You limited your search to:

  Partner: UNT Libraries
 Decade: 2000-2009
 Year: 2007
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
Around the Fibonacci Numeration System

Around the Fibonacci Numeration System

Date: May 2007
Creator: Edson, Marcia Ruth
Description: Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
Contributing Partner: UNT Libraries
Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis

Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis

Date: May 2007
Creator: Brooks, Evan
Description: A "complex" system typically has a relatively large number of dynamically interacting components and tends to exhibit emergent behavior that cannot be explained by analyzing each component separately. A biological neural network is one example of such a system. A multi-agent model of such a network is developed to study the relationships between a network's structure and its spike train output. Using this model, inferences are made about the synaptic structure of networks through cluster analysis of spike train summary statistics A complexity measure for the network structure is also presented which has a one-to-one correspondence with the standard time series complexity measure sample entropy.
Contributing Partner: UNT Libraries