Combinatorics
Papers
Fresh from arXiv, typeset properly. Highlighted words trade on the market.
All of arXiv
Monday 5 October
We formally initiate the study of $\lambda$-fold $(s,t)$ near-factorizations in association schemes. Namely, given an association $(X, \mathcal{A})$, we consider the existence of a factorization of $\lambda(J-I)$ into 01-matrices $S$ and $T$ with the constraint that $S$ and $T$ must belong to the adjacency algebra of $(X, \mathcal{A})$. We establish basic properties of $\lambda$-fold $(s,t)$ near-factorizations in association schemes and calculate bounds for $\lambda$, $s$, and $t$ relative to the order of the association scheme. We completely determine all near-factorizations in symmetric and asymmetric 2-class association schemes. Furthermore, we construct near-factorizations in certain Hamming schemes, cyclotomic association schemes, Schurian schemes on small primitive groups, and the folded cube and halved cube association schemes. Finally, we establish that certain Hamming schemes, Johnson schemes, and Grassmann schemes do not admit a $\lambda$-fold near-factorization.
Quantum Physics
Benchmarking exchange-only control of a 48-spin singlet manifold
Exchange-only quantum computing benefits from high fidelity and straightforward control afforded by the exchange interaction. However, independently controllable qubits must be encoded into subsystems of at least three electron spins, restricting computation to only a fraction of the available spin Hilbert space. The remaining states are treated as leakage and used only transiently in gate sequences. By contrast, a quantitative, system-wide measure of exchange-only performance can exploit the full available Hilbert space, including states conventionally treated as leakage. Here, we apply this approach to arrays of up to 48 electron spins, accessing a total-spin-zero Hilbert space with dimension exceeding $2^{40}$. Measurements of out-of-time-order correlators (OTOCs) reveal rich scrambling dynamics and demonstrate access to regimes relevant to quantum computational advantage. Using generalized forms of cross-entropy and mirror randomized benchmarking, we also assess the aggregate performance of the full exchange-only system per fundamental two-body interaction: the two-spin exchange. We obtain an effective system-level error of $3 \times 10^{-4}$ per exchange, incorporating the complete experimental control sequence and all associated noise sources. This value is up to an order of magnitude lower than those reported from comparable benchmarks on other platforms at the time of writing.
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Statistical Methodology
Multiple Change Point Detection in the Mean and Covariance of High-Dimensional Matrix Time Series
This paper studies simultaneous change point detection in the first- and second-order structures of high-dimensional matrix-valued time series. Specifically, we extend the framework of main effect factor models to accommodate multiple change points so that shifts in the mean and covariance structures are characterized by changes in the trend-stationary main effects main effects and in the factor-driven common components, respectively. Under this framework, the two types of changes are not necessarily aligned and can be arbitrarily large without masking the effects of each other, and each of the detected change points is identified either with the row or column categorizations which improves their interpretability. We propose a unified procedure based on moving-sum statistics to detect and localize both types of changes. Under general regularity conditions that allow for temporal and cross-sectional dependence, we derive detection and localization guarantees for the proposed method. The finite-sample performance of the method is demonstrated through extensive experiments, and its practical usefulness is illustrated by a real data application to New York City Yellow Taxi trip records.
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Statistical Methodology
A perspective note on likelihood approximation and inference for complex simulation models using a chain of aggregated normalizing flows
We present a new perspective on the problem of likelihood approximation within the framework of simulation-based inference that promotes scalable and controllable simulation routines for large-scale data analysis, allows efficient parameter space exploration or smooth interpolation in high-dimensions and, thus, supports valid statistical treatments of hypothesis testings as well as uncertainty quantification. In particular, we consider a chain of $n$-aggregated normalizing flows for likelihood approximation scheme, where a set of upfront replicated observation datasets from the forward complex simulation model pass through the first set of bijective transformations, and then subsequently pass to the other sets of bijective transformations. Here, we assume that, for any $k \in \{1,\,2, \ldots, n\}$, the parameters corresponding to the first $k$ sets of bijective transformations are estimated sequentially, in some sense of optimality, for constructing flexible probability distributions, regardless of the remaining $(n-k)$ sets of bijective transformations. Moreover, our objects of interest are to highlight two complementary mathematical arguments that leverage an informatics-theoretic formalization, based-on empirical likelihood estimators under moment restrictions, and a sequential decision-making paradigm, with mixing distributions, for updating and aggregating the estimated parameters of the overall normalizing flows. As a by-product, the framework provides a reliable surrogate model, conditioned on the model parameters defining the forward computational simulation, that allows samples generation, with statistical powers, and facilitates computationally tractable scheme in the Bayesian paradigm for inference, hypothesis testings and uncertainty quantification.
