Papers

Motivated by applications to low-dimensional worldsheet string constructions, we analyze $\mathcal{N} = 1$ super Liouville theory on the torus. Specifically, we re-examine the recursive representations of the torus one-point super Virasoro blocks that have been constructed in the literature and correct several of their ingredients. In the process we identify a new block in the odd spin structure, associated with a privileged superdescendant whose torus one-point function transforms like that of a Virasoro primary. We then demonstrate that the structure constants for both spacelike and timelike super Liouville theory satisfy modular crossing. Furthermore, we use a bootstrap argument to construct modular crossing kernels for all four spin structure sectors, valid for central charges $c \in \mathbb{C}\setminus(-\infty,\tfrac{3}{2}]$, and verify that they correctly implement the crossing transformations of the blocks. As a concrete application of the technology, we analyze the super Virasoro minimal string. There are four such theories, $\mathrm{0A}^{\pm}$ and $\mathrm{0B}^{\pm}$, which are distinguished by the GSO projection together with the choice of worldsheet supercharge. The resulting NS-sector sphere three-point and torus one-point amplitudes are shown to agree with topological recursion on the spectral curves of the dual matrix integrals, which were recently derived from 3d supergravity. Notably, the one-point function of the privileged superdescendant plays an essential role in the contribution of the odd spin structure to the torus amplitude via a careful treatment of the picture changing operator. We also identify an exceptional zero-momentum Ramond insertion in the $\mathrm{0A}^{-}$ theory that we interpret geometrically as a Ramond puncture, and match its mixed sphere three-point amplitude to the corresponding intersection theory prediction.

Reinforcement learning with verifiable rewards (RLVR) improves vision-language benchmark scores even without visual information during training. With images at test, blind-trained models recover roughly half of the real-image gain at 3B and nearly four fifths at 7B. Prolonged real-image training can erode grounding while benchmark gains persist. Both findings expose the same gap: an image in the prompt is not an image in the learning signal. Our design rule, visual resolvability, asks that visual evidence be necessary for a correct answer and that the task remain learnable. We test it on counterfactual coordinate scenes in which the question stays fixed and the target is never named, so a correct answer requires finding the target in the image. With standard GRPO and correctness-and-format rewards, a 7B model raises its accuracy at finding the target (discovery) from 0.425 to 0.875 on held-out scenes denser than any it trained on, and it improves on question types it never trained on. Two controls locate the source of the gain. Replacing test images with gray canvases drops discovery to zero; training on gray canvases instead, at matched step 30 and in each of four seeds, yields essentially none of the gain even when the model is then tested with real images. The learned skill carries over to grounding tasks built independently of the training corpus. A caption that answers the training question, added to the same images, reward and budget, cuts the gain by nearly two thirds. Changing what reward requires changes what RL learns.

Differential privacy implementations rely on precise sampling from noise distributions to provide formal privacy guarantees. We report the discovery of systematic artifacts in OpenDP's discrete Laplace sampler that manifest as periodic distortions in the output distribution. Through systematic testing, we trace these artifacts to a faulty implementation in the rational arithmetic library used by the bernoulli_exp1 function, a low-level primitive that implements sampling from Bernoulli(e^(-x)) distributions. We present a diagnostic methodology that isolates the faulty component in the nested sampling hierarchy and propose an alternative implementation based on exact rational arithmetic that eliminates the artifacts. Statistical validation with 10^6 samples confirms that the corrected sampler produces outputs indistinguishable from the theoretical distribution at the tested precision level.

