Papers

Anterior-posterior polarization in the Drosophila oocyte requires posterior localization of oskar mRNA. oskar mRNA is produced in the anteriorly situated nurse cells, moved into the oocyte, and assembled into oskar-Staufen ribonucleoprotein particles (RNPs). These RNPs then move through the oocyte and interact with the cortex, where myosin-V binds them to the actin network and kinesin-1 removes them along cortically anchored microtubules. This cortical tug-of-war takes place against an anterior-to-posterior decrease in microtubule density. How the interplay between cytoplasmic transport and cortical binding and unbinding produces a stable posterior cap is unclear. Here, we combine quantitative microscopy, photoconversion experiments, experimental perturbations, and biophysical modeling to show that posterior localization emerges from position-dependent cortical exchange coupled to cytoplasmic diffusion. Our model, which accounts for the tendency of RNPs to demix, suggests that two key parameters that determine the observed localization pattern are the total amount of oskar and the ratio of cortical unbinding to binding rates (the exchange equilibrium constant). Given oskar volume fractions in wild-type, the measured exchange constant is such that oskar localizes to the posterior cortex without demixing. If the balance is broken, say by increasing unbinding rates, oskar irreversibly demixes into cytoplasmic droplets. This is consistent with observations from our experimental perturbations. Our results show how bulk diffusion and cortical exchange, in the face of oskar RNPs' self-attraction, convert a cytoskeletal asymmetry into robust developmental polarity.

We resolve the remaining cases of a longstanding problem on the lower and upper Lie nilpotency indices of modular group algebras. Equality of the two indices has been known in characteristics greater than three since 1992; we establish it in the remaining characteristics two and three, thereby completing the problem for finite groups of prime-power order over finite fields. The proof gives a uniform argument for every prime and introduces a terminal restricted Poincare-Birkhoff-Witt construction that converts the lower-Lie problem into a chronological reachability argument, with no structural hypothesis on the derived subgroup.

Decisions that will shape future fusion facilities, including the production of waste, the management of tritium, the achievement of safety, and impacts on land, water, and local communities, are increasingly becoming sociotechnical in nature. For prior energy technologies, fission among them, such decisions were made top-down and met sustained public opposition. Research shows such opposition is rarely a deficit of public understanding and is instead rooted in place-specific environmental, health, sociocultural, and economic concerns and in distrust of how technologies are selected and sited. We argue that fusion developers have an opportunity to design differently, and we propose an ecology of participation: multiple, complementary modalities of engagement sustained over time, replacing the one-off public consultations now typical of large infrastructure projects. We synthesize human- and environment-centered design frameworks and introduce a framework that reinterprets opposition as a divergence between communities and technology developers in values, norms, or design characteristics. We present six case studies from our work: participatory technology assessment focus groups, participatory design workshops, immersive virtual-reality models of a fusion facility, the Global Fusion Forum platform, the Imaginary Energies speculative design platform, and Heartbeat, an arts-based sound installation. Mapping these onto the values-norms-design framework shows how each interrogates or closes a different part of the expert-public gap, and exposes two limitations of fusion public engagement efforts writ large: developers are seldom asked to articulate their own values and norms, and the environment is represented only indirectly. We close with five guiding questions for fusion researchers building their own participatory engagements.

Objective: To develop and validate a framework for spatially resolved ascending aortic strain estimation from 4D computed tomography angiography (CTA) and characterize reliability across segmentation sources and spatial scales. Methods: We constructed patient-specific aortic strain maps using nnU-Net segmentation, optimized surface remeshing, deformable registration, and mesh-based strain estimation. Finite element (FE)-derived synthetic 4D CT sequences provided controlled reference deformations for registration validation. Strain reliability was characterized across segmentation sources and Laplace-Beltrami (LB) spectral scales. Associations with diameter, aortic height index (AHI), and age were assessed. Results: Registration-derived median strain showed minimal bias relative to FE-reference strain for observer-derived (0.0013) and nnU-Net-derived meshes (0.0056). Median strain exhibited low bias and narrow 95% limits of agreement (LoA) across segmentation sources (interobserver: bias = -0.0045, LoA [-0.0490, 0.0399]; nnU-Net versus observer: bias = -0.0052, LoA [-0.0340, 0.0237]). Differences were greater for 95th-percentile strain, particularly in the interobserver comparison. LB spectral analysis showed preferential preservation of low-frequency strain organization, with k = 5 reconstructions reducing segmentation-related disagreement by 52-56%. The 95th-percentile areal strain was inversely associated with maximum ascending aortic diameter (r = -0.493, p = 0.005), AHI (r = -0.488, p = 0.005), and age (r = -0.479, p = 0.006). Three high-grade AR cases showed heterogeneous regional strain patterns. Conclusion: This framework reproducibly estimates ascending aortic strain from 4D CTA, characterizes its reliability across segmentation sources and spatial scales, and demonstrates its potential for noninvasive assessment of patient-specific aortic mechanics.

