Chemical reaction networks: Computability, complexity, and randomness

Abstract

Their friendship made the journey full of joy. Adam introduced me effective dimension and mutual dimension when I first entered LAMP and knew nothing about these topics. Don and I published our first paper together. I will miss the days we spent in front of the chalk boards discussing Math. Titus talked to me about Chemical Reaction Networks (CRNs) even before I entered LAMP. I learned a lot of tricks on constructing CRNs from him. The workflow and software tools he introduced to me made me much more efficient. Andrei proofread a lot of my English writings, including my job applications, my postdoctoral fellowship proposal, and paper drafts. Xiaoyuan asked me a lot of questions, sometimes challenging ones, which often forced me to find better answers and better explanations. She actually brought the topic of CRN-computable numbers to my attention. It is a story worth telling. It started with an exercise Jack assigned in his COM S 533 class that she took. I solved the exercise and found that it is not hard to compute algebraic numbers. Jim then challenged me to compute π. Titus and Jim first answered that through an experimental method and later I came up with a constructional solution. Of course, finally transforming everything into proofs took us a lot more time. It all started with an exercise problem and I ran into it by accident! I thank Dr. Zhilin Wu in Institute of Software, Chinese Academy of Sciences, who encouraged me to go abroad and jump on this journey. I thank my former advisor Dr. Ting Zhang, who recruited me into his lab and supported my first year's study in Iowa State. I thank Dr. Simanta Mitra for nominating me for the Teaching Excellency Award. I thank all friends in the Computer Science Department, who made me feel at home. vii I thank my colleagues Dr. David Voorhees and Dr. Aparna Das at Le Moyne College where I spent my last year as a visiting assistant professor. I learned a great deal about teaching from both of them. Dave also helped in cover my classes when I was away for job interviews and took a caring interest in my progress on teaching, research, and job hunting. I thank Dr. Tim McNicholl, Dr. Jim Lathrop, and needless to say, Jack, for the enormous help in my academic job hunting in year 2019 and especially, in 2020, during this once-in-a-century pandemic. Many positions had been canceled due to COVID-19, including some that I applied and interviewed for. Luckily, I landed a tenure-track position at University of Illinois at Springfield before everything became much worse. Last but not least, I'd like to thank my parents and siblings back in China. I am always indebted to them for their love and support.

Randomness and dimension in computational learning and analog computation

“…The main body of Chapters 3-6 is taken from the publications below, and from unpublished work (the results of Chapter 5 are unpublished joint work with Xiang Huang, Jack H. Lutz, Neil Lutz, and Elvira Mayordomo, and I am solely responsible for any mistakes that appear in this dissertation. Chapter 4 reviews some of the results of Algorithmic Randomness in Continuous Time Markov Chains, which appear in Huang et al (2019) and in Xiang Huang's dissertation Huang (2020). Chapter 4 includes a simplified proof of one of these results contained in the journal version.…”

“…We will see that randomness can also be formulated for SCRNs (in terms of the more general continuous-time Markov chains discussed in the next section) and used to reason about the inherent complexity of particular trajectories of such systems. Much of the basis of this work has already been discussed in Huang (2020). We will review some of these definitions and notions as a foundation for the next chapter's discussion of the randomness properties of sojourn time sequences.…”