation assumes that pinning a judge to a fixed model version and decoding at temperature zero yields reproducible verdicts. We show this assumption fails as a property of how LLM-as-Judge is operationalized on cloud serving infrastructure, not of any particular model family. Across four frontier judges served via a single major enterprise cloud platform and three standard benchmarks (Arena-Hard, AlpacaEval 2, MT-Bench), identical inputs to the same temperature-zero judge, at a constant serving-reported model version, produce different verdicts across re-runs: per-item flip rates of roughly 5% on average and about 40% on the close-call items that decide leaderboard margins, with a per-judge magnitude spanning a 40x range (0.13% to nearly 10%). We introduce metrics tailored to this instability: per-item flip rate, a two-part stability profile (waver fraction and conditional intensity), and adjacency separability. For the principal judge the aggregate ranking is stable (0% top-K instability, 0% pooled winner flip); what degrades is precision: under a paired hierarchical bootstrap, roughly one-fifth to three-quarters of adjacent leaderboard positions are statistically indistinguishable, a noise floor driven mainly by finite prompt sampling rather than the judge. Across judges, leaderboards agree on the coarse ordering but diverge in the middle (Kendall's tau of 0.42-0.64 between Gemini and Sonnet judges on Arena-Hard, values sensitive to answers truncated at the generation cap). Of 15 expected head-to-head orderings we re-judge, 12 survive every re-run of the principal judge but only 8 survive every judge. Leaderboards thus report unhedged point estimates that overstate their precision. We propose a minimal, low-cost reporting protocol: several judge re-runs, published stability profiles and adjacency intervals, and results under at least two judges from different families.

The lower asymptotic proportion of distinct nontrivial zeros of the Riemann zeta function, relative to the total number counted with multiplicity, is at least $0.8369928814\ldots$. Earlier work proves $0.83625\ldots$, and a report we have not verified claims $0.83672\ldots$. As in the proof of the bound $0.83625$, an unconditional version of Montgomery's pair-correlation theorem gives an asymptotic energy estimate. The new ingredient is a short matrix inequality with a free clipping parameter. It strengthens the lower bound for this energy in terms of the number of distinct zeros. The gain is a nonnegative correction from overlaps between different nearby zeros on the critical line, which is retained even when some of these zeros are double. The matrix inequality, the threshold lemma, the block dichotomy, the counting assembly and the exact arithmetic are proved formally in Lean 4. The constant relies on a computer-assisted local inequality from recent work that has not yet been refereed. That computation was re-run independently, and every imported input is listed. This paper is primarily an experiment in AI-assisted mathematical research (Section 4).

Plume-laden convection plays a fundamental role in thermal transport in geophysical and industrial flows. While the dynamics of isolated laminar plumes have been extensively studied, their collective interactions and evolution in a multi-plume system remains poorly quantified due to the lack of four-dimensional (4D, in space and time) flow measurements for viscous convection, common in the turbulence community. Here we present a time-resolved experimental study of clustered plume dynamics in a high-Prandtl-number Rayleigh-Bénard system with temperature-dependent viscosity from 4D velocity measurements. Building on our companion methodology (Bao and Lithgow-Bertelloni, 2025), we characterize the spatiotemporal distribution, morphological evolution, and interaction modes of tens of coexisting plumes. We identify a wide spectrum of dynamical behaviors–merging, splitting, branching, pulsing, and head detachment–that arise from coupled interactions among plumes, multiscale flow, and the evolving thermal boundary layers. We synthesize prior behaviors into a unified, time-resolved framework of plume evolutionary pathways. Characteristic length and timescales, including spacing and initiation times, are compared with previous theoretical and experimental studies. We find thinner plumes with greater minimum spacing. The fraction of isolated plumes (e.g., Hawaii-like) varies dramatically (0–60%) as the flow evolves. Our results provide new insight into plume self-organization and spatiotemporal variability under Earth-like conditions, crucial for understanding geochemical evolution and mapping geochemical anomalies from hotspot lavas to deep sources. These results quantitatively complement previous experimental work and numerical studies on interacting plumes, serving as a benchmark for comparison with geodynamical simulations of mantle convection.

