Papers

A two-dimensional electron gas in a uniform neutralizing background forms a triangular Wigner crystal at low density. In a strongly mass-asymmetric electron-hole bilayer, localized heavy holes instead provide a nonuniform positive background that supports an electron crystal at densities two orders of magnitude higher than for a homogeneous electron gas in the same material. Here we show that correlated mobile electrons can overturn the preference for triangular order, stabilizing a honeycomb electron-hole crystal. Using the powerful real-space neural-network variational Monte Carlo in the Born-Oppenheimer limit with fixed holes, we find that increasing the density drives a transition from a triangular electron-hole crystal to a honeycomb crystal, which eventually melts into itinerant electrons coexisting with the honeycomb or the triangular hole lattice at fixed interlayer separation. Relative to triangular order, honeycomb order emerges when gains in electronic kinetic energy and electron-hole attraction outweigh its higher intralayer Coulomb repulsion, a threshold never reached in the rigid point-dipole model. Moreover, the honeycomb hole lattice supports paramagnetic, antiferromagnetic, and stripe-ordered spin states. Complex polarization indicates a metal-insulator transition, while the states on the honeycomb hole lattice are consistent with a stripe-ordered Dirac semimetal and paramagnetic or antiferromagnetic Mott insulators via mapping to the half-filled Hubbard model. We further propose a BLG/hBN/WS$_2$-WSe$_2$ heterostructure as a platform for the predicted honeycomb crystal, at an experimentally feasible density $n\sim10^{11}~\text{cm}^{-2}$.

Neural operator splitting composes a library of neural operators, one per physical mechanism, into zero-shot simulators of new equations. Existing approaches, however, require these mechanisms and their labels to be specified in advance. We ask whether a pretrained library can instead be adapted and grown from unlabeled trajectories in which multiple mechanisms act simultaneously. We introduce SPLICE, a framework that discovers operators without mechanism labels on mixture data. The contributions of the candidate operators to each trajectory are inferred by solving a convex optimization problem. A calibrated test then assigns each discovered operator the mechanism it implements. Failure cases are also detectable, when the library lacks the required physics or when mechanisms are insufficiently separable. Across one and two dimensional systems, the discovered operators recover mechanisms from unlabeled mixtures and compose into zero-shot simulators of unseen equations; a frozen library can also grow an operator for physics absent from pretraining, without labels and without forgetting. On Navier-Stokes, the discovered operators compose about as accurately as their supervised counterparts.

By virtue of their relation to Fulton–MacPherson compactifications, the cohomological field theory of Hilbert schemes of points on a surface, in extremal curve classes, is universally and effectively determined by the characteristic numbers of the surface and by the corresponding theory of Hilbert schemes of the affine plane. As a consequence, we compute the extremal genus 1 Gromov–Witten invariants of Hilbert schemes of all surfaces.

Detecting credit card fraud is notoriously difficult because fraudulent charges make up less than 0.2% of total transactions. Quantum Machine Learning (QML), particularly Quantum Kernel Support Vector Machines (QSVM), promises richer feature representations by embedding classical data into high-dimensional Hilbert spaces. However, whether this theoretical advantage holds up when managing real-world financial data bottlenecks remains unclear. We designed a controlled benchmark comparing three quantum encodings, Angle, ZZFeatureMap, and IQP against classical models while keeping sample sizes, feature counts, and scaling strictly matched. To handle class skew without corrupting quantum state overlaps, we embedded synthetic minority oversampling (SMOTE) directly into the quantum Gram matrix workflow, raising PR-AUC scores by roughly +0.04 across feature maps. When trained on the full European credit card dataset with 30 features, classical baselines reached a top PR-AUC of 0.983. However, restricting classical models to match QSVM hardware constraints (500 samples, 4 PCA features) dropped their PR-AUC to 0.750. This puts our best quantum result 0.730 PR-AUC using IQP encoding on 150 samples into realistic context. Testing on physical quantum hardware reduced performance further to 0.62 due to CNOT gate errors and thermal noise. Overall, our findings pinpoint two main operational bottlenecks for near-term quantum kernels: the scaling of Gram matrix evaluation and heavy information loss from squeezing features onto small qubit registers.

