Papers

In science and engineering, many physical laws and scientific principles naturally arise as variational problems of minimizing an energy functional over an appropriate functional space. In many cases, it is more advantageous to directly discover the minimizer of the energy functional than to solve the associated Euler-Lagrange equations. Conventional numerical solvers, such as the finite-element method (FEM), often lack the flexibility to incorporate prior knowledge or noisy observational data. In recent years, machine learning approaches, particularly kernel-based methods, have attracted growing attention in scientific computing. Unlike FEM, which requires domain discretization and mesh generation, kernel-based methods construct solutions from scattered nodes, thereby avoiding the complexity of meshing, especially in high-dimensional or geometrically complex domains. This works presents a two-step procedure for variational energy minimization based on the optimal recovery formulation in a reproducing kernel Hilbert space (RKHS), providing a unified framework for seamlessly incorporating both physical constraints and noisy data. On the computational side, we employ the sparse Cholesky decomposition for Matérn kernels to alleviate the well-known cubic complexity bottleneck of kernel methods. On the theoretical side, we rigorously establish the existence and convergence theory of the proposed method using $\Gamma$-convergence theory. Numerical experiments on benchmark problems demonstrate the efficiency, robustness and accuracy of the approach.

If a language model can recognize code it wrote, it may favor that code as a judge, and instances of one model monitoring each other could collude. We test this zero-shot on current commercial models. Five LLMs generate solutions to MBPP, HumanEval, and DS-1000, seven more to MBPP, and models act as evaluators in four tasks: picking their own solution from a pair, judging whether a single solution is their own, identifying which of two solutions a named model wrote, and judging quality blind. In the single-solution task, balanced accuracy is 49-58% for all 15 model-benchmark combinations, while raw accuracy (38-67%) mostly reflects how readily a model claims authorship. In the pairwise task, accuracy across 14 evaluator-opponent combinations correlates at r=0.93 with how often the evaluator's solution is longer. Attribution to a named model succeeds on some pairs and is consistently inverted on others. A rule-based normalization that strips docstrings, comments, type hints, and local names preserves Pass@1 and leaves ten of twelve re-tested results at chance; the other two follow a length difference it leaves, although a trained classifier still separates most normalized pairs. Claude Haiku's self-preference also disappears. We recommend reporting balanced accuracy, heuristic baselines, and label consistency.

Resistive switching in oxide-based devices is widely governed by stochastic defect processes, yet a predictive link between fabrication conditions and functional behavior remains elusive. Here, we establish a multiscale framework connecting plasma-defined deposition conditions to macroscopic device functionality in sputtered SiO$_x$/Cu/SiO$_x$-based systems. By combining large-scale statistical analysis of more than 50,000 experimentally characterized devices with physics-based plasma and atomistic simulations, we show that device behavior does not emerge from deterministic process-to-performance mappings, but from a probabilistic cascade spanning defect formation, defect-state evolution, and functional-regime emergence. Data-driven clustering reveals a continuous functional state space composed of operational switching types, while inverse modeling identifies the reconstructed oxygen-vacancy density as an effective latent descriptor capturing the combined influence of structural disorder and defect topology. This latent descriptor is strongly coupled to both Cu redistribution and electrical response, linking otherwise hidden material properties to observable device characteristics. Furthermore, macroscopic switching behavior is argued to arise from ensemble integration across spatially heterogeneous subdomains, providing a physical explanation for the pronounced variability of large-area devices. These findings shift the perspective from deterministic defect engineering toward probabilistic defect-state design and establish a physically grounded framework for understanding and controlling functional variability in such oxide-based systems, such as memristive or resistive-switching devices.

Thin plate splines are highly attractive smoothers. However, they have cubic computational cost, which severely limits their use in practice. As a remedy, Wood (2003) suggested thin plate regression splines (TPRS), which provide a low rank approximation. The key step of the TPRS approximation is a truncated eigendecomposition of the radial basis function (RBF) design matrix. However, as Wood (2003) writes, the optimality of the TPRS approximation is a slightly weak one. This is because the RBF coefficients are subject to orthogonality constraints and the TPRS approximation is only optimal if these constraints are ignored. To address this shortcoming, we suggest a slightly different low rank approximation. The suggested approximation is based on a truncated Demmler-Reinsch basis (TDRB), which provides a best low rank approximation of the smoother matrix in terms of Frobenius and spectral norm. We prove that the TDRB smoother achieves the optimal rate of convergence and suggest an efficient algorithm for its construction. This algorithm is based on a truncated Karhunen-Loève (KL) expansion of the equivalent Bayesian smoothness prior and it has the same computational cost as required for TPRS. We demonstrate the applicabilty of our approach through simulations and a real data example. We find that the performance is very similar to that of TPRS but the suggested approach has some advantages.