Learning-rate warmup is a standard technique in language-model training, yet its duration remains largely heuristic. Common approaches use either a fixed number of updates or a fixed fraction of the training horizon, two choices that imply very different scaling as training gets longer. When should warmup stay fixed, and when should it grow with the horizon? We address this question with a quadratic model whose modes respond differently to the peak learning rate. Warmup slows progress in directions that already contract well at the peak rate, but can remove persistent error in directions near the stability edge, with higher peak rates shifting the balance toward longer warmup durations. This yields a compact horizon scaling law that captures regimes ranging from essentially no warmup, through fixed-duration warmup, to durations that grow with the training horizon, and explains how the preferred regime changes with peak learning rate. Because the law captures the tradeoff between giving up early progress and improving the trajectory that follows, it can be fit using shorter runs and used to predict warmup at substantially longer horizons. Together, our results explain several familiar properties of warmup through a single tradeoff and suggest treating warmup duration as a horizon-dependent hyperparameter rather than a fixed training heuristic.

Reliability in medical Q&A is often pursued by grounding responses in authoritative medical information. We show that when Q&A is embedded within ongoing care, reliability depends on more than what the system knows medically. In a study with 73 skin cancer patients practicing postoperative wound care, 41.9% of response-requiring questions depended on information beyond the procedure, including visual or physical state, environmental context, or prior actions. These demands varied across patients, consistent with patients recruiting the assistant into different informational roles. We then replayed the questions to seven LLMs while adding procedural and postoperative guidance. Errors remained substantial, including treating unknown states as known, even under explicit guardrails; with full procedural context, six of seven models more often introduced later steps prematurely. Based on these findings, we propose a design space for situated medical assistance that connects what the assistant and patient can each reliably establish to the form of assistance provided.

Language model agents can now perform sophisticated sequences of actions via tools and harnesses, which has increased the scope of the damage they can cause. Guard models, however, are mainly built for content moderation and thus are not well-suited to detecting this agentic risk. To address this, we proceed by first conducting a representational analysis, then use the resulting insights to build a solution. In our analysis, we focus on two types of trajectory-level agentic harms: harmful content, which is expressed directly, and unsafe tool use, which depends on whether an action is consistent with the interaction that produced it. We investigate how open-source guard models represent these two types of harm and find that they are linearly readable inside the model, even though guard models predict no better than chance on pairs that differ only in the called tool's schema. The two harm types also follow nearly orthogonal internal directions, and neither reliably serves as a proxy for the other. These results motivate reading trajectory safety directly from internal states. We introduce TACIT, a readout of a frozen backbone's internal states that decodes no tokens. Trained on six trajectory-safety benchmarks, a linear probe raises mean macro-F1 from 62.3 for the strongest open guard to 80.7, and refined readouts reach 86.2. With each benchmark held out of training entirely, the refined readouts still lead the strongest guard (65.7 vs. 61.1). With the same backbone, training data and test split, the frozen readout is on par with full safety fine-tuning, and it improves the fine-tuned model further when applied on top. The probe trains about one millionth as many parameters as full fine-tuning in about a sixth of the time, and TACIT has the lowest latency of the guards we evaluate.

We propose DAST (Diversifying Arithmetic Sampling with TokenTour), a method that increases the diversity of LLM outputs without any change to the marginal distribution and with negligible generation-time overhead (a few microseconds). We observe that token IDs are often arranged in a meaningless order and reassign them so that tokens with similar meanings appear consecutively. This can be done in advance in a few hundred seconds per model, and the resulting order can be reused for all subsequent generations. By combining this order with arithmetic sampling (or quasi-Monte Carlo methods), we make similar tokens less likely to be generated across runs while preserving the distribution. Our method not only produces qualitatively good ideas but also significantly improves performance on the downstream task of ProtoQA.