We study the boundary corrector $\theta_\epsilon$ in the two-scale expansion for periodic elliptic problems with Dirichlet conditions. By results of Gérard-Varet–Masmoudi and Prange, on smooth uniformly convex domains $\theta_\epsilon$ converges to the solution $\theta^*$ of a homogenized problem with boundary data given by the boundary layer tail $d(n)$, which is determined by a half-space problem for each normal $n$. In the lifted form of Gérard-Varet and Masmoudi, $d(n)$ is given explicitly by the cell correctors and the Dirichlet-to-Neumann operator $N_n$ of this half-space problem. Our main result is that $N_n$ satisfies a nonlinear equation on the period cell alone, so that $d(n)$ and the boundary density that represents it can be computed on the cell. This equation is a Riccati equation in which the derivative in depth is replaced by a commutator with the derivative along $n$. This cell problem can therefore be solved by a Riccati doubling algorithm, and we can compute $d(n)$ at irrational normals without rational approximation. Dropping the commutator term in the cell equation gives an operator square root approximation for $N_n$ that captures the leading term of $d(n)$ for small contrast, for the truncated problem. Finally, we approximate $\theta_\epsilon$ at finite $\epsilon$ by the sum of two solutions of constant coefficient problems, one with oscillatory boundary data and the other $\theta^*$, and test it on the disk.

This paper investigates a shift-sum decoding algorithm that employs dual codewords. Existing dual codeword shift-sum decoding schemes mainly rely on minimum-weight dual codewords. However, the number of such codewords is often limited, which restricts the amount of reliability information available to the decoder. To address this issue, we extend the component counting mechanism from minimum-weight dual codewords to dual codewords whose Hamming weights lie within a prescribed upper bound. We further introduce a normalized component counting rule to suppress the overcounting bias caused by the much larger populations of higher-weight classes. Based on this framework, we develop a hard-decision iterative error reduction decoder and a soft information-aided iterative error reduction decoder. Numerical results show that the proposed method consistently outperforms existing minimum-weight shift-sum baselines especially for short codes where additional dual codeword information is particularly valuable.

We present CLASSO, a path-following method for the LASSO subject to general linear equality and inequality constraints. The local direction is obtained from a quadratic programme on an augmented active set, which determines both the coefficients that leave zero and the weakly active inequalities that remain binding. For a positive-definite Hessian and a nonempty feasible set, this programme has a unique primal minimiser, even when the binding constraint rows are dependent, and gives the local derivative of the solution path. The construction recovers the LASSO-modified LARS direction without constraints, and over the full cone gives the segment leaving the origin. We prove that the primal path is piecewise affine with finitely many kinks, without a constraint qualification or unique multipliers. A finite path does not imply a finite traversal: re-certifying at each kink can fail to terminate. CLASSO instead follows the minimum-norm certificate along a lexicographic rate; we prove that this rule reaches $\lambda=0$ in exact arithmetic within an explicit bound and traverses the whole path. These results are machine-checked in Lean~4, and the floating-point implementation agrees with an exact rational one on all $210$ small test problems. We assess the implementation on a $39$-case synthetic suite and six constrained versions of the diabetes benchmark. On the $31$ nontrivial synthetic cases with $n\ge p$, sampled relative objective differences from numerical reference solves are below $10^{-9}$ in magnitude; unnormalised endpoint differences reach $1.5\times10^{-7}$ in magnitude. For $n<p$, matched differences range from $-3.6\times10^{-7}$ to $2\times10^{-9}$ across five ridge strengths. Across the synthetic and diabetes benchmarks, checks of all $580$ recorded segments found no missed interior event and all checked KKT residuals within the stated tolerances.

