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In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods., Comment: 49 pages, 21 figures

Numerous researchers have utilized GPS-enabled vehicle data and SafeGraph mobility data to analyze human movements. However, the comparison of their ability to capture human mobility remains unexplored. This study investigates differences in human mobility using taxi trip records and the SafeGraph dataset in New York City neighborhoods. The analysis includes neighborhood clustering to identify population characteristics and a comparative analysis of mobility patterns. Our findings show that taxi data tends to capture human mobility to and from locations such as Lower Manhattan, where taxi demand is consistently high, while often underestimating the volume of trips originating from areas with lower taxi demand, particularly in the suburbs of NYC. In contrast, SafeGraph data excels in capturing trips to and from areas where commuting by driving one's own car is common, but underestimates trips in pedestrian-heavy areas. The comparative analysis also sheds new light on transportation mode choices for trips across various neighborhoods. The results of this study underscore the importance of understanding the representativeness of human mobility big data and highlight the necessity for careful consideration when selecting the most suitable dataset for human mobility research.

We demonstrate the Patterns of Life Simulation to create realistic simulations of human mobility in a city. This simulation has recently been used to generate massive amounts of trajectory and check-in data. Our demonstration focuses on using the simulation twofold: (1) using the graphical user interface (GUI), and (2) running the simulation headless by disabling the GUI for faster data generation. We further demonstrate how the Patterns of Life simulation can be used to simulate any region on Earth by using publicly available data from OpenStreetMap. Finally, we also demonstrate recent improvements to the scalability of the simulation allows simulating up to 100,000 individual agents for years of simulation time. During our demonstration, as well as offline using our guides on GitHub, participants will learn: (1) The theories of human behavior driving the Patters of Life simulation, (2) how to simulate to generate massive amounts of synthetic yet realistic trajectory data, (3) running the simulation for a region of interest chosen by participants using OSM data, (4) learn the scalability of the simulation and understand the properties of generated data, and (5) manage thousands of parallel simulation instances running concurrently., Comment: Accepted paper to SIGSPATIAL 2024 main conference

Federated Learning(FL), in theory, preserves privacy of individual clients' data while producing quality machine learning models. However, attacks such as Deep Leakage from Gradients(DLG) severely question the practicality of FL. In this paper, we empirically evaluate the efficacy of four defensive methods against DLG: Masking, Clipping, Pruning, and Noising. Masking, while only previously studied as a way to compress information during parameter transfer, shows surprisingly robust defensive utility when compared to the other three established methods. Our experimentation is two-fold. We first evaluate the minimum hyperparameter threshold for each method across MNIST, CIFAR-10, and lfw datasets. Then, we train FL clients with each method and their minimum threshold values to investigate the trade-off between DLG defense and training performance. Results reveal that Masking and Clipping show near to none degradation in performance while obfuscating enough information to effectively defend against DLG., Comment: 13 pages, 5 figures, to be submitted to Applied Intelligence

We study the (ambi-)twistor model for spinning particles interacting via electromagnetic field, as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. We compute the momentum kick and spin kick up to one-loop order and show precisely how they are encoded in the classical eikonal. The all-orders-in-spin effects are encoded as a dynamical implementation of the Newman-Janis shift, and we find that the expansion in both spins can be resummed to simple expressions in special kinematic configurations, at least up to one-loop order. We confirm that the classical eikonal can be understood as the generator of canonical transformations that map the in-states of a scattering process to the out-states. We also remark that cut contributions for converting worldline propagators from time-symmetric to retarded amount to the iterated action of the leading eikonal at one-loop order., Comment: 74 pages, 15 figures; (v2) 76 pages, 15 figures; additional references; extended discussions on singularity structures of axial scattering eikonal

It is shown that a complex coordinate transformation maps the Taub-NUT instanton metric to a Kerr-Schild metric. This metric involves a semi-infinite line defect as a gravitational analog of the Dirac string, much like the original metric. Also, it corresponds to self-dual dyon in electromagnetism through three versions of classical double copy, one of them being a novel nonlocal operator form. The relevance to Newman-Janis algorithm is briefly noted., Comment: (v1) 9 pages, 2 figures; (v2) 10 pages, 2 figures, more references and added discussion on split signature; (v3) 10 pages, 2 figures, clarifications and added appendix on the geometric origin of the diffeomorphism

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator $U_\alpha$ labeled by a center element $\alpha$ of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator $W_\rho$ is the holonomy in a spin representation $\rho$, which is the gravitational analog of a Wilson loop. The topological linking of $U_\alpha$ and $W_\rho$ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries., Comment: 60 pages, 13 figures

This paper presents a contact-implicit model predictive control (MPC) framework for the real-time discovery of multi-contact motions, without predefined contact mode sequences or foothold positions. This approach utilizes the contact-implicit differential dynamic programming (DDP) framework, merging the hard contact model with a linear complementarity constraint. We propose the analytical gradient of the contact impulse based on relaxed complementarity constraints to further the exploration of a variety of contact modes. By leveraging a hard contact model-based simulation and computation of search direction through a smooth gradient, our methodology identifies dynamically feasible state trajectories, control inputs, and contact forces while simultaneously unveiling new contact mode sequences. However, the broadened scope of contact modes does not always ensure real-world applicability. Recognizing this, we implemented differentiable cost terms to guide foot trajectories and make gait patterns. Furthermore, to address the challenge of unstable initial roll-outs in an MPC setting, we employ the multiple shooting variant of DDP. The efficacy of the proposed framework is validated through simulations and real-world demonstrations using a 45 kg HOUND quadruped robot, performing various tasks in simulation and showcasing actual experiments involving a forward trot and a front-leg rearing motion., Comment: This is the accepted version for The International Journal of Robotics Research (2024); published version at https://journals.sagepub.com/doi/10.1177/02783649241273645 / Videos at https://youtu.be/SXD4BJIfyoY