Papers

Multi-cancer segmentation in computed tomography (CT) is fundamentally limited by the scarcity of tumor masks across different organs. We present Merlin Plus, the first large-scale CT dataset with radiologist-created tumor masks across 9 organs. Merlin Plus extends the Merlin dataset by adding 1,153 per-voxel tumor masks and longitudinal metadata. To create these tumor masks, we developed a report-based active-learning framework in which radiology reports identify tumor cases for annotation and support training of a tumor segmentation model. The model generates initial masks, which radiologists review and correct to produce the final masks, reducing annotation burden while maintaining high-quality annotations. Besides tumor masks, the longitudinal metadata in Merlin Plus enables temporal modeling of cancer progression. By directly addressing the major bottleneck of limited multi-cancer segmentation masks, Merlin Plus supports scalable multi-organ cancer detection, segmentation, and longitudinal analysis in CT. Dataset is available at: https://github.com/MrGiovanni/MerlinPlus

An assistant that serves the same user over a long horizon has to answer from what that user has revealed: which preferences still hold, which were revised, and which constraints apply now. Retaining that information is not the same as acting on it, and the two are usually optimized as if they were. Keeping the information as text makes the reader's input grow with the retained history, while compressing it into a fixed number of latent vectors bounds the interface but is typically trained to reconstruct text or imitate reference answers, both of which are scored on sequences the reader never produced. We present MemFold, which optimizes a fixed-budget soft memory by the behavior it supports. A query-conditioned textual memory is compressed into K continuous vectors that form the reader's memory interface, and the reader is then trained on its own rollouts under two complementary signals: group-relative rewards for task outcomes, and confidence-gated on-policy distillation in which a frozen textual-memory teacher re-scores the student's sampled tokens under the textual memory. The teacher is never sampled from, so supervision stays on the student's current distribution and adds no autoregressive decoding; at inference it is removed entirely. Across three Qwen backbones, MemFold attains the highest accuracy we measure on PersonaMem-32K and PersonaMem-128K, with margins that widen at the longer history length, and transfers to PrefEval and LongMemEval without target-domain training. Ablations attribute most of the task gain to the reward term and a smaller additional gain to the teacher signal, and memory interventions show that the reader depends on the instance-specific content of its soft memory.

Context tokens in a transformer-based language model can be absorbed into the model's weights as a multiplicative operator. We study this operator in the setting of safety instructions and show that influencing its dominant eigenvalue modulates how strongly the instruction shapes generation. We derive a Contrastive Safety Loss with a suppression weight that controls the tradeoff between emphasizing the safety instruction on harmful queries while suppressing it on harmless queries. Varying the suppression weight maps a relationship between the attack success and the over-refusal rates, supporting the hypothesis that the operator's eigenvalue acts as a continuous dial for the instruction's influence. Moreover, this relationship holds relatively independently of how the Safety Loss is parameterized, yielding Pareto-improved safety instructions for appropriate values of suppression weight.

Diffusion models enable high-quality visual generation, but iterative denoising remains computationally expensive, especially under classifier-free guidance (CFG), which requires both conditional and unconditional evaluations. Training-free caching reduces this cost by reuse of previously computed features or predictions. However, existing branch-local reuse criteria do not explicitly account for how cache errors combine under CFG or how local perturbations affect the final output. We identify two misalignments in cache control: a branch-guided mismatch, where guided error depends on both the magnitudes and alignment of branch errors, and a local-final mismatch, where the downstream impact of a local error varies across timesteps. We propose RA-CFGCache, a Risk-Aligned Caching framework under CFG that incorporates both factors while keeping the sampling schedule and guidance rule fixed. CFG-aware Guided-Risk Composition combines existing branch-wise proxies using CFG coefficients and offline-calibrated cross-branch alignment. Propagation-Aware Rescaling further weights the resulting guided-risk estimate with a timestep-dependent propagation prior calibrated from isolated reuse perturbations. An online threshold controller then determines when to jointly refresh or reuse both branches. Experiments on FLUX.1-dev, Wan2.1-T2V-1.3B, and CogVideoX-2B demonstrate improved efficiency–fidelity trade-offs over evaluated training-free caching baselines. Moreover, RA-CFGCache is compatible with diverse base proxy families, including TeaCache-, DiCache-, and MagCache-style estimators, and consistently improves fidelity at nearly unchanged latency. Code is available at https://github.com/yiming-l21/RA-CFGCache.git.