Recovering piecewise-smooth functions with jump discontinuities from noisy, indirect, and incomplete data is a central task in computational inverse problems. Bayesian neural networks (BNNs) with heavy-tailed weight priors have emerged as effective edge-preserving priors for such problems. However, posterior inference for these models remains computationally challenging, and existing approaches settle for point estimates obtained by directly optimizing heavy-tailed log-densities. We propose GSBL-BNNs, which model the neural network parameters hierarchically using sparsity-promoting priors from generalized sparse Bayesian learning (GSBL). The hierarchical formulation recovers several popular marginal priors, including Laplace and Student's $t$ (including Cauchy). A key modeling ingredient, novel among edge-preserving BNNs and native to the hierarchical formulation, couples each neuron's bias to its weights through a shared hyperparameter, so that the induced jump discontinuities are free to occur anywhere in the domain while the conditionally Gaussian structure underlying efficient inference is preserved. Furthermore, we develop a block-coordinate descent (BCD) algorithm for maximum a posteriori (MAP) estimation. This BCD approach alternates between standard network training with iteratively reweighted $\ell^2$-regularization and exact, closed-form hyperparameter updates for gamma and inverse gamma hyperpriors. Building on the BCD algorithm, we perform approximate Bayesian inference and uncertainty quantification (UQ) using deep ensembles. Computational experiments—including signal denoising, deblurring, and inverting a two-dimensional hyperbolic conservation law— show that GSBL-BNNs deliver accurate, edge-preserving reconstructions with built-in UQ. Compared with Gaussian- and Cauchy-BNNs, they yield more accurate predictive means and avoid overconfident uncertainty estimates.

The Square Kilometre Array (SKA) will observe our Universe on the largest scales and so enable the study of fundamental assumptions in cosmology, such as cosmic homogeneity and isotropy. Observations over recent years have reaffirmed an unexpected challenge to the Cosmological Principle first seen in measurements of the cosmic radio dipole. This dipole anisotropy is thought to be caused by our local observer motion, however, it is observed to be about three times larger than predicted, with significances exceeding 5$\sigma$. The SKA is in a unique position to shed light on this anomaly by measuring this and other effects related to our observer motion. To quantify this, we forecast the capability of large-angle HI and continuum surveys of the SKA to constrain the kinematic matter dipole in galaxy number counts, the modulation of the matter power spectrum by a kinematic dipole, and kinematic spectral distortions of diffuse radio emission.

Nitrite photochemistry in atmospheric aerosols and natural waters is a major source of hydroxyl radicals and reactive nitrogen oxides. Contrary to the prevailing view that in the environment aqueous nitrite photochemistry proceeds exclusively through photoexcitation followed by homolytic bond cleavage, we show that visible light directly ionizes aqueous nitrite in individual micron-sized droplets. Although the photoionization cross section is exceptionally small, this pathway is observable at the high photon flux densities accessible in single-droplet experiments. Molecular simulations reveal that this is because photoionization absorption has an exceptionally long wavelength tail due to the large solvent reorganization energy in aqueous solutions. Kinetic modeling of an aqueous-phase reaction mechanism quantitatively accounts for the observed chemistry and predicts the formation of nitrate, hydroxyl radicals, and solvated electrons. The overlap of the predicted broad photoionization continuum with the visible solar spectrum further suggests that visible-light photoionization is an overlooked source of nitrogen oxides, solvated electrons, and oxidants in atmospheric aerosols, snowpack, and natural waters. Under dilute conditions, where dissolved oxygen is the main sink for solvated electrons, photoionization is expected to be the dominant photochemical loss pathway for nitrite.

Cybersecurity evaluations of AI agents have focused largely on offense, yet a working exploit does not show that an agent can make software safe. An attacker needs to exploit only one vulnerability; a defender must find and fix all of them. We introduce CWE-bench, a private benchmark of 120 held-out repository audit-and-repair tasks spanning 73 CWE types, eight languages, and all OWASP Top 10 2025 categories. Agents are given a repository to audit and a description of its threat model, but are not told the weakness, where it occurs, or how many vulnerable sites there are. Each patch must block the exploit while preserving original functionality, as checked by a programmatic verifier. We validated the verifier against a panel of agentic judges, manually reviewing disagreements during development and refining the checks. The best agents reach 68% pass@1 and 81% pass@4. We further conduct analyses showing that (i) agents with the same pass@1 differ widely in retry gains and cost, and (ii) no single agent is best across languages or vulnerability categories, and difficulty varies far more by vulnerability category than by language. As the offensive capabilities of agents improve, CWE-bench provides a broad and rigorous measure of whether their defensive capabilities keep pace.

