Papers

Valley excitations are considered one of the biggest challenges for a coherent spin shuttling in Si/SiGe heterostructures. In this work we theoretically investigate the valley dynamics during spin shuttling in a Si/SiGe heterostructure by considering a two-level system given by the two low-lying valley states of the mobile quantum dot. We assume that the electron is initially in the valley ground state and analyze the evolution of this state during shuttling. We find that, depending on the shuttling velocity, the system can be in three distinct regimes. In one of these regimes, the quantum information is preserved even in the presence of the valley excitations, allowing for coherent spin shuttling independently of the shuttling distance. This regime is obtained for a shuttling velocity of tens of m/s, a desired regime where dephasing mechanisms, such as spin-valley hotspots and spatially varying spin splitting, can be suppressed. This result is in accordance with recent experimental work that obtained a high spin shuttling fidelity after a fast and long shuttling. We also propose strategies based on the Partial Landau-Zener model to enhance the valley shuttling fidelity, which was found to be much more efficient than previously proposed strategies based on the standard Landau-Zener model.

Generative inpainting of brain MRI volumes is essential for synthesizing healthy tissue in pathological regions, improving the accuracy and reliability of automated downstream brain analysis applications such as image registration, brain extraction, and segmentation. However, standard 3D approaches are computationally prohibitive, while efficient 2D slice-wise methods suffer from severe inter-slice discontinuities. Furthermore, traditional models rely on conditional training, requiring task-specific learning of masked inputs. We propose a zero-shot brain MRI inpainting framework utilizing 2.5D unconditional flow priors to capture spatial context along the superior-inferior axis without the overhead of full 3D convolutions. During training, our flow matching model learns the joint distribution of adjacent axial slice triplets, modeling the manifold of healthy brain anatomy while explicitly excluding pathological regions from the loss function. At inference, the model processes the input triplets autoregressively along the depth axis. We employ the Restora-Flow solver to constrain the unconditional prior using the input mask, achieving accurate zero-shot inpainting. Evaluations show our 2.5D strategy resolves the structural discontinuities of 2D baselines, synthesizing plausible healthy tissue while maintaining volumetric consistency across the axial, sagittal, and coronal planes. As a final step, we generate and average an ensemble of multiple stochastic reconstructions to form the final prediction. Quantitative results benchmarked on the official BraTS 2026 Inpainting Challenge validation set demonstrate the effectiveness of our proposed approach, yielding an SSIM of 0.816 $\pm$ 0.112, MSE of 0.007 $\pm$ 0.005, and PSNR of 22.923 $\pm$ 4.343. Code is available at https://github.com/imigraz/brats2026-inpainting.

Magnetic field-based positioning is a resilient positioning technology that requires no external infrastructure and is hard to jam at scale. To facilitate research on magnetic field-based positioning for aerial platforms operating close to the Earth's surface, an open dataset is presented with measurements collected using an unmanned aerial vehicle carrying two optically pumped magnetometers, a type of quantum magnetometer, and a global navigation satellite system-aided inertial navigation system. The dataset includes measurements for both magnetic-field map learning and validation. Along with the dataset, a probabilistic framework for magnetic-field map learning and validation is presented and used to illustrate how the dataset may be used. Finally, we outline research directions that may be explored using the dataset.

Molecular ions are crucial in initiating and regulating the formation of molecules in the interstellar medium, and are expected to be sensitive tracers of evolution in star-forming regions. Within the framework of the project `CHemical Evolution of MassIve star-forming COres' (CHEMICO), we investigate the temporal evolution of molecular ions towards three high-mass star-forming cores that represent three sequential evolutionary stages. CHEMICO is based on an unbiased spectral line survey of the bandwidth at 3, 2, and 1.2~mm carried out with the 30m telescope of the Insitut de Radioastronomie millimétrique. We detect 19 molecular ions, including isotopologues. From a local thermodynamic equilibrium analysis, we derive the following main results: (i) Overall, the physical parameters of sulphur-bearing ions are the most sensitive to evolution, whereas those of nitrogen-bearing ions are the least; (ii) The molecular abundances that exhibit the most pronounced temporal variations are those of SO+, DCO+, and N2D+; (iii) A simple analytic approach tailored for warm gas conditions provides cosmic-ray ionisation rates of H2 several orders of magnitude above the canonical values measured in the interstellar medium and with a marked increase with evolution; (iv) The abundance ratio of protonated-to-neutral species increases with the proton affinity of the neutral regardless of the evolutionary stage of the source, indicating that proton-transfer appears to proceed similarly in both cold and warm interstellar environments. Molecular ions exhibit distinct evolutionary trends in high-mass star-forming regions, with sulphur-bearing species and the abundances of N2D+, DCO+, and SO+ emerging as particularly sensitive tracers of evolution. Measured electron fractions and cosmic-ray ionisation rates are in line with an internal production of cosmic-rays that becomes increasingly efficient with time.

