Papers

We present several geometric constructions of graphs with rapidly growing chromatic numbers, most of which are triangle-free or have large girth.

World action models (WAMs) have advanced robot control by predicting how observations and actions evolve over time. Despite this progress, RGB and action based future prediction does not explicitly address the spatial understanding needed for robot manipulation. Existing efforts often add a limited set of spatial prediction tasks through specialized heads or branches, leaving both the range of spatial supervision and the model architecture fragmented. We introduce XGenAct, a world action model that represents RGB observations, robot actions, metric depth, surface normals, and functional role segmentation as RGB videos through deterministic codecs. By sampling perception and action tasks during training, XGenAct uses one video diffusion transformer and one objective to learn temporal prediction across these spaces without modality specific learned heads. On held out RLBench tasks, structured perception training improves average closed loop success over RGB only training, and XGenAct achieves 52% success in the five task external comparison, versus 26% for the strongest evaluated baselines. It also predicts future depth and segmentation more accurately than the evaluated pipelines that generate RGB first and then apply a frozen perception expert.

On-policy self-distillation (OPSD) uses reference solutions as privileged hindsight to supervise student-generated reasoning trajectories. However, reference-based guidance may explain a correct solution without addressing why the student's own reasoning fails. This reasoning mismatch between the guidance provided and the correction needed can encourage the student to borrow correct conclusions while leaving its reasoning errors unresolved. Moreover, applying the same hindsight throughout the trajectory risks a distillation trap, where unnecessary constraints on valid reasoning compete with correction of substantive errors. To address these issues, we propose Root-Cause-Guided On-Policy Distillation (RC-OPD), which uses repairs of the student's own reasoning to provide guidance that addresses its specific errors while building on valid progress. For each failed attempt, RC-OPD locates the earliest substantive error, develops a local correction, and uses the corrected intermediate result as an anchor for the valid prefix. An iterative diagnosis–repair–continuation process tests the repairs through student continuation, identifying further errors within a fixed repair budget. For repair chains that reach a correct answer, root–cause–guided distillation uses failure diagnoses and corrective goals to supervise the erroneous segments, while anchor-guided distillation supports the corresponding valid prefixes with reasoning chains leading to the repaired intermediate results. We evaluate RC-OPD across multiple datasets and model scales. Extensive experiments and analyses show that it mitigates reasoning mismatch and the distillation trap, yielding substantial performance gains.

We develop a Fock-space formulation that reduces expectation values of vacuum-family quasi-primaries in qKdV eigenstates of arbitrary highest-weight conformal families to a free-bosonic problem, and employ it to test the generalized eigenstate thermalization hypothesis (GETH), in 2D conformal field theories with large central charge $c$. We demonstrate that the first two quantum Korteweg–de Vries (qKdV) charges $Q_1$ and $Q_3$ lift all degeneracies except along at most countably many curves in the $(c,\Delta)$ plane, where $\Delta$ is the highest weight of the conformal family, so that the full-qKdV simultaneous eigenstates are unambiguously determined by $Q_1$ and $Q_3$. Based on this, a near-complete toolkit for testing in the vacuum conformal family or falsifying the general form of GETH, i.e. equating qKdV eigenstates and thermal states of the generalized Gibbs ensemble in the sense of expectations of local observables, is provided in this paper, through the infinite tower of qKdV charges. A stronger form of the GETH, namely that all expectations of local observables of a definite level should be expressible of qKdV charges but not contain microscopic eigenstate information, is directly falsified at subleading order in the large-$c$ expansion. At levels 6 and 8 in the vacuum family, expectation values of quasi-primaries in simultaneous eigenstates of the qKdV charges are not fixed by first finitely many qKdV charges, and microscopic information of the eigenstate is required.