Shortcut learning is a prevalent issue in robot learning. The limited diversity of robot demonstration datasets can mislead policies into exploiting spurious correlations between tasks and irrelevant features, such as viewpoint or background. Collecting sufficiently diverse robot demonstrations is costly and inefficient, motivating algorithmic alternatives. We focus on vision-language-action (VLA) models and discover that different vision-language model backbones exhibit substantially different levels of susceptibility to visual shortcut learning. We find that model behavior correlates with our proposed representation-level metric, action margin, which requires no policy rollouts. Visual shortcuts consistently enter action representations in early layers, with models differing in the extent to which later layers correct them by incorporating language information. To boost models' attention to language, we introduce task scrubbing, a new domain-adversarial training method that decreases models' likelihood of using visual shortcuts and improves VLAs' generalization. Experiments in both simulation and the real world across multiple VLAs and visual cues show that task scrubbing improves out-of-distribution robustness and often eliminates visual shortcut learning.

A rational polyhedron has Chvátal rank at most one if a single round of Chvátal-Gomory cuts yields its integer hull. In 1973, Chvátal asked whether 0/1 integer programs over polytopes of bounded Chvátal rank can be solved in polynomial time. For polyhedra of bounded Chvátal rank, integer feasibility is in NP $\cap$ coNP, so it is unlikely to be NP-hard. We answer Chvátal's question negatively already in its most restricted form: for Chvátal rank one, for integer feasibility, and even for the SAT polytopes of formulas whose clauses have at most three literals. Our answer holds under either of two standard assumptions from lattice-based cryptography. First, a polynomial-time algorithm for integer feasibility on such SAT polytopes of Chvátal rank one would solve bounded distance decoding with polynomial factors in deterministic polynomial time, contradicting the conjectured hardness of approximating lattice problems within polynomial factors. Second, assuming the hardness of learning with errors, an average-case analog of bounded distance decoding, the problem is also hard on average, for a polynomial-time samplable distribution of formulas. This also gives negative answers to related questions of Cornuéjols, Lee, and Li. We first prove these results for parallelepipeds, where they rest on an elementary sufficient condition: a polyhedron has Chvátal rank at most one if its width is less than one along every row of some unimodular matrix. For our parallelepipeds, such a matrix exists but is hard to find. For SAT polytopes, we represent candidate lattice vectors by their residues modulo small integers, and binary arithmetic on additional 0/1 variables checks that these vectors lie in the lattice.

The magnetic field of the Sun is a key driver of coronal heating and solar wind acceleration. In tandem, these influence the observable morphology of the corona, along with defining the magnetic connectivity and magnitude of open magnetic flux. Here,we investigate how coronal heating affects the magnetothermal state of the 3D global corona by analyzing a series of data-constrained, thermodynamic magnetohydrodynamic (MHD) simulations for solar minimum conditions. We vary the overall heat deposited in the corona via modifying the input Poynting flux of a wave-turbulence-driven (WTD) model for coronal heating and by scaling the inner boundary magnetic field. We quantify the magnetic, thermodynamic, and combined magnetothermal effects on our simulations. We find that increasing the overall amount of heat leads to a higher magnitude of open flux and a more visibly open white-light morphology in the K-Corona between 1.5 and 6 Rsun. We quantify how plasma beta evolves and drives morphological differences between simulations. We also compare these runs to an extremely high-resolution reference solution that includes small-scale magnetic information in the surface boundary condition. This latter comparison provides insight into the further development of 'subgrid' corrections for low(er) resolution models to best represent the structure and observables of the corona and inner heliosphere.

