Alexandrov meets Lott-Villani-Sturm

Here I show the compatibility of two definitions of generalized curvature bounds: the lower bound for sectional curvature in the sense of Alexandrov and the lower bound for Ricci curvature in the sense of Lott-Villani-Sturm

Sweeping out sectional curvature

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Ramification conjecture and Hirzebruch's property of line arrangements

The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral metrics on the complex projective plane with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a CAT[0] ramification and prove this in several cases. In the latter case we prove that the ramification is CAT[0] if the metric is non-negatively curved. We deduce that complex line arrangements in the complex projective plane studied by Hirzebruch have aspherical complement.Comment: 19 pages 1 figur

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension

Drone model identification by convolutional neural network from video stream

We present a convolutional neural network model that correctly identifies drone models in real-life video streams of flying drones. To achieve this, we show a method of generating synthetic drone images. To create a diverse dataset, the simulation parameters (such as drone textures, lighting, and orientation) are randomized. This synthetic dataset is used to train a convolutional neural network to identify the drone model: DJI Phantom, DJI Mavic, or DJI Inspire. The model is then tested on a real-life Anti-UAV dataset of flying drones. The benchmark results show that the DenseNet201 architecture performed the best. Adding Gaussian noise to the training dataset and performing full training (as opposed to freezing layers) shows the best results. The model shows an average accuracy of 92.4%, and an average precision of 88.6% on the test dataset

Orientation and symmetries of Alexandrov spaces with applications in positive curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous versio

Drone model classification using convolutional neural network trained on synthetic data

We present a convolutional neural network (CNN) that identifies drone models in real-life videos. The neural network is trained on synthetic images and tested on a real-life dataset of drone videos. To create the training and validation datasets, we show a method of generating synthetic drone images. Domain randomization is used to vary the simulation parameters such as model textures, background images, and orientation. Three common drone models are classified: DJI Phantom, DJI Mavic, and DJI Inspire. To test the performance of the neural network model, Anti-UAV, a real-life dataset of flying drones is used. The proposed method reduces the time-cost associated with manually labelling drones, and we prove that it is transferable to real-life videos. The CNN achieves an overall accuracy of 92.4%, a precision of 88.8%, a recall of 88.6%, and an f1 score of 88.7% when tested on the real-life dataset

Crystal Undulator As A Novel Compact Source Of Radiation

A crystalline undulator (CU) with periodically deformed crystallographic planes is capable of deflecting charged particles with the same strength as an equivalent magnetic field of 1000 T and could provide quite a short period L in the sub-millimeter range. We present an idea for creation of a CU and report its first realization. One face of a silicon crystal was given periodic micro-scratches (grooves), with a period of 1 mm, by means of a diamond blade. The X-ray tests of the crystal deformation have shown that a sinusoidal-like shape of crystalline planes goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in CU, a novel compact source of radiation. The first experiment on photon emission in CU has been started at LNF with 800 MeV positrons aiming to produce 50 keV undulator photons.Comment: Presented at PAC 2003 (Portland, May 12-16

Integrating GRU with a Kalman filter to enhance visual inertial odometry performance in complex environments

To enhance system reliability and mitigate the vulnerabilities of the Global Navigation Satellite Systems (GNSS), it is common to fuse the Inertial Measurement Unit (IMU) and visual sensors with the GNSS receiver in the navigation system design, effectively enabling compensations with absolute positions and reducing data gaps. To address the shortcomings of a traditional Kalman Filter (KF), such as sensor errors, an imperfect non-linear system model, and KF estimation errors, a GRU-aided ESKF architecture is proposed to enhance the positioning performance. This study conducts Failure Mode and Effect Analysis (FMEA) to prioritize and identify the potential faults in the urban environment, facilitating the design of improved fault-tolerant system architecture. The identified primary fault events are data association errors and navigation environment errors during fault conditions of feature mismatch, especially in the presence of multiple failure modes. A hybrid federated navigation system architecture is employed using a Gated Recurrent Unit (GRU) to predict state increments for updating the state vector in the Error Estate Kalman Filter (ESKF) measurement step. The proposed algorithm’s performance is evaluated in a simulation environment in MATLAB under multiple visually degraded conditions. Comparative results provide evidence that the GRU-aided ESKF outperforms standard ESKF and state-of-the-art solutions like VINS-Mono, End-to-End VIO, and Self-Supervised VIO, exhibiting accuracy improvement in complex environments in terms of root mean square errors (RMSEs) and maximum errors