Scuba divers are taught to control their depth to avoid rapid ascents and descents, which could result in serious injuries such as gas embolisms and barotrauma. However, many underwater tasks necessitate lateral control, maintaining distance between subsea structures such as coral reefs, submerged drilling instrumentation, or unexploded ordnance. In this work, we discuss a first-of-its-kind wearable robotic solution providing thruster-actuated directional guidance to a diver, as distinct from prior propulsive-assistance exoskeletons. We introduce “Robotic Assisted Diver Movement in Confined Spaces” (RADMCS), a wearable robot that assists divers in maintaining a fixed distance from subsea structures by leveraging perception techniques in monocular depth estimation and force-feedback from submersible thrusters to provide haptic feedback. Its small and compact form factor creates a foundational platform that could be expanded to include more sophisticated control and navigation behaviors. We present results from Institutional Review Board (IRB) in-water studies with eight human scuba diver participants on threshold sensitivity tests in both a closed-water swimming facility and ocean environments; distance-maintaining experiments in a closed-water facility; and form, fit, and function testing in the ocean. We demonstrate that relatively low thrust values (10 percent of maximum) allow robotic direction of a human's movement using the physical sensation of the robot's guidance.

Online vectorized HD map construction is essential for scaling safe autonomous driving and requires accurate, real-time inference. Prior methods typically rely on dense bird's-eye-view (BEV) grids as the intermediate representation. We propose MapLightning, which replaces the dense BEV grid with a compact set of 1D learnable map tokens. To construct map tokens from image features, we choose self-attention over vanilla cross-attention because it enables joint interactions and contextual aggregation among image and map tokens. Our transformer-based mapper concatenates map and image tokens, applies full self-attention, discards the image tokens, and retains the updated map tokens for decoding. This design offers three advantages. First, our representation is efficient, using fewer tokens, consuming less memory, and running faster. Second, the lightweight design allows the map decoder to use full rather than deformable cross-attention for better global context. Third, unlike BEV-based methods, our network does not use camera projection parameters, making it robust to camera-extrinsic perturbations. MapLightning uses up to 16.7$\times$ fewer intermediate tokens than dense BEV-based methods and achieves state-of-the-art accuracy and efficiency on nuScenes and Argoverse~2. Its lightweight variant surpasses MapTRv2 by +10.1 mAP on nuScenes and +16.2 mAP on Argoverse~2, while delivering 1.73$\times$ faster inference (40+ FPS) with 53% less memory. We further show improvements on uncertainty-aware map construction and downstream trajectory prediction. Code and models will be released.

Constrained combinatorial optimisation provides a mathematical framework for modelling a wide range of practical decision making problems, including energy network operation, financial portfolio optimisation, logistics, routing, and resource allocation. This paper studies parameter optimisation for the multi angle quantum approximate optimisation algorithm (maQAOA) applied to the maximum independent set problem, a canonical constrained graph based optimisation task. We propose a coordinate wise training framework for maQAOA that updates one variational parameter at a time by solving a sequence of one dimensional optimisation subproblems. For each selected coordinate, the method reconstructs the objective dependence on that parameter and moves directly to the parameter value that minimises the training objective, or equivalently maximises the corresponding expected solution quality. While demonstrated specifically on maQAOA, the underlying theoretical principle, that the expectation value with respect to a given parameter can be analytically expressed as a finite Fourier series, is broadly applicable to general tasks solved via parameterised quantum circuits. Empirical evaluations on connected ErdHos Renyi graph benchmarks demonstrate that this analytic approach significantly reduces the computational training cost required to reach target approximation ratios and yields superior convergence reliability compared to standard gradient based, stochastic, and derivative free baselines.

Many real-world systems exhibit higher-order interactions among groups of entities that cannot be captured by pairwise relationships alone. Graph Transformers and Graph Neural Networks increasingly rely on positional encodings to enrich graph representations, yet existing positional encodings are computed solely from the original graph and therefore cannot directly capture observed higher-order interactions. Topological Deep Learning addresses this limitation by lifting graphs to simplicial complexes, but typically requires performing message passing or attention on higher-order neural network representations. We introduce a representation learning paradigm that enriches graph representations with higher-order topology through positional encodings, enabling standard graph learning models to exploit lifted incidence structure without modifying the backbone. We derive a theoretical characterization of the expressivity of higher-order positional encodings, proving that node-level operators induced by higher-order lifts can mix graph Laplacian frequencies in ways that scalar graph spectral filters cannot. Guided by this theory, we instantiate higher-order positional encodings using Hodge Laplacians derived from clique complexes. Experiments with Graph Transformers on ZINC and controlled synthetic benchmarks demonstrate improvements in predictive performance, while a fixed-1-skeleton experiment shows that the pipeline can transmit higher-order information when cells are supplied independently of the graph. Together, our results establish higher-order positional encodings as a principled bridge between graph positional encodings and topological deep learning.