Membership inference attacks (MIAs) threaten the privacy of machine learning (ML) training data by determining whether a sample was used to train a target model. Existing MIAs rely on model outputs, ranging from prediction probabilities to predicted labels, an assumption that can be restrictive for on-device ML systems with limited or inaccessible outputs. However, suppressing model outputs does not eliminate the data-dependent computations that produce them, which may remain observable through physical side channels. We present PSCMIA, a power side-channel membership inference attack against embedded ML models that can infer membership directly from power traces without requiring prediction probabilities or even the predicted labels. We evaluate PSCMIA across multiple datasets (MNIST, FMNIST, CIFAR10, CINIC10), fully connected (FC) and convolutional neural network (CNN) architectures, and two embedded platforms (STM32F3, XMEGA). PSCMIA achieves ROC-AUC values of up to 0.907 on FC models. For CNN models, the ROC-AUC gap between PSCMIA and probability vector-based shadow MIA ranges from 0.006 to 0.116. Across the FC and CNN evaluations, PSCMIA outperforms label-only MIA in 11 of 16 model-dataset-hardware configurations, demonstrating that physical execution can expose membership information even when conventional model outputs are unavailable through unintended power side-channel leakage.

We study the relation between the saddle property and local metric minimality for smooth surfaces in Euclidean spaces. Anton Petrunin and Stephan Stadler proved that every smooth strictly saddle surface in $\mathbb{R}^3$ is locally metric-minimising and expressed the expectation that this phenomenon fails in $\mathbb{R}^4$. We confirm this expectation and prove a stronger density result: Every smooth strictly saddle embedding of a closed disc into $\mathbb{R}^4$ can be approximated arbitrarily closely in the $C^\infty$-topology by smooth strictly saddle embeddings that are nowhere locally metric-minimising. In particular, nowhere locally metric-minimising saddle embeddings exist in $\mathbb{R}^d$ for every $d \geq 4$. The main ingredient is the construction of non-trivial infinitesimal isometric deformations of saddle immersions in $\mathbb{R}^4$ supported in arbitrarily small discs. We also provide an explicit twisted quadratic surface that is saddle in a neighbourhood of the origin but fails to be locally metric-minimising there, by deriving a necessary condition for metric minimality.

Real-world data often exhibit nonlinear, interactive associations between predictors and an outcome. For example, in public health studies, environmental exposures and demographic variables can have nonlinear associations with health outcomes and modify the associations of other predictors. Parametric regression models facilitate interpretable inference and hypothesis testing with Type I error rate control, but may be misspecified when associations are nonlinear. In contrast, flexible nonparametric regression models such as Gaussian processes (GPs) can capture complex nonlinearity, but are often more difficult to interpret and do not readily provide hypothesis tests with Type I error rate control. To bridge this gap, we propose a hypothesis testing framework based on additive GPs restricted to pairwise interactions, allowing tests of variable associations and interaction effects with Type I error rate control. We further establish contraction rates for additive GPs, providing theoretical support for their reduced dependence on predictor dimension when higher-order interactions are absent. Through simulations, we show that restricting the model to pairwise interactions can substantially improve testing power relative to methods based on standard GPs. Applications to environmental health studies identify nonlinear associations between metal exposures and health outcomes as well as effect modification by demographic factors.

Human communities are governed by normative systems: shared standards that produce norms dictating acceptable behavior, enforced through community sanctioning. Aligning increasingly autonomous AI systems with these norms is a central alignment challenge, complicated by the fact that norms are vast in number, change quickly, and are often arbitrary (e.g., dress or language conventions). Thus, alignment requires normative competence: the ability to discern from interaction alone what norms a community enforces without relying on static pretrained knowledge. We introduce a multi-agent community debate setting, where access to debate is governed by synthetic norms, to study normative competence in isolation from pretraining exposure. We show that baseline LLM agents fail to learn norms even when doing so would improve their accuracy. We then experiment with various normative modules – architectural components for norm inference – finding that norm-following is highly sensitive to both the style of norm and the model powering the normative module, suggesting a lack of generalizability. Furthermore, when idiosyncratic, non-normative behaviors accompany the true norm, LLM agents exhibit an unselective attribution failure: they indiscriminately copy idiosyncratic noise alongside enforced rules, a pattern that persists even when imitating unnecessary behaviors is explicitly penalized. To the best of our knowledge, our work is the first to operationalize and evaluate normative competence in LLMs, demonstrating that current AI systems excel at behavioral mimicry but lack the capacity to discern socially enforced order.