We prove that the planar balanced excited random walk $M(2,1,2)$ is recurrent. This walk takes a horizontal simple random walk step on its first departure from each vertex and a planar simple random walk step on every later departure. Moreover, the number of distinct vertices visited before time $n$, multiplied by $(\log n)/n$, converges to $\pi$ almost surely and in every $L^p$, $1\le p<\infty$, the same limit as for the planar simple random walk. More generally, we prove recurrence of balanced excited random walks in spatially inhomogeneous cookie environments whenever the total positive and negative cookie strengths at each vertex are bounded by constants $A, B$ with $A+B<1+1/(2\pi +1)$.

The Komlós conjecture, now a theorem, asserts that whenever the columns of a matrix $A\in\mathbb{R}^{m\times n}$ have Euclidean norm at most one, some signs $\varepsilon\in\{-1,1\}^n$ make every coordinate of $A\varepsilon$ bounded by an absolute constant. Guo, Fang, and Lu gave the first polynomial-time algorithm for finding such signs, a deterministic spectral signing procedure with discrepancy $8272$ and running time $O((mn^9+n^{10})\log(m+n))$. We give a deterministic algorithm that finds signs with $\|A\varepsilon\|_\infty<99$ using $O(mn+n^{\omega+2}\log^3 n)$ arithmetic operations, where $\omega>2$ is any fixed attainable matrix-multiplication exponent; with the current bounds on $\omega$ this is $\widetilde O(mn+n^{4.372})$. Our algorithm uses the same framework: it rounds a single fractional coloring and watches all rows through the top eigenvalue of a Gram matrix of energy-corrected barriers. Steps follow flat directions, rescaled so that no barrier near its threshold moves faster than a constant, and the regularizer grows as coordinates freeze; together these bound the number of updates by $O(n^2\log n)$. A weak quadratic charge on the tracked row sums leaves $O(n\log^2 n)$ rows to evaluate at any time, and a motion clock bounds when any other row could approach its barrier. Each update is a short sequence of matrix products. Its direction is read off by conditional expectations from a polynomial soft projector, its small constraint residual is repaired in affine row representations, and one identity accounts for every change of representation. For rational input the algorithm has polynomial bit complexity.

Dense vessel annotation in digital subtraction angiography (DSA) is labor-intensive, yet every unlabeled sequence records how contrast passes through the vessels. Semi-supervised methods take their targets from the current model, and generic self-supervised pretexts reconstruct static appearance, so this signal goes unused. We propose ConPro, a self-supervised pretraining scheme whose target is a contrast projection, the normalized drop of every pixel below its temporal median over the sequence. On DIAS and DSCA, with 10%, 20% and 50% of the training cases labeled, ConPro improves on training from scratch at every label fraction and is the best of the compared methods on DSCA at 20% and 50% labels. Controlled comparisons show that the gain comes from the target. A temporal-median target with the same input, loss and budget stays at scratch level, and using the projection directly instead of learning it, as an input channel or a pseudo-label, helps little or hurts. ConPro provides pretrained weights without changing the segmentation architecture, so it combines with semi-supervised training, and UniMatch, the strongest baseline, gains 0.5 to 2.0 Dice and 0.9 to 2.3 clDice at every label fraction when started from ConPro weights, reaching 75.4 Dice on DIAS and 81.3 on DSCA.

We study the computational complexity of peak-oriented rationalizability, a survey based revealed-preference test introduced by Seror (2026). We provide a polynomial-time algorithm for testing rationalizability and recovering a utility function, establishing that peak-oriented preference elicitation is computationally tractable. In contrast, we show that computing the peak-oriented Houtman-Maks index is NP-hard. These results delineate the precise computational boundaries of peak-oriented revealed-preference analysis.

