Papers

The Fourier Neural Operator (FNO) learns solution operators of partial differential equations (PDEs) through Fourier-space kernel parameterization, but frequency truncation can limit the learning of high-frequency variations. AM-FNO and SirenFNO generate kernels for all grid modes from spectral coordinates using shared networks, making coordinate encoding and generator design important. Recent work on implicit neural representations (INRs) has proposed constructing frequency interactions through explicit feature composition rather than relying on subsequent MLPs to form them implicitly. Building on this approach, we propose CAFE+FNO, which incorporates Content-Aware Frequency Encoding+ (CAFE+) into Fourier kernel generation. CAFE+ combines Fourier–Chebyshev features through parallel affine branches and a Hadamard product, forming interactions within and across the two feature families. A kernel MLP maps the resulting representation of each normalized spectral coordinate to a complex channel-mixing matrix. Each layer shares its generator across all stored modes, making the number of trainable parameters independent of the number of modes for a fixed architecture. We compare CAFE+FNO with existing FNO variants on five PDE benchmarks and conduct ablation studies on basis configuration, multiplicative composition, and bandwidth learnability. Code and experimental configurations are available at https://github.com/fabsk101/CAFEPlusFNO.git.

We investigate short-range correlation (SRC) scaling of nuclear gluon modifications using nCTEQ SRC abundances and EPPS21 gluon distributions. Rescaling the EPPS21 central modifications by these abundances yields an approximately common curve for six nuclei from carbon to lead over $0.1\leq x\leq0.4$ at $Q^2=10$ and $100\,\mathrm{GeV}^2$. The SRC interpretation is supported by the broad agreement between the fitted abundances and high-momentum proton fractions from variational Monte Carlo calculations. Using an SRC proton fraction of approximately $20\%$ in carbon, the measured EMC-SRC correlation also gives a pure-SRC EMC slope of $1.94\pm0.12$, consistent with the nCTEQ estimate $2.02\pm0.20$. To test the connection between this scaling and SRC configurations, we propose recoil-tagged charm-production in deuteron deep-inelastic scattering (DIS), combining a backward high-momentum proton tag with a gluon-sensitive hard process. We formulate leading-power collinear factorization through an extended fracture function, which reduces within the plane-wave impulse approximation to a deuteron light-front spectral factor times a recoil-conditioned neutron gluon distribution. The tagged charm reduced cross section and its ratio to inclusive tagged DIS provide complementary observables for comparing gluon modifications in SRC-enriched configurations with the scaling inferred from inclusive nPDFs.

Let $f:\mathbf P^n_{\mathbb C}\to\mathbf P^n_{\mathbb C}$ be an endomorphism of degree greater than one. We prove that every irreducible Zariski closed subset $V$ with $f^{-1}(V)=V$ is a linear subspace.

Molecular communication (MC) is a communication paradigm in which information is conveyed through the release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside the human body, where the cardiovascular system (CVS) may serve as the physical propagation environment and molecular transport is governed by diffusion and blood flow. Although blood flow is inherently pulsatile, most analytical MC channel models assume steady flow. In this paper, we develop a time-variant analytical model for dispersive MC channels with pulsatile flow. We derive the straight-duct response as a Normal distribution with time-variant mean and variance, capturing the combined effects of diffusion and pulsatile flow, and extend it to closed-loop channels through a wrapped-Normal representation. The model is validated against three-dimensional (3D) particle-based simulations (PBSs) for synthetic and physiologically motivated velocity waveforms. We further derive a closed-form first-order approximation for the first-arrival peak time and introduce the nondimensional indicator $S_{\mathrm{Rx}}$ for assessing the applicability of the reduced one-dimensional (1D) model. Our results show that pulsatility has the strongest influence when molecular transport is predominantly advective and the temporal flow variations are not averaged out, whereas stronger diffusion and faster pulsations reduce its impact on the received signal. Moreover, a PBS-based parameter sweep supports $S_{\mathrm{Rx}} \ge 2$ as a practical criterion for the applicability of the proposed analytical model. Finally, relating the analytical assumptions to representative blood-vessel classes shows that model applicability depends not only on the transport conditions but also on physiological properties such as vessel rigidity, geometric uniformity, and blood rheology.