Sampling-based system identification estimates physically meaningful parameters by tuning a simulator to reproduce the target system dynamics, providing an interpretable approach to improving sim-to-real transfer. Yet when the collected trajectories do not distinguish the effects of different parameters, multiple parameter combinations can reproduce those trajectories, leading to unreliable parameter estimates. To address this challenge, we introduce an Informationally Decoupled Trajectory Design framework (IDTD), which formulates the objective for the exploration policy built on the Schur complement score derived from the Fisher information matrix. To faithfully reflect parameter separability in the exploration objective, IDTD normalizes the score against the per-parameter information, selects the most favorable trajectory segment for each parameter, and aggregates the resulting scores logarithmically. The optimized trajectory is therefore composed of complementary intervals, each exposing a distinct subset of parameters whose contribution to the motion over that interval can be attributed unambiguously. Across diverse simulation environments, ranging from a linear-dynamics system to the Go2 quadruped, G1 humanoid, and Crazyflie quadrotor, IDTD reduces the parameter identification error by 39.6% on average relative to the strongest prior active-exploration baseline and attains improved downstream policy transfer. Furthermore, we validate the proposed trajectory design on a real K1 humanoid, demonstrating that the resulting identified parameters accurately capture the real-system dynamics. Code is available at https://github.com/jsw7460/IDTD.

We prove an $\Omega((\log n/\log\log n)^2)$ unconditional lower bound on the maximum of the update time and the query time for Pătraşcu's multiphase problem [STOC 2010] with Disjointness, in its insert-only form. Through his reductions, we obtain the same lower bound for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions, improving the $\widetilde{\Omega}(\log^{3/2} n)$ lower bound of Larsen and Yu [SICOMP 2025], and matching the strongest lower bound known for any dynamic problem. The same bound holds for many other dynamic problems: in directed graphs, for incremental $s$-$t$ reachability, strong connectivity and cycle detection; in undirected graphs, for incremental shortest paths, subgraph connectivity and triangle detection; and for dynamic set disjointness, range mode, and Langerman's, Pagh's and Erickson's problems. Ko [FOCS 2026] recently proved this bound for a variant of the multiphase problem with Inner Product in place of Disjointness, via a 2.5-round multiphase communication game; we bring this framework to the original problem. Our main technical contribution is to show that verification in this game makes a one-sided corruption bound suffice in place of discrepancy, which Disjointness lacks.

In this paper we propose lifted Markov Chains (MCs) as a new paradigm for deriving patrol strategies for mobile agents on an environment represented as a graph. Lifted MCs operate on a state space that can be larger than the set of nodes of the graph, and a projection operation maps the MC state to the corresponding node of the graph. We prove bounds on the performance improvement of lifted MCs over non-lifted MCs, where the performance is measured by the Kemeny constant, and show a corresponding monotonicity for the Stackelberg game capture probability and return-time entropy. These bounds yield a result of independent interest that relates the Kemeny constant and the MC conductance for general MCs. We also provide a tractable method for optimizing lifted MCs on general graphs with edge weights encoding travel times. Simulation results on randomly generated and real-world graphs verify that lifted MCs achieve substantial improvements, particularly on sparse graphs.

We investigate the symplectic geometry of homogeneous spaces associated with semisimple Lie groups, with particular emphasis on cotangent bundles of generalized flag manifolds. Our approach gives an explicit description of the Liouville symplectic form on these spaces in terms of the connections and curvature forms of principal bundles naturally arising from the Lie group structure. This provides a geometric link between the Lie-theoretic properties of generalized flag manifolds and the symplectic structures carried by their cotangent bundles.