LiDAR relocalization aims to estimate the global 6-DoF pose of a sensor in the environment. However, existing regression-based approaches often encounter limitations in dynamic or ambiguous scenarios, as they typically prioritize single-frame inference, leaving the potential of spatio-temporal consistency across scans not fully explored. In this paper, we propose a Temporal-aware Localization framework (TempLoc) designed to enhance the robustness of outdoor localization by effectively modeling sequential consistency. Specifically, a Global Coordinate Estimation module is first introduced to predict point-wise global coordinates and associated uncertainties for each LiDAR scan. A Prior Coordinate Generation module is then presented to estimate inter-frame point correspondences by the attention mechanism. Lastly, an Uncertainty-Guided Coordinate Fusion module is deployed to integrate both predictions of point correspondence in an end-to-end fashion, yielding a more temporally consistent and accurate global 6-DoF pose. Experimental results on the NCLT and Oxford RobotCar benchmarks show that our TempLoc outperforms state-of-the-art methods by a large margin, demonstrating the effectiveness of temporal-aware correspondence modeling in LiDAR relocalization.

Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum $\hat p_x$, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to $\sy$. The CD term of a two-waveguide coupler is itself proportional to $\sy$, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the $\sigma_z$–$\sigma_x$ plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as $\dot{\xo}=\dot\theta/(\gamma\dbeta^{2})$. The expression agrees with the numerical offset search to $0.3\%$ and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.

We study the computational cost and stability of positive cubature and hyperinterpolation on a truncated conic surface with a Jacobi-type weight. A classical quadratic disk-to-cone map is formulated as a measure-preserving $\mathbb Z_2$ quotient. It identifies degree-$m$ conic traces with even disk polynomials of degree at most $2m$ and gives a two-way correspondence between positive degree-$2n$ cone cubature and centrally symmetric positive degree-$(4n+1)$ disk cubature. Consequently, Möller's lower bound and the node excess above it transfer exactly, producing compressed non-product cone rules from near-minimal disk formulas. The quotient also transfers reproducing kernels and hyperinterpolation operators. Every positive degree-$2n$ cone rule yields an exact $L^2$ sampling isometry on $\Pi_n(V)$, so the weighted sampling matrix has condition number one, independently of the number and geometry of its nodes. The associated Lebesgue constants satisfy the rule-independent bound $\Lambda_{n,\gamma}^V\ge c_\gamma n^{\gamma+1}$ for every $\gamma>-1$. For nonnegative half-integer $\gamma$, the matching upper bound holds, giving the sharp universal order $\Lambda_{n,\gamma}^V\asymp n^{\gamma+1}$; in particular, $\Lambda_n^V\asymp n$ when $\gamma=0$. Thus node compression preserves exact $L^2$ conditioning and, in this parameter range, optimal-order $L^\infty$ stability. Low-degree near-minimal rules and higher-degree optimized disk schemes illustrate the reduction in sampling cost.

Predicting gene expression from H&E-stained histology images offers a scalable alternative to costly spatial transcriptomics, yet most existing methods operate at the spot level, where signals from multiple cells are aggregated and critical cellular heterogeneity is obscured. Extending this paradigm to single-cell resolution is non-trivial. Naively applying pathology foundation models faces a scale mismatch: their patch-level representations mix multiple cells, whereas per-cell cropping or resizing distorts morphology and removes local context. Conversely, segmentation-based models without strong pretrained visual encoders often lack the morphological representation capacity needed for accurate molecular prediction and inherit errors from imperfect cell boundary masks. Here, we present CELLO, an efficient end-to-end framework that performs a single pathology foundation model forward pass per image and uses grid sampling to extract location-specific features for all cells simultaneously. We further introduce a distance-decay cross-attention module that refines each cell representation using spatially biased local morphological context. Using 52 public Xenium-H&E pairs from HEST-1k that span 12 organs and approximately 10 million cells, CELLO improves the average predictive accuracy over the evaluated baselines while reducing the mean whole-slide inference time compared to DeepSpot2Cell, a 14.0x speed-up on average that excludes upstream cell segmentation. Our work establishes a scalable foundation for single-cell gene expression prediction from H&E images.