We analyze solutions to a one-dimensional periodic linear model for peridynamic waves, focusing on the setting where the natural energy space allows for spatial discontinuities. Exploiting the high-frequency asymptotics of the peridynamic dispersion relation, we construct an explicit solution whose initial displacement has a single jump discontinuity but becomes continuous at every positive time. By time reversibility, this yields a continuous initial displacement whose evolution develops a jump at any prescribed time and is continuous at every other time. We further quantify the formation of this singularity through a sharp Hölder-norm blow-up estimate obtained via a Littlewood-Paley characterization of Hölder spaces. Finally, by superposing suitably weighted solutions, we construct an evolution exhibiting jump discontinuities on a dense set of times.

A time-domain representation for ultrabroadband optical pulses that includes chirp, stretching, and absolute phase is presented. This is accomplished by holomorphic Fourier transform of a class of spectra that include spectral phase up to second order, resulting in derivatives of the Faddeeva function $w(\zeta)$. Relating the real part of this pulse to physical quantities, its shape is investigated. The derivative order $\eta$ is shown to dictate relative spectral bandwidth. The absolute phase determines the mixing of more localized (Gaussian decay) and less localized (algebraic decay) components of $w(\zeta)$. Second order spectral phase accounts for linear dispersion and is shown to cause a sheering of the Wigner-Ville distribution of the pulse, akin to the linear chirp that would be seen in the quasi-monochromatic case. Along with $\eta$ it determines the pulse length and number of oscillations. A correspondence with the slowly varying envelope approximation is derived for large order $\eta$, although the algebraic decay persists.

Gradient-based design of large optical surfaces hits a memory wall: a stored-history time-domain adjoint needs $24N_t$ bytes per cell for $N_t$ steps, and every field update is bound by memory bandwidth. Here we present a validated framework that removes this wall and makes globally optimized freeform meta-optics practical. Its finite-difference time-domain adjoint reconstructs interior fields backwards from two recorded planes, so volume memory no longer grows with $N_t$, and fused kernels raise memory-bandwidth use on an H200 GPU from 6.4% to a remarkable 56% of peak. Overlapping tiles, coupled by angular-spectrum propagation and distributed over GPUs, keep tile memory independent of the aperture. Within hours on one GPU node, we optimize, against one global objective, every density variable of single-layer metasurfaces 100 to 200 $\mu$m across, and design a nine-wavelength lens, a color hologram and a polarization-switched hologram. Confirmed by an independent solver within 1.6%, they substantially outperform meta-atom designs, reaching 1.64, 1.65 and 1.24 times their objectives.

We aim to constrain the dynamical masses of the four confirmed transiting planets orbiting the infant ($20\pm10$ Myr) star V1298,Tau (orbital periods $P_b\sim$24.1 d, $P_c\sim$8.2 d, $P_d\sim$12.4 d, and $P_e\sim$48.7 d), through a new analysis of a homogeneous radial velocity dataset. This system is a key benchmark for testing formation and early-stage evolutionary models of planets. We analysed more than 380 high-resolution spectra collected with the HARPS-N spectrograph over a time span of 4.5,yr. To account for dominant stellar activity and transit-timing-derived planet-planet interactions, we analysed radial velocities extracted using two different approaches, and combined N-body simulations with multi-dimensional Gaussian process regression. We tested a set of spectroscopic and photometric activity diagnostics to mitigate the variability due to the stellar magnetic activity in the radial velocity time series. The mass determinations are sensitive to the choice of the radial velocity extraction method and activity diagnostics. For some specific models, we measured masses with a significance of 3.5–4$\sigma$ for planets b ($0.52^{+0.12}{-0.14}$, $0.65^{+0.21}{-0.18}$, $0.67\pm0.16$, and $0.78^{+0.19}{-0.20}$ $M_{\rm Jup}$) and e (0.40$^{+0.14}{-0.13}$, 0.66$^{+0.17}{-0.18}$, and $0.71\pm0.20$ $M_{\rm Jup}$). These values are compatible with masses of giant planets, and are notably higher than those recently derived from transit timing variations alone, which indicate that these are low-density “super-puffy” planets. Injection-and-recovery simulations moderately support this conclusion for planet b. For planets c and d, we primarily provide updated mass upper limits. Our analysis represents an exploratory study to address the complex issue of mass measurement in a multi-planetary system characterised by high levels of stellar activity.