We study the stellar, black hole, and satellite galaxy populations of group- and cluster-scale halos in the IllustrisTNG, TNG-Cluster, and FLAMINGO cosmological hydrodynamical simulations. We characterize the mass-conditioned scaling relations, covariance, conditional likelihoods, and mass proxy quality (MPQ) of integral properties within $R_{\rm 500c}$: total stellar mass ($M_{\star,\,\rm tot}$), brightest central galaxy stellar mass ($M_{\star,\,\rm BCG}$), intracluster light mass ($M_{\star,\,\rm ICL}$), total black hole mass ($M_{\rm BH}$), satellite occupation ($N_{\rm sat}$), and satellite velocity dispersion ($\sigma_{\rm sat,\,1D}$), at $z\in \{0,0.5,1,2\}$. While normalization differences of up to a factor of two emerge among simulations, many properties exhibit remarkably similar mass-localized slopes, intrinsic scatters, and MPQs across halo samples and redshifts. Correlations among stellar, satellite, and gas properties are generally consistent in sign and their dependence on halo mass and redshift, whereas those involving $M_{\rm BH}$ and $N_{\rm sat}$ show greater variation, particularly in TNG-Cluster. Conditional likelihoods are nearly lognormal for many properties, including $M_{\star,\,\rm tot}$, $N_{\rm sat}$, and $\sigma_{\rm sat,\,1D}$, while $M_{\star,\,\rm BCG}$ and $M_{\star,\,\rm ICL}$ are negatively skewed. Among the properties considered here, total stellar mass is the best mass proxy, with a halo mass scatter of $7$-$14\%$, followed by $N_{\rm sat}$ with a mass scatter of $9$-$18\%$. The consistent correlation behavior of $M_{\star,\,\rm ICL}$ highlights its potential for next-generation observational studies. Finally, $\sigma_{\rm sat,\,1D}$ exhibits highly consistent scaling, with mass-independent slope and scatter and a largely neutral correlation structure, suggesting that it is relatively insensitive to astrophysical complexity.

We report a systematic ab initio investigation of the excited states and absorption spectra of small mercury clusters (Hg$_{\mathrm{2-5}}$). Benchmarking multi-reference configuration interaction (MR-CISD) and equation-of-motion coupled-cluster (EOM-CCSD) methods shows that EOM-CCSD/aug-cc-PVTZ-PP reproduces atomic excitation energies within $\pm$500 cm$^{-1}$ of experiment, whereas MR-CISD deviates by about $\pm$1100 cm$^{-1}$. For the mercury dimer, EOM-CCSD potential energy curves yield absorption bands in excellent agreement with experimental transitions, while asymptotic excitation energies closely match atomic references. Extending this methodology, we present the first systematic ab initio study of absorption spectra of Hg$_{\mathrm{3}}$, Hg$_{\mathrm{4}}$, Hg$_{\mathrm{5}}$, which display broad bands in the ranges of 37000-60000 cm$^{-1}$. The consistent agreement with experimental benchmarks and diagnostics confirming single-reference character validates EOM-CCSD as a robust approach for describing excited states and optical spectra of mercury clusters.

Speech quality predictors are increasingly used as rewards, yet no agreed measure of their hackability exists. The usual measurement has two flaws. First, the perturbation reaches the predictor through a processing chain – here a neural codec – that shifts the score on its own, which scoring against the raw input charges to the attack. Referencing the unperturbed round trip instead changes measured hackability by up to a factor of four (0.31 to 0.08 for one defence). Second, one trained attacker is a sample, not a measurement: five attackers differing only in random seed reach success rates from 0.00 to 0.38 against one fixed predictor, so a defence claim needs the worst case over several. Under this protocol, four published predictors differ widely: NISQA is hacked on 90% of utterances, SSL-MOS on 21%, DNSMOS on 14% and UTMOS on 6%. We then audit a closed attack-detect-patch loop. It hardens the predictor only in its own attack space, by less than the spread between attackers; a random-perturbation baseline matches it; and it costs up to 0.30 system SRCC out of domain. Enhancers post-trained against patched predictors hack them far less (PESQ -0.03 versus -0.23). Code, preregistration and run outputs are released.

