Papers

We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at each vertex. We prove the existence of absolutely continuous spectrum and the absence of singular spectrum on a deterministic set of positive measure at weak disorder, and for $0<\lambda\le2$ when the single-site density is bounded below on $[-1,1]$. Truncated Cauchy distributions and controlled perturbations give purely absolutely continuous spectrum on intervals.

We prove a $1/e$ guarantee for Matroid Secretary on linear matroids: each element of a fixed optimal basis is selected with probability at least $1/e$. This settles the strong secretary conjecture for this class of matroids. Our result holds both when the matroid is known in advance and when a linear representation is given online. In the known-matroid model, the result extends to fully modular extendable matroids. We also obtain $1/e$ guarantees for a more general model on linear matroids, both when the matroid is known and when its representation is revealed online. In XOS Matroid Secretary, agents with XOS valuations over the elements arrive in uniformly random order, and the algorithm must assign each arriving agent a bundle of elements. The bundles must be pairwise disjoint, and their union must be an independent set of the matroid. We obtain an expected total value of at least $1/e$ times the offline optimum. This model contains Group Matroid Secretary, in which the elements are adversarially partitioned into groups that arrive in uniformly random order, and the algorithm selects a subset of each arriving group. For this special case, we select each element of a fixed optimal basis with probability at least $1/e$

For every $0 < \varepsilon \le 1$, we give a randomized $(3+\varepsilon)$-approximation to weighted edit distance when the costs form a metric on the alphabet augmented with a gap symbol. For strings of total length $N$, the running time is $\widetilde{O}(N^{8/5}/\varepsilon^{16/5})$, where $\widetilde{O}$ suppresses factors polynomial in $\log(N/\varepsilon)$. The dependence on $N$ matches that of the fastest known $(3+\varepsilon)$-approximation for unit-cost edit distance. The algorithm never underestimates the edit distance and achieves the approximation guarantee with inverse-polynomial failure probability in $N$. The running time bound assumes constant-time exact arithmetic operations and metric queries, and it is independent of the numerical range of the edit costs. We build on three tools: the sampling framework of Chakraborty, Das, Goldenberg, Koucký, and Saks (J. ACM, 2020), with subsequent refinements by Andoni (2020); Kuszmaul's removal of inexpensive characters (ICALP 2019); and Klein's data structure for distances in planar graphs (SODA 2005). Our new ingredients include, among others, a decomposition of one string into pieces of bounded length with highly structured total deletion costs. This decomposition lets us compare all pieces against a small family of substrings of the other string.

Constraints on neutron star radii provide insight into the properties of the cold, dense matter in their interiors. Previous studies using synthetic Neutron star Interior Composition Explorer (NICER) pulse waveform data have demonstrated that radius inferences derived therefrom are robust against several classes of modeling systematics. Here we explore the consequences of assuming the wrong atmospheric composition, using synthetic data based on the $\sim 2.1~M_\odot$ pulsar PSR~J0740$+$6620. We find that the assumption of a hydrogen atmosphere when the synthetic data assumed a helium atmosphere, or vice versa, produces little bias in the inferred radius at the spot-to-background ratio of the actual PSR~J0740$+$6620 data. However, when we increase the spot-to-background ratio by a factor of $\sim20$ while keeping the total number of counts fixed at the observed $\sim 5.5\times 10^5$, we find that composition mismatch can produce significantly biased radius estimates while remaining hidden inside a fit with statistically acceptable residuals. Even in these cases, the Bayesian evidence consistently identifies the correct atmospheric model. Our findings reinforce the importance of using the Bayesian evidence for model comparison and goodness-of-fit tests.

Generative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations. In these settings, a method can achieve strong pointwise accuracy while still failing to capture the true posterior through mode collapse, overconfident uncertainty, or averaging incompatible solutions. We introduce PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers. PosteriorBench evaluates four physics-based inverse problems: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. For each task, we construct high-fidelity reference posteriors using computationally heavy but established procedures such as rejection sampling and Markov chain Monte Carlo, enabling direct assessment of whether solvers recover the full set of solutions rather than the single best sample. We pair these references with a five-metric posterior evaluation suite: posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error. These metrics assess pointwise accuracy, marginal uncertainty, distributional alignment, and global frequency fidelity. The benchmark spans sparse sensing, low-resolution observations, nonlinear forward models, varying noise levels, and multimodal priors, with a unified pipeline for distribution matching and uncertainty quantification. Our experiments reveal substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness, and guidance weights and generation noise are key to posterior-variance calibration.