Many mechanical systems, such as the Newtonian $n$-body system, are invariant under rotations. The rotational symmetry of the system gives rise to two commuting actions: the dynamical action and the action of the symmetry group. In this paper, we exploit this symmetry to construct families of periodic and quasi-periodic trajectories. In the strong-force setting, we extend Montgomery's variational approach to free homotopy classes of curves that are periodic up to a prescribed nontrivial rotation. In the weak-force setting, we establish, under suitable hypotheses, global and local variational persistence results for action minimizers in loop spaces defined by general finite symmetry-group actions under sufficiently small rotations. As applications, we apply these results to the figure-eight orbit, under a numerically supported assumption of strict local minimality, to double choreographic loops with $q$-fold rotation symmetry, and to counter-rotating double choreographic loops in planar $(N+3)$-body problems.

Multi-Agent Path Finding (MAPF) is the problem of planning conflict-free paths for multiple agents in a shared space, each from its start to its goal. Classical MAPF has been the dominant formulation for many years, with its assumptions of discrete time and graph-based conflicts presumably easing the search for solutions. These assumptions limit the physical environments and agents for which a solution is truly collision-free, and also place an upper bound on solution quality that no algorithmic improvements can lift. This work investigates how much solution quality, and in what contexts, the classical MAPF formulation forfeits. Continuous-time MAPF (MAPF$_R$) relaxes these assumptions, making it a natural counter-formulation to compare against across various agent counts and sizes, and graph connectedness, topologies, and resolutions. We find that continuous time and agent shape consideration are worth relatively little on their own; their value comes from enabling an expanded range of move actions, on average improving solution quality by at least $5\%$ on narrow and constrained maps and $17\%$ on maps with open spaces. In some cases, the improvements exceed $20\%$. Doubling the map resolution with classical MAPF recovers less than $3\%$, meaning that little of what is forfeited can be bought back through more compute. This work therefore provides insight on when classical MAPF is a reasonable simplification, and when MAPF$_R$ unlocks significantly higher-quality solutions.

Filamentous cyanobacteria form extensive kilometer-scale mats in aquatic environments, yet the physical mechanisms driving their macroscopic self-organization remain elusive. Here, we investigate the dynamics of filamentous cyanobacterial assemblies within a quasi-two-dimensional confinement. Our observations reveal that chiral gliding drives active tangling between individual filaments, inducing rapid network contraction and the formation of densely packed aggregates. By quantifying single-contact forces, we demonstrate that these mechanical interactions generate significant contractile stresses. Together, our findings sug- gest that chiral gliding has evolved as a physical mechanism to maximize inter-filament interactions and drive large-scale collective organization.

We study a family of liftings $\mathfrak U(\lambda)$ of the super Jordan plane over the infinite cyclic group in characteristic zero. For a nonzero lifting parameter $\lambda$, we identify a natural subalgebra $\mathfrak B$ with the bosonization of $U(\mathfrak{osp}(1|2))$, also known as $sl_{-1}(2)$, and show that the lifting $\mathfrak U(\lambda)$ is obtained from $\mathfrak B$ by an Ore localization at a single distinguished element. This structural description provides a unified approach to the representation theory and ideal structure of $\mathfrak U(\lambda)$. We classify the finite-dimensional simple modules of $\mathfrak B$ and prove that every finite-dimensional $\mathfrak B$-module is completely reducible; the localization then yields the corresponding results for $\mathfrak U(\lambda)$. We determine the prime, primitive, and completely prime ideals of both algebras. Finally, we compute their classical quotient rings, showing in particular that the classical quotient ring of $\mathfrak U(\lambda)$ is a $2\times2$ matrix algebra over the skew field of fractions of the tensor product of its centre and the first Weyl algebra.

