Papers

c-Polynomials are polynomials whose (non-zero) coefficients are all equal to 1. Taking a theorem by Carlitz and Moser as a motivation, we prove a structure theorem for the factorisations of the c-polynomial $(x^n-1)/(x-1)$ into c-irreducible factors by relating c-torisations into c-polynomials to joint ordered factorisations arising from the integer n. The question of how many different joint ordered factorisations there are leads to the precise chromatic polynomial for path graphs, counting the ways of path graph colourings with $m$ colours under the condition that all colours are used. Moreover, we give similar counting formulae for joint ordered factorisations under the constraints that all factors are primes, or that all factors are square-free.

The Ariel mission will conduct a population level survey of hundreds of exoplanet atmospheres, requiring observations to be scheduled across a large and diverse catalogue of potential targets. By framing Ariel scheduling as a long-horizon optimisation problem in which individual decisions affect both mission time and the scientific opportunities available later in the survey, Reinforcement Learning (RL) can be utilised as a framework for target selection. We introduce aRieL, a simulated observing environment coupled to a Set Transformer Proximal Policy Optimisation (PPO) agent that is trained to generate a scheduling policy. The RL policy consistently finds a strong compromise between competing survey objectives, producing large Tier~1 samples while maintaining high Tier~3 completion, population coverage, and observing efficiency when compared to a set of baseline heuristic polices. This behaviour is retained when the candidate catalogue is substantially expanded, while modifications to the reward function produce corresponding changes in the learned observing strategy. We further show that a policy trained on the baseline mission scenario can generalise without retraining to a modified scenario requiring repeated Tier~3 observations, revealing the resulting trade-off with the wider survey. These results demonstrate that reinforcement learning provides a flexible approach to large-scale astronomical scheduling, in which the observing strategy can respond directly to changes in mission state and to the scientific priorities, and motivate its wider exploration for observatories with similarly complex, state dependent scheduling problems.

Over the past 25 years, sketching and sampling have become widely used tools for accelerating large-scale regression. In iterative randomized solvers, a basic design choice is whether to $\textit{reuse}$ the same sketch or draw $\textit{fresh}$ randomness at every step. For (under-constrained) iterative ridge regression with column sampling, whether fresh sketches offer provable advantages has remained open: $\textit{We show that they do.}$ Fresh sketching lets us analyze error only along the current residual solution, rather than uniformly over the entire Gram matrix. This directional view yields sharper convergence guarantees for leverage score and ridge leverage score sampling and, more importantly, leads to residual-aware sampling rules. By minimizing the variance of the relevant sketched matrix-vector product, we derive an oracle distribution and practical approximations to the oracle distribution, including a mixture sampling distribution with (somewhat weaker) convergence guarantees. Experiments on synthetic and real data, including ridge probes on Qwen2.5 representations, support our theory, showing substantially faster convergence.

Matter-wave interferometers are sensitive probes of low energy physics and have been used for precise tests of gravity and quantum mechanics. These applications would benefit from interfering particles of higher mass, but observing the interference of a large particle is challenging due to the need to control its initial state and to avoid decoherence. Here we propose to demonstrate matter-wave interference of a microparticle with an embedded rare-earth ion. Optical transitions of the rare-earth ion will impart momentum to the microparticle's center of mass. The use of a time-symmetric interferometer geometry and a rare-earth ion state with angular momentum $J = 1/2$ will eliminate sensitivity to the initial conditions of the microparticle. We show that the rates of all relevant external decoherence mechanisms either decrease or remain constant as the microparticle mass is increased, allowing decoherence to be avoided by using sufficiently large particles. An apparatus at moderate vacuum levels will support microparticle interferometry with up to $10^3$ photons per beam splitter and millisecond coherence time. This demonstration will establish microparticle interferometry as a new platform for quantum sensing, improving searches for minimal modifications of quantum mechanics by up to three orders of magnitude in the near term and laying the foundation for future gravitational tests.