Decoded quantum interferometry (DQI) is a polynomial-time quantum algorithm introduced by Jordan et al. (Nature 2025). For a natural optimization problem, known as optimal polynomial intersection (OPI), it achieves approximation guarantees in regimes where all known classical algorithms require exponential time. Besides time, space is another central resource: storing and manipulating a massive input can be very challenging, especially when logical qubits carry substantial fault-tolerant implementation overhead. This motivates the following question: does DQI yield quantum advantages in memory, and can we prove it unconditionally? We give an affirmative answer to this question in the streaming setting. In particular, we consider a natural generalization of OPI using Hermite interpolation and Hasse derivatives, which asks for a low-degree polynomial satisfying as many constraints on its values and derivatives as possible. As a concrete example, we show [Quantum efficiency.] An adaptation of the DQI algorithm produces a polynomial satisfying $93\%$ of the constraints; moreover, it only reads the input stream in one pass, uses polylogarithmic space, and has polylogarithmic computation time per stream entry. [Classical hardness.] Any classical algorithm that produces an answer satisfying just $76\%$ of the constraints requires polynomial space, even if it can read the input stream with polynomially many passes and can use unlimited time. Our result provides a complete tradeoff curve for the tunable parameters, and implies that DQI has provable quantum advantages for the original OPI problem.

We study classical and quantum superintegrability of a resonant three-dimensional Hamiltonian with indefinite kinetic energy and three Poisson descriptions of the same flow. Besides three commuting quadratic Hamiltonians, the polynomial first-integral ring contains two primitive degree-four generators, $I_4^{\rm o}$ and $I_4^{\rm e}$, of odd and even momentum parity. A single octic relation leaves the polynomial invariant ring with transcendence degree four. Solving the complete first-integral equation shows that every rational first integral is a rational function of $H_1,H_2,H_3,I_4^{\rm o}$, so that the rational invariant field likewise has generic functional rank four. A branch-free transcendental invariant raises the generic smooth functional rank to five on the invariant open set $\Delta>0$. The system is therefore minimally superintegrable in the polynomial and rational classes and maximally superintegrable on this invariant domain when transcendental integrals are admitted. Weyl quantisation yields exact higher-order differential symmetries in all three Poisson realisations. The branch-free fifth classical invariant also admits a densely defined nonlocal quantum counterpart, providing a concrete quantum realisation of the transcendental completion.

In distributed storage systems, redundancy enables a single data object to be reconstructed using several disjoint groups of servers. The resulting service rate region (SRR) captures all combinations of object request rates that the system can support simultaneously without overloading any individual server. We analyze the SRR of binary codes obtained via the Plotkin-type construction. We demonstrate that each recovery set for an information object of the Plotkin-type code $\mathcal{C}_p$ induces a corresponding recovery set for the same data object characterized by the underlying code $\mathcal{C}$. Furthermore, by characterizing the recovery sets structure of $\mathcal{C}_p$ in terms of the recovery set structure of $\mathcal{C}$, we identify the additional recovery sets introduced by this construction. Using the associated recovery hypergraphs, we establish bounds on the SRRs of $\mathcal{C}_p$ and iterated code $\mathcal{C}_{p^m}$ in terms of the SRR of $\mathcal{C}$. We consider the family of first-order binary Reed-Muller codes and show how the recovery structure, and consequently, the service rates of R$(1,m)$ for arbitrary $m$ can be recursively derived from a generator matrix of R$(1,2)$ through our results for successive Plotkin-type constructions.