We study the emergence of a mutual giant component in a multiplex network comprised of two one-dimensional long-range networks on a lattice. The probability that two nodes on one lattice, with a distance $r$ between them, are connected with an edge falls algebraically with distance as $Cr^{-(1+\sigma)}$, where $0 < \sigma < 1$ and $0 < C \leq 1$. A mutual giant component exists if $C > C_c^{\mathrm{mul}}$, where $C_c^{\mathrm{mul}}(\sigma)$ is a critical value of $C$ that is dependent on $\sigma$. We find rigorous lower bounds on $C_c^{\mathrm{mul}}$, and a tree approximation whose estimate of $C_c^{\mathrm{mul}}$ agrees with simulations within 0.6% for $\sigma \leq 0.5$. The multiplex network is significantly less stable than the single network case, as is evident by the larger value of $C_c^{\mathrm{mul}}$, which is up to 2.4 times the single-layer value. Our simulations indicate that the order of the transition depends on $\sigma$. For $\sigma \leq 0.35$ the mutual giant component collapses abruptly, in a first-order phase transition, while for $\sigma \geq 0.4$ the transition is continuous. When the dependency links connect random pairs of nodes, the transition is first order for all $\sigma$.

Energy landscapes of non-convex optimization problems are high-dimensional surfaces that are difficult to reveal, visualize, or analyze. Message-passing algorithms, or equivalently cavity approaches in statistical physics, may fail to identify local minima as messages do not converge owing to the ruggedness of the energy landscapes. Here we aim to reveal the characteristics of these complex energy landscapes by limiting the amount of information passed in local messages, improving the convergence of messages for local minima. By studying a routing optimization problem with its convexity governed by a single parameter, we introduce a cavity message-passing algorithm with a trust region, and sample ensembles of converged local minima of rugged energy landscapes across many independent realizations of the same problem instances. We observe three regimes with different characteristics of the energy landscapes: (1) a maximally rugged regime with a peak in the diversity of low-energy minima; (2) an intermediate regime with a hierarchical multi-cluster organization of low-energy solutions; and (3) a smooth regime dominated by a single minimum. Additional tests show that the converged energies are largely insensitive to the size of the trust region if the size is small or moderate, demonstrating the robustness of the proposed approach in identifying characteristics of rugged energy landscapes.

Start with the number $2$. At each move, combine two numbers already made, but the operations must be used in the fixed repeating order $+,\times,-,\div$. We ask for the fewest moves needed to make every integer from $1$ to $N$. Since $2$ is already one of the numbers we want and each move makes at most one new number, at least $N-1$ moves are needed. We show that $N-1$ moves are also enough for every $N\ge 9$. Conventional induction cannot work, because a division that comes right after a completed interval $\{1,\dots,P\}$ produces numbers already made. Instead we extend a completed interval $\{1,\dots,P\}$ to $\{1,\dots,3P\}$ all at once, which counting shows is the smallest multiplicative extension $P\to kP$ that can work, and then adjust the last few moves to reach every other $N$. For $9\le N\le 33$ we give explicit sequences, found by computer search.

Speech deepfake detectors often lose accuracy when the distribution of the test data differs from that of the training data. Meta-learning for domain generalization (MLDG) shows promise by simulating domain shifts with episodic meta-train and meta-test splits. However, the MLDG meta-objective considers only a single clean adaptation trajectory and does not account for the local loss landscape around its endpoints. To address this limitation, we first propose an explicit worst-case MLDG variant, dubbed WC-MLDG-4P, which perturbs both the meta-train and meta-test states but requires four gradient evaluations per episode. We then introduce WC-MLDG-2P, a source-directed alternative to the explicit robust objective. It shifts the clean MLDG endpoint toward a locally higher source-loss state and evaluates the meta-test gradient there, retaining the two-evaluation cost of the first-order MLDG. A first-order expansion relates the resulting gradient change to meta-test directional curvature along the source gradient without explicitly computing a Hessian. Relative to MLDG, WC-MLDG-2P achieves relative mean-EER reductions of 23.4% with XLSR-AASIST and 7.6% with XLSR-Conformer-TCM, respectively.

We prove that the peripheral spectrum of every positive operator on a complex Banach lattice is cyclic, thereby resolving the cyclicity conjecture without additional growth assumptions. Our proof is based on a spectral domination theorem derived from Vesentini's theorem on the subharmonicity of the spectral radius: when two positive operators have the same spectral radius and one dominates the other, the peripheral spectrum of the smaller operator is contained in that of the larger one. This extends an earlier result of Räbiger and Wolff. After passing to a suitable lattice extension, an averaging procedure based on torsion operators produces a decreasing sequence of positive minorants which retain the spectral radius and become asymptotically rotationally self-similar. An ultrapower argument turns this asymptotic relation into exact rotational self-similarity, allowing us to deduce cyclicity from spectral domination. The same approach also yields an alternative proof of Lotz's cyclicity theorem for Abel solvable operators.

