Papers

Benchmark gains are often mechanism-ambiguous: reproducing an improvement does not by itself identify why it occurs. We study finite-library mechanism discrimination, where posterior-weighted candidate mechanisms, executable probes, and a limited experimental budget define a sequential experiment-selection problem. MECHVAR selects the next probe by maximizing the posterior-weighted variance of its predicted responses. Under a shared-Gaussian predictive model, this score is exactly proportional to the classical Box–Hill posterior-weighted pairwise-KL criterion, yet it admits O(KE) vectorized rescoring and a transparent additive audit over mechanism pairs. A local expansion further links the score to expected information gain (EIG) when predicted response separations are small. In a 25-block stress audit, MECHVAR outperforms confirmation-first in several moderate misspecification regimes, while its primary comparisons with EIG remain statistically unresolved. In a held-out Digits loop, normalized mechanism-identification AUC is 0.8975 for MECHVAR, 0.7825 for a score-greedy policy, and 0.9092 for EIG. At K = 100, E = 200, median single-thread full-library scoring is 10.36 microseconds for MECHVAR versus 57.69 ms for six-node quadrature EIG in the recorded environment. MECHVAR therefore provides a lightweight, auditable acquisition rule for finite-library experiment selection when a shared predictive scale is a defensible approximation.

The predictively oriented posterior offers principled uncertainty quantification, even under model misspecification. However, it does not admit an explicit density and therefore cannot be computed using classical Monte Carlo sampling algorithms. We remedy this by deriving an approximation to the predictively oriented posterior whose density can be evaluated point-wise, and whose approximation error decays rapidly. These results are illustrated on case studies from epidemiology, spatial statistics, and low-energy nuclear physics.

Sensors deployed in real-world conditions often produce measurements corrupted by outliers due to model uncertainties, changes in the surrounding environment, and/or data loss. As a result, managing these outliers becomes crucial for state estimation to avoid inaccurate estimations and a reduction in the reliability of results. To address this issue, we introduce a novel form of extended Kalman filter (EKF) based on the maximum a posteriori (MAP) principle for scenarios where outliers simultaneously occur in multiple dimensions. For detecting outliers during the filtering process, we introduce a novel variant of the normalized innovation ratio (NIR) test and embed it within the EKF framework. Our approach enhances the estimation accuracy and computational efficiency of state estimation process even when data from several sensors simultaneously contain outliers.

We present the results from follow-up spectroscopy of three protocluster candidates at $z\sim3$, selected as overdense regions of $U$-dropout galaxies in the wide-field imaging of the Hyper SuprimeCam Subaru Strategic Programme. All three targets exhibit tight clustering in three-dimensional space, i.e. on the sky ($>4\sigma$ overdensity) and in redshift ($>98.4\%$ confidence), making for clear evidence of genuine protoclusters. Since these three protoclusters are identified by the same dataset and technique, they represent a good sample to study the diversity of protocluster properties with minimal observational biases. Although the average population across the three protoclusters is consistent with field galaxies, each protocluster individually exhibits distinguishing properties from each other or from field galaxies. In one protocluster, member galaxies stand out by a higher Ly$\alpha$ equivalent width ($EW_0$), and massive members that are still highly star-forming. In contrast, relatively more suppressed star formation appears in another protocluster where the Ly$\alpha$ $EW_0$ of member galaxies is systematically lower. These variations can be attributed to differences in the developmental phase of protoclusters. If the presence of quenching galaxies indicates a more mature system, galaxies with stronger Ly$\alpha$ emissions may be more prevalent in the earlier stages of cluster formation. The uniform approach to searching protoclusters on which this study builds enables us to link observed variations at the onset of cosmic noon to different pathways in the history of cluster formation.