Entering the post-pandemic era, cities navigate a new normal shaped by hybrid work and space-time flexibility, but existing evidence is spatially scattered and temporally limited. Here we develop an analytical approach that examines this reorganization through three dimensions: remote work adoption via sector composition, daily travel behavior via trip-level metrics, and functional urban form via mobility-derived measures. To capture the interplay of urban dynamics, we synthesize three complementary spatial metrics. In particular, coupling overall trip centrality with work-trip concentration differentiates whether employment and daily activity organize around the same centers. Applied to population-scale data across 15 U.S. metropolitan areas spanning 2019-2024, our approach shows that daily car travel increased despite elevated remote work, a pattern consistent across cities with distinct spatial structures. Decomposition and regression identify trip frequency as the primary contributor to VKT growth, moderated by compact urban form and concentrated employment. The approach provides a replicable framework for comparative study of post-pandemic urban mobility.

We study the distribution of $A_\alpha$-eigenvalues of a tree. We extend the works \cite{Jacobs2021} and \cite{SIN2020} by proving that the number of $A_\alpha$-eigenvalues, for $0\leq \alpha \leq \frac{1}{2}$, less than or equal to the average degree $d_\alpha= \alpha (2- 2/n)$ is, at least, $\lceil \frac{n}{2} \rceil$ for a tree with $n$ vertices. Several counterexamples for $\frac{1}{2} < \alpha \leq 1$ are exhibited. We also derive the same result for other well-known families such as the Deformed Laplacian and the matrix $B_\beta$.

A detector pretrained on a broad corpus is fine-tuned on a narrow domain, its in-domain accuracy improves, and it ships. We ask what happens meanwhile to its coverage of objects the vocabulary never names, which in obstacle detection and inspection carry the risk. No in-domain test set holds an example of one. We give a longitudinal protocol: one pretrained checkpoint against its own fine-tuned descendants. It tracks held-out top-$K$ proposal coverage $C_\tau$: of categories pretraining covered and the vocabulary omits, the share of boxes a detector's top $K$ regions still cover. The quantity is the open-world proposal literature's; the longitudinal reading is not. $C_\tau$ falls while in-domain accuracy rises, on four architectures and three domains, by $5.12$ to $63.35$ points on boxes above $1024$ px$^2$. No in-domain number identifies the fall, and neither does detection average precision, which charges a missed and a misnamed box alike. On the one architecture scoring both, adaptation costs $87\%$ of the AP against a fifth of the coverage, and the naming goes first at all six depths of its freeze ladder, every run. What breaks is structured: three architectures sharing no pretraining run agree on which categories lose coverage, and those a model never learned do not lose any. A repair follows and needs no training: mixing a quarter of the pretrained state back, normalisation statistics included, raises coverage on every cell swept for at most $2.47$ points of in-domain accuracy. Seeing it costs one extra evaluation pass.

In this paper, we prove that the rational Chow ring $A^*(\mathcal{M}_{5,10})$ is finitely generated as a $\mathbb{Q}$-algebra.