We determine the thermal melting phase diagram of the electron solid by measuring the onset density of the double-threshold voltage-current curves in the insulating state in the ultra-high mobility two-dimensional electron system in SiGe/Si/SiGe quantum wells at different temperatures in perpendicular magnetic fields. The introduction of a magnetic field leads to a considerable increase in the onset density, which is strongest at the lowest temperatures and decreases with increasing temperature, and the melting temperature increases with magnetic field. These data are in agreement with theoretical predictions. Unexpectedly, the melting temperature as a function of electron density in a fixed magnetic field reveals a plateau, which can be interpreted in terms of resonance modes in the crystallites.

Humans draw progressively: a few strokes, a look at the result, a stroke erased, a prompt revised. Image generators do not work this way. They typically take a finished sketch and produce the image in a single pass, so every edit starts the picture again, and the models that do keep state across turns are driven by text, cannot take a stroke, and are too slow to draw with. We present ProgressNet, a training-free framework that lets a frozen text-to-image model follow a drawing session as it unfolds: strokes are added and erased, the prompt is revised, and the image keeps up at about a second per turn. It needs no new parameters because the frozen model already has what a progressive generator needs, a pathway through which the previous turn can be remembered, layers that can carry appearance forward without freezing structure, and an internal signal of how far to trust an unfinished sketch; three inference-time mechanisms (Previous-Concept Memory, Layer-Selective K/V Injection and Banded Adaptive Control) use each in turn. As a sketch fills in, every existing method degrades, the FID of the FLUX+ControlNet baseline doubling between 10% and 100% completion on FS-COCO, while ProgressNet's barely moves; it maintains strong fidelity and progressive coherence across three sketch domains and is preferred by users over five competitors, most widely on erasure.

Machine learning risk models are increasingly being used in patient-facing health tools, but it remains unclear how well users understand the information these systems present. In this work, we study how people interpret an interactive Type 2 Diabetes (T2D) risk interface and whether interacting with it influences their attitudes toward behavioural change. Through an exploratory mixed-methods study with 15 participants, we compare participants' perceived understanding with their actual understanding and identify key themes from qualitative interviews. We find that participants often understood the interface better than they initially believed, but still faced important barriers related to unclear terminology, ambiguous risk framing, and limited explanations of model inputs. Finally, we propose relevant design guidelines and discuss broader issues surrounding trust and fairness. Our findings highlight the importance of intuitive visual design, familiar presentation, and clear explanations in patient-facing ML interfaces.

Recent advances in autoregressive video generation have improved temporal consistency over extended durations, yet interactive storytelling requires more than continuous scene extension: a new shot may combine characters and backgrounds from different historical shots. Whole prompt retrieval can overlook the distinct reference needs of individual components, while directly combining all historical memories may introduce unrelated visual content. To address these problems, we present Weave Forcing, a training-free framework for compositional memory reuse in interactive long video generation. First, we use an LLM for semantic slot routing to decompose user prompts into character and background descriptions and explicitly select suitable historical references for each component. To isolate the required content, masked memory weaving uses contrasting attention maps conditioned on semantic slots to construct refined semantic masks, selectively exposing relevant tokens from compressed historical KV memories to guide the generation of the current shot. We further introduce coverage adaptive RoPE to adjust temporal offsets and memory retention according to no, partial, or full reference coverage, addressing visual artifacts observed when incomplete historical references are positioned close to the current generation. Extensive experiments demonstrate that Weave Forcing improves cross-shot subject and background consistency while maintaining competitive visual quality and text alignment.

Chain-of-thought (CoT) reasoning allows humans to inspect how large language models reach their answers, and oversee model behaviour. This reasoning comes at an increased inference cost, motivating efficient methods that train models to solve tasks using fewer tokens. However, a common concern is that such training may cause models to skip important reasoning steps, so the CoT no longer faithfully reflects the model's decision. It is unclear whether or when this occurs in practice, since different efficiency methods apply length pressure to models' CoT in distinct ways, and faithfully explaining a model's decision takes more tokens on some tasks than others. To understand these dynamics, we fine-tune a variety of models with three methods that apply length pressure differently, namely a fixed generation budget, a per-example length target, and a group-relative length reward. We evaluate how efficient reasoning affects CoT faithfulness (i.e., how well the CoT reflects model decisions on related inputs) and monitorability (i.e., whether the CoT reveals when input interventions alter the output). We find that it affects faithfulness and monitorability differently. Faithfulness falls in most settings, primarily because the trained models are less consistent. Monitorability is more robust, as models keep acknowledging the influence on their answer even when the CoT is much shorter.

