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We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computing the Littlewood-Richardson coefficients. The corresponding multiplication on the Clifford algebra side is, in a convenient basis given by projections of the spin module, simply the componentwise multiplication of vectors in $\mathbb{C}^N$, also known as the Hadamard product., Comment: 10 pages

Misclassification in binary outcomes is not uncommon and statistical methods to investigate its impact on policy-driving study results are lacking. While misclassifying binary outcomes is a statistically ubiquitous phenomena, we focus on misclassification in a public health application: vaccinations. One such study design in public health that addresses policy is the cluster controlled randomized trial (CCRT). A CCRT that measures the impact of a novel behavioral intervention on increasing vaccine uptake can be severely biased when the supporting data are incomplete vaccination records. In particular, these vaccine records more often may be prone to negative misclassification, that is, a clinic's record of an individual patient's vaccination status may be unvaccinated when, in reality, this patient was vaccinated outside of the clinic. With large nation-wide endeavors to encourage vaccinations without a gold-standard vaccine record system, sensitivity analyses that incorporate misclassification rates are promising for robust inference. In this work we introduce a novel extension of Bayesian logistic regression where we perturb the clinic size and vaccination count with random draws from expert-elicited prior distributions. These prior distributions represent the misclassification rates for each clinic that stochastically add unvaccinated counts to the observed vaccinated counts. These prior distributions are assigned for each clinic (the first level in a group-level randomized trial). We demonstrate this method with a data application from a CCRT evaluating the influence of a behavioral intervention on vaccination uptake among U.S. veterans. A simulation study is carried out demonstrating its estimation properties.

Towards the role of humanoid robots as squad mates in urban operations and other domains, we identified doors as a major area lacking capability development. In this paper, we focus on the ability of humanoid robots to navigate and deal with doors. Human-sized doors are ubiquitous in many environment domains and the humanoid form factor is uniquely suited to operate and traverse them. We present an architecture which incorporates GPU accelerated perception and a tree based interactive behavior coordination system with a whole body motion and walking controller. Our system is capable of performing door traversals on a variety of door types. It supports rapid authoring of behaviors for unseen door types and techniques to achieve re-usability of those authored behaviors. The behaviors are modelled using trees and feature logical reactivity and action sequences that can be executed with layered concurrency to increase speed. Primitive actions are built on top of our existing whole body controller which supports manipulation while walking. We include a perception system using both neural networks and classical computer vision for door mechanism detection outside of the lab environment. We present operator-robot interdependence analysis charts to explore how human cognition is combined with artificial intelligence to produce complex robot behavior. Finally, we present and discuss real robot performances of fast door traversals on our Nadia humanoid robot. Videos online at https://www.youtube.com/playlist?list=PLXuyT8w3JVgMPaB5nWNRNHtqzRK8i68dy., Comment: 15 pages, 23 figure, for submission to Elsevier RAS

Hierarchical sorting is a fundamental task for programmable matter, inspired by the spontaneous formation of interfaces and membranes in nature. The task entails particles of different types, present in fixed densities, sorting into corresponding regions of a space that are themselves organized. By analyzing the Gibbs distribution of a general fixed-magnetization model of equilibrium statistical mechanics, we prove that particles moving stochastically according to local affinities solve the hierarchical sorting task. The analysis of fixed-magnetization models is notoriously difficult, and approaches that have led to recent breakthroughs in sampling the low-temperature regime only work in the variable-magnetization setting by default. To overcome this barrier, we introduce a new approach for comparing the partition functions of fixed- and variable-magnetization models. The core technique identifies a special class of configurations that contribute comparably to the two partition functions, which then serves as a bridge between the fixed- and variable-magnetization settings. Our main result is an estimate of the Gibbs distribution that unifies existing and new results for models at fixed magnetization, including the Ising, Potts, and Blume--Capel models, and leads to stochastic distributed algorithms for hierarchical sorting and other self-organizing tasks, like compression and separation.

