Papers

Quantum programming requires concepts and intuition that differ substantially from those used in traditional programming languages. Multiple quantum programming frameworks address these requirements through different abstractions and execution models, creating tradeoffs in programmability, portability, and performance. Because quantum software is less prevalent in the training data available to large language models, autonomous coding agents might be expected to face additional challenges when working with these frameworks. We present a case study in autonomous migration of the QED-C Application-Oriented Benchmarks from Qiskit to CUDA-Q. Opus, GPT, and Gemini models were each tasked with porting thirteen benchmark methods spanning foundational algorithms, amplitude estimation, Monte Carlo methods, variational optimization, linear-system solving, and factoring. In all cases, the models were able to generate satisfactory ports with little direct coding help and there was a drastic reduction in the time required compared to a human engineer. However, in all cases, the agents resorted to shortcuts when implementation challenges surfaced and multiple prompts were required to force appropriate coding directions. Assessment of the generated implementations showed that no single model consistently produced the best port across all benchmarks, indicating that multi-agent ensemble strategies could mitigate challenges associated with quantum software. The effort resulted in publicly available, near-complete CUDA-Q support in the QED-C benchmarks along with model-generated skills designed to improve agent performance when implementing CUDA-Q applications. When tested on an unseen benchmark, these skills reduced the required model turns by up to 85% and token usage by up to 96%. We conclude by distilling lessons from the case study.

After decades of microfinance expansion and despite charging higher interest rates, moneylenders continue to exist alongside microfinance institutions (MFIs). We develop a dynamic model with ex post moral hazard, in which borrowers use MFI loans for production and can rely on moneylenders for bridge loans after shocks to repay MFIs and preserve future access to MFI credit. We then study how MFI competition shapes the coexistence between MFIs and moneylenders. The effect of competition on MFI credit is ambiguous: it may weaken repayment incentives or replace moneylenders as bridge lenders. By contrast, competition unambiguously reduces moneylender credit. In a village-level randomized expansion in Bangladesh, stratified by baseline MFI presence, one additional MFI reduces the number of moneylender loans by roughly 30-40% two to three years later, with no detectable effect on MFI or overall borrowing. This suggests that, in markets where MFIs rely primarily on the threat of exclusion to induce repayment and moneylenders provide emergency finance, gains from additional MFI entry may be greater in less saturated areas.

Reliable robotic manipulation requires timely intervention to correct emerging deviations and restore progress after execution errors. However, recovery methods based on repeated vision-language reasoning or iterative online optimization can incur substantial latency, delaying intervention. To address these challenges, we introduce RESETTLE(Robotic rEcovery through diSagrEement-Triggered reTrievaL and Efficient Corrective Control), a model-agnostic framework that provides computationally efficient recovery at the action-execution interface of frozen robot policies. RESETTLE triggers recovery when two action proposals independently sampled under identical conditioning persistently disagree. It retrieves a same-task demonstration reference using an adapted V-JEPA encoder and combines a state-servo prior with a guarded visual residual to execute one corrective action without online trajectory optimization or additional vision-language reasoning, then returns control to the base policy. Across six base policies in simulation, RESETTLE achieves up to 8.70%, 6.28%, and 6.83% absolute success-rate gains on LIBERO-Plus, Meta-World, and RoboCasa Tabletop, respectively, with further improvements on four real-world tasks using two policies. In QwenPI-based comparisons, its monitoring-and-recovery computation latency is 74.04%–93.57% lower than VoLoAgent's monitoring-and-planning latency for grasp and place tool calls. It also raises Harness VLA's LIBERO-Pro Swap success from 42% to 50%, demonstrating compatibility with high-level agentic planning. Code available at: https://github.com/JIA-Lab-research/RESETTLE