Whisper-style ASR models provide strong zero-shot transcription, but their residual errors are not evenly distributed across datasets, recording conditions, and metadata-based groups. We study when lightweight low-rank adaptation (LoRA) improves Whisper and whether observed gains require group-specific adapters. Across Common Voice, LibriSpeech, and VoxPopuli, we compare zero-shot Whisper, pooled LoRA, and group-specific LoRA under matched within-group splits. We find that adaptation is not uniformly beneficial: gains are concentrated in difficult Common Voice groups, are consistent on VoxPopuli, and largely disappear on low-error LibriSpeech. Crucially, pooled LoRA often matches, and sometimes clearly outperforms, group-specific LoRA. Gains over zero-shot should therefore be tested against matched pooled adaptation before being interpreted as evidence of personalization.

Standard procedure in machine learning is to randomly split train and test data, emulating IID draws from one underlying data distribution. In practice, models are trained on past data and deployed in the future, which may come from distinct distributions. In this paper, we find that web text is indeed highly non-stationary, as text distributions shift over time. We further observe that model performance changes continuously over time across diverse benchmarks. Consequently, future model performance is better predicted by measurements made on recent evaluation data, and is best predicted by time series forecasters applied to historic performance rather than by historic performance itself. Choosing which model to deploy based on forecasted accuracy enables more reliable selection of performant models, thus improving downstream accuracy in the regime practitioners care about: deployment. Taken together, our experiments suggest that time should be treated as a fundamental variable in LLM evaluation. We release our code and data.

Bosonic codes often read out their syndrome with a transmon ancilla whose computational levels $g$ and $f$ have equal parity and matched dispersive shifts: a decay $f\to e$ is then heralded and leaves the code intact, while the direct $f\to g$ is forbidden by parity. We show that the photons of the code open this decay at first order in the ancilla's decay rate. Dressing by the code mode lets the charge noise that limits the ancilla's $T_1$ drive a photon-stimulated Raman decay $|f,n\rangle\to|g,n+1\rangle$, at $(n+1)(\chi_{ge}/2g_{01})^2$ times the $f\to e$ rate for a smooth noise spectrum. When the matching is set by the detuning, the decay costs $\approx\Gamma_{fe}/\alpha$ per gate and photon, whatever the coupling strength; a deliberate mismatch or matching by a drive lowers this cost, and a qubit ancilla has no such channel. The opened decay is unheralded and flips a cat with probability $\approx 1/2$; being first order, it overtakes the second-order double decay $f\to e\to g$ as the ancilla improves. In a microscopic model of the Ocelot repetition cat code, it makes the bit-flip floor of the gates grow linearly with the cat size, by a factor 1.2-1.7 from four to ten photons, which would limit the noise bias to $\sim 10^3$. The published gate data end at four photons and do not yet test this growth.

Evaluating model uncertainty on real-world data is challenging because each instance provides only a single observed label, leaving true conditional class probabilities unknown. To address this, we introduce ProbabilityBench, a benchmark that provides exact, instance-level class probabilities across three simulated text-based domains: peer review, covert information transfer, and credit risk. By explicitly defining the full data-generating process for each environment, we analytically compute both exact class probabilities and Bayes error. Furthermore, we provide a theoretical guarantee that rendering these cases into natural-language memos strictly preserves their underlying generative probabilities. This exactness enables direct measurement of reported probability quality via KL divergence. Across 16 evaluated models, most models on the observed cost-quality Pareto frontiers are decision models, including Jev and Perplexity Decider. Finally, ProbabilityBench serves as a meta-evaluation framework, leveraging known ground-truth values to benchmark the accuracy of standard calibration metrics and Bayes-error estimators themselves.

Scaling up data and model capacity has driven substantial progress in visual representation learning. However, conventional pretext tasks exhibit diminishing returns on fine-grained facial analysis. We attribute this to a scaling bottleneck: these tasks model each image's appearance and are dominated by identity, pose, and illumination, so subtle within-identity facial differences contribute little to the training signal. We introduce DIME, a differential masked autoencoder for large-scale facial representation learning. DIME builds on a simple observation: two images of the same person share identity-specific appearance, so their difference exposes facial changes. DIME reconstructs both masked images in an identity-matched pair and, through an Explicit Differential Direction Supervision (EDDS) objective, aligns the direction of their reconstructed difference with the true difference, while source isolation makes each reconstruction depend only on its own image. Shared appearance cancels in this difference, and because EDDS ignores magnitude, subtle facial changes count as much as large pose or illumination changes. DIME uses identity labels only to form pretraining pairs, requires no dense annotations, and learns dense facial representations with emergent part-level semantics. We pretrain DIME on 20 million high-resolution facial images consolidated from existing face datasets. DIME's AU detection performance continues to improve as pretraining data scales from 6M to 20M images, with its BP4D F1 increasing by 5.9 points, while MAE gains only 0.5 points on the same subsets. DIME also outperforms specialized facial methods on AU detection, AU intensity estimation, cross-domain anti-spoofing, landmark localization, head pose estimation, face parsing, and face generation.