For better or worse, LLMs are by now used routinely for scientific writing.\footnote{This paper is no exception; we did use AI to assist with writing some of the sections (see Acknowledgments).} Many have noticed that recent models fill papers with unnecessary antithesis, stating over and over what the work does not do, in ways that do not contribute to its precision or quality of expression and annoy reviewers rather than impressing them. We study the construction rather than in ACL papers from 2019, ACL-style arXiv papers from 2026, and papers written by GPT models from the same titles and abstracts. Its rate in 2026 is seven times the 2019 rate, and higher still in the GPT papers. Two annotators, blind to the source, find almost no 2019 use annoying and about one in ten 2026 uses; they seldom agree on which, yet about half of 2026 papers contain a use that annoys each of them. Annoying uses present the rejected alternative less favorably than legitimate uses. Raters of preference data and open reward models favor the construction, and an instruction to be honest promotes it. We conjecture that it is a side effect of post-training on pairwise preferences, which credit a disavowal in a single response and cannot register its cost across a text.

Knowledge-intensive tasks require answering many questions by reasoning about a shared corpus of artifacts (e.g., court cases, or scientific literature). As humans interact with these corpora, they naturally accumulate experiential knowledge about artifacts, enabling them to quickly identify the complete set of relevant artifacts for each new task. However, existing AI agents lack appropriate memory solutions to build or reuse such artifact-grounded experience, leading to lower answer quality and higher online cost. Existing memory solutions extract and reuse information from prior task-solving traces, but they primarily focus on user preferences, factual attributes, or abstract reasoning patterns rather than persistent artifact-specific knowledge. We introduce ExperienceIndex, a novel experience layer for AI agents that captures and reuses knowledge about artifacts based on prior reasoning traces. ExperienceIndex stores two complementary forms of experience: (i) single-artifact experiences that summarize an artifact's contribution to prior tasks and (ii) artifact-pair experiences that encode structural relationships discovered during past reasoning. Integrated as lightweight middleware, ExperienceIndex uses an experience retrieval mechanism to guide agents toward the complete set of relevant artifacts for new tasks, improving both answer quality and efficiency. Across diverse corpora and agentic solutions with different search frameworks, ExperienceIndex delivers consistent gains, raising answer quality by up to 11.0 points and reducing online dollar cost by up to 50.5%. We further demonstrate two benefits: (i) cross-task generalization, where experiences accumulated from text-to-SQL tasks transfer to factoid QA tasks over the same artifact corpus, and (ii) teacher-student learning, where experiences from a stronger model enable a weaker model to reach comparable performance.

Collaborative perception extends the sensing range of autonomous vehicles, but its performance degrades when shared features arrive stale or incomplete. Most latency-robust methods compensate delayed collaborator features through flow-guided alignment or direct feature transport. In this work, we formulate asynchronous collaborative perception as temporal residual prediction. Our Temporal Residual Bottleneck keeps a deterministic pose-warped collaborator feature as a conservative anchor and uses a $\Delta t$-conditioned xLSTM to extract residual temporal evidence from the available history. A detector-facing residual bottleneck then applies only gated, regularized corrections before ego-side fusion, reducing the risk of overwriting reliable static structure when temporal correspondence is uncertain. Experiments on DAIR-V2X and OPV2V show that our method is especially effective under severe fixed/irregular delays and packet drops. On DAIR-V2X, the reported checkpoint trades a small amount of synchronized peak accuracy for better robustness under stronger communication degradation. Controlled diagnostics further indicate that direct feature transport has oracle headroom but can become unreliable when deployed without accurate correspondence. These results support temporal residual fusion as a practical alternative for asynchronous and incomplete collaborative perception. Code will be publicly released at https://url.fzi.de/8dk38.

It is proved that there exists a language $L$ such that its $\omega$-power has infinite rank in the difference hierarchy of open sets. The same holds for the decreasing difference hierarchy of $\Pi^0_2$ sets.