We give a randomized reduction from global minimum cut in a directed graph with $n$ vertices and $m$ weighted edges to maximum-flow computations on graphs of total size $\widetilde{O}(m)$. For polynomially bounded integral weights, this yields the first almost-linear $m^{1+o(1)}$-time algorithm [vdBCK+23], improving the previous $m^{1+o(1)}\min\{\sqrt{n},n/m^{1/3}\}$ bound [CLN+22]. Previous work reduced finding the minimum cut to constructing a 1-respecting arborescence, a directed spanning tree with exactly one edge crossing a minimum cut [CLN+22]. They then construct such a tree by sampling from a $(1+\epsilon)$-approximate arborescence packing, which currently requires superlinear time. Our algorithm sidesteps constructing the packing entirely and relies on a novel iterative arborescence sampling procedure. We show that, after $O(\log n)$ rounds of sampling, our final arborescence 1-respects the minimum cut with constant probability.

Physics-Informed Neural Networks (PINNs) are a widely used data-free method for solving Partial Differential Equations (PDEs) using machine learning. With recent advances in Generative Adversarial Networks (GANs), adversarial learning has shown strong capabilities for modeling complex data-driven problems; however, the use of GANs in deterministic physics-informed PDE solutions remains limited. In this work, we first identify limitations of standard PINNs for solving PDEs, including spectral bias, loss imbalance, and optimizer stagnation. We then propose Generative Adversarial Physics-Informed Neural Networks (Gen-PINNs), a unified deterministic residual-adversarial framework designed to improve data-free solutions of PDEs with sharp or shock-front behavior. The generator learns the underlying PDE solution using dynamically weighted physics-informed loss components, while separate discriminators evaluate complementary PDE residual features against ideal zero-residual states. The framework further develops and adapts several methodological components, including a Fourier representation for resolving high-frequency spatial content, an orthonormal spectral diagnostic for quantifying frequency-dependent solution errors, and a modified gradient-based dynamic weighting system for physics, initial-condition, boundary-condition, and adversarial loss objectives. Gen-PINNs is tested against standard PINNs on nonlinear and higher-order PDEs, including the Burgers, Allen-Cahn, and Kuramoto-Sivashinsky equations. The results demonstrate substantial improvements in accuracy and convergence across sharp-front, stiff, and higher-order PDE solutions, highlighting the potential of deterministic residual-adversarial learning as an effective approach for solving challenging nonlinear PDEs.

Let $f:(\C^n,0)\to(\C,0)$ be a holomorphic germ with an isolated critical point at the origin, and let $\varphi_f$ be the negative gradient flow of $\re f$ with respect to a Riemannian metric. We show that the origin is an isolated invariant set of $\varphi_f$ and that its Conley index is the suspension of the Milnor fiber, \[ h(\varphi_f,\{0\})\;\simeq\;\Sigma F_f\;\simeq\;\bigvee_{\mu(f)}S^n , \] so that $\mu(f)=\rank \CH_n(\varphi_f,\{0\};\Z)$: the Milnor number is the rank of the homological Conley index of the flow in degree $n$. The proof uses continuation to a holomorphic morsification of $f$. Since $\im f$ is a first integral of the flow, after a rotation of the target through an angle avoiding finitely many values there are no connecting orbits between the $\mu(f)$ nondegenerate rest points that result, and the sum property of the Conley index applies. McCord's theorem then recovers the Poincaré–Hopf index of $-\nabla\re f$.

During an infectious disease outbreak, accurate estimates of epidemiological parameters such as the reproduction number and infection duration can inform the public health response. Recently, neural simulation-based inference (NSBI) methods have become popular for estimating these parameters due to lower computational costs and more input data flexibility than traditional methods. Input data modalities that have been evaluated independently in an NSBI framework include case counts and transmission trees. Here, we evaluate whether combining information from these two data types outperforms using information from each individually with NSBI. To do so, we simulated stochastic susceptible-infectious-recovered (SIR) outbreaks across a range of basic reproduction numbers (R0) and average infection durations (D) to generate training, validation, and testing datasets. We then calculated, for each simulated outbreak, summary statistics from case count trajectories and from transmission trees. Using these features, individually and in combination, we performed a type of NSBI called neural ratio estimation (NRE) to estimate R0 and D. We also calculated maximum likelihood estimates of the parameters by fitting a deterministic SIR model using the case count trajectory. All three NRE models outperformed the baseline method. Furthermore, incorporating tree summary statistics improved the estimation of both R0 and D over case count summaries alone. This suggests that trees provide valuable additional information for estimating epidemiological parameters above and beyond case counts alone.