Toeplitz matrices are among the simplest structured models of translation invariance, arising naturally in convolution, stationary covariance models, and discretizations of translation-invariant operators. For a pair of real matrices, the Böttcher–Wenzel form (BW form) is a nonnegative quartic measuring the gap in the corresponding commutator inequality. László conjectured that, when both matrices are Toeplitz, this quartic is a sum of squares for every matrix order. We show that the conjecture is false. More precisely, we identify an explicit family of corner-supported Toeplitz pairs, retaining only the outermost diagonals on the two sides, for which the associated BW form is not a sum of squares at all sufficiently large orders. The proof reduces the complete family of Gram representations to a finite complex test: its Gram-invariant part develops a strictly negative limiting direction, while the remaining Gram-dependent contribution vanishes. We also give an explicit sufficient threshold for the matrix order. The negative result is complemented by two positive regimes. If either Toeplitz factor is symmetric or skew-symmetric, then the corresponding BW form is SoS for every order, with the other factor allowed to be an arbitrary real Toeplitz matrix. For unrestricted Toeplitz pairs, we further prove SoS representability for every $2\le N\le50$, with formal Lean~4 verification through order 20. The large-order non-SoS theorem, including the explicit sufficient threshold, has also been formally verified in Lean 4.

Experience with invariant finite-difference schemes for one-dimensional hydro\-dynamic-type equations for a function $u(t,x)$ suggests that nonlinear polynomial schemes on orthogonal uniform meshes with the 9-point stencil cannot simultaneously preserve difference analogues of the energy and momentum conservation laws, with the multipliers given by the standard difference approximations of $u_t$ and $u_x$. For the 9-point stencil this hypothesis is proved for polynomials of arbitrary degree. On larger stencils it is investigated by means of the difference analogue of the direct method: for polynomials of bounded degree, such schemes are found to exist only on sufficiently large stencils, and the second-order equations they approximate are of Monge–Ampère type. As a by-product, a scheme for the homogeneous Monge–Ampère equation is obtained that has five conservation laws, admits most of the symmetries of the differential equation, and is invariant under the discrete dihedral group $D_4$. Numerical tests on exact solutions confirm its second order of approximation and show that the conservation laws are satisfied on these solutions with the same order of accuracy.

Streaming 3D reconstruction requires more than a sequence of geometric predictions: it requires a persistent scene state that can incorporate new evidence and remain renderable as observations arrive. Latent spatial tokens offer a promising representation for this purpose, but constructing them from an image collection leaves open how to maintain them online, where each observation may both revisit known regions and reveal new content. We introduce S2Tok, a feed-forward framework that maintains a size-adaptive, persistent scene state from uncalibrated image streams. Its central idea is to distinguish updates to the existing representation from selective expansion. A spatially informed transformer integrates each incoming observation with the persistent scene tokens, while a learned admission module selectively expands the representation to limit redundant storage. A hierarchical decoder and Gaussian head convert the evolving state into non-pixel-aligned 3D Gaussians, enabling novel-view rendering without caching previous frames. Experiments across four benchmarks demonstrate competitive streaming rendering quality with compact Gaussian representations. These results support latent spatial tokens as a persistent computational state for online 3D reconstruction, combining learned scene updates with explicit Gaussian rendering.