Teleoperation plays a crucial role in enabling robot operations in challenging environments, yet existing limitations in effectiveness and accuracy necessitate the development of innovative strategies for improving teleoperated tasks. This article introduces a novel approach that utilizes mixed reality and assistive autonomy to enhance the efficiency and precision of humanoid robot teleoperation. By leveraging Probabilistic Movement Primitives, object detection, and Affordance Templates, the assistance combines user motion with autonomous capabilities, achieving task efficiency while maintaining human-like robot motion. Experiments and feasibility studies on the Nadia robot confirm the effectiveness of the proposed framework., Comment: IEEE Robotics and Automation, Volume: 9, Issue: 2

The integration of autonomous vehicles (AVs) into transportation systems presents an unprecedented opportunity to enhance road safety and efficiency. However, understanding the interactions between AVs and human-driven vehicles (HVs) at intersections remains an open research question. This study aims to bridge this gap by examining behavioral differences and adaptations of AVs and HVs at unsignalized intersections by utilizing two comprehensive AV datasets from Waymo and Lyft. Using a systematic methodology, the research identifies and analyzes merging and crossing conflicts by calculating key safety and efficiency metrics, including time to collision (TTC), post-encroachment time (PET), maximum required deceleration (MRD), time advantage (TA), and speed and acceleration profiles. The findings reveal a paradox in mixed traffic flow: while AVs maintain larger safety margins, their conservative behavior can lead to unexpected situations for human drivers, potentially causing unsafe conditions. From a performance point of view, human drivers exhibit more consistent behavior when interacting with AVs versus other HVs, suggesting AVs may contribute to harmonizing traffic flow patterns. Moreover, notable differences were observed between Waymo and Lyft vehicles, which highlights the importance of considering manufacturer-specific AV behaviors in traffic modeling and management strategies for the safe integration of AVs. The processed dataset utilized in this study is openly published to foster the research on AV-HV interactions., Comment: This work has been submitted to Transportation Research Record for potential publication

The rapid development of automated vehicles (AVs) promises to revolutionize transportation by enhancing safety and efficiency. However, ensuring their reliability in diverse real-world conditions remains a significant challenge, particularly due to rare and unexpected situations known as edge cases. Although numerous approaches exist for detecting edge cases, there is a notable lack of a comprehensive survey that systematically reviews these techniques. This paper fills this gap by presenting a practical, hierarchical review and systematic classification of edge case detection and assessment methodologies. Our classification is structured on two levels: first, categorizing detection approaches according to AV modules, including perception-related and trajectory-related edge cases; and second, based on underlying methodologies and theories guiding these techniques. We extend this taxonomy by introducing a new class called "knowledge-driven" approaches, which is largely overlooked in the literature. Additionally, we review the techniques and metrics for the evaluation of edge case detection methods and identified edge cases. To our knowledge, this is the first survey to comprehensively cover edge case detection methods across all AV subsystems, discuss knowledge-driven edge cases, and explore evaluation techniques for detection methods. This structured and multi-faceted analysis aims to facilitate targeted research and modular testing of AVs. Moreover, by identifying the strengths and weaknesses of various approaches and discussing the challenges and future directions, this survey intends to assist AV developers, researchers, and policymakers in enhancing the safety and reliability of automated driving (AD) systems through effective edge case detection., Comment: Preprint submitted to IEEE Transactions on Intelligent Transportation Systems

In this paper, we present a novel data-driven approach to quantify safety for non-linear, discrete-time stochastic systems with unknown noise distribution. We define safety as the probability that the system remains in a given region of the state space for a given time horizon and, to quantify it, we present an approach based on Stochastic Barrier Functions (SBFs). In particular, we introduce an inner approximation of the stochastic program to design a SBF in terms of a chance-constrained optimisation problem, which allows us to leverage the scenario approach theory to design a SBF from samples of the system with Probably Approximately Correct (PAC) guarantees. Our approach leads to tractable, robust linear programs, which enable us to assert safety for non-linear models that were otherwise deemed infeasible with existing methods. To further mitigate the computational complexity of our approach, we exploit the structure of the system dynamics and rely on spatial data structures to accelerate the construction and solution of the underlying optimisation problem. We show the efficacy and validity of our framework in several benchmarks, showing that our approach can obtain substantially tighter certificates compared to state-of-the-art with a confidence that is several orders of magnitude higher.