We establish matching lower bounds for deterministic first-order optimization of globally Lipschitz geodesically convex functions on hyperbolic space. A global minimizer lies within distance $r$ of a known point, each query returns an exact function value and a selected Riemannian subgradient, and the target objective gap is $\varepsilon Lr$, where $L$ is the Lipschitz constant. For sectional curvature $-k^2<0$, let $\rho=kr$ and $\zeta=\rho/\tanh\rho$. The optimal worst-case query complexity $Q^\star$, taken uniformly over dimensions, satisfies $Q^\star(\rho,\varepsilon)=\Theta(\zeta\varepsilon^{-2})$ for every $\rho>0$ and $0<\varepsilon\le1/64$. The new lower bound covers arbitrary adaptive deterministic queries and arbitrary outputs, matching the projected-subgradient upper rate of Zhang and Sra (2016). It removes the geodesic-span and historical-halfspace restrictions of earlier matching lower bounds. The construction extends a radial source from a convex carrier with boundary. A small residual cut selects minimizer candidates while an exact hyperbolic persistence inequality keeps every historical contact valid under future carrier growth. One fixed globally convex objective and one fixed subgradient selection consequently realize all exact replies simultaneously. Each query consumes $O(\varepsilon^2)$ of a geometric potential whose available budget is $\Theta(\zeta)$, yielding the product lower bound in a dimension linear in the query horizon.

Black-box optimization (BBO) arises in many scientific and engineering problems where objective evaluations are expensive and limited. Recent large language model (LLM) agents offer a new way to approach BBO by combining task semantics, computation, optimization tools, and feedback-driven decision making, showing great potential due to the integration with mathematically rigorous tools. However, existing agentic BBO studies use different task domains and system configurations, making their results difficult to compare and the effects of individual design choices hard to isolate. We therefore introduce AgenticBBO-Bench, a cross-domain benchmark for agentic BBO spanning synthetic functions, hyperparameter optimization, database tuning, chip design, and molecular design under a unified finite-budget evaluation protocol. In our experiments, agentic BBO achieves higher family-averaged scores than direct LLM-based methods in all five domains and outperforms the best numerical optimizers in four. We further study three factors shaping agent performance: optimization tools, task information and prior knowledge, and the role of the LLM during search. Our results show that additional numerical tools do not consistently improve performance, task semantics are broadly useful while more specific priors are less reliable, and numerical optimizers can effectively absorb gains from search trajectories established by the agent. Finally, we introduce a five-task frontier challenge within AgenticBBO-Bench and evaluate seven LLMs under the Codex agent harness, where GPT-6 Astra and DeepSeek-V4.1-Flash lie on the Pareto frontier of performance and cost among the evaluated models. Our code is available at https://github.com/lamda-bbo/agentic-bbo.

Very-high-resolution Earth-observation satellites acquire more data than they can store and downlink, while in maritime surveillance the vessels cover a tiny fraction of each scene. We study onboard vessel detection as a way to select what is downlinked, which reduces the data according to its content rather than coding every pixel; it is complementary to conventional onboard compression. The work follows three axes. (i) Data and algorithm: a controlled dataset is generated from 68 annotated Maxar scenes with 43 vessel classes, and a YOLOX-S detector is trained on it. (ii) Embedded deployment: the detector is quantized and deployed on the DPU of a Versal VC1902, with a limited loss of detection quality and a processing time of a few seconds per scene. (iii) Data reduction: we propose several downlink modes, from metadata only (box, class and score of each detection) to image crops around vessels, tiles holding detections, or the whole scene with a degraded background, and estimate from the measured detection errors the trade-off each offers between the vessels kept and the volume downlinked. On our dense harbor and coastal scenes, tiles keep 98% of the vessels with 29% of the scene volume, and crops 83% with 3%.

In 2008, Jacobi and Madden proved that $a^4+b^4+c^4+d^4=e^4$ has infinitely many primitive solutions with the linear relation $e=a+b+c+d$. We extend their result to relations with rational cubes $e=a+k^3(b+c+d)$ and prove infinitude for $k=3$ and $10$ other $k\ne 1$. We compile $30$ starting solutions. In the spirit of Jacobi and Madden's original paper, everything here is simple algebra except one theorem of Mazur.