Functional brain connectome represents neural connectivity as a matrix of pairwise interactions between brain regions. Generation of functional connectomes is not only a question of validity; rather, having satisfied the constraints on the correlation matrix, the next step is to recover the class-conditional geometry buried under coarse labels. We propose MAGNET, a Manifold-Aware Graph Diffusion Network which uses a normalized-Cholesky representation of the manifold of correlation matrices that guarantees validity. MAGNET lifts noisy latent states into ROI-level region tokens and performs denoising with a relational inductive bias over brain atlas regions. To deal with structural problems induced by coarse labels, MAGNET employs class-anchored conditioning, amortized structural bridge, and relevance-preserving corruption. Across ABIDE, ADNI, and OASIS-3, MAGNET consistently achieves favorable results compared to previous manifold-aware approaches, demonstrating improvements of 7-21% in class-conditional fidelity ($\alpha,\beta$-F1) across three cohorts and better sampling efficiency. Moreover, while training only with strict binary labels, MAGNET is capable of maintaining clinical heterogeneity through fine substructure of the connectomes in a zero-shot setting, improving subclass covariance alignment ($\lambda$-MSE) by over 30%. These results suggest that geometric validity is a necessary but insufficient condition for clinical utility in connectome synthesis. Moreover, efforts in making the diffusion denoising class-conditional manifold aware finds utility beyond the highly curved brain connectome generation as this is a critical problem in various general settings. The code repository can be found at https://github.com/protyayofficial/MAGNET.

Indirect searches for dark matter (DM) span gamma rays, charged cosmic rays, neutrinos, X-rays, radio emission, the cosmic microwave background (CMB), and the 21~cm signal, but reported constraints and anomalies vary in evidential strength. This critical review synthesizes peer-reviewed literature from January 2000 through October 2026 using a structured search strategy. We assess observations through a framework linking particle interactions and halo source terms to propagation or cosmological energy deposition, instrumental response, background modeling, and statistical inference. Fermi-LAT observations of dwarf spheroidal galaxies provide robust GeV-scale benchmarks for DM annihilation, whereas Galactic-center searches offer higher expected signals but depend more on foregrounds and halo profiles. Charged-cosmic-ray measurements are precise but limited by propagation and source uncertainties, while neutrino searches offer complementary sensitivity through solar capture, directional and flavor information, and high-mass annihilation or decay. Several widely discussed signals, including the 3.5~keV line, 511~keV emission, the Galactic-center GeV excess, charged-particle features, cluster radio excesses, and candidate gamma-ray lines remain inconclusive because of limited independent confirmation, uncertain target scaling, spectral degeneracies, or background-modeling limitations. Cosmological observations provide complementary constraints from CMB energy-injection limits and 21~cm measurements of the intergalactic medium. Artificial intelligence increasingly supports reconstruction and inference but requires rigorous calibration and domain-shift validation. The strongest case for DM discovery would require statistically consistent evidence across independent targets, instruments, or messengers, under common particle-physics parameters, and with well-characterized uncertainties.

We study the geometry of positive Dirichlet solutions on smooth, uniformly geodesically convex domains $\Omega\subsetneq\mathbb S^n$, $n\ge2$. Set $p_n^*=2n/(2n-3)$. For the Lane–Emden equation $-\Delta_g u=u^p$, $1<p\le p_n^*$, we prove that the set of positive solution pairs $(p,u)$ has a connected component containing the near-linear solution curve and projecting onto $(1,p_n^*]$. Every pair on this component satisfies $\nabla_g^2(u^{-(p-1)/3})>0$ in $\Omega$. For the torsion equation $-\Delta_g u=1$, we establish $\nabla_g^2\sqrt{u}<0$ for its unique Dirichlet solution in all dimensions $n\ge2$, without an additional diameter or circumradius assumption. In both settings, the solutions specified above have a unique nondegenerate maximum and strictly geodesically convex positive superlevel sets. For the non-power reaction $f(s)=s^p/(1+\lambda s^\delta)$, with $1<p\le p_n^*$, $\lambda>0$, and $0<\delta\le(p-1)/3$, we also prove the existence of at least one positive solution $u$ for which the transform $\left(\int_u^\infty ds/f(s)\right)^{1/3}$ has positive definite Hessian. The proofs combine a spherical Schur-complement estimate with a priori bounds and continuation.

