Papers

Sparse attention mechanisms estimate attention over $n$ tokens using a small subset of keys. Many existing approaches use maximum inner product search (MIPS) to retrieve the heaviest keys, which motivates the following question: given black-box access to a MIPS oracle, how many keys must be retrieved to output an $\varepsilon$-accurate attention estimate? We answer this question by unifying prior approaches through the framework of priority sampling. With a single MIPS index, we show that $\Theta(\sqrt{n}/\varepsilon)$ retrieved keys are both sufficient and necessary. With $\Theta(\log n)$ indices, we give an algorithm that retrieves only $O(\log n+1/\varepsilon^2)$ keys and prove that this is near-optimal. More generally, we design algorithms that establish a smooth tradeoff between the number of MIPS indices and number of retrieved keys. We then show that if we allow augmentation of keys and queries, we can bypass the above lower bounds: there exists a simple priority-sampling estimator using a single MIPS index and $O(1/\varepsilon^2)$ retrieved keys. When integrated into LLM inference, our algorithms outperform top-$k$ and sampling approaches used in prior work and yield attention approximation that scales favorably to long contexts.

Hierarchical Archimedean copulas (HACs) admit redundant tree representations: when adjacent internal nodes have equal parameters, contracting the connecting edge leaves the copula unchanged. This creates a structural overparametrization. For homogeneous one-parameter families, we remove this redundancy and identify the resulting reduced model class with the ultrametric fan. We treat the Clayton, Frank, Ali-Mikhail-Haq, Gumbel and Joe families. Using the negative logit of normalized Kendall's tau as a common node-height coordinate, reduced hierarchies form polyhedral strata, binary hierarchies index maximal cones, and multifurcating hierarchies lie on common contraction faces. The induced cophenetic metric generates the same topology as uniform convergence of copulas. We also show that informative pairwise dependence summaries act componentwise on cophenetic coordinates and hence provide global coordinates for the reduced model. This representation yields a global estimator obtained by inverting estimated pairwise summaries and projecting onto the fan, without preselecting a hierarchy. We prove consistency and convergence-rate transfer. At binary truths, the unthresholded estimator recovers the hierarchy with probability tending to one; at multifurcating truths, it asymptotically selects a binary refinement, while vanishing thresholding consistently recovers the reduced hierarchy. Under a joint central limit theorem for the pairwise summaries, the projected estimator has a root-$n$ limit given by Euclidean projection of a Gaussian vector onto the tangent fan. The limit is Gaussian at binary hierarchies and generally non-Gaussian at multifurcating ones. For empirical Kendall's tau, we verify the required regularity conditions and obtain the corresponding singular limit.

Real-world low-quality images suffer from complex mixed degradations, including but not limited to noise, blur, atmospheric effects, etc. Recent agentic methods usually model real-world image restoration (Real-IR) as a sequential tool calling problem over task-specific single-degradation restoration models. This paradigm, however, is fundamentally limited because complex real-world degradations cannot be cleanly undone degradation by degradation, and the tool used for task-specific models caps the capability of the agent system. In this work, we present HarnessIR, an agentic framework for Real-IR by harnessing a multimodal foundation model (MFM) as the executor. HarnessIR consists of five stages: perception and diagnosis, on-demand tool invocation, prompt composition, execution, and verification-driven refinement. Unlike prior agentic Real-IR methods that rely on tool chains assembled from task-specific models, HarnessIR feeds the restoration requirements, the perceptual diagnosis, and the evidence into an MFM that performs restoration in a single pass, followed by verification stages to determine whether the result warrants further processing. Under our harness, off-the-shelf MFMs handle restoration tasks remarkably well, achieving state-of-the-art results on the widely used MiO100 synthetic benchmark. More importantly, by exploiting the strong generalization ability of MFMs, HarnessIR delivers compelling restoration quality on challenging real-world scenes where previous agentic IR systems often struggle. Codes is available at https://github.com/PolyU-VCLab/HarnessIR.