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Robotics
AeroBuoy: A Drone Deployable, 3D Printed, Autonomous Robotic Buoy for Environmental Inspection in Remote and Hazardous River Systems
Monitoring of waterways such as remote and hazardous rivers and streams is important so as to assess the impact of external factors including construction runoff or climate change. Versatile, autonomous robotic boats can offer excellent environmental inspection and monitoring solutions for remote, dangerous, or access protected water bodies but they have several shortcomings in terms of maneuverability. This paper proposes an environmental inspection system consisting of an autonomous data collection buoy which is designed to be deployed to inaccessible river systems using a drone. The system can perform a drop off and pickup of the buoy depending on the requirements of a particular location and monitoring task. Utilising the natural flow of the river the buoy autonomously steers down, using GPS and magnetometers so as to maintain the desired trajectory. The buoy is capable of measuring water temperature but it can also be equipped with a range of sensors such as water oxygen meter, sonar for river bed inspection, or turbidity for water clarity. This paper describes the system design, presents an analysis of the self-righting capabilities of the buoy, and shows a full system demonstration at the Ōrewa River in Auckland, New Zealand.
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Machine Learning
Inference and learning in sparse autoencoders as natural gradient flow
Sparse autoencoders are widely used to uncover interpretable features in neural networks, yet reliable recovery remains difficult when features overlap or activate infrequently. These challenges involve both inferring which features explain an input and learning the dictionary that represents them. Here, we unify inference and dictionary learning as natural-gradient flows on a shared variational free energy. We instantiate this framework as BeFOND, an encoder-free sparse coding model with closed-form inference and learning dynamics. We show how recurrent explaining away reduces interference between overlapping features, while Fisher preconditioning can compensate for the slow learning of rare features. On synthetic data, BeFOND improves dictionary recovery and rare-feature detection, with a growing advantage over amortized baselines as superposition increases. On language-model activations, it improves single-feature concept detection and selective intervention, outperforming pretrained reference SAEs with substantially less training data. Its feature quality continues to improve with dictionary width, whereas the evaluated baselines largely plateau. Together, these results show how improving inference and learning within a unified probabilistic framework can make better use of data and dictionary capacity to interpret and intervene on neural representations.
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Statistics Applications
DeepAJM: Deep Association Joint Model for Irregularly Sampled data
Joint Models simultaneously model longitudinal and survival outcomes, leveraging patterns in patients' longitudinal trajectory to improve the prediction of survival outcomes. The classical parametric joint models, however, rely on fixed parametric assumptions, making them susceptible to bias under model misspecification and smaller sample sizes. We propose a deep joint model, DeepAJM, that does not require any parametric assumptions, while retaining a partially interpretable, per-longitudinal-outcome association structure. The joint model uses an encoder-decoder (sequence-to-sequence) architecture to learn the latent structure in patients' time-varying covariate trajectories. The model links the longitudinal processes to the survival processes through a learned interpretable association structure, in which each longitudinal output from the decoder gets remodulated by baseline covariates before it contributes to the risk scores from the survival head of the architecture. The model was evaluated on three datasets ( a cardiovascular-disease EHR cohort, a primary biliary cirrhosis (PBC2) dataset, and a simulated dataset) against a classical parametric joint model, TransformerJM, DA-LSTM and a Cox-based survival-only model. All models were assessed using C-index, integrated brier score (IBS), time-dependent AUROC, and time-dependent AUPRC. Our model achieved the best discrimination in terms of the C-index, time-dependent AUROC, and AUPRC across all datasets.