Multi-timescale systems present a fundamental challenge, where fast operational decisions must coexist with long-horizon sustainability targets. In this work, we propose a new hierarchical control framework via Model Predictive Control (MPC) and Reinforcement Learning (RL) to separate decision-making on two distinct timescales. The high-level MPC optimizes long-horizon setpoints at the slow dynamic and on a fast timescale, a low-level pretrained RL agent tracks these setpoints in real time to maximize short-term objectives. RL is introduced to learn nonlinear control policies, without relying on model linearizations or requiring the heavy online computation from solving repeated optimal control problems. The framework is applied to a Battery Energy Storage System (BESS) operating in frequency regulation markets to balance fast profit opportunities (seconds) and slow battery degradation (weeks to months). The design employs a degradation-aware RL agent trained offline to generate safe long-horizon setpoints, and a degradation-unaware agent fine-tuned from it for fast runtime setpoint tracking. Compared to MPC baselines, the proposed approach successfully extends battery lifetime by 84% and increases operational profit by 34%.

At the low densities encountered in the inner crust of neutron stars, neutron matter becomes superfluid, directly influencing macroscopic phenomena such as star cooling. However, a precise quantitative understanding of this system has been hindered by uncontrolled many-body approximations. In this letter, we exploit the nonperturbative Gorkov algebraic diagrammatic construction method to provide a unified ab initio description of the equation of state and the single-particle spectral functions of homogeneous neutron matter, spanning from the dilute regime to saturation density. We identify clear microscopic signatures of superfluidity in the excitation spectrum and quantify the pairing gaps associated with realistic chiral Hamiltonians, estimating for the first time their sensitivity to the many-body truncation. Our robust handling of both dynamical and pairing correlations paves the way for exploring electroweak processes across the regimes relevant to neutron stars.

Decision making under uncertainty requires balancing the value of additional information against the cost of delaying the decision until that information becomes available. This challenge is especially prevalent for embodied decisions such as those faced by animals moving between food sources and robots selecting navigation targets, where movement through space shapes both the quality of information and the cost of acting. We consider a version of this problem, where the decision is on choosing among rewards of uncertain value, and those rewards can only be attained through changing the decision maker's state sufficiently. Our focus is on interactions between reward learning and state evolution, restated as a deterministic optimal control problem with two terminal alternatives, one with a known reward and the other learned gradually through noisy observations. We demonstrate that delayed reward attainment is often optimal in a variety of systems, especially so when the alternatives are initially difficult to distinguish and the cost of waiting is relatively low. For a subset of problems, we also derive sufficient conditions that allow shortening the planning horizon a priori, guaranteeing that further observations would not affect the value function. Finally, when observation quality depends on the state, we show that it is often optimal for a controller to evolve the state strategically toward more informative sensing locations before making a decision, in line with the behavior broadly observed in biological and engineered systems.