For $n\ge2$ let $F(n)$ be the least $k\ge2$ such that $n!$ is the largest factor in a product of $k$ distinct factorials that is a perfect square, and let $D_k(X)$ be the number of $n\le X$ with $F(n)=k$. Erdos and Graham asked for the order of growth of $D_k(X)$ for $3\le k\le6$, and conjectured that $D_6(X)\gg X$. We prove that $D_3(X)=\kappa_3\sqrt X+O_\varepsilon(X^{2/5+\varepsilon})$ with an explicit constant $\kappa_3=2.7097\ldots$, and that $D_5(X)\asymp D_6(X)\asymp X$. Together with classical facts, this determines the order of growth of $D_k(X)$ for every $k$. The exponent $2/5$ comes from balancing a uniform bound for Pell equations against Gallagher's larger sieve, with residue restrictions supplied by the Weil bound. For five and six factors we restrict to integers with a prime factor exceeding $X^{1-\alpha}$, where $\alpha>0$ is small and fixed. We exclude shorter representations by combining an equidistribution estimate for primes of Matomaki, Radziwill, Shao, Tao and Teravainen with the large sieve. In an appendix we use a zero-sum theorem for finite abelian groups to construct, for every $m\ge2$, perfect $m$-th powers that are products of a bounded number of distinct factorials with arguments given by fixed affine functions.

Most known inorganic crystals exhibit symmetric atomic arrangements, yet generative models often fail to reproduce them. Explicitly enforcing these symmetries has so far yielded fewer stable and novel structures than unconstrained generation. We introduce Generative Equivariant Orbit Diffusion Engine (GEODE), to our knowledge the first model to combine coordinate and lattice diffusion in Cartesian space. GEODE first samples symmetry templates, then jointly generates the lattice, atomic coordinates and atom types while preserving the specified symmetry with a novel Wyckoff-constrained loss. Cartesian diffusion gives coordinate noise a consistent physical scale that we empirically demonstrate improves performance. Unconditional generation achieves a metastable, unique and novel (mSUN) rate of 11.9%, compared with 7.7% for the next best symmetry-aware model. We also introduce sampling time template filtering, which increases mSUN by ~6% without retraining, making GEODE competitive with leading symmetry-agnostic models. Template selection also enables joint symmetry and property guidance, which we demonstrate through classifier-free guidance of permittivity.

We study whether model diversity survives selection into trading. In synthetic markets with a fixed mixture of three language-model families, news presentation changes their representation among submitted orders. At the announcement round, Qwen's share of submitted orders shifts by 48 percentage points in the financing event, with little change in net order counts. In the workforce-reduction event, Mistral's share shifts by 40 percentage points while net counts reverse sign. Homogeneous populations remove opposing flow when their active decisions share a direction. An analytical decomposition shows why selection can improve or worsen price accuracy even at unchanged aggregate demand sensitivity. The evidence concerns presentation bundles and submitted flow; cleaner replication and a known-value validation are specified prospectively.

Asynchronous reinforcement learning (RL) improves the efficiency of large language model post-training but introduces stale rollouts generated by earlier policies. Theoretical understanding of how this staleness affects convergence and how to mitigate its impact remains limited. We derive a convergence bound for GRPO-style algorithms that explicitly characterizes the tradeoff between the gradient estimator's second moment and bias. For trajectory-level importance-weighted estimators, our analysis shows that once the second moment is uniformly controlled, delay enters the bound through the bias introduced by clipping or rescaling. Guided by this insight, we propose a novel group mass capping GRPO (GMC-GRPO) method, which minimizes a ratio-based bias bound within a class of weighted estimators sharing a common second-moment guarantee. We establish convergence guarantees for asynchronous GMC-GRPO and show that, compared with TIC-GRPO, it improves the threshold dependence of the fourth-order delay term from $O(\epsilon^{-4})$ to $O(\epsilon^{-2})$ as $\epsilon\to0$, where $1+\epsilon$ is the ratio threshold. Under local policy overlap, the delay-dependent term decreases as $G^{-2/5}$ after tuning the step size, where $G$ is the group size. For fixed behavior and current policies, the bias introduced by group rescaling also vanishes as $G\to\infty$, whereas the bias from trajectory-wise clipping can persist. Experiments across Qwen3 models and reasoning benchmarks demonstrate improved robustness to stale rollouts, with GMC-GRPO achieving the best performance among stable baselines under large rollout delays.