Which pure states give uniform outcomes in several mutually unbiased measurements, and when can they form another measurement basis? We distinguish common unbiased states, their orthonormal completion, and further extension. For a displayed phase-deformed Fourier pair in dimension $2m$, a clock symmetry and skew antiunitary complete every prescribed common unbiased state to an explicit orthonormal basis. In dimension six, an amplitude-profile obstruction proves strong unextendibility of a given mutually unbiased triple when its original third-basis rays are invariant under the ternary clock. We give an exact nonproduct example and an application to a companion whose columns are localized at single Fourier frequencies. For every exact Hadamard matrix in a specified closed entrywise neighborhood of a fixed reference matrix, the coordinate and Hadamard bases have exactly 48 common unbiased rays but no third measurement basis, with a quantitative lower bound on the squared Gram defect of every six-column candidate. We also study auxiliary complex equations for common states, retaining algebraic multiplicities. For a flat unitary of order six with all $3\times3$ minors nonzero, the projective ray scheme is finite; each singular two-minor contributes two reduced isolated boundary points, and the affine coordinate algebra is finite-dimensional over $\mathbb{C}$. In every order, a critical-algebra identity preserves multiplicities; in dimension six it gives finiteness for a fixed phase fibre. Specialization over a discrete valuation ring controls complete reciprocal-orthogonal collections. A nonphysical Tao/Potts collection separates algebraic from physical solutions. These results do not determine the global maximum number of mutually unbiased bases or classify all triples.

In the present work we develop a model–independent method to reveal the underlying patterns of anisotropy and geometry in CMB temperature maps. This method, based on the rho-statistics and a process of mask–sweeping, unveils faint but persistent geometrical and periodic structures characterising the anisotropy of the CMB in a universe with 3-torus topology. We assess that the patterns detected over large ensembles of toroidal maps match geometrically to the layouts of expected circles-in-the-sky. The mask–sweeping method explores the whole CMB over 768 mask orientations. Thus we are able to re-verify the linear relation between L the size of the cubic torus and rho the standard deviation of the normalised variance of the CMB temperature gradient. This confers a finite size s of approximately 3 Hubble lengths to our Universe with toroidal topology. Furthermore, it is shown that the violation of statistical isotropy is so faint that this has almost no influence on the linear relation between rho and L. A topology like the cubic toroidal one imposes to our Universe periodic conditions (that can be seen as periodic boundary conditions) which constrain the global degree of inhomogeneity and a zero average curvature. We demonstrate here that rho is not only a statistical signature of the spatial finiteness and size of our Universe (may its topology be simply or multiply connected) but also outlines the patterns of anisotropy of the CMB with the help of the mask–sweeping process.

In this work, we propose a unified localization framework, termed UNILocMP, that combines model-based geometry and channel charting (CC) for multi-panel massive multiple-input-multiple-output (MIMO) under clock asynchronism. Owing to the multi-panel architecture, users are classified into multi-line-of-sight (LoS) users, which maintain LoS links with at least two panels, and single/non-LoS users, which maintain a LoS link with only one panel or with none of the panels. For multi-LoS users, a joint position and clock bias estimation is developed; while for single/non-LoS users, an unsupervised CC model is trained with a two-stage data augmentation strategy, where a clock-bias aware dissimilarity metric is introduced. It is numerically validated that the proposed UNILocMP outperforms model-based and CC-based baselines and achieves acceptable performance compared with fully-supervised fingerprinting. Moreover, for a fixed total number of antennas, the multi-panel architecture significantly improves localization accuracy and robustness compared with a single-panel base station (BS) deployment, particularly in the presence of clock asynchronism.