Deployment-oriented compression is attractive for resource-constrained brain–computer interfaces (BCIs), but whether it changes adversarial vulnerability remains unclear. On BCI Competition IV-2a, we compare 32-bit floating-point (FP32) EEGNet and ShallowConvNet models with global magnitude pruning and simulated INT8 post training quantization (PTQ) and quantization-aware training (QAT) across nine subjects and three seeds. Simulation provides differentiable quantize–dequantize models for white-box attacks and gradient analysis, while native TensorRT deployment is used for validation. Accuracy-preserving compression does not improve direct robustness: at $\epsilon=0.005$, EEGNet PGD accuracy remains 22–24% across FP32, 50% pruning (P50), PTQ, and QAT. However, P50 reduces bidirectional transfer efficiency to 0.963/0.928 (FP32$\rightarrow$P50/P50$\rightarrow$FP32), versus 0.994/0.997 for PTQ; the same trend holds for ShallowConvNet. Gradient alignment shows a corresponding separation, while native PTQ agrees with simulated clean/adversarial predictions in 95–98% of cases. These results show that direct robustness, adversarial transfer, and deployment efficiency are distinct properties of compressed EEG decoders.

Latent world models plan toward goal images with a frozen pretrained predictor, without task rewards or extra trained heads. However, their planners struggle with long-range goals, and prior work addresses this by training extra components such as value functions or subgoal models. We show that the planning target itself can cause this failure: even with exact dynamics and globally optimal short-horizon search, scoring predictions by their distance to the final goal rejects the first steps of a route that initially moves away from the goal. Building on this insight, we propose Anchored Planning (AP), a training-free method that reuses the world model's own offline trajectories. AP retrieves a segment that leads from the current observation toward the goal and aims the frozen planner at an observation shortly after the segment's start. Across four diverse tasks, AP substantially improves frozen LeWM planners for both action synthesis and action ranking, and it outperforms both additional final-goal search and the LeWM planner on long-range goals.

A graph $G=(V,E)$ is called smooth (respectively, strongly smooth) if for any two vertices $u,v\in V$, the distance point-shadow $v|u := \{ x\in V: d(u,x)=d(u,v)+d(v,x)\}$, respectively, the point-shadow $v/u := \{ x\in V: v\in\mathrm{conv}(u,x)\}$, is geodesically convex. Smooth graphs have been introduced by Nebeský (2005) in the context of step systems. Graphs with convex point-shadows and convex distance point-shadows also naturally occur in convexity theory. Brešar et al. (2026) recently showed that several classes of graphs are smooth and that smoothness is preserved by Cartesian products, gated amalgams, and isometric subgraphs. Weakly modular graphs comprise the most important classes of graphs from Metric Graph Theory: median, modular, Helly, bridged, and dual polar graphs. In this note, we characterize smooth and strongly smooth weakly modular graphs in terms of forbidden isometric subgraphs on 5 and 7 vertices. This settles Problem 1 of the paper by Brešar et al. We also characterize prime strongly smooth weakly modular graphs, i.e., strongly smooth weakly modular graphs that cannot be obtained from smaller graphs by Cartesian products and gated amalgams.

In this paper, we consider a three-dimensional non-homogeneous incompressible fluid in a bounded periodically perforated domain at the critical Stokes-capacity scale. The density obeys a transport equation. The viscosity depends on a quasi-static temperature perturbation, which solves a uniformly elliptic transmission problem with insulated outer boundary conditions and zero spatial mean. The limiting momentum equation contains a Brinkman resistance term generated by the critical perforation regime. For each fixed perforated domain, we construct global finite-energy weak solutions and derive a quantitative relative-energy stability estimate with respect to regular solutions of the homogenized system. As long as a regular effective solution exists, the squared relative error between any microscopic weak solution and the effective solution is bounded by the initial mismatch plus $O(\eps^{2})$. For well-prepared data, the density and uncorrected velocity converge at order $O(\eps)$ in $L^\infty(0,T;L^2)$, the temperature at the same order in both $L^\infty((0,T)\times\Omega)$ and $L^2(0,T;H^1)$, and the corrected velocity in $L^2(0,T;H^1)$. The key estimates are an $O(\eps)$ cell-capacity residual in the dual energy norm, an $O(\eps)$ corrector-gradient bound in $L^{6/5}$, and fixed-domain thermal stability. The critical boundary layers retain order-one viscous energy, represented in the limit by the Brinkman dissipation, so the uncorrected velocity gradient does not converge strongly to the effective gradient whenever the effective velocity is nonzero. Finally, we prove local existence of regular effective solutions for smooth data satisfying a finite set of boundary compatibility conditions, which closes the stability argument.

