Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.Comment: some minor updates and revisions; 18 pages, no figures; to appear in the Pacific Journal of Mathematic

Identifying optimal paths for purchasing cryptocurrencies.

Increase of trend in trading cryptocurrencies, ease of use, surge in media attention and the idea of making quick money were contributing factors for massive growth in users in the year 2017. To start trading, the user must rst register on the desired exchange to which he transfers his funds and exchanges them for the chosen cryptocurrency. In the event that the target cryptocurrency is not available on this exchange, he must create another account on a di�erent exchange, send the currency there and execute another trade. Many times users do not realise all the fees that take place during this process. The goal of this Bachelor's thesis is to create an algorithm that provides the end user with optimal path for purchasing a speci�c cryptocur- rency. Based on data, provided by API points, the algorithm generates a network of trading pairs in which it �nds the optimal path for purchase. The user can then make actions based on the provided path. The algorithm is made in programming language Python, using MongoDB database and set up as a web application using Flask and Vue frameworks

Identifying optimal paths for purchasing cryptocurrencies.

Increase of trend in trading cryptocurrencies, ease of use, surge in media attention and the idea of making quick money were contributing factors for massive growth in users in the year 2017. To start trading, the user must rst register on the desired exchange to which he transfers his funds and exchanges them for the chosen cryptocurrency. In the event that the target cryptocurrency is not available on this exchange, he must create another account on a di�erent exchange, send the currency there and execute another trade. Many times users do not realise all the fees that take place during this process. The goal of this Bachelor's thesis is to create an algorithm that provides the end user with optimal path for purchasing a speci�c cryptocur- rency. Based on data, provided by API points, the algorithm generates a network of trading pairs in which it �nds the optimal path for purchase. The user can then make actions based on the provided path. The algorithm is made in programming language Python, using MongoDB database and set up as a web application using Flask and Vue frameworks

Understanding Complex Design Models through Bayesian Networks and Network Theory

Like the design of many large and complex systems, modern ship design often involves the automated creation of thousands of viable design alternatives developed through computer driven design models and optimizations. The models used to develop these designs are often multi-disciplinary and contain highly interconnected engineering systems. Consequently, even the most experienced designer has a limited ability to develop complete mental models for a large number of complex and varied design alternatives. Furthermore, when design decisions are made and need to be communicated to non-technical stakeholders, the complex relationships driving the design model become even more difficult to effectively communicate. Automated learning of Bayesian networks can offer designers an opportunity to quickly analyze a large set of designs with the efficiency with which they are created. As sets of nodes, edges and conditional probabilities, Bayesian networks can identify and quantify the influential relationships between design parameters. Transforming the learned Bayesian networks into simpler weighted edge networks further aids communication of the driving factors of a complex design model to all stakeholders by presenting the learned information visually and through simple to understand network metrics. This dissertation presents a framework for learning Bayesian networks, transforming them into weighted edge networks and analyzing those networks with metrics from network science. Additionally, an algorithm for identifying and chunking redundant variables is presented. Two case studies, a simple multi-objective function from Osyczka and Kundu and more complex ship design model from Sen and Yang, are presented and analyzed with the proposed framework. Each is sampled with a Latin hypercube to develop ten design trials of 100,000 design alternatives each. The variables of the more complex ship design model are analyzed for redundancy and chunked using the proposed chunking algorithm. Bayesian networks are learned from each design database and transformed into weighted edge networks using two scoring methods, derived from log gamma K2 and match distance. Finally the weighted edge networks are analyzed to identify communities and compute degree, betweenness, closeness and Eigenvector centralities. These metrics identify disciplines and driving factors of the design space at progressive stages of design.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169959/1/cwincott_1.pd