Retrieval-augmented generation (RAG) lets language models answer questions more accurately by consulting relevant documents. Many valuable collections, such as medical records, cannot be pooled because of privacy rules. Federated RAG leaves each collection with its owner, or node, which scores candidate answers from its own documents; a central hub combines the scores. Some nodes, called Byzantine, may be compromised, faulty, or misled by instructions hidden in documents, and report arbitrary scores. Conformal prediction returns a set containing the correct answer with a chosen probability, using a cutoff set in a calibration step on questions with known answers. An unknown group of nodes, no larger than a declared bound, may misreport both in this step and at query time. Existing methods assume every node is honest or protect only the calibration step. We observe that the honest nodes are the same in both steps. The hub therefore has all nodes score the same calibration questions, and keeps a candidate only if some plausible group of honest nodes, using its own scores in both steps, would keep it. We prove that the resulting sets contain the correct answer with the chosen probability in finite samples, whatever the Byzantine nodes report. No method using the same information can return smaller sets without risking the loss of an answer the honest nodes support. If nodes fail at random, the guarantee weakens only by the probability that more nodes fail than declared. In simulations, on real question-answering tasks including medical exams, and with language models as nodes, some hijacked, our sets reached the target whenever no more nodes misbehaved than declared, while plain averaging could miss it. They were also clearly smaller than those of simpler methods with the same protection, most of all when the declared bound was generous, so a cautious bound costs little.

Laboratory investigation of convective flow in viscous fluids is crucial for various engineering and geophysical applications, including vigorous convection in planetary mantles, which involves multiple rising plumes. Many experimental techniques have been developed to visualize the flow and plumes, but most previous measurements remain largely qualitative. Here we present a method to measure and analyze four-dimensional (4D) plume-bearing viscous fluid flow, extending volumetric velocimetry approaches to the high Prandtl-number laminar regime relevant to mantle convection. First, a customized three dimensional (3D) Scanning Stereoscopic Particle Image Velocimetry (SSPIV) system is applied to a Rayleigh-Bénard experiment suitable to study the dynamics of Earth's interior. We report the first quantitative 4D velocity measurements of multiple interacting laminar plumes at high Prandtl numbers. The raw velocity data are postprocessed with a Lagrangian Coherent Structure (LCS) and cluster analysis pipeline, tailored for clusters of viscous plumes, which allows quantitative, transport-based material boundary tracking of the plumes in space and time. We show example results to demonstrate the power of our method while fully exploring the dynamics in a companion paper Bao and Lithgow-Bertelloni (2025). Our analysis quantifies the rich dynamical behavior of multiple interacting plumes. We suggest our method of measurement and analysis can help better quantify the morphology, interaction, and evolutionary pathways of plumes feeding Earth's volcanic hotspots and other planetary interiors.

A graph G is uniquely C_t-saturated if G contains no cycle of length t and, for every edge e of the complement, G+e contains exactly one cycle of length t; it is nontrivial if it has at least t vertices. Wenger and West proved that no nontrivial uniquely C_6- or C_7-saturated graphs exist, and conjectured the same for every t >= 6; the case t=8 was verified but never published, and t >= 9 has remained open. We prove the conjecture for t=9: there is no nontrivial uniquely C_9-saturated graph. The proof is a case analysis on the length L of a longest even cycle of length at most 12 (L is 4, 6, 8, 10, or 12). The cases L=12, L=10, and L=4 are settled by hand; for L=6 and L=8, hand classifications of the components outside the cycle reduce each case to a bounded finite family of configurations, eliminated by a short, replayable computer enumeration with known-answer controls and completeness certified by zero cap hits. Along the way we prove, in sharpened form, the t=9 instance of a structural lemma Wenger and West stated without proof.

A global classification of the asymptotic oscillatory dynamics is established for a symmetric zero-divergence class of three-dimensional piecewise-linear Filippov systems, up to a set of initial conditions of zero Lebesgue measure. The affine fields are related by an involution, and the switching plane contains a visible–visible two-fold. In canonical coordinates, the eigenvalues are \(\mu\pm i\) and \(-2\mu\), while \(H\) measures the focal-line inclination. For every \(\mu>0\), a simple-period crossing cycle exists if and only if \(H\in\mathcal I_\mu\), and is unique, symmetric, hyperbolic, and orbitally asymptotically stable. Its half-period parametrizes \(\mathcal I_\mu\) and determines the crossing points, period, and Floquet multipliers. Global dissipation excludes crossing cycles with any higher number of crossings and makes the classified cycle the \(\omega\)-limit set of every crossing-only trajectory. If attractive sliding has no interior pseudo-equilibria, sliding is transient unless the trajectory reaches the two-fold. The initial conditions leading to the two-fold lie in a countable union of analytic surfaces and curves. Under sufficiently small perturbations in the Whitney \(C^1\) topology, the cycle persists as the unique simple-period crossing limit cycle and remains hyperbolic and orbitally asymptotically stable.

