Papers

Generative models are increasingly trained in self-consuming iterative loops, where users curate preferred samples from model-generated candidates and the curated samples are used to train future generations of the model. Prior work has largely assumed fixed user preferences, but in practice exposure to model outputs gradually reshapes what users perceive as desirable, creating a feedback loop in which model distributions and user preferences co-evolve. We take a first step toward understanding the long-term behavior of such coupled dynamics. We show that when training relies entirely on user-curated synthetic data, iterative curation amplifies initial biases and drives the system toward one of multiple singleton equilibria in which the instance holding an initial advantage eventually dominates. In contrast, injecting reference data into training at a sufficiently large rate fundamentally changes the dynamics and yields a unique globally attracting equilibrium. Building on this insight, we study how reference-data injection can be used to control long-term outcomes, and propose an efficient algorithm that jointly selects a reference distribution and its mixing weight to steer the coupled system toward equilibria that preserve desired attributes while minimizing data collection costs.

CXL memory expands single-node memory capacity for in-memory databases but has higher latency and lower bandwidth than local DDR. Hybrid DDR–CXL databases require joint indexing and data distribution design. Indexing designs differ in access and migration paths and constrain the placement of indexes and tuples, creating trade-offs in runtime performance, DDR memory efficiency, and system integration complexity. Their performance impact is thus difficult to determine. Indexes and tuples may differ in access characteristics: placing them in the same tier may reduce DDR efficiency, while separate management adds tracking and decision overhead. We propose five indexing designs based on two approaches: treating the two tiers as a unified data space or managing them separately. We analyze their trade-offs and underlying causes and develop adaptive data distribution optimization for single-index designs in which the database explicitly manages distribution. The method manages index objects and tuples separately, reduces metadata overhead through hierarchical hotness tracking and an index object residency policy, and extends benefit-aware admission and randomized eviction to determine and adjust their placement according to each type's expected benefits and memory footprints. We implemented the designs in a hybrid DDR–CXL database prototype and evaluated them using YCSB. The single-index design with direct addressing achieves the best performance under most workloads and system configurations. The dual-index design performs better mainly when DDR capacity is limited or accesses are highly concentrated, and has relatively low integration complexity. Adaptive distribution optimization improves DDR memory efficiency and system performance, enabling single-index designs to achieve up to $1.59\times$ the throughput of their counterparts with non-separated management.

Conventional Chern insulators rely on breaking time-reversal symmetry via magnetic fields or synthetic gauge fields. Here we introduce a fundamentally different paradigm: a static lattice without any gauge field becomes a Chern insulator solely through the cooperation of two non-Hermitian ingredients: on-site loss and non-reciprocal coupling. Neither effect alone suffices; only their synergy opens a topological gap and gives rise to robust chiral edge states with a nonzero Chern number. The underlying mechanism originates from a non-Hermitian chiral molecule formed by the lossy sites, whose dynamically dominant mode carries an orbital angular momentum that effectively generates a synthetic flux after the fast-decaying degrees of freedom are eliminated. Our results establish non-Hermitian cooperation as a versatile resource for inducing Chern topology without external fields or temporal modulations, opening a new route to topological phases in open classical and quantum systems.

Retrieval diversification is widely available in retrieval-augmented generation (RAG) frameworks, yet prior studies disagree on whether it improves retrieval and answer quality. We show that its effectiveness varies primarily with candidate-pool redundancy, in a pattern consistent with the number of distinct evidence pieces a query requires. Using controlled near-duplicate injection and production-style overlapping chunking, we find that diversification harms relevance, evidence coverage and answer quality on clean pools, but becomes beneficial on multi-evidence tasks when redundancy causes nearest-neighbor retrieval to select repeated passages. We therefore introduce a query-adaptive rule that diversifies only when the effective number of distinct documents in the nearest-neighbor top-$k$ selection falls below the query's evidence requirement. Computed from existing embeddings, the rule captures most of the achievable gain, transfers across datasets and encoders and automatically reduces to nearest-neighbor retrieval for single-evidence queries. We also introduce RNG-Score, a geometric reranker with an exact nearest-neighbor fallback whose margin indicates duplicate structure. Overall, we conclude that diversification should be used selectively, based on observable redundancy and evidence requirements.