We study a Monge normal form of a surface in $\mathbb{R}^4$ based on the principal axes of its curvature ellipse. The curvature-ellipse-based Monge normal form is obtained using only Euclidean motions of the ambient space and local reparameterizations of the surface, and preserves the Euclidean invariants of the curvature ellipse, including its semi-axis lengths up to their ordering. We also give applications of this normal form to the $2$-jet geometry of surfaces in $\mathbb{R}^4$ and to the geometry of their orthogonal projections.

Centralized admissions platforms grant priority based on self-reported facts such as residence, sibling status, or family income, and a false claim can cost another applicant her seat. Verifying every claim before matching is expensive, yet checking only admitted applicants afterward is unsafe: a false claim by an applicant who ends up unmatched may already have triggered a chain of rejections. We show how a platform can check far fewer claims without changing any outcome. A claim matters only if it can move its applicant across a school's admission cutoff, and we give an exact, easily computed test for when this happens. Checking only such claims, and only when they could change a school's tentative choice, reproduces every application, rejection, and assignment of deferred acceptance under full verification. When claims are truthful, checking the highest claimed priority first minimizes checks among such policies at each school decision, and the number of checks never exceeds the school's capacity. Truthful reporting of preferences and eligibility is a weakly dominant strategy, so incentives deliver the conditions under which this audit order is optimal. In simulated markets, the policy cuts verification by 76 percent relative to checking every claim upfront and by 36 percent relative to checking each claim when it first reaches a school. The design principle is to verify decisions, not files.

Extreme debris disks are signposts of violent rocky collisions, but it remains unclear whether their mid-infrared variability traces transient dust clouds or longer-lived post-impact reservoirs. We analyze a 19 yr mid-infrared record of the young solar analog NGC 2547 ID8, combining four spectra from 2007-2024 with 3-5 micron monitoring through 2026. The optically thin mineral surface remains compositionally stable: broad fits spanning multiple grain sizes give 550-577 K, and a common-basis decomposition with T_surf fixed at 560 K is dominated by 1 micron olivine/Mg-olivine and 0.1 micron forsterite. The W2-equivalent 4.5 micron excess, traced across six recurrent high states, is instead driven mainly by changes in the hot-base continuum component and defines a 956.8 d infrared recurrence timescale with cycle-to-cycle variations in timing and amplitude. This combination supports the interpretation of ID8 as an early post-impact stage in which material on eccentric orbits repeatedly interacts with a warm rocky reservoir, preserving the impact's mineral fingerprint while the interaction geometry evolves. Material on eccentric orbits can persist for decades, and possibly longer, while interacting with debris disks. Longer-baseline, higher-cadence infrared monitoring of ID8 will further constrain the stability of its recurrence timescale and the detailed evolution of its infrared variability.

As EDA researchers, we conducted eight deliberate trials of agentic algorithm exploration, selecting several topics outside our areas of depth. One faculty member and seven students participated, including students without publication experience. With limited intervention in the algorithms, agents developed mathematical constructions, analyzed existing tools, and implemented improvements; some efforts fell short of their practical goals. We also used AI to collect, classify, and analyze 8,420 papers from four EDA conferences and two journals over 2022-2026. Among 2,380 primary-core papers, we classified 97.7% from titles and abstracts as computationally closed, including work on new formulations. Together, these observations suggest that much of EDA offers an executable environment for increasingly accessible algorithm research. We see an opportunity for tool developers to investigate ideas they previously lacked time to pursue. We also ask how EDA should validate and reward research when results become easier to produce than to examine, and what papers and venue labels will continue to tell us about a contribution.

We show upper and lower bounds on the regret of $m$-set adversarial bandits for different utilities (winner reward or sum of rewards) and feedback models (winner index, winner reward, sum of rewards, and their combinations). By comparing to standard bounds for combinatorial and MNL bandits, our results reveal how subtle changes in the setting can have a dramatic impact on the learning rates. Our main technical contributions are the information-theoretic lower bounds on the regret. Experiments on synthetic data confirm our theoretical analyses.