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Data Structures and Algorithms
Stronger Hardness for Submodular Maximization Subject to a Matroid Constraint
Maximizing a submodular function subject to a matroid constraint is a cornerstone problem in combinatorial optimization. The state-of-the-art algorithm for this problem obtains $0.401$-approximation~\cite{buchbinder2024constrained}, and the state-of-the-art hardness result shows that no polynomial time algorithm can obtain better than $0.478$-approximation for this problem~\cite{oveisgharan2011submodular}. In this work, we present the first improvement in $15$ years for the hardness result, showing that no polynomial time algorithm in the value-oracle model can obtain better than $8/17 \approx 0.471$-approximation, even for the special case of a cardinality or (simplified) partition matroid constraint.
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Cryptography and Security
NetAgent: Multi-Task Agentic Network Traffic Analysis Made Practical
Network traffic analysis is central to network security, spanning tasks from intrusion detection to encrypted traffic classification. Existing approaches either train task-specific models that generalize poorly or rely on costly traffic foundation models that still struggle under distribution shift. We present NetAgent, the first agentic framework for multi-task traffic analysis. Through a carefully designed agent loop, NetAgent supports complex task understanding, on-the-fly decomposition and orchestration, dynamic replanning, and long-horizon analysis, without task-specific training. It introduces five key designs: (1) knowledge-augmented workflow planning that maps attack knowledge to traffic features to bridge the semantic gap; (2) a comprehensive tool action space with 150+ verified tools extracted from 50+ published systems; (3) a unified code execution space for flexible action composition; (4) a three-tier memory for long-term knowledge consolidation; and (5) sandboxing and runtime repair for reliable execution. Across 9 major benchmarks, NetAgent outperforms all baselines (23 single-task and 5 multi-task) on nearly all tasks and generalizes substantially better to unseen traffic distribution (90.04% F1 vs. 2.74% and 3.04% for the best single-task and multi-task baselines) and under realistic background shift (4.85-point F1 drop vs. 74.88-point and 74.80-point drop for the best single-task and multi-task baselines). These results reveal that existing methods owe much of their reported success to overfitting dataset-specific patterns and degrade sharply in realistic network environments, while NetAgent's agentic design remains accurate, generalizable, and robust.
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Computer Vision
Semantic Capability Acquisition and Specialization During Vision-Language Model Fine-Tuning
Fine-tuning vision-language models (VLMs) is typically evaluated at a single downstream checkpoint, obscuring whether a semantic capability was never acquired or emerged earlier and later declined during specialization. We ask how semantic capabilities are acquired, when they peak, how well they transfer, and what remains at deployment. We study these dynamics as a semantic capability trajectory, tracking identity- and attribute-based capabilities over training. We formulate a trajectory-based framework that separates capability acquisition, capability-specific optima, and later specialization, and introduce Structured Semantic Routing (SSR) to study how the representation of supervision shapes what is acquired. Across six pretrained backbones spanning DFN, MetaCLIP, and OpenAI CLIP, we show that fine-tuning can acquire semantic capability beyond the pretrained state, including gains observed on held-out evaluations. Unstructured name-and-attribute supervision produces strong name-and-attribute retrieval with comparatively weak name-free attribute-profile retrieval, whereas SSR yields substantially stronger name-free attribute-profile retrieval and is further strengthened by stochastic name-branch dropout. Different capabilities can peak at different stages, so a checkpoint selected by target class-name retrieval need not coincide with a transferable semantic optimum. Continued optimization can therefore preserve strong target class-name retrieval while reducing previously acquired transferable semantic capability. In a representative diagnostic study, this late specialization is consistent with reduced cross-modal semantic accessibility while substantial image-only class structure remains available.
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Computer Vision
WildMatch: Weakly Supervised Image Matcher Adaptation for Wildlife Re-Identification
Individual animal re-identification from camera-trap imagery is an instance retrieval problem central to non-invasive wildlife monitoring: a query image must retrieve the correct individual from a reference set of known animals. This requires computer vision models to recognize distinctive local patterns in fur, skin, or other visual markings. Current approaches either learn global embeddings as a classification problem, requiring many labeled images per individual while largely ignoring local evidence, or apply off-the-shelf, domain-agnostic image matchers. Although such matchers are pretrained on large and diverse image collections, adapting them to wildlife imagery is challenging because available datasets are small and lack correspondence-level annotations. We study weakly supervised adaptation of a pretrained keypoint matcher using only identity labels, without keypoint-level or geometric correspondence ground truth. We mine informative image pairs with the pretrained matcher, derive weak positive and negative supervision from identity agreement, and contrastively fine-tune the matching network to strengthen correspondences for same-identity pairs and suppress them for different identities. Across open-source wildlife re-identification datasets, our approach improves accuracy over off-the-shelf matchers and a state-of-the-art local–global fusion method. Under an open-world protocol with held-out individuals, it learns a transferable correspondence prior rather than memorizing training identities. To our knowledge, this is the first study of matcher-level, identity-supervised adaptation for animal re-identification. Our method enables data-efficient specialization of image matching models to wildlife domains using identity annotations already available in typical monitoring datasets.