The interaction of moose (Alces alces) and wolf (Canis lupus) populations in ecosystems such as Isle Royale National Park is a canonical benchmark for ecological modeling of prey-predator dynamics. Mathematical modeling is a useful tool for modeling these interactions. A central challenge in this domain is the inverse problem, recovering governing system parameters from observational data. Although classical parameter estimation methods have seen considerable progress, they mostly rely on data rather than physics and therefore largely fall short in capturing the time-varying nature of ecological interactions driven by environmental fluctuations, seasonal forcing, and habitat change. This study addresses that gap by solving the inverse problem for a non-autonomous prey-predator system that incorporates theta-logistic prey growth with temporally varying intrinsic growth and natural death rates, as well as Holling type-II and ratio-dependent functional responses. A deep learning framework (self-adaptive bc-PINN with transfer learning) is employed to estimate time-dependent and constant parameters directly from population time series data (1959-2019). Before estimating the parameters, we performed a structural identifiability analysis to ensure that the model parameters are identifiable. The framework demonstrates good reconstruction and prediction results across both functional responses. The ratio-dependent model has shown the better prediction trend beyond the training data. Our framework successfully predicts the sudden decline in the moose population in 2020.

We introduce a unified framework for supervised and unsupervised learning through density estimation using reproducing kernel Hilbert spaces (RKHSs). To this end, we introduce the notion of a nested RKHS, that is, an increasing sequence of RKHSs whose union is dense in an ambient $L^2$-space. This construction allows us to exploit the computational structure of RKHS methods at each finite approximation level while preserving the approximation power of the entire $L^2$-space. We first study statistical learning in a fixed RKHS. In both unsupervised and supervised settings, we establish strong convergence results for empirical averages of random elements taking values in an RKHS continuously embedded in $L^2$. We then use the nested RKHS structure to combine these statistical convergence results with the density of the union of the RKHSs in the ambient $L^2$-space. We apply this construction to probability density estimation and binary Bayesian classification. For density estimation, we construct explicit empirical estimators of the orthogonal projections of the target density onto the RKHSs and establish their almost sure convergence. A diagonal selection procedure then yields a sequence of estimators converging almost surely to the target density in $L^2$. For binary Bayesian classification, we formulate the approximation of the Bayes target as the minimization of suitable population and empirical risk functionals. We prove consistency of the empirical minimizers and use the nested structure to obtain convergence towards the Bayes target in $L^2$. We further provide a geometric interpretation in terms of hyperplanes and weighted distances in the ambient $L^2$-space. Finally, we show that the population risk admits a direct probabilistic interpretation in terms of the probability of misclassification.

Hierarchical planning frameworks combine skills from multiple robot control policies for long-horizon task execution, where determining when to terminate the current skill and advance to the next subtask is essential. Existing approaches often rely on pre-designed completion signal checkers that are hard to obtain in real-world execution. Large-scale vision-language models (VLMs) offer strong reasoning capabilities, but their decision boundaries are not inherently aligned with task completion criteria, while cloud deployment and lengthy reasoning introduce substantial latency, limiting real-time monitoring. We propose StageGuard, an agentic distillation framework for accurate and efficient stage-transition decisions. StageGuard combines teacher-model reasoning with demonstration trajectories to generate structured explanations of subtask completion and policy switching. A lightweight student VLM uses these explanations to generate compact self-explanations, which are used for supervised fine-tuning. We evaluate stage-transition prediction on trajectories from two benchmarks and assess closed-loop task success through integration into hierarchical robot control on BEHAVIOR-1K, with further validation on real robots. Results show substantial improvements in stage-transition prediction while supporting efficient online monitoring.