Transmission silicon detectors are widely used in $\Delta E$–$E$ telescope configurations for particle identification and timing in nuclear physics experiments. Variations in signal rise time can introduce time-walk effects that degrade time-of-flight measurements, as recently observed in light-ion production experiments at the Neutrons For Science (NFS) facility at GANIL using the Medley setup. This work investigates the influence of particle energy and detector non-uniformity on signal rise time.

Multi-agent LLM systems coordinate task execution through exchanges of information among agents. When coordination breaks down, similar symptoms in execution traces can reflect different problems in how information is passed, used, or verified. Communication topology captures how agents exchange information and provides structural cues for distinguishing coordination failure modes. Using these cues for diagnosis requires establishing how topology relates to failure patterns and recovering the relevant structure from execution traces that lack explicit topology labels. We analyze the relationship between communication topology and failure patterns and introduce MAScope, a two-stage framework for topology-conditioned diagnosis. Its Trace Structural Extractor TSE recovers communication topology from heterogeneous execution traces by grounding an interaction graph in message evidence. The Topology-Conditioned Judge TC-Judge then classifies failures using the trace, predicted topology, an empirical failure prior estimated from separate labeled traces, and a short description of topology-specific failure patterns. Under a fixed orchestration structure, the recovered topology can be reused across executions. Experimental results show a statistically significant association between communication topology and failure type, with $\chi^2 = 409.9$ and $p = 1.2 \times 10^{-70}$. On the \num{851} MAST-clean traces, ground-truth topology context raises gpt-mini's Macro-F1 from $0.173$ to $0.350$. With predicted topology, the pipeline achieves $0.346$, approaching the trace-only gpt-5.4 baseline of $0.372$. For \num{1000} traces under a fixed orchestration structure, the projected pipeline cost, including one topology extraction, is approximately $6\%$ of repeated gpt-5.4 diagnosis cost. These results show that topology-conditioned context improves failure diagnosis and supports lower-cost deployment.

Household robots need to continually navigate to different objects in the same environment, many of which are small and portable, such as tools and toys. Their small visual footprint and frequent occlusion make reliable observation difficult, and they may be moved by people without the robot observing the changes. We formulate this challenging task as Lifelong Small-object Navigation in Changing Object Layouts (LiSoNav-COL). Agents must seek suitable viewpoints for reliable observation, accumulate and reuse scene knowledge to efficiently locate subsequent targets, and update outdated memory after object relocation. To eliminate the need for prior scene scanning, we also require agents to start navigation with empty scene memory. Although practical, this task still lacks benchmarks designed around its defining assumptions. To bridge this gap, we introduce LiSoNav-Eval, a dedicated benchmark spanning 28 indoor scenes with 45 small-object categories. Its lifelong navigation sequences include both unchanged and relocated targets to evaluate memory reuse and adaptation to object relocation. To address this challenging task, we propose a navigation method based on multi-view Inspection with Viewpoint-Anchored Memory, dubbed IVAM-Nav. IVAM-Nav actively observes supporting surfaces from complementary viewpoints for reliable small-object perception and anchors the resulting memory to their observation viewpoints, supporting relational memory reuse and revalidation under similar viewing conditions. Extensive experiments on LiSoNav-Eval demonstrate favorable performance of IVAM-Nav against representative methods. Benchmark analyses also show that smaller objects, larger environments, and longer relocation distances pose greater challenges. The dataset and code are available here.

Generative recommenders return a limited candidate set and may omit observed targets before reranking. A training strategy appends these missed targets to reranker training lists, although inference still ranks only original candidates. This operation simultaneously changes retrieved-target weight, adds supervision over appended targets, and makes the two groups compete for probability. An append/no-append comparison therefore cannot explain changes in returned-item rankings. We construct three matched losses that hold retrieved-target weight fixed while introducing appended-target supervision and group competition separately. The intermediate loss trains within both groups but normalizes them separately, preventing training-only targets from competing with inference candidates. Experiments with a released OneRec model and locally trained Amazon generators show that this competition can harm returned-item ranking. In four prespecified Amazon Video Games comparisons, removing it improved full-target normalized discounted cumulative gain (FT-NDCG) by 7.8–22.2%; 95% intervals over users and three of four intervals over training runs excluded zero. A conservative development-set rule selected appended-target training for two of three generators in one held-out category and rejected it for all three in another, avoiding a 1.7% loss. Candidate completion should therefore be evaluated for each generator rather than applied automatically.