Accurate and low latency channel estimation is critical for modern MIMO systems, particularly under mobility, where channels exhibit structured sparsity and strong temporal correlation. This paper proposes a time-series conditioned diffusion framework for channel estimation that performs denoising in the angular domain. Starting from least squares (LS) observations, we train a diffusion denoiser whose conditioning information is encoded by a long short-term memory (LSTM) network over a short observation sequence, enabling the model to exploit temporal dynamics beyond per-snapshot estimation. To robustly balance observation fidelity and learned generative priors across a wide signal-to-noise ratio (SNR) range, we introduce a learnable SNR-gated late-fusion shortcut that injects the network input into the final decoding stage through a sigmoid gate with trainable center and scale. To reduce inference latency, we adopt deterministic denoising diffusion implicit model (DDIM) style reverse updates with SNR-adaptive truncation and step allocation, which significantly reduces the number of reverse diffusion steps at high SNR while maintaining strong performance in low SNR regimes. Simulations on time-evolving standardized channel models demonstrate that the proposed method achieves consistent performance gains over existing diffusion-based channel estimation baselines, while retaining low latency through SNR-adaptive inference.

We prove a spectral multiplier theorem for the standard sub-Laplacian on the Engel group under a scale-invariant local $H^s$ condition with $s>2$. The multiplier operators $F(\mathcal L)$ are of weak type $(1,1)$ and bounded on $L^p$ for every $1<p<\infty$. Together with the known lower bound, this identifies the sharp threshold as $2$, half the topological dimension. The proof combines a weighted Plancherel estimate for quartic oscillators with a decomposition into rank-two spectral subspaces, which controls parameter derivatives uniformly as one well escapes to infinity. For fixed smooth multipliers compactly supported in $(0,\infty)$, we also determine the leading term and first correction for the localized kernels. Whether the weak type $(1,1)$ estimate holds under the local $H^2$ condition remains open.

A plethora of new adaptive optimizers are designed to efficiently estimate and use minibatch gradient statistics to shape parameter updates, but they are typically benchmarked at a single batch size. Hyperparameter scaling rules promise to preserve performance as batch size and gradient noise change, suggesting that the best optimizer at one batch size should remain the best at another. We challenge this approach to developing and evaluating optimizers by showing: (1) no principled scaling rule for Muon works consistently across training settings, and (2) the best optimizer for language model pretraining changes with batch size even after extensive hyperparameter tuning. To understand these failures, we analyze a noisy quadratic model and show that the batch-size scaling rule that preserves performance is direction-dependent, shifting from square-root to linear as a direction's curvature-to-noise ratio rises. We further prove that gradient noise drives a bias-variance tradeoff in preconditioning that can reverse optimizer rankings across batch sizes, even under optimal learning rate and momentum tuning. Consistent with this, when we increase the batch size $16\times$ partway through language model pretraining, keeping small-batch updates in only the sharpest $0.001\%$ of directions removes up to $59.5\%$ of the resulting loss gap over the next $8\%$ of training, while a random subspace of the same size barely helps. Taken together, our results show that principled optimizer design must account for batch size and empirical benchmarking should be performed across batch sizes.

We develop a computationally tractable statistical framework for angular data supported on a recursively embedded curved torus $\mathbb{T}^n\hookrightarrow\mathbb{R}^{n+1}$. Due to the recursive structure we build an exact uniform sampler by generalizing the process from the curved 2-torus. We generalize projected normal distributions to the curved $n$-torus and we develop inference theory for these distributions. We utilize both maximum-log-likelihood estimates and energy-based Fréchet estimates for the projected normal distribution for this purpose. This is done by establishing identifiability for isotropic projected normal distributions and by applying theory of maximum likelihood and intrinsic statistics for the curved tori. We numerically verify the geometry, sampler, density transformation, and energy solver. Lastly, we demonstrate the applicability of the proposed model using real data.

This paper investigates a reconfigurable intelligent surface (RIS)-assisted backscatter non-orthogonal multiple access (NOMA) network operating as the secondary system of an underlay cognitive radio network. A multi-antenna base station serves several user clusters through the RIS, each containing a backscatter device (BD). We maximise the weighted sum rate of the secondary network by jointly optimising the transmit beamformers and the RIS reflection matrix, subject to the power budget, the interference-temperature limit and minimum rate requirements. The non-convex problem is solved by alternating optimisation, using semidefinite relaxation and sequential rank-one constraint relaxation. Interference-normalised user ordering makes the successive interference cancellation constraints redundant. A closed-form equal-rate power split is derived; it agrees closely with simulation and costs about 4.5% of the sum rate. Supporting the BDs reduces the NOMA sum rate by 8.7% relative to a no-BD design, while a larger BD reflection coefficient raises the backscatter rate with little NOMA loss.

