Papers

Hybrid terrestrial-satellite quantum networks combine terrestrial fiber infrastructure with free-space links to enable long-distance entanglement distribution. Entanglement can be routed over different combinations of terrestrial and satellite links, resulting in paths with different entanglement generation rates (EGRs) and fidelities. Existing routing algorithms, however, typically reduce routing to a single-objective problem by optimizing either EGR or fidelity, or by optimizing one while constraining the other, and thus do not explicitly capture the trade-off between the two. In this paper, we present a bi-objective routing framework for hybrid quantum networks that jointly optimizes end-to-end EGR and fidelity. We formulate routing as a Pareto optimization problem and show that it possesses a special mathematical structure: the bottleneck nature of end-to-end EGR and the multiplicative nature of end-to-end fidelity allow the problem to be transformed into a MAXMIN-MINSUM bi-criterion path problem. This transformation enables the exact polynomial-time computation of a minimal complete Pareto set using Martins' bicriterion routing algorithm. Our results demonstrate that hybrid networks expose substantially richer Pareto frontiers than terrestrial-only networks and that the proposed framework outperforms representative single-objective routing policies by allowing applications to select paths based on their EGR and fidelity requirements.

Let $A$ be a finite dimensional algebra and let $\rmHH^*(A)$ be its Hochschild cohomology ring, which is a Gerstenhaber algebra. Denote by $\calN$ (resp. $G$, $\calG$) the ideal (resp. weak Gerstenhaber ideal, Gerstenhaber ideal) generated by all homogeneous nilpotent elements. Motivated by their work on support varieties via Hochschild cohomology, Snashall and Solberg conjectured that $\rmHH^*(A)/\calN$ is a finitely generated algebra. Xu constructed a counterexample to the Snashall-Solberg conjecture over a base field of characteristic two, and Snashall generalized this example to arbitrary characteristic. Hermann further asked whether $\rmHH^*(A)/G$ is a finitely generated algebra and suggested considering first the Xu–Snashall algebra. In this paper, we answer this question for the Xu–Snashall algebra. In fact, by explicitly computing the Gerstenhaber algebra structure on the Hochschild cohomology ring, we show that $G=\calN$; hence $\rmHH^*(A)/G=\rmHH^*(A)/\calN$ is not a finitely generated algebra. Furthermore, we show that $\rmHH^*(A)/\calG\cong K$. Therefore, one may ask whether, for a finite dimensional algebra $A$, $\rmHH^*(A)/\calG$ is always a finitely generated algebra. Our main tools are two-sided Anick resolutions and weak self-homotopies.

Heterogeneous federated learning requires clients with diverse computational capacities to collaboratively train a global model, where each client trains a capacity-constrained submodel. Existing methods select submodel parameters using heuristic importance measures—most prominently parameter magnitude—without theoretical justification for why these measures support convergence. We identify a fundamental gap: existing parameter selection criteria lack theoretical grounding in the convergence framework, partial client participation introduces additional estimation effects in the Fisher scores. We propose FedFIbOS: Fisher Importance-based Optimal Submodelling for heterogeneous federated learning, using Fisher Information in a principled criterion derived from minimizing submodel masking error. %We formally establish when magnitude selection is equivalent to Fisher selection fail under non-IID heterogeneous federated learning. We theoretically formulate submodel selection through a Fisher-weighted quadratic masking surrogate and show that the raw Fisher top-$k$ rule implemented by FedFIbOS solves this surrogate under a Fisher-dominant ranking condition. The resulting method retains the convergence structure of the underlying masked federated optimization bound. Fisher scores are efficiently estimated from empirical diagonal Fisher information using squared gradients, enabling stable and adaptive parameter selection without additional optimization overhead. Experiments on CIFAR-10, CIFAR-100, and AGNews under pathological and Dirichlet non-IID settings show FedFIbOS achieves ${\approx}10\%$ higher accuracy than the state of the art, with improvements becoming more pronounced under stronger heterogeneity.