Understanding the non-equilibrium dynamics of quantum many-body systems plays a central role in modern many-body physics. Intriguing insights emerge from investigating how quantum resources, which are essential for achieving unambiguous quantumness, are generated and spread under chaotic quantum dynamics. In fermionic systems, non-Gaussianity constitutes an important resource beyond entanglement, characterizing the deviation of generic quantum states from free-fermion states. In this Letter, we propose using the replica twist entropy, defined through the expectation value of a replica rotation operator with a tunable angle $\alpha$, as a natural probe of non-Gaussianity in pure fermionic states. After deriving its behavior for typical many-body states, we establish a general framework for analyzing the replica twist entropy in solvable Sachdev-Ye-Kitaev models in the large-$N$ limit. Applying this framework to the dynamics of the thermofield double state, we uncover a novel dynamical phase diagram in the parameter space of $\alpha$ and evolution time $t$, exhibiting spontaneous $Z_2$ symmetry breaking at $\alpha=\pi/4$ and universal cusps as a function of $\alpha$ in the long-time regime. Our results pave the way for studying non-Gaussianity in strongly correlated fermionic systems and reveal a new class of dynamical transitions probed by non-Gaussianity.

A Gaussian process (GP) model can agree with the data for two reasons: its assumptions are right, or the chosen inputs could never have shown that they are wrong. The distinction can be checked from the design before any responses are observed. Every model implies relations that its noiseless responses must satisfy at the chosen inputs, such as the middle value lies on the line through its two neighbours. For GPs built from finitely many features, these relations are exactly the null space of the kernel matrix. Gale duality gives them a geometric interpretation, in which each observation has a vector and the smallest groups of observations that can expose an error are the circuits. For other kernels the relations become soft: response patterns may be improbable under the prior rather than algebraically impossible. A standard test then combines two kinds of evidence. Structural evidence comes from a violated relation and grows without limit as the noise falls. Prior-based evidence only says that a departure is improbable under the prior. With all inputs at the two ends of an interval, for example, a GP can reject a straight line against a large curvature, but only because the implied intercept is improbable, never because curvature was seen. In simulations the predicted power matched the observed rejection rates. Choosing the next input by predicted power raised the power against a localised discrepancy from 0.48 to 0.72, against 0.51 when choosing by predictive variance, and a grid in two dimensions contained exact tests of additivity that a Latin hypercube lacked. The test itself is classical. The contribution is the prospective reading of that test: before observing the responses, the design already determines what kind of contradiction it can produce.

Previous speech deepfake detectors can adaptively capture spectro-temporal dependencies through graph attention, yet they largely overlook the co-variation between spectral and temporal representations. To address this gap, we construct a normalized affinity graph from their joint covariance and apply polynomial graph filtering to capture higher-order covariance-induced dependencies. We first develop Cov-ST to isolate the contribution of covariance-based relational modeling. Although it improves detection performance, its sensitivity to the polynomial order suggests limited robustness when covariance relations are modeled alone. We therefore propose DuRe-ST, which jointly exploits covariance-induced and graph-attention-induced relations to capture complementary second-order co-variation and adaptive spectro-temporal dependencies. Experiments show that DuRe-ST achieves an average relative EER reduction of 25.9% over XLSR-AASIST on the ASVspoof benchmarks and 28.4% across four cross-dataset benchmarks with only 4-8k additional trainable back-end parameters. It further outperforms the strongest publicly available comparison models by 2.2-13.2% in relative EER on four benchmarks, while remaining smaller than the publicly available models considered.