We prove the convergence of the isoparametric Barrett–Garcke–Nürnberg (BGN) method for mean curvature flow of closed surfaces. For finite elements of degree $k\ge6$ and time steps $\tau=O(h^2)$, the numerical surfaces converge to the exact surfaces in the manifold distance with order $h^2$. The proof relies on two ingredients. First, we construct approximation flows by an expansion in time, whose interpolations satisfy the BGN method with an improved defect. Second, we derive a refined estimate for the tangential error from an algebraic identity for tangential test functions.

We show that a single Lagrangian trajectory encodes not only temporal but also spatial cascade structure–recoverable without access to a spatially resolved Eulerian velocity field. We report a Markov-Switching Multifractal (MSM) framework that infers hidden multi-scale cascade states directly from single-particle trajectories. Kolmogorov scaling fixes the model's switching rates, leaving a single calibrated intermittency parameter; exact Bayesian filtering then returns the posterior of the layer-resolved cascade state along the trajectory. When we apply the MSM framework independently to each trajectory of a particle pair, we find that the inferred states carry genuine spatial information: consistent with Richardson's locality picture, the Kolmogorov $r^{1/3}$ scaling is preserved when fine-scale layers are randomized, but collapses once the randomization crosses the layer set by the pair separation. Single trajectories thus encode the spatial organization of the cascade, opening a route to cascade diagnostics for turbulent flows accessible primarily through sparse or individual Lagrangian trajectories–from particle-tracking velocimetry to atmospheric and oceanographic tracking–where the instantaneous Eulerian field is out of reach.

Humanoid loco-manipulation of large, heavy objects demands forceful interaction across the entire body. However, such payloads shift a humanoid's center of mass and impose sustained loads across the upper body, challenging balance and command tracking. We present HULK, a whole-body control framework for forceful loco-manipulation. Using model predictive control (MPC) to guide reinforcement learning with predictions of the loaded dynamics, we train two teachers: one tracks arm motions under wrist forces, and the other locomotes while holding large objects against the body. A capture-point control barrier function augments the wrist-force teacher during training to improve balance under load. We distill both teachers into a single policy. Evaluation spans simulation and the Unitree G1. In simulation, the teacher with the barrier function achieves the lowest forward and lateral velocity tracking errors at 10 kg per arm among evaluated controllers and reduces aggregate divergent component of motion (DCM) excursion magnitude by 35.7% relative to MPC-guided reinforcement learning alone. Our wrist-force teacher withstands torso push disturbances of up to 130 N.

Black-box optimization problems are ubiquitous across science and engineering, often dealing with expensive objective functions. This objective latency has two consequences during optimization: (i) the objective evaluation dominates execution time, and (ii) sample-efficient algorithms are crucial to accelerate development and avoid wasting resources. Bayesian optimization (BO) methods are the de facto choice of planners for suggesting the next point to try. Standard BO fits the surrogate model's hyperparameters with a point estimate. Alternatively, a fully Bayesian approach uses model averaging to account for uncertainty over the hyperparameters, leading to better uncertainty estimates—useful in the low-data regime that is pervasive in BO. However, it is often prohibitively expensive and thus rarely used. In this work, we propose ELF-BO, an algorithm that uses the objective evaluation latency to headstart the computation of the next suggestion, allowing for fully Bayesian optimization without incurring substantial decision-time costs. This is done by sampling from the hyperparameter posterior while the objective is being evaluated, only requiring reweighting of the samples once the objective value is observed. Across synthetic functions and real-world applications, we show that ELF-BO matches the performance of fully Bayesian methods while only incurring decision latency on par with or better than standard BO. Thus, ELF-BO makes fully Bayesian optimization practical in real-world use cases.