Let $M^{n+1}$ be a closed, connected smooth manifold, where $n\geq 1$. For each prescribed volume fraction $s\in(0,1)\setminus\{\frac12\}$, we prove that the isoperimetric region of volume $s \operatorname{Vol}_g(M)$ is unique for a generic set of smooth Riemannian metrics $g$. At half volume, a generic metric has exactly two minimizers, a region $E$ and its complement $E^c$. As consequences, for every $m>0$, uniqueness holds for a generic set of metrics $g$ satisfying $m<\operatorname{Vol}_g(M)$, and it also holds for a generic set of pairs $(g,m)$ with $0<m<\operatorname{Vol}_g(M)$. The proof is variational and requires neither boundary regularity nor nondegeneracy of the constrained Jacobi operator. In particular, the results apply even when isoperimetric boundaries are singular.

This article introduces mutual evaluation of a replicable task worker and a critic that incentivizes truthful reporting, both modeled as strategic agents. The critic chooses a finite-valued rule that induces an evaluation score on joint report laws. Their common payoff is analyzed through regret relative to the unrestricted critic envelope. The critic rule is distinct from the evaluation score. This class enables a peer-free information elicitation mechanism using conditionally independent replications of a worker on the same task. This replication-loop mechanism implements a type-agreement payoff using same-task replications and new-task samples. In contrast to the peer-prediction and scoring-rule literature, implementations are shown that produce unbiased Pearson and Shannon information scores without requiring peers, a ground-truth reference, or likelihood-ratio estimation. A valid binary critic also can be represented by shared finite type annotations of worker returns. One runtime restriction is that the number of required replicas is random and can depend on the critic rule. Other timing effects, such as commitment and reoptimization, yield distinct incentives, connecting the framework to variational peer prediction. This mechanism class illustrates why strategic considerations matter for both critic and worker agents.

Quantum effects are expected to modify a black hole's interior structure, particularly near the singularity. We show how to extract the scaling exponent of the singularity from the quasinormal mode (QNM) spectrum of a massless scalar probe in the asymptotic large-overtone limit. We apply our method to a family of exact quantum black holes in (2+1)-dimensional anti-de Sitter (AdS) space and explicitly uncover a transition deep in the interior when quantum effects become dominant.

Some long duration gamma-ray bursts (LGRBs) are not associated with bright supernovae (SNe), indicating that their explosion mechanism differs from the traditional collapsar channel. SN-less LGRBs are rare, thus it remains unclear whether they are sporadic outliers or a substantial component of the GRB population. In this work, we use two decades of Swift observations to conduct a systematic search for nearby ($z\lesssim$0.35) LGRBs without a confirmed SN association. Our analysis reveals a heterogeneous population linked, in part, to star-forming or dusty environments and, in part, to quiescent galaxies. Through the analysis of their high-energy properties, afterglows, and environments, we identify a sample of LGRBs with robust SN limits and distance scales, more than doubling the number of candidate SN-less events. From our fiducial sample, we derive a volumetric rate, not corrected for beaming, of $R = (0.5 \pm 0.2) {\rm~Gpc^{-3}\ yr^{-1}}$, comparable to the apparent rate of short duration GRBs (SGRBs) and standard LGRBs with SNe with luminosities $L \gtrsim\,10^{50}\,{\rm erg\,s^{-1}}$. For plausible beaming factors, the inferred rate of SN-less LGRBs is consistent with several compact binary merger channels, although the allowed parameter space is already narrow if the entire population is attributed to a single progenitor channel. Owing to the small number of candidate events and the uncertainties in their distance scale, our sample leaves the low-luminosity tail unconstrained. A larger sample will be needed to determine whether they are the faint tail of known progenitor channels or evidence of a distinct route to relativistic explosions.

Active nematics can spontaneously develop flow beyond a critical activity in confined geometries. We show analytically that the onset of flow is governed by two competing instabilities: a long-wavelength mode leading to unidirectional flow and a finite-wavelength instability producing transverse rolls. A reduced description reveals how activity, flow alignment, and nematic elasticity control the competition between these modes. We identify regimes in which the finite-wavelength instability has a lower critical activity than the long-wavelength instability, causing vortices to emerge before unidirectional flow. This establishes wavelength selection as an intrinsic feature of the onset of spontaneous flow in active nematics.