Although diffusion models produce high-quality images, they also reproduce and amplify demographic imbalances in their training data. Debiasing their generation process post-training w.r.t. some sensitive attribute usually relies on classifier guidance or explicit text extra-conditioning, but this reduces methods' applicability and output diversity. Conversely, methods promoting diversity alone do not ensure fair attribute representation. In this paper, we propose a method tackling fairness and diversity jointly that is generally applicable to any diffusion model and any sensitive attribute. To this end, an adapter connects the frozen diffusion model to a pretrained vision-language embedding space, enabling fairness and diversity guidance without sensitive-attribute annotations. For fairness, pairs of text prompts define attribute directions which guide batch composition towards specific proportions. For diversity, we introduce a score measuring disagreement between the semantic estimates derived from this representation. The formulation supports unconditional and text-conditional diffusion models, while requiring no prior knowledge or data of sensitive attribute. Experiments confirm that our method improves quality and diversity scores at comparable fairness levels.

Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a $p$-impurity model is non-Markovian, then the corresponding $(p+1)$-impurity model is also non-Markovian, implying the existence of a critical $p$ at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical $p$, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.

Mitotic counting is an important component of tumour grading, diagnosis and prognostic assessment across several tumour types, but manual assessment is time-consuming and subject to inter-pathologist variability. To help address these challenges, we developed MitPro, an AI tool designed to improve consistency and efficiency by directing pathologists towards regions with the highest predicted mitotic activity and highlighting mitotic figures for review, while retaining pathologist control over region selection and the final count. We evaluated its effect on the reproducibility and efficiency of mitotic counting in a retrospective, non-interventional, paired reader study comprising 385 whole-slide images from 3 centres in 3 countries and 7 tumour types using 3 different scanners. 13 pathologists participated, with each slide assessed independently by 3 pathologists without AI assistance and again with AI assistance after a minimum 2 week washout period. Across all slides, AI-assisted counting increased the intraclass correlation coefficient from 0.589 to 0.949. Mean pathologist-level median assessment time decreased from 286.4 to 127.8 seconds, corresponding to an average saving of 151.8 seconds per assessment. Improvements in agreement and efficiency were also observed in supporting analyses using HALO AP and Sectra image management systems and in 2 additional tumour types outside the main study population. AI-assisted assessment was associated with a subtle shift towards higher mitotic counts and scores, consistent with identification of more active mitotic hotspots and fewer missed mitotic figures. The frequency of score change between unassisted and AI-assisted assessment was comparable with inter-pathologist variation during routine counting. These findings support the use of MitPro as an assistive tool for more consistent and efficient mitotic assessment in routine practice.

Signomials—finite sums of generalized monomials with real exponents—are a natural machine learning model, combining parsimonious representations of power laws, inverse relationships, and multiplicative interactions with universal approximation and interpretable parameters. In fact, 45 of the 100 equations in the AI Feynman benchmark admit signomial representations. Moreover, signomial optimization is widely used in engineering design, communications, economics, and machine learning, but is computationally intractable in general. Convexity, the gold standard for efficient optimization, offers three routes to tractability for signomials: a signomial may be convex in its original variables, become convex after a logarithmic change of variables, or, when positive, become convex after additionally taking the logarithm of its value—the structure underlying disciplined geometric programming. We show that recognizing each form is strongly NP-hard, both on compact domains and globally. Our proofs start from gap-promise variants of polynomial convexity and develop polynomial-to-signomial reductions that preserve curvature gaps under the relevant logarithmic transformations.