Multimodal representations enable zero-shot classification and retrieval, but aligning independently trained models usually requires large amounts of paired data. Yet, the Platonic Representation Hypothesis suggests that models trained on different modalities may converge spontaneously toward a shared representation geometry. But then, do we even need paired examples for cross-modal alignment? Remarkably, we show that paired examples are unnecessary for coarse cross-modal alignment. Our simple Wasserstein Procrustes method with a coarse geometric initialization aligns two disjoint embedding sets by estimating a single orthogonal map without seeing any pairs. Across datasets, modalities, and unimodal models, we show that we can consistently align independently trained representations without pairs, and standard geometric alignment metrics accurately predict when this is possible. Nevertheless, we can naturally benefit from paired examples. In the very few-pair regime, our method substantially outperforms existing ones, while staying competitive with pair-based methods with more added examples. Finally, we demonstrate that the resulting alignments can enable text-to-image generation without paired examples. These results show that independently trained models often share enough geometry to establish cross-modal correspondence with little or no paired data.

A graph $G$ is $k$-degenerate if there exists an ordering $v_1, v_2, \dots, v_n$ of its vertices such that each vertex $v_i$ has at most $k$ neighbors $v_j$ in $G$ with $j < i$. A well-ordered $k$-degenerate graph is a labeled graph on the vertex set $\{1, 2, \dots, n\}$ in which every vertex $i$ has at most $k$ neighbors among $1, 2, \dots, i-1$. We present the first simple algorithms that generate, rank, and unrank cyclic pivot Gray codes for well-ordered $k$-degenerate graphs, where consecutive graphs differ by the addition, removal, or pivoting of a single edge. Our algorithm generates each well-ordered $k$-degenerate graph in constant amortized time per graph, using $O(n^2)$ space, while ranking and unranking take $O(n^2)$ time and $O(n^2)$ space.

The widespread deployment of generative AI has made it increasingly difficult to distinguish synthetic content from real data. Consequently, synthetic data is inevitably incorporated into the training pipelines of future model generations, forming a self-consuming training loop. Prior work has studied the effects of such recursive self-consuming training, but analyses have largely been limited to isolated models, where a model consumes only its own synthetic data, or to simplified interactions between two models. This paper takes a first step toward understanding networked self-consuming generative models, in which multiple models consume synthetic data generated by one another through complex interaction pathways. We introduce a theoretical framework representing models as nodes in a directed, weighted graph, with edge weights governing the flow of synthetic data among models. Using this framework, we analyze the long-term behavior of networked models under retraining dynamics, establishing conditions for convergence and characterizing the resulting fixed points. We further investigate how the system's long-term stability and diversity are shaped by each model's access to real data, cross-model data consumption, and the structure of the interaction graph.

Audio-visual multi-segment grounding (AV-MSG) in untrimmed videos, reasoning over audio-visual evidence and predicting multiple segments for a query, is a fundamental problem but remains challenging. Visual-only models overlook complementary acoustic cues, while audio-visual models often fail to calibrate the number of events - a phenomenon we refer to as count miscalibration. We present TiTok, an audio-visual large language model (AV-LLM) that localizes an arbitrary number of temporal event segments for each query. For precise boundary prediction, we introduce the Time Token Interleaving (TTI) method, which explicitly injects special time tokens into the audio-visual stream to align input-side temporal perception with output-side temporal prediction. We further propose decoupled, multi-segment-oriented rewards for reinforcement learning, consisting of global, local, count, precision, and format rewards, optimized with Group reward-Decoupled Normalization Policy Optimization (GDPO). To assess the performance on AV-MSG, we establish a new UnAV-100-based evaluation protocol, and propose the CountF1 metric for quantifying count miscalibration that overlap metrics fail to capture. TiTok reaches 65.7 mIoU and 0.58 CountF1, achieving state-of-the-art performance. Our code is available at this link.

Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard. We introduce diffusion waltz, an MCMC method using SDEdit-style noising-denoising as a proposal, corrected via Metropolis-Hastings for exact posterior sampling without prior evaluation. We further propose injecting observations into the proposal while preserving exactness, using a gradient-free ensemble Kalman update. On a non-differentiable Navier-Stokes initial condition recovery task, diffusion waltz outperforms existing baselines across different noise and nonlinearity regimes.

We prove a single-logarithm bound for the eigenvalues in the plunge region of Fourier concentration operators, removing the extra logarithmic factor in the Kulikov–Dam Larsen bound for two general admissible sets throughout each fixed exponential window. For bounded spatial and frequency sets $A,B\subset\mathbb{R}^d$ of positive measure with finite upper codimension-one Minkowski boundary content, the number $\Lambda_\varepsilon(cA,B)$ of eigenvalues in $(\varepsilon,1-\varepsilon)$ satisfies $\Lambda_\varepsilon(cA,B)\le C(d,A,B,\beta)c^{d-1}D(1+\log_+(c/D))$, where $D=\log(1/(\varepsilon(1-\varepsilon)))$, for every fixed $\beta>0$, $c\ge2$, $0<\varepsilon<1/2$, and $D\le\beta c$, with $\log_+t=\max(0,\log t)$. The argument uses positive band-limited smoothing and requires no symmetry, convexity, or connectedness. In dimension two, the corresponding exponential-window estimate has a constant uniform in the window parameter. We also determine the optimal coordinate-Lipschitz constant $d-1$ for recursive decompositions of balls and standard simplices in every dimension, and obtain box-frequency estimates with explicit geometric constants. For $C^1$ convex bodies in three dimensions, the optimal infimum of recursive coordinate slopes is $2$. Uniform real-order Bessel estimates give independent disk and ball bounds at every spectral threshold, including an explicit deep-tail term. For smooth strictly convex planar frequency bodies with positive curvature, we prove correlation estimates for aligned Gaussian packets at arbitrary relative scales and quantitative lower bounds on the cost of estimating spatial blocks separately. Together these results connect the global spectral bound with sharp geometric constructions and the cancellation retained by grouping boundary interactions.

Resolving the anomalous conductivity exponent of the symmetric $\beta$-Fermi–Pasta–Ulam–Tsingou chain by molecular dynamics can require very large systems because of long finite-size crossovers and thermal-contact resistance. Motivated by this computational challenge, we derive a long-wavelength continuum description and investigate whether the kinetic-theory scaling $\kappa\propto L^{2/5}$ becomes accessible with a moderate number of numerical degrees of freedom. The nonlinear elastic field retains the cubic stress of the microscopic interaction and exchanges heat with Langevin reservoirs. A flux-conservative spatial discretization constructs the force and energy current from the same stress, providing a consistent interior transport estimator. For $L>8$, corresponding to approximately $10^3$ mesh nodes and above at the reference resolution, the fitted exponent is $0.399\pm0.004$. Mesh refinement supports the stability of this exponent between the two finer resolutions, although the conductivity amplitude remains resolution-dependent. The main result is thus an accessible finite-size regime near $2/5$, rather than convergence of the absolute conductivity as the mesh spacing vanishes. This formulation provides a practical route to studying anomalous transport in anharmonic systems and a conservative continuum framework for investigating energy flow in nonlinear elastic media.

In this paper, we establish an $L^2$ maximal inequality for partial sums of Gaussian-subordinated random variables. More precisely, let $f:\mathbb{R}\to\mathbb{R}$ belong to $L^2(\gamma)$ and have Hermite rank at least $d$, where $\gamma$ denotes the standard Gaussian measure. If the covariance matrix of the underlying Gaussian family, with standard normal marginals, satisfies a uniform $d$th-power row bound $K$, then the $L^2$ norm of the maximal partial sum is bounded by $C_{d,K}\sqrt n\,\|f\|_{L^2(\gamma)}$. The constant $C_{d,K}$ is independent of $(f,n)$ and depends on the covariance structure only through $K$. As a consequence, our $L^2$ maximal inequality controls Hermite tails uniformly in the path norm. In discrete time, this yields the Breuer–Major–Donsker principle under the sole finite-variance assumption, removing both the additional $L^{2+}$-integrability assumption of Nourdin and Nualart (Probab. Theory Related Fields, 2020) and the prediction-theoretic or decimation assumptions of Mansanarez, Poly, and Zheng (arXiv:2607.11469). In continuous time, we likewise obtain the Breuer–Major–Donsker principle under finite variance alone, removing the additional moment assumption of Campese, Nourdin, and Nualart (Ann. Probab., 2020). For the nonstationary self-similar setting considered there, we remove the same extra moment assumption in the subcritical regime, while a separate leading-chaos argument yields the corresponding logarithmically normalized critical limit. [Abstract shorten to meet arXiv requirement]