Aircraft equipped with delta wings are designed to be aerodynamically efficient in high-speed flight. However, at low-speed flight conditions with sufficiently high angle of attack, these vehicles often have lightly damped, close to unstable lateral-directional dynamics, such as the dutch roll mode. As a result, a delta wing aircraft often exhibits the so-called wing rock (WR) phenomenon, with a back and forth rocking motion, while the aircraft sideslip angle, the roll and the yaw angular rates remain small. In this paper, the WR dynamics are defined as a lightly damped dutch roll mode excited by airmass vortical external input, acting at or near the dutch roll natural frequency. The vortical signal comes from Fourier-Galerkin approximation of the Navier-Stokes equation, with no-penetration boundary conditions and the resulting airmass velocities are calculated by the Lorenz dynamical system of three coupled bilinear ordinary differential equations. In that context, the Lorenz bilinear dynamics become the disturbance-generator exosystem, acting on the lightly damped lateral-directional aircraft mode at or near its natural frequency, and thus exciting it to produce near oscillatory wing rocking motion. Using the proposed model, a flight control design trade study is conducted to mitigate and suppress the WR phenomenon.

The acoustic Faraday effect probes phonon Hall viscosity through the rotation of transverse acoustic polarization, conventionally interpreted in terms of circular birefringence. We show that magnetic order breaking rotational symmetry generates anisotropic phonon responses and elliptically polarized eigenmodes, so that Faraday rotation cannot be attributed to Hall viscosity alone. To elucidate their microscopic origin and consequences, we derive spin-phonon couplings from a generic $J$-$K$-$\Gamma$-$\Gamma'$ model with interlayer coupling, identifying transverse strain couplings for propagation along the $c$-axis arising from the interplay of Kitaev $(K)$ and $\Gamma$ interactions, along with strain-induced $g$-tensor contributions. Incorporating these couplings into our theory for the Kitaev spin-liquid candidate $\alpha$-RuCl$_3$, we find that symmetry breaking modifies the Faraday response, revealing a Hall viscosity approximately twice the value inferred assuming rotational symmetry. Our results establish a microscopic framework beyond circular birefringence, refining the connection between acoustic Faraday rotation and phonon Hall viscosity in symmetry-broken spin-orbit-coupled magnets.

Reinforcement learning (RL) has shown strong potential for aligning generative models with human intent, but adapting RL to masked generative models (MGMs) remains largely underexplored. Existing approaches that directly adapt Group Relative Policy Optimization (GRPO) to MGMs leave a foundational conflict unaddressed: MGMs' exploitative decoding nature is inherently at odds with the exploratory diversity that GRPO presupposes. In this work, we reveal a structural decoding bias termed the visual exploration trap: confidence-based sampling trades the exploration of diverse subject realizations for the greedy resolution of low-uncertainty background regions, causing premature collapse of the generative exploration space and starving GRPO of the rollout diversity it depends on. To this end, we propose MaskSense, a novel RL framework for MGMs that confronts the visual exploration trap at both the sampling and optimization stages. Specifically, we introduce a semantic anchored routing sampling mechanism that leverages semantic priors to preserve high-entropy subject token exploration while amplifying intra-group reward variance through exploratory-exploitative routing to yield more discriminative advantage estimates. Furthermore, we design a global entropy transition anchoring strategy to identify the most consequential decoding steps and concentrate gradient updates on them. Extensive experiments on multiple text-to-image benchmarks demonstrate that MaskSense substantially improves upon the base model, with GenEval accuracy improving from 54% to 86% and HPS from 28.89 to 36.39, achieving state-of-the-art performance.