We prove new small-ball inequalities for boolean matrix-series. The leading example is $\mathbb E_s[{\text{det}(I-S^2)^\beta\,\mathbf 1_{\{\|S\|<1\}}}]\ge e^{-O(\beta\tau)}$, which holds for boolean matrix-series $S=\sum_i s_iA_i$ formed using symmetric matrices $A_1,\dots,A_n$ and uniformly random signs $s\in\{\pm1\}^n$. Specifically, this inequality holds for all $\beta\ge1$ with $\tau=\sum_i\text{Tr} A_i^2$, as soon as the maximum of $(\text{Tr} A_i^2)_{i=1}^n$ and a certain variance term are bounded above by universal constants. The proof combines the Gaussian reciprocal estimate of (Akbas and Sra 2026), the directional-variation signing theorem of (Guo, Fang, and Lu 2026), and a replica argument that turns existence into a Gibbs law on good signings. Most notably, boolean small-ball delivers a new, interlacing-free proof of Kadison-Singer (most general case); it also recovers Matrix Spencer and Komlós as quick corollaries, while yielding more than six almost immediate proofs of an assortment of discrepancy theoretic problems.

Multi-turn agents trained with reinforcement learning (RL) receive a single scalar reward per trajectory, which motivates self on-policy distillation (OPD) to supply dense token-level supervision from a self-teacher with privileged task skills, letting a skill-free student internalize them. This recipe, however, is undermined by two findings in agentic tasks: privileged information alone does not always make a teacher reliable, and the benefit of teacher supervision is stage-dependent. We therefore propose RetireOPD (Self-Retiring On-Policy Distillation), which first optimizes a decoupled, skill-conditioned teacher with environment rewards and then trains a skill-free student jointly with RL and OPD. Rather than following a predefined distillation schedule, RetireOPD adopts Adaptive Retirement: the student drops the teacher on its own once their discrepancy stops shrinking and it reaches a target fraction of the teacher's success rate, after which training proceeds with RL alone. Across Qwen2.5 models from 1.5B to 7B, RetireOPD improves ALFWorld success rate over RL baseline by 14.1% to 18.8% and WebShop accuracy by 11.8% to 19.0%, and surpasses its own skill-conditioned teacher in every setting.

For $r> 2$, we study the moduli space parameterising fixed degree morphisms $\mathbb P^r\to X$ where $X$ is a smooth hypersurface of low degree. More precisely, we prove the following result: let $n\geq 2, e\geq 1$ and $X\subset \mathbb P^{n-1}$ a smooth degree $d\geq 2$ hypersurface over an algebraically closed field of characteristic zero or greater than $d$, then $\mathrm{Mor}_e(\mathbb P^r, X)$ is irreducible of the expected dimension if \[ n> 2^d(d-1)\binom{de+r-1}{r-1}. \] Our result extends the result of Browning-Yamagishi for $r=2$ via multiblock Weyl differencing.

Research data quality is multidimensional and purpose-dependent: it emerges from the interplay of data, intended use, contextual knowledge, documentation, intervention decisions, and traceability. This concept paper presents the Data Hospital, a human-in-the-loop control and interaction model for research data quality. Using a hospital metaphor, datasets are admitted, contextualized, assessed, reviewed in specialized stations, modified only through approved interventions, validated, documented, and made replayable where interventions are sufficiently specified. The concept combines deterministic profiling and inspectable evidence with optional evidence-bound explanation by Dr. Data and explicit user decisions. Preserved Raw Data and controlled working states separate observation from intervention. The contribution is not a new cleaning or imputation algorithm, but a ten-stage workflow that makes assessability, uncertainty, intervention authority, provenance, and process reproducibility visible. The prototype is an implementation-backed demonstrator rather than a released research artifact and illustrates selected parts of the concept through representational standardization, imputation, Patient File documentation, and replay. The paper concludes with a staged agenda for subsequent technical and user-centered evaluation.