Existing models of mixed-autonomy weaving ramps characterize how altruistic connected and automated vehicles (CAVs) can improve traffic efficiency at the population level, but provide limited insight into how such behavior emerges from decentralized vehicle interactions or how it is affected by finite populations, heterogeneous preferences, and imperfect information. We develop an agent-based model of a macroscopic weaving-ramp framework in which individual vehicles adapt their lane choices using an evolutionary game-theoretic update rule and altruism-based objectives providing a microscopic interpretation of the original Wardrop model. We prove convergence of the decentralized dynamics to the unique equilibrium predicted by the macroscopic theory. Beyond reproducing aggregate equilibrium behavior, the framework enables the study of deployment-level questions that cannot be addressed by static analysis. Simulation results demonstrate close agreement with the macroscopic predictions while revealing how convergence rates, adaptation to changing traffic conditions, heterogeneous altruism levels among CAVs, and imperfect state information influence system performance and the distribution of altruistic burden across vehicles. These results provide a bridge between equilibrium traffic theory and decentralized mixed-autonomy deployment.

We study the realization problem for discrete-time input/output polynomial systems. These are formalized using tools from commutative algebra and algebraic geometry as systems whose state spaces are algebraic varieties, or more abstractly the set of k-points of an affine k-scheme, where k is an arbitrary infinite field. The input/output behaviors of such systems are described by "polynomial response maps" in which outputs are polynomial functions of past inputs. The main results show that every polynomial response map admits a canonical (quasi-reachable and algebraically observable) realization, which is unique up to isomorphism. The key to the approach is to linearize dynamics by considering a "dual" system in which states are functions defined on states. Finite dimensionality of the canonical realization, and its polynomiality, are characterized in terms of the space, algebra, and field of observables of the map, as well as in terms of algebraic input/output difference equations, and by a Jacobian rank criterion. A particular subclass consists of the maps that we call "bounded," defined by the property that their degree in the past inputs is uniformly bounded. Bounded maps are shown to be finitely realizable if and only if they are realizable by finite-dimensional state-affine systems, whose theory in turn reduces to that of rational formal power series. We also study the lattice of quasi-reachable realizations of a given map, including normal realizations. This work is an update of the PhD thesis written by the author in 1976; connections to recent work are briefly discussed in the last section.

Information-flow theory quantifies directional coupling through the rate of change of a target's Shannon entropy, a bulk functional insensitive to the tail of the distribution. We ask instead how a source variable contributes to the probability that the target exceeds a threshold. For source-additive drift the source's share of the marginal probability current is exact, and it separates into a mean-forcing part and a conditional-excess part that vanishes under independence. An identity links the two descriptions: the Liang information flow is the density-weighted mean of the derivative of the specific source current, whereas the exceedance current is its level at the threshold. This explains why entropy-based coupling collapses in saturated regimes where the source contributes most to the extreme; the Rényi information flow, a higher-order expansion and a Fisher-normalised response fail for the same reason. The flux decomposition, although exact, does not attribute: its terms are gross transports that nearly cancel. The quantity that does attribute is an adjoint response built from the backward generator which, read as a relative change, is uniformly accurate across two decades of event probability. We map the operating envelope of the estimator under omitted drivers, hidden slow memory, state-dependent coupling and multiplicative noise. Under correct specification the attribution carries a reproducible shortfall of ten to twenty-five per cent; the misspecifications we test bias it upward by up to ninety per cent. Applied to the 2003 European and 2010 Russian heatwaves in reanalysis, the attributed contribution of soil moisture is strongly threshold dependent, rising from the per cent level at moderate thresholds to a factor of two at the rarest, so a contribution quoted without its threshold is underspecified.

Reinforcement learning (RL) is a powerful framework for robotic control, yet its practical application is often hindered by high sample complexity. This is particularly restrictive in physical domains where interaction data is costly. While the world often exhibits geometric and physical symmetries, standard RL algorithms typically fail to exploit this structure. In this paper, we demonstrate that exploiting group symmetries significantly reduces the sample complexity of RL. Focusing on finite-horizon Markov decision processes, we find that leveraging homomorphisms induced by group symmetries significantly reduces the theoretical upper and lower bounds on the number of environment interactions required to reach an optimal return. We further extend these bounds to continuous state and action spaces, providing corresponding sample-complexity guarantees under appropriate regularity assumptions. Beyond theory, we validate our findings through controlled experiments and demonstrate the advantages of symmetry-aware policy learning on high-dimensional continuous robotic simulations. Our results show that integrating symmetry into the learning pipeline yields substantial gains in sample efficiency and performance, offering a principled path toward more data-efficient robotics.