We study minimum-time navigation between two points in a known two-dimensional fluid flow for a vessel with fixed-magnitude slip velocity and controllable direction. The navigation policy is parameterized by a neural network and optimized using a genetic algorithm that evolves an ensemble of candidate strategies through Darwinian selection and parameter mutation, without crossover. The method recovers analytical and numerical optimal-control solutions in several benchmark cases, including two-dimensional turbulence, and outperforms Q-learning and one-step actor-critic method. We further show that the learned navigation strategies are robust to variations in the starting position and to unresolved small-scale turbulent fluctuations, provided that the characteristic velocity of these fluctuations remains small compared to the vessel's slip velocity. The proposed approach provides a compact representation of the navigation policy, is readily parallelizable, and eliminates the need for reward shaping, offering an efficient alternative to existing analytical and numerical methods for computing minimum-time trajectories in complex flows.

Recursive self-improvement (RSI) of a model on non-verifiable tasks, such as open-ended research, faces a supervision bottleneck when its outputs exceed what even human experts can reliably assess, leaving the model itself (optimizee) as the best available optimizer and evaluator. However, a single model instance struggles to critique and improve its own complex reasoning under this homogeneous loop. To address this, we propose Multi-Agent Self-Supervision (MASS), an RSI method that alternates between evolutionary workflow optimization and supervised fine-tuning on self-generated trajectories. Guided by early findings that multi-agent topologies excel at complex reasoning, MASS prompts a single base model to iteratively propose, execute, and self-evaluate multi-agent workflows. Through an evolutionary search constrained by structural guardrails, the model optimizes these computational-graph-like orchestrations, discovering the most effective distinct roles and information routing for a given task. Over two MASS cycles with Qwen3.6-27B, the model achieves 1.2-1.6x higher performance per output tokens on four open-ended public benchmarks. Because the improved model subsequently acts as a better optimizer and evaluator, this alternating framework enables a continuous, recursive bootstrapping of the model's capabilities. Moreover, multi-agent traces are also more training-efficient: a student trained on them outperforms a single-agent student trained on 1.4x more training tokens. These findings suggest that jointly learning orchestration and bounded subagent execution from multi-agent trajectories can provide an effective signal for RSI.

We prove that every weakly pseudoconvex Oka manifold admitting a positive line bundle is elliptic in the sense of Gromov, thereby proving Gromov's ellipticity conjecture. The proof establishes a cohomological construction of local sprays. Given a bundle morphism $\varphi\colon E\to T_X$, we introduce quadratic $\varphi$-vector fields on $E$ whose flows yield local sprays with fibre derivative $\varphi$. Their existence is characterized by the vanishing of the symmetrized $\varphi$-Atiyah class of $E$. This gives a local dominating spray on every weakly pseudoconvex manifold admitting a positive line bundle, without any Oka assumption. The positivity hypothesis is essential even for local existence: blow-ups at a single point of complex tori of algebraic dimension zero, and Kummer surfaces of algebraic dimension zero, admit no local dominating spray. The torus examples give compact Kähler Oka manifolds that are not elliptic and show that ellipticity is not preserved under blowing up, and that it is neither open nor closed in holomorphic families of compact Oka manifolds. Combined with the work of Xie and Zhao, the Kummer examples yield Oka K3 surfaces that are not elliptic. Under the additional Oka assumption, we globalize the local dominating sprays constructed above. The proof combines Oka approximation with a gluing argument based on weighted $L^2$ estimates for the $\bar\partial$-equation.

Jackiw-Teitelboim (JT) gravity with positive cosmological constant is a toy model to study the emergence of expanding de Sitter universes from a quantum state. Its density matrix is a superposition of double-trumpet amplitudes which are solutions of a Wheeler-DeWitt equation. We compare predictions of such mixed states for classical expanding universes with the corresponding predictions of no-boundary wavefunctions. Double-trumpet amplitudes consistent with holography, whose semiclassical limit matches the result from Schwarzian boundary fluctuations, lead to a flat probability distribution for the size of the universe, consistent with models of inflation. This is in contrast to the suppression of large universes predicted by no-boundary wave functions.

