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Introduction: Michael Knap

HI all. I am first-quarter graduate student at The University of California, Riverside. I moved to California from Nashville, Tennessee where I did undergraduate work at Tennessee State University. At TSU I was working with an applied mathematician and a control theorist. We mostly looked at linear dynamical systems with uncertainty. Most of my contribution to the research was numerical and computational. We looked at Markovian switched systems, very few networked systems, stochastic systems, parametrically uncertain systems, and some hybrids of these. The focus was always the stability analysis of the systems (that is what control theorists want: stability and stabilizability.) I could go on and share some of this work, but that is not my current topic.

Though the research was in the field of "applied mathematics" we studied no actual applications. All of the models we investigated were purely numerical and abstract - perhaps a better word is fictitious. This was quite frustrating to me. While I was working on this research, I started to read Dr. John Baez's blog; I started to think about how cool it would be to learn more about the environmental issues facing humanity while (hopefully) using some of the tools of systems analysis and control theory to further understand and disseminate this science.

My first mini-project I've taken on recently is learning how to use javascript for modeling as is done in Erskine et al’s temperature dynamics. The stochastic variant of the previous model is still a work in progress, but can be found here.

My current interests are

  • Networked systems
  • Tipping points or critical transitions in dynamical systems
  • Switched or hybrid dynamical systems
  • Stability analysis
  • Relationships between any of the above
  • Modeling any of the above

Comments

  • 1.

    I sort of share what you're feeling, but from a slightly different viewpoint: there's a tendency to

    1. Have some good "in its own right" maths work but feel the need to suggest it's applicable.

    2. A tendency to assume all problems that could be solved with mathematics are solvable in an "upward analytical-understanding pathway" from the simplest models to actual data. I'm not convinced this is true, particuarly for very complex systems like climate and population biology. Ironically, number theory (which is arguably less applicable than most things, modulo stuff like ciphering) seems more open to experimental maths than other stuff.

    Anyway, hope this mix of approaches here at Azimuth works for you. Got to run or I'd write a longer comment.

    Comment Source:I sort of share what you're feeling, but from a slightly different viewpoint: there's a tendency to 1. Have some good "in its own right" maths work but feel the need to suggest it's applicable. 2. A tendency to assume all problems that could be solved with mathematics are solvable in an "upward analytical-understanding pathway" from the simplest models to actual data. I'm not convinced this is true, particuarly for very complex systems like climate and population biology. Ironically, number theory (which is arguably less applicable than most things, modulo stuff like ciphering) seems more open to experimental maths than other stuff. Anyway, hope this mix of approaches here at Azimuth works for you. Got to run or I'd write a longer comment.
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