Context. Protoclusters at reionization are thought to host a significant fraction of the cosmic star formation rate density, making them crucial for the timing and topology of reionization. The gas-phase metallicity, a key tracer of galaxy evolutionary stage, can now be measured directly in the early Universe with JWST. Aims. We measure the gas-phase metallicity of Lyman-$\alpha$ emitters (LAEs) in the LAGER-z7OD1 protocluster at $z\approx6.93$ via the direct ($T_e$-based) method using the [O III]$\lambda$4363 auroral line, and combine it with stellar masses to constrain the mass-metallicity relation (MZR) in dense environments. Methods. We use JWST/NIRSpec MSA G395H spectroscopy, derive metallicities with self-consistent analytic prescriptions, and propagate the dust-extinction uncertainty into an asymmetric error budget via Monte Carlo simulations based on the observed Balmer decrements. Stellar masses come from BEAGLE SED fitting of JWST/NIRCam and UltraVISTA photometry. Results. We obtain five secure [O III]$\lambda$4363 detections and one upper limit, with 12+log(O/H) $\approx$ 7.2-8.0. The weighted spectral stack yields 12+log(O/H) = $7.76^{+0.06}_{-0.05}$, ~0.26 dex higher than stacks of LAEs at similar redshifts from JWST surveys. However, the MZR fit gives a slope $\gamma$ = 0.232 +/- 0.214 and normalization $Z_0$ = 7.888 +/- 0.199, placing our sources below the established MZR of normal galaxies and recent protocluster baselines at $z\sim5-7$. Conclusions. The higher metallicity relative to general LAEs suggests accelerated assembly driven by the overdensity, while the offset below the MZR points to a complex interplay between mass build-up and gas accretion. Since we target actively star-forming LAEs, we are likely capturing a phase of pristine gas inflow from the intergalactic medium that fuels star formation but dilutes the interstellar media of these protocluster members.

We study continuous-time Galton–Watson trees whose offspring generating function takes the form \begin{align} \label{eq:gen} f(s) = s - (1-s)^\alpha L(1-s), \end{align} where $\alpha \in (0,1)$ and where $L:[0,1] \to [0,\infty)$ is slowly varying at zero. Processes with this offspring generating function explode in finite time. We observe that, conditional on explosion at time $T$, at each earlier time $t < T$ there is a unique particle $\xi_t$ alive at time $t$ who is an ancestor of all but finitely many particles at the explosion time. We call $(\xi_t)_{t \in [0,T)}$ the spine to explosion, and show that the births off the spine admit a Poissonian description, where they become both more frequent and larger as $t \uparrow T$. We undertake a careful study of the size of the population leading up to explosion, showing in particular that near explosion, the rescaled population is approximately gamma distributed. More generally, conditional on explosion at time $T$, define a stochastic process $Z^\varepsilon := (Z_t^\varepsilon)_{t \in \mathbb{R}}$ by setting \begin{align*} Z_t^\varepsilon := E(\varepsilon e^{-t})N_{T-\varepsilon e^{-t}}, \qquad E(t) = \mathbf{P}(N_t = \infty). \end{align*} We show that as $\varepsilon \downarrow 0$, $Z^\varepsilon$ converges in finite-dimensional distributions to a stationary continuous-state branching process with immigration whose branching mechanism is subcritical and whose immigration mechanism corresponds to spine events. Finally, we show that this limiting process has a Markovian time reversal, and that the coalescent process associated with it is a stochastically time-changed Beta$(2-\alpha,\alpha)$-coalescent.

We develop a variational framework for state-dependent diffusion on adaptive multiresolution representations in which the diffusion operator is generated by the adaptive state itself. The state consists of an admissible multiresolution tree, its active approximation space and basis, and the corresponding coefficient representation. It determines a symmetric nonnegative interaction form and an associated positive semidefinite intrinsic diffusion operator. In contrast to classical adaptive wavelet methods, where a prescribed operator is represented on an evolving approximation space, refinement and coarsening here modify simultaneously the representation, interaction graph, and operator. Because the adaptive hierarchy evolves through discrete topological changes, the coupled dynamics are formulated through a time-discrete variational principle rather than a differential evolution on a fixed space. We establish existence of the discrete updates, a discrete energy inequality, the coefficient-space null mode, and contractivity for frozen adaptive states. For regularized inverse problems, the construction yields Adaptive Multiresolution Diffusion Imaging (AMDI), combining data fidelity, intrinsic diffusion, coefficient sparsity, and tree complexity in a state-dependent energy. Numerical experiments verify the assembled operator identities, examine refinement-commutator decay, and confirm discrete energy dissipation. Adaptive Haar and higher-order multiwavelet calculations demonstrate localization of resolution on heterogeneous data. In denoising, AMDI retains high structural reconstruction quality with less than 10% of the full active representation, with stable behavior across held-out noise realizations.