Step-index few-mode fibers (FMFs) provide a compact passive platform for high-speed photonic information processing by exploiting modal dispersion to map temporal inputs into spatiotemporal representations with short-term memory. In previous studies, we have demonstrated linear classification tasks with such FMFs, such as ultrafast multibit header recognition. Here, we extend the computational capability of such architectures towards solving nonlinear tasks by introducing an optical nonlinearity at the output of the dispersive medium. The FMF output is processed through parallel direct and nonlinear branches, with the latter implemented using a nonlinear semiconductor optical amplifier (SOA). We experimentally evaluate the architecture at 28.5 Gb/s on two delayed XOR and higher-order parity tasks. We show that combining the direct and SOA-transformed representations reduces classification errors and broadens the range of operating conditions supporting low-error classification. In addition, by exploiting multiple temporal samples within each bit period as independent classifier features, we increase the dimensionality of the photonic representation and improve the computational performance.

Learning how actions change scene geometry can provide complementary supervision for goal-directed manipulation. We introduce Spatial Language Modeling, which represents scene contours, goals, action targets, and future states with a shared vocabulary of discrete coordinates and semantic tokens. A task-specific grammar organizes these elements into spatial sequences, allowing one autoregressive Transformer to learn action generation and action-conditioned state prediction through a common next-token objective. We train the model from scratch using random-play transition pretraining followed by joint action and state training on expert demonstrations. During pretraining, recorded action coordinates condition subsequent state predictions and are excluded from the prediction loss. During control, the model decodes only executable action targets and updates its history with newly observed states. We evaluate the approach on Push-T in simulation and on a real robot. The model achieves competitive simulation performance and higher task success and target coverage than the evaluated real-robot policy baselines. Training ablations show improved control with joint action and state sequences, with further gains from random-play pretraining. Given supplied action trajectories, the same model also predicts successive scene states, capturing the geometric effects of pushing.

This article establishes a sharp singular Moser-Trudinger type inequality in a new function space and explores a concentration-compactness principle in the Heisenberg group, inspired by P.\textcolor{blue}{-}L. Lions. We analyze the equivalence of sharp critical and subcritical singular Moser-Trudinger inequalities, focusing on their asymptotic behavior and connections between their suprema. Additionally, we apply the mountain pass theorem to demonstrate the existence of positive ground state solutions for zero mass $(p, Q)$-Laplace subelliptic equations with singular exponential nonlinearity for the following equation: $$ -\Delta_{H,p} u-\Delta_{H,Q} u=\frac{f(\xi,u)}{r(\xi)^\vartheta}\quad\text{in}\quad \mathbb{H}^n, $$ with $1<p<Q$, $\vartheta\in(0,Q)$, $Q=2n+2$, the function $r(\cdot)$ is called the Korányi norm in $\mathbb{H}^n$ and the nonlinearity $f:\mathbb{H}^n\times \mathbb{R}\to \mathbb{R}$ is a Carathéodory function, which behaves like $\exp{(\alpha|s|^{\frac{Q}{Q-1}})}$ as $|s|\to~+\infty$ for some $\alpha>0$.

Large Eddy Simulation (LES) resolves only the large, energy-containing structures of turbulent flows while modeling the effects of unresolved subgrid scales. As a result, the ac- curacy of LES strongly depends on the subgrid-scale closure. This work investigates the online calibration of a spectral viscosity closure for forced two-dimensional turbulence using ensemble Kalman Inversion (EKI). The closure consists of a wavenumber-dependent viscosity function, which is parameterized by a 16-dimensional vector. An ensemble of potential parameter vec- tors is passed through coarse resolution LES simulations, and the resulting kinetic energy spec- tra are compared with a DNS reference spectrum up to the LES-resolved wavenumber range. Then, ensemble statistics iteratively update the spectral viscosity parameters in order to reduce the model-data discrepancy. The convergence of the spectral mismatch is used to assess the accuracy of the calibrated closure by comparing LES with the filtered DNS data in spectral space. The results demonstrate the potential of EKI-based online calibration as a derivative- free framework for constructing data-driven turbulence closures with multiple parameters.