This paper establishes a unified non-linear regularization framework for high-dimensional $M$-estimation, encompassing both linear regression and Cox's proportional hazards models. Rather than relying on traditional additive non-convex penalties, the proposed paradigm embeds sparsity directly into the parameter mapping using a smooth ($C^2$) component-wise ReParametrization map for Sparsity (RePS). This geometric formulation dynamically adapts to local parameter scales, successfully suppressing high-dimensional noise and recovering unbiased oracle asymptotic normality under the large-sample limit. Through the Primal-Dual Witness method, we establish a unified oracle equivalence for both model classes under a liberated micro-penalty scaling regime $\lambda \ll n^{-1/2}$, effectively accommodating model-specific structures such as the shift-invariance in survival analysis. Extensive Monte Carlo simulations demonstrate that the RePS framework consistently achieves near-perfect false-positive control and optimal 95% confidence interval coverage, outperforming conventional non-convex regularizers (SCAD and MCP) which suffer from severe variance inflation and under-coverage due to post-selection noise leakage.

Large-scale nonconvex quadratic programming remains challenging because the sparse matrix factorizations used by many existing solvers can incur substantial computational and memory costs and are difficult to parallelize efficiently on GPUs. We present PDNQP, a factorization-free first-order solver for finding stationary points of large-scale nonconvex quadratic programs. The method combines a proximal augmented-Lagrangian framework with restarted accelerated primal–dual hybrid gradient to solve the resulting strongly convex QP subproblems. Its key ingredients are a residual-form reformulation that avoids penalty-dependent normal matrices and preserves a fixed sparse constraint operator across outer iterations, and an adaptive strategy that coordinates inner-solve accuracy with outer progress. The resulting computations rely on sparse matrix–vector products, projections, and vector operations suited to GPU execution. On $107$ nonconvex CUTEst instances, PDNQP achieves the highest success rate among the tested solvers at both accuracy levels. With absolute and relative tolerances set to $10^{-4}$, it achieves speedups of $2.6\times$–$6.0\times$ in shifted geometric mean runtime; at $10^{-6}$, its aggregate runtime remains comparable to that of the fastest tested solvers. On $30$ large-scale synthetic nonconvex QPs with approximately one million variables each, PDNQP returns points satisfying the common external termination criteria on $27$ instances, while none of the other tested solvers succeeds under the same experimental protocol.

Security practitioners burn out at high rates, and the resulting attrition is itself a security problem. This workforce is hard to study: security operations centers are closed to outside researchers, studies that reach practitioners recruit through employers, and those who have disengaged most may have the least reason to answer an employer's survey. The same practitioners discuss their working conditions openly in online communities. We adapt the Burnout Assessment Tool, a validated clinical instrument, into a text annotation scheme and apply it to 354,861 posts and 296,442 replies from five online communities of cybersecurity practitioners. Checked against two trained coders on 100 posts, the annotation reaches a macro F1 of 0.75 across the four symptoms and 0.98 for detecting any burnout signal. We find that the four symptoms point to different problems at work, not to the same problem at different levels of severity. Exhaustion appears in almost any complaint about staffing or workload. Mental distance, a loss of belief that the work is worthwhile, is the only symptom unrelated to operational problems, and among posts with a single symptom it is accompanied by a stated intention to leave roughly twice as often as any other. Peer responses show the opposite pattern. When a poster says they are considering leaving, the mix of replies shifts toward career advice, but this shift is smallest for mental distance. The symptom most strongly associated with leaving is thus the one peers adjust to least, and a single burnout score obscures both patterns.

Artificial intelligence for plant disease analysis has advanced from task-specific classifiers to multi-modal models capable of jointly interpreting visual and textual information. However, practical deployment in precision agriculture remains limited because most existing approaches treat disease understanding as isolated prediction tasks, failing to capture the complementary relationships among symptom recognition, severity assessment, and question-driven diagnostic reasoning. In tomato pathology, accurate interpretation of diseased leaves requires more than label prediction; it demands integrating visual symptoms with semantic context to support a comprehensive and explainable understanding. Here, we present SOLAR, a multimodal generative model that understands tomato disease spanning six question-answering tasks. SOLAR learns to align visual features with task-aware language representations by Fusion Expert module based on mixture-of-expert, enabling it to generate contextually relevant answers across diverse diagnostic tasks. By formulating tomato disease analysis as a generative Visual Question Answering (VQA) task, SOLAR provides a flexible framework that supports multi-task inference within a single model while improving performance and cross-task knowledge sharing. We evaluate SOLAR on $41,677$ images, including $216,209$ Question-Answering (QA) pairs to understand tomato leaf disease under both closed and open-ended QA settings. Experimental results show that SOLAR consistently outperforms state-of-the-art vision-only, vision-language, and task-specific models across all tasks, demonstrating superior accuracy, robustness, and multimodal reasoning. These findings highlight the potential of generative multimodal modeling as an effective direction for understanding of plant disease. The code for this study is available at https://github.com/EnalisUs/SOLAR.