Paleo-detectors aim to exploit the damage tracks left in natural minerals by cosmic messengers over geological times to reconstruct past fluxes of energetic particles. For cosmic rays, the expected signal is abundant, and the tracks are micron-scale, so they can be revealed by etching and read out with conventional optical microscopy; what remains challenging is turning a bulk sample into a calibrated track-length spectrum that can be quantitatively confronted with theoretical predictions. In this work we present the experimental pipeline we developed for this purpose within the INFN PRImuS experiment, from sample preparation and automated multi-focus microscopy to track recognition with OptimusPrimus, a two-stage machine-learning algorithm, and to a forward-folding model that propagates geometric sectioning, etching and the measured detection response into simulated spectra. The pipeline was built and validated on chemically etched obsidian where the recovered track-length distribution is statistically compatible with expert annotation. In parallel, we developed and characterized a dry argon-plasma etching protocol for halite, an evaporite mineral of particular interest as a low-background cosmic-ray paleo-detector. Since every stage of the pipeline is mineral-agnostic, with only the trained networks and the detection response to be re-derived from annotated data, we are now applying it to plasma-etched halite with the aim of identifying cosmic-ray-induced tracks.

Generative Flow Networks (GFlowNets) learn a policy that samples compositional objects in proportion to an unnormalized reward $R(x)$. This makes them useful wherever many diverse, high-reward candidates are needed and oracle queries are expensive. In practice, a single GFlowNet often fails to cover all modes of a complex distribution, and the obvious ways to scale compute saturate: larger batches and data-parallel gradient averaging draw every trajectory from one, possibly biased, policy, so extra rollouts rediscover known modes instead of finding new ones. We explore whether this mode-bias problem (mode collapse in the extreme) can be addressed with a population of asynchronously trained policies which divide the state space between them. Mixture of GFlowNets (MoG) replaces the single forward policy with a community of $K$ independent GFlowNets coupled through one jointly trained soft classifier, which assigns each member its own region of the state space through reward shaping. Mixing the members under their learned partition functions provably recovers the target $p(x)\propto R(x)$. MoG exchange (MoGX) also lets the classifier route sampled trajectories: a trajectory the classifier assigns to another member is sent to that member and trained on there, with no importance sampling. We evaluate both methods by keeping the environment-interaction budget fixed while scaling the community size, turning parallel compute into mode coverage without extra oracle calls. On HyperGrid, across six reward landscapes and communities of up to $K{=}64$, MoG and MoGX keep finding new modes as $K$ grows, while data-parallel training saturates. On a genomic ideotype-design task, MoGX covers $39%$ of the $1024$ optima at $K{=}64$, against $31\%$ for independent agents and $20\%$ for data-parallel training. MoG also has a lower per-iteration synchronization cost than data-parallel training.

Rotation symmetric Boolean functions are Boolean functions invariant under cyclic permutation of their variables and can be represented by binary necklaces. We express local sensitivity as a weighted bichromatic degree in the necklace quotient and derive an exact formula for the multiplicities between neighboring necklaces. For an odd prime number of variables, we obtain explicit sensitivity formulas and show that multiplicity corrections occur only on an asymptotically negligible family of necklaces. For monomial rotation symmetric Boolean functions, we prove that every odd-degree function has maximum sensitivity, determine the sensitivity of every quadratic function, and determine the sensitivity of the consecutive quartic family. We also determine exactly the sensitivity of cyclic run-threshold functions for arbitrary length and threshold.

We provide several results showing that sums of “small” Cantor sets can turn into an interval or a finite union of intervals. Specifically, we show that 1) There exists a Cantor set $C\subset [0,1]$ of zero logarithmic capacity such that $C+C=[0,2]$. 2) For any $n\ge 2$ there exists a Cantor set $C\subset [0,1]$ of zero logarithmic capacity such that a Minkowski sum of $n$ copies of $C$ is an interval $[0,n]$, while a sum of any smaller number of copies of $C$ is still a Cantor set. 3) For any $n\ge 2$ there exists a collection of Cantor sets $C_1, C_2, \ldots, C_n\subset [0,1]$ of zero lower box-counting dimension such that a Minkowski sum of any $n-1$ sets from this collection is a Cantor set of zero lower box-counting dimension, while the sum of all $n$ sets is an interval $[0,n]$. 4) There is an uncountable family of Cantor sets of zero lower box-counting dimension such that the sum of any two different sets from this family is a finite union of intervals. 5) For each of the properties above, there are examples of Cantor sets with the same property having zero Hausdorff $h$-measure for an arbitrary given gauge function $h$.