We argue that a detailed analysis of semileptonic decays can test the possibility of a massive neutrino. The key observable, related to the forward-backward asymmetry, is exactly zero for a massless neutrino but becomes non-zero if the neutral lepton is heavy and interacts with Standard Model fields via left-handed operators. For right-handed interactions, this quantity differs significantly from zero even for a massless right-handed neutrino. We demonstrate this explicitly using the example of a pseudoscalar meson decaying into another pseudoscalar meson.

Reliable clinical deployment of deep medical image models is hindered by distribution shifts across scanners, sites, and acquisition protocols. Existing domain generalization (DG) methods often focus on style or intensity diversification, but they can still leave networks dependent on domain-specific texture correlations. Inspired by evidence that Fourier phase encodes semantic structure, we introduce PhaseAT, a phase-aware adversarial training framework for medical DG. PhaseAT forms phase-perturbed training views in the Fourier domain by iteratively updating a bounded phase perturbation while keeping the amplitude spectrum unchanged, thereby stressing spatial organization under matched appearance statistics. Perturbations are applied only to the luminance channel in YCbCr color space to avoid chromatic artifacts. Additionally, a simple phase-saliency mask concentrates updates on the most influential frequencies. The model is trained with a weighted combination of losses on clean and phase-perturbed samples, supporting both single-source and multi-source DG. We validate our method on two challenging medical datasets and demonstrate that PhaseAT achieves over 20% improvement in single-source domain generalization, outperforming several state-of-the-art DG methods. The code implementation is available at: https://github.com/ahmed-sharshar/PhaseAT.

We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Prasad-Yeung, and Cartwright-Steger.

The article reviews the robust design and analysis of auctions, focusing on the predominant paradigm in the computer science literature, which quantifies robustness by the worst-case, over environments, ratio between the robust auction's performance and that of an optimal auction for the environment. Applications include robust analysis of canonical auctions such as the first-price auction for the welfare objective, prior-robust auction design for the revenue objective, and prior-robust design of exchange mechanisms for the gains-from-trade objective. Finally, the revelation principle is not without loss in robust mechanism design. The potential loss can be quantified by the revelation gap, the fraction of the optimal robust guarantee that is lost when restricting from all mechanisms to revelation mechanisms.

Jurij Volčič conjectured that a noncommutative polynomial $g$ belongs to the two-sided ideal generated by $f_1,\ldots,f_l$ if and only if, for matrices of every size, the rank of the evaluation of $g$ is bounded by a constant times the maximum rank of the evaluations of $f_1,\ldots,f_l$. In this paper, we show this equivalence when the generators $f_1,\ldots,f_l$ are homogeneous. We then give an explicit counterexample in the non-homogeneous case.

Consider the circular beta-ensembles, Jiang and Matsumoto computed the moments of traces, and proved central limit theorems for polynomial linear statistics using Jack functions. We give a direct proof of the Gaussian limits for the traces of powers of circular beta-ensembles using the theory of orthogonal polynomials on the unit circle and Stein's method. The proof relies on an explicit coupling of the Verblunsky coefficients of circular beta-ensembles, which also allow us to obtain almost sure and $L^2$ convergence.

These are the slightly edited notes from a 10-hour course I taught at Institut Henri Poincaré in January-February 2025 in the framework of the thematic semester "Representation theory and noncommutative geometry".