This is the third paper in a series where we study arithmetic applications of the higher elliptic Gamma functions. In the first two articles in this series, we defined geometric families of these functions and proved that they satisfy coboundary and cocycle relations under the action of special linear groups and associated congruence subgroups. The main purpose of the present paper is to present a construction of conjectural higher elliptic units above number fields with exactly one complex place as special values of higher elliptic Gamma functions, upgrading the construction carried out by Bergeron, Charollois and García for complex cubic fields. These higher elliptic units are obtained by evaluating a multiplicative $(n-2)$-cocycle built from higher elliptic Gamma functions against a $(n-2)$-cycle associated to some group of totally positive units of a given number field of degree $n$ with exactly one complex place. We conjecture that these higher elliptic units are algebraic units which belong to prescribed abelian extensions of the base field where they are evaluated and that they satisfy a Kronecker limit formula which relates the logarithm of their modulus to values of derivatives of partial zeta functions at $s = 0$ in the base field. We showcase our conjecture on various examples for number fields of degree 3, 4 and 5.

We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.

Generalist graph anomaly detection (GAD) aims to build a foundation model that detects anomalies on arbitrary unseen graphs without retraining or fine-tuning. Sufficient data are essential for foundation model training, yet generalist GAD still faces a data shortage, as real-world anomalous graphs are scarce and costly to collect and annotate. To fill this gap, we propose AG-FORGE, an Anomalous Graph generation Forge for automatic synthesis of anomalous graphs, exploring the feasibility of synthetic data-driven training for generalist GAD. Empirically, we find that synthetic data can achieve performance comparable to real-world training, but fail to push the performance boundary further due to the limited capacity of existing methods. To further unlock model capacity as training data scale up, we develop TS-GGAD, a Topology-Semantic coordinated Generalist GAD that captures complementary topological and semantic anomaly evidence, together with a curriculum learning strategy tailored to large-scale synthetic training. Extensive experiments on 14 real-world datasets demonstrate that TS-GGAD, trained on data generated by AG-FORGE, significantly outperforms state-of-the-art methods.

Equity correlation matrices are foundational to quantitative risk, yet the operational default of a single Gaussian-copula structure fit to the full sample has a structural defect: it forces asymptotic tail-independence and so cannot represent the joint moves that drive risk in stress episodes. We argue that the dependence of equity returns is not one object but three distinct under lower-tail, central, and upper-tail conditions, and that any estimator aimed at tail-sensitive applications should be regime-aware. We develop a decomposition that fits a dedicated dependence matrix to each regime, using a tail-dependence estimator grounded in multivariate regular variation in the two tails and a time-varying conditional-correlation model in the central regime, and recombines the three at the unconditional regime probabilities to form a steady-state matrix. The construction identifies tail-regime dependence that the Gaussian-copula benchmark structurally suppresses. Demonstrated on water- and energy-sector Exchange Traded Funds (ETF) constituents, the tail regimes reorganize the commodity partition produced by the central regime, identifying the pairs where the Gaussian-copula default systematically fails to identify joint extreme co-movement.

On any bounded convex domain $\Omega\subset\mathbb{R}^n$ with a $d$-dimensional flat boundary piece $F\subset\partial\Omega$, we consider convex solutions with zero boundary values to the Monge-Ampère equations $$ \det\mathsf{D}^2 u= \mathrm{dist}(\,\cdot\,,\mathrm{Aff}(F))^\alpha,\quad\det\mathsf{D}^2 u=\mathrm{dist}(\,\cdot\,,\partial\Omega)^\alpha,\quad \det\mathsf{D}^2 u=(-u)^\alpha, $$ where $\mathrm{dist}$ stands for Euclidean distance and $\mathrm{Aff}(F)$ is the affine hull of $F$. We show that the threshold of the exponent $\alpha\in\mathbb{R}$ for $u$ to have infinite slope at $F$ is $\alpha\leq 2d-n$. For the first two equations, we also show that no solution exists when $\alpha\leq 2d-2n$. Moreover, when $\Omega$ satisfies the “exterior cone condition with a $d$-dimensional ridge” at $F$, both thresholds are sharp for the first equation, and the infinite-slope threshold is sharp for the last equation.