We develop an intrinsic rigidity theory for bar-and-joint frameworks whose vertices are constrained to a Riemannian manifold and whose edges are given by minimizing geodesic arcs. Such frameworks are called rigid if they cannot be deformed beyond the ambient isometries, while preserving the geodesic edge lengths. For admissible placements, for which adjacent vertices are joined by unique minimizing geodesics, we define a coordinate-free rigidity operator as the differential of the squared geodesic distance of the edges. By the first-variation formula, its edge rows are expressed in terms of the Riemannian logarithm, providing an intrinsic analogue of the classical Euclidean rigidity matrix. Trivial motions are characterized by orbits of the diagonal action of the isometry group, leading to notions of infinitesimal and local rigidity. We further develop a covariant second-order rigidity theory using the Riemannian Hessians of the edge constraints and characterize second-order rigidity through self-stresses and associated quadratic forms. Finally, we show that infinitesimal and second-order rigidity can be used as sufficient conditions for the local rigidity of an intrinsic framework. Our overarching goal is to provide a unified differential-geometric formulation of intrinsic framework rigidity on smooth manifolds.

We study multi-agent terminal interception when one of several moving candidates is the unknown target and both target identity and candidate terminal locations are uncertain. We develop a receding-horizon deferred-decision trajectory optimization (DDTO) controller that combines conformal terminal-location prediction, sequential candidate rejection, capacity-constrained assignment, and candidate-contingent planning. Under exchangeability conditions for terminal and identity residuals, with predictable querying, we establish fixed-time terminal-location coverage and anytime-valid target retention. At the final replan, when one control step remains, we bound the joint probability that a tightened-set DDTO plan passes nonlinear rollout verification but capture fails. The closed-loop controller applies fallback guidance to any agent without a verified DDTO plan and, across 100 paired scenarios, captures 79% of targets under the strict control-effort budget and 85% when that budget is relaxed.

Large language models are trained on collections that may include scholarly works, while authors generally lack work-level information about whether and how their works were used. This paper asks how copyright governance frames and operationalises the protection of such authors, and what a responsible alternative would require. Forty legislative, judicial and soft-law instruments issued between 2019 and 2026 were coded deductively against a framework derived from Responsible Research and Innovation theory, yielding 1,337 category assignments across 835 segments. The European Union and the United States are the primary cases; the United Kingdom, China and international bodies serve as comparators. Normative orientation and the distribution of responsibility dominate the corpus, while reflexivity is the least represented category and reaches its minimum in the US sub-corpus. Both primary jurisdictions frame protection procedurally rather than as an entitlement, and no instrument in the corpus creates a general author-facing attribution duty for the use of works in AI training. From the coded gaps, the paper derives a six-instrument governance design and a capacity-based allocation of responsibility among developers, publishers, collecting societies, funders, institutions, regulators, and individual authors.

Generative policies such as diffusion models provide expressive data-driven priors for robot behavior, yet the situations a robot faces at execution time rarely match its training data and impose constraints and objectives the policy never learned. Existing inference-time guidance methods either rely on gradients that can push samples away from the learned prior, or on sampling procedures that can be inefficient, collapse modes, or average them into out-of-distribution predictions. We introduce MOSAIC, a mode- and support-aware framework for gradient-free inference-time control of robotic diffusion models. MOSAIC treats the initial noise and all stochastic reverse-step perturbations as a joint input to the pretrained denoising process and adapts a distribution over this input using importance weights computed from fully denoised outputs. Physical feasibility and consistency with the learned support are balanced using adaptive penalties, while mode-wise importance-weighted updates preserve modes and avoid destructive averaging. The same formulation can jointly steer multiple independently trained diffusion models through shared coupling costs, enabling coordinated behavior without requiring a joint model. We evaluate MOSAIC on navigation, dexterous grasping, motion planning with unseen geometry, and collaborative box manipulation with independently trained robot priors. Across these settings, MOSAIC adapts and composes frozen diffusion priors under new deployment constraints without retraining.