Higgs bundles for the Lorentz group

Using the Morse-theoretic methods introduced by Hitchin, we prove that the moduli space of \SO_0(1,n)-Higgs bundles when $n$ is odd has two connected components

TARP: Indication of a Potential Target? Evaluating Market to Book Ratios and Their Relationship to TARP

This paper examines to what extent banks with outstanding Troubled Asset Relief Program (TARP) debt are perceived as potential takeover targets. Each bank\u27s price-to-tangible-book value is related to a series of fundamental bank ratios and market index as well as a series of TARP variables that capture if a bank took TARP and for how long. The results show that middle tiered banks (with assets between 500 million and 5 billion) are positively associated with retaining TARP, which may suggest they are perceived as takeover targets. In addition, banks with higher valuations have lower non-performing assets, net charge offs, loan loss reserves, tier 1 capital ratios, real estate and development loans. A higher price-to-tangible-book value is also associated with higher returns on average tangible common equity and interest income

TARP: Indication of a Potential Target? Evaluating Market to Book Ratios and Their Relationship to TARP

This paper examines to what extent banks with outstanding Troubled Asset Relief Program (TARP) debt are perceived as potential takeover targets. Each bank\u27s price-to-tangible-book value is related to a series of fundamental bank ratios and market index as well as a series of TARP variables that capture if a bank took TARP and for how long. The results show that middle tiered banks (with assets between 500 million and 5 billion) are positively associated with retaining TARP, which may suggest they are perceived as takeover targets. In addition, banks with higher valuations have lower non-performing assets, net charge offs, loan loss reserves, tier 1 capital ratios, real estate and development loans. A higher price-to-tangible-book value is also associated with higher returns on average tangible common equity and interest income

A Mathematical Approach to Gomoku

This goal of this thesis is to design and implement a light weighted AI for playing Gomoku with high level intelligence. Our work is built upon an innovative algebraic monomial theory to help assess values for each possible move and estimate chances for the AI to win at each move. With the help of the monomial theory, we are able to convert winning configurations into monomials of variables that represent the underlying board positions. In the existing approaches to building an AI for playing Gomoku, one common challenge is about how to represent the present configuration of the game along with the history of the moves of the two players. Compared with the usual 2D matrix of the board positions, our monomials can make the AI easily understand the current state and the history of the game, and they also allow the AI to compute the potential values for future moves from the current state and the history of moves made by the players. In addition, when we adopt the Monte Carlo Tree Search to probe for a possible winning strategy for the AI, those monomials help reduce the search space, in addition to help estimate rates for exploration of the historical moves and exploitation of the future moves. Based on the proposed algebraic monomial theory, we have implemented a lightweight powerful AI that is capable of playing Gomoku at highly competitive level. At this stage, our AI can win top rated AIs (up to top 7) from the most recent Gomocup rating