Spatial intelligence requires more than describing object locations. Under incomplete observation, models must identify and acquire missing evidence, interpret it in a common spatial frame, and act on it. We introduce VA-Bench to evaluate the complete observe-reason-act-revise loop. General-purpose MLLMs learn procedural context from RGB-only demonstrations, actively select camera viewpoints, issue metric Cartesian commands, and revise them from execution feedback. Models receive no privileged object poses, oracle trajectories, or learned action heads. A fixed model-agnostic controller executes only model-specified targets. VA-Bench contains 14 base task families (11 single-arm and three dual-arm), seven held-out geometry/layout variants, and a long-horizon five-object composition track. We evaluate 12 primary model conditions in three independent runs over the same 20 physically verified seeds per base task, reporting terminal success, nine trajectory-level behavioral diagnostics, and subtask progress. First, the best-performing model scores 100.0% on target localization and 78.9% on spatial relations in the annotated run. Its three-run macro-average task success is only 53.93+/-3.17%. Second, active camera control significantly improves task success over passive multi-view observation. In one matched comparison, success rises from 27.86% to 57.50%. Third, held-out geometric transfer can reduce task success by over 30 percentage points. No model completes a strict long-horizon episode, despite substantial partial progress. VA-Bench thus tests whether general-purpose MLLMs can turn visual demonstrations and actively acquired evidence into successful embodied action.

Model fusion integrates the capabilities from source models into a single target model. As of June 2026, Hugging Face hosts more than 2M models. This growing pool provides a rich base for model reuse and capability integration. Yet existing surveys often cover only separate parts of this space, and they do not provide a unified definition or a systematic taxonomy. This survey defines model fusion and organizes prior work into three levels: parameter-level, representation-level, and behavior-level fusion. We also review related metrics, benchmarks, and applications, summarize current challenges, and identify future directions. Our goal is to provide a clear map of this area and support future work on model fusion. A comprehensive list of papers about model fusion is available at https://github.com/Baicaihaochi/Awesome-Model-Fusion-Survey.

A golden ticket allows one reviewer to advance a proposal that the rest of a panel would reject. We assess its score-based rationale by comparing minority-support ranking with other rules for allocating the same number of places. We do so on 10,625 rejected submissions to a computer-science conference between 2017 and 2024, using later citation percentiles as the outcome. Minority-support ranking measured the gap between the two highest scores after adjustment for the panel mean and reviewer count. At a budget of 10% of the year's accepted count, panel-mean ranking selected submissions with a mean citation percentile 7.75 points higher than minority-support ranking (95% bootstrap interval 4.35 to 11.09). The difference was larger in the other sample periods and citation windows examined. At that budget, minority-support ranking was equivalent to a lottery within a margin of plus or minus 5 percentile points. Two further analyses, adjusted highest-score ranking and a matched comparison, found no clear citation advantage from minority support once the panel mean was accounted for. Ranking on score variance also outperformed minority-support ranking in a paired comparison. Estimates cover the 69.8% of eligible rejections whose later citations could be verified. These comparisons identify panel-mean ranking as a benchmark for evaluating whether golden tickets select work that would otherwise be overlooked.

In an enterprise system, updating one field can set another, create a record, or start an approval. These effects are produced by business rules that are not built into the platform but written by each organization and revised over time. An agent working in such a system cannot predict the result of its own actions without knowing these rules. We study continual enterprise world model discovery, where an agent starts without knowledge of these business rules and discovers them by interacting with records and observing the outcomes. From those observations it builds a world model, which it revises as the rules change. To evaluate this, we introduce EnterpriseWorldShift, built on a live ServiceNow environment with nine tables, 25 hidden rules and 600 evaluation actions. It presents four versions of the same enterprise world, with the tables and records held fixed while a rule is modified, then added, then removed, so that discovery, revision, extension and retirement are each tested in turn. Our Continual Discovery Agent (CDA) builds such a model and carries it from one world to the next. It predicts the effects of the hidden rules more accurately than looking them up for each question, the approach taken by prior work, by up to 8.98 IoU points, and it answers from its own model without querying the running system.