Self-evolving agents distill task-solving experience into skills for future reuse, but these skills can encode incorrect procedures or non-transferable knowledge. It is therefore critical to verify each skill's reusability: whether its guidance remains useful beyond the experience from which it was distilled. Such verification requires observing how a skill affects execution in new tasks, yet existing tasks may not expose the situations where the target skill can actually be exercised. To construct such situations, we propose SkillSandbox, a framework that dynamically synthesizes a task and its environment for each skill that are skill-relevant yet novel. A Proposer specifies the conditions to preserve and the source-specific details to vary, a Builder constructs an executable scenario, and a Verifier compares executions with and without the skill. The Verifier assesses executability, utility, and efficiency to assign a Keep or Reject verdict, determining whether the skill enters the library. Across ALFWorld and WebShop with three models, SkillSandbox consistently yields the strongest downstream performance and improved execution efficiency. Further analyses examine whether these gains reflect accurate assessment of skill reusability and identify which components of SkillSandbox contribute to them.

Offline MARL increasingly relies on generative policies to model multimodal joint behavior, typically by distilling a centralized teacher into decentralized one-step actors under the CTDE. We identify a failure mode at the teacher training stage: standard flow-based teachers pair noise with replay targets independently, so nearby noise samples can be routed toward conflicting coordination modes. The teacher then produces samples between valid modes, and because the distillation loss regresses each local actor onto the conditional mean of the teacher's output given local input, this error is not absorbed but propagated to the student. To remove this teacher-side artifact, we propose Mode-Support Semi-Discrete Optimal Transport (MoSDOT), which summarizes multimodal replay into a finite mode support with prescribed capacities and uses conditional semi-discrete optimal transport to assign each noise sample to a single mode before teacher training. We additionally study a shared-randomness variant that uses a shared noise component at execution to expose the residual gap intrinsic to strict-product execution. On controlled diagnostics and offline MARL benchmarks, MoSDOT improves endpoint quality and routing consistency, particularly on datasets exhibiting multimodal joint behavior.

\noindent Let \(\Om\subset\R^2\) be a smooth bounded simply connected domain. We prove that all positive solutions of \(-\Delta u=\theta ue^{u^2}\), with \(\theta>0\) and zero Dirichlet boundary data, have Dirichlet energy bounded by a constant depending only on \(\Om\). Consequently, the Trudinger–Moser functional has no nonnegative constrained critical points at sufficiently large prescribed energies. The proof combines a weighted Pohozaev identity obtained after conformal change of variables, concentration analysis of normalized measures, and local radial comparison. The comparison hypotheses are obtained from local integral estimates, without an a priori energy bound. An estimate for the exterior Green potential then excludes sequences of unbounded energy.

Post-training tensor-network compression replaces Transformer linear layers with Tensor Train (TT) or Tree Tensor Network (TTN) operators, but standard decompositions minimize weight-space Frobenius error rather than functional error under the layer's activation distribution. We propose Activation-aware Weight Tensorization (AWT), a training-free calibration wrapper that preconditions each weight matrix with a diagonal activation-derived scale before an unchanged TT/TTN solver and deploys the result with only an input-side elementwise rescaling. Across Llama 3.1 8B, Ministral 8B, and Qwen2.5 7B, AWT consistently improves vanilla TT/TTN tensorization at 2-6 times compression: under single-operator replacement, AWT closes 12-35% of the WikiText perplexity gap to the dense baseline across the three model families and 2-6 times compression settings; while under multi-operator Llama suffix replacement it closes 27-60% across attention-group and all-seven-matrix settings. The gains also transfer to downstream HellaSwag and ARC-Challenge evaluations. We further show that diagonal preconditioning is a robustness-modularity tradeoff rather than a diagonal-covariance assumption: a dense full-covariance oracle wins its own weighted objective in 80/81 cases, yet diagonal AWT gives better held-out functional fidelity in 53/81 cases. Together, these results position AWT as a principled, modular preconditioner for improving functional fidelity in fixed TT/TTN compression pipelines without modifying the decomposition solver.