Optimal control of open quantum systems governed by the Lindblad master equation requires the repeated solution of forward and adjoint evolution equations. For large Hilbert spaces, these computations demand numerical methods that are structure-preserving, accurate, and computationally efficient, while remaining compatible with nonsmooth optimization techniques. In this work, a unified framework for optimal control of Lindblad equations is presented. The continuous optimality system is derived from the Pontryagin maximum principle and solved by a sequential quadratic Hamiltonian (SQH) method. Its numerical realization is based on second-order exponential midpoint propagators for the forward and adjoint Lindblad equations with time-dependent Hamiltonians. Full-rank schemes preserving the Hermitian and positive-semidefinite structure of the density matrix are developed together with low-rank formulations that substantially reduce storage requirements and computational cost. Rigorous error estimates are established for the full- and low-rank forward and adjoint propagators. Numerical experiments confirm the predicted convergence rates, demonstrate the effectiveness of the low-rank approximations, and illustrate the performance of the proposed FREM-SQH and LREM-SQH algorithms for optimal control problems with smooth and nonsmooth control costs.

We study the problem of sampling from a target distribution $\pi(x)\propto e^{-f(x)}$ supported on a convex set $ X\subseteq\mathbb R^d$, when the potential $f$ is accessible only through a stochastic first-order oracle. Mirror Langevin algorithms provide a natural approach to constrained sampling by transporting the problem to an unconstrained dual space and discretizing the resulting Mirror Langevin diffusion. Existing implementations, however, typically use a fixed discretization step size and consequently retain a nonvanishing discretization bias at any fixed step size. Moreover, their direct extension to settings with noisy gradient information entails the challenge of controlling both discretization and stochastic-oracle error. We study a stochastic first-order version of the Mirror Langevin Algorithm (sFO-MLA) and, as our main contribution, develop a warm-started two-loop implementation in which an outer loop progressively decreases the step size while an inner loop runs sFO-MLA (with a fixed step size) for an appropriately chosen epoch length. The construction provides a principled schedule linking step sizes and epoch lengths, so that successive epochs warm-start from increasingly accurate distributions rather than repeatedly paying the cost of mixing from a cold start. We establish finite-time Wasserstein guarantees for sFO-MLA that explicitly separate mixing, Euler–Maruyama discretization, and stochastic-gradient errors. These bounds yield a fixed horizon rate of $\widetilde O(T^{-1/2})$ and show that the two-loop scheme removes the associated logarithmic penalty, attaining the canonical $O(T^{-1/2})$ rate under a geometric step-size schedule and corresponding epoch lengths. We illustrate the methodology in two statistically distinct settings.

LLM-based formal provers can retrieve relevant lemmas and prior proofs, but relevance alone does not say whether a mathematical method can be used on the current theorem. A method has prerequisites, a target, an intended action, and obligations that its use leaves to prove. Methods that look equally related to a theorem may therefore differ substantially in whether they offer a plausible next step. We formulate this as an applicability-aware method-selection problem and introduce self-advertisement: before candidates are ranked, a model generates a problem-specific proposal for each one, stating what part of the goal it targets, what action it would take, and what conditions that action requires. We organize 82 reusable methods from Putnam 2000-2014 as Method Contracts, which pair applicability descriptions with Mathlib anchors, a checked example or scaffold, and expected proof obligations. A single batched call elicits proposals across the library; vague or unsupported proposals are demoted, yielding a ranked shortlist accompanied by inspectable claims about each candidate's use. We analyze when similarity-based representations cannot distinguish methods with different applicability, how errors in applicability estimates affect shortlist quality, and what a checked scaffold guarantees under its stated assumptions. Against lexical, embedding, and embedding-plus-LLM reranking baselines, self-advertisement achieves 95.0% hit@5 on Putnam 2015-2025, compared with 84.2% for the strongest reranker. On IMO ProofBench, it achieves 91.7% compared with 88.3%. These results indicate improved coverage of annotated methods in the retrieved shortlists, particularly on Putnam.