It is known that completeness of the coalitional ($C$-)desirability relation in a simple game does not imply the existence of a weighted-majority representation. We show that weightedness is implied in an approximate sense. Call an $n$-player simple game $\varepsilon$-weighted if, for some weight vector in the $(n-1)$-simplex, any losing coalition weight exceeds any winning coalition weight by at most $\varepsilon$; let $\varepsilon^{\ast}$ be the smallest such $\varepsilon$. We establish an upper bound on $\varepsilon^{\ast}$ in a general $C$-complete game, and deduce that, if all classes of equally desirable players become large asymptotically but the number of classes is bounded, then $\varepsilon^{\ast}=O(1/n_{\min})$ for the minimal player class size $n_{\min}$, and the bound is tight. Importantly, the minimal attainable fraction $\delta$ of coalitions mislabeled by a weighting rule also tends to $0$ when $n_{\min}\rightarrow\infty$ and the number of player classes is bounded, with $\delta=O(1/\sqrt{n_{\min}})$.

Simulating individual behavior requires large language models (LLMs) to preserve persona traits while adapting to dynamic social contexts. However, general-purpose LLMs often flatten distinct personas, while task-specific tuning suffers from fragmentation and generalization. To overcome these challenges, we organize individual simulation into the FONTS Taxonomy, comprising five complementary capability dimensions: persona fidelity (F), outcome realization (O), behavioral naturalness (N), trajectory coherence (T), and social grounding (S). Grounded in this taxonomy, we curate a standardized training corpus library of approximately 10 million instances across 14 representative datasets and present Socio-Foundation. Socio-Foundation decouples specialization from integration via a three-stage pipeline: learning task experts via DAPO, consolidating them into capability experts via off-policy distillation, and unifying them via multi-teacher on-policy distillation (MOPD). We also establish IndiEval, consolidating 29 metrics across the FONTS dimensions. Experiments show that Socio-Foundation outperforms its Qwen3-8B base by 11.0 points and approaches frontier models such as GLM-5.2, with ablations and out-of-distribution evaluations further demonstrating the effectiveness and generalization of our model.

Humans perceive far more in a scene than what is explicitly depicted: a single glance captures past causes and future trajectories; a quick peek determines if a vehicle can fit between two parked cars; a few seconds of video reveals who holds authority in a room; and a fleeting clip highlights subtle abstract patterns like unwritten rules or hidden labels. This capacity reflects a form of humanity's sixth sense: an intuitive reasoning mechanism that recovers implicit information beyond raw sensory perception. Crucially, this rapid, zero-shot visual intuition underpins everyday navigation and social interaction, making it a vital capability for Multimodal Large Language Models (MLLMs) deployed alongside people. Existing visual benchmarks, however, target either deliberate expert-level analysis in academic and mathematical domains or low-level perception, leaving the intuitive reasoning that people perform largely untested. To bridge this gap, we introduce Humanity's Sixth Sense (HSS), a benchmark for intuitive visual reasoning. HSS spans diverse image and video inputs, organizes items under a structured taxonomy, and pairs each with human-written prompts probing the implicit temporal, spatial, social, and abstract structure that people infer at a glance. Frontier MLLMs fall short of human performance: participants reach 93.1% accuracy, while the strongest model, GPT-6-astra, reaches only 53.6% even at maximum reasoning effort. Despite excelling in many complex tasks that require advanced perception and knowledge, current models still struggle significantly on these visual tasks that are intuitive for humans. We further explore agentic setup that apply dynamic visual manipulation to HSS, which narrows but does not close the gap. HSS establishes intuitive visual reasoning as a measurable axis and directs attention to a capability that scaling on current benchmarks has so far left behind.

Let N(T) count the nontrivial zeros of the Riemann zeta function up to height T with multiplicity, N_d(T) the distinct ones, and N_0^s(T) those that are simple and on the critical line. We prove liminf N_d(T)/N(T) >= 1645064/1960733 = 0.83900...; earlier work proves 0.83699..., and a report we have not verified claims 0.83805.... Hence more than 67.80% are simple. Also liminf N_0^s(T)/N(T) >= 0.67353...; earlier work proves 0.67250..., and reports we have not verified claim 0.673492. Two estimates of Lamzouri are improved: at least 88.93% of the zeros are simple or on the critical line, and the proportions of simple zeros and of zeros on the line average at least 83.67%. By the unconditional form of Montgomery's pair-correlation theorem the energy, a sum of a test function over pairs of zeros, is known asymptotically. A zero of multiplicity d contributes d^2 to it and nearby zeros contribute too, so a lower bound for such pairs leaves less energy for multiple zeros. The proof has three steps. First, for zeros at least a fixed fraction of the mean spacing apart, a large sieve inequality lets their pairs be used in full, with multiplicities. Second, their contribution is bounded below by a computer-assisted inequality for seven or eight consecutive zeros which distinguishes simple and double zeros. Its correction terms telescope, as increments of a storage function. Third, the test function is chosen to make this contribution large, at the cost of more energy. We also prove upper limits for what such inequalities can give with the two main test functions. The lower bounds and these limits are proved in Lean 4, analytic inputs included. The proofs use three axioms beyond those of Mathlib, one per inequality. Each records that a search program returned true; Lean's kernel does not check the run itself. This work is an experiment in AI-assisted mathematical research.