Reinforcement learning with verifiable rewards (RLVR) has driven substantial progress in domains where task outcomes can be reliably evaluated, but long-horizon interaction remains challenging due to sparse terminal feedback and difficult credit assignment. Process rewards provide denser supervision, yet the capabilities most relevant for training can change as the policy evolves: a behavior that is easy to evaluate or frequently deficient need not be the bottleneck currently limiting task success. We introduce RewardWeaver, a self-evolving reward adaptation framework for language agents in long-horizon interaction. RewardWeaver maintains a validated capability space in which the semantics of admitted Rubrics remain fixed, and closes the loop between policy optimization, task evaluation, failure attribution, and reward adaptation. After each training stage, it performs outcome-grounded backward attribution on low-outcome trajectories, aggregates recurrent and policy-controlled capability bottlenecks, and dynamically selects the corresponding process rewards for the next stage. Recurrent failures not covered by the existing capability space trigger a separate, controlled expansion procedure. We evaluate REWARDWEAVER on SOTOPIA, Amazon?HistoryPrice, and a newly constructed Sales Benchmark. Across social interaction, bilateral bargaining, and domain-specific sales, REWARDWEAVER establishes new state-of-the-art (SOTA) results. Ablations further demonstrate the importance of dynamic reward allocation, failure-grounded attribution, and stable semantics for admitted capabilities.

We prove a sharp Szegö-Weinberger-type inequality for balanced doubly connected domains in $\mathbb S^2$, $\mathbb R^2$ and $\mathbb H^2$. More precisely, the first positive Neumann eigenvalue is bounded above by that of the corresponding rotationally symmetric annulus, determined by the area of the domain and the area of the smallest component of the complement. Equality holds only for the rotationally symmetric annulus. We also show that the balancing assumption is essential: if we drop it, the inequality fails in general.

We present EdgeRock, a family of multimodal models that deliver strong reasoning at constant memory. Most models keep reasoning history in a key-value (KV) cache that grows with every token, consuming accelerator memory, limiting concurrent requests, and competing with perception and control on edge devices. With fixed history, memory is allocated once and never runs out, however long the model reasons. Constant memory alone is not new: bounded-state models (recurrent, state-space, and sliding-window) already achieve it, but often at the cost of reasoning, because they cannot keep the distant details that later reasoning needs. We therefore introduce Rock Memory Anchors (RMA): the model learns what is worth remembering and stores it as KV records in a fixed-size bank, directly readable however far back the source lies. EdgeRock-4B, our first open-source release, supports text and image reasoning and reaches 82.9% mean pass@1 on AIME 2024-2026, while the bounded-state models we evaluate reach at most 18.8%, even at 14B scale. This result is on par with leading compact models whose memory grows with reasoning. Compared with its source model, EdgeRock-4B uses up to 99.1% less KV cache and delivers up to 6.42$\times$ higher end-to-end batch throughput.

We use the MUSE-ALMA Haloes sample to build a census of the condensed baryons (stars and cold gas) to study the multiphase interstellar medium and circumgalactic medium (CGM). The sample includes 79 gas-rich galaxies at 0.2<z<1.2 located near strong HI Ly-alpha absorbers along quasar sightlines within projected separations of ~5-270 kpc and radial velocity separations of up to 500 km/s. HST spectroscopy characterises the absorbers, while HST imaging, MUSE and ALMA observations trace the stars, ionised gas and molecular gas. We find the following results. (i) HI masses inferred from optical properties show broad agreement with those derived from the CGM absorber properties for impact parameters <100 kpc, although group environments can significantly influence these estimates. (ii) The molecular gas fraction declines more steeply with stellar mass than the HI fraction. This suggests that stars build up more rapidly than the cold gas reservoir, while massive galaxies either consume their molecular gas more efficiently or convert HI into H2 less efficiently. (iii) Galaxies with high stellar surface densities exhibit the highest baryon fractions. This may reflect baryonic feedback, which can produce flatter inner dark matter profiles in high surface density systems, or aperture effects, where the ionised gas kinematic tracer probes only the innermost, baryon-dominated regions in compact sources, but extends further into the dark matter halo in sources with extended baryonic distributions. (iv) A few galaxies are consistent with being the baryon-dominated descendants of the low mass z~6 galaxies detected by JWST, while many appear to be substantially more dark matter dominated, lower mass systems with progenitors beyond JWST detection limits. This study provides a multiscale, multiphase view of the gas in and around galaxies, allowing us to probe the baryon budget across cosmic time.