Materials discovery and design campaigns can be formulated as constrained multi-objective Bayesian optimization (CMOBO) problems, within which each experimental decision negotiates between two coupled but competing goals: discovering feasible candidates and refining the underlying Pareto front. Here we recast acquisition-function choice as an adaptive policy-selection problem over a portfolio of conventional and feasibility-focused acquisition functions. This was done using two controllers: UCB-Bandit, a modified UCB multi-armed bandit, and Agentic-Switch, a multi-agent decision system driven by a large language model (LLM). Both were evaluated against fixed-policy baselines in silico across five synthetic benchmark functions and two materials design case studies. The adaptive policies performed competitively in terms of both cumulative feasibility count and feasible hypervolume improvement, while each individual acquisition function performed well for only one metric, suggesting that adaptive policies are better suited for constrained materials science problems.

Communication is made possible by common ground—the unspoken knowledge that people share and presuppose of one another, whether that be online or offline. In his conception of common ground, Clark (1996) distinguishes between personal and communal common ground, and asserts that the latter is graded: the more community affiliations two people share, the more common ground they share as well. Social media research has invoked this mechanism to explain how users connect, but it has gone largely untested because community memberships are rarely visible and, where they are, they are coupled to user interactions in a way that leads to conflating effects. To circumvent these challenges, this study repurposes Bluesky starter packs (SPs) as user-curated community affiliation labels. Across 191,648 pairs of users, we show that shared lexical repertoire—our proxy for common ground—grows monotonically with the number of SPs that users share, with users sharing a single pack being roughly twice as similar as equally connected strangers. A semantic renormalization of SP co-membership shows furthermore that it is more so the number of topically distinct communities, rather than the raw count, in which common ground is graded. Finally, we show that community co-membership adds to common ground independently of proximity in the Bluesky follow network. These results lead to the conclusion that community membership is a measurable, separable, and semantically structured carrier of common ground. Reading it as such makes common ground observable before an exchange rather than inferred from it, and thus opens the door for large-scale observational approaches to a set of questions that have so far only been posed in the laboratory.

The mapping $ \chi_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=\chi_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$. We also determine their compositional inverses explicitly.

Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1,093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence.

For every prime power $q$ and integer $n\ge1$, we give a single Kummer equation defining an $\mathbb{F}_{q^{2n}}$-maximal curve $\mathcal X_{q,n}$. The family recovers the Hermitian curves for $n=1,2$, the Giulietti–Korchmáros curve for $n=3$, and the Beelen–Montanucci curves for odd $n\ge5$. For $q>2$ and even $n\ge4$, it gives new maximal curves of genus $(q^2-1)q^n/2$ that are not covered by the Hermitian curve over $\mathbb{F}_{q^{2n}}$. We compute the genus for both parities of $n$ and give a uniform proof of maximality by counting rational places. For $q>2$ and odd $n\ge5$, we remove the Galois hypothesis from the known non-covering results for the Beelen–Montanucci and Garcia–Güneri–Stichtenoth curves. For even $n\ge4$, we determine the full automorphism group,of order $(q^n+1)q(q^2-1)$, and give explicit equations and genera for all Galois quotients, with closed-form equations for several classes of subgroups.

Systems that turn natural-language descriptions of optimization problems into solver-ready code generally use a language model at every stage, including the final translation from a mathematical formulation into executable model-building code. We propose the ANVIL compiler architecture, where we separate these concerns. A language model is called only once, assisted by constraint guidance based on problem type, to produce a LaTeX formulation. A deterministic compiler then translates that LaTeX into code with no language model involvement. We describe the deterministic compiler (a normalizer, a recursive-descent parser producing a typed intermediate representation, analysis passes that bind symbols to a dataset schema, and a code emitter) and evaluate it on the 354 easy and hard problems of the NLP4LP benchmark. The compiler produced code for 329 of 354 formulations (92.9%), taking the deterministic path in every one of those cases and never falling back to model-generated code. Median compile time was below the 10ms resolution of our timer. Overall, our formulations achieved an accuracy of 98.9% over easy problems and 91.1% for hard problems. The gap between these compilation and accuracy figures is a key point of analysis, and we analyze it: formulations that failed to compile, problems that returned as infeasible, problems raising errors at runtime, and problems returning a wrong objective. Almost all of these errors trace back to the formulation rather than to the translation. ANVIL performs exceptionally well on leading benchmarks by using language models purely where they are effective, rather than as a catch-all tool.