The antenna-elements that make up a radio interferometer form a spatial filter that samples components of the Fourier transform of a target radio astronomical source brightness. Along the signal path, there are multiplicative and additive perturbation effects that alter the signal and that should be corrected. The process of mitigating these perturbation effects is called calibration. In this work, we develop a new and fast Maximum Likelihood based estimator of these perturbation effects using the Exponential Map and Lie groups. To evaluate its performance, we compare it to the Cramér-Rao Lower Bound and, to test the estimation time, we compare it with the Expectation Maximization algorithm, another fast Maximum Likelihood estimator. Finally, we apply our estimator to a real observation of the protoplanetary disk AS 209 made with the Submillimeter Array. We found that our proposed estimator meets the Cramér-Rao Lower Bound and it was approximately 40 times faster than the Expectation Maximization algorithm.

Machine learning (ML) has emerged as a promising approach for improving diffusion MRI (dMRI) tractography, a task that remains limited by the intrinsic tension between local diffusion information and global anatomical plausibility. In this work, we systematically evaluate recurrent neural networks (RNNs) and Transformer models for iterative tractography, with particular attention to training strategies, input representations (including convolutional neural network (CNN)-based embeddings and end-of-sequence (EOS) tokens), and hyperparameter selection. We introduce a generation-validation phase enabling supervision at the streamline level during training, allowing supervision despite the mismatch between local loss functions and global streamline quality. Using the ISMRM2015 tractography challenge dataset, our models achieve the highest reported performance to date. Through controlled experiments, we quantify the impact of missing bundles, noisy or imperfect training streamlines, and invalid fibers in the training set. Finally, we demonstrate the applicability of our best-performing models for in vivo data from the Tractoinferno database. Overall, our results highlight both the potential and the limits of sequence-based deep learning models such as Transformers and RNNs for tractography, and emphasize the need for improved phantoms and evaluation methods for in vivo validation. We provide takeaways and recommendations for future researchers training and validating sequence-based supervised methods for tractography.

By 2030, Internet of Things (IoT) devices are projected to reach 40 billion, with fast-paced technological advancements in fields such as industry, healthcare, agriculture, automobiles, and building/home automation systems. This expansion has created a large attack surface for cybercrime, as the majority of these devices open the door for cybercriminals to exploit vulnerabilities, as they lack adequate built-in security. Cybercriminals launch malware attacks to compromise systems or steal sensitive data, and once a system is compromised, a ransom is typically demanded for its release. Current cybersecurity measures in place are being outpaced by the rapid growth of the IoT, which is accompanied by a subsequent growth in malware variants being created per day. Recognizing this pitfall, this research examines and proposes a novel approach to malware detection and classification to safeguard devices from further attacks and make IoT systems more robust and secure. The framework proposed utilizes a Structured State Space Sequence (S4) model, which discretizes sequences of malware samples in a sequence and captures long-range dependencies, essentially identifying the "cause" and "effect" hidden within malware execution flow. This study presents two novel contributions: the first empirical application of the S4 model for malware analysis, and a comprehensive comparison of its performance against other deep learning architectures, laying the stepping stone for future research in this new paradigm.

Multimodal agents commonly generate free-form reasoning before each action. For small models, limited model capacity can result in lengthy reasoning that provides little useful guidance for action generation while incurring substantial inference cost. To address this challenge, we introduce Selection-based Structured Reasoning (SSR), a framework that reformulates reasoning as selection instead of open-ended generation. SSR represents recurring high-level reasoning as pre-specified, reusable natural-language candidates. At each turn, the model selects from these reasoning candidates based on their likelihoods given the current context, without requiring an auxiliary task head. Using pre-specified reasoning traces enables parallel scoring, where teacher-forced prefilling computes token likelihoods concurrently within and across candidates using a shared context KV cache. We evaluate SSR on seven multimodal search benchmarks using 2B and 4B models. Across multiple reinforcement learning objectives and supervised fine-tuning, SSR delivers significant efficiency gains without sacrificing task performance. SSR achieves an average success rate competitive with leading search agents of the same scale, while reducing per-turn reasoning latency by over 90% and total per-question model inference latency by 28-54%. Project page: https://zfy0314.github.io/ssr-webpage/.