Quantum channel discrimination plays a crucial role in quantum information theory. Of particular interest is the case in which the channels can be discriminated perfectly. In this work, we focus on the perfect quantum channel discrimination task in a parallel scheme. We develop an SDP formulation combined with a bisection procedure to compute a quantum state for perfect discrimination in time linear in the number of copies. In addition, we obtain the minimal number of copies of quantum channels to achieve perfect discrimination. Thanks to that, we settle in the affirmative Conjecture 1 of Duan, Guo, Li and Li [arXiv:1605.02294, IEEE ISIT 2016], which characterizes the number of parallel uses needed to discriminate perfectly a distinguished family of operator subspaces. All our results are obtained using the notion and basic properties of the numerical range. In particular, the key fact that we prove and use is that the minimal angle of the numerical range of a tensor product of matrix subspaces equals the sum of the minimal angles of the numerical ranges of the individual subspaces.

We construct explicit families of asymptotically good quantum locally testable codes over qubits. More precseily, we construct explicit quantum LDPC CSS codes over qubits having constant rate, constant relative distance and constant weight local testers with constant soundness.

Safety evaluations for large language models rely on surface-form classifiers that report declining harm scores across model generations. We provide evidence that this methodology is systematically incomplete: explicit discriminatory content is transformed rather than removed. We call this harm laundering. Analysing 450,000 gender-directed completions across 15 models spanning GPT-2 through to GPT-5 (OpenAI GPT lineage; three demographic conditions), we show that sexual violence clusters prevalent in GPT-2 women-directed output disappear by GPT-4, while men-directed completions gain positive representational territory (caregiving, emotional range, ally identity) that women-directed completions do not. The pattern is most visible at GPT-5: Topic~5 (1,997~documents) frames breast cancer as a men's rights debate, while zero equivalent clusters appear in women-directed output. Three independent classifiers score this content as non-toxic. Sentiment scores invert at GPT-4: early models demean women; later models over-correct. Topic diversity in women-directed completions falls 36% relative to men at the GPT-4 alignment boundary (W/M~$= 0.58$, from $0.91$ at GPT-2). REGARD representational harm disparity correlates with release date ($\rho = +0.55$, $p = .034$) while Detoxify does not ($\rho = -0.23$, $p = .42$): toxicity scores fall as representational harm grows. We formalise harm laundering as a three-criteria test and provide a three-stage detection protocol applicable to any generative model. Within the OpenAI GPT lineage, toxicity score reduction is not a sufficient proxy for harm reduction.

We study a singular Dirichlet problem driven by a regularized $p(x)$-Laplacian under a prescribed modular constraint. Using growth and differentiability estimates for the regularized energy, together with coercivity and modular compactness, we construct nonnegative constrained minimizers for a family of nonsingular approximating functionals. Under the admissibility of signed constrained variations, each minimizer satisfies an approximate Euler–Lagrange equation with a uniquely determined constraint multiplier. An explicit uniform boundary lower barrier and a compatible weight condition, combined with a variable exponent Hardy inequality, provide global dual control of the singular sources and convergence against every zero-trace Sobolev test function. For these approximate minimizing pairs, the singular-limit result gives subsequential strong Sobolev convergence of the states and convergence of their multipliers, while preserving positivity and the prescribed modular. The limiting pair is therefore a positive normalized weak solution of the singular problem, obtained by removing the reaction regularization while keeping the gradient regularization fixed.

We report improved global-minimum configurations for the classical Thomson problem of $N=60$, $61$, $92$, and $99$ repulsive Coulomb charges confined to a disk. By combining the quenched molecular dynamics (QMD) method with the fixed-border heuristic introduced by Amore and Zarate, we systematically obtain configurations with energies $E_{\mathrm{QMD}}(60)=2159.3584240930$, $E_{\mathrm{QMD}}(61)=2237.19264190$, $E_{\mathrm{QMD}}(92)=5358.35353314$, and $E_{\mathrm{QMD}}(99)=6254.83029083$, which improve upon the previously best-known values. For $N=60$, the Voronoi diagram of our configuration differs from the one reported earlier. The symmetries for $N=61$ $(C_{2})$ and $N=99$ $(D_{1})$ are confirmed and are consistent with the known symmetry patterns for these configurations. For $N=92$, whereas the previously reported Voronoi diagram has lower symmetry, our solution exhibits a clear $D_{1}$ (axial) symmetry of defects. The results are highly reproducible across multiple independent runs, providing strong evidence that these configurations are robust global-minimum candidates.

