In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what it means for an individual trajectory of a CTMC to be random. CTMCs have discrete state spaces and operate in continuous time. This, together with the fact that trajectories may or may not halt, presents challenges not encountered in more conventional developments of algorithmic randomness.Although we formulate algorithmic randomness in the general context of CTMCs, we are primarily interested in the computational power of stochastic chemical reaction networks, which are special cases of CTMCs. This leads us to embrace situations in which the long-term behavior of a network depends essentially on its initial state and hence to eschew assumptions that are frequently made in Markov chain theory to avoid such dependencies.After defining the randomness of trajectories in terms of a new kind of martingale (algorithmic betting strategy), we prove equivalent characterizations in terms of constructive measure theory and Kolmogorov complexity. As a preliminary application we prove that, in any stochastic chemical reaction network, every random trajectory with bounded molecular counts has the non-Zeno property that infinitely many reactions do not occur in any finite interval of time.

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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.

The frequent cross-ship communication has raised the complexity of ship network, therefore raised the requirements of monitoring system on the complicated local network on board. The traditional monitoring system is expensive and can hardly monitor cross-OS local network. Aimed at the specifications of ship network, this paper puts forward using embedded web server to design monitoring system. Through designing monitoring layer with LibPcap, designing application layer with CGI and designing user layer with JavaScript and REST, this paper finish the complete monitoring system and high improves the performance on latency and threat identification success rate.

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Image registration is one of the fundamental tasks within image processing. It has wide applications in the fields of medical imaging, computer vision, statistical modeling etc. It is required when one wants to combine valuable statistical information from multiple images, possibly acquired using different modalities, at different time points or from different subjects, or to compare or integrate the data obtained from same or different measures. The subject of this article is nonrigid image registration. In particular, the main focus is on the application of fluid dynamics and mutual information (MI), and the comparison of two different similarity measures, i.e. mutual information and sum of squared differences (SSD). Numerical experiments show that fluid registration using SSD is ideal for mono-modal image registration, while fluid registration using MI does a better job in multi-modal image registration.