Let $F$ be a totally real field of degree $n$ and discriminant $\Delta_F$, and let $X_1(\eta)$ be the cover of the Hilbert modular variety parametrizing abelian varieties with real multiplication by $\mathcal O_F$, together with a torsion point having annihilator $\eta$. Let $L=K_{\overline X_1(\eta)}+D$ be the log-canonical bundle on a smooth toroidal compactification, and let $H_L$ be an associated multiplicative height. We prove that rational points on $X_1(\eta)$ become sparser as $|\mathrm{Nm}(\eta)|\to\infty$, with $(\eta,\Delta_F)=1$. More precisely, for every number field $K$, set $$ N_{\eta,K}(B)=\#\{x\in X_1(\eta)(K):H_L(x)\leq B\}. $$ If $|\mathrm{Nm}(\eta)|\ge 5^n$ and $(\eta,\Delta_F)=1$, we prove $$ \limsup_{B\to\infty}\frac{\log\max\{1,N_{\eta,K}(B)\}}{\log B} \leq\delta_{\eta,K,n},\qquad \delta_{\eta,K,n}\ll_{[K:\mathbb Q],n}|\mathrm{Nm}(\eta)|^{-1/(2n)}. $$ In particular, $\delta_{\eta,K,n}\to0$ uniformly when $n$ and $[K:\mathbb Q]$ are bounded and $|\mathrm{Nm}(\eta)|\to\infty$. The main geometric result is a uniform lower bound, growing with the level, for the log-canonical degree of subvarieties of $X_1(\eta)$. Combining this estimate with recent progress derived from determinant-method, due to Ellenberg–Lawrence–Venkatesh and Brunebarbe–Maculan, we obtain the sparsity result above. We also prove that, for sufficiently large $|\mathrm{Nm}(\eta)|$, every subvariety of $X_1(\eta)$ is of general type, and establish a higher-dimensional generalization of the geometric torsion theorem of Bakker–Tsimerman. Namely, for a family of abelian varieties with real multiplication over a quasi-projective base of arbitrary dimension, we bound the torsion subgroup of its Mordell–Weil group in terms of the canonical volume of the base, uniformly in the totally real multiplication field of fixed degree.

A private semantic computation primitive enables parties to privately compute over structured and unstructured data that requires understanding its semantics, context, and relationships. Standard cryptographic primitives (e.g., multiparty computation) do not readily support such computation. Generative models are well suited for such tasks but typically process data in plaintext, while cryptographic private inference remains inefficient and difficult to scale. Thus, we need a new primitive for private semantic computation. We introduce trusted model environments (TME), the first such primitive that executes generative models inside trusted execution environments (TEEs) while controlling output leakage. TME is designed to be (i) effective (correctly performs the semantic task); (ii) confidential (protects computation and sensitive inputs); (iii) utility-preserving (retains utility on other tasks); (iv) verifiable (provides tamper-resistant evidence of the computations); (v) efficient (incurs low overhead compared to baseline model computations); and (vi) scalable (supports multiple participating parties). Effectiveness follows from the generative models, while TEEs provide confidential computation. For confidentiality of sensitive inputs, we combine adversarial training to resist verbatim leakage with an information flow control module to suppress semantic leakage. For verifiability, we introduce novel attestations that let parties verify TME operations on their data and queries, along with optimizations (e.g., batching) for efficiency and scalability. We design and evaluate the proof-of-concept for TME across three applications, showing that it meets all the requirements.