In this paper, we generalize Guan's sharp effective strong openness theorem to the case of several plurisubharmonic weights. The proof uses a generalized Skoda-type $L^2$ division theorem for multiplier ideal sheaves. We also discuss the relationships among the $L^2$-division theorem, the $L^2$-extension theorem and the effective openness theorem.

We develop a structure-preserving parametric finite element framework for geometric flows whose energy density couples the unit normal and the curvature. This class includes bending energies with orientation-dependent rigidity or spontaneous curvature. A common fully discrete formulation treats closed curves in two dimensions and closed surfaces in three dimensions, and accommodates the $L^2$ flow, curve or surface diffusion, and the area- or volume-constrained $L^2$ flow. The formulation couples the geometric and curvature updates so that their contributions satisfy a discrete energy inequality. It uses continuous piecewise linear elements, a surface energy matrix, and a mass-lumped projection of the curvature derivative of the density. For positive densities satisfying a directional condition and convexity in curvature, we prove energy dissipation without a time-step restriction. The diffusion and constrained flows also preserve the enclosed area or volume exactly. The analysis allows non-even anisotropies and nonseparable dependence on orientation and curvature. Numerical experiments exhibit approximately second-order convergence in the manifold distance and confirm the discrete structural properties. Shape relaxation under an anisotropic Helfrich-type energy illustrates the use of the framework for coupled directional and bending effects.

Let $(M^{2m},g,f,J)$ be a complete gradient Kähler–Ricci shrinker satisfying \[ \operatorname{Ric}+\nabla^2 f=\frac12 g. \] We prove that if the scalar curvature is constant, then the soliton is rigid. More precisely, there exists an integer $k\in\{0,\ldots,m\}$ such that \[ R\equiv k \] and \[ (M^{2m},g,J)\cong \bigl(N^{2k}\times\mathbb C^{m-k}, g_N+g_{\mathrm{Euc}},J_N\oplus J_0\bigr), \] where $(N^{2k},g_N,J_N)$ is Kähler–Einstein and \[ \operatorname{Ric}_{g_N}=\frac12 g_N. \] As part of the proof, we establish a Riemannian rigidity criterion: for a complete nonsteady gradient Ricci soliton with constant scalar curvature, the condition $\mathcal{L}_{\nabla f}\operatorname{Ric}=0$ implies radial flatness and hence rigidity.

Relational in-context learning (ICL) uses labeled support examples and their linked relational context to predict labels for new queries. This creates a failure mode when target-derived features are present in the support context but unavailable for the query. We study this setting as support-set target leakage. We construct 20 controlled target-derived features that vary in signal fidelity, representation, semantic transparency, coverage, and zero-, one-, and two-hop relational placement, and evaluate them across 13 RelBench tasks and five relational ICL configurations that vary the ICL head, message-passing depth, pretraining cohort, or relational encoder architecture. We evaluate matched 0-hop, 1-hop, and 2-hop leakage settings, together with a Full leakage condition containing all 20 leaker columns. Within the tested configurations, target-table (0-hop) and Full leakage produce the largest aggregate deviations from clean evaluation, while higher-hop effects are often weaker, consistent with differences in effective exposure associated with temporal reachability, sampling, and aggregation fidelity. Leakage effects are strongly task- and model-dependent and can reverse relative conclusions between model variants even when aggregate changes are small. For leaker detection, we compare an Integrated Gradients (IG)-based screening method with mutual information (MI) and leave-one-column-out (LOCO) on a common Baseline subset. Ranking quality is strongest in the high-impact 0-hop and Full leakage conditions, but detector-based removal does not consistently restore the clean evaluation. A four-task rel-salt case study further shows the same evaluation concern with native-schema leakage candidates from the original relational schema. These results identify the support/query information boundary as an important component of reliable relational ICL evaluation.