Online knowledge communities rely on a division of epistemic labor between users who seek information and those who produce it. Generative AI may blur these roles, but how it reallocates knowledge-seeking and knowledge-producing activities and reshapes the nature and returns of participation remains unclear. We examine changes in question-asking and answering among Stack Overflow user groups, focusing on consumers and producers, following the release of ChatGPT. Consumers shifted from asking questions to producing answers, but their answers were less likely to be accepted relative to the pre-ChatGPT period, suggesting that increased production did not yield equal standing in the community. By contrast, producers did not change the number of questions they asked, but increasingly asked about novel and emerging topics. Although they produced fewer answers, their answers received greater recognition. These findings show that access to generative AI does not necessarily translate into equal opportunities for successful participation.

World models, game simulators, and long-take video creation require coherent scene evolution and sustained dynamics over extended durations. Autoregressive (AR) video diffusion provides a natural framework for long-horizon generation, yet extended rollouts often become near-static or lose visual quality. We hypothesize that these failures reflect the limited guidance provided by short-video supervision on how ongoing scene dynamics develops over longer durations. This motivates us to introduce LongTake, a two-stage training pipeline built around Long-Horizon Teacher Forcing (TF) on curated real long videos. Long-Horizon TF trains the AR model to predict later frames conditioned on long ground-truth video prefixes, extending direct supervision beyond the short training horizon. This supervision is designed to help the model sustain dynamics and preserve visual quality during long-horizon generation. Our central finding is that this training stage strengthens direct initialization for distribution matching distillation (DMD) under student self-rollout, without the intermediate few-step distillation stage used in standard pipelines. Under the same five-second DMD training setup, our initialization yields substantially higher dynamic degree than short horizon TF initialization on 30-second rollouts at comparable aesthetic quality, and surpasses the evaluated baselines in both measures. Hybrid DMD further reuses this teacher to extend supervision to later frames of the self-rollout while retaining bidirectional joint supervision over the initial window. On long-horizon self-rollouts, LongTake lies on the Pareto front of dynamic degree and aesthetic quality, and Hybrid DMD attains the highest dynamic degree among evaluated methods at both 30s and 60s.

Zeroth-order optimization methods are essential for solving black-box problems where gradient information is unavailable or expensive to compute. This paper presents POEM-ES, a novel parameter-free stochastic zeroth-order algorithm that extends the recent POEM method by integrating subspace preconditioning with ellipsoidal randomized sampling. In contrast to traditional zeroth-order approaches that rely on isotropic random directions, POEM-ES performs anisotropic sampling guided by a fixed structural symmetric positive semi-definite (SPSD) preconditioner $\hat{\Sigma}$ that encodes the underlying low-dimensional geometry. Under a standard structural spectral normalization where $\lambda_{\max}(\hat{\Sigma}) = 1$, we introduce the use of the empirical effective dimension $d^* = \operatorname{tr}(\hat{\Sigma})$, which reflects the intrinsic dimensionality of the problem and guides both the sampling and randomized smoothing parameter schedules. In practice, such a preconditioner can be effectively obtained via pilot sampling, historical trajectories, or domain-specific expert knowledge. We prove that POEM-ES achieves a dimension-reduced convergence rate under low-rank structural assumptions, requiring only $\tilde{\mathcal{O}}\left( \frac{\left( r^2 \kappa(\hat{\Sigma}) + d^* \right) L^2 D_{\mathcal{X}}^2}{\varepsilon^2} \right)$ stochastic zeroth-order oracle queries. The method remains fully parameter-free and demonstrates significant improvements over the original POEM in problems with low-rank structure where $d^* \ll d$. Numerical experiments on hinge-loss binary classification tasks using LibSVM datasets confirm the practical superiority of the proposed approach.

Mycosis fungoides (MF) is a rare form of cutaneous T-cell lymphoma that is often misdiagnosed in early stages due to its visual similarity to benign inflammatory dermatoses. Early and accurate diagnosis is critical for improving patient outcomes. In this paper, we propose a comprehensive diagnostic framework for automated MF detection that combines dual- scale histopathological image analysis with deep learning. To distinguish MF from other lymphoproliferative skin conditions, the proposed approach leverages a late-fusion ensemble of dual- magnification (10x and 20x) convolutional neural networks (CNNs), complemented by a random forest classifier trained on 16 clinical features. Experimental results on an expanded dataset of 6,267 images (4,306 MF; 1,961 Non-MF) across 463 patients demonstrate that strong detection performance is obtained by prioritizing higher-resolution cytological details (20x) within broader architectural context (10x). The image-based late-fusion model achieves an accuracy of 83.58% and a sensitivity of 89.13%, while the clinical random forest model achieves an accuracy of 96.6% and sensitivity of 93.8%, highlighting the po- tential of this multimodal framework as a robust clinical decision support system in dermatology. This framework addresses two distinct clinical objectives: an image-based dual-scale pipeline optimized for the early diagnostic screening of MF versus non- MF dermatoses, and a complementary clinical metadata model designed for the subsequent staging of confirmed MF cases (patch/plaque versus tumor)