Mathematical modeling helps us identify and investigate complex mechanisms of function. This is especially useful for understanding inflammation, which is a complex, multiscale process that interacts nonlinearly with other physiological systems. The full potential of these models can only be realized when combined with experimental data through parameter estimation. However, uniquely determining model parameters requires that they are practically identifiable, which can be assessed by multiple, possibly inconsistent, methods. Identifiability can also vary with experimental designs and observation operators. This study investigates this issue by assessing parameter identifiability in a coupled model of the neuroendocrine-inflammatory system. We compare three workflows following a global sensitivity analysis: Fisher-information matrix based identifiability, global optimization with frequentist confidence intervals, and the profile-likelihood. We compare results across six observation operators with and without measurement noise, all of which are experimentally feasible given prior literature. Our results show that Fisher-information-based methods typically lead to larger sets of identifiable parameters while profile-likelihood analyses lead to a smaller number of identifiable parameters. This suggests that, while computationally expensive, the profile-likelihood is necessary for accurately assessing identifiability, and must be recalculated when the experimental design is altered.

A synthetic survey can reproduce the average answer while misrepresenting how people differ, how their answers relate to one another, or how they respond to changes in conditions. We introduce the Artificial Societies Benchmark to help researchers assess whether synthetic populations support their intended analyses. The framework combines eleven tests across internal, construct, and external validity, drawing on twenty human sources and comparing nine language models. It connects each research use to the evidence it requires and tests how results change with the information we supply about respondents. Importantly, strong performance in one domain does not establish fidelity in the others. Models often answer too consistently, compress response scales, and alter relationships between traits whilst richer profiles improve prediction for some models and worsen it for others. The resulting scorecard helps researchers identify which aspects of a synthetic population can support their analysis and where researchers need further human evidence.

Multi-turn, multi-audio temporal question answering requires models to track target events across follow-up questions, recording switches, and historical references, recovering complete instances and their boundaries for temporal calculation and comparison. We propose TEMA, which connects event perception with evidence-based answering through Route, specifying the audio scope, and Span, describing all relevant intervals as conditional audio captions. We construct TEMA-Dialog with 40,704 dialogs and per-turn evidence and answer supervision, and TEMA-Bench for joint evaluation of evidence and final answers. Training combines temporal grounding initialization, full-dialog supervised fine-tuning, and completeness-first Span-only GRPO. Experiments on Qwen2.5-Omni and AF-Next show improved temporal question answering, particularly event localization and cross-audio comparison. Reinforcement learning applied solely to evidence further improves interval recovery and answer accuracy.

Multi-agent deliberation can improve performance, but what happens when some agents do not act in good faith? In practice, an agent may be deceptive and work to subvert the group, whether through its own objectives or external instruction. We study how susceptibility to deception scales as groups increase in size and deceivers become more prevalent. It is not the number of agents in the group that matters, but the proportion of deceivers. We observe that the defection rate, how often initially correct agents switch to an incorrect final answer, rises linearly with this proportion. Whereas humans in comparable conformity studies are reliably swayed only when misleading confederates form a majority, LLM agents defect regularly even when deceivers remain a minority. Susceptibility also depends on which models are interacting, especially on the honest agent side. Unexpectedly, allowing deceivers to coordinate privately can make them less effective. Altogether, our results show that adding more agents is therefore not a sufficient defense, because the adversary can simply scale with the group.

Frontier language models are rarely used in clinical workflows because the realistic, longitudinal benchmarks needed to develop them are scarce. Real electronic health record (EHR) data cannot be openly shared due to privacy, ethics or data use issues and it does not contain verifiable ground truth since the chart records only reflect what clinicians documented. We introduce Synthetic Hospital, an open, fully synthetic, fact-grounded longitudinal EHR benchmark that resolves the open sharing and verifiable ground truth barriers. Built entirely from public medical-education material with no protected health information, it comprises 1,268 longitudinal patients and 5,602 encounters, where every diagnosis, finding, and temporal relation is grounded in standard ontologies (ICD-10-CM, SNOMED CT, LOINC) and with a complete provenance chain back to its source medical education material. Synthetic Hospital is served through a simulated hospital record system that mirrors real EHR infrastructure (standard interoperability APIs, role-based access and function-calling interface). In a blinded review, physicians distinguished its records from real patient charts at near-chance rates (53%). Across 10 frontier and open models, none approaches ceiling: the best model reconstructs a patient's longitudinal problem list with a severity-weighted F1 of 0.73, level with the mean of seven physicians on a matched subset but well below the best of them (0.89), and misses roughly half of clinically relevant findings when summarizing a chart. Overall, these results highlight that Synthetic Hospital is a difficult and realistic test of clinical AI performance.