Robots operating in real-world environments must often execute complex, multi-step bimanual tasks over long horizons rather than single, isolated actions. Current manipulation datasets provide limited support for this capability: although single-arm datasets reach hundreds of thousands of trajectories, they typically provide only one high-level instruction per episode, while existing bimanual datasets provide subtask annotations for only part of their recorded hours. We present FineART, a densely annotated bimanual manipulation dataset comprising 40,543 episodes (1,718 hours) and 533,913 subtasks across 151 tasks. We also introduce FineART-VLA, a vision-language-action policy that predicts its own next subtask to guide its actions. Mid-training on FineART's subtask annotations improves FineART-VLA's success at following spatial instructions from 32.0% to 100.0%. With step-by-step human subtask guidance, success on unseen long-horizon tasks increases from 16.0% to 76.0%. Furthermore, FineART-VLA matches baseline performance on a new robot with 10x less fine-tuning data and generalizes zero-shot to unseen tasks. We open-source the full dataset, model weights, and training code.

We give a self-contained elementary proof of the known result that every set $A\subset\R$ of cardinality seven satisfies $|A+A|\le |A-A|$. The argument adapts Hegarty's method, using representation counts and the largest positive differences. An exact counting identity, two applications of the Cauchy–Schwarz inequality, and an analysis of a symmetric six-element set with one point added complete the proof, with no computer enumeration. This answers in the affirmative a question of Chu for the seven-element case.

We consider persistent LLMs that accumulate memories of their interactions with a user over time. Such LLMs maintain memories using external storage, which they can query to overcome the limitations of a fixed context window. Such systems have numerous practical applications, as they can draw on all past interactions when responding to user queries. In this paper, we ask whether LLMs can forget information shared with them upon a user's request. We find that current LLMs fail to delete such information—even when they claim to have forgotten it and even when operating with a limited context. To this end, we consider a new direction of study: Deletion of LLM Memories. We show that naively removing messages that match a user's deletion request is insufficient, since conversations naturally introduce message dependencies that cause information to persist. To correctly handle deletion requests, we propose the DeLLM framework. It dynamically constructs relevant context for each LLM query and maintains a provenance graph of messages to determine which ones must be removed during deletion. Our experiments show that DeLLM achieves a high deletion rate while maintaining utility.

A pretrained video world model admits many plausible futures for a scene, but a robot must realize the exact task-conditioned one. To turn world models into executable robot policies, existing methods fine-tune the heavy world model backbone using large-scale robot data and computational resources. Challenging this status quo, we argue that the expensive part has already been paid in the world model pretraining since the representation space of a video world model lays out the diverse potential futures. In this case, what remains is to select the future that accomplishes the task and to read out the actions that realize it. We formalize this task as actualization, which learns a task-conditioned selection and realization on top of a prior supplied by a frozen world model. This can be solved by a tiny actualizer model. We implement RoboActualizer with as few as 60M parameters on top of a frozen world model encoder. The actualizer is composed of two lightweight DiT experts that jointly predict future latents and actions by flow matching. The model can be trained entirely on a single GPU with 32 GB peak memory. With up to 100x fewer trainable parameters than existing WAMs and VLAs, RoboActualizer reaches great performance on simulation benchmarks including LIBERO, LIBERO-Plus, RoboTwin 2.0 and five tasks on two real-world platforms, with a low latency of 39 ms that allows real-time control.

We develop a general method for uniform twisted metric Diophantine approximation with an arbitrary fixed real matrix. Using all successive minima of the associated diagonal lattice trajectory, we estimate lattice-point counts, accounting for clustering in every direction. Ratios of these counts give exact Hausdorff dimensions of sets of twisted $\psi$-Dirichlet vectors for a large class of functions $\psi$, including all except finitely many power functions {$T^{-\tau}$, $\tau>0$}. We obtain Hausdorff dimension formulae for the endpoint sets obtained by taking the intersection and union of the sets of twisted $c\psi$-Dirichlet vectors over $c>0$, and prove that taking the intersections causes no dimension drop. Furthermore, we obtain Hausdorff dimensions of level sets of the uniform Diophantine exponent. In addition, we prove zero-full laws for general Hausdorff measures of $\psi$-Dirichlet sets. Applications recover the one-dimensional Kim-Liao formulae, strengthen Aggarwal's escape-of-mass upper bound, reproduce the metric criteria of Moshchevitin and the second author and give certain extensions of the above statements.