Post-exposure microscopy is central to qualification of fusion materials. However, manual analysis does not scale to the volume, heterogeneity, and multiresolution character of modern fusion-materials campaigns. To address this challenge, we present a reproducible workflow, implemented in the Galaxy scientific workflow environment, for automated crack identification and quantitative damage assessment from scanning electron microscopy images. The workflow processes SEM images and experimental metadata to identify cracks, quantify damage, and retain the intermediate products and processing history needed for reproducibility. Outputs include crack masks, skeletonized crack networks, quality-control visualizations, and scalar damage descriptors. The method is designed to operate without image-specific parameter tuning across tungsten grades, microstructures, magnifications, and damage states. We demonstrate the workflow on a sparse electron-beam thermal-shock dataset containing 418 images from 114 experiments spanning five tungsten grades and three microstructural states. We define a crack-density descriptor, which provides standardized inputs for downstream machine-learning prediction and physics-based crack simulation. These predictive components are exposed in the same Galaxy environment and are intentionally treated here as extensible workflow modules. The principal contribution is therefore an end-to-end, shareable, and computationally portable workflow that links experimental characterization, automated image analysis, preliminary damage prediction, and simulation-guided data acquisition for fusion-materials research.

Accurate transient B-H modeling under pulsewidth-modulated (PWM) excitation is challenging since the magnetic-field response depends on both the instantaneous flux density and the preceding magnetisation trajectory. Although sequence-to-sequence models enable waveform prediction, existing studies have not jointly addressed how much magnetic history is required, how saturation region should be handled, and how trained models can be adapted to unseen materials. To address these gaps, this paper presents MagLearn 2, a condition-aware, short-window LSTM-based sequence-to-sequence framework for reconstructing the future H(t) response from the historical B(t) and H(t) trajectories. A saturation-aware auxiliary module selectively replaces saturation-dominated predictions within the complete waveform forecast. In a representative saturated 3C90 case, the auxiliary module reduces the sequence-level relative RMSE from 67.84% to 9.19%. To understand how much the history samples contributes to the predictions, an occlusion-based sensitivity analysis is conducted to quantifies the contribution of magnetic history and reveals that that the information most relevant to prediction is concentrated near the forecast boundary. In the independent evaluation for MagNet Challenge II, the proposed framework's best-performing model achieved the lowest reported average RMSE to date on the sequence-prediction task at 2.2%.

Training-free posterior sampling methods, also known as Plug-and-Play methods, leverage pretrained unconditional diffusion or flow-matching models to solve inverse problems. Most existing approaches rely on guidance weights to balance, at each time step, prior information from the unconditional score or velocity network with measurement consistency, yet the tuning of these weights is often not discussed and is largely left to heuristics. We introduce a simple and principled offline strategy for automatically tuning these guidance weights. Our key observation is that, at each time step, the conditional denoising score-matching objective for diffusion models, or the conditional flow-matching objective for flow-matching models, is a least-squares objective. Therefore, when the conditional prediction is expressed as a weighted sum of the unconditional network output and a measurement-guidance term, optimizing over these weights reduces to a two-dimensional linear least-squares problem. The resulting time-dependent guidance weights can be optimized offline for a given measurement operator, noise level and sampler at the cost of a single minibatch of sampling trajectories, without retraining or fine-tuning the pretrained generative model. Instantiated with the standard Tweedie-based measurement-consistency term, our approach improves posterior sampling and achieves state-of-the-art reconstruction performance across diffusion- and flow-matching-based methods. Moreover, the optimized guidance weights enable diffusion samplers to reduce the number of sampling steps from 1000 to 50 with no significant degradation in reconstruction quality. Code will be made available.

Mechanistic edits (ablations, weight edits, activation steering) are the standard tools for unlearning a harmful capability from a neural network while preserving useful ones. Current approaches validate their effects only by testing, which can never cover an entire continuous region of inputs. Prior work at the interpretability-verification boundary certifies descriptions of a model: what a circuit computes, or whether it faithfully explains the whole. We instead certify the behavioral effect of an edit: that disabling a circuit removes one skill and provably preserves another, for every input in a region; a feature non-interference guarantee in the information-flow-security sense. We demonstrate such certified edits from toy ReLU networks up to a standard softmax + LayerNorm transformer, proving removal and preservation over continuous embedding-space regions and reaching roughly 9x the input-perturbation dimension an exact solver can handle by switching to sound bound propagation. Furthermore, we prove that no finite deterministic black-box test can certify removal, exhibiting an edit that passes exhaustive testing yet provably fails on a survivor pocket that can be made arbitrarily small. Guarantees hold on small, standard-architecture networks and, like any removal claim, presuppose that the target skill admits a decidable specification, a property which real-world harms may not have.