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Machine Learning (Statistics)
HyperNSDE: Personalized Neural SDEs for Joint Static-Longitudinal Clinical Data Generation
Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learning. Realistic synthesis of patient-level clinical data requires jointly modeling heterogeneous static covariates, irregularly sampled longitudinal trajectories, and informative observation times - three tightly coupled components in practice yet rarely addressed together. We propose HyperNSDE, a continuous-time generative model that conditions a latent Neural SDE on static patient representations through a hypernetwork, allowing baseline characteristics to shape trajectory evolution beyond the initial condition without requiring a trajectory encoder, while stochastic latent dynamics capture realistic variability in generated paths. Observation times are modeled jointly through a latent-state-dependent intensity process, and training on irregular stochastic paths is stabilized via a deterministic-stochastic path decomposition with a non-adversarial signature-kernel objective. Experiments on simulated and real clinical datasets show improved observation-time fidelity and competitive performance, while matched-grid analyses reveal that forecasting and correlation metrics are affected by observation-grid regularity and trajectory smoothness.
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Robotics
Toward Trustworthy Physical AI for Human Interaction
Robots are entering human spaces faster than we can establish when they deserve trust. We propose a framework for trustworthy physical AI that integrates Safety, Behavioral Intelligibility, and Perceptual Alignment across embodiment, control, cognition, and design. Trustworthiness emerges from aligning physical capabilities, observable behavior, and expectations people form during interaction.
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Computer Vision
GeoWM: Efficient Direct World Modeling in Explicit Geometry
Modeling 3D scene geometry and its evolution over time is essential for autonomous driving and robotics. A common paradigm is to use world models to predict future images or latent representations of the environment and subsequently recover geometry from these predictions. However, this paradigm does not explicitly model geometric structure and typically relies on recursive rollouts to reach longer prediction horizons, leading to error accumulation and increasing computational cost. To address these limitations, we present GeoWM, a geometry world model that directly forecasts future scene geometry at specified future horizons without recursive rollout. The key idea is to leverage a geometry foundation model to transform observed RGB frames into a geometric history, which conditions a flow-matching transformer to predict the scene geometry at a specified future horizon. We further show that a lightweight camera-motion predictor can accurately estimate the future viewpoint, and that projecting the observed geometry into the predicted viewpoint provides an effective geometric prior for future geometry forecasting. Extensive experiments on four datasets spanning urban driving, aerial flight, and dynamic manipulation demonstrate that GeoWM outperforms the evaluated world models in forecasting depth, camera pose, and 3D scene geometry, while substantially reducing inference time at longer horizons.
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Probability
Quantitative averaging of Markov-modulated additive functionals and Wentzell boundary homogenization
Let $A$ be a positive continuous additive functional of a strong Markov process and $\alpha$ an independent finite-state Markov chain. For bounded $h$, we study \[ J_\varepsilon(t)=\int_0^t\bigl(h(\alpha_{s/\varepsilon})-\pi(h)\bigr)\,dA_s . \] If $\sup_y \mathrm E_y A_t\le C_T t^\vartheta$, then for every bounded random time determined by the base process, not necessarily a stopping time, \[ \mathrm E|J_\varepsilon(\tau)|^2=O(\varepsilon^\vartheta),\qquad \mathrm E\sup_{t\le T}|J_\varepsilon(t)|^2 =O\!\left(\varepsilon^\vartheta(1+|\log\varepsilon|)^2\right). \] For reflected Brownian boundary local time, the exponent $1/2$ is sharp at fixed time. We apply this principle to reflected Brownian motion with rapidly switching Wentzell boundary dynamics. The homogenized boundary condition is again of Wentzell type, with stickiness and killing coefficients given by invariant averages. For bounded Lipschitz observables, the quenched Feynman–Kac error has every polynomial rate below $1/8$, uniformly over deterministic times and in expected uniform norm. For smooth Neumann-compatible observables with proportional killing and stickiness, the rate improves to $O(\varepsilon^{1/4})$, up to a logarithmic factor in the uniform-in-time estimate. We also construct the switching process, derive quenched and annealed backward evolutions, and transfer the estimates by duality to the forward measure evolution. For the forward evolution, we obtain quantitative convergence in bounded-Lipschitz distance and the sharper $1/4$ rate for smooth observables, including surviving mass. Numerical experiments illustrate the finite-scale convergence.