Teleoperation of humanoid robots has long been a challenging domain, necessitating advances in both hardware and software to achieve seamless and intuitive control. This paper presents an integrated solution based on several elements: calibration-free motion capture and retargeting, low-latency fast whole-body kinematics streaming toolbox and high-bandwidth cycloidal actuators. Our motion retargeting approach stands out for its simplicity, requiring only 7 IMUs to generate full-body references for the robot. The kinematics streaming toolbox, ensures real-time, responsive control of the robot's movements, significantly reducing latency and enhancing operational efficiency. Additionally, the use of cycloidal actuators makes it possible to withstand high speeds and impacts with the environment. Together, these approaches contribute to a teleoperation framework that offers unprecedented performance. Experimental results on the humanoid robot Nadia demonstrate the effectiveness of the integrated system.

Local interactions of uncoordinated individuals produce the collective behaviors of many biological systems, inspiring much of the current research in programmable matter. A striking example is the spontaneous assembly of fire ants into "bridges" comprising their own bodies to traverse obstacles and reach sources of food. Experiments and simulations suggest that, remarkably, these ants always form one bridge -- instead of multiple, competing bridges -- despite a lack of central coordination. We argue that the reliable formation of a single bridge does not require sophistication on behalf of the individuals by provably reproducing this behavior in a self-organizing particle system. We show that the formation of a single bridge by the particles is a statistical inevitability of their preferences to move in a particular direction, such as toward a food source, and their preference for more neighbors. Two parameters, $\eta$ and $\beta$, reflect the strengths of these preferences and determine the Gibbs stationary measure of the corresponding particle system's Markov chain dynamics. We show that a single bridge almost certainly forms when $\eta$ and $\beta$ are sufficiently large. Our proof introduces an auxiliary Markov chain, called an "occupancy chain," that captures only the significant, global changes to the system. Through the occupancy chain, we abstract away information about the motion of individual particles, but we gain a more direct means of analyzing their collective behavior. Such abstractions provide a promising new direction for understanding many other systems of programmable matter.

Current approaches to identifying driving heterogeneity face challenges in comprehending fundamental patterns from the perspective of underlying driving behavior mechanisms. The concept of Action phases was proposed in our previous work, capturing the diversity of driving characteristics with physical meanings. This study presents a novel framework to further interpret driving patterns by classifying Action phases in an unsupervised manner. In this framework, a Resampling and Downsampling Method (RDM) is first applied to standardize the length of Action phases. Then the clustering calibration procedure including ''Feature Selection'', ''Clustering Analysis'', ''Difference/Similarity Evaluation'', and ''Action phases Re-extraction'' is iteratively applied until all differences among clusters and similarities within clusters reach the pre-determined criteria. Application of the framework using real-world datasets revealed six driving patterns in the I80 dataset, labeled as ''Catch up'', ''Keep away'', and ''Maintain distance'', with both ''Stable'' and ''Unstable'' states. Notably, Unstable patterns are more numerous than Stable ones. ''Maintain distance'' is the most common among Stable patterns. These observations align with the dynamic nature of driving. Two patterns ''Stable keep away'' and ''Unstable catch up'' are missing in the US101 dataset, which is in line with our expectations as this dataset was previously shown to have less heterogeneity. This demonstrates the potential of driving patterns in describing driving heterogeneity. The proposed framework promises advantages in addressing label scarcity in supervised learning and enhancing tasks such as driving behavior modeling and driving trajectory prediction.

