Applications of position-based coding to classical communication over quantum channels

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Renyi-2 entropies and conditional quantum entropies.Comment: v4: 44 pages, v4 includes a simpler proof for an upper bound on one-shot entanglement-assisted capacity, also found recently and independently in arXiv:1804.0964

APPLICATION OF REAL-TIME DETECTION SYSTEM IN EPIDEMIC PREVENTION

The number of confirmed cases of the covid-19 virus have skyrocketed since November 2019. Now researchers are beginning to realize that due to the continuous change in the mode of virus transmission, it is too slow to rely on outdated news from the government. This project focused on solving the following question: How can we use a cost effective real-time regional diagnosis to slow down the spread of the virus and save more lives? .This project developed a real-time monitoring system model that had four main modules: (1) the data receiving, processing and transmission module, (2) the real-time analysis module, (3) the remote control module, and (4) the mobile terminal module. The real-time monitoring system collected confirmed cases in specific areas (e.g. Fontana area) and rendered them through a mobile terminal module. Through the data receiving, processing and transmission module and the real-time analysis module, people in the region are reminded not to crowd too densely, resulting in accelerated virus transmission. The combination of the remote control module and mobile platform module dynamically obtained the diagnosis position, without setting a fixed sampling point. The main conclusion is that compared with manual sampling, the cost of a case monitoring system 5was more effective, and the monitoring results were more accurate. Future studies should explore more effective prevention of the virus. For example, the development of facial recognition systems can remind users to wear masks when unlocking mobile phones

Experimental and numerical study of Taylor-Couette flow

Taylor-Couette flow between in a gap of two coaxial cylinders is studied using a combination of particle image velocimetry (PIV) experimental data and computational fluid dynamics (CFD). Wavy vortex flow and modulated wavy vortex flow which are two flow regimes of Taylor-Couette flow are investigated using the PIV technique and power spectral density. In addition, the turbulent Taylor-Couette flow is studied by means of Reynolds-average Navier-Stokes (RANS) simulations and stereo-PIV. Two main turbulence models of Reynolds-average Navier-Stokes simulations are used in the investigation and verified with the PIV experimental data. The investigations provide in-depth evaluation of the simulation schemes. This work shows that computational fluid dynamics in combination with PIV data is an excellent tool to study turbulent structures in the Taylor-Couette flow. Furthermore, this work demonstrates the in-depth evaluation of RANS simulation

Evaluation of the Effects of Bottom-Up Management in Preserving Values of Historic Hutong Neighborhood in Beijing: A Case Study of Community-Based Organization (CBO) - Shijia Hutong Historic Preservation Society

Preservation of traditional urban neighborhoods in China has long been a government-oriented process. In particular, since the “Old and Dilapidated Housing Renewal Program” implementation in the late 1990s, the Beijing Hutong neighborhood renewal has become an important trigger for the municipal governments to engage with the real estate market. Yet over the years, the official forces have been facing increasing challenges in the development of politics, socio-culture, and economy. As a complement to the current top-down management, the bottom-up approach could improve the recognition of a holistic spectrum of site values in the fast changing environments. However, the lack of on-the-ground community collaborations has limited the ability to test a grassroots-oriented preservation mechanism. The projects dedicated to renovating the courtyard built environments and promoting the neighborhood’s intangible values by applying a resident-centered decision-making process create valuable opportunities for the preservation practitioners to experiment with a bottom-up approach. The establishment of Shijia Hutong Historic Preservation Society (SHHPS) as the first registered community-based organization (CBO) in Beijing, has facilitated the transformation of decision-making roles between the officials and grassroots. My research probes into the effectiveness of a bottom-up management approach relative to the current top-down system in preserving the values of the Hutong neighborhood. The evaluation adopts a value-centered methodology for identifying, documenting and categorizing multiple values of the study area. Comparative analysis of the renovation project demonstrates the differences between the two approaches in the integration of interests, implementations and subsequent reviews. The efforts of promoting preservation mediated through a dedicated CBO have a beneficial effect on pursuing a more adaptive and sustainable system for the historical Chinese social contexts within the Hutong neighborhood

Optimal Smoothed Analysis and Quantitative Universality for the Smallest Singular Value of Random Matrices

The smallest singular value and condition number play important roles in numerical linear algebra and the analysis of algorithms. In numerical analysis with randomness, many previous works make Gaussian assumptions, which are not general enough to reflect the arbitrariness of the input. To overcome this drawback, we prove the first quantitative universality for the smallest singular value and condition number of random matrices. Moreover, motivated by the study of smoothed analysis that random perturbation makes deterministic matrices well-conditioned, we consider an analog for random matrices. For a random matrix perturbed by independent Gaussian noise, we show that this matrix quickly becomes approximately Gaussian. In particular, we derive an optimal smoothed analysis for random matrices in terms of a sharp Gaussian approximation

Resampling Sensitivity of High-Dimensional PCA

The study of stability and sensitivity of statistical methods or algorithms with respect to their data is an important problem in machine learning and statistics. The performance of the algorithm under resampling of the data is a fundamental way to measure its stability and is closely related to generalization or privacy of the algorithm. In this paper, we study the resampling sensitivity for the principal component analysis (PCA). Given an $n \times p$ random matrix $\mathbf{X}$, let $\mathbf{X}^{[k]}$ be the matrix obtained from $\mathbf{X}$ by resampling $k$ randomly chosen entries of $\mathbf{X}$. Let $\mathbf{v}$ and $\mathbf{v}^{[k]}$ denote the principal components of $\mathbf{X}$ and $\mathbf{X}^{[k]}$. In the proportional growth regime $p/n \to \xi \in (0,1]$, we establish the sharp threshold for the sensitivity/stability transition of PCA. When $k \gg n^{5/3}$, the principal components $\mathbf{v}$ and $\mathbf{v}^{[k]}$ are asymptotically orthogonal. On the other hand, when $k \ll n^{5/3}$, the principal components $\mathbf{v}$ and $\mathbf{v}^{[k]}$ are asymptotically colinear. In words, we show that PCA is sensitive to the input data in the sense that resampling even a negligible portion of the input may completely change the output.Comment: 38 pages, 6 figures. Fix some typos. Add numerical simulation