Can response safety be scored by cosine similarity to the mean embedding of known-safe responses? A recent sleeper-agent detector proposes exactly this score, yet the raw positive-centroid rule is not identified: positive observations locate the safe class relative to an encoder origin, but do not determine which direction separates safe from unsafe responses. We audit the rule on two prompt-controlled, human-labeled corpora and one auxiliary jury-labeled source control, using four frozen encoders and prompt-grouped splits. On the human-labeled corpora the safe prototype reaches ROC-AUC 0.457-0.545, with two cells significantly below chance and one above, while an explicit safe-minus-unsafe reference reaches 0.588-0.738 on the same embeddings; on the jury control the prototype is inverted (0.358-0.405) and the reference reaches 0.754-0.793. At validation-calibrated 5% false-safe thresholds, the reference accepts more safe responses on PKU-SafeRLHF (0.153-0.263 versus 0.039-0.061 across encoders) and Aegis (0.189-0.291 versus 0.004-0.045), but not reliably on BeaverTails. A fully unlabeled held-out reference recovers part to most of the referenced ranking, much less when only 5% of the pool is unsafe, whereas 80-634 labeled unsafe responses recover most of it. Prompt-only ablations show that prompt-label composition can inflate uncontrolled evaluations. This is a bounded result about a raw positive centroid, not all one-class methods or safety-specialized guards. A class mean is a location, not necessarily a safety direction; a declared reference with enough unsafe mass identifies orientation.

Time series captioning is a fundamental step in time series understanding and can also serve as the bridge between signal and natural language. Supervised fine-tuning (SFT) relies on a larger model's captions and cannot exceed their quality. Reinforcement learning (RL) can, but its rewards were designed for other modalities and other tasks, and they transfer poorly to open-ended generation in the time series domain. We address this by proposing LineupRL, a reinforcement learning with verifiable rewards (RLVR) pipeline whose reward is caption-to-series identification. The reward model is a frozen large language model (LLM) verifier that reads the generated caption and the candidate time series as raw values, never the chart, and must pick the described time series from multiple distractors. Matching is a far lighter demand on the verifier than writing questions or judging a caption, so an off-the-shelf LLM can supply the reward. Across two captioning benchmarks, and on forecasting and reconstruction where the predictor sees only the caption, LineupRL outperforms SFT and RL baselines on every metric. The 3B vision language model (VLM) trained by LineupRL also outperforms, at 1/24 of the parameters, the 72B VLM whose captions the SFT baseline is distilled from. Our case study shows that LineupRL resists reward hacking, and that the captioner it trains both traces the trend and names the values at key points.

Skill evolution offers a promising way to improve large language model agents without updating their parameters, but its use in formal theorem proving remains underexplored. Existing methods mainly target natural-language reasoning, improving skills by analyzing successful and failed trajectories and incrementally revising solving strategies. Although the Lean verifier provides reliable execution feedback, when all sampled trajectories fail, existing skill evolution methods lack successful trajectories from which to infer effective update directions. Furthermore, these methods also focus mainly on the root instruction file, thus underexploring the evolution of reference knowledge including mathematical concepts and proving techniques. To address these limitations, we propose a mutation-enhanced skill self-evolution framework for building skill-augmented Lean provers. The framework jointly evolves a high-level solving policy and its reference knowledge through progressive and mutation-based updates. Progressive evolution derives local improvements from successful and failed trajectories, while mutation is triggered when no complete proof can be generated, sampling mathematical concepts to produce and select new skill candidates under verifier feedback. We evaluate our method on MiniF2F, PutnamBench, the 2025 International Mathematical Olympiad (IMO 2025), and the 2026 USA Mathematical Olympiad (USAMO 2026). Under the same backbone model, trajectorysampling budget, and test-time compute, our method achieves proof success rates of 100.0%, 90.6%, 4/6, and 4/6, respectively, with GPT-5.5, outperforming the baseline methods. Further analysis shows that concept-guided mutation outperforms random-text-guided mutation by 6.9 and 8.2 percentage points on MiniF2F and PutnamBench, respectively, while solving one additional problem on both IMO 2025 and USAMO 2026.

We establish that, for a binary operad Var, the Hadamard product of Var and the operad Nov of Novikov algebras is a binary operad (i.e., coincides with their Manin white product Nov $\circ$ Var) if and only if the quadratic part of Var governs a 2-variety. The condition Nov $\circ$ Var $=$ Nov $\otimes$ Var is known to be equivalent to the existence of an easily verifiable characterization of those differential Var-polynomials which lie in the free derived Var-algebra. For a binary quadratic operad, these conditions are also equivalent to the Dong property of formal distributions. We distinguish the white product defined as a generated sub-operad from its quadratic approximation and give an example in which the canonical epimorphism between them is not injective.

