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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.

David resides primarily in the diner capital of the world.

Education and affiliations

University of California, San Francisco, San Francisco, CA 94143
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 also listed on David's Google Scholar profile.
  1. Haskell R C, Liao D, Pivonka A E, Bell T L, Haberle B R, Hoeling B M, and Petersen D C (2006). Role of beat noise in limiting the sensitivity of optical coherence tomography. J. Opt. Soc. Am. A 23(11), 2747-2755. doi:10.1364/JOSAA.23.002747 PMID 17047700.
  2. Liao D, Galajda P, Riehn R. Ilic R, Puchalla J L, Yu H G, Craighead H G, and Austin R H (2008). Single molecule correlation spectroscopy in continuous flow mixers with zero-mode waveguides. Opt. Express 16(14), 10077-10090. doi:10.1364/OE.16.010077 PMID 18607415.
  3. Keymer J E, Galajda P, Lambert G, Liao D, and Austin R H (2008). Computation of mutual fitness by competing bacteria. Proc. Natl Acad. Sci. USA 105(51), 20269-20273. doi:10.1073/pnas.0810792105 PMID 19074280. PMCID PMC2600899.
  4. Austin R H, Tung C K. Lambert G, Liao D, and Gong X (2010). An introduction to micro-ecology patches. Chem. Soc. Rev. 39(3), 1049-1059. doi:10.1039/b911230h PMID 20179824.
  5. Lambert G, Liao D, and Austin R H (2010). Collective escape of chemotactic swimmers through microscopic ratchets. Phys. Rev. Lett. 104(16), 168102. doi:10.1103/PhysRevLett.104.168102 PMID 20482083.
  6. Liu L, Loutherback K, Liao D, Yeater D, Lambert G, Estévez-Torres A, Sturm J C, Getzenberg R H, and Austin R H (2010). A microfluidic device for continuous cancer cell culture and passage with hydrodynamic forces. Lab Chip, 10(14), 1807-1813. doi:10.1039/c003509b PMID 20424729. PMCID PMC3248645.
  7. Lambert G, Liao D, Vyawahare S, and Austin R H (2011). Anomalous spatial redistribution of competing bacteria under starvation conditions. J. Bacteriol. 193(8), 1878-1883. doi:10.1128/JB.01430-10 PMID 21317322. PMCID PMC3133049.
  8. Lambert G, Estévez-Salmerón L, Oh S, Liao D, Emerson B M, Tlsty T D, and Austin R H (2011). An analogy between the evolution of drug resistance in bacterial communities and malignant tissues. Nature Rev. Cancer 11(5), 375-382. doi:10.1038/nrc3039 PMID 21508974. PMCID PMC3488437.
  9. Zhang Q, Lambert G, Liao D, Kim H, Robin K, Tung C K, Pourmand N, and Austin R H (2011). Acceleration of emergence of bacterial antibiotic resistance in connected microenvironments. Science 333(6050), 1764-1767. doi:10.1126/science.1208747 PMID 21940899.
  10. Zhang Q, Robin K, Liao D, Lambert G, and Austin R H (2011). The Goldilocks principle and antibiotic resistance in bacteria. Mol. Pharm. 8(6), 2063-2068. doi:10.1021/mp200274r PMID 22085251. PMCID PMC3235521.
  11. Cleveland C, Liao D, and Austin R H (2012). Physics of cancer propagation: A game theory perspective. AIP Adv. 2(1), 11202. doi:10.1063/1.3699043 PMID 22489277. PMCID PMC3321518.
  12. Liao D, Estévez-Salmerón L, and Tlsty T D (2012). Conceptualizing a tool to optimize therapy based on dynamic heterogeneity. Phys. Biol. 9, 065005. doi:10.1088/1478-3975/9/6/065005 PMID 23197078. PMCID PMC3618714.
  13. Liao D, Estévez-Salmerón L, and Tlsty T D (2012). Generalized principles of stochasticity can be used to control dynamic heterogeneity. Phys. Biol. 9, 065006. doi:10.1088/1478-3975/9/6/065006 PMID 23197162. PMCID PMC3618713.
  14. The Physical Sciences - Oncology Centers Network: Agus D B, Alexander J F, Arap W, Ashili S, Aslan J E, Austin R H, Backman V, Bethel K J, Bonneau R, Chen W-C, Chen-Tanyolac C, Choi N C, Curley S A, Dallas M, Damania D, Davies P C W, Decuzzi P, Dickinson L, Estévez-Salmerson L, Estrella V, Ferrari Mauro, Fischbach C, Foo J, Fraley S I, Frantz C, Fuhrmann A, Gascard P, Gatenby R A, Geng Y, Gerecht S, Gillies R J, Godin B, Grady W M, Greenfield A, Hemphill C, Hempstead B L, Hielscher A, Hillis W D, Holland E C, Ibrahim-Hashim A, Jacks T, Johnson R H, Joo A, Katz J E, Kelbauskas L, Kesselman C, King M R, Konstantopoulos K, Kraning-Rush C M, Kuhn P, Kung K, Kwee B, Lakins J N, Lambert G, Liao D, Licht J D, Liphardt J T, Liu L, Lloyd M C, Lyubimova A, Mallick P, Marko J, McCarty O J T, Meldrum D R, Michor F, Mumenthaler S M, Nandakumar V, O'Halloran T V, Oh S, Pasqualini R, Paszek M J, Philips K V, Poultney C S, Rana K, Reinhart-King C A, Ros R, Semenza G L, Senechal P, Shuler M L, Srinivasan S, Staunton J R, Stypula Y, Subramanian H, Tlsty T D, Tormoen G W, Tseng Y, van Oudenaarden A, Verbridge S S, Wan J C, Weaver V M, Widom J, Will C, Wirtz D, Wojtkowiak J, and Wu P-H (2013). A physical sciences network characterization of non-tumorigenic and metastatic cells. Sci. Rep. 3, 1449. doi:10.1038/srep01449 PMID 23618955. PMCID PMC3636513.
  15. Wu A, Liao D, Tlsty T D, Sturm J C, and Austin R H (2014). Game theory in the death galaxy: interaction of cancer and stromal cells in tumour microenvironment. Interface Focus 4, 20140028 (In press). PMC Journal- In Process.
  16. Liao D and Tlsty T D (2014). Evolutionary game theory for physical and biological scientists: I. Training and validating population dynamics equations. Interface Focus 4, 20140037 (In press). PMC Journal- In Process.
  17. Liao D and Tlsty T D (2014). Evolutionary game theory for physical and biological scientists: II. Population dynamics equations can be associated with interpretations. Interface Focus 4, 20140038 (In press). PMC Journal- In Process.


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).