We study the mixing between a generic axion-like particle (ALP) and the light pseudoscalar mesons within chiral perturbation theory ($\chi$PT), and its consequences for low-energy scattering and decay processes. Starting from the most general ALP effective Lagrangian, we derive the ALP-meson kinetic and mass mixing induced at leading order in the ALP decay constant and isospin breaking for arbitrary ALP masses. As a result, we obtain the physical ALP mass to $\mathcal{O}(F^2/f_a^2)$, recovering the QCD-axion limit and finding that any ALP with a vanishing bare mass shares the QCD-axion mass. We provide a compact parameterization of every four-body amplitude involving pseudoscalar mesons and an arbitrary number of ALPs. As an illustration, we show the $K\bar{K}\to P^0a$ scattering. The framework applies for general ALP masses and couplings and consistently incorporates isospin breaking, essential for otherwise forbidden processes.

We establish sharp two-point function asymptotics for the two dimensional Villain model at sufficiently low temperatures, confirming a central prediction in the Berezinskii-Kosterlitz-Thouless theory. We characterise the power law exponent through the renormalisation group flow of a marginal line defect observable in the dual high-temperature Discrete Gaussian model.

Optical cavities can enhance atom-light coupling in atom interferometry, but free-fall geometries require large transverse modes. Marginally stable resonators provide such modes, yet aberrations and alignment imperfections turn their near-degenerate response into detuning-dependent transverse ring modes, strongly limiting the usable interaction volume under static excitation. Here, we turn this limitation into a resource. By chirping the interrogation frequency across the cavity resonance while dynamically shaping the input amplitude, we map laser detuning onto the transverse position and scan the cavity-enhanced coupling across the atomic cloud. In a cavity-enhanced Bragg diffraction experiment with $^{87}$Rb atoms, this produces a nearly uniform effective interaction region of about 15 mm and increases the transfer efficiency from about 5% to 28%. We also demonstrate phase-coherent operation of a three-pulse atom interferometer using chirped cavity-enhanced Bragg pulses. These results establish scanning-cavity interrogation as a route to large-area, cavity-enhanced atom interferometry.

Plagioclase is the most abundant mineral group of the crust and will therefore either control or strongly influence crustal rheology. Yet, we still know little about crystal plasticity in plagioclase as brittle deformation dominates under most laboratory conditions. To overcome past challenges in quantifying crystal plastic deformation in plagioclase, we used micropillar compression to quantify the strength of specific slip systems as well as the stresses necessary for mechanical twinning in anorthite. Pillars with diameters of around 1 micrometre were milled from three differently oriented cuts of the same anorthite single crystals using focused-ion beam. Uniaxial deformation of 36 pillars in total was then conducted inside a scanning-electron microscope under either 25, 300, or 800 degrees Celsius. Most pillars were deformed with a constant displacement rate that corresponds to a strain rate of around 0.001 1/s on the pillars. We find that the critical resolved shear stress (CRSS) for mechanical (pericline) twinning lies at around 300 MPa and is, as expected from previous studies on other materials, insensitive to changes in temperature or strain rate. Pillar deformation in crystals oriented to activate slip exhibit a strong decrease in yield stress with increasing temperature. Among the deformation mechanisms active during pillar deformation, twinning is the easiest under the applied conditions, followed by slip on (011)[100] regardless of temperature. Slip on (011)[0-11] or (0-11)[011] is consistently the hardest mechanism to activate in our anorthite pillars.

Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the kernel parameters are routinely estimated by the maximum likelihood estimators (MLEs), as implemented by standard GP software. Despite this widespread use, the asymptotic behavior of the MLEs remains poorly understood under fixed-domain asymptotics, even for the RBF kernel. The main difficulty arises from the increasingly strong dependence among densely sampled observations and the nonlinear dependence of the covariance matrix on the kernel parameters. In this paper, we address this gap by providing, to the best of our knowledge, the first complete asymptotic characterization of the joint MLE of the spatial variance, lengthscale, and nugget variance under fixed-domain asymptotics. We establish consistency, derive convergence rates for all three parameters, prove joint asymptotic normality, and show that these rates are minimax optimal.

