With tangent space optimization, we can use standard Euclidean optimization techniques, and respect the geometry of the manifold. All experiments were run on Intel Cascade Lake CPUs, with microprocessors Intel Xeon Gold 6230 (20 Cores, 40 Threads, 2.1 GHz, 28MB Cache, 125W TDP). The red dot corresponds to the relation addition R . Datasets: Stats about the datasets used in Knowledge graph experiments can be found in Table 4. Results: In addition to the results provided in 6.1, in Table 5 we provide a comparison with other We include ComplEx [77], Tucker [9], and Quaternion [92]. In Figure 6 we add equivalent plots to the ones explained in 6.4 for other relations from Same grid search is applied to baselines.

We propose CatEquiv, a category-equivariant neural network for Human Activity Recognition (HAR) from inertial sensors that systematically encodes temporal, amplitude, and structural symmetries. We introduce a symmetry category that jointly represents cyclic time shifts, positive gain scalings, and the sensor-hierarchy poset, capturing the categorical symmetry structure of the data. CatEquiv achieves equivariance with respect to the categorical symmetry product. On UCI-HAR under out-of-distribution perturbations, CatEquiv attains markedly higher robustness compared with circularly padded CNNs and plain CNNs. These results demonstrate that enforcing categorical symmetries yields strong invariance and generalization without additional model capacity.

With tangent space optimization, we can use standard Euclidean optimization techniques, and respect the geometry of the manifold. All experiments were run on Intel Cascade Lake CPUs, with microprocessors Intel Xeon Gold 6230 (20 Cores, 40 Threads, 2.1 GHz, 28MB Cache, 125W TDP). The red dot corresponds to the relation addition R . Datasets: Stats about the datasets used in Knowledge graph experiments can be found in Table 4. Results: In addition to the results provided in 6.1, in Table 5 we provide a comparison with other We include ComplEx [77], Tucker [9], and Quaternion [92]. In Figure 6 we add equivalent plots to the ones explained in 6.4 for other relations from Same grid search is applied to baselines.

This document is in supplement to the paper titled "Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers", available at [1]. The purpose of this document is to show how IMU biases can be incorporated into the framework presented in [1], while maintaining the differential Sylvester equation form of the process model.

ABSTRACT We demonstrate the potential of the state-of-the-art OpenAI GPT-4 large language model to engage in meaningful interactions with Astronomy papers using in-context prompting. To optimize for efficiency, we employ a distillation technique that effectively reduces the size of the original input paper by 50%, while maintaining the paragraph structure and overall semantic integrity. We then explore the model's responses using a multi-document context (ten distilled documents). Our findings indicate that GPT-4 excels in the multi-document domain, providing detailed answers contextualized within the framework of related research findings. INTRODUCTION Large language models (LLMs) have significantly advanced natural language processing, allowing machines to process and generate intricate text with remarkable quality (e.g., Devlin et al. 2018; Brown et al. 2020; Chowdhery et al. 2022; Bubeck et al. 2023).

The navigation systems of autonomous aircraft rely on the readings provided by a suite of onboard sensors to estimate the aircraft state. In the case of fixed wing vehicles, the sensor suite is composed by triads of accelerometers, gyroscopes, and magnetometers, a Global Navigation Satellite System (GNSS) receiver, and an air data system (Pitot tube, air vanes, thermometer, and barometer), and is often complemented by one or more digital cameras. An accurate representation of the behavior and error sources of each of these sensors, together with the images generated by the cameras, in indispensable for flight simulation and the evaluation of novel inertial or visual navigation algorithms, and more so in the case of low SWaP (size, weight, and power) aircraft, in which the quality and price of the sensors is limited. This article presents realistic and customizable models for each of these sensors, which have been implemented as an open-source C ++ simulation. Provided with the true variation of the aircraft state with time, the simulation provides a time stamped series of the errors generated by all sensors, as well as realistic images of the Earth surface that resemble those taken from a real camera flying along the indicated state positions and attitudes.