This paper examines human-AI interactions (HAIIs) in clinical trials and presents a multidimensional categorisation framework that classifies interactions according to AI tasks, human-AI relationships, interaction configurations and interacting human groups. We define HAII, examine existing taxonomies and extend existing categorisation approaches through this novel multidimensional framework. We purposively sampled 15 clinical trials from a previously reported dataset. Each trial was independently categorised by two human reviewers and six large language model (LLM) classifiers. The proposed categorisation provides a structured method for the consistent identification, comparison and synthesis of human-AI interactions across clinical-trial records. The framework is intended to support more consistent comparison and synthesis of AI-related clinical trials and to make explicit the different forms of human involvement associated with AI interventions. The results demonstrate the potential for LLM-assisted categorisation while indicating the continuing importance of human judgement where trial records are incomplete or ambiguous. The principal contribution is a proposed multidimensional framework that brings together AI tasks, human-AI relationships, interaction configurations and interacting human groups within a single approach designed for clinical-trial records. Its significance lies in its potential to support more systematic identification, comparison and synthesis of how humans and AI interact in clinical trials.

Let $p\geq 5$ be a prime, and let $f$ be a $p$-ordinary cuspidal newform of even weight $k = 2r \geq 2$ and level $N$, with $p \nmid N$ and trivial nebentype. In this article, we prove Kato's Iwasawa main conjecture for $f$, formulated in terms of the $p$-adic $L$-function of $f$, under the sole assumptions that the associated Galois representation of $f$ satisfies the big-image hypothesis and that its residual representation is absolutely irreducible. This generalises the main result of Burungale–Castella–Skinner, which treats elliptic curves over $\mathbb{Q}$ with good ordinary reduction at $p$. Our proof follows their general strategy. A key new ingredient is the construction, over an imaginary quadratic field in which $p$ splits, of a zeta element attached to $f$, together with a proof of its explicit reciprocity laws, generalising the corresponding work of Burungale–Skinner–Tian–Wan. These results provide the higher-weight analogue of a crucial input in the argument of Burungale–Castella–Skinner and allow their method to be carried out for higher-weight modular forms.

We compute the one-loop breaking of the Slavnov-Taylor (ST) identities in a massive Abelian chiral gauge theory with spontaneous symmetry breaking, regularized in the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) scheme. We also provide the one-loop finite counter-terms required to restore the one-loop ST identities. The recent formulation of spontaneously broken models based on the Fröhlich-Morchio-Strocchi (FMS) gauge-invariant and dynamical (i.e. propagating inside loops) fields is used. The proposed algebraic approach holds true to all orders in the loop expansion and allows for a consistent decomposition of the ST breaking into independent sectors. By using cohomological techniques we eventually constrain the dependence of the ST breaking on the vacuum expectation value of the Higgs field. This yields a set of differential equations that provide a useful check of the mass-dependent terms in the ST breaking terms in the broken phase. They can be generalized to the non-Abelian case, both in the gauge-invariant formalism and in the conventional one. In the massless limit we find agreement with previous calculations present in the literature.

We determine the intrinsic mirror of an orbifold cubic surface with three nodes and interpret the resulting geometry through mirror symmetry between the $PGL(2,\mathbb{C})$ and $SL(2,\mathbb{C})$ character varieties of the once-punctured torus. We further construct a quantization of the mirror using higher genus Gromov-Witten theory and show that it recovers the $A_1$ spherical double affine Hecke algebra.