Let $\Gamma<\mathrm{SU}(n,1)$, $n\ge2$, be Zariski-dense and contain a regular loxodromic element $A$. The splitting-field problem asks how far traces and spectra determine a field of definition for $\Gamma$. We show first that traces together with the spectrum of $A$ always give a linear realization over $K=\mathbb{Q}(\textrm{tr}\Gamma,E(A))$. We also prove that every complex-irreducible subgroup of $\mathrm{SU}(n,1)$ with real trace field is conjugate into $\mathrm{SO}(n,1)$; in particular, no discreteness hypothesis is required for this real-trace conclusion. In higher dimension, however, linear descent does not by itself give the standard unitary form: a Hermitian similarity obstruction remains, described over imaginary quadratic fields by Landherr's local invariants. In $\mathrm{SU}(3,1)$ we give a Zariski-dense example for which the one-spectrum field is $\mathbb{Q}(i)$ but does not yield the standard unitary form. This leads naturally to the total spectral field. We prove that the obstruction disappears for arithmetic groups and under suitable local openness hypotheses, and we give an even-degree local criterion. In dimension four we analyze the discrete branch through explicit Schottky groups and rank-one local geometry. There the full Bruhat cocycle recovers anisotropic Levi holonomy and forces a non-split rotational word. The remaining quasi-split rank-two case is not reached by this method, so the general $\mathrm{SU}(3,1)$ problem remains open.

Video-language models commonly assume that more temporal observations lead to more reliable reasoning. We question this assumption and argue that the key challenge is not merely processing more video frames efficiently, but learning to reason reliably under limited temporal evidence. We propose SAVER, a dense-to-sparse post-training framework that uses dense video views as training-time references for sparse-frame inference. During reinforcement post-training, paired dense and sparse views are optimized with grounding rewards and a reliability-gated reference reward, encouraging sparse view predictions to preserve task-relevant temporal evidence. Notably, SAVER is trained only on 1,250 randomly sampled temporal grounding examples, without using any video question answering annotations. Across three temporal grounding benchmarks and six video question-answering benchmarks, SAVER consistently improves performance across frame budgets. In particular, SAVER can match or surpass dense-frame Qwen3.5 baselines while using substantially fewer frames. These results show that temporal grounding can serve as an effective evidence-localization proxy for learning sparse video reasoning that transfers to broader video understanding tasks.

Femtoscopic correlations in proton-proton and heavy ion collisions are commonly calculated using emission sources from microscopic transport models, where emitted particles are represented by classical phase-space points with simultaneously specified positions and momenta. This point-emitter picture neglects the finite phase-space localization required by quantum mechanics, which can become relevant when the localization scale approaches the femtoscopic source size, particularly in small collision systems. We formulate a quantum treatment by replacing each transport phase-space point with a minimum-uncertainty Gaussian phase-space distribution. Finite localization then induces both spatial and momentum smearing; in the presence of coordinate-momentum correlations, the latter produces a nontrivial modification of the emission source. Using proton–proton collisions at $\sqrt{s}=7~\mathrm{TeV}$ simulated with the microscopic Parton–Hadron–String Dynamics transport approach, we show that this effect significantly modifies the proton-pair source and its momentum correlation. Our results expose a quantum localization effect overlooked in transport-based femtoscopy and establish the regime in which the classical point-emitter approximation is valid.

We develop a machine learning assisted workflow for the rapid screening of permanent magnet candidates within the CaCu$_5$ structure family. We generated more than 60,000 structures through substitutions. These compositions were screened using a combination of pretrained materials models, Materials Project data, and a machine-learning model for magnetization prediction. Four criteria, namely, metallicity, negative formation energy, energy above the convex hull $\leq 50$~meV/atom, and predicted magnetization above the adopted $\geq 0.75$~T threshold reduced the initial chemical space to 439 candidates for first-principles calculations. Density functional theory calculations revealed that 159 compounds exhibit positive axial magnetic anisotropy energy, favoring [001] over the tested in-plane directions. The resulting dataset reveals chemical trends in magnetic anisotropy across the CaCu$_5$ compositional space and provides a set of candidates for further investigation. More broadly, this work demonstrates a practical strategy for combining existing machine learning models with first-principles calculations to systematically reduce large chemical spaces to tractable sets for computationally intensive materials screening.