Protein mutation effect generation asks a model to describe the functional consequence of a point mutation in natural language. Existing protein-to-text systems typically encode mutation information into undifferentiated representations, overlooking the organization of mutation-induced evidence across structural and biochemical factors. We propose RipplePLM, a mutation-aware generation framework centered on Direct-Distal Cross-Attention (DDCA). By constructing a residue-level Mutation Perturbation Field from pre-trained protein language models, DDCA leverages predicted contact maps to organize mutation representations into two pathways: the mutation site's immediate contact neighborhood and its multi-hop distal context. To complement this structural decomposition, we further introduce the Property Latent Chain (PLChain), which injects expert-guided supervision of biochemical property changes (e.g., thermostability and optimal pH) into the LLM hidden-state pathway through latent property tokens. On MutaDescribe, RipplePLM improves over mutation-specific baselines on temporal and structural splits; under a matched-backbone comparison, average structural-split ROUGE-L increases from 22.23 to 35.65. Expert evaluation further shows a higher proportion of biologically accurate or relevant descriptions than the mutation-specific baseline. Additional ablations, representation diagnostics, and low-$N$ fitness regression experiments further support the effectiveness of the learned mutation-aware representations. Code: https://github.com/Lyu6PosHao/RipplePLM.

Deep generative networks have recently achieved unprecedented performance in precise image and video editing using sophisticated textual prompts. However, the effectiveness of such models heavily depends on access to very large supervised and annotated image datasets, which can be very difficult to obtain. This is particularly true for satellite instruments, which very rarely overlap with labelled data, and suffer from domain shifts in the rare occasions they do. In this paper, we investigate the potential of flow matching models for unsupervised domain adaptation of satellite radiometer images. Our main contribution is a novel unsupervised method that achieves precise domain alignment by leveraging parts of the deterministic ordinary differential equations in flow matching models, conditioned on different satellite instruments. A key strength of our approach is its ability to preserve essential information while adapting across any domains since the perturbations are in theory bijective. Extensive experiments conducted on the GPM-Core constellation show the benefit of our conditional domain adaptation, particularly in improving rain precipitation estimation from radiometer imagery.

Should low-precision transformer inference use stochastic rounding (SR) or round-to-nearest (RN)? The answer depends on where in the network you look. We isolate this effect by holding the numerical format fixed and varying only the rounding rule at individual operation sites. To enable experiments at freely chosen precisions, we extend the PRISM vectorized rounding library to arbitrary virtual precision via a variable-precision stochastic rounding (VPSR) algorithm, proving that the rounding decision is evaluated exactly in hardware floating point. We develop two analyses providing complementary insight into this site-level trade-off. First, a probabilistic forward-error bound for linear projections shows that SR's error envelope grows as $O(\sqrt{n} u)$ in reduction length $n$, versus $O(n u)$ for RN, a gap that widens rapidly at low precision and is most pronounced in the long multilayer perceptron (MLP) down-projection. Second, a second-order decomposition of expected cross-entropy loss change at the output softmax into signed drift, drift curvature, and a Fisher-weighted variance penalty reveals why the two sites behave oppositely: MLP noise is predominantly a uniform logit shift to which softmax is invariant, so SR's variance is largely discounted; head noise is non-uniform across the vocabulary and is not. On DistilGPT-2 at $t=6$ significand bits, observations match theory: SR in the MLP raises perplexity to 1.15x the full-precision reference, versus 2.21x for RN. At the language-model head, the ordering reverses because SR introduces non-uniform variance, whereas deterministic RN carries none. In a mixed-precision configuration (MLP output at $t=6$), assigning SR to the MLP and RN to the head brings perplexity within 1.10x of the full-precision reference, a 28% reduction over matched-bit RN.