Over the past three decades, generalized parton distributions (GPDs) have emerged as one of the most active and important areas of research in nucleon structure and quantum chromodynamics (QCD). Since the last comprehensive review two decades ago, substantial progress has been made in experimental measurements of hard exclusive processes, such as deeply virtual Compton scattering and near-threshold $J/\psi$ production, as well as in increasingly sophisticated phenomenological analyses of GPDs that enable three-dimensional nucleon tomography. Theoretical advances in perturbative coefficient functions, scale evolutions, and kinematic and power corrections have considerably improved the precision of GPD phenomenology, while new hard exclusive processes for probing GPDs have been explored. More interestingly, lattice QCD can now directly access GPDs at fixed parton momentum fractions $x$ and skewness $\xi$ through large-momentum expansions, in addition to the traditional calculations of their moments, or generalized form factors. Significant progress has also been made in exploring the QCD energy-momentum tensor that encodes fundamental information on the nucleon's mass distribution, complete spin structure, and spatial distributions of momentum current and color-Lorentz forces acting on quarks and gluons.

By constructing Lax operators in the loop algebra of the $\mathbb{Z}_2^2$-graded extension of the Lie superalgebra $\mathfrak{osp}(1|2)$, we derive a $\mathbb{Z}_2^2$-graded extension of the Camassa-Holm equation. The resulting equation is an integrable nonlinear PDE for a system of four $\mathbb{Z}_2^2$-graded commutative functions, each associated with a distinct $\mathbb{Z}_2^2$-degree. We further show that the $\mathbb{Z}_2^2$-Camassa-Holm equation admits a bi-Hamiltonian structure. As a consequence, it possesses infinitely many conserved quantities, including one with non-trivial $\mathbb{Z}_2^2$-degree, which are mutually in involution with respect to the $\mathbb{Z}_2^2$-graded Poisson brackets.

Open-vocabulary segmentation enables rich semantic perception for UAVs, but frame-wise predictions can remain temporally inconsistent across repeated observations and changing viewpoints. We present PerSeM, a training-free persistent semantic memory framework for long-horizon open-vocabulary UAV mapping. PerSeM associates frame-wise semantic observations with persistent world-space voxels and constructs a majority-based semantic memory, which is conservatively refined through history-preserving spatial refinement, trust-aware replay, and context-guided verification. Experiments on the Forest and UAVScenes benchmarks show that persistent 3D memory provides substantial gains in semantic correctness and temporal stability over frame-wise predictions. Beyond this strong persistent-memory baseline, PerSeM provides consistent additional improvements, improving both semantic accuracy and temporal stability across all five evaluated UAVScenes sequences. Analysis using regions identified independently of the final PerSeM predictions further shows that these gains are concentrated in semantically difficult and temporally unstable regions, where majority-based memory is most likely to remain uncertain. These results demonstrate that persistent 3D aggregation provides a strong foundation for long-horizon semantic mapping, while conservative refinement of uncertain memory states can provide additional improvements without retraining or additional neural-network inference.

Conventional robot planning methods seek collision-free paths to a goal but fail when all paths are blocked. In these cases, the robot must determine which objects to relocate, in what order, and where to place them to clear a path—a problem known as Navigation Among Movable Obstacles (NAMO). Most NAMO planners assume a known environment, while existing approaches for unknown environments typically reason locally about relocations and cannot plan interdependent relocation sequences. We consider NAMO in unknown environments revealed through onboard sensing, where the robot must decide whether a blocked route requires relocation or a feasible path may exist through unexplored space. We propose an online framework that addresses this ambiguity by selecting between navigation and relocation using shortest paths that treat discovered movable objects as obstacles or as removable. Navigation relies on existing motion planners, while relocation uses a sampling-based approach that, unlike existing approaches for unknown environments, searches over interdependent relocation sequences and uses an LLM to bias sampling. Numerical experiments demonstrate scalability to cluttered environments requiring interdependent relocations and improved plan quality over existing baselines.

A peeling sequence of a finite planar point set is an ordering of its points, such that when the points get removed in this order, each removed point is a vertex of the current convex hull of the set. Write $g(S)$ for the number of such sequences, and $g(n)$ for the minimum of $g(S)$ over $n$-point sets in general position. We present a method which can be used to prove better upper bounds on the previously analysed recursive 3-block constructions $S_n$. In fact, we prove $g(n)\leq g(S_n)=O(6.57^n)$, using directional restrictions and a weighted prefix-tree form of the Kraft–McMillan inequality. From the other direction, we show that the same construction cannot attain the current best known lower bound of $c\cdot3^n$. In fact, $g(S_n)\geq 5.22^n$ when $n$ is a large enough power of $3$. Improving the general lower bound on $g(n)$ is still an open question.