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Discrete Mathematics
Property B for random non-uniform hypergraphs
We show that, in random hypergraphs with several permitted edge sizes, non-uniformity affects existential and algorithmic bounds for 2-colorability (Property B) in fundamentally different ways. Assigning weight $2^{-k}$ to each $k$-edge, we obtain upper and lower bounds in terms of the total edge weight that asymptotically match the uniform bounds as the minimum permitted edge size grows, regardless of how edges are distributed among sizes. We also extend the best-known algorithm for 2-coloring random uniform hypergraphs to the non-uniform setting. With weight $\frac{k}{2^k}$ assigned to each $k$-edge, we construct non-uniform instances whose expected total edge weight per vertex is arbitrarily large, yet the algorithm finds a proper coloring asymptotically almost surely. In the uniform setting, the algorithm fails with high probability once this quantity exceeds a constant. Our construction uses sufficiently separated edge sizes, so that edges of different sizes become relevant at well-separated stages of the execution and their effects are essentially independent.
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Computer Vision
SimCortex v2: Joint Cortical Surface Reconstruction with Near-Zero Collisions and Self-Intersections
Reconstructing cortical WM and pial surfaces from structural magnetic resonance imaging (MRI) is a prerequisite for surface-based neuroanatomical analysis, yet remains challenging because the cortex is thin and tightly folded. Reconstruction methods can produce geometric artifacts such as mesh self-intersections and collisions between cortical surfaces, and although recent deep learning methods have reduced reconstruction time from hours to minutes, these artifacts persist. We propose SimCortex v2, a deep learning framework for simultaneous reconstruction of the left and right WM and pial surfaces from T1-weighted MRI. SimCortex v2 estimates topologically correct initial surfaces from a volumetric segmentation and refines all four jointly using multi-scale stationary velocity fields predicted by a ribbon-conditioned, U-Net-like network. We evaluated SimCortex v2 on 560 cases from 14 cohorts, thirteen of them unseen during training, spanning ages 6-89, healthy and clinical populations, and scanners from three vendors. SimCortex v2 matched the surface-distance accuracy of the strongest baseline (average symmetric surface distance 0.253 mm) while showing no detected inter-surface collision in 92.14% of cases and the lowest self-intersection fraction (0.044%) among learning-based methods, whereas every baseline produced at least one collision in every case. Source code, configuration files, pretrained weights, preprocessed data, and the exact evaluation splits are publicly released.
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Networking
High Speed Network Processing for Scientific Computing in the Open Cloud Testbed
This paper presents an FPGA-based SmartNIC architecture designed to address critical network challenges in data-intensive scientific computing. As scientific workflows increasingly demand high-bandwidth data movement and real-time monitoring across wide-area networks, the Open Cloud Testbed (OCT) provides an ideal platform for investigating in-network processing solutions at line rate. Our approach focuses on implementing network visibility, optimization, and orchestration capabilities through FPGA acceleration. The proposed system leverages P4-programmable data-plane functions to support packet parsing, marking, telemetry extraction, traffic steering, and machine learning inference, all without requiring host CPU intervention or modifications to application servers. As a concrete example, our framework integrates the SciTags standard, which enables associating network traffic with scientific context through packet marking. We implement a high-performance network bridge that counts packets by their SciTag values, as identified in the IPv6 Flow Label. Experimental evaluation on AMD U280 FPGAs in OCT demonstrates the feasibility of this approach, showing imperceptible processing latency and line-rate packet handling, while accurately monitoring scientific data flows.