We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|\Psi|^2$. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].

Deep tabular generative models are benchmarked on datasets with tens of thousands of rows; clinical datasets have hundreds. We preregistered and ran a size-ladder benchmark to find where the two regimes diverge: 8 public datasets subsampled from 200 to 20,000 training rows, seven generators (independent marginals, Gaussian copula, SMOTE, unconditional SMOTE, CTGAN, TVAE, TabDDPM) with a fixed 20-trial tuning budget and 5 evaluation seeds, plus 4 natively small clinical datasets at true size, for 2,220 committed runs in total. The primary metric is the AUROC of fixed classifiers trained on synthetic and tested on real data. In 23 of 24 (dataset, deep model) pairs no deep model ever beats the best trivial baseline by more than seed noise, at any training size we measured. The best baseline wins 40 of 49 (dataset, size) cells. Our preregistered prediction that the deep models' ranking would be unstable at small sizes is falsified: mean Kendall tau between adjacent rungs below 5,000 rows is 0.806, above our 0.8 threshold, and stability is highest at the smallest sizes rather than lowest. One caveat bounds all of this: in 81% of cells the gap between the top two methods is smaller than the variation between seeds. Finally, method rankings on natively small clinical datasets agree only moderately with rankings on subsampled large ones (mean tau 0.57 to 0.64), which questions whether a subsampled large dataset can stand in for a small one. All 2,220 result files, the preregistration and its hash, and the code that regenerates every figure and number from those files are public.

We give two alternate formulations for the second moment formula of the Siegel transform over $\mathrm{Sp}(2n, \mathbb Z) \backslash \mathrm{Sp}(2n,\mathbb R)$, previously established by Athreya-Konstantoulas and Kelmer-Yu. We also provide several applications that demonstrate their usefulness.

Adversarial patches can disrupt Vision-Language-Action (VLA) models by manipulating visual observations, leading to failures in robot control. However, it remains poorly understood which internal mechanisms underlie these failures and how targeted interventions can mitigate them. In this work, we mechanistically analyze VLA representations using a sparse autoencoder (SAE) and identify a feature whose activation strongly correlates with the presence of an adversarial patch. Based on this analysis, we suppress the identified feature at inference time only when a linear probe detects an attack. This intervention improves robustness without the cost of fine-tuning the VLA. We evaluate our method against VLA adversarial patch attacks on LIBERO-10. Conditional intervention improves success rate under intermittent attacks, whereas continuously applying the same intervention substantially degrades policy performance. These results show that attack-related internal representations can provide useful targets for VLA adversarial defense and that controlling when to intervene is important for limiting disruption to nominal policy behavior.

In this paper we study a discrete homotopy theory for undirected graphs. More precisely, we consider $A$-homotopy groups, first defined in the work of Barcelo, Kramer, Laubenbacher and Weaver. For every degree $n$ and every group $G$ (Abelian if $n\geq 2$), we construct a graph whose $n$-th $A$-homotopy group is isomorphic to $G$ and whose other $A$-homotopy groups all vanish. Using these, we show that for every infinite sequence of groups $G_1,G_2,\ldots$, with $G_i$ Abelian for $i\geq 2$, there is a graph $X$ such that the $i$-th $A$-homotopy group of $X$ is isomorphic to $G_i$ for all $i$. Along the way, we identify relative $A$-homotopy groups with relative classical homotopy groups, and prove a discrete version of the Blakers-Massey theorem. We then construct partial Postnikov systems and (full) Whitehead towers.