Researchers often read before they can articulate what they are looking for. As AI increasingly mediates scholarly search and synthesis, understanding and preserving the idiosyncratic judgments guiding early exploration become important. We call these evolving orientations scholarly sensibilities. To understand curiosity-driven reading, we first examined Wikipedia rabbitholing, a self-directed browsing practice, then designed Wistful, a research probe for open-ended scholarly exploration that captures reading paths as creative reading traces. We studied Wistful with 16 HCI researchers—eight junior and eight senior—in comparison with their usual workflows. Researchers approached the same scholarly landscape differently, with familiarity and personal interests shaping what they pursued and semantic proximity and scholarly links shaping their paths. Their traces made these differences visible and let readers revisit and compare their paths. We position creative reading traces as artifacts for reflection and exchange and as a means of studying how scholarly sensibilities are expressed through reading.

Vision-Language (VL) reasoning requires a model to both extract relevant and accurate information from an image (visual reasoning, VR), and to infer the answer from it (language reasoning, LR). Reinforcement learning with verifiable rewards typically trains both through a single chain-of-thought with a final-answer reward. This gives every CoT token the same sequence-level advantage, failing to distinguish capability specific errors. We propose SPLIT-RL, a staged post-training approach that trains VR and LR in disjoint phases. Because a group's rollouts differ along one capability at a time, the group-relative advantage isolates it, and each phase is optimized using phase-specific reward. We further introduce Claim-Level Advantage (CLA-GRPO), which decomposes VR-phase rollouts into atomic visual claims and provides a fine-grained advantage at claim level based on visual-type group formation. Although trained in two phases, trained policy is evaluated like GRPO model, with a single CoT call at inference time. Under this protocol, SPLIT-RL improves average accuracy over GRPO by 1.4-6.1 points across Qwen3-VL models from 2B to 30B-A3B and InternVL3.5-8B. Evaluating each capability using an oracle based diagnostic shows that answer-only GRPO leaves perception unchanged, whereas SPLIT-RL improves both VR and LR.

Chekuri, Gupta, Newman, Rabinovich, and Sinclair [SODA'03] showed that $k$-outerplanar graphs can be embedded into trees and $\ell_1$ with distortion $2^{O(k)}$. Their result is perhaps the strongest evidence supporting the still-open planar $\ell_1$-embedding conjecture: planar metrics can be embedded into $\ell_1$ with constant distortion. However, the exponential dependency on $k$ in their distortion bound remains the state of the art. Their embedding is obtained by a so-called onion-peeling approach: removing one layer of the graph at a time at the cost of incurring $O(1)$ distortion multiplicatively, and recursively embedding the resulting $(k-1)$-outerplanar graph. In this paper, we devise a new onion peeling approach that peels $k/2$ layers off the input $k$-outerplanar graph at every step. As a result, we obtain the first embedding of $k$-outerplanar graphs into trees and $\ell_1$ with distortion $\operatorname{poly}(k)$, an exponential improvement over the best-known distortion bound [SODA'03]. Our result of embeddings into trees comes closer to the distortion lower bound $\Omega(k)$ for $k$-outerplanar graphs.

We prove an invariant identity relating the curvature operators of the first and second kind in dimension four. Under the natural identification $S^2_0\cong\Lambda^+\otimes\Lambda^-$, the trace-free Ricci tensor contributes through a single commutator term. As a consequence, we relate the curvature operator of the second kind on products of unit self-dual and anti-self-dual two-forms to biorthogonal sectional curvature. We then classify closed oriented four-manifolds satisfying $K^\perp_{\max}\leq S/6$, where $K^\perp_{\max}$ denotes the maximum biorthogonal sectional curvature and $S$ is the scalar curvature. The classification includes the cases in which the scalar curvature vanishes.