World Action Models (WAMs) combine visual dynamics modeling with action generation, but their high inference latency limits responsive robot control. Recent efforts accelerate inference by removing explicit future-video generation at test time, as in FastWAM, an approach that requires a specially tailored architectural design. More general caching strategies exploit feature redundancy, but redundancy alone does not capture the changing computational demands of closed-loop control. To address these challenges, we present RealtimeWAM, a general, training-free framework that coordinates parallel execution with adaptive computation for low-latency inference across diverse WAM architectures. We exploit layerwise dependencies to overlap observation processing with prediction. However, concurrent branches still compete for GPU resources, limiting the benefit of parallel execution. We therefore adapt computation throughout the pipeline through selective reuse, caching observation features in visually stable regions and reusing Transformer residuals while reserving additional refinement for small predicted adjustments. We evaluate RealtimeWAM on FastWAM and OpenWAM across RoboTwin, LIBERO, and LIBERO-Plus. On an RTX 4090, measured mean inference latencies are 24.09 and 63.09 ms, corresponding to average speedups of 8.90$\times$ and 10.67$\times$. Average success rates are 82.75% and 87.41%, respectively, within 0.02 and 0.53 percentage points of native inference. Across five real-world tasks, RealtimeWAM improves average success rates over native inference by 17.2 and 37.2 percentage points on FastWAM and OpenWAM, respectively.

We study exact fillings of Legendrians and contact manifolds using Floer theory of universal covers. We prove vanishing results on wrapped Floer homology of the universal cover and symplectic (co)homology with $k[\pi_1]$ coefficients by using lifted versions of Ritter's TQFT operations. We use these results to show that an exact Maslov zero Lagrangian filling of the standard Legendrian $\Lambda_{std}$ in any Liouville filling of $(S^{2n-1},\xi_{std})$ is diffeomorphic to a ball in dimension at least 5. We show that the existence of a topological simple exact filling $W$ with vanishing symplectic homology for a dynamically convex contact manifold $M^{2n-1}$ reveals information about homotopy groups of $W$ and $M.$ We also strengthen a theorem of Zhou for ADC-contact manifolds as an application of universal covers.

We study bijective nonexpansive maps in $T_0$-quasi-metric spaces, distinguishing preservation of directed distances from pointwise rigidity. Our focus is their behaviour under passage to the $q$-hyperconvex hull. The upper quasi-metric integers are $q$-plastic and bicomplete, but their hull is the non-$q$-plastic upper real line. An explicit hull calculation and an established metric dense-rigidity theorem give the same failure of inheritance for a $q$-rigid original space. Tightness propagates distance preservation from the canonical copy throughout the hull. Under compactness and a bounded lattice structure for the zero-distance order, identifying that copy with the complemented elements gives a sufficient condition for inheritance of $q$-rigidity. A four-vertex asymmetric rectangle verifies this criterion. We also record metric transfer mechanisms and show that a directed interval condition gives an endpoint-coordinate representation, automatic $q$-plasticity, and $q$-rigidity under uniqueness of the ordered diametral pair.

Calibration is an essential requirement for probabilistic predictions to be useful for decision making. While state-of-the-art prediction methods often yield miscalibrated predictive distributions, several post-hoc recalibration schemes have been proposed to generate calibrated predictions. However, popular recalibration schemes can conceal miscalibration in specific regions of the outcome space. Since particular outcomes, such as extreme events, often matter most for decision making, probabilistic predictions should be calibrated when evaluation is restricted to these outcomes. Hence, in this paper, we introduce outcome-conditional recalibration, a post-hoc method to recalibrate probabilistic predictions on user-defined regions of the outcome space. The method is simple, easy to implement, and can be applied to arbitrary predictive distributions. It works by applying the quantile recalibration approach of Kuleshov et al. (2018) to forecast conditional distributions, before rescaling these conditional distributions so that forecast event probabilities match empirical occurrence frequencies. This produces valid and continuous predictive distributions that are calibrated within each region of interest. Across regression benchmarks, we demonstrate that existing recalibration schemes do not necessarily yield calibrated predictions when interest is on particular outcomes, and that our approach improves outcome-conditional calibration relative to existing conditional and unconditional recalibration methods, while retaining competitive calibration overall. In an application to day-ahead electricity price forecasting, the approach substantially improves calibration when predicting negative prices, at negligible cost to forecast accuracy.