The Mumford–Morita–Miller classes on the moduli space of Riemann surfaces may be defined not only in ordinary cohomology but in any complex-oriented cohomology theory. We begin their investigation, emphasising the new phenomena that arise.

Dynamic resource assignment, the real-time allocation of task streams to heterogeneous processing nodes, is the backbone of modern computing infrastructure. While learning-based schedulers excel in research, industrial deployments still rely on hand-written rules that operators can read, audit, and execute within tight latency budgets. LLM-based Automatic Heuristic Design (AHD) promises to automate writing such rules. However, existing AHD frameworks were developed for combinatorial problems fully specified to the LLM, and they learn only from a scalar fitness score. In real systems, the behaviour that determines a good heuristic, such as processor speeds or power consumption, is unknown a priori: the score reveals which heuristic performs better, but not why. This missing information is recorded in the system logs that every evaluation produces. Exploiting it is non-trivial: logs are massive and noisy, the relevant signals depend on the objective, and their content and format vary across hardware and software stacks, so they can neither be fed to an LLM as is nor processed by a fixed parser. We propose TRACE, which couples an evolutionary AHD loop with an agentic knowledge-extraction workflow. A Reasoner agent analyzes the log schema in light of the objective and formulates hypotheses about the system dynamics; a Coder agent writes and executes schema-specific code to test them, producing insights or executable tools for the evolved heuristics. We evaluate TRACE on a synthetic cloud benchmark and a 5G vRAN scenario built from industrial testbed measurements and operational traffic traces. TRACE consistently outperforms state-of-the-art AHD methods in resource assignment problems and yields more auditable heuristics at under 2% overhead.

Subsurface hydrogen storage in porous geological formations is a promising strategy for balancing temporal mismatches between renewable energy generation and demand. The viability of large-scale hydrogen storage depends on predicting hydrogen distribution, trapping, and recovery during cyclic injection and withdrawal operations. However, these multiphase flow processes are influenced by rock heterogeneity, capillary hysteresis and trapping at the pore-scale. In this work, fast in-situ synchrotron X-ray tomography was used to directly visualise hydrogen mobilisation during brine imbibition in a heterogeneous sandstone. By systematically varying the brine injection rate, the influence of flow conditions on hydrogen recovery, and the evolution of trapped hydrogen were quantified. Significant mobilisation of disconnected hydrogen clusters was observed during imbibition, even at low capillary numbers ($< 10^{-6}$). Rock heterogeneity influenced trapping behaviour, particularly during the early stages of imbibition. Our results highlight the importance of incorporating pore-scale heterogeneity and transient trapping mechanisms into hydrogen storage predictions.

The design of satellite constellations for Earth observation requires balancing spatial coverage, revisit time, cost, and operational complexity. This paper considers the problem of designing the orbits of a given number of Low Earth Orbit (LEO) or Very Low Earth Orbit (VLEO) satellites to maximize the spatial and temporal resolution achieved over a prescribed set of ground targets. This kind of problem is inherently nonconvex and possibly combinatorial, making its solution computationally demanding for large constellations and target sets. To address this challenge, we propose a two-stage optimization strategy that separates spatial-coverage design from temporal-resolution optimization, thereby reducing the complexity of the overall problem. Two variants of the method are developed. The first employs continuous decision variables during the spatial-optimization stage, whereas the second discretizes these variables and reformulates the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The latter formulation enables the use of efficient classical QUBO solvers and is directly compatible with quantum-annealing hardware. The proposed framework provides a scalable approach to the design of heterogeneous LEO and VLEO Earth-observation constellations and establishes a pathway for exploiting emerging quantum-optimization technologies in satellite mission design. Preliminary simulation results are presented to demonstrate the effectiveness of the strategy.