Multi-tiered memory systems combine fast, small upper tiers with slow, large lower tiers to improve performance and cost efficiency. Existing designs, such as AutoTiering and MTM, rely on greedy promotion and stepwise demotion, which can intensify contention for limited capacity in faster tiers. We observe that promotions directly improve performance, whereas demotions primarily reclaim space. Based on this asymmetry, we propose Mole, a memory tiering system that separates promotion and demotion destinations. Mole employs staging demotion to move cold pages directly to the lowest tier, bypassing intermediate tiers, and targeted promotion to place hot pages in tiers that match their current hotness. The lowest tier serves as a staging area from which pages can be promoted when they become hot again. This separation preserves intermediate-tier capacity for promotions, reducing tier contention and migration failures. However, staging demotion requires timely identification of pages that become hot after demotion. To meet this requirement with low profiling overhead, Mole uses tier-specific profiling: it profiles the lowest tier at high frequency to detect reactivated hot pages, while profiling upper tiers at lower frequency to identify cold pages. Experimental results show that Mole reduces migration failures and improves performance under dynamic access patterns.

Generating large attributed graphs requires reproducing the topology, generating attributes jointly with the structure, and remaining scalable. Many real-world graphs exist as a single large graph, so a generative model has to generalize from the one graph it is fit on, without independent samples. We present Schema, which recursively decomposes a reference graph into a hierarchy of soft communities, assigning each node a membership distribution. Generation is then split into three stages, each trained independently: (1) synthesizing node attributes conditioned on soft memberships, (2) generating intra-community edges from local structural context, and (3) modeling inter-community connections over bridge nodes whose membership mass is distributed across several communities. No stage forms the full adjacency matrix, and each stage operates on a subgraph bounded by the community size. We also introduce an evaluation protocol that covers structural fidelity, memorization, downstream utility, and scalability. On four real-world attributed graphs, Schema recovers the balance between local and long-range structure more closely than any other model that generates attributes, while reproducing only a small fraction of the reference edges. It retains the downstream accuracy of the reference graph without raising it artificially above that level. Baselines that match its structural fidelity memorize the reference, while those with higher downstream accuracy either exceed the reference accuracy or fail to complete on the larger graphs. We measure scalability on six additional graphs with up to 10 million nodes.

Random communication symbols allow integrated sensing and communications (ISAC) systems to exploit payload signals for sensing, but the resulting matched-filter response varies with the transmitted data. Existing statistical analyses of sensing with random orthogonal frequency division multiplexing (OFDM) waveforms have largely focused on delay and Doppler, while the spatial dimension introduced by multi-input multi-output (MIMO) arrays and precoding has received much less attention. This paper develops a three-dimensional ambiguity function (3D-AF) for random MIMO-OFDM waveforms over delay, Doppler, and angle domains. For point-target sensing, we express the 3D-AF as a quadratic form of the random communication symbols, with a deterministic matrix that captures the delay and Doppler shifts, the transmit and receive array responses, and the precoders on different subcarriers. Based on this representation, we derive a closed-form expression for the expected squared 3D-AF and show explicitly how the constellation fourth-order moment (or kurtosis) affects the ambiguity sidelobes. The same characterization yields expected integrated sidelobe level (EISL) and expected sidelobe level (ESL) metrics over mixed delay-Doppler-angle search domains. The framework is further extended to coherent multi-symbol processing with slow-time Doppler, leading to the corresponding fast-slow time (FST) approximation. These results provide a statistical characterization of the sensing ambiguity induced by random MIMO-OFDM communication signals in delay, Doppler, and angle.

Why does removing reference-policy KL regularization sometimes improve group policy optimization? This motivates studying how reference-policy information should enter group-relative updates. We analyze seven potential failure modes in the interactions between KL and rewards: residual KL updates after reward clipping, after gradient cancellation, and in groups with identical rewards; KL growth with response length and an imbalance in its relative contribution; KL concentration on a small number of tokens; and sampling noise when k1 is incorporated into rewards. We propose Zero-Sum Calibrated Policy Optimization (ZCPO), which uses relative drift measured by conditional KL to calibrate within-group reward coefficients and integrates them into the base surrogate. Mathematical reasoning experiments and ablations support this design's effectiveness in our settings.