The Little Red Dots (LRDs) are compact, broad-line sources that appear to contain accreting black holes (BHs) embedded in dense gas. Proposed models for their central environments (including quasi-stars, radiative BH envelopes and super-Eddington accretion discs) predict gas densities at the radii probed by an extreme-mass-ratio inspiral that differ by many orders of magnitude. We compute the inspiral of a $10$–$30\Msun$ BH for a range of LRD interior models, including environmental effects from the gas, and test with a mismatch criterion whether the resulting waveforms can be distinguished from vacuum and from one another. Dense interiors (Bondi-like free-fall cavities and radiative envelopes) produce measurable deviations from vacuum in essentially every detectable event. Convective quasi-star interiors are measurable for $\MBH\lesssim10^5\Msun$ and $z\lesssim0.6$, while a co-rotating disc leaves no measurable imprint. In favorable cases the models are also mutually distinguishable. None of the 14 JWST LRDs at $z>3.9$ would be detectable with a $10\Msun$ companion, but 30 of 31 LRDs at $z<0.9$ would be if their black holes are $\sim100$ times less massive than their virial estimates, and in many of them the interior's imprint would be measurable. Across the LRD population to $z=6$, a 4-yr LISA mission would yield $0.08$–$0.8$ detectable events for $10^5\Msun$ hosts and $10\Msun$ companions ($1.5$–$15$ for $30\Msun$) if LRD nuclei host inspirals at the rate of ordinary galactic nuclei. In dense clusters, where captures are plunges, this falls to $\lesssim10^{-4}$.

Asynchronous reinforcement learning (RL) for large language model (LLM) agents trains one policy on trajectories generated by another: rollouts come from stale checkpoints, and the inference engine's probabilities differ from the trainer's even at identical parameters. Standard remedies either clip importance ratios, which biases the update, or, as in GRPO, sample a group of responses per prompt, which is costly when episodes are long. We propose KL-Regularized Policy Optimization (KLPO), a framework that anchors the KL regularizer at the sampler. The regularized improvement step then has a closed-form Gibbs solution, and KLPO fits its log-ratio optimality condition by least squares on the sampler's own trajectories, so the sampler probability enters through a log-ratio and no importance weights are needed. Profiling out the regression intercept replaces the intractable log-partition function with the signal's sampler mean plus a sampler-to-trainer KL divergence. For token-level policy mirror descent targets, we show that the resulting gradient can be computed from terminal returns without a critic, via sampler-centered scores or a single trajectory residual, even under stochastic tool outputs. We further prove that independent Monte Carlo estimates of the KL term keep these gradients unbiased, derive the exact KL gap of cheaper top-$K$ and binary approximations, and show that SPPO, GPO, REBEL, and BPO arise as special cases of KLPO. The result is a critic-free update that uses one rollout per prompt and requires neither a learned normalizer nor a group of responses.

The Go programming language provides a lightweight abstraction for concurrent programming through goroutines, which are prone to deadlocks. Go includes a runtime detector that aborts execution when all threads are blocked (a global deadlock). However, due to nondeterministic thread scheduling, this runtime mechanism only detects global deadlocks that manifest during execution and cannot identify partial deadlocks, where a subset of goroutines is permanently blocked while at least one remains runnable. Statically detecting local deadlocks is essential for developing dependable concurrent software. While several tools statically detect deadlocks in concurrent programs, few assist developers in fixing them. Detecting and resolving partial deadlocks requires reasoning about complex interleavings and communication patterns, an inherently challenging task. In this paper, we present GoDDaR, a tool that detects unobserved global or partial deadlocks in Go programs and suggests concrete fixes. GoDDaR translates Go source code into an intermediate representation reflecting message-passing communication events and composition patterns. Partial deadlocks are identified through symbolic analysis over this representation. To resolve detected deadlocks, our algorithms transform the intermediate representation to eliminate problematic synchronization patterns, allowing GoDDaR to generate fix suggestions for the original Go source code as a diff. We evaluate GoDDaR on a benchmark suite of representative deadlock examples from literature and git repositories to validate algorithm correctness and compare performance against the state of the art. Results demonstrate that GoDDaR is competitive with top approaches in partial deadlock detection and advances the state of the art in automated deadlock fixing.