We introduce an approach for collection-grounded B-roll sequence generation. Given a user's video collection, a directive given in natural language, and a target duration, the goal is to produce a multi-shot sequence that complements the user's primary footage (A-roll) while preserving the collection's characters, settings, objects, and style. This task is challenging as one must choose the visual evidence from hours of captured footage that should guide the generation of each shot in the sequence. We address this challenge with MemComposer, a three-stage system that turns raw footage into a structured memory with visual references (characters, settings, objects, and style) and uses it to plan, retrieve, and generate grounded B-roll sequences. First, in a one-time offline stage, MemComposer constructs an entity-centric memory from raw video. Second, it uses the memory and user directive to plan a grounded sequence and retrieve conditioning frames for each shot. Third, it iteratively generates and critiques the sequence to enforce identity, setting, and sequence-level consistency. We evaluate MemComposer in a user preference study along two dimensions: prompt adherence and visual alignment to the user's collection. Against an ungrounded text-to-video planner, MemComposer wins 60.0% of prompt-adherence and 92.8% of visual-alignment comparisons, showing the grounding benefit of collection memory and reference retrieval. Against retrieval-only sequences assembled from captured footage, MemComposer wins 94.5% of prompt-adherence comparisons, showing the value of generating missing shots, while retrieval-only sequences are preferred for visual alignment in 58.2% of comparisons.

In this paper, we consider the existence of small- and large-amplitude compressible water waves. These are solutions of the two-dimensional free boundary isentropic Euler equations subjected to a constant gravitational force and neglecting the effects of surface tension. We study periodic and solitary waves beneath vacuum as well as front-type solutions of the two-phase problem in a channel. Using local and global bifurcation techniques, we construct large families of these waves beginning at an incompressible solution and treating the Mach number (defined in a suitable sense) as the bifurcation parameter. This gives a rigorous version of the classical Janzen–Rayleigh expansion, but also furnishes solution curves that may limit to transsonic flow.

Multi-agent reinforcement learning (MARL) provides a powerful framework for learning coordinated behaviors through interactions with the environment. Developing MARL policies requires balancing expressive modeling of complex and multimodal action distributions with efficient training and execution. Generative policies, particularly diffusionbased policies, can faithfully capture complex and multimodal behaviors, but costly iterative sampling hinders their scalability in online multi-agent settings. We propose an Online MARL framework via one-step Flow model (OMAF) that combines expressive generative policies with efficient one-step action generation. OMAF employs a Transformer-based flow policy to capture complex coordination behaviors, while its approximate path score surrogate provides a principled route to synchronized flow policy optimization. To enable stable and sampleefficient learning, we further develop a joint optimization scheme coupling softmax Q-value estimation with a joint flow policy objective for coordinated policy learning. By eliminating iterative sampling, OMAF dramatically reduces training overhead without sacrificing policy expressiveness. Extensive experiments across 10 standard tasks from MPE and MAMuJoCo show that OMAF consistently achieves superior performance, with up to 3.4x higher returns and 10.5x sample efficiency improvement compared with baseline methods. These results validate the effectiveness of OMAF as an expressive and computationally efficient one-step flow policy paradigm for online MARL.

We study webs on surfaces for the $\rm{PGL}_2$ skein theory specialized at roots of unity. We construct the $\rm{PGL}_2$ analogue of Chebyshev polynomials and use them to construct central elements in the skein algebra. We then focus on the cases of the 3-punctured sphere and the closed torus. We compute the Frobenius homomorphism for these two surfaces and show that the $\rm{PGL}_2$ Frobenius homomorphism for the torus is not injective when the quantum parameter $q^2$ is a root of unity of even order $n.$

The chirality-induced spin selectivity (CISS) effect, the coupling between structural chirality and electron spin polarization, has been experimentally observed across many diverse systems. However, despite extensive theoretical effort, a unified mechanistic understanding remains elusive. In this perspective, we demonstrate how some of the basic properties of the fascinating effects of CISS can be understood based on straightforward symmetry considerations commonly employed in fundamental particle physics. In particular, we show that CISS does not violate any fundamental symmetries including parity and time-reversal. By anchoring CISS within the universal language of symmetry, we offer a robust conceptual foundation for interpreting experiments and guiding future theoretical and experimental designs.