Large language models (LLMs) are increasingly used in culturally sensitive settings, where alignment requires representing diverse preferences within populations. Yet existing methods model populations at coarse demographic or community levels and overlook within-group variation. We introduce Demographic Pluralism, an inference-time framework that estimates population-level opinion distributions without opinion-distribution training data or task-specific fine-tuning by generating multiple perspectives within demographically grounded groups. Across four backbones on GlobalOpinionQA and VITAL, it reduces Jensen-Shannon distance by 8.4%-26.4% over Modular Pluralism. Among weighted, equal-weighted, and inverse-weighted aggregation, equal weighting performs best overall; group-level error also increases with group weight, helping explain weighted aggregation's weaker performance.

We design auctions for the sale of a single item with unlimited supply given a single prediction of the revenue-maximizing uniform price. This departs from prior work on auctions with predictions which typically assumes predictions of every bidder's value. Our main result is a characterization of the Pareto frontier for consistency and robustness attainable by any universally truthful auction. We show that a mechanism that randomizes between posting the predicted price and conducting an optimal prior-free fallback auction is Pareto-optimal. We then extend our results to achieve graceful degradation of revenue as a function of the prediction accuracy. Finally, we study how such a prediction can be obtained from historical market data through the lens of learning theory. Together, our results give an end-to-end account of how a price prediction can be learned and used robustly to maximize auction revenue.

Recent millimeter wavelength observations at 230 GHz by the Event Horizon Telescope have resolved the innermost structure of the Galactic Center, Sgr A*, revealing a ring-like structure consistent with synchrotron emission from a magnetized torus surrounding a supermassive black hole. These observations reveal two key features: three prominent hotspots near the photon ring and low light-curve variability, with a modulation index of $\bar{\sigma}/\bar{\mu} \lesssim 0.1$. State-of-the-art general relativistic magnetohydrodynamic and radiative transfer simulations cannot simultaneously reproduce the three hotspots and low light-curve variability observed in Sgr A*. We propose that an orbiting hot blob, formed in the accretion disk, could account for hotspots. We systematically explore its physical properties, including size, emission amplitude, orbital radius, eccentricity, velocity, and orbital plane orientation. The results – applying two observational constraints–show that the preferred model corresponds to a black hole with dimensionless spin $a_{\star}=0.5$, a magnetically arrested disk configuration for the magnetic field, and the presence of a hotspot with size $\sigma_{\rm hs}=2\,M$ and intensity amplitude $A=10$, orbiting circularly at $r_{\rm orb}=6 M$ with Keplerian velocity in the black holes equatorial plane, and an inclination view angle of $i^\circ=20$.

Public institutions increasingly procure AI systems whose design they cannot inspect or change. In higher education, proprietary Early Warning Systems (EWS) leave colleges with few options beyond adjusting model outputs to address inequity. This raises the question of how fairness work is coordinated among vendors, institutions, advisors, and students with unequal power to change these systems? Using student records from a public college in Ontario, Canada, we evaluate six post-hoc fairness interventions on a research EWS under simulated procurement constraints. We compare fairness, accuracy, and demographic disparities, introducing error-type profiling to trace how interventions redistribute false positives and false negatives. Interventions redistributed disparities without consistently reducing them. Two implementations favored already-advantaged groups because they used group size to define disadvantage; small, marginalized groups remained poorly served. These findings show how procurement constraints and implementation choices shape the possibilities for fairness work. We call the resulting condition fairness theatre; dashboard metrics converge while groups' error burdens persist or worsen.

We study a two-parameter deformation of scalar curvature associated with the Gauduchon connections on compact Hermitian manifolds. A central identity expresses its dependence on the connection parameter through the squared norm of the trace-free part of the torsion of the Chern connection. We establish existence criteria for metrics of constant deformed scalar curvature and analyze the global dependence of the deformed Yamabe invariant on the connection parameter, including when the critical threshold is reached. We also study a prescribed-curvature problem in positive conformal classes. Applications include attainment of the critical threshold for an explicit Hopf example in every complex dimension at least two and on non-locally conformally Kähler Iwasawa products.

