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3 results on '"Thirey, Benjamin"'

1. Distribution of Euclidean Distances Between Randomly Distributed Gaussian Points in n-Space

Author

Thirey, Benjamin and Hickman, Randal

Subjects
60D05 (Primary) 52A38, 53C65 (Secondary), Probability (math.PR), FOS: Mathematics, Mathematics - Probability
Abstract

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms which are heavily dependent upon distances between points, such as nearest-neighbor and $k$-means clustering. Given that contributing variables follow Gaussian distributions, this research derives the probability distribution that describes the distances between randomly generated points in n-space. The theoretical results are extended to examine additional properties of the distribution as the dimension becomes arbitrarily large. With this distribution of distances between randomly generated points in arbitrarily large dimensions, one can then determine the significance of distance measurements between any collection of individual points., 13 pages, 4 figures

Published
2015

2. Network Models of Entrepreneurial Ecosystems in Developing Economies.

Author

Evans, Daniel, Thirey, Benjamin, and Boguchwal, Louis

Subjects
ENTREPRENEURSHIP, SMALL business, ECONOMIC development, ECOSYSTEMS, ECONOMIC policy
Abstract

Development of Small and Medium Enterprises (SMEs) has been recognized as a key step in the progressive development of frontier and emerging economies. The social and economic environment is critical to the creation and success of the SMEs. Our project methodology seeks to develop insight into the establishment of social and economic criteria which facilitates the creation and success of SMEs. We have developed a quantitatively-oriented network methodology that accurately evaluates a local entrepreneurial ecosystem in terms of potential for growth and expansion. This innovative, yet simple, methodology is a variation of the Position Generator technique currently used to measure social capital. The results enable the identification of the most influential roles in a given local ecosystem. We further develop a model that illustrates the connections between these influential roles which then allows us to compare and contrast different local communities utilizing a uniform standard of measurement. [ABSTRACT FROM AUTHOR]

Published
2015

3. The Touchy-Feely Integral: Using Manipulatives to Teach the Basic Properties of Integration.

Author

Thirey, Benjamin and Wooster, Robert

Subjects
*CALCULUS, *MATHEMATICS education, *INTEGRALS, *RIEMANN integral, *LEARNING
Abstract

Elementary education makes use of manipulatives in the teaching of fundamental mathematical concepts. As the age of the students progress, mathematics becomes much more abstract and concepts such as the integral become harder for some students to visualize. One approach we have implemented is the use of construction paper as a manipulative. This simple hands-on object can be used to demonstrate the basic properties of integrals to students who struggle greatly with the underlying ideas, especially when they are first encountered. Through the treatment of the integral as something that can be held in the hand and modified with the use of scissors, many of the basic properties of integrals can be demonstrated, as well as the intuition behind the Fundamental Theorem of Calculus. [ABSTRACT FROM PUBLISHER]

Published
2013
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