Let f:2^N –> \cZ^+ be a polymatroid (an integer-valued non-decreasing submodular set function with f(emptyset) = 0). A k-polymatroid satisfies that f(e) <= k for all e in N. We call a subset S of N independent if f(S) equals the sum of f(e) over the elements e of S and f(e) > 0 for all e in S. Finding a maximum-size independent set in a 2-polymatroid has been studied and polynomial-time algorithms are known for linear polymatroids. For k >= 3, the problem is NP-hard, and an approximation algorithm with ratio approaching 2/k is known and is obtained by swapping as long as possible a "large" subset from the current solution by a set with one more element. Here we give a simple analysis of the more particular two-for-one repeated swapping heuristic, obtaining a (weaker) 2/(k+1)-approximation.

Predictive world models provide compact visual representations for control. Control requires a latent geometry aligned with temporal reachability rather than predictive similarity alone. We introduce Directed Temporal Representations for Control (DTRC), which learns such a geometry from offline visual trajectories on top of frozen LeWorldModel (LeWM) features. DTRC constructs a directed temporal quasimetric over the learned control representation. Short-range temporal offsets calibrate the distance scale. Bootstrapped targets extend temporal reachability across longer horizons. Action-conditioned consistency aligns the representation with local transition dynamics. The resulting distance estimates temporal reaching cost, and its change across a transition defines goal-relative temporal progress. We use this progress signal as a temporal critic for direct goal-conditioned policy learning. Model-assisted targets provide an additional training-time refinement under behavior-support and dynamics-agreement constraints. Across ten visual control tasks, DTRC achieves strong goal-conditioned control performance relative to planning and direct-policy baselines. Held-out diagnostics on the four LeWM tasks show consistent short-range temporal calibration, task-dependent long-range and directional structure, and positive transition-level progress. Temporal supervision improves the same flow-policy parameterization across all four LeWM tasks, while the resulting policy acts directly without iterative trajectory search at test time.

On-policy distillation post-trains large language model agents by supplying dense, step-level guidance from a teacher policy when the reinforcement-learning reward is sparse and arrives only once per trajectory. Existing instantiations allocate this guidance by the size of the teacher-student divergence at each step, on the single-turn intuition that a large disagreement marks a mistake worth correcting. Once decisions chain over many turns, that rule misfires, since an early drift enters every later context both policies condition on, leaving the teacher consistent with the drifted trajectory instead of flagging its cause, while interchangeable steps register large but outcome-irrelevant divergences. We demonstrate this on an agentic benchmark, where distilling the highest-divergence steps brings no consistent benefit over random selection. To this end, we introduce GraphOPD, the first method to bring graph-based structural augmentation into on-policy distillation for agent capabilities. It reads which steps enabled which later ones from the environment's own record of state changes, immune to the drift that corrupts the teacher-student gap, organizes them into a dependency graph, scores each step by a random-walk stationary distribution over it, and fuses that structural credit with the divergence signal into a trajectory-relative mask concentrating supervision on each rollout's highest-aptitude steps. Across three model scales and eleven baselines on ALFWorld, WebShop, and SearchQA, GraphOPD shows competitive performance throughout, improving over the strongest baseline by up to +5.8 pp. An executed-replay audit further shows that this structural credit score tracks true causal impact far above chance, that both fused signals are independently necessary, and that the same signal transfers to out-of-domain tool-integrated reasoning.

