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1. Low-latency Visual SLAM with Appearance-Enhanced Local Map Building

   https://doi.org/10.1109/ICRA.2019.8794046  

   Zhao, Yipu ; Ye, Wenkai ; Vela, Patricio A. ( May 2019 , IEEE International Conference on Robotics and Automation)

   A local map module is often implemented in modern VO/VSLAM systems to improve data association and pose estimation. Conventionally, the local map contents are determined by co-visibility. While co-visibility is cheap to establish, it utilizes the relatively-weak temporal prior (i.e. seen before, likely to be seen now), therefore admitting more features into the local map than necessary. This paper describes an enhancement to co-visibility local map building by incorporating a strong appearance prior, which leads to a more compact local map and latency reduction in downstream data association. The appearance prior collected from the current image influences the local map contents: only the map features visually similar to the current measurements are potentially useful for data association. To that end, mapped features are indexed and queried with Multi-index Hashing (MIH). An online hash table selection algorithm is developed to further reduce the query overhead of MIH and the local map size. The proposed appearance-based local map building method is integrated into a state-of-the-art VO/VSLAM system. When evaluated on two public benchmarks, the size of the local map, as well as the latency of real-time pose tracking in VO/VSLAM are significantly reduced. Meanwhile, the VO/VSLAM mean performance is preserved or improves. 

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2. Sufficient conditions and constraints for reversing general quantum errors

   https://doi.org/https://doi.org/10.1103/PhysRevA.102.062415  

   Gonzales, Alvin ; Dilley, Daniel ; Byrd, Mark ( December 2020 , Physical review and Physical review letters index)

   Abstract Reversing the effects of a quantum evolution, for example, as is done in error correction, is an important task for controlling quantum systems in order to produce reliable quantum devices. When the evolution is governed by a completely positive map, there exist reversibility conditions, known as the quantum error correcting code conditions, which are necessary and sufficient conditions for the reversibility of a quantum operation on a subspace, the code space. However, if we suppose that the evolution is not described by a completely positive map, necessary and sufficient conditions are not known. Here we consider evolutions that do not necessarily correspond to a completely positive map. We prove that the completely positive map error correcting code conditions can lead to a code space that is not in the domain of the map, meaning that the output of the map is not positive. A corollary to our theorem provides a class of relevant examples. Finally, we provide a set of sufficient conditions that will enable the use of quantum error correcting code conditions while ensuring positivity. 

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3. Guaranteeing completely positive quantum evolution

   https://doi.org/10.1088/1751-8121/ac2e28  

   Dilley, Daniel ; Gonzales, Alvin ; Byrd, Mark ( November 2021 , Journal of Physics A: Mathematical and Theoretical)

   Abstract In open quantum systems, it is known that if the system and environment are in a product state, the evolution of the system is given by a linear completely positive (CP) Hermitian map. CP maps are a subset of general linear Hermitian maps, which also include non completely positive (NCP) maps. NCP maps can arise in evolutions such as non-Markovian evolution, where the CP divisibility of the map (writing the overall evolution as a composition of CP maps) usually fails. Positive but NCP maps are also useful as entanglement witnesses. In this paper, we focus on transforming an initial NCP map to a CP map through composition with the asymmetric depolarizing map. We use separate asymmetric depolarizing maps acting on the individual subsystems. Previous work have looked at structural physical approximation (SPA), which is a CP approximation of an NCP map using a mixture of the NCP map with a completely depolarizing map. We prove that the composition can always be made CP without completely depolarizing in any direction. It is possible to depolarize less in some directions. We give the general proof by using the Choi matrix and an isomorphism from a maximally entangled two qudit state to a set of qubits. We also give measures that describe the amount of disturbance the depolarization introduces to the original map. Given our measures, we show that asymmetric depolarization has many advantages over SPA in preserving the structure of the original NCP map. Finally, we give some examples. For some measures and examples, completely depolarizing (while not necessary) in some directions can give a better approximation than keeping the depolarizing parameters bounded by the required depolarization if symmetric depolarization is used. 

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4. Urban Map Inference by Pervasive Vehicular Sensing Systems with Complementary Mobility

   https://doi.org/10.1145/3448076  

   Fang, Zhihan ; Wang, Guang ; Xie, Xiaoyang ; Zhang, Fan ; Zhang, Desheng ( March 2021 , Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies)

   Accurate and up-to-date digital road maps are the foundation of many mobile applications, such as navigation and autonomous driving. A manually-created map suffers from the high cost for creation and maintenance due to constant road network updating. Recently, the ubiquity of GPS devices in vehicular systems has led to an unprecedented amount of vehicle sensing data for map inference. Unfortunately, accurate map inference based on vehicle GPS is challenging for two reasons. First, it is challenging to infer complete road structures due to the sensing deviation, sparse coverage, and low sampling rate of GPS of a fleet of vehicles with similar mobility patterns, e.g., taxis. Second, a road map requires various road properties such as road categories, which is challenging to be inferred by just GPS locations of vehicles. In this paper, we design a map inference system called coMap by considering multiple fleets of vehicles with Complementary Mobility Features. coMap has two key components: a graph-based map sketching component, a learning-based map painting component. We implement coMap with the data from four type-aware vehicular sensing systems in one city, which consists of 18 thousand taxis, 10 thousand private vehicles, 6 thousand trucks, and 14 thousand buses. We conduct a comprehensive evaluation of coMap with two state-of-the-art baselines along with ground truth based on OpenStreetMap and a commercial map provider, i.e., Baidu Maps. The results show that (i) for the map sketching, our work improves the performance by 15.9%; (ii) for the map painting, our work achieves 74.58% of average accuracy on road category classification. 

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5. Invariant theory for the commuting scheme of symplectic Lie algebras

   Chen, Tsao-Hsien ; Ngo, Bao Chau ( October 2024 , Tata Institute of Fundamental Research Publications)

   We prove the Chevalley restriction theorem for the commuting scheme of symplectic Lie algebras. The key step is the construction of the inverse map of the Chevalley restriction map called the spectral data map. Along the way, we establish a certain multiplicative property of the Pfaffian which is of independent interest. 

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