We formalize in Lean 4 the Galerkin construction of global Leray–Hopf weak solutions for the unforced two-dimensional Navier–Stokes equations on arbitrary bounded open domains with no-slip boundary conditions. For every initial datum in the solenoidal \(L^2\) velocity space, the solution has a weakly continuous velocity path, satisfies the weak equation locally in time, and obeys the energy inequality at every time. For rectangles, we also formalize finite-horizon solutions with continuous forcing in the dual energy space. The development includes divergence-free graph spaces, compact spectral coordinates, transport cancellation, Ladyzhenskaya estimates, and simultaneous space–time compactness. The abstract Hilbert-space results apply to evolution equations with a compact energy-to-velocity embedding and a skew trilinear nonlinearity.

We introduce neuro-distillation (Neuro-Dist), a technique designed to directly transfer computationally useful neural population structure from biological brains into artificial controllers. Using three macaque motor-cortical datasets as neuro-distillation teachers, we align controller internal states with cortical neural population geometry during training; controller deployment requires no neural data. We evaluate gated recurrent unit (GRU) networks and Transformers controlling a simulated arm. Neuro-Dist achieves the lowest median error among five methods, including distillation from movement kinematics, in 10 of 18 comparisons across trained, student-held-out, and new target directions. Seed-split aggregate statistical comparisons significantly favor Neuro-Dist over all six controls on trained and new targets, and five on student-held-out targets (Holm-corrected familywise p<0.05). We furthermore find that Neuro-Dist can substantially improve controller robustness to sensory feedback noise. Mechanistically, Neuro-Dist induced low tangling of trajectories in internal controller state space—a functionally important characteristic of motor cortex, demonstrating successful transfer of a known motor-cortical population geometry feature. These findings establish neuro-distillation as a complement to behavioral distillation and point to a novel class of neuro-interfaces that tap biological neural population structure as a computational resource for improving the control of goal-directed behavior in robotics and embodied AI.

Heart failure is a serious medical condition associated with risk of acute deterioration, recurrent hospitalizations and high mortality making accurate mortality prediction potentially valuable for patient care and healthcare planning. Numerous prognostic models have been developed using conventional statistics (CS), machine learning (ML) and deep learning (DL), but variation in study populations, heart failure definitions, prediction horizons and development practices may limit interpretation of applicability. We conducted a systematic review of mortality prediction models published between 2009 to the start of 2026 searching three databases (PubMed, IEEE and Scopus) for studies predicting all-cause mortality over a 1-60 months prediction horizon among patients with heart failure. Data extracted were cohort characteristics, heart failure definitions, model development, cohort size, validation practices, mortality, computational model design and reported performance. The risk of bias and applicability were assessed using the Prediction Model Risk of Bias Assessment Tool (PROBAST). Of 1516 publications identified, 56 met the inclusion criteria. Publication numbers increased over the observation period, alongside increasing use of ML/DL models and decreasing use of CS approaches. Most development cohorts (64%) were classified as Unknown/Undefined heart failure, reflecting inconsistent reporting and terminology that did not correspond with established heart failure guidelines. External validation was reported in 23% of studies. Overall, research in modeling heart failure mortality has grown alongside increasing adoption of ML/DL approaches. Greater standardization of study design and reporting is needed for meaningful comparison, reproducibility and evaluation of models for clinical application.