Detecting which holds a climber uses, and when, underpins automated scoring, movement analysis, and assistive systems for sport climbing. Existing approaches train task-specific models or repurpose 2D pose estimators whose hand keypoint sits at the wrist and foot keypoint at the ankle i.e. offset from the fingertips and toes that actually contact the holds, and whose hands are occluded in roughly half of all frames. We show that a frozen, off-the-shelf pose foundation model is sufficient: using the fingertip and toe keypoints of Sapiens, a per-frame proximity test against the annotated holds, per-limb mutual exclusion, and a short temporal-persistence rule, we detect hold usage without any climbing-specific training. On the The Way Up dataset (22 videos, 10 athletes, two routes), our method reaches an event F_1 of 90.2% on a held-out split (89.8% under leave-one-participant-out cross-validation) and 79.9% over all 22 videos at any temporal overlap, and performs best on footholds (F_1,89.8% overall, 96.6% held-out). Under an identical protocol it exceeds our reproductions of the YOLOv8-pose and ViTPose pipelines at every temporal threshold, with the margin widening under strict timing. An ablation shows that two intuitively helpful additions—dense foundation-feature change gating and body-part segmentation—both hurt, arguing that a minimal, keypoint-only design is the right one for this task. Finally, standard coaching statistics computed from our automatic predictions track ground truth closely (Pearson r=1.00 for climb time, 0.94 for pace), turning ordinary single-camera video into reliable performance metrics with no instrumentation.

Janus-particle arrays provide a soft-matter platform in which particle orientations act as classical spins with anisotropic, bond-dependent interactions. Motivated by recent experiments on triangular arrays of metallodielectric Janus particles exhibiting sixfold orientational order and directly observable vortices and antivortices, we study effective models beyond the isotropic XY description. A classical $120^\circ$ compass model captures the minimal bond-directional interaction, while an effective Kern–Frenkel model incorporates the geometry of the Janus surface interaction more directly. Monte Carlo simulations show that both models exhibit a low-temperature sixfold ordered phase, a high-temperature disordered phase, and an intermediate quasi-long-range-ordered regime consistent with two Berezinskii–Kosterlitz–Thouless transitions. In both cases, the sixfold order arises through thermal order-by-disorder from a continuously degenerate ferromagnetic manifold. We further show that higher-order extensions of the $120^\circ$ interaction can alter the orientational selection: a quadratic term reverses the fluctuation-induced sixfold anisotropy, while a cubic term lifts the degeneracy energetically and selects the lattice-aligned directions that coincide with those observed experimentally. These results connect the microscopic anisotropy of Janus-particle interactions to emergent XY-like vortex physics and illustrate how distinct microscopic mechanisms can produce similar sixfold orientational order.

Manipulation requires not only reasoning about the external environment, but also about the robot's physical condition. A strategy may remain geometrically feasible while becoming physically unsuitable due to increased joint load or limited mobility, yet internal physical state is typically used only for low-level control. We propose body-grounded high-level replanning, which uses internal physical state to adapt manipulation strategies during execution. Body-state events trigger strategy replanning, and an LLM interprets the underlying joint-level state, recent execution statistics, and execution history to select a context-dependent alternative, while leaving the task objective and low-level controller unchanged. We evaluate the framework on a reaching task under controlled load and asymmetric mobility constraints in simulation and on a real robot. Our experiments show that body-grounded replanning maintains high task success while reducing physical effort and enabling more efficient strategy adaptation. Additional contact-rich manipulation experiments demonstrate the applicability of the same replanning interface beyond reaching. These results show that internal physical state can inform not only low-level control, but also high-level decisions about how a manipulation task should be performed.