Semantic segmentation networks operate on a fixed set of classes and therefore fail when out-of-distribution (OOD) objects appear during deployment, a critical limitation for safety-critical applications such as autonomous driving. Reliably identifying OOD objects requires well-calibrated epistemic uncertainty, yet common softmax-based confidence scores remain overconfident, while Bayesian alternatives such as Monte Carlo dropout or deep ensembles require costly repeated forward passes. Evidential Deep Learning (EDL) offers an efficient alternative by modeling class probabilities as a Dirichlet distribution learned from a single deterministic forward pass. Existing EDL formulations rely on Euclidean objectives that push predictions towards the simplex vertices, encouraging overconfidence rather than preserving uncertainty for unfamiliar inputs. We instead employ Wasserstein-based objectives, which respect the geometry of the probability simplex, and study the influence of the Wasserstein order on segmentation accuracy and OOD detection within a unified evidential framework. We evaluate this framework on a convolutional (DeepLabV3+) and a transformer-based (SegFormer) architecture on the SegmentMeIfYouCan benchmark, including LostAndFound, RoadObstacle21, RoadAnomaly21, and Fishyscapes. Our results show the optimal Wasserstein order is architecture-dependent: second-order objectives dominate on the convolutional backbone, third-order objectives on the transformer backbone, and our framework surpasses comparable baselines on most metrics, with a single deterministic forward pass.

We show that no meaningful version of the Cone Conjecture holds for non-generic Sakai surfaces.

The architectural design of Large Language Models (LLMs) is shifting from traditional full-attention-only models to hybrid models, which combine different attention modules to improve long-context efficiency and performance in length extrapolation and context extension. To explain why hybrid models work and how to design them better, we propose Mechanics of Long-Context Hybrid Models. As Part 1.1 of this series, we begin with hybrids of full attention and either sliding-window attention (SWA) or gated variants of linear attention (LA), represented by GLA and GDN. We first observe a Seesaw Effect in Context Extension: LA hybrids benefit more from long-context continual pretraining, whereas SWA hybrids perform better under length extrapolation. We attribute this behavior to differences in the positional inductive biases induced by these attention mechanisms. We find that SWA hybrids suffer from a Short-Context Learning Trap, Short-Window Weariness, and Long-Window Laziness, and require extended windows to enhance performance in continual long-context pretraining. For LA hybrids, we summarize the Matthew Effect of Hybrid Position Extrapolation and propose Sliding-Window Linear Attention, achieving 16$\times$ training-free length extrapolation while maintaining 100% accuracy on NIAH-SK1 in 64k context length.

