This thesis examines the interpretations derived from the Kac Ring Model, and the adding of a modification to the original model via “kick backs,” which can be interpreted to represent time reversals in the individual Kac rings. The results of this modification are analyzed, and their implications explored. There are three main parts to this thesis. Part 1 is a literature review which explains the working principles of the original Kac ring and explores its numerous applications. Part 2 describes the software and the theoretical & computational methodology used to implement the model and gather data. Part 3 analyzes the data gathered and makes a conclusion about its implications. There is an appendix included which contains some figures from Part 3 in a larger size, as it wasn’t possible to make the figures bigger within the text due to formatting.

This research explores Amazons growth amidst the COVID-19 pandemic and how it impacted its innovation initiatives. It examines the strategies employed by Amazon to drive innovation, explores the challenges encountered during this period of expansion, and identifies opportunities for innovation in a post-pandemic era. Additionally, this study offers insights and recommendations for organizations navigating similar circumstances.

Social media has not always been a traditional form of business strategy for the fashion industry, therefore a study on the role of social media on user engagement for different tiers of fashion brands was conducted. A combination of multiple regression models, ANOVA analysis, and hashtag analysis was done to understand various aspects of the research question. Tests were run against different post types to gain deeper insights on engagement levels and statistical significance. Post frequency and correlation analysis was conducted to understand how followers respond to the content. Overall, reels and carousel media were the most successful in increasing and maintaining user engagement. Prada has the most inactive users and ineffective social media strategies to increase engagement. While they have a high following they are unable to sustain engagement levels through their posts. Whereas, Teddy Fresh, despite being a smaller brand has been successful in maintaining engagement levels through their niche target market. Lastly, SKIMS has the fastest growth rate and has been able to increase following through their high frequency post schedule. For each of the brands, this information can be used to further strategize the marketing content. Social media is dynamic and therefore the approach for curating content will differ; being able to understand which types of posts are doing well is helpful for the brands as they can continue to run analysis when needed.

Social media has not always been a traditional form of business strategy for the fashion industry, therefore a study on the role of social media on user engagement for different tiers of fashion brands was conducted. A combination of multiple regression models, ANOVA analysis, and hashtag analysis was done to understand various aspects of the research question. Tests were run against different post types to gain deeper insights on engagement levels and statistical significance. Post frequency and correlation analysis was conducted to understand how followers respond to the content. Overall, reels and carousel media were the most successful in increasing and maintaining user engagement. Prada has the most inactive users and ineffective social media strategies to increase engagement. While they have a high following they are unable to sustain engagement levels through their posts. Whereas, Teddy Fresh, despite being a smaller brand has been successful in maintaining engagement levels through their niche target market. Lastly, SKIMS has the fastest growth rate and has been able to increase following through their high frequency post schedule. For each of the brands, this information can be used to further strategize the marketing content. Social media is dynamic and therefore the approach for curating content will differ; being able to understand which types of posts are doing well is helpful for the brands as they can continue to run analysis when needed.