Frequency-bin encoding provides a scalable platform for photonic quantum information processing by enabling high-dimensional qudit states compatible with the telecommunications infrastructure. However, characterizing these systems remains challenging, as conventional quantum state tomography requires measurement resources that increase rapidly with dimensionality, compounded by the difficulty of implementing controllable measurements across many frequency modes at once. Here, we address these challenges and demonstrate threshold quantum state tomography of entangled frequency-bin qudits using adaptive measurements that exploit the sparsity of highly entangled biphoton frequency combs. Combined with Bayesian inference, we experimentally demonstrate full state estimation of biphoton frequency combs with Hilbert space dimensions up to $d^2=100$—a 56% increase over the previous record—all while performing a mere 1.9% of the measurements required by conventional tomographically complete approaches. This work confirms the promise of measurement-aware approaches for characterizing high-dimensional photonic quantum systems, unlocking new tools for full tomography that are hardware-efficient, state-aware, and free from a priori assumptions about state structure.

Null string theory (NST) is a two-dimensional (2d) sigma-model on a Carrollian worldsheet with 2d diffeomorphisms, Weyl and Carroll-Weyl (CW) scalings as gauge symmetries whereas the Isberg-Lindström-Sundborg-Theodoridis (ILST) theory on a generic target space only realizes the first two and not the CW gauge symmetry. We show in this work that NST on the Carrollian target spaces (CTS) is well-defined if the background admits a homothetic kernel generator and that, it is described by the ILST theory on the same CTS. To this end, we formulate a minimal null string theory on CTS, starting from first principles and then discuss beyond minimal theories as deformations away from minimality. We study some classes of such deformations involving the clock one-from for ruled Carrollian spaces and/or connection on the Carrollian space. We discuss implications of this for the recently introduced null string holography. As examples CTS, we briefly discuss null strings probing black hole horizons and the null string holography in this context.

Long-term forecasting models commonly process all patches in a look-back window using the same fixed stack. Older contextual patches and recent evidence therefore receive the same computational depth. Yet the information closest to the forecast and the more distant context do not contribute equally. Uniform processing leaves this distinction unexpressed in the architecture. We propose MARO, a Most-Recent Anchoring with Recurrent Ordering model that processes the look-back window from the most recent patch to the oldest. The most recent patch serves as the anchor. It initializes the latent state and conditions each subsequent step, so older patches are folded into a representation that remains centered on recent evidence. A single shared module is reused at every step, so extending the scan further into the past introduces no additional parameters. Intermediate states retained during the scan allow the forecast head to weigh short and long portions of the history separately. This expresses recency through the order of recurrent refinement. Extensive experiments across multiple real-world time series datasets show that MARO achieves state-of-the-art performance on both long-term and short-term forecasting tasks.Ablation studies examine the contribution of the main architectural components.

Multicore optical fibers (MCFs), developed to scale classical telecommunications, are gaining traction as a quantum platform for high-dimensional key distribution, entanglement, and photonic quantum walks. So far, quantum light has occupied these fibers only as single-mode path channels; the spatial-mode structure within each core has remained untouched. Here we operate a telecom-grade 39-core fiber far from its design wavelength, where each core supports exactly two LP mode groups (LP01, LP11), and measure heralded photon-number states |1> and |2>, resolving the photon number simultaneously with the intra-core spatial mode or with the core index. Displacing the launch prepares a coherent LP01-LP11 superposition whose single-sided intensity pattern shows that the intermodal phase is preserved over the fiber: a drift-resolved joint fit gives a pixel asymmetry (0.4% vs 47%) incompatible with an incoherent mode mixture. Because the two modes couple to neighboring cores at different rates (kappa_LP11/kappa_LP01 = 2.4), the launched mode content acts as a state-selectable coupling knob: the effective inter-core coupling of the passive fiber is set by the launch alone (3.9-13.1%), a tunability that otherwise requires electro-optic, thermo-optic, or mechanical reconfiguration. The propagation is photon-number independent: the per-photon crosstalk of heralded |2> states equals that of |1>, bounding any Fock-state dependence to |dx/x| < 6.1% (95% CL), and the imaged mode distributions of |1> and |2> agree to better than 1%. This measured linear-optics null, validated against exact Fock-space simulation, is the baseline against which genuine multiphoton interference in fiber quantum walks must be certified; we also show how coincidence-based event selection produces spurious photon-number-dependent crosstalk if accidentals are not subtracted.

Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with $\mathcal O(nD^3)$ time, where $n$ and $D$ denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.

Most long-term time-series forecasting models map the look-back window directly to the full horizon in a single pass. While efficient, this design does not explicitly identify which historical states are most relevant to different future segments or exploit what followed those states. Analog forecasting addresses this by retrieving past states similar to the present and using their observed continuations, but single nearest matches can be unreliable and overlapping patches may produce redundant candidates. We propose DuoTS, a Dual-Context Time Series forecasting model that uses retrieved evidence without relying on it exclusively. DuoTS first produces a base forecast with a parallel patch encoder and linear prediction head, then progressively refines it one future patch at a time. Each refinement combines two views: a current context that attends to recent tokens and captures the latest dynamics, and a detail context that provides distinct retrieved analogs together with their subsequent trajectories. Patch-wise refinement allows the model to balance these views across the forecast horizon and associate each future segment with evidence appropriate to its temporal distance from the present. Experiments on multiple real-world datasets show that DuoTS achieves state-of-the-art performance, while ablations confirm the contribution of each context. The refinement mechanism is also model-agnostic, requiring only an encoded look-back window and the future-patch position, and can therefore be integrated into existing forecasting models.

Let $M^n$, $n\ge3$, be the smooth, connected, complete, noncompact boundary of a closed convex set with nonempty interior in $\mathbb{R}^{n+1}$. We prove that its normalized scalar-curvature integral at infinity is at most $4\pi\omega_{n-2}(1-\operatorname{AVR}(M))$, except when, up to an ambient rigid motion, $M$ is the product of a smooth closed convex surface in $\mathbb{R}^3$ and $\mathbb{R}^{n-2}$. These exceptional products have zero asymptotic volume ratio and limit $8\pi\omega_{n-2}$. We also characterize the equality case for the $4\pi\omega_{n-2}(1-\operatorname{AVR}(M))$ bound. The proof uses exterior tube volumes together with the cone Steiner and Gauss–Bonnet formulas. An elementary comparison of intrinsic and Euclidean radial distances proves existence of the intrinsic limit and identifies its exact value from the cone coefficients. The same conclusions extend to orientable convex submanifolds of arbitrary codimension

A search for pair-produced vector-like top quarks, T, decaying into a new scalar boson $\phi$ and a standard model (SM) top quark is presented. The search targets events containing a photon pair originating from the decay of one of the scalar bosons, accompanied by all-hadronic decays of the SM top quark pair. The analysis is optimized for boosted top quark signatures in which the decay products of the top quarks are reconstructed as large-radius jets. The search is based on proton-proton collision data at $\sqrt{s}$ = 13 TeV, collected by the CMS experiment at the CERN LHC during 2016$-$2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is performed for an array of T and $\phi$ masses. No significant deviation from the predicted background is observed. The largest local excess has a significance of 2.7 standard deviations, reduced to 1.5 standard deviations after accounting for the look-elsewhere effect. Upper limits at 95% confidence level are set on the product of $\mathrm{T\bar{T}}$ production cross section and the branching fraction.

The paper contains three results. First, we give a global quotient presentation of the supermoduli space of genus $g>1$ super Riemann surfaces. Second, we prove that the moduli stack of marked super Riemann surfaces, which we call super Teichmüller space, is a complex analytic Deligne Mumford superstack. Third, we construct an étale atlas for super Teichmüller space whose underlying topological space is a disjoint union of $2^{2g}$ contractible unit balls.