Characterization of affine automorphisms and ortho-order automorphisms of quantum probabilistic maps

In quantum mechanics, often it is important for the representation of quantum system to study the structure-preserving bijective maps of the quantum system. Such maps are also called isomorphisms or automorphisms. In this note, using the Uhlhorn-type of Wigner's theorem, we characterize all affine automorphisms and ortho-order automorphisms of quantum probabilistic maps

Fast Parallel Algorithms for Basic Problems

Parallel processing is one of the most active research areas these days. We are interested in one aspect of parallel processing, i.e. the design and analysis of parallel algorithms. Here, we focus on non-numerical parallel algorithms for basic combinatorial problems, such as data structures, selection, searching, merging and sorting. The purposes of studying these types of problems are to obtain basic building blocks which will be useful in solving complex problems, and to develop fundamental algorithmic techniques. In this thesis, we study the following problems: priority queues, multiple search and multiple selection, and reconstruction of a binary tree from its traversals. The research on priority queue was motivated by its various applications. The purpose of studying multiple search and multiple selection is to explore the relationships between four of the most fundamental problems in algorithm design, that is, selection, searching, merging and sorting; while our parallel solutions can be used as subroutines in algorithms for other problems. The research on the last problem, reconstruction of a binary tree from its traversals, was stimulated by a challenge proposed in a recent paper by Berkman et al. ( Highly Parallelizable Problems, STOC 89) to design doubly logarithmic time optimal parallel algorithms because a remarkably small number of such parallel algorithms exist

NLP Modeling and Analysis of Popular Vloggers

Vlog, or video blog, is the chicest form of personal production on YouTube First appearing at the beginning of the 21 st century, vlogs saw an enormous rise in popularity around 2005 Differing from other forms of production, vlogs allow their producers more freedom in expressing themselves without the limitation of content, word count, and forms of expression The absence of censorship and early stage marketing allows an almost free market effect in the sense that the most popular vloggers and videos are purely the choice of people Therefore, analyzing viral vlogs and vloggers can offer a more accurate representation of where the general population’s interests lie. In the project, I focused on 4 vloggers of different genres to analyze the reasons behind their successes using NLP techniques