We establish an exact zero-one law for twisted Diophantine approximation with an arbitrary fixed real matrix and a positive non-increasing approximation function satisfying dyadic regularity. The criterion is the convergence or divergence of a dyadic series whose summands are Khintchine-Groshev block volumes divided by homogeneous lattice-point counts. An equivalent formulation is using all successive minima of the associated diagonal lattice trajectory, capturing homogeneous clustering in every direction. We also obtain an almost-sure zero-infinity law for inhomogeneous $\psi$-Lagrange constants, separate Hausdorff-measure criteria, and dimension results. Within this regularity class, our theorem recovers the Kurzweil and Fuchs-Kim criteria. At the critical exponent, this series determines whether the set of badly approximable shifts has zero or full Lebesgue measure.

We construct a smooth projective family of rational surfaces and an effective line bundle on its total space that give a negative answer to Păun's metric-extension question. The restricted bundle on the central fibre carries a semipositively curved singular Hermitian metric with analytic and minimal singularities, but this metric admits no semipositive extension to any neighbourhood of the whole fibre, even up to singularity type. The construction uses four-point blow-ups of the plane, with three centres becoming collinear on the central fibre. This change produces a nonzero integrable adjoint section on the central fibre, whereas the corresponding adjoint systems vanish on nearby noncentral fibres. If a metric extension existed, an $L^2$ extension theorem would extend that section, contradicting this vanishing.

Longitudinal data are valuable because people change. Yet the objectives used to learn from these data can inadvertently erase that change. In person-level contrastive learning, observations from the same person are treated as positives; as records grow, those positives can span increasingly distant—and increasingly different—behavioral states. More history can therefore produce not only more data, but broader invariance. We show that this distinction is fundamental. We separate record span, how much history the learner sees, from supervision span, how far across that history positive-pair supervision reaches. Across in-home sensing records spanning up to 2.7 years, broader supervision systematically suppresses recoverable changing-state information, even when the available history is held fixed. At the broadest span, less than 10% of the information recoverable from an untrained encoder remains. Yet keeping positives local is not sufficient: as records grow, even distant states that are never paired become increasingly similar. Explicitly contrasting other observations from the same person reverses this loss without shortening the record, revealing a second route by which longitudinal scale can broaden invariance. Finally, we prospectively reproduce the supervision-span effect in 199 GLOBEM participants. Longitudinal scale therefore presents a choice: more history need not mean more invariance. By controlling what is held invariant as records grow, we can preserve the change that made the longitudinal data valuable in the first place.

Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.

Cross-resolution knowledge distillation aims to improve low-magnification whole- slide analysis by transferring high-magnification representations, yet the conditions for useful transfer remain unclear. We develop a decomposition-based analysis of teacher access, representation loss, and model excess, motivating three questions: whether (a) teacher targets help the task, (b) low-magnification students can predict them, and (c) slide models benefit from those predictions. We investigate them through controlled experiments across ten pathology cohorts spanning classifi- cation, grading, and survival prediction. In the main comparison, providing teacher regional means alongside native low-magnification features improves downstream performance in all ten cohorts. Direct prediction achieves lower reconstruction error than residual prediction, yet the predicted features underrepresent variation in the teacher targets. Moreover, better reconstruction does not consistently improve downstream scores, and retaining native features changes performance even when the predicted teacher features are held fixed. Together, these findings expose a gap between reconstructing teacher representations and realizing their downstream value. They challenge the sufficiency of reconstruction error as a measure of cross-resolution transfer and provide a diagnostic framework for examining where that transfer breaks down. Future distillation designs must account for both what students can predict and how slide models use those predictions.