Active subspace methods provide a framework for quantifying predictive uncertainty in high-dimensional models by identifying and performing inference along parameter directions that have the greatest influence on the model output. However, the construction of active subspaces requires storing many full-dimensional model gradients, which becomes prohibitive as model size increases. We address this limitation by proposing Compressed Active Subspaces (CAS), a scalable approach that first maps the model parameters to a compressed space using a structured isometric embedding and then constructs the active subspace within this reduced parameterization. Our approach substantially reduces the memory required for active subspace construction and enables Bayesian inference for large models where standard active subspace methods become impractical. We demonstrate the scalability of CAS on neural networks of increasing size while maintaining predictive performance and robust uncertainty estimates.

Low-altitude wireless networks (LAWNs) are emerging as a key infrastructure for heterogeneous unmanned aerial systems that support concurrent services within a shared three-dimensional airspace. Their coexistence creates strong coupling among mobility, connectivity, and shared network resources, while heterogeneous services impose distinct and time-varying requirements. These interactions naturally form a dynamic non-cooperative game in which both operating conditions and coordination objectives evolve over time. Conventional optimization and learning-based controllers typically rely on predefined objectives, limiting their ability to adapt autonomously to changing service requirements and resource priorities. To address this challenge, we propose a hierarchical hybrid large language model (LLM)- multi-agent reinforcement learning (MARL) architecture organized as a dual-loop structure. Specifically, an outer adaptation loop employs LLM-assisted game orchestration to interpret service requirements and operator intent, and reconfigure objectives and resource priorities, while an inner loop executes decentralized, parameter-conditioned MARL policies under the configured game. A logistics-monitoring case study illustrates how the proposed framework facilitates coordinated coexistence among heterogeneous services, adapting to evolving operating conditions without retraining the underlying MARL policies. Finally, we discuss key challenges and research directions toward scalable, trustworthy, and adaptive agentic LAWNs.

The metric traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization that asks for a minimum-cost tour covering all clients in a metric graph. The metric multiple-depot TSP (MD-TSP) is a natural extension, where the graph contains depots and clients, and the objective is to compute a minimum-cost set of tours covering all clients, with each tour starting and ending at the same depot. When the number of depots is part of the input, an adaptation of the Christofides–Serdyukov heuristic yields an approximation ratio of $2$. In this paper, we introduce a $(1+1/\sqrt{2})$-approximation algorithm. Like the Christofides–Serdyukov heuristic, our algorithm first computes a rooted spanning forest (RSF), then a matching to correct its odd degrees, and finally obtains a solution by shortcutting. However, instead of using a minimum-cost RSF, we construct an RSF by a primal-dual algorithm for a natural cut relaxation. The algorithm grows rootless components and the component containing all depots at different rates, adding an edge when its dual constraint becomes tight. Vertex labels record the times at which clients first become connected to a depot. The two-speed growth provides a joint bound on the forest cost and two label-dependent terms that also arise in bounding the parity-correction cost. Balancing the coefficients of these two terms by setting both to $\sqrt{2}-1$ yields the claimed approximation ratio.

Croft, Falconer and Guy ({Unsolved Problems in Geometry}, Problem~C5) exhibit a tiling of the $27\times27$ square by eight pairwise incomparable integer rectangles and remark that it is not known whether $27$ is the smallest side length of a square that can be tiled by pairwise incomparable integer rectangles, no restriction being placed on the number of tiles. We show that it is: for every integer $n\le26$ and every $k\ge2$, the $n\times n$ square admits no tiling by $k$ pairwise incomparable integer rectangles. The proof combines two structural reductions with an exhaustive search over the $167\,538$ surviving candidate tile sets, carried out by two independently written programs. The complete software, build instructions and output logs are included as ancillary files.