Spatially resolved galaxy kinematics are well studied at z $\sim$ 0 and z > 1, revealing that disks are common out to z $\sim3-6$, albeit with higher velocity dispersions. z $\sim$ 0.5 marks a key transition in the drivers of disk turbulence and baryonic-dark matter mass budgets, yet multi-tracer resolved kinematic studies remain rare beyond the local Universe. We exploit a unique dataset combining ALMA CO observations with MUSE ionised gas and stellar continuum data to study the resolved kinematics of six galaxies at 0.43 < z < 0.83, part of the MUSE-ALMA Haloes program, selected via their association with H I absorption systems and spanning stellar masses from log$(M_\star/M_\odot) = 10.1 - 11.8$. Combining new ALMA/CO data with existing MUSE H$\beta$ kinematics and HST morphologies, we classify galaxies using morpho-kinematic criteria. For rotating disks, we jointly model H$\beta$ and CO(2-1) kinematics with DYSMALPY and compare results to theoretical predictions for pressure support, while pPXF is used to fit stellar absorption features. Four of the six galaxies are classified as disks, with two having known group members. These disks show elevated gas velocity dispersions relative to z $\sim$ 0 disks, consistent with interpolated trends between z $\sim$ 0 and z > 1. The results support marginally stable gaseous disks where gravitational instability still contributes alongside stellar feedback, with tentative evidence for a dynamically hotter warm ionised phase relative to cold gas ($\sigma_{0, H\beta} \sim 1.7 \times \sigma_{0, CO}$). We derive an average dark matter fraction $\langle f_{DM} \rangle = 0.42\pm0.14$, consistent with observations at similar redshifts, stellar masses, and surface densities. This work demonstrates the value of self-consistent, multi-wavelength analyses for probing disk settling physics in a relatively unexplored redshift range.

The interactions between gas and galaxies are of paramount importance to our understanding of structure formation. A fundamental element of such baryon cycle studies is a complete census of the condensed matter (stars and cold gas) in both galaxies and their immediate surroundings, the so-called circumgalactic medium. Of particular importance are the processes of converting molecular gas into stars and deciphering whether this <100K gas is tracing gas flows. The MUSE-ALMA Haloes survey has assembled probes of the neutral atomic gas HI, ionised gas and stellar component for a sample of 79 $z\sim0.5$ galaxies. This is achieved by combining absorption line spectroscopy of background quasars with projected impact parameter as low as 5 kpc and up to 250 kpc to probe the low density circumgalactic gas with emission line tracers of both ionised gas and stars. This paper presents the Large Programme observational set-up and releases the data characterising the molecular phase of some of the MUSE-ALMA Haloes targets so as to reach a complete census of their condensed baryons. ALMA's unique millimetre coverage and high sensitivity is ideal to characterise the CO emission of these $z\sim0.5$ HI-selected galaxies. By measuring the molecular mass, kinematics, gas flows and gas fractions, this project then: i) quantifies the role of molecular gas in HI-rich galaxies, ii) characterises the molecular phase of gas flows from morpho-kinematics analyses, and iii) establishes a census of the condensed baryons in the interstellar and circumgalactic media. Ultimately, these results will provide unique insights into the baryon cycle - a crucial component of galaxy formation.

We disprove the classical version of the Borsuk-Ulam-flavored conjecture, due to Baum-Dąbrowski-Hajac, that free actions $X\times \mathbb{G}\to X$ on non-empty compact Hausdorff spaces by non-trivial compact groups admit no equivariant maps $X*\mathbb{G}\to X$. Specifically, among non-trivial compact abelian $\mathbb{G}$, the conjecture fails precisely when $\mathbb{G}$ is torsion-free profinite.

Quasi-periodic eruptions (QPEs) are repeating X-ray transients from galactic nuclei potentially caused by a stellar-mass orbiter repeatedly colliding with the accretion disk of a supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI). In this picture, the eruption arrival times encode the orbit and its relativistic precessions, while the quiescent spectral energy distribution (SED) probes the same disk and SMBH, providing two independent constraints on the same orbit-disk system. We present a joint spectral-timing framework that takes advantage of this by simultaneously fitting an analytic QPE timing model built on Kerr geodesic frequencies and a warped disk geometry, coupled to a self-irradiated disk SED model sharing the same SMBH mass, spin, and disk parameters. We apply it to the QPE sources GSN 069 and eRO-QPE2, showing that the QPE timings and quiescent spectra can be reproduced simultaneously in each, providing circumstantial support for the EMRI model and warped disks in these systems. However, given the sparse timing data in both sources, neither admits a unique solution. In eRO-QPE2, we identify six physical modes which reproduce the timings and SED comparably well, motivating denser observing campaigns to identify one unambiguously. Our results demonstrate both the promise of QPE spectral-timing as a precision probe of SMBHs, their accretion disks, and orbiting companions, and the aliasing subtleties of sparsely sampled QPE timings.