There has long been a tension between the stellar ages in the Orion Nebula Cluster and the rapid external photoevaporation of its protoplanetary discs. Recently, the shell of the Orion Nebula has similarly been found to be dynamically younger than the stars. We propose a new scenario to resolve both age problems. In our scenario the ONC's most massive star, $\theta^1$~Ori~C1, formed from the merger between two binary stars induced by vZLK oscillations due to the present-day binary companion $\theta^1$~Ori~C2. This merger, happening between the last episode of star formation and today, resulted in an increased luminosity, leading to stronger external photoevaporation and accelerated expansion of the shell. {We use Monte Carlo simulations to explore both whether a sudden brightening of $\theta^1$~Ori~C1 could reconcile the stellar ages and shell expansion, and whether triple progenitors to $\theta^1$~Ori~C\, could result in stellar mergers on the relevant timescale. A sudden brightening of $\theta^1$~Ori~C1 a few hundred thousand years ago can reproduce today's shell while maintaining a system age close to the stellar age. However, the required increase in stellar wind luminosity is greater than a simple merger can explain. At lower luminosity, the mixing of a relatively greater amount of cool photoevaporative wind material into the hot bubble could result in the required increase, and we identify a lower limit on the required strength of this effect. Additionally, we find that progenitor triples merge readily, on timescales even shorter than the scenario would require. These mergers could be deferred by increased pre-main sequence tidal effects, rotation, and perturbing encounters with other cluster members. Our proposed scenario with a merger driven by von Zeipel-Lidov-Kozai evolution solves two problems; the Orion Nebula's proplyd problem and the shell lifetime problems.

We investigate how the Yarkovsky effect created by one flat surface element on the asteroid depends on the thermal parameter. Then we integrate the Yarkovsky force over the surface of a spherical asteroid. In the next articles of the series, we will investigate the Yarkovsky force for bodies of more complicated shape and compute the change of the asteroid's orbit. Using perturbation theory, we analytically solve the one-dimensional heat conduction equation under the surface element and use the solution to analytically compute the Yarkovsky effect in the limiting cases of big and small thermal parameters. Then we analytically sew the two solutions to obtain an approximate expression for the Yarkovsky effect valid for both large and small thermal parameters. We verify it by comparing it to the results of the numerical solution of the heat conduction equation. Finally, we fit the parameters in an approximate analytical expression to improve the agreement with the numerical results. We obtain a fully analytical expression for the Yarkovsky effect of one surface element, which is composed of 4 terms and is precise for any value of the thermal parameter up to the accuracy of 15%. We also propose a fitted expression of the same form, which is precise up to 0.15%. They both much supersede the traditionally used 3-parameter fit, which produces an error up to 50% and, in particular, is about a factor of 2 wrong for small values of thermal parameters. Finally, we apply the new formalism to evaluate an analytical expression for the Yarkovsky force acting on a spherical asteroid, ending up in a 0.1%-accurate fitted expression for an asteroid with 0 obliquity on a circular orbit and a less accurate expression for the general case.

Lagrangians of the moduli space of Higgs bundles are a fundamental piece of its study under the lens of mirror symmetry. We construct a new class of Lagrangians defined via a zero 'velocity condition' imposed on the natural action of the non-zero complex numbers on the moduli space, motivated by a certain 'infinitesimal conormal principle'. These are Lagrangian subvarieties analogous to the upward flows considered by [CW19] and [HH22], but which fiber over the $\mathbb{C}^*$-fixed point subvarieties. We then prove a formula for the number of intersection points of this Lagrangian with the generic fiber of the Hitchin map, and build a vector bundle over the dual moduli space which we conjecture to correspond to its mirror hyperholomorphic bundle.

Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called Wasserstein barycenters. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the Wasserstein simplex, remains underexplored. We refer to this problem as Universal Barycenter Approximation, and propose BaryFM, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. BaryFM achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.