We present TutorLoop, a sensor-in-the-loop system that regulates student learning behaviors by delivering adaptive feedback based on real-time cognitive states. Unlike prior large language model (LLM) tutors that directly depend on scenario-specific content, TutorLoop operates on sensor-derived signals captured via webcams. Moreover, unlike direct cognitive-to-feedback mappings that are short-sighted, the system employs a deep reinforcement learning (DRL) agent to optimize the feedback type across the entire learning process. Finally, another LLM tutor refines feedback into human-like, context-aware messages. We evaluate TutorLoop in a large-scale user study (N=187), where a model trained offline is directly applied to a new learning task without retraining. Results show that TutorLoop provides less frequent yet more effective interventions, improving attention, reducing workload, increasing engagement, and ultimately enhancing learning outcomes. These findings highlight the potential of closed-loop, sensor-driven feedback for scalable human-AI integrated systems to support learning.

Quantum electrodynamics (QED) currently features prominently at the precision frontier in describing the structure of atoms and molecules. Dominant QED effects are governed by the electronic structure in the vicinity of the nucleus and are therefore generally regarded as atomic in origin, with molecular contributions largely arising from additive atomic contributions. By studying the nuclear magnetic resonance shielding tensors of thallium in Tl$X$, we reveal genuinely molecular QED effects that strongly depend on the bonding partner ($X$ = F, Cl, Br, I, At) and are absent in the Tl$^+$ ion.

In tropical regions, their agricultural sectors remain highly dependent on manual labor for fruit harvesting. On large-scale farms, this dependency often results in significant labor cost and logistic complexities. This project presents the development and simulation of a voice-controlled Unmanned Aerial Vehicle (UAV) system designed to automate harvesting tasks in extensive plantations. The proposed system integrates speech recognition using Whisper [1] and LLM, computer vision-based ripeness classification, and adaptive path planning within a unified framework. The entire system is modeled and validated in a Gazebo simulation environment, allowing performance evaluation under controlled agricultural scenarios

Cine cardiovascular magnetic resonance (CMR) analysis relies on multi-frame sequences capturing the full cardiac cycle. However, standard multi-frame acquisition depends heavily on electrocardiogram (ECG) gating and repeated breath-holds, posing challenges in uncooperative populations, resource-limited settings, and temporally corrupted datasets. Existing methods that synthesize full cardiac sequences either rely on explicit ECG signals to parameterize myocardium function, or employ deformable registration without physiological constraints, failing to faithfully reproduce clinically relevant dynamic metrics such as ejection fraction (EF) and ventricular contraction magnitude. We present PhaseFlow, a unified generative framework that overcomes both limitations. PhaseFlow estimates a non-linear cardiac phase signal directly from the input sequence via a segmentation-derived left-ventricular (LV) area curve, capturing the asymmetric dynamics of systole and diastole without any ECG dependency. At inference, this phase signal is provided by a pathology-specific template, informing phase-specific frame generation. A rectified flow model conditioned on the phase and slice position synthesizes the full cardiac motion trajectory in the latent space, decoded into a diffeomorphic displacement field that warps end-diastole pixel intensities directly, eliminating the reconstruction blur often accompanying the variational autoencoder. On the ACDC benchmark, PhaseFlow achieves superior physiological fidelity and image realism, with best LV volume curve $R^2$, structural similarity (SSIM) and generative quality (FID) among all baselines. Ablation studies confirm that each proposed component contributes measurably to the overall performance.

