The limit of the Yang-Mills-Higgs flow on Higgs bundles

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact K\"ahler manifold $(M, \omega )$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle.Comment: 33 pages. arXiv admin note: text overlap with arXiv:math/0410055, arXiv:1206.5491 by other author

Design of VR Engine Assembly Teaching System

Virtual reality(VR) is a hot research topic, and it has been effectively applied in military, education and other fields. The application prospect of virtual reality in education is very broad. It can effectively reduce labor cost, resource consumption, stimulate students' interest in learning, and improve students' knowledge level. New energy vehicles have also been widely promoted in recent years, and the production of new energy vehicles has played a key role in it. However, the teaching of car engine disassembly and assembly still retains a more traditional way. That's why applying VR technology has high significance. This project uses the Unity 3D engine to develop a VR-based engine teaching software, which aims to allow users to use VR headsets, handles and other accessories to simulate the disassembly and assembly of car engines in a virtual environment. We design a modular system framework and divided the software into two layers, the system layer and the function layer. The system layer includes a message system and a data configuration system. The functional layer includes the user interface system, disassembly and assembly function, and data module. In addition to fulfilling functional requirements , we used the Unity UPR tool to check out performance issues, and optimized product performance by turning off vertical sync and turning on static switches for some scene objects.Comment: 8 pages, 4 figures, 4 table

Succinct Blind Quantum Computation Using a Random Oracle

In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few resources as possible. This problem, first raised by Broadbent, Fitzsimons and Kashefi [FOCS09, arXiv:0807.4154], has become fundamental to the study of quantum cryptography, not only because of its own importance, but also because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computation verification). Known protocols on this problem are mainly either information-theoretically (IT) secure or based on trapdoor assumptions (public key encryptions). In this paper we study how the availability of symmetric-key primitives, modeled by a random oracle, changes the complexity of universal blind quantum computation. We give a new universal blind quantum computation protocol. Similar to previous works on IT-secure protocols (for example, BFK [FOCS09, arXiv:0807.4154]), our protocol can be divided into two phases. In the first phase the client prepares some quantum gadgets with relatively simple quantum gates and sends them to the server, and in the second phase the client is entirely classical -- it does not even need quantum storage. Crucially, the protocol's first phase is succinct, that is, its complexity is independent of the circuit size. Given the security parameter $\kappa$, its complexity is only a fixed polynomial of $\kappa$, and can be used to evaluate any circuit (or several circuits) of size up to a subexponential of $\kappa$. In contrast, known schemes either require the client to perform quantum computations that scale with the size of the circuit [FOCS09, arXiv:0807.4154], or require trapdoor assumptions [Mahadev, FOCS18, arXiv:1708.02130].Comment: 231 pages, 8 figures, 1 table. Add a separate section for extended technical overview; several readability improvement