We study the local geometry, singularity classification, and wavefront dynamics of complex evolutoids for regular holomorphic curves in $\mathbb{C}^2$ equipped with the standard complex bilinear metric. By integrating the generating family of rotated complex affine lines, we derive an explicit parametrization for the 1-parameter family of complex wavefronts $\Gamma^{\theta, w}$ and establish that their singular cusp locus sweeps out the complex evolutoid $E^\theta$. Using a square-root-free formulation, we classify the local behavior of $E^\theta$, proving that evolutoids remain regular and tangent to the curve at isotropic points ($q=0$) while escaping to infinity at complex inflections ($\kappa=0$). Finally, we analyze the three-dimensional complex discriminant surface $\mathcal{D}_F \subset \mathbb{C}^3$ formed by the evolving family $E^\theta$. We prove that $A_2$ cusps are versally unfolded by spatial parameters, whereas $A_3$ swallowtail singularities are holomorphically versally unfolded by $(x_1, x_2, \theta)$ if and only if the complex non-degeneracy condition $\kappa^4 + \kappa_s^2 \neq 0$ holds. Crucially, we demonstrate that simple isotropic points drive the breakdown of this versality condition, inducing degenerate, non-transverse sections of the complex swallowtail surface.

Machine-learning signals built from financial text treat what institutions say, and what the media repeat, as evidence about value. But whoever shapes a narrative may be trading against it. We study markets with three observable voices: institutional statements (Say), media repetition (Echo) and revealed positioning (Do). We ask when words should be followed and when they should be faded. In a linear-quadratic model of an informed institution that speaks and trades before a partly credulous crowd, talking an asset down while buying it is optimal exactly when $\varphi^2<2\lambda k<\varphi$. A distribution-free identity then shows that when the observable Say-Do covariance is negative, words carry negative predictive content and should be faded. For measurement, we derive (i) an exact factorised posterior over which articles are echoes, combining arrival times with embedding similarity; (ii) a return-aligned contrastive objective that attains its bound exactly when squared embedding distances are an increasing affine function of squared outcome distances, with the tightest loss-based certificate of which neighbour rankings survive imperfect training; and (iii) a path-signature statistic for who moved first. In a controlled market with known ground truth, echo sentiment predicts returns with a significantly negative sign in all 29 simulated markets, the rolling Say-Do correlation flags false-alarm events with an AUC of 0.90, and return-aligned embeddings organise headlines by consequence rather than topic. We also report where the tools fail.

In this paper we study Euclidean triangles associated with Diophantine $D(4)$-triples. For a $D(4)$-triple $\{a,b,c\}$, $a<b<c$, we prove that the lengths $r=\sqrt{ab+4}$, $s=\sqrt{ac+4}$ and $t=\sqrt{bc+4}$ associated with this $D(4)$-triple form a non-degenerate triangle if and only if the triple is regular and $r>b-a$. For a fixed shortest side $r$, we describe all triangles associated with $D(4)$-triples in terms of the factorisations of $r^2-4$, give a divisor criterion for their number, and determine their angle type. We also prove that two similar triangles associated with $D(4)$-triples are necessarily congruent. Finally, for the family of $D(4)$-triples $\{r-2,r+2,4r\}$, we obtain a Pell-equation characterisation of the Heronian triangles associated with these $D(4)$-triples.

Constantly evolving real-world knowledge necessitates models to be updated continuously. Especially in medicine, as clinical evidence changes over time, outdated knowledge can pose safety risks. Existing evaluations of knowledge integration focus on factual recall, offering limited insight into whether newly integrated knowledge is actually usable. Our benchmark MedKIT (Medical Knowledge Integration and Transfer) provides a granular evaluation of how models integrate and apply knowledge under realistic sequences of clinical updates. Each instance corresponds to a factual update derived from clinical evidence, paired with targeted probes that assess transfer across lexical variation, relational transformations, compositional reasoning, and open-ended operationalization, as well as locality tests for knowledge preservation. Using MedKIT, we conduct a large-scale empirical study of 12 knowledge integration strategies across 5 diverse models, including both general-purpose and medical LLMs. Our results reveal a consistent gap between recall and usable knowledge: while most methods achieve strong gains on the original update task and under lexical variation, relational generalization is limited, and no method yields meaningful improvements on compositional or operational tasks. These findings highlight a fundamental challenge in knowledge integration and position MedKIT as a testbed for developing methods that make newly integrated knowledge more consistently usable across tasks and contexts.