As text-to-SQL systems move beyond demonstrations toward real-world deployment, ambiguity in user questions becomes a primary source of errors. Such ambiguities are often subtle, domain- or data-specific, and can silently cause system outputs to deviate from the user's true intent. Ambiguity is traditionally addressed through conversational clarification, which is often inefficient, cognitively demanding, and poorly aligned with real-world user workflows. We propose structured disambiguation, a new paradigm in which ambiguity is resolved through explicit, constrained interactions rather than free-form dialogue. We construct ARCS (Ambiguity Resolution Corpus for SQL), the first text-to-SQL benchmark featuring naturally occurring, unconstrained ambiguities over real-world databases, with complete annotations of all valid ambiguity points, interpretations, and SQL queries. Experimental results show that text-to-SQL remains challenging in the presence of ambiguity: gpt-6-sol achieves only 51% end-to-end execution accuracy, and no open-source model exceeds 27%.

This paper develops a distributionally robust optimization (DRO) framework for identifying the frequency response function (FRF) of an unknown linear time-invariant system from repeated noisy non-steady-state input-output measurements. Building on a recent frequency-domain extension of Willems' fundamental lemma, we formulate FRF estimation as a DRO problem, wherein robustness is desired with respect to the unknown probability distribution generating the noisy data. The proposed estimator computes FRF estimates by minimizing a convex upper bound on the DRO cost and allows for frequency-dependent calibration of the Wasserstein metric; the tractable upper bound consists of an empirical fit and a regularizer that penalizes the largest weighted sensitivity to spectral perturbations. Under suitable assumptions, we prove that the FRF estimation error is upper bounded by the optimal value of the DRO problem. The method is validated via a simple numerical study, which demonstrates improved performance under severely heavy-tailed noise.

Studies with 1-m class telescopes have now established that glints from satellites and space debris are the main obstacles to searches for sub-minute optical transients. Here, we report a study of this foreground using observations from the Legacy Survey of Space and Time (LSST) with the Simonyi 8.4-m telescope at the Vera C. Rubin Observatory. From 2,955 pairs of consecutive 30-s exposures, spanning 4,755 deg$^2$ of unique sky area and an area-time coverage of 472 deg$^2$ hr, we identified a population of faint, PSF-like, sub-minute events, including isolated events with no linear sequences of repeated flashes (tracklets) indicative of a tumbling satellite. We extended measurements of this population to the faintest magnitudes yet probed, finding a lower-bound to the occurrence rate of $(9.55 \pm 0.14) \times10^6\,$sky$^{-1}\,$day$^{-1}$ to $\sim23$ mag (median of $\sim22.3$ mag). The large aperture of the Simonyi 8.4-m telescope provides an additional discriminator: orbital debris in low-Earth orbit are sufficiently out of focus that they are filtered out. We find that, for a $1^{\prime\prime}$ PSF, unresolved events are constrained to distances beyond 1,732 km, and identify a previously unreported population of glints consistent with medium-Earth-orbit altitudes with estimated sizes of order $\sim1$-3 mm. We also report two isolated events observed along sight lines deep within the Earth's shadow, for which a sunlit-debris origin is disfavored. The scant evidence is consistent with an eclipsing binary and a stellar flare. The robust way forward for sub-minute transients is simultaneous observations of the same field by two (or more) widely separated telescopes. The resulting measurement of parallax will cleanly eliminate local (primarily orbital) debris, clarifying the nature of this transient foreground. This understanding will help astronomers probe truly celestial optical bursts.

Artificial Intelligence (AI) data centers are emerging as converter-dominated, parameter-rich electrical systems whose dynamic response depends on fast workload-driven demand variations, tightly regulated data-hall converters, and coordinated on-site sources. Assessing such systems by repeatedly solving nonlinear time-domain models for every outage, load realization, and parameter perturbation is computationally expensive and provides limited insight into response sensitivity. This paper presents a trajectory sensitivity (TS)-based dynamic assessment framework for a self-contained AI data center supplied by a 2 kV DC microgrid with a grid-tied interface. The model includes time-varying data-hall load profiles, a voltage source converter (VSC), battery energy storage systems (BESS) units, supercapacitors, and synchronous-generation-side sources. For each disturbance, firstly, TS are computed along the nonlinear disturbance trajectory, capturing the local effect of source trips, data-hall outages, converter controls, and load ramps. Later, the computed TS data is used to estimate system trajectories under simultaneous parameter perturbations. Validation against full nonlinear ODE simulations with $\pm 15\%$ perturbations shows close agreement. In addition, the TS-based approach reduces computational time of dynamic-response evaluations from seconds to milliseconds, demonstrating its potential as a scalable screening tool for AI data center dynamics.