Physics-based models provide skillful subseasonal forecasts but suffer from systematic biases, weakened teleconnections, and parameterized physics, while very large ensembles remain computationally expensive. Purely data-driven models also see too few realizations of the low-frequency modes that provide subseasonal predictability. We introduce methodname, a hybrid framework that converts modelshort subseasonal ensemble guidance into 90-member stochastic forecasts of weekly precipitation and 2 m temperature on a global 1-degree grid using a lead-aware flow-matching U-Net. Its stochastic prior initializes members with EOF perturbations conditioned on the Madden-Julian Oscillation, North Atlantic Oscillation, El Nino-Southern Oscillation, and lead week, allowing the learned flow to refine large-scale covariance rather than create it from white noise. On held-out 2021-2025 forecasts, empirical CRPS improves by 22.0% for precipitation and 25.6% for temperature in a same-initialization four-versus-four comparison, and by 32.2% and 34.0% in the 90-versus-four production comparison. Ablations across five training seeds show distinct gains from the structured prior and a learned error-variance pathway, with the prior contributing more. Verification over 120 observed-extreme cases shows positive CRPS skill, but the ensemble remains underdispersive, four-member upper quantiles are poorly resolved, and precipitation exceedance BSS is near neutral after week 1. Results support improved probabilistic skill and tail representation, but not calibrated operational rare-event probabilities. Case studies of the 2022 UK heatwave, 2023 California atmospheric rivers, and 2022 Pakistan floods illustrate the reach and limits of dynamically informed refinement.

Medicine occupies a singular position in the open access economy: It is the field with the highest number of OA journals with APCs in DOAJ, the second largest by global APC expenditure with high rates of APC adoption among researchers in the Global South. This article analyses APC trajectories in medicine from a comparative disciplinary perspective, drawing together evidence from multiple studies to position medicine in relation to other scientific fields over the period 2009-2023. It documents price gaps between medical and biomedical subcategories, the particularly acute affordability challenges associated with publishing in global health journals and the structural asymmetry between the public urgency of medical knowledge and the cost of its dissemination. The article concludes with a reflection on alternative models and the conditions required for an equitable and sustainable open access transition in medicine.

Contact-rich insertion requires precise geometric alignment despite uncertainty in perception, geometry, and con- trol. When this uncertainty causes unintended contact, the re- sulting contact provides local information that can guide correc- tive motion. Sampling-based Model Predictive Control (SMPC) is well suited to this setting because it optimizes through forward simulation without requiring gradients through contact dynamics. However, standard SMPC methods typically use generic proposal distributions that do not exploit observed contact to determine where to search next. We introduce ContactKernels, a contact-adaptive proposal kernel that uses geometry-conditioned wrench measurements to estimate contact location and local contact geometry. The estimated contact state directly adapts the proposal distribution: contact location biases the search toward corrective motions, while the contact normal shapes the sampling covariance. We evaluate ContactKernels with Predictive Sampling (PS) and Model Predictive Path Integral (MPPI) control across multiple insertion geometries in simulation and on a real robot. In simulation, ContactKernels improves mean insertion success by over 50 % points across both controllers. On the real robot, it increases insertion success from 53.3 % to 90.0 % and reduces mean time to insertion by 33 %. These results show that contact information can improve sampling-based control not only as feedback, but also by directly determining where the controller searches

End-to-end autonomous driving systems have achieved rapid progress by learning unified policies that map sensor observations directly to driving trajectories. However, once deployed, these systems typically remain frozen: they may repeat similar decisions in similar scenes, and failures can only be addressed through costly data collection and retraining. This sharply contrasts with human drivers, who improve lifelong through experience, memory, and reflection. In this work, we ask whether autonomous driving systems can achieve similar post-deployment self-evolution to human drivers. We propose EvoAD, a self-evolving autonomous driving framework via latent world-model guided post-hoc reflection. EvoAD stores driving experiences in a bird's-eye-view feature memory pool, retrieves scene-relevant precedents according to geometric and semantic similarity, and uses a latent world model to evaluate the future consequences of candidate trajectories in a compact planning-oriented space. Instead of treating memory as external textual contexts or using world models only for pre-action simulation, EvoAD transforms executed driving outcomes into reusable improvement signals for future decisions. This enables the system to diagnose how prior trajectories could have been improved and to refine behavior in similar future scenarios without retraining the base driving policy. Experiments on NAVSIM v1 and v2 show consistent improvements across reflection rounds and state-of-the-art performance, demonstrating the potential of world models as reflective mechanisms for post-deployment self-evolution in autonomous driving.