Floquet engineering controls material responses via a time-periodic electromagnetic drive. An important task in practice is to reduce the driving strengths required to implement Floquet protocols. We show that in systems with strong phase-space constraints, where the response is dominated by a small region of momentum space, the relative impact of a resonant Floquet drive is enhanced. We demonstrate this idea on the example of the orbital Hall effect, where equilibrium occupations restrict the interband coherence to a narrow momentum interval $\hbar\Delta k$. The ratio $eE_0/(\Omega_0\hbar\Delta k)$, where $\Omega_0$ is the frequency of the drive, is considerable even at modest field amplitudes $E_0$, leading to a large relative change in the orbital Hall conductivity. Due to the non-trivial orbital texture, the circularly polarized drive induces an inverse orbital Faraday effect by magnetizing the electrons. We show that the corresponding susceptibility is controlled by the interband quantum metric that determines the resonant Floquet hybridization.

The undirected multiple-unicast conjecture [LL04] asserts that network coding offers no throughput advantage over multicommodity flow. We refute this conjecture by constructing a deterministic linear network code over $\mathbb{F}_9$ on a 182-vertex bipartite subgraph of the point-line incidence graph of $\mathrm{PG}(2,9)$. The construction supports $157$ independent unicast sessions at common coding rate at least $1$, while every fractional multicommodity flow has common rate at most $147/157$. By the amplification theorem of~[BGS17], this yields a family of undirected multiple-unicast instances with coding gap $\Omega((\log n)^\varepsilon)$ for some $\varepsilon>0$. We also introduce a nondeterministic model of network coding based on locally verifiable certificates, which guides our construction and may be of independent interest. Building on the high-girth graph and error-correcting code framework of [BH25], we use GPT-6 to find a nondeterministic counterexample based on a new choice of Reed–Solomon local codes, and then convert this example into a causal code using an edge orientation and local search.

We introduce a weighted adjacency-degree matrix \(A_{fg}(G)\) with edge weights \(f(d_i,d_j)\) and diagonal entries \(g(d_i)\), unifying adjacency, Laplacian, signless Laplacian, \(A_\alpha\), ABC, Randić, Sombor and related matrices. For dendrimer trees \(D_{n,k}\) and Bethe trees \(B_{n,k}\), the characteristic polynomial is factorized through one recursive sequence \(P_{fg,n}\). When \(f^2(1,k)=f^2(k,k)\), this sequence admits a Chebyshev reduction to \( U_{j+1}(x)+\delta U_j(x)=0, \) covering \(L/L^+\) and \(A_\alpha\); explicit cosine spectra occur only in special cases, such as the adjacency matrix and the \(L/L^+\) end factor of \(B_{n,k}\). We derive positive-semidefinite energy formulas, Gershgorin criteria, spectral-gap estimates, interlacing and non-interlacing results, partial eigenvalue-coincidence information, and McClelland- and Koolen–Moulton-type bounds. Several known results are recovered as special cases of this unified framework.

This paper proposes a progressive Bayesian multiple-input multiple-output (MIMO) sensing framework for multiple targets over multiple stages. We consider a practical yet challenging scenario where the targets' angles are unknown and random parameters to be estimated, while the targets' reflection coefficients are unknown nuisance parameters. With an initial prior probability density function (PDF) for the targets' angles, we progressively update the prior PDF for each sensing stage as the posterior PDF obtained from the previous stage, based on which Bayesian transmit beamforming optimization is performed to minimize the sum posterior Cramér-Rao bound (PCRB) in estimating the targets' angles and Bayesian sensing is performed with the help of new observations in this stage. To analytically characterize the intractable and high-dimensional posterior PDF with low complexity, we propose a variational Bayesian inference based approach which derives a surrogate posterior PDF in closed form with only polynomial complexity over the number of targets, in sharp contrast to existing numerical calculation approaches with exponential complexity. Numerical results validate the efficacy of our proposed framework in progressively refining sensing performance.