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About the course

To fully realize the potential benefit of collaboration between the biological and physical sciences, the initiatives of the Office of Physical Sciences Oncology must accomplish more than simply continuing the development of measurement technologies. Moore et al. remark that previous "contributions [i.e. x-rays, PET, and MRI] leverage[d] the technology development aspect from the physical sciences . . . but not other important aspects like methodology, practices and thought processes. What is different about the NCIís PS-OC Program is the conviction that unique physical sciences and engineering approaches and principles can be integrated . . . in cancer research to yield a more fundamental understanding of the disease."

Physical sciences "thought processes" commonly involve quantitative reasoning. Resources for developing this skill currently include introductory courses in quantitative biology. For example, Los Alamos Natl Laboratory hosts the invaluable q-Bio summer school. Unfortunately, mathematical prerequisites for these courses pose a challenge for investigators trained in many life sciences fields. A mathematical way to think about biology was developed to help address this challenge. This website is a collection of video tutorials to help biologists, clinicians, and patient advocates prepare for courses in quantitative biology. The purpose of these videos is to provide familiarity with introductory topics often presented in quantitative biology courses and confidence to pursue more sophisticated concepts developed from these foundations.

α: Caveat spectator

This website does not replace live interaction. This website is in α (alpha) and made available without charge on an "AS IS" basis. Viewers are cautioned against relying on this website for professional clarity, accuracy, or completeness. The following problems illustrate that this website remains a work in progress.

As a first example, the video "DEs I: Numerical integration" mentions a simplistic adaptive algorithm. The algorithm was contrived merely to persuade students of the formal possibility of inventing a method to readjust stepsize by comparing different orders of approximation. The author's study of numerical integration in formal courses concluded with little more than the Euler method (which is practically useless outside of teaching), and he has no idea whether any production-quality numerical integration routine adapts stepsizes in any way even remotely resembling the method in the video. As a second example, part of the section on uncertainty propagation had to be re-recorded because a previous version confused the terms "sample" and "measurement." Instructors commonly use the word "sample" to refer to a finite collection of individual measurements, rather than to refer to any individual measurement (datum).

It was important to release this curriculum in α to provide the following benefits as soon as possible.

  1. Videos provide a quick way to browse for interesting topics
  2. Oversimplistic propositions clearly litter the videos, serving as warnings against taking mathematical models too seriously
  3. What conceptual foundations the videos do provide are indispensable for efficient conversations in mathematical collaborations
  4. It is easier to learn mathematical concepts by seeing their representations performed than by reading manuscripts

About the author

David Liao develops mathematical and physical concepts, assists experimental planning, interprets data, and communicates findings in physical biology.

David's participation in the National Cancer Institute Physical Sciences Oncology Network has included studying the consequences of dynamic heterogeneity for optimizing therapy and developing video tutorials to help interdisciplinary scientists model biological systems using mathematical and physical methods. David's illustrations have been published in journals including Science, Phys. Rev. Lett., and the Proc. Natl Acad. Sci. USA. He also designed the logo of the Princeton Physical Sciences Oncology Center.

Education and affiliations

University of California, San Francisco, San Francisco, CA 94143
Associate Professional Researcher (2015-present)
Analyst I (2012-2014)
Postdoctoral Scholar (2010-2012)

Princeton University, Princeton, NJ 08544
PhD, Physics (2005-2010)
MA, Physics (2005-2007)

Harvey Mudd College, Claremont, CA 91711
BS, Physics (2001-2005)


National Science Foundation
Graduate Research Fellowship Program (Fellow, 2009-2010)

Department of Defense
NDSEG Fellowship Program (Fellow, 2006-2009)


  1. Tlsty T D and Liao D (2012). Conceptualizing a tool to optimize therapy based on dynamic heterogeneity. Princeton Physical Sciences Oncology Center Workshop on Failures in Clinical Treatment of Cancer, Princeton, 2012 September 4-5: Session V: Rethinking chemotherapy effectiveness: Must it fail? 2012 September 5.
  2. Liao D (2013). (Developing and disseminating a mathematical way to think about biology). Fourth Annual NCI Physical Sciences-Oncology Centers (PS-OCs) Network Investigators' Meeting, Scottsdale, 2013 April 17-19: Education, Outreach, and Advocate Joint Working Group (Scottsdale, AZ) 2013 April 18.
  3. Liao D (2013). Evolutionary game theory for biologists. Princeton Physical Sciences-Oncology Center Workshop on Game Theory and Cancer, Baltimore, 2013 August 12-13: (Dinner talk) 2013 August 12. (get the slides and handouts)
  4. Liao D (2014). Evolutionary game theory for physical and biological scientists. Princeton Physical Sciences-Oncology Center Micro-Habitat-Patch Workshop, University of California, San Francisco, 2014 April 10-12: Morning session: Physical-sciences tutorials, 2014 April 10.

Peer-reviewed publications

Manuscripts are listed on David Liao's MyBibliography.


David's watercolor of Cleveland Tower featured on Wikipedia's front page 2007 July 31
David Liao is listed as "David L of Holmdel, NJ," the threshold 25,000th signature on the open-access petition at the Whitehouse

David Liao also has a personal page.
Creative Commons License © Copyright 2011-2015 David Liao. These videos and slides are open course ware made available under a Creative Commons license (CC BY-SA 4.0). The lightbox and social sharing effects are scripts by Stéphane Caron (CC BY 2.5).