We derive a generalized fluctuation-dissipation theorem (FDT) for vector fields in rotating thermal equilibrium from an exact phase-space Kubo-Martin-Schwinger (KMS) relation. The resulting FDT contains rotation-induced tensorial contributions beyond a scalar thermal factor. In the local transport limit, we obtain a model-independent generalized Einstein relation with rotation in which, through second order in thermal vorticity, symmetric momentum diffusion depends on low-frequency spectral information beyond that encoded in the rotation-dependent dissipative drag. Remarkably, we find a new Einstein-type relation linking zero modes in the spectral function to the nonrotating drag coefficient. These zero modes underlie a new mechanism for the orbital polarization of heavy quarkonium. The same FDT constraint yields a modified detailed-balance relation whose first-order vortical correction is governed by transition polarization, without explicit dependence on the bath model. Our findings establish microscopic equilibrium constraints for studying rotating quantum matter in various fields.

A dominating set $D$ of a graph is called $1$-limited if every vertex of $D$ has at most one neighbor outside $D$, while a $(1,2)$-dominating set is a dominating set in which every vertex of the set has at least two neighbors within the set. These two notions coincide on cubic graphs. We prove that the decision problem 1-Limited Dominating Set is $\mathsf{NP}$-complete even when restricted to $2$-connected planar cubic graphs, thereby completing the known complexity results for $k$-Limited Dominating Set for all fixed positive integers $k$. We also determine the exact $1$-limited domination number of the entire Goldberg family. This provides a further infinite family of cubic graphs supporting several open conjectures and proposed bounds concerning $(1,2)$-domination and induced cycles.

Let $p$ be an odd prime, let $m\geq1$ be an integer, and let $Q$ be a nondegenerate quadratic form on $\mathbb F_p^{2m}$. For a nonempty set $E\subseteq\mathbb F_p^{2m}$, write $\Delta_Q(E)=\{Q(x-y):x,y\in E\}$. We prove that, whenever $|E|>p^m$, \[ |\Delta_Q(E)|\gg \min\left\{\frac{p}{L_E},\, \frac{|E|}{p^{m-1}L_E^2}\right\}, \qquad L_E=\log\left(2+\frac{p^{m+1}}{|E|}\right), \] with an absolute implied constant independent of $p$, $m$ and $Q$. This confirms the Erdős–Falconer distance conjecture up to a logarithmic factor. In the anisotropic planar case $m=1$, for small sets, we also prove that \[ |\Delta_Q(E)|\gg\frac{|E|}{\log(2|E|)}, \qquad (1\leq |E|\leq p), \] which is also optimal up to a logarithmic factor.

Vision-Language-Action (VLA) models rely strongly on language for describing task information, despite having multimodal inputs. We hypothesize that other modalities in the state space may present opportunities for supplemental task conditioning, which may be particularly relevant in cluttered or otherwise ambiguous scenes. We introduce two tuned models to test this hypothesis: (1) an electrophysiology-conditioned VLA (EC-VLA) that incorporates 8-channel electromyography envelopes as continuous conditioning input concatenated to the proprioceptive vector, and (2) a visually-annotated VLA (VA-VLA) that incorporates visual segmentation annotations to the image inputs. On a cube-selection task evaluated across three participants, EC-VLA matches a language-prompted baseline in uncluttered, in-distribution conditions and substantially outperforms it in cluttered, out-of-distribution scenes. Similarly, VA-VLA shows modest improvements over a language-prompted baseline in in-distribution scenes with substantial improvement in cluttered, out-of-distribution trials. Together, these results provide strong evidence for the potential benefit of task-conditioning beyond language.

We prove that if the product of two class transpositions has finite order, then its order divides 840. This gives a complete affirmative answer to Question 18.48 in the Kourovka Notebook. We also obtain a criterion for the product of two class transpositions to have infinite order. In addition, we construct a pair of class transpositions whose product has order 840, showing that the bound is sharp.