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Artificial Intelligence
MemCo: Memory-Centric Collaboration for Generalizing LLM Agents to Unseen Environments
Large language model (LLM) agents increasingly operate in interactive environments, where they need to make sequential decisions through observation, action, and feedback. Although memory can help agents reuse experience, existing work designs memory in isolation, where collecting enough trajectories to populate it is expensive. Existing shared-memory approaches mitigate isolated experience by pooling episodic memories across tasks and environments. However, retrieving shared memory is challenged by the granularity, where retrieved memories can be either too specific to preserve current grounding or too coarse to support the next action. In this work, we propose MemCo, a memory-centric collaboration framework for generalizing LLM agents to unseen interactive environments. It maintains complementary local and global memory spaces, preserving environment-specific details locally while promoting transferable workflows induced from local trajectories to global memory. During online interaction, MemCo routes relevant local and global memories in terms of the agent's current state and decision phase, enabling agents to reuse the experience of other agents without blindly transferring environment-specific details. Experiments on interactive decision-making benchmarks show that MemCo improves task success and reduces redundant exploration compared with isolate-memory and shared-memory baselines. Our code is available at https://github.com/SYannL/nvdamas.
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Number Theory
On eutactic forms
We prove two new results about the number of classes of positive definite eutactic forms in n variables.
Machine Learning
Multigroup Fairness and Omniprediction: Separations and Equivalences
Omniprediction is a learning guarantee which requires a single predictor to be competitive relative to the best hypothesis from a benchmark class for any loss chosen from a family of loss functions. Loss Outcome Indistinguishability (loss OI for short) is a stronger notion that implies omniprediction. It requires the predicted distribution on labels to be indistinguishable from the true distribution to tests that depend on the loss functions and the benchmark class. Multiaccuracy and multicalibration are multigroup fairness notions that generalize classical notions of calibration and accuracy in expectation. Most known learning algorithms for omniprediction (both for the standard notion and for strengthenings like loss OI) rely on some version of these multigroup fairness notions, or on an intermediate notion called calibrated multiaccuracy. We ask if this is necessary: Does omniprediction require some form of multigroup fairness? We show that the answer is no for (plain) omniprediction, and yes for loss OI. First, a sequence of works shows that multicalibration or calibrated multiaccuracy imply omniprediction. We rule out even a weak converse, by showing that omniprediction for proper losses does not imply even accuracy in expectation, a much weaker notion than any of calibration, multiaccuracy, or multicalibration. Second, prior work showed how to achieve loss OI from a combination of calibration and multiaccuracy. We show a converse: loss OI is equivalent to a form of calibrated multiaccuracy.
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Optimization and Control
A continuous-time limit for particle swarm optimization
Particle swarm optimization (PSO) is a popular class of gradient-free methods for global optimization. We study a continuous-time model for momentum-free PSO with personal-best memory and global-best interaction. Unlike previous models which rely on smooth approximations, we keep the original discontinuous personal- and global-best processes. We study the small-step limit and show that weak limit points satisfy a stochastic differential inclusion: personal-best variables obey a relaxed record condition, while fast switching of the global-best selector leads to a convexified interaction. We then give conditions under which the true original selectors are recovered. Under suitable regularity and nondegeneracy assumptions, Brownian noise allows us to identify the personal-best processes with the latest record positions of the limiting trajectories and to prove that the particle attaining the global best is unique at almost every time. The resulting continuous-time dynamics retain both selection rules without smoothing them.
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Soft Condensed Matter
Mechanics of a Model Frictional Knitted Fabric
We present a study of the shapes and mechanical properties of a knitted loop made of elastic and frictional yarns. First, for non-frictional yarns, we investigate how the elastic energy of a loop varies with its shape. This allows us to quantify the energetic contributions of stretching and bending, and to identify energetically favorable loop configurations. We then consider the case of thin frictional yarns. In this case, the stability of a loop can be reduced, even in the presence of friction, to a simple planar elastica problem. Friction gives rise to a multiplicity of stable loop shapes in a knitted fabric at rest, i.e., in the absence of externally applied forces. We show that, in the limit of thin yarns, a 2D elastica model can predict these rest shapes. Furthermore, the force-deformation curves under uniaxial stretching can be obtained straightforwardly within this framework. Measurements of loop dimensions and forces during uniaxial stretching of nylon knitted fabrics allow us to assess the qualitative and quantitative validity of the planar elastica model. Finally, we examine the limitations of this model for dense knitted fabrics.
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Robotics
Expressiveness, Equivalence, and Uncertainty in Velocity Obstacles and Closest Point of Approach Metrics
Time to Closest Point of Approach (TCPA), Distance to Closest Point of Approach (DCPA), and Velocity Obstacles (VOs), are widely used to assess and mitigate collision risk in autonomous navigation, yet their relationship and behavior under uncertainty remain largely unexplored. Assuming perfect state information, we establish a relationship between these representations over finite and infinite prediction horizons and derive conditions under which they provide equivalent characterizations of collision risk. Under bounded uncertainty, we extend the Closest Point of Approach (CPA) metrics and VO to convex relative-state sets. We show that in this setting, independently computed TCPA and DCPA bounds lose the joint relationship required for VO membership, while uncertainty-aware VOs preserve this relationship through a set-valued representation of collision-inducing velocities.
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Information Theory
Optimal Codes for the Coverage Depth Problem and the Performance of Random Codes
DNA storage systems retrieve information by randomly sampling synthesized DNA strands, making the number of reads required for successful recovery a fundamental performance measure. This motivates the coverage depth problem: for given code parameters, determine a linear code that minimizes the expected number of randomly sampled columns required to span the entire information space. While MDS codes are known to be optimal whenever they exist, identifying optimal codes in parameter regimes where MDS codes do not exist remains largely open. In this work, we derive a general formula for the expectation in the coverage depth setting, and apply this result to establish the optimality of the $q$-ary simplex code for the parameters that allow its existence. Moreover, we show the optimality of the $q$-ary Hamming code by relating coverage depth to independent sets in the dual code and exploiting log-concavity properties of matroid basis-generating polynomials. We further analyze random linear codes, derive an exact expression for their expected coverage depth, and show that, in the constant-rate regime, their additive gap from the MDS benchmark remains bounded independently of the code length.
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Systems and Control
Exact-Safe MPPI: Safety-Aware Sampling with Nonsmooth Control Barrier Functions
Model predictive path integral (MPPI) control plans actions by sampling and evaluating trajectories, but standard MPPI does not guarantee safety. Incorporating control barrier function (CBF) filters into each rollout allows the planner to account for safety corrections. However, combining multiple CBFs through a soft-minimum approximation can exclude states that satisfy the original safety constraints, restricting the trajectories available to the planner. This paper proposes Exact-Safe MPPI, which uses the exact minimum of multiple barrier functions and applies a CBF-based quadratic program during both planning and control execution. To handle nondifferentiability where multiple barriers attain the minimum, the filter simultaneously enforces the CBF conditions for all $\delta$-active barriers, whose values lie within a prescribed tolerance $\delta>0$ of the minimum. Under suitable feasibility and regularity assumptions, we establish forward invariance of the certified safe set without the shrinkage introduced by soft-minimum smoothing. We also characterize the state-dependent approximation gap and explain how multiple barriers with values at or near the minimum increase this shrinkage. Furthermore, we show that increasing the number of MPPI samples cannot recover trajectories excluded by the soft-minimum filter. We demonstrate the effectiveness of the proposed approach in a navigation task requiring passage through a narrow gap between two obstacles. Video demonstrations are available at https://github.com/lc-lab25/Exact-Safe-MPPI .
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Distributed Computing
Byzantine-Tolerant Causal Unicast with Constant Message Space Overhead
Causal message ordering provides essential semantics for distributed applications, yet ensuring it within an asynchronous system subject to Byzantine failures presents fundamental theoretical and practical challenges. Prior research establishes that algorithms cannot guarantee both strong safety and liveness without using cryptography under these conditions. Existing Byzantine-tolerant solutions make synchrony assumptions or suffer from $O(n)$ message space overheads and $O(n^2)$ message complexity, where $n$ is the number of processes in the system, or use cryptography, but may not guarantee strong safety. In this paper, we present a novel Byzantine-tolerant causal ordering algorithm that achieves an optimal $O(1)$ application message space overhead for point-to-point messages. Our approach uses a Sender Permission to Send (SPS) invariant and an Isolated-Buffer Optimistic Model for the memory management architecture. To circumvent Byzantine state-pinning and head-of-line blocking attacks, instead of unified causal buffers, we use isolated, per-peer queues equipped with event-driven Cascading Space Evictions. We formally prove that our algorithm guarantees system-wide liveness and satisfies a weakened causal safety abstraction called Congestion-Relaxed Causal Delivery. Under this model, weak causal safety is strictly preserved for all honest-to-honest communications unless extreme network latency or Byzantine withholding attacks exceed quantifiable local buffer capacities, forcing optimistic queue evictions. This formal guarantee successfully balances causal ordering with high throughput, constant message space overhead, low computational overhead, and strictly bounded local space.
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Astrophysics of Galaxies
Occam's Razor and a Three-Family Ultralight Fermionic Dark Matter Model
Inspired by the three generations in the Standard Model, we propose that dark matter particles are simply three non-interacting ultralight fermions. This model is tested at galactic scales with the SPARC catalog of rotational velocity curves. This is done by modeling the dark matter halo as the self-gravitating configuration of three gravitationally coupled fermion species. This configuration is capable of forming more complex rotational curves which gives it flexibility to describe more complex and diverse morphologies of galaxy rotation curves. The core of the halos will be described by degenerate fermions and the transitions from a degenerate core to a non-degenerate halo will be described by either a perfect-fluid-like halo or a NFW density profile. In order to construct the priors of the three-fermion model, first we performed a single-fermion analysis and obtained three characteristic mass regions around 20, 40, and 65-70 eV, for both halo types. It is found that the three-component fermion model improves the goodness of fit for 94.9% of the galaxies considered. To estimate if the additional parameters are favored despite the added complexity by the corresponding improvement in the fit, the information criteria of AICc and BIC were computed and we found that more than $50\%$ of the galaxies analyzed prefer the three-component fermion model over a single fermion model. The three-fermion model is particularly favored for galaxies with larger radial extent and more complex rotation curves. The multicomponent fermionic dark sector is able to describe a large diversity of rotation curves while maintaining characteristic fermion mass scales across the galaxy sample.
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Computer Vision
Identity-Conditioned Score Fusion for Open-Set Person Re-Identification
Robust person re-identification often combines complementary cues such as face, gait, and body shape. While adaptive fusion typically targets query quality, model strength also varies across identities. We introduce identity-conditioned score fusion, a framework that tailors weights to each gallery identity without training. By contrasting intra-identity consistency against cross-identity impostors, it extracts identity-specific profiles that couple with query-conditioned adaptation via a parameter-free rule. This widens the separation between true and false matches while preserving score calibration. Evaluations on three clothes-changing person re-identification benchmarks show that our method consistently outperforms statistical, rank-based, and learned baselines, achieving up to an 8.8% absolute reduction in the false non-identification rate and demonstrating the value of identity-conditioned fusion in open-set person re-identification.
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Computation and Language
Who Wrote It Is Not Enough: Detecting Who Contributed the Insight
As LLMs increasingly assist scientific writing and peer review, detecting who wrote the text is no longer sufficient: we need to determine who contributed the underlying insight. We introduce Insight Provenance, the task of identifying whether a review insight originates from a human, an LLM, or their hybrid contribution. We construct InsightProv-v0 from 4,057 scientific papers and 12,660 human reviews, simulating different levels of LLM involvement with GPT-4o, Gemini, and DeepSeek and annotating provenance at the sentence level. We show that strong performance on raw data can be misleading, as models exploit linguistic and textual-authorship shortcuts that degrade substantially under progressively debiased evaluation. We therefore propose a two-stage adversarial framework that suppresses shortcut signals while preserving provenance-relevant information. Beyond detection, extensive analyses reveal what makes intellectual authorship identifiable: paper grounding and neighboring review context provide complementary provenance signals, while human, hybrid, and AI insights systematically differ in their information sources and failure modes. Most strikingly, AI insights predominantly remain close to generic or paper-provided information, whereas human insights more often introduce external knowledge and independent judgment. These findings suggest that while wording can be rewritten by an LLM, the provenance of an idea leaves a deeper and more persistent signal.