We study a semiflexible magnetic polymer in which each monomer carries a two-state spin, giving rise to coupled conformational, stiffness, and magnetic degrees of freedom. The model provides a minimal representation of nucleoprotein complexes in vivo, in which DNA bending rigidity and bridging proteins must be simultaneously accommodated. We employ Monte Carlo simulations on a face-centered-cubic (FCC) lattice, complemented by a variational free-energy upper-bound approach, to characterize the zero-field phase diagram as a function of bending stiffness and temperature. At low stiffness, we identify a first-order transition combining coil-to-globule collapse with a ferromagnetic-to-paramagnetic transition. At lower temperatures, an additional first-order transition separates the disordered globule from an ordered crystal characterized by nematic-like orientational order of the bond tangents. At high stiffness, the globule disappears, resulting in a direct first-order coil-to-crystal transition. These results demonstrate how chain stiffness and magnetic degrees of freedom couple to polymer conformation and reorganize the zero-field phase diagram. Our model connects the two limiting cases of flexible magnetic polymers and semiflexible homopolymers, the latter corresponding to the strong-field limit in which all spins are aligned.

Determining magnetic exchange interactions is vital for understanding the magnetic behavior of materials. The standard method for exchange interaction determination involves performing inelastic neutron scattering experiments on single crystals to measure spin wave dispersions from a long-range-ordered magnetic ground state. However, the influence of exchange interactions is not limited exclusively to spin waves in ordered states, but also governs magnetic behavior in all magnetic states, including the short-range spin correlations that persist into the paramagnetic regime. Exchange parameters have been successfully recovered in the past from energy-integrated diffuse neutron scattering data from paramagnets, indicating that the diffuse scattering and underlying short-range magnetic correlations are rich in information. Consequently, magnetic pair distribution function (mPDF) analysis, which directly probes short-range magnetic correlations in real space, is expected to be well suited for extracting exchange parameters from correlated paramagnets. Here, we demonstrate a robust mean-field theory approach incorporating the Onsager reaction field for determination of exchange parameters from the results of mPDF analysis. We successfully apply this approach to several relevant materials to recover exchange interaction values comparable to literature values.

We propose an algorithm for the numerical solution of the time-dependent Schrödinger equation for N >> 1bosons interacting via a two-body interaction potential in the mean-field scaling regime. Unlike existing numerical algorithms for quantum dynamics, the proposed algorithm has a computational complexity that is independent of the number N of particles. It is based on an ansatz for the wave function inspired by the Bogoliubov theory, which is an asymptotic theory for large N. In a first part, we follow Bogoliubov theory in evolving the condensate function by the Hartree equation, but we use the Dirac–Frenkel time-dependent variational principle to derive nonlinear equations of motion for the excitation functions in the Bogoliubov ansatz. By carefully exploiting the bosonic symmetry, the so obtained approximate wave functions are shown to have derivatives bounded independently of N apart from a time-dependent global phase factor which rotates with a frequency proportional to N. In the second part, we numerically approximate the wave function (modulo the phase) by a composite algorithm, which employs an appropriate splitting of the equations of motion and uses a dynamical low-rank approximation of the fundamental two-particle excitation function by linear combinations of products of single-particle functions. The low-rank excitation function is evolved in time by a basis update and Galerkin (BUG) integrator that is robust to small singular values of the coefficient matrix and allows for rank adaptivity. Numerical results are provided to assess the performance of the proposed algorithm.

Effective descriptions of quantum materials rely on a separation of energy scales that identifies their low-energy degrees of freedom. When kinetic energy, lattice potential, and interactions compete, this hierarchy breaks down, and both the microscopic state and its effective description are unknown. Continuum neural quantum states (NQS) can find the ground state directly without projecting onto prescribed bands, orbitals, or spins, but their microscopic wavefunctions are difficult to interpret in terms of effective variables. Here, we introduce a wavefunction readout that maps the continuum NQS onto site-resolved charge and spin statistics, allowing effective degrees of freedom to emerge from the microscopic solution. Focusing on moiré transition metal dichalcogenides at filling $\nu = 3$, the NQS reveals a low-spin ground state below the ferromagnetic crystal of spin-polarized Wigner molecules. Although the charge density retains triangular molecular motifs, our readout reveals significant charge fluctuations through bound nearest-neighbor doublon–hole pairs. Each molecular charge state has an inert spin-singlet core and rim electrons that carry the spin. Charge and spin fluctuations are therefore intertwined, with antiferromagnetic spin-correlations between sites, motivating an effective description by a spinful two-orbital Hubbard model. More generally, our results demonstrate a route from continuum wavefunctions to effective lattice models when competing scales preclude a controlled reduction.