Noncommutative Choquet theory

We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply these ideas to develop a noncommutative Choquet theory that generalizes much of classical Choquet theory. The central objects of interest in noncommutative convexity are noncommutative convex sets. The category of compact noncommutative sets is dual to the category of operator systems, and there is a robust notion of extreme point for a noncommutative convex set that is dual to Arveson's notion of boundary representation for an operator system. We identify the C*-algebra of continuous noncommutative functions on a compact noncommutative convex set as the maximal C*-algebra of the operator system of continuous noncommutative affine functions on the set. In the noncommutative setting, unital completely positive maps on this C*-algebra play the role of representing measures in the classical setting. The continuous convex noncommutative functions determine an order on the set of unital completely positive maps that is analogous to the classical Choquet order on probability measures. We characterize this order in terms of the extensions and dilations of the maps, providing a powerful new perspective on the structure of completely positive maps on operator systems. Finally, we establish a noncommutative generalization of the Choquet-Bishop-de Leeuw theorem asserting that every point in a compact noncommutative convex set has a representing map that is supported on the extreme boundary. In the separable case, we obtain a corresponding integral representation theorem.Comment: 81 pages; minor change

Credit Scoring Using Machine Learning

For financial institutions and the economy at large, the role of credit scoring in lending decisions cannot be overemphasised. An accurate and well-performing credit scorecard allows lenders to control their risk exposure through the selective allocation of credit based on the statistical analysis of historical customer data. This thesis identifies and investigates a number of specific challenges that occur during the development of credit scorecards. Four main contributions are made in this thesis. First, we examine the performance of a number supervised classification techniques on a collection of imbalanced credit scoring datasets. Class imbalance occurs when there are significantly fewer examples in one or more classes in a dataset compared to the remaining classes. We demonstrate that oversampling the minority class leads to no overall improvement to the best performing classifiers. We find that, in contrast, adjusting the threshold on classifier output yields, in many cases, an improvement in classification performance. Our second contribution investigates a particularly severe form of class imbalance, which, in credit scoring, is referred to as the low-default portfolio problem. To address this issue, we compare the performance of a number of semi-supervised classification algorithms with that of logistic regression. Based on the detailed comparison of classifier performance, we conclude that both approaches merit consideration when dealing with low-default portfolios. Third, we quantify the differences in classifier performance arising from various implementations of a real-world behavioural scoring dataset. Due to commercial sensitivities surrounding the use of behavioural scoring data, very few empirical studies which directly address this topic are published. This thesis describes the quantitative comparison of a range of dataset parameters impacting classification performance, including: (i) varying durations of historical customer behaviour for model training; (ii) different lengths of time from which a borrower’s class label is defined; and (iii) using alternative approaches to define a customer’s default status in behavioural scoring. Finally, this thesis demonstrates how artificial data may be used to overcome the difficulties associated with obtaining and using real-world data. The limitations of artificial data, in terms of its usefulness in evaluating classification performance, are also highlighted. In this work, we are interested in generating artificial data, for credit scoring, in the absence of any available real-world data

Development of a Low-Noise High Common-Mode-Rejection Instrumentation Amplifier

Several previously used instrumentation amplifier circuits were examined to find limitations and possibilities for improvement. One general configuration is analyzed in detail, and methods for improvement are enumerated. An improved amplifier circuit is described and analyzed with respect to common mode rejection and noise. Experimental data are presented showing good agreement between calculated and measured common mode rejection ratio and equivalent noise resistance. The amplifier is shown to be capable of common mode rejection in excess of 140 db for a trimmed circuit at frequencies below 100 Hz and equivalent white noise below 3.0 nv/square root of Hz above 1000 Hz

Alien Registration- Kennedy, Kenneth L. (Livermore Falls, Androscoggin County)

https://digitalmaine.com/alien_docs/27055/thumbnail.jp

How Much is E-Commerce Worth to Rural Businesses?

The probability of a business paying for an e-commerce presence ultimately depends on demographic features, experiences with e-commerce, technological expertise, and knowledge of e-commerce opportunities and limitations. Results allow for the assignment of probabilities associated with various business profiles to determine the willingness to pay for an e-commerce presence.Research and Development/Tech Change/Emerging Technologies,

Website Usage Information for Rural-Based E-Commerce Start-Ups

Usage patterns for start-up agricultural and non-agricultural websites, as well as product and service oriented websites, were studied to determine differences in the number of unique visitors, usage based on the day and time of the week, total time spent on the website, and how the visitor found the website.Research and Development/Tech Change/Emerging Technologies,