Quantum key distribution (QKD) links are provisioned from security analyses of stationary channels, whereas the devices that determine the channel drift between recalibrations. Whether an eavesdropper who cannot alter the channel's own noise gains by following that drift has not been quantified. Adaptive eavesdropping is posed here as a constrained Markov decision process in which the attacker selects one circuit per round while the noise level follows an Ornstein–Uhlenbeck process and the abort condition is a budget over each block of rounds. The value of adaptation is bounded by the best fixed circuit and a dynamic-programming upper bound. The actions are learnt attacks. Whereas Decker et al. trained a parametrised circuit on a fixed gate template against a fixed channel, here the gate structure and rotation angles are searched jointly. This yields circuits compact enough to form a discrete action set, extending the construction to noise models lacking a known template, including the amplitude damping channel. On device-independent E91 under bilateral depolarising noise, a reinforcement-learning attacker raises her Holevo information from $0.135$ for the best fixed circuit to $0.348$ at zero detection, $98\%$ of the upper bound. On BB84 under a drifting bit-flip channel, she exceeds a conservative noise-indexed rule by $0.024$ in fidelity, reaching $99\%$ of the upper bound. Under stationary noise, the attacker's gain from basis asymmetry changes sign between an averaged and a per-basis error-rate constraint. The search, started from random gate sequences, recovers the analytical cloners and the collective-attack key rate, and meets the lower bound of the Winick–Lütkenhaus–Coles objective from above.

Heavy-quark spin dynamics in the quark-gluon plasma provides a potential probe of the interaction between heavy quarks and the medium. We develop a stochastic framework in which the random momentum kicks responsible for heavy-quark diffusion also induce spin rotation through Thomas precession. Starting from the Thomas-Bargmann-Michel-Telegdi equation and a Langevin equation for heavy-quark momentum, we derive a novel coupled spin-momentum Fokker-Planck equation. In the heavy-quark limit, where momentum equilibrates faster than spin, the momentum degrees of freedom can be integrated out, yielding a rotational Fokker-Planck equation for the spin orientation. This establishes a direct relation between the Thomas precession contribution to the spin-relaxation time $\tau_{s}$ and the heavy-quark momentum-diffusion coefficient $\kappa$. In the non-relativistic limit, we find $\tau_s=2\tau_p(m_Q/T)^2$, with $\tau_p$ being the momentum relaxation time. Using recent determinations of $\kappa$ from lattice QCD, strong-coupling estimates, $T$-matrix calculations, and heavy-flavor phenomenology, we obtain the corresponding Thomas precession contribution to spin relaxation times for charm and bottom quarks. Relativistic kinematics modify the result by only a modest amount over the temperature range relevant for heavy-ion collisions, while the uncertainty is dominated by that of $\kappa$. We emphasize that the result represents the Thomas precession contribution to heavy-quark spin relaxation; direct coupling to the chromomagnetic field provides an additional channel.

We discuss the triality between stochastic growth models in the KPZ universality class, the DSSYK model, and low dimensional dilaton gravity. The TASEP model, which will be our primary focus, is identified with the strong-coupling limit of two-dimensional quantum gravity. The Hamiltonian of DSSYK and the transfer matrix of ASEP coincide up to an additive constant, and we derive the exact expression for the resolvent of the corresponding transfer matrix in ASEP on a finite interval. We also mention the relation of cumulants with the Tutte polynomial $T(1,q)$ of the crossing graph dual to the chord diagram, which implies the relationship of the models considered with the $Q=0$ Potts model coupled with gravity. We further exploit the realization of all these models in terms of different versions of discrete and continuous random walks on two-dimensional manifolds, which parameterize the Hilbert spaces of the respective theories. The representation of TASEP as the growth model of heaps provides new insight into strong-coupling gravity, suggesting its interpretation as an emerging phenomenon. The new dualities between ASEP and q-TASEP models and heap models providing a useful growth interpretation have been developed.