We present an analytical study of the spatial structure of correlations in periodic fermionic systems at the single Slater determinant level, focusing on the cyclic case. Exploiting cyclic symmetry, the transformation from localized orbitals to molecular orbitals is simultaneously a discrete Fourier transform, a Vandermonde matrix on the roots of unity, a complex Hadamard matrix, and the character table of the cyclic group $C_m$. Within this framework, the spatial structure of correlations is fully determined by the occupied irreducible representations (Fourier modes), independently of the specific Hamiltonian generating them. In particular, the fermionic two-point correlator is expressed as a truncated Fourier sum over the occupied orbitals, leading to exact analytical expressions for symmetric occupation patterns of Fourier modes ($\ell$ and $-\ell$ pairs), corresponding in quantum chemistry to aromatic fillings, i.e. fillings satisfying Hückel's $4n + 2$ rule. For the half filling case, we derive exact spatial selection rules. In particular, the two-point correlator vanishes identically for all even distances along the ring. This property propagates to reduced density matrices and implies a complete absence of mutual information between the corresponding orbitals. These results reveal that, despite the global delocalization of molecular orbitals, the correlation structure in cyclic systems is highly non-uniform and governed by symmetry-induced interference. Although formulated in terms of cyclic lattice systems, the present results extend straightforwardly to one-dimensional fermionic chains with periodic conditions, reflecting the underlying translational symmetry of the problem. The framework therefore provides a Hamiltonian-independent and universal reference for understanding correlation patterns in one-dimensional periodic fermionic systems.

To extract complete information about experimental noisy quantum states, as well as correlations among different physical parameters, we develop an efficient machine learning-assisted framework with the normalizing flow based Bayesian parameter estimation (BPE). By embedding a physically interpretable parameter vector, ${s}$, into the quantum state ansatzes, $\rho({s})$, the corresponding parameter distribution $p({s}|D)$ is induced from BPE, based on the available experimental data $D$. The BPE allows us to perform parameter correlation analyses, providing powerful insights about how experimental parameters and related noise sources affect quantum features of the system. As an example, the flexibility of our framework is demonstrated using two different physical ansatzes on the optical cat state experiments, where a noisy single-photon state is added to impure squeezed state. With correlations among the Wigner function negativity, photon-addition fraction, noisy fraction, and pump powers, our framework gives interpretations for complicated experimental mechanisms in generating noisy non-Gaussian states. By leveraging normalizing flow-based neural networks and Bayesian uncertainty estimation, along with physical and experimental constraints incorporated naturally, the valuable information inferred in the posterior learning provides guidelines for experimentalists, as well as theorists, in identifying promising parameters to enhance desirable features.

Simultaneous localization and mapping (SLAM) is one of the services running on an autonomous robot. It is typically run to assist other tasks such as planning, manipulation, etc. All these tasks are run on edge hardware and are subject to severe resource constraints. However, most SLAM systems are built and tested in isolation, and their performance is reported as if they are the only task running on a system. We observe that existing benchmarks lack a common mechanism for comparing SLAM systems under realistic resource constraints. To address this limitation, we have developed SLAMSqueezeBench, a framework that allows testing of SLAM systems under realistic workloads on edge hardware. It does so by imposing constraints on compute and memory resources available for the SLAM system during execution. It also simulates realistic camera frame acquisition with frame drops when a finite buffer is full. Using SLAMSqueezeBench, we compare nine SLAM systems spanning classical systems, learning-based systems, and approaches for Gaussian splatting. Our testing framework will be available for use by the community upon publication.

This paper introduces the mollified-sharp decomposition, a probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is treated as a random variable with a prescribed probability density. Averaging over this artificial distribution replaces the localized pressure change by a smooth transition whose spatial extent is set by the density width, rather than by direct filtering of the pressure field. Each snapshot is decomposed exactly into a regularized mollified field and a local sharp correction that restores the shock. This probabilistic construction and exact additive split define the general method; the detector, kernel, treatment of multiple shocks, alignment coordinates, and regression are implementation choices. In the present realization, a calibrated indicator detects shocks, a compactly supported Wendland kernel mollifies them, and a peak-normalized and, where necessary, partitioned weight derived from each shock-location probability density defines the centroid, principal axes, and scales of its local alignment domain. Separate POD-GPR models represent the mollified field and aligned corrections, with additional regressions for shock presence and alignment. The method is demonstrated on the transonic airfoil pressure data of Catalani et al. (2023) and compared with a standard POD-GPR model constructed from the same data and POD-energy criterion. The mollified-sharp model reduces the mean test-set relative $L^2$ pressure error by 31.2% and the mean test-set surface-pressure-coefficient error by 33.2%, while also improving the predicted shock locations and pressure changes; the trade-off is a median online evaluation time 2.24 times as long. The construction is applicable in principle to other parameter-dependent fields with moving sharp features, such as moving material interfaces in multiphase flows.