Action chunking is widely used for action generation and execution in Vision-Language-Action (VLA) policies, yet existing approaches commonly use a fixed action horizon. During a rollout, different task stages may require different levels of action continuity, control precision, and closed-loop feedback, making a fixed horizon unable to accommodate changing control requirements. We propose GeoAAC, a geometry-based adaptive action chunking method for flow-based VLA policies that adjusts the action horizon according to the reliability of the current action prediction. We show that the geometry of Flow Matching denoising trajectories provides process-level information for characterizing prediction reliability, with geometric variation across action prefixes remaining positively correlated with predictive uncertainty. GeoAAC uses this prefix-wise geometry to construct a horizon-wise geometric profile and adaptively determine the action horizon from a single generation without additional training. Experiments with GR00T N1.5 and {\pi}0.5 on LIBERO, LIBERO-Pro, RoboCasa365, and real-world manipulation tasks show consistent improvements over fixed-action-horizon baselines and existing adaptive methods, including up to 8.7 percentage points in simulation and an increase in average real-world success rate from 53.3% to 74.4%.

Hole spin qubits in semiconductor quantum dots (QDs) enable high-fidelity all-electric control, but conventional electric dipole spin resonance (EDSR) can require substantial rf drive power at the low magnetic fields that are favorable for qubit coherence and readout. In planar Ge hole spin qubits, this can reach -27 dBm at the device, posing challenges for scalable architectures due to heating and crosstalk. Here, we demonstrate a flopping-mode (FM) qubit in Ge, where a single spin is delocalized in a double QD, combining first-order protection against charge noise with exceptionally efficient electric driving. By mapping out coherence sweet-spots as a function of magnetic field orientation we achieve $T_2^*= 1.4\mu\mathrm{s}$, $T_2^{\mathrm{Hahn}}= 11.5 \mu\mathrm{s}$, $T^{\phi, \mathrm{CPMG32}}_2= 130 \mu\mathrm{s}$, and $T_1= 226 \mu \mathrm{s}$, and a single-qubit gate fidelity of up to 99.76$\%$ for a gate time $t_{X\pi} = 88$ ns. Importantly, these results are obtained at a nearly in-plane magnetic field of 5 mT using only -52 dBm drive power at the device. We further find that qubit relaxation in this regime is consistent with a two-photon Orbach process, providing a route for further optimization. Our results demonstrate that FM-EDSR supports ultra-low-power, high-fidelity single-qubit operations, improvements that could benefit scalable hole-spin-based architectures and hybrid spin-photon interfaces.

The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)]. We resolve an open problem from these earlier works by showing – using a novel "coherent teleportation technique" – that a sufficient condition for causal separability identified in [Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)] is also necessary, and thus provides a complete characterisation of multipartite causal separability. A consequence of this result is that all causally separable processes admit a realisation as generalised quantum circuits in which the order between the operations is classically controlled, known as "quantum circuits with classical control of causal order".