Time-modulated metasurfaces offer a magnet-free route to nonreciprocal wave control, but existing realizations modulate only the electric response of the structure, and proposals for simultaneous electric-magnetic modulation have so far remained theoretical. We experimentally demonstrate a space-time-periodic meta-transceiver whose omega-topology unit cell integrates varactor-loaded electric (dipole) and magnetic (ring) resonators, both modulated by a common unidirectional traveling-wave bias. This modulation gives rise to two independent, experimentally resolved manifestations of nonreciprocity: on transmit, the incident field is efficiently converted into a polychromatic comb of harmonics that radiate at distinct, bias-reconfigurable angles, while on receive, the same modulation instead suppresses frequency conversion and routes the incoming wave preferentially toward one port over the other. These two effects - nonreciprocal polychromatic conversion and unidirectional wave routing - arise from a single unidirectional space-time modulation but act on distinct physical observables, frequency content and spatial direction, respectively. Measured near the electric resonance with a shared bias, these effects characterize the complete cell and do not separate its electric and magnetic contributions. Our results establish the space-time-modulated omega-topology cell as an experimentally viable platform for reconfigurable, full-duplex nonreciprocal wave transformation.

Instruction-guided video editing has made significant progress, yet existing methods use multimodal large language models (MLLMs) primarily as semantic encoders, so they often fall short in working with implicit edits that require causal or semantic reasoning. To bridge this fundamental gap in video editing, we propose ThinkV2V, a reasoning-driven framework for complex instruction-guided video editing, explicitly activating MLLM thinking before visual generation. At its core, ThinkV2V builds on a practical MLLM-to-DiT architecture to turn explicit thinking over the source video and instruction into refined conditioning signals for video editing. Further, we equip it with a dedicated training and inference recipe, combining Progressive Curriculum Training, which gradually cultivates the model from basic editing to reasoning-intensive cases, with Inference-Time Thinking Scaling, which iteratively refines candidate prompts and selects the most reliable one, to better elicit reasoning in challenging editing scenarios. We also curate the ThinkV2V-150K dataset and introduce ThinkV2V-Bench to support training and evaluation of video editing with implicit intent and causal reasoning. Experimental results demonstrate the state-of-the-art performance of ThinkV2V on both complex and standard editing scenarios, in which our 5B-scale DiT model substantially outperforms larger 10B-scale baselines.

A valid curvature upper bound need not justify either a robustness certificate or an intervention on an intrinsic predictor property. We demonstrate this distinction for a last-layer relative-flatness proxy used in both settings. First, empirical-risk stationarity does not eliminate pointwise first-order loss terms: at a finite global empirical-risk minimum, the retained certificate expression underestimates a loss increase by over $210\times$. We derive a globally valid, gauge-invariant feature-space repair. Second, common-row softmax shifts preserve predictions and the exact contraction while making the proxy unbounded. Even standard reference-class choices double it on average relative to the centered representation. For a single fixed-feature example with at least three classes, scalar retuning generically cannot align the induced probability updates. Row centering gives the orbit-minimized bound and restores value and full-model gradient invariance under this symmetry. Across 45 paired one-step tests on algorithmic and image models, amplified shifts separate raw-regularized predictors while quotient-regularized predictors remain aligned. Long-horizon CIFAR-10 experiments show substantial, reversible suppression of generalization, while evidence for selective delay after memorization is less consistent. Together, these results show that validity as a curvature upper bound does not by itself justify either inversion into a robustness certificate or differentiation into an intrinsic training intervention.

We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is preserved by an affine bijection. The matrix size is of order $\sqrt{d}$, where $d$ is the dimension of the original system. This also gives a three dimensional (smallest) counterexample to Arveson's hyperrigidity conjecture.

Random splitting can yield non-independent train–test subsets when a dataset contains related samples, as is common in certain applications such as biochemical studies. This leads to overly optimistic generalization estimates. Here, we introduce ReLaG, a modality-agnostic framework that models sample relatedness through a hierarchical latent-variable process and infers groups of related samples using proximity graphs and community detection to produce independent train–test subsets. Across molecular and protein datasets, ReLaG matches existing relation-aware methods while scaling substantially better, enabling splits at previously impractical dataset sizes. We further introduce a label-free procedure that adapts the splitting resolution to production data, aligning evaluation with the intended deployment setting. ReLaG's inferred groups provide a cheap estimate of effective dataset size, enabling diversity-aware dataset scaling. ReLaG is open source and can be installed with pip install relag.