Reliable volumetric segmentation is critical for clinical diagnostics, yet foundation models such as MedSAM remain deterministic and lack calibrated uncertainty under distribution shift. Existing conformal prediction methods offer statistical guarantees but are frequently applied in 2D and assume symmetric error distributions, so they do not capture the class-specific biases that arise in 3D multi-class segmentation. We propose Class-Aware Asymmetric Weighted Conformal Prediction (CA-WCP), which combines latent-space density-ratio weighting for covariate shift with directional quantiles for the lower and upper volume bounds, and scales each bound by a class-specific asymmetry factor derived from validation-set false-positive and false-negative rates. We prove that CA-WCP retains the weighted-exchangeability marginal coverage guarantee for every class, and we evaluate it on 3D brain tumor segmentation (BraTS 2020) and on a synthetic multi-organ CT benchmark constructed under covariate shift. On both benchmarks the 95% Clopper–Pearson interval for the observed coverage of CA-WCP contains the nominal 90% level for every semantic class, while interval width is reduced by 8–14% relative to symmetric weighted conformal prediction. We further encode the calibrated intervals into structured prompts for a multimodal large language model to produce uncertainty-conditioned radiology reports, linking distribution-shift-aware uncertainty quantification to interpretable clinical communication.

An adaptive system can retain an earlier estimate while changing what that estimate is used to guarantee. The guarantee depends on the experiment that produced the evidence, including how its target was selected and which assumptions connect it to the current claim. We show that past-measurable selection preserves future martingale dynamics without preserving a unit expected starting value. An exact finite counterexample, using a strictly positive family, refutes a published changing-prior extension as stated with probability one and rules out unrestricted bounds based only on switch count and the error level. We give a paid-start multi-switch correction and establish $m$ as the sharp worst-case expected starting-moment cost for an unstructured family of $m$ hypotheses. We then develop Adaptive Assurance, a framework in which statistical events retain their experiment, funding and outcome bindings while claims and premise dependencies change. Compatible-outcome projection supports reuse, selective invalidation, fresh acquisition and auditable decisions. Two histories can have identical current regions yet require different responses to a later edit, making evidence origin part of the assurance state. Studies in six public-recorded domains exercise heterogeneous outcomes and access contracts. Component interventions expose erroneous inheritance and unnecessary resets. The framework separates conditional guarantee recovery from competence adaptation, with explicit costs for evidence, computation and verification.

We prove Z-stability for all simple, separable, pure, nuclear C*-algebras. Combining this with very recent work of Thiel completes the proof of the Toms-Winter conjecture. We do this through the framework of II_1 factorial tracially complete C*-algebras. We characterise regularity for these algebras in various terms. In particular they are regular if and only if they have real rank zero and the Murray-von Neumann equivalence classes of projections correspond to continuous affine functions from the designated traces to [0,1]. As an application of our analysis of ultrapowers of tracial completions, we show simple pure C*-algebras whose quasitraces are traces are K-stable. In the amenable setting we give a local quantisation result, a la Popa, for II_1 factorial amenable tracially complete C*-algebras, which obtains hyperfiniteness from regularity conditions. Our Z-stability results follow from this together with a theorem of Matui and Sato. An initial version of an essential lemma in the Bauer trace simplex case was obtained from ChatGPT Astra.

