Cellular Neural Networks with Switching Connections

Artificial neural networks are widely used for parallel processing of data analysis and visual information. The most prominent example of artificial neural networks is a cellular neural network (CNN), composed from two-dimensional arrays of simple first-order dynamical systems (“cells”) that are interconnected by wires. The information, to be processed by a CNN, represents the initial state of the network, and the parallel information processing is performed by converging to one of the stable spatial equilibrium states of the multi-stable CNN. This thesis studies a specific type of CNNs designed to perform the winner-take-all function of finding the largest among the n numbers, using the network dynamics. In a wider context, this amounts to automatically detecting a target spot in the given visual picture. The research, reported in this thesis, demonstrates that the addition of fast on-off switching (blinking) connections significantly improves the functionality of winner-take-all CNNs. Numerical calculations are performed to reveal the dependence of the probability, that the CNN correctly classifies the largest number, on the switching frequency

The Effects of a Platform Digital Game-Based Learning Environment on Undergraduate Students Achievement and Motivation in a Multivariable Calculus Course

This study examined the effects of a researcher-designed digital game-based learning (DGBL) environment called Adventures of Krystal Kingdom on undergraduate students’ mathematics achievement and motivation in a Multivariable Calculus course. Multivariable Calculus is a specific area of computational and applied mathematics that focuses on the differentiation and integration of functions of several variables in fields like physics and engineering. The study employed a single exploratory embedded case study design with quantitative and qualitative techniques. A case study is the appropriate methodology for this study, which is a bounded system that facilitates a deeply contextualized understanding of a case through giving descriptions, analyses, and interpretations (Yin, 2014). The quantitative sample comprised 29 undergraduate students, and the qualitative sample included 6 students selected through stratified sampling based on the level of achievement. Quantitative data was collected using two surveys: demographic and motivation surveys, and two tests: academic achievement test and a game performance test. Analysis of quantitative data used a paired sample t-test. Qualitative data were collected from interviews, observations, and artifacts. Analysis of qualitative data used coding procedures suggested by Creswell (2014) where patterns were identified and grouped to allow the emergence of themes. The results of the study indicated no statistical significance in achievement (p=0.88 \u3e0.05), however, there was overall improvement found in achievement scores of the students who played the game. Three themes emerged from the study: 1) Undergraduate students saw the use of the Adventures of Krystal Kingdom as learning tool to enhance their understanding of concepts in Multivariable Calculus.; 2) Undergraduate students saw the use of the Adventures of Krystal Kingdom as a way to engage themselves in mathematical fun in a digital environment; and 3) Undergraduate students saw input semiotics, automated reflexes, Task Relevant Support and other core mechanics as components that affect students’ gameplay. Results of the interviews, observations, and artifacts revealed that students benefited from using DGBL as an alternative approach to learning mathematics and to use such advanced techniques in biology, engineering, and computational neuroscience. The overall results indicate that DGBL used in the study was an appropriate teaching and learning tool to improve students\u27 mathematics skills

Cellular Neural Networks with Switching Connections

Artificial neural networks are widely used for parallel processing of data analysis and visual information. The most prominent example of artificial neural networks is a cellular neural network (CNN), composed from two-dimensional arrays of simple first-order dynamical systems (“cells”) that are interconnected by wires. The information, to be processed by a CNN, represents the initial state of the network, and the parallel information processing is performed by converging to one of the stable spatial equilibrium states of the multi-stable CNN. This thesis studies a specific type of CNNs designed to perform the winner-take-all function of finding the largest among the n numbers, using the network dynamics. In a wider context, this amounts to automatically detecting a target spot in the given visual picture. The research, reported in this thesis, demonstrates that the addition of fast on-off switching (blinking) connections significantly improves the functionality of winner-take-all CNNs. Numerical calculations are performed to reveal the dependence of the probability, that the CNN correctly classifies the largest number, on the switching frequency.Master of Science (MS)Mathematics and Statistic

‘Round ‘n’ ‘Round We Go!

New attractions—including Martin Luther King Jr. National Historic Site, Atlanta History Center, World of Coca-Cola, and SkyView Ferris wheel—have made Atlanta, Georgia, a destination city. SkyView is one of the top five attractions for Atlanta tourists (see photographs 1 and 2). This Ferris wheel sits 200 feet tall and contains 42 climate-controlled gondolas, each of which can hold a maximum of six people. We can analyze and identify many mathematical features of this attraction that will lead us to a discussion of circumference, angles of polygons, the parametric form of conic sections, periodic functions, and related rates.</jats:p

Digital Game-Based Learning in Advanced Mathematics and its Effects on Achievement and Motivation

This study will examine the effects of a computer game on students\u27 mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skills, and English language skills on their achievement and motivation as they play the game. A case study embedded with a quantitative approach using a paired sample t-test will be used to analyze the data. Viewing this presentation will provide mathematics instructors or teachers with a supplemental or an additional instructional approach to engage students to be motivated to participate in the their classroom learning environments. We expect that there will be a significant improvement with students\u27 achievements and motivation with the use of the computer game