For a finite set $A\subseteq\mathbb Z^d$, we study the capacities of a sausage obtained by transporting $A$ along the Minkowski sum of simple or critical branching random walks. We first establish quantitative capacity estimates for the random walk sausage and the branching sausage. This in turn, gives us estimates for the probability that Minkowski sums of a mixture of walks hit a finite set in high dimensions. Our approach is based on an annular decomposition of a critical branching random walk into successive waves, which may have further applications.

We present a post-processing pipeline that predicts CO line luminosities, molecular hydrogen masses, and CO abundances for galaxies in the Feedback in Realistic Environments (FIRE-2) simulations, as a first step toward CO response functions for line intensity mapping mocks. SKIRT gives the radiation field reaching each gas cell. CLOUDY, tabulated on a five-parameter grid (metallicity, density, turbulent velocity, radiation field, cloud scale) and interpolated, gives $L'_{\rm CO(1-0)}$ and the $\rm H_2$ and CO masses. In this first of three papers we validate the pipeline against observations. For Milky Way (MW) molecular clouds, the predicted $L'_{\rm CO(1-0)}$ rises sharply at $A_V\sim1$ and matches the observed values above that column. For a uniform $3\,Z_\odot$ the summed luminosity is within 35% of the observed total. A factor of three increase in metallicity changes the total $L'_{\rm CO(1-0)}$ by an order of magnitude. Along MW sight lines, the predicted $N_{\rm CO}/N_{\rm H_2}$ reproduces the observed upturn within 0.3 dex in $N_{\rm H_2}$ but falls below the data at higher columns. At $z=0$ our molecular gas masses agree with xCOLD GASS for ${\rm SFR}\gtrsim0.3\,M_\odot\,yr^{-1}$ and are converged across our simulation resolutions. At $z\gtrsim1$ observed gas masses exceed ours at fixed stellar mass, though selection effects and conversion-factor assumptions limit this comparison. CO luminosities are compared with extragalactic observations in Paper II. Capturing the metallicity-dependent dust shielding of CO from photodissociation is essential for modeling CO emission in low-mass and high-redshift galaxies.

We report a direct measurement of the 21-cm signal from neutral hydrogen (HI) via the intensity mapping technique at redshift $z = 0.42$ through its power spectrum at cosmological scales $0.095\,h\,{\rm Mpc}^{-1}<k<0.245\,h\,{\rm Mpc}^{-1}$. We analyse intensity maps observed in the frequency range $971.2\,{\rm MHz}<\nu<1023.6\,{\rm MHz}$ during the 2021 observational campaign of the MeerKAT Large Area Synoptic Survey (MeerKLASS) spanning an area of approximately $236\,{\rm deg}^2$. Capitalising on the depth of this survey, we divide the data set into multiple observationally independent subsets. After performing blind contaminant separation independently on each subset, we exploit internal cross-correlations to suppress the instrumental noise plateau and isolate the cosmological signal from residual systematics. Although the subsets' auto-spectra show the presence of excess power that we deem linked to still unresolved systematics, the cross-spectra measurements satisfactorily pass a battery of null and robustness tests. We introduce a multi-subset formalism to infer the amplitude of the HI auto-spectrum from our internal cross-spectra measurements while marginalising the potential signal loss that occurs during data processing, reaching a detection with signal-to-noise ratio of 6.2. We constrain the clustering amplitude of the signal in terms of the HI cosmic abundance and its linear bias, measuring $10^3\,\Omega_{\rm HI} b_{\rm HI}=1.271^{+1.080}_{-0.598}$. This direct measurement marks a milestone in demonstrating the effectiveness of the HI intensity mapping technique for future surveys with the SKA Observatory, of which MeerKAT is a precursor.