Predicting the dynamic polarizability tensor of organic molecules is essential for simulating light-matter interactions in optoelectronic devices, yet conventional quantum-chemical methods such as time-dependent density functional theory (TD-DFT) are computationally expensive and limit large-scale screening. We present an equivariant graph neural network architecture that predicts frequency-dependent, complex-valued dynamic polarizability tensors directly from readily available molecular information, such as 3D geometry and UV-vis spectra. The model learns to approximate the shape and magnitude of the dynamic polarizability tensor, capturing both dispersive and absorptive features that define the molecular optical response. We evaluate the model on molecules from both the QM9 dataset and the Harvard organic photovoltaic dataset using various metrics, including the earth mover's distance, which is suitable for comparing spectral quantities. For both datasets, the model successfully reproduces the main features of the dynamic polarizability tensor and generalizes across diverse molecules. To assess the applicability, we further validated the model using a downstream workflow to calculate the optical properties of organic photovoltaic devices. We used the model-predicted polarizabilities to perform device-level optical simulations, yielding charge carrier generation rates in agreement with TD-DFT-based results ($R^2 = 0.94$). Our approach offers a promising complement, or even an alternative, to conventional methods such as TD-DFT, enabling faster and more efficient screening of photoactive organic molecules for optoelectronic applications.

Poly(1,3-dioxolane) (pDXL) is a chemically recyclable polyether that can be synthesized by living cationic ring-opening polymerization with precise control of chain length into the ultra-high-molecular-weight (UHMW) regime, where it acquires enhanced mechanical properties. Like most polymers, however, it has amorphous condensed-phase structure, and diffraction measurements alone cannot resolve the atomistic microstructure that underlies them. In this work, we predict the ensemble of the pDXL microstructures by applying a recently developed AI-accelerated ab initio bottom-up polymer structure prediction (AI$^{2}$-BPSP) framework that simulates the living polymerization of pDXL under experimental synthetic conditions with machine-learning force fields trained within van der Waals-corrected hybrid density functional theory. Partitioning the predicted X-ray and neutron diffraction signal between the growing chain and the surrounding monomer resolves its dominant feature into two counteracting modes: a monomer contribution near $q \approx 1.5$ Å$^{-1}$ that decays as monomer is consumed, and a polymer contribution near $q \approx 1.6$ Å$^{-1}$ that is absent in oligomers and grows with chain length. This work paves the way to direct accuracy validation of these statistically significant, first-principles, and chain-length resolved diffraction predictions against experiments.

Non-reciprocal lattices offer a flexible setting for directional wave transport, raising the question of how enhanced internal scattering translates into transmission between fixed external ports. We address this question for non-reciprocal Su–Schrieffer–Heeger (SSH) chains with staggered gain and loss by relating the reference-dependent insertion kernel $K_p=VG_pV$ to the coherent transmission intensity $T$. On a fixed finite graph, a strong-insertion expansion gives a contribution proportional to $\gamma^{1-d}$, whose coefficient is the signed sum of shortest directed paths of length $d$. When this sum is nonzero, it sets the leading behavior independently of fixed diagonal losses; when it cancels, those losses can enter the first surviving higher-order term. For a fixed cross-sublattice endpoint channel, transmission has a strictly negative slope at every nonzero differentiable stationary point of the kernel magnitude. In the weak-insertion regime, the reference-system coefficient $\chi=-\mathrm{Re}\,\mathrm{Tr}[(G_{0p}Z)^2]$ predicts the initial transmission change for symmetric SSH ports, and $\chi>0$ together with a strictly stable baseline guarantees local stable enhancement. Finite-chain calculations and driven dynamics connect these results to observable response and distinguish asymptotic convergence from transient settling. A strictly dissipative short-chain example exhibits local enhancement without net power gain. Together, these results separate graph-path structure, coherent port response, and dynamical establishment, providing channel-specific criteria for interpreting internal scattering.

We study the uniqueness of optimal $1$-embeddings on closed surfaces up to weak equivalence. Answering a question of Suzuki in the negative, we show that for every closed surface other than the sphere, the projective plane and the Klein bottle, there exists an optimal $1$-embedded graph admitting two weakly inequivalent optimal $1$-embeddings. Our construction is given explicitly on the torus and is then extended to other surfaces through a suitable connected-sum construction that preserves weak inequivalence. As a consequence, we also obtain optimal $1$-embedded graphs with exponentially many pairwise weakly inequivalent optimal $1$-embeddings as the genus increases.