Imitation learning enables robots to acquire manipulation skills from demonstrations, but the resulting policies can fail outside the training data, while collecting more demonstrations requires substantial human effort. Human-in-the-loop reinforcement learning uses corrective feedback during online training, but typically learns the complete task policy rather than refining a pretrained imitation policy. We introduce Res-HIL, a human-in-the-loop residual reinforcement learning framework that learns corrective actions on top of a frozen imitation policy. Each human intervention provides two complementary learning signals: direct supervision of the residual policy and reward shaping of preceding autonomous behavior. Res-HIL combines these signals with zero initialization of the residual policy to stabilize and accelerate online learning. We evaluate Res-HIL on five contact-rich manipulation tasks spanning high-precision and long-horizon behaviors. With only 20 initial demonstrations, Res-HIL outperforms state-of-the-art full-policy human-in-the-loop reinforcement learning and residual fine-tuning without human guidance on every task after ten minutes of online training. Res-HIL improves its pretrained base policies and outperforms imitation policies trained with five times more demonstrations. An ablation study shows that direct residual supervision is critical to performance, while intervention-aware reward shaping substantially improves training efficiency.

We introduce a new secondary operation on Lawson homology of smooth complex projective varieties. It refines the Lawson intersection product by retaining null-homotopy data that are invisible at the level of the graded Lawson intersection algebra. Intrinsically, the operation is the Toda bracket in multiplicative morphic cohomology transported through Friedlander–Lawson duality; in an associative cochain model it is represented by the classical Massey formula. For every defined triple, the affine bracket modulo its full indeterminacy gives a well-defined secondary invariant. The new structure is genuinely nontrivial and strictly finer than its singular-homology realization. On a smooth projective eightfold we construct integral Lawson–Massey brackets whose quotient classes are nonzero, while specified values have exact order two and map to zero under the Lawson cycle map to singular homology. A square-zero perturbation makes all three associated singular-homology classes nonzero without changing the secondary values. Infinitely many such values remain independent even after quotienting by the sum of all their indeterminacies, over one fixed singular-homology triple. Projection-formula transfers preserve the phenomenon under projective bundles and odd-degree generically finite morphisms, and cyclic triple covers give examples with ample canonical bundle in every dimension at least eight. The same defining systems yield nonzero motivic Massey values, scalar-indecomposable higher Chow torsion, and obstructions to integral and two-local formality.

We extend a previous study of the radial stability of solitonic boson stars by nonlinearly evolving them under aspherical perturbations, and by studying their formation from the collapse of scalar clouds. We focus in particular on models previously identified as radially stable, despite having positive binding energy, which ordinarily suggests that dispersion of all scalar matter is energetically preferred. A mode analysis of our 3+1 evolutions produces no evidence for the presence of a non-radial instability in any radially stable model, including those with positive binding energy. However, we do find evidence that such models do not generically form via gravitational cooling. We also find that it is possible to form another kind of compact object, which undergoes long-lasting radial oscillations and hence cannot be described as a stationary boson star. These objects may be characterized, we suggest, by energetically favoured multi-oscillating solutions to the Einstein-Klein-Gordon equations, present in certain regions of the parameter space.

We analyze the radiative properties of a general class of static and spherically symmetric black holes described by three independent shape functions, that encompass a broad family of regular and quantum-corrected geometries. We consider a minimally coupled massless scalar field, and derive the Hawking temperature and graybody factor for the different geometries. While the Hawking temperature is determined by the near-horizon geometry, the graybody factor depends on the scattering properties of the entire exterior spacetime, and therefore exhibits a richer dependence on the deformation parameters, frequency, and angular mode. Then we particularize to geometries that describe slight deformations of the Schwarzschild black hole, and obtain analytic expressions for the leading corrections to the graybody factor. Finally, we apply our results to several specific well-known black-hole models, including Reissner-Nordström, Bardeen, Hayward, Simpson-Visser, as well as geometries inspired by loop quantum gravity. In general, the deformations lead to colder horizons than Schwarzschild, and their effect on the graybody factor is frequency-dependent: the transmission of low-frequency modes is suppressed, whereas it is enhanced for high-frequency modes. This behavior is found for all but one of the geometries considered, which exhibits just the opposite trend. The analyzed modifications to the Hawking spectrum may therefore have relevant observational consequences, potentially providing signatures of deviations from the Schwarzschild geometry.