We present an exploratory numerical model for the thermal evolution and fragmentation of pristine interstellar comets on a first passage through the inner Solar System, applied over a grid of perihelion distances ($q=0.25$–$1.5$~AU) and tensile strengths ($\sigma_t=50$–$500$~Pa). A single nucleus ($M_0=2\times10^{12}$~kg, $R_0\approx1.06$~km, dust/ice $=1$, ices 35% CO, 30% CO$_2$, 15% CH$_4$, 20% H$_2$O) follows a hyperbolic trajectory from an initially 30~K state, with heat conduction, energy-balanced multi-species sublimation, dust lifting and lag-mantle growth, and a subsurface gas-pressure failure criterion, so that fragmentation is emergent rather than prescribed. In the primary case ($q=1$~AU, $\sigma_t=100$~Pa) splitting begins at the 3~AU starting distance, once a sub-millimeter lag deposit partially confines the warming CO front; 63 binary splittings follow, with a self-limited plateau at 53 bodies before perihelion and the 64-body tracking cap reached near perihelion. Sublimation is energy-limited: total mass loss is 1.3%, volatile depletions are at most a few per cent, and most of the mass survives as a fragment swarm; the mass budget closes to machine precision. Across the grid, mass loss (0.8–1.7%) depends weakly on $q$ and $\sigma_t$ but strongly on composition, falling to 0.1% for depleted, 67P-like ices. Yet every case, including the depleted class, disaggregates, whereas Jupiter-family comets of similar composition survive repeated perihelia, so the sealing prescription over-fragments. We regard the composition ranking, the insensitivity to $\sigma_t$, percent-level mass loss, and an onset beyond 3~AU as robust, and defer absolute survival predictions to calibration against well-observed comets. Mantle insulation suppresses outbound activity, producing an inbound–outbound asymmetry.

We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects from associations driven by common external processes, supporting reliable decision-makings in applications such as finance, neuroscience, and climate science. While traditional approaches assume a linear vector autoregressive (VAR) model and are vulnerable to misspecification, we instead address a model-free version of the problem. We propose nonlinearly regressing both the outcome and exposure on the joint history of $Y$ and $Z$, and calculating a test statistic based on the sample covariance of residuals, we call the Generalised Temporal Covariance Measure (GTCM). To account for heteroscedasticity and improve power against local alternatives, we incorporate variance weights and employ a data-adaptive test based on polynomial lag expansions.The type I error control of the test relies on the relatively weak assumption that user-chosen regression procedures estimate conditional means at a sufficiently fast rate that is slow enough to accommodate nonparametric settings. By further assuming stability of the regression procedures and weak dependence in the time series, we can utilise the entire dataset to estimate the conditional means without splitting the time series into subsets.

Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampling and membership-oracle access to a set $A \subseteq \mathbb{F}_2^n$ with doubling constant at most $K$, our algorithm outputs a subspace of size at most $|A|$ whose $K^{O(1)}$ translates cover $A$. The algorithm runs in $\textsf{poly}(n,K)$ time. As applications, we obtain polynomial-time algorithms for a variety of learning problems, including quadratic Goldreich-Levin, improper agnostic tomography of stabilizer states, and tomography of quantum states with bounded stabilizer extent.

We investigate the sensitivity of solutions to multi-dimensional scalar balance laws with respect to perturbations of the initial data analytically and numerically. Reliable first-order sensitivity information is essential in gradient-based optimization and inverse problems constrained by hyperbolic balance laws. In hyperbolic problems, such perturbations affect both the smooth components of the solution and the locations of shocks. Consequently, classical difference quotients of the solution operator generally fail to converge in $L^1$, even in one space dimension. Although generalized tangent-vector techniques have been developed for one-dimensional problems, extending these ideas to multiple space dimensions is considerably more challenging because it requires a geometric description of hypersurfaces of discontinuity. We represent perturbations of hypersurfaces of discontinuity by normal displacements and account for the induced variation of the normal direction. This representation yields evolution equations for the components of a generalized tangent vector. Based on this calculus, we develop a numerical method for computing first-order variations with respect to the initial data. Numerical experiments in two space dimensions confirm the expected first-order accuracy of the resulting approximation.

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers make simplifying approximations in posterior sampling and/or assume linear forward models. In contrast, principled diffusion-based methods exist but are computationally expensive. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) with annealed coupling, and make flow-specific interventions to the prior sampling and annealing steps, theoretically grounded in the Stochastic Interpolants (SI) framework. Using a novel timestep correction and accelerated warm-up with one-step flow models, our method is faster and more accurate than the state of the art across a range of imaging problems. We demonstrate the first use of flow-based samplers for a nonlinear inverse problem (Fourier phase retrieval) and apply one-step flow models to principled Bayesian inverse imaging.