Traffic conflict detection is essential for proactive road safety by identifying potential collisions before they occur. Existing methods rely on surrogate safety measures tailored to specific interactions (e.g., car-following, side-swiping, or path-crossing) and require varying thresholds in different traffic conditions. This variation leads to inconsistencies and limited adaptability of conflict detection in evolving traffic environments. Consequently, a need persists for consistent detection of traffic conflicts across interaction contexts. To address this need, this study proposes a unified probabilistic approach. The proposed approach establishes a unified framework of traffic conflict detection, where traffic conflicts are formulated as context-dependent extreme events of road user interactions. The detection of conflicts is then decomposed into a series of statistical learning tasks: representing interaction contexts, inferring proximity distributions, and assessing extreme collision risk. The unified formulation accommodates diverse hypotheses of traffic conflicts and the learning tasks enable data-driven analysis of factors such as motion states of road users, environment conditions, and participant characteristics. Jointly, this approach supports consistent and comprehensive evaluation of the collision risk emerging in road user interactions. Our experiments using real-world trajectory data show that the approach provides effective collision warnings, generalises across distinct datasets and traffic environments, covers a broad range of conflict types, and captures a long-tailed distribution of conflict intensity. The findings highlight its potential to enhance the safety assessment of traffic infrastructures and policies, improve collision warning systems for autonomous driving, and deepen the understanding of road user behaviour in safety-critical interactions., Comment: Officially published in Analytic Methods in Accident Research

Lane-changing (LC) is a challenging scenario for connected and automated vehicles (CAVs) because of the complex dynamics and high uncertainty of the traffic environment. This challenge can be handled by deep reinforcement learning (DRL) approaches, leveraging their data-driven and model-free nature. Our previous work proposed a cooperative lane-changing in mixed traffic (CLCMT) mechanism based on TD3 to facilitate an optimal lane-changing strategy. This study enhances the current CLCMT mechanism by considering both the uncertainty of the human-driven vehicles (HVs) and the microscopic interactions between HVs and CAVs. The state-of-the-art (SOTA) DRL algorithms including DDPG, TD3, SAC, and PPO are utilized to deal with the formulated MDP with continuous actions. Performance comparison among the four DRL algorithms demonstrates that DDPG, TD3, and PPO algorithms can deal with uncertainty in traffic environments and learn well-performed LC strategies in terms of safety, efficiency, comfort, and ecology. The PPO algorithm outperforms the other three algorithms, regarding a higher reward, fewer exploration mistakes and crashes, and a more comfortable and ecology LC strategy. The improvements promise CLCMT mechanism greater advantages in the LC motion planning of CAVs., Comment: 6 pages, 5 figures, IEEE conference

The use of partially automated driving systems raises concerns about potential responsibility issues, posing risk to the system safety, acceptance, and adoption of these technologies. The concept of meaningful human control has emerged in response to the responsibility gap problem, requiring the fulfillment of two conditions, tracking and tracing. While this concept has provided important philosophical and design insights on automated driving systems, there is currently little knowledge on how meaningful human control relates to subjective experiences of actual users of these systems. To address this gap, our study aimed to investigate the alignment between the degree of meaningful human control and drivers' perceptions of safety and trust in a real-world partially automated driving system. We utilized previously collected data from interviews with Tesla "Full Self-Driving" (FSD) Beta users, investigating the alignment between the user perception and how well the system was tracking the users' reasons. We found that tracking of users' reasons for driving tasks (such as safe maneuvers) correlated with perceived safety and trust, albeit with notable exceptions. Surprisingly, failure to track lane changing and braking reasons was not necessarily associated with negative perceptions of safety. However, the failure of the system to track expected maneuvers in dangerous situations always resulted in low trust and perceived lack of safety. Overall, our analyses highlight alignment points but also possible discrepancies between perceived safety and trust on the one hand, and meaningful human control on the other hand. Our results can help the developers of automated driving technology to design systems under meaningful human control and are perceived as safe and trustworthy., Comment: 8 pages

We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the $\Sigma_{\alpha+2}$ level for any $\alpha\in\omega_1^{ck}$ the set of linear orderings with generically or coarsely computable copies is $\mathbf{\Sigma}_1^1$-complete and therefore maximally complicated. This development is new even in the general analysis of generic and coarse computability of countable structures. In the process of proving these results we introduce new tools for understanding generically and coarsely computable structures. We are able to give a purely structural statement that is equivalent to having a generically computable copy and show that every relational structure with only finitely many relations has coarsely and generically computable copies at the lowest level of the hierarchy., Comment: 35 pages

Precise robotic weed control plays an essential role in precision agriculture. It can help significantly reduce the environmental impact of herbicides while reducing weed management costs for farmers. In this paper, we demonstrate that a custom-designed robotic spot spraying tool based on computer vision and deep learning can significantly reduce herbicide usage on sugarcane farms. We present results from field trials that compare robotic spot spraying against industry-standard broadcast spraying, by measuring the weed control efficacy, the reduction in herbicide usage, and the water quality improvements in irrigation runoff. The average results across 25 hectares of field trials show that spot spraying on sugarcane farms is 97% as effective as broadcast spraying and reduces herbicide usage by 35%, proportionally to the weed density. For specific trial strips with lower weed pressure, spot spraying reduced herbicide usage by up to 65%. Water quality measurements of irrigation-induced runoff, three to six days after spraying, showed reductions in the mean concentration and mean load of herbicides of 39% and 54%, respectively, compared to broadcast spraying. These promising results reveal the capability of spot spraying technology to reduce herbicide usage on sugarcane farms without impacting weed control and potentially providing sustained water quality benefits., Comment: 33 pages, 17 figures, 4 tables. Submitted to the Computers and Electronics in Agriculture journal

Normal numbers were introduced by Borel. Normality is certainly a weak notion of randomness; for instance, there are computable numbers which are absolutely normal. In the present paper, we introduce a relativization of normality to a fixed representation system. When we require normality with respect to large sets of such systems, we find variants of normality that imply randomness notions much stronger than absolute normality. The primary classes of numbers investigated in this paper are the supernormal numbers and the highly normal numbers, which we will define. These are relativizations of normality which are robust to all reasonable changes of representation. Among other results, we give a proof that the highly normal numbers are exactly those of computable dimension 1, which we think gives a more natural characterization than was previously known of this interesting class.

We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic fields which are not random. We also partially characterize the index set, relative to an oracle, of the set of random algebraic fields computable relative to that oracle. In order to carry out this investigation of randomness for fields, we develop computability in the context of infinite Galois theory (where the relevant Galois groups are uncountable), including definitions of computable and computably enumerable Galois groups and computability of Haar measure on the Galois groups.

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent work demonstrates that a local property of configurations called "rattling" predicts the global steady states of a broad class of nonequilibrium systems. We interpret this emerging physical theory in terms of Markov processes to generalize and prove its main claims. Surprisingly, we find that the idea at the core of rattling theory is so general as to apply to equilibrium and nonequilibrium systems alike. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global "parts" of an arbitrary steady state. We show how these key quantities characterize the local-global relationships of random walks on random graphs, various spin-glass dynamics, and models of animal collective behavior., Comment: 26 pages, 12 figures

We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a parabolic subgroup of $\mathbb{G}$ with abelian unipotent radical. The same Grassmannians can also be realized as (classical) compact symmetric spaces $G/K$. We give explicit generators and relations for the de Rham cohomology rings of $\mathbb{G}/\mathbb{P}\cong G/K$. At the same time we describe certain filtered deformations of these rings, related to Clifford algebras and spin modules. While the cohomology rings are of our primary interest, the filtered setting of $K$-invariants in the Clifford algebra